Description
Venture Capital and Finance of Innovation
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VENTURE CAPITAL &
THE FINANCE OF
INNOVATION
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VENTURE CAPITAL &
THE FINANCE OF
INNOVATION
SECOND EDITION
ANDREW METRICK
Yale School of Management
AYAKO YASUDA
Graduate School of Management, UC Davis
John Wiley & Sons, Inc.
EDITOR Lacey Vitetta
PROJECT EDITOR Jennifer Manias
SENIOR EDITORIAL ASSISTANT Emily McGee
MARKETING MANAGER Diane Mars
DESIGNER RDC Publishing Group Sdn Bhd
PRODUCTION MANAGER Janis Soo
SENIOR PRODUCTION EDITOR Joyce Poh
This book was set in Times Roman by MPS Limited and printed and bound by Courier Westford. The
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Copyright 2011, 2007 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be
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Library of Congress Cataloging-in-Publication Data:
Metrick, Andrew.
Venture capital and the ?nance of innovation / Andrew Metrick, Ayako Yasuda. — 2nd ed.
p. cm.
Includes index.
ISBN 978-0-470-45470-1 (hardback)
1. Venture capital. 2. Technological innovationsÀFinance. I. Yasuda, Ayako. II. Title.
HG4751.M48 2010
332u.04154—dc22
2010020655
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
BRIEF CONTENTS
PREFACE TO 2
ND
EDITION—A READER’S GUIDE vii
ACKNOWLEDGMENTS xiii
CONTENTS xvii
PART I
VC BASICS
CHAPTER 1 THE VC INDUSTRY 3
CHAPTER 2 VC PLAYERS 21
CHAPTER 3 VC RETURNS 46
CHAPTER 4 THE COST OF CAPITAL FOR VC 65
CHAPTER 5 THE BEST VCs 83
CHAPTER 6 VC AROUND THE WORLD 99
PART II
TOTAL VALUATION
CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS 123
CHAPTER 8 TERM SHEETS 146
CHAPTER 9 PREFERRED STOCK 163
CHAPTER 10 THE VC METHOD 178
CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES 195
CHAPTER 12 COMPARABLES ANALYSIS 214
v
PART III
PARTIAL VALUATION
CHAPTER 13 OPTION PRICING 231
CHAPTER 14 THE VALUATION OF PREFERRED STOCK 252
CHAPTER 15 LATER-ROUND INVESTMENTS 272
CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK 290
CHAPTER 17 IMPLIED VALUATION 305
CHAPTER 18 COMPLEX STRUCTURES 320
PART IV
THE FINANCE OF INNOVATION
CHAPTER 19 R&D FINANCE 339
CHAPTER 20 MONTE CARLO SIMULATION 357
CHAPTER 21 REAL OPTIONS 378
CHAPTER 22 BINOMIAL TREES 400
CHAPTER 23 GAME THEORY 419
CHAPTER 24 R&D VALUATION 445
APPENDIX A SAMPLE TERM SHEET 466
APPENDIX B THE VCFI SPREADSHEETS 484
APPENDIX C GUIDE TO CRYSTAL BALL
s
487
GLOSSARY 512
INDEX 535
vi BRIEF CONTENTS
PREFACE TO 2
ND
EDITION—
A READER’S GUIDE
Many interesting developments have occurred in the world of venture capital since
the publication of the first edition of this book in 2006, which prompted us to revise
the book for the second edition. While the organization of the book remains
unchanged, many of the chapters are substantially rewritten. For example, in Chapter
5, we re-ranked top VC firms, incorporating the latest performance statistics, fun-
draising and investment activities, notable exits, and (as always) our subjective
opinions. In Chapter 6, we examine further evidence of the deepening globalization
of the industry. In Chapters 3, 4, and 7, we analyze the impact of the 1999À2000
Internet bubble years on the VC risk and returns, as investments made in those years
are finally mature and thus now a part of the performance evaluation analysis. We
also incorporated expositional improvements throughout the book based on reader
feedback on the first edition.
Another feature of the new edition is that the VCV model, used extensively in
Part III of the book, is now available as a Web-based application available on http://
VCVtools.com. Significant collaborative efforts went into developing this tool,
which we believe will be of interest to a broad audience, including practitioners
interested in valuing VC-backed company stocks and employee stock options.
THE ORGANIZATION OF THIS BOOK
The book is divided into four parts, with six chapters each. Each of these four parts
has a major finance theme: the theme of Part I is the relationship between risk and
return; the theme of Part II is the valuation of high-growth companies; the theme of
Part III is the analysis of capital structure; and the theme of Part IV is the rela-
tionship between strategy and finance. Overall, Parts I and II are heavy on data
and definitions and are intended to provide students with the vocabulary of VC and
knowledge of the key industry facts. Although these two parts contain some new
definitions and approaches, most of the material should seem familiar to a VC
practitioner. In contrast, Parts III and IV are more theory based and provide a new
perspective on the evaluation of VC and other high-technology investments.
Although these latter two parts might seem experimental to a practicing VC,
financial economists will recognize the material as a straightforward translation of
well-known methods.
vii
In Part I, “An Introduction to VC”, we provide an overview of the VC
industry, with discussions of history (Chapter 1), major players (Chapters 2 and 5),
performance measurement (Chapters 3 and 4), and global patterns (Chapter 6). The
discussion of risk and return in Chapters 3 and 4 provide a key translation between
the language of VC and the language of financial economics—a translation that we
rely on heavily throughout the book.
In Part II, “Total Valuation”, we provide data and methods used to value a
high-growth company. We first review the investment process used by VCs and
provide data on their historical performance (Chapter 7). We next describe the
structure of VC transactions (Chapters 8 and 9) and then demonstrate the industry-
standard technique for the valuation of VC investments (Chapter 10). This technique,
known loosely as “the venture capital method”, requires that analysts estimate
company values far into the future. Although such estimates will always contain a
fair amount of guesswork, we show how to use a “reality-check” model to frame
these estimates (Chapter 11) and how to use evidence from comparable companies to
provide an additional input for the investment decision (Chapter 12).
In Part III, “Partial Valuation”, we take the total valuation (Part II) as given
and analyze the special features of VC transactions. In most VC transactions, the
investors receive preferred stock with several special features. When there are
many VC investors, the capital structure of the company grows quite complex, with
each investor holding a unique place in the capital-structure hierarchy of the
company. In Part III, we show how to divide the total valuation of the company into
its component parts (partial valuation) for each investor. The key step in this
analysis is the recognition that all flavors of preferred stock can be represented as a
portfolio of options. In Chapter 13, we show how the classic option-pricing analysis
of Black and Scholes can be extended to VC settings. We then apply this extended
analysis to the valuation of preferred stock (Chapters 14, 15, and 16). The tech-
niques used in these chapters can also be used to refine some industry-standard
measures of company valuation (Chapter 17) and to estimate the partial valuation
of complex nonstandard transaction structures (Chapter 18).
Parts II and III of the book take the perspective of a venture capitalist making
an investment in a high-technology company. In Part IV, we take the perspective of
the company deciding what to do with VC money or other capital. Specifically, we
develop a framework for modeling investment in “research and development”
(R&D). Since VC-backed companies typically spend a significant fraction of their
capital on R&D, an understanding of R&D finance is crucial for both VCs and for
financial decision-makers at technology companies of all sizes. After introducing
typical kinds of R&D investment problems (Chapter 19), we study several of the
most interesting and cutting-edge techniques in finance, including Monte Carlo
analysis (Chapter 20), real options (Chapter 21), binomial trees (Chapter 22),
and game theory (Chapter 23). In Chapter 24, we pull all of these tools together and
solve the investment problems originally posed in Chapter 19.
Several appendices supplement the text. Appendix A provides an example
“term sheet” VC contract developed by the National Venture Capital Association.
viii PREFACE TO 2
ND
EDITION—A READER’S GUIDE
Appendix B provides some basic documentation for the companion spreadsheets
and the web-based valuation model used in the book. Appendix C is a brief primer
on Crystal Ball
s
software, a commercial product from Oracle that is useful for
solving some of the models in Part IV. Finally, a glossary at the end of the book
gives definitions for all key terms used in the book.
WHAT THIS BOOK COVERS . . . AND WHAT
IT DOESN’T
To be successful, VCs must have a broad general knowledge of business and all its
disciplines: marketing, management, finance, operations, accounting, and so on. In
addition, most VCs must acquire specialized knowledge in one or more high-
technology industries. It is not possible to cover all these areas in one textbook, nor
is it advisable to even try. This book focuses almost exclusively on finance, spe-
cifically on the valuation of high-technology investments. The ideal reader is an
MBA student or advanced undergraduate who is both interested in VC and intel-
lectually curious about finance. We wrote the book for this prototypical reader;
your distance from this prototype will likely predict your satisfaction with this
book. In particular, readers looking for a “how to” guide for being a successful VC
are sure to be disappointed. We doubt such a book is even possible, and we are sure
that we could not write it.
For instructors, the 24 chapters of the book can provide for 24 class meetings
with 75 minutes each (530 hours) for a course of the same name as the book. That
is how we taught it at Wharton.
1
Alternatively, a finance course on “Venture
Capital” could omit Part IV of the book and include six additional case-study classes
to fill out a full semester course. For a quarter-length course that meets 20 times for
90 minutes each (530 hours), some chapters can be combined (for example,
chapters 1 and 2, 3 and 4, and 11 and 12) or omitted (e.g., 18, 22À24). For a six-
week course (515 class hours) on “Venture Capital”, the first two parts of the book
can provide a self-contained framework.
For any of these VC courses, many instructors may choose to combine this
book with case studies. At Wharton, we used this book as the main text, with case
studies from the books by Josh Lerner and Felda Hardymon of Harvard Business
School used to illustrate the practical applications of the concepts. Alternatively,
one could use the case studies as the main classroom topics, with this textbook as
background. A companion instructor’s manual suggests some cases that work well
with each of the chapters.
For VC courses taught outside of a finance department, instructors will
rightly want to emphasize different aspects of VC practice. At Yale and UC Davis,
we have a highly successful VC course taught by management faculty—a course
1
Both authors previously taught at Wharton, 1999À2008 for Metrick and 2001À2009 for Yasuda.
PREFACE TO 2
ND
EDITION—A READER’S GUIDE ix
that has virtually no overlap with this book. Furthermore, as one might expect,
courses taught by VC practitioners are often much more “practical”, with many
class sessions dedicated to the nuts and bolts of working with young companies.
While we believe that some chapters of this book could provide useful background
for these practitioner courses, we are certain that most of the book would be useless.
We have found that students can learn a tremendous amount from these practice-
based courses, and have made no attempt to substitute for these valuable lessons.
There are several related topics for which this book has some imperfect
overlap. For example, for courses in “entrepreneurial finance”, students typically
need some exposure to VC. For these students, Part I should be useful, while the
other parts are likely to be overkill. This book takes the perspective of a venture
capitalist—not the perspective of an entrepreneur. The latter perspective requires a
careful study of non-VC sources of capital for young companies, a perspective that
this book does not cover at all. Furthermore, the financial management of young
growth companies is another important topic in entrepreneurial finance. While such
a topic could conceivably have been included in this book, we chose instead to
focus on the valuation aspects of VC finance.
Another topic of some overlap would be a general course on “private equity”.
As will be discussed in Chapter 1, private equity is a broad class of investing that
includes VC as well as investments in leveraged buyouts, mezzanine structures, and
distressed companies. (All these terms will be defined in Chapter 1.) For instructors
of such classes, the usefulness of the book depends on the relative emphasis on VC.
Six weeks (515 hours) of VC can be supported by Parts I and II, supplemented
with (or supplementing) case studies. For private equity courses with less than six
weeks of VC, the reductions can be accomplished in Parts I and II by omitting some
combination of Chapter 5, Chapter 6, and Chapter 9, and combining Chapters 11
and 12 into a single class meeting.
NOTES ON TERMINOLOGY, STYLE,
AND MATHEMATICS
The text assumes that readers have familiarity, but not mastery, of the basic con-
cepts from first-year MBA courses in finance, statistics, and accounting. (For
example, the book assumes that readers know the definitions for “mean” and
“standard deviation”,
2
but does not assume that readers have memorized formulas
for the mean and standard deviation of any specific probability distributions.) Most
of the mathematics in the book goes no further than simple algebra. In Parts III and
IV of the book, we use some basic calculus in a few places, but even there it is more
2
This book follows British style in the “logical” placement of some punctuation marks outside of
quotation marks. This annoys some people. Sorry.
x PREFACE TO 2
ND
EDITION—A READER’S GUIDE
important that readers know what an integral “does” rather than know how to solve
any specific integrals.
The book assumes no prior knowledge of venture capital. All key terms are
given in bold type in their first appearance in the text. Because this book is
attempting to provide a bridge between the language of VC and the language of
finance, it is sometimes helpful to introduce new terminology in order to ease the
translation. Such new terminology is given in bold italic type in its first appearance in
the text. All key terms are listed at the end of the chapter of their first appearance.
At the end of the textbook, a glossary provides definitions for all key terms. The text
uses many acronyms to shorten the exposition. Each acronym is spelled out in its first
appearance, followed by the acronym given in parenthesis: for example, venture
capital (VC). All acronyms are also listed in the glossary.
PREFACE TO 2
ND
EDITION—A READER’S GUIDE xi
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ACKNOWLEDGMENTS
This book would not have been possible without the guidance, encouragement, and
support of many of our academic colleagues; special gratitude goes to Paul
Gompers, Steve Kaplan, Josh Lerner, and David Scharfstein for their continuous
generosity with their knowledge and insights.
We are also indebted to our friends in the VC industry for their willingness to
help us with their time, knowledge and resources. Special thanks to Susan
Woodward, who graciously made available to us the venture capital database at
Sand Hill Econometrics, Mike Holt of Holt Private Equity Consultants for sharing
with us the coveted compensation data from his annual compensation survey, and
John Taylor of National Venture Capital Association for his help with the LP data.
We also thank Louis Radovich for his superb assistance with the analysis of the
Sand Hill Econometrics data.
We continue to rely on the dedication of highly skilled students for development
of the VCVmodel, used inPart III tovalue deal structures withpreferred stockandnow
newly offered as a Web-based application. This valuation model in its current
incarnation would not have been possible without the contribution of Tony Curnes,
Holland Gary, Jonathan Reinstein, David Smalling, and Rebecca Yang. We also thank
Garris Shipon for building the Web application and designing the site (VCVtools.com)
that houses the VCV model, and Greta Lin for co-authoring Appendix C.
The book benefited greatly from the feedback on the first edition from many
individuals, including our former Wharton colleague David Wessels, who taught
courses using the book, and generations of students at Wharton and Yale. Ayako
thanks her colleagues at UC Davis Graduate School of Management for supporting
her in creating a new VC finance course in her first year there, and her MBA
students for being test-marketed for the pre-publication manuscript of the second
edition. Several of our students and colleagues made important contributions to the
first edition of this book, and these contributions are still evident in this new
version: Izhar Armony, Albert Cheng, Christine Chou, Colleen Pontious, and Yin
Yin. We also would like to thank the Mack Center for Technological Innovation at
the Wharton School of the University of Pennsylvania for their generous financial
support for the first edition of the book.
We would also like to thank Lacey Vitetta, Jennifer Manias, Emily McGee, and
Joyce Poh at Wiley for their contributions to the completion of this book. Finally, we
each are most indebted to our families, for making this all possible and worthwhile.
Andrew dedicates the book to: his wife Susie, his son David, and his daughter Amy;
Ayako dedicates the book to: her husband Garris, and her daughter Miumi.
xiii
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For Susie, David, and Amy
AM
For Garris and Miumi
AY
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CONTENTS
PART I
VC BASICS
CHAPTER 1 THE VC INDUSTRY 3
1.1 What Is Venture Capital? 3
1.2 What Do Venture Capitalists Do? 9
1.3 The History of Venture Capital 10
1.4 Patterns of VC Investment in the United States 14
1.4.1 Investments by Stage 14
1.4.2 Investments by Industry 16
1.4.3 Investments by U.S. Region 18
Summary 19
Key Terms 20
References 20
CHAPTER 2 VC PLAYERS 21
2.1 Firms and Funds 21
2.2 The Limited Partners 27
2.3 VC Partnership Agreements 30
2.3.1 Management Fees 30
2.3.2 Carried Interest 32
2.3.3 Restrictive Covenants 39
Summary 41
Key Terms 42
References 42
Exercises 42
Appendices: Key Terms and Conditions for Three VC Funds 43
Appendix 2.A: EarlyBird Ventures I 43
Appendix 2.B: Talltree Ventures IV 44
Appendix 2.C: Owl Ventures IX 45
xvii
CHAPTER 3 VC RETURNS 46
3.1 Industry Returns 46
3.1.1 De?nitions 46
3.1.2 A Gross-Return Index 48
3.1.3 A Net-Return Index 50
3.2 Fund Returns 53
3.2.1 De?nitions 53
3.2.2 Evidence 59
Summary 62
Key Terms 63
References 63
Exercises 63
CHAPTER 4 THE COST OF CAPITAL FOR VC 65
4.1 The Capital Asset Pricing Model 65
4.2 Beta and the Banana Birds 69
4.3 Estimating the Cost of Capital for VC 74
Summary 79
Key Terms 80
References 80
Exercises 80
CHAPTER 5 THE BEST VCs 83
5.1 The Economics of VC 83
5.2 The Best VCs: A Subjective List 86
5.3 VC Value Added and the Monitoring of Portfolio Firms 95
Summary 98
Key Terms 98
References 98
CHAPTER 6 VC AROUND THE WORLD 99
6.1 The Global Distribution of VC Investing 99
6.2 The Cost of Capital for International VC 111
6.2.1 Baseline Model: The Global CAPM 112
6.2.2 Objective and Extensions to the Global CAPM 114
6.2.3 A Global Multifactor Model for Venture Capital 118
Summary 119
Key Terms 119
References 119
Exercises 120
xviii CONTENTS
PART II
TOTAL VALUATION
CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS 123
7.1 VC Investments: The Historical Evidence 123
7.2 The Investment Process 135
Summary 144
Key Terms 145
References 145
CHAPTER 8 TERM SHEETS 146
8.1 The Basics 147
8.1.1 Investors 148
8.1.2 Price Per Share 149
8.1.3 Pre-Money and Post-Money Valuation 149
8.1.4 Capitalization 150
8.2 The Charter 151
8.2.1 Dividends 153
8.2.2 Liquidation Preference 153
8.2.3 Voting Rights and Other Protective Provisions 154
8.2.4 Mandatory Conversion 154
8.2.5 Redemption Rights 154
8.3 Investor Rights Agreement 155
8.3.1 Registration Rights 158
8.3.2 Matters Requiring Investor-Director Approval 158
8.3.3 Employee Stock Options 158
8.4 Other Items 159
8.4.1 Rights and Restrictions 160
8.4.2 Founders’ Stock 161
Summary 161
Key Terms 161
References 162
Exercises 162
CHAPTER 9 PREFERRED STOCK 163
9.1 Types of Preferred Stock 163
9.2 Antidilution Provisions 173
Summary 176
Key Terms 177
CONTENTS xix
Reference 177
Exercises 177
CHAPTER 10 THE VC METHOD 178
10.1 The VC Method: Introduction 178
10.1.1 Exit Valuation 179
10.1.2 Target Returns 180
10.1.3 Expected Retention 182
10.1.4 The Investment Recommendation 183
10.2 The Standard VC Method 184
10.3 The Modi?ed VC Method 185
Summary 192
Key Terms 192
References 192
Exercises 192
CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES 195
11.1 DCF Analysis: Concepts 196
11.2 DCF Analysis: Mechanics 198
11.3 Graduation Value 204
11.4 DCF Analysis: The Reality-Check Model 207
11.4.1 Baseline Assumptions for the
Reality-Check DCF 207
Summary 212
Key Terms 212
References 213
Exercises 213
CHAPTER 12 COMPARABLES ANALYSIS 214
12.1 Introduction to Comparables Analysis 215
12.2 Choosing Comparable Companies 219
12.3 Using Comparable Companies to Estimate the Cost of Capital 224
Summary 226
Key Terms 227
References 227
Exercises 227
Appendix 12.A: Potential Comparables for Semico 228
xx CONTENTS
PART III
PARTIAL VALUATION
CHAPTER 13 OPTION PRICING 231
13.1 European Options 232
13.2 Pricing Options Using a Replicating Portfolio 234
13.3 The Black-Scholes Solution 238
13.4 American Options 242
13.5 Random-Expiration Options 243
13.6 Reading Exit Diagrams 245
13.7 Carried Interest as an Option 247
Summary 248
Key Terms 249
References 249
Exercises 249
Appendix 13.A RE Options: Technical Details 250
CHAPTER 14 THE VALUATION OF PREFERRED STOCK 252
14.1 Base-Case Option-Pricing Assumptions 253
14.2 RP Valuation 254
14.3 Excess Liquidation Preferences 257
14.4 Dividends 259
14.5 CP Valuation 261
14.6 CP with Excess Liquidation Preferences or Dividends 263
14.7 Combining RP and CP 266
14.8 Comparing RP and CP 268
Summary 269
Key Terms 270
References 270
Exercises 270
CHAPTER 15 LATER-ROUND INVESTMENTS 272
15.1 Series B 272
15.2 A Conversion Shortcut 277
15.3 Series C 278
15.4 Dividends in Later Rounds 282
15.4.1 Accrued Cash Dividends 282
15.4.2 PIK Dividends 284
15.5 Beyond Series C 285
CONTENTS xxi
Summary 288
Key Terms 288
Exercises 288
CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK 290
16.1 Binary Options 291
16.2 The Valuation of PCP 292
16.3 The Valuation of PCPC 294
16.4 Series B and Beyond 296
Summary 303
Key Terms 303
References 303
Exercises 303
CHAPTER 17 IMPLIED VALUATION 305
17.1 Post-Money Valuation Revisited 306
17.2 Measurement of Portfolio Value 310
17.3 Down Rounds? 314
17.4 How to Avoid Valuation Confusion 317
Summary 318
Key Terms 318
Exercises 319
CHAPTER 18 COMPLEX STRUCTURES 320
18.1 Management Carve-outs 320
18.2 Dealing with Partners 327
18.3 A Complex Example 329
Summary 334
Key Terms 334
Exercises 334
PART IV
THE FINANCE OF INNOVATION
CHAPTER 19 R&D FINANCE 339
19.1 R&D Around the World 339
xxii CONTENTS
19.2 Two Touchstones 345
19.2.1 Drug Development 345
19.2.2 Energy Innovation 348
19.3 How Is R&D Financed? 349
19.4 Where Do We Go from Here? 354
Summary 355
Key Terms 356
References 356
CHAPTER 20 MONTE CARLO SIMULATION 357
20.1 Event Trees 357
20.2 Simulation with Continuous Probability Distributions 362
20.3 Simulation with Multiple Sources of Uncertainty 373
Summary 376
Key Terms 376
Exercises 376
CHAPTER 21 REAL OPTIONS 378
21.1 Decision Trees 379
21.2 Real Options in R&D 381
21.3 The Valuation of Real Options 382
21.4 Risk-Neutral Probabilities 388
21.5 Drugco, Revisited 395
Summary 398
Key Terms 398
Exercises 398
CHAPTER 22 BINOMIAL TREES 400
22.1 The Black-Scholes Equation, Revisited 400
22.2 Multiple Strike Prices and Early Exercise 409
22.3 Dividends 411
Summary 417
Key Terms 418
References 418
Exercises 418
CHAPTER 23 GAME THEORY 419
23.1 What Is Game Theory? 419
23.2 Simultaneous Games 423
CONTENTS xxiii
23.3 Sequential Games 433
23.4 Game Theory and Real Options 438
Summary 443
Key Terms 443
Exercises 444
CHAPTER 24 R&D VALUATION 445
24.1 Drug Development 445
24.2 Energy 455
24.3 The Forest and the Trees 464
Summary 464
References 465
Exercises 465
APPENDIX A SAMPLE TERM SHEET 466
APPENDIX B THE VCFI SPREADSHEETS 484
APPENDIX C GUIDE TO CRYSTAL BALL
s
487
GLOSSARY 512
INDEX 535
xxiv CONTENTS
PART I
VC BASICS
1
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CHAPTER 1
THE VC INDUSTRY
IN THIS CHAPTER, we provide a de?nition of venture capital (Section 1.1),
take a preliminary look at the activities of venture capitalists (Section 1.2), explore the
history of venture capital (Section 1.3), and review a variety of statistics on the patterns
of venture capital investment (Section 1.4). Throughout this text, we use the abbre-
viation VC to refer to both the venture capital industry and to an individual venture
capitalist.
1.1 WHAT IS VENTURE CAPITAL?
A VC has ?ve main characteristics:
1. A VC is a ?nancial intermediary, meaning that it takes the investors’
capital and invests it directly in portfolio companies.
2. A VC invests only in private companies. This means that once the invest-
ments are made, the companies cannot be immediately traded on a public
exchange.
3. A VC takes an active role in monitoring and helping the companies in its
portfolio.
4. A VC’s primary goal is to maximize its ?nancial return by exiting invest-
ments through a sale or an initial public offering (IPO).
5. A VC invests to fund the internal growth of companies.
Characteristic (1) de?nes VCs as ?nancial intermediaries. This is similar to a
bank, because just as a bank takes money from depositors and then loans it to
businesses and individuals, a VC fund takes money from its investors and makes
equity investments in portfolio companies. Typically, a VC fund is organized as a
limited partnership, with the venture capitalist acting as the general partner
(GP) of the fund and the investors acting as the limited partners (LP).
1
If all goes
1
The organization structure of VC funds will be discussed at length in Chapter 2.
3
well, the VC eventually sells its stake in the portfolio company, returns the money
to its limited partners, and then starts the process all over again with a different
company. Exhibit 1-1 illustrates the key players and the ?ow of funds in the VC
industry.
VCs are often compared to—and confused with—angel investors. Angel
investors, often just called angels, are similar to VCs in some ways but differ
because angels use their own capital and, thus, do not satisfy characteristic (1).
There are many types of angels. At one extreme are the wealthy individuals with no
business background who are investing in the business of a friend or relative. At the
other end are groups of angels with relevant business or technical backgrounds who
have banded together to provide capital and advice to companies in a speci?c
industry. In the latter case, the angel groups look very much like VCs, but the fact
that they use their own capital changes the economics of their decisions: Since they
can keep all the returns to on their labor, they have a correspondingly lower cost of
capital and can invest in deals that would not work for a VC. Although it is dif?cult
to get reliable ?gures on angel investing, the best available survey evidence for
recent years suggests that total angel investments are approximately the same
magnitude as total VC investments.
2
Although the total ?ow of capital is similar,
angels tend to focus on younger companies than do VCs and make a larger number
of smaller investments.
EXHIBIT 1-1
THE FLOW OF FUNDS IN THE VENTURE CAPITAL CYCLE
Portfolio
companies
VC funds
managed by
general partners
(VCs or GPs)
Exits: IPO or
sale of
portfolio
companies
Limited partners
(investors or LPs)
2
The most comprehensive data on the angel market is maintained by the Center for Venture Research at
the University of New Hampshire: http://wsbe.unh.edu/cvr/. Their annual reports on the state of the angel
market provide the evidence cited in this paragraph.
4 CHAPTER 1 THE VC INDUSTRY
Characteristic (2) de?nes VC as a type of private equity. Although the
de?nitions of “private company” and “public company” have some nuances,
the key distinction is that a public company’s securities can be traded in a formal
market, like the NYSE or the NASDAQ, whereas a private company’s securities
cannot. Any company that is publicly traded in the United States must also ?le
regular reports with the Securities and Exchange Commission (SEC) detailing its
?nancial position and material changes to its business. When combined with the
activities of professional traders in public markets, this requirement to ?le creates
signi?cant amounts of information about public companies. In comparison, infor-
mation about private companies is practically nonexistent. Private equity is considered
to be a category of alternative investing, where “alternative” stands in contrast to
“traditional” investing in stocks and bonds.
Characteristic (3) is central on our list—and central to the success of any VC.
Without (3), a VC would only be providing capital, and his success (or failure)
would be entirely due to his ability to choose investments. Although success can, of
course, be entirely built on these choices, the comparative advantage of the VC
would be greatly improved if the investor could also help the company directly.
This help takes many forms. Most notably, VCs typically take at least one
position on the board of directors of their portfolio ?rms. Having board repre-
sentation allows them to provide advice and support at the highest level of the
company. (More than one VC has remarked that his job could be described as being
“a professional board member”.) In addition to board service, VCs often act as
unof?cial recruiters and matchmakers for their portfolio ?rms. Young companies
often have a dif?cult time attracting high-quality talent to a ?edgling operation,
and VCs can signi?cantly mitigate this problem by drawing on their reputation and
industry contacts. A VC who performs these value-added services well has a
sustainable form of competitive advantage over other investors.
Because VCs are ?nancial intermediaries, they need some mechanism to give
money back to their investors. Thus, a savvy VC will only make an investment if he
can foresee a path to exit, with proceeds of this exit returning to the VC and his
investors. Exits can occur through an IPO, with a subsequent sale of the VC stake in
the open market, through a sale of the company to another investor, or through the
sale of the company to a larger company. Because of the need to exit, VCs avoid
investments in “lifestyle” businesses (companies that might provide a good income
to the entrepreneurs, but have little opportunity for a sale or IPO).
Characteristic (4), the requirement to exit and the focus on ?nancial return, is
a key distinction between venture capital and strategic investing done by large
corporations. As a perpetual entity, a corporation can afford to take stakes in other
businesses with the intention of earning income, forming long-term alliances, and
providing access to new capabilities. It is possible for the corporation to maintain
this stake inde?nitely.
A strategic investor may satisfy all the other characteristics, but without the
need to exit, the strategic investor will choose and evaluate investments very dif-
ferently from a VC. In some cases, a corporation may set up an internal venture
1.1 WHAT IS VENTURE CAPITAL? 5
capital division. In the industry, this is referred to as corporate venture capital.
This label can be confusing, as only sometimes do such divisions satisfy
characteristic (4). These corporate VC efforts will often have strategic objectives
other than ?nancial returns and will have neither dedicated supplies of capital nor
an expectation that capital will be returned within a set time period. When (4) is not
satis?ed, the investment activity can take on a very different ?avor than the type
studied in this book.
The requirement to exit provides a clear focus for VC investing activities.
There are over 20 million businesses in the United States; more than 99 percent of
these businesses would meet the government de?nition of a “small business”.
3
In
general, small businesses are dif?cult to exit, and only “large businesses”—those in
the top 1 percent of all businesses—have a realistic chance to go public or be sold
in a liquid acquisition market. It is therefore typical for VCs to invest in small
businesses—but they only do so when these small companies have a realistic
chance to grow enough to become a large company within ?ve to seven years after
the initial investment. Such rapid growth is dif?cult to attain in most industries;
therefore, VCs tend to focus on high-technology industries, where new products can
potentially penetrate (or even create) large markets.
Characteristic (5) refers to “internal growth”, by which we mean that the
investment proceeds are used to build new businesses, not to acquire existing
businesses. Although the legendary VC investments tend to be those adventurous
VCs who backed “three guys in a garage”, the reality of VC investing is much
more varied. As a simple classi?cation, we divide portfolio companies into three
stages: early-stage, mid-stage (also called expansion-stage), and late-stage. At
one extreme, early-stage companies include everything through the initial
commercialization of a product. At the other extreme, late-stage companies are
businesses with a proven product and either pro?ts or a clear path toward pro?t-
ability. A late-stage VC portfolio company should be able to see a plausible exit on
the horizon. This leaves mid-stage (expansion) companies, who represent the vast
landscape between early-stage and late-stage. With all this territory to cover, it is
not surprising that mid-stage investments make up the majority of VC investment.
In Section 1.4.1 of this chapter, we give more precise de?nitions of these stages,
along with evidence about the investment patterns by stage.
Characteristic (5) also allows us to distinguish VC from other types of private
equity. Exhibit 1-2 illustrates the overlapping structure of the four main types of
private equity investing and also shows the intersection of these types with hedge
funds, another category of alternative investments. The relationship between
private equity and hedge funds will be discussed below.
The largest rectangle in the exhibit contains all of alternative investing, of
which private equity and hedge funds are only two of many components. These
components are represented by two smaller rectangles within alternative investing.
3
See http://www.sba.gov/size/
6 CHAPTER 1 THE VC INDUSTRY
The different types of private equity investing are represented by the overlapping
circles within private equity, with some overlap with hedge funds. The sizes of
the circles and rectangles are not matched to the scale of the investing categories,
but rather are intended to illustrate the relative scopes of overlap.
Venture capital sits on the far left of Exhibit 1-2 and intersects with the
mezzanine category. The term mezzanine has developed two distinct meanings
within the private equity industry. The ?rst meaning is a form of late-stage (often
very late-stage) venture capital. Some VC funds do this kind of investing (hence the
intersection); but so do other ?nancial intermediaries, including hedge funds, banks,
insurance companies, specialty ?nance corporations, and non-VC private equity
funds. This ?nancing is typically in the form of subordinated debt (junior to bank
loans), with some additional equity participation in the form of options (warrants)
to buy common stock. Some ?rms refer to this kind of investing as growth capital.
The second meaning of “mezzanine” ?rst arose in the mid-1980s, when investors
began to use the same capital structure—subordinated debt with some equity
participation—to provide another layer of debt ?nancing for highly leveraged
buyout (LBO) transactions. Today, most private equity ?rms with “mezzanine” in
their title are doing this second type of investing.
EXHIBIT 1-2
PRIVATE EQUITY AND HEDGE FUNDS
Venture
Capital Mezzanine
ALTERNATIVE INVESTMENTS
Private Equity
Hedge Funds
Buyout
Distress
1.1 WHAT IS VENTURE CAPITAL? 7
Because the subordinated debt in mezzanine investing will often be attached
to some equity ownership, mezzanine investing can also intersect with the pure
equity investing done in buyouts, the next category in Exhibit 1-2. Buyout investing
is the largest category of private equity, with total funds under management about
three times as great as for venture capital. Buyout investors pursue a variety of
strategies, but a key feature of buyout investors is that they almost always take
majority control of their portfolio companies. (In contrast, VCs usually take
minority stakes in their portfolio companies.) Large buyouts of public companies
typically garner the biggest headlines, and the most famous buyout of all time—the
$25 billion purchase of RJR Nabisco by Kohlberg, Kravis, and Roberts (KKR) in
1989—was the largest transaction of its kind until 2007, when KKR, Texas Paci?c
Group, and Goldman Sachs bought TXU Corp. for $45 billion. In these large
buyouts, the investors put up the equity stake (these days it is usually between 20
and 40 percent of the total purchase price) and then borrow the rest from banks,
public markets (noninvestment grade or “junk bonds”), and mezzanine investors—
hence the term leveraged buyouts (LBOs).
Despite the publicity generated by these large buyouts, most buyout ?rms are
engaged in more everyday deals involving the purchase of “middle-market”
companies. Although some of these so-called middle-market companies may
qualify among the largest 1 percent, many of them still lack the growth potential to
generate much interest from public markets. This is typically because the company
is in an older industry that has more stable cash ?ows and limited potential for
internal growth. In this case, private equity investors can create liquidity for the
current owners through a buyout. Such buyouts do not always include leverage. A
related strategy is “buy-and-build”, where a buyout investor will acquire a series of
?rms in a fragmented industry for the purpose of taking advantage of changes in the
optimal industrial scale. Although buy-and-build is a growth investment strategy,
the growth comes externally from the purchase of existing businesses.
The ?nal category of private equity is distress investing, also called special
situations. As the name suggests, distress investors focus on troubled companies.
Because many distress investments are buyouts, this category intersects with the
previous one. Some private equity investors do both traditional leveraged buyouts
and distress buyouts, but most investors specialize in either one or the other.
A separate category of alternative investing, hedge funds, is also included
in Exhibit 1-2. Hedge funds are ?exible investing vehicles that share many
characteristics of private equity funds, including the limited partnership structure
and the forms of GP compensation. The main difference, however, is that hedge
funds tend to invest in public securities. A good example of this distinction can
be seen in the area of distress investing, the area with the greatest overlap for private
equity and hedge fund investors. The private equity funds that engage in distress
investing usually do so with the intention of gaining control of the distressed
company (or some subset of the company). These investors then operate and
restructure the company before reselling it to another investor or to the public
markets. Hedge funds also engage in distress investing, but their main strategy is to
8 CHAPTER 1 THE VC INDUSTRY
trade in the public securities of distressed companies with the intention of making a
trading pro?t by quickly reselling these securities. In recent years, the distinction
between hedge funds and private equity funds has grown more blurred, with some
hedge funds beginning to invade the traditional private equity territory, particularly
in the buyout and distress space. For now, traditional VC investing, with its long
holding periods and relatively small investments, remains relatively free of hedge
fund involvement.
Although there are exceptions to this pattern, the basic distinction is that
while private equity funds are long-term investors, hedge funds are short-term
traders. Both strategies have the potential for outstanding returns, but the skill sets
and investment approaches are different enough that it is rare that a single indi-
vidual can excel at both. However, because their investments are more liquid than
those for private equity investors, hedge funds can offer their investors faster access
to their money, with withdrawals usually allowed on a quarterly or annual basis.
This is a case of form following function: if you have an investment strategy in
illiquid assets, then you need to lock up your investors for a long period of time
(private equity); if you have an investment strategy in liquid assets, then you can
allow for quicker withdrawals (hedge funds). Although hedge funds have occa-
sionally crossed over to private equity, any large-scale crossover would require a
change of contractual form toward a longer lockup. At that point, they would
become private equity funds.
1.2 WHAT DO VENTURE CAPITALISTS DO?
VC activities can be broken into three main groups: investing, monitoring, and
exiting. In later chapters, we will describe these activities in more detail. For now,
we will give brief summaries of each group and use these summaries to de?ne the
scope of this book.
Investing begins with VCs prospecting for new opportunities and does not end
until a contract has been signed. For every investment made, a VC may screen
hundreds of possibilities. Out of these hundreds, perhaps a few dozen will be worthy
of detailed attention, and fewer still will merit a preliminary offer. Preliminary offers
are made with a term sheet, which outlines the proposed valuation, type of security,
and proposed control rights for the investors. If this term sheet is accepted by the
company, then the VC performs extensive due diligence by analyzing every aspect
of the company. If the VC is satis?ed, then all parties negotiate the ?nal set of terms
to be included in the formal set of contracts to be signed in the ?nal closing. These
investing activities—especially the term sheet valuation and structure—are ideal
topics for ?nancial analysis and are the main subjects of this book.
Once an investment is made, the VC begins working with the company
through board meetings, recruiting, and regular advice. Together, these activities
comprise the monitoring group. Many VCs argue that these activities provide the
best opportunity to add value and are the main source of comparative advantage for
1.2 WHAT DO VENTURE CAPITALISTS DO? 9
a successful VC. This argument may indeed be correct, but monitoring activities do
not lend themselves well to quantitative analysis. Thus, aside from a discussion of
the academic literature in Chapter 5, we will not go into monitoring in this text.
The ?nal group of activities is exiting. As discussed earlier, VCs are ?nancial
intermediaries with a contractual obligation to return capital to their investors. How-
ever, the exit process itself requires knowledge and skills that are somewhat distinct
from the earlier investment and monitoring activities. VCs plan their exit strategies
carefully, usually in consultation with investment bankers. A typical IPO underwritten
by a top investment bank will sell at least $50 million of new stock and have a total
equity value of at least $200 million. Historically, the IPO has been the source of the
most lucrative exits. The mainalternative tothe IPOis a sale toa strategic buyer, usually
a large corporation. Sometimes these sales can be very pro?table for the VC, but only if
there is signi?cant competition for the deal, which often includes the possibility of an
IPO. Financial analysis is crucial for the valuation of IPO ?rms and acquisition can-
didates, and this analysis is discussed at length in the rest of this book.
1.3 THE HISTORY OF VENTURE CAPITAL
Equity investments in risky new ventures are as old as commerce itself. The
modern organizational form of venture capital, however, dates back only to 1946.
Bank lending rules then (and now) looked for evidence that borrowers had
collateral and could make timely payments of interest and principal. Most entre-
preneurial ?rms, however, didn’t meet these standards, so they required risk capital
in the form of equity. There was usually no regular source of such capital, meaning
that entrepreneurs without wealthy friends or family had little opportunity to fund
their ventures. Along came George Doriot to solve this problem. General Doriot, so
called for his rank in the U.S. Army quartermaster’s of?ce during World War II,
recognized the need for risk capital and created a ?rm to supply it. His ?rm,
American Research and Development Corporation (ARD), began operations in
1946 as the ?rst true VC ?rm. Unlike modern funds, it was organized as a cor-
poration and was publicly traded. In its 25-year existence as a public company,
ARD earned annualized returns for its investors of 15.8 percent.
4
ARD also set a
standard for generating these returns that has persisted to the present day. Excluding
the $70,000 investment in their biggest “home run”, the Digital Equipment
Corporation, ARD’s 25-year annualized performance drops to 7.4 percent. Many
modern venture capitalists spend their days searching for their own home runs, now
with more fanciful names like Yahoo!, eBay, and Google—all ?rms that started as
venture capital investments and made legendary reputations for their investors.
Today, venture capital is a well-established business throughout the developed
world, but remains quite geographically concentrated both across and within
4
Fenn, Liang, and Prowse (1998).
10 CHAPTER 1 THE VC INDUSTRY
countries, with the United States still comprising nearly half the VC activity in the
world.
5
Because the United States represents so much of the worldwide VC industry,
the data providers have followed the money, and we now know much more about
American VCs than we do about those of the rest of the world. In this chapter, we
focus on the history and statistics from the well-studied U.S. market, and most of this
book will refer to U.S. data and legal structures. This focus on the United States does
not limit the applicability of the analysis, because most global VCs follow U.S.
practices. Most importantly for our purposes, the ?nancial concepts of VC investing
are universal, and all the quantitative analysis in this book can be applied to VC
investments anywhere in the world. In Chapter 6, we provide statistics on the world
distribution of VC and discuss some reasons for the observed patterns.
General Doriot’s innovationin1946didnot changetheworldovernight, andeven
ten years later the VClandscape remained barren. In recognition of this problem faced
bysmall-growthbusinesses, the U.S. government beganits ownVCefforts as part of the
Small Business Act of 1958, which was legislation that created the Small Business
Administration and allowed the creation of Small Business Investment Companies
(SBICs). Perhaps the greatest success of the SBICprogramwas to provide a vehicle to
train a pool of professional VCs for the later decades. SBICs still exist today and share
many characteristics of modern VC ?rms; however, regulatory restrictions af?liated
with SBICs keep it from becoming the dominant institutional form.
An important milestone for the VC industry came in the 1960s with the
development of the limited partnerships for VC investments. In this arrangement,
limited partners put up the capital, with a few percentage points of this capital paid
every year for the management fees of the fund. The remaining capital is then
invested by the general partner in private companies. Successful investments are
exited, either through a private sale or a public offering, before the ten-year life of
the partnership expires. The most common pro?t-sharing arrangement is an 80À20
split: after returning all the original investment to the limited partners, the general
partner keeps 20 percent of everything else.
This pro?t sharing, known as carried interest, is the incentive that makes
private equity investing so enticing for investment professionals. In recent years,
the most successful general partners have demanded—and received—as much as
30 percent carried interest on new partnerships. Limited partnerships are by far the
most common form of organization in the VC industry, and in Chapter 2 we will
discuss these partnerships in detail.
Despite inroads made by SBICs and the new limited partnerships, total VC
fundraising in the United States was still less than $1 billion a year throughout the
1970s. The next big change for VC came in 1979, when the relaxation of investment
rules for U.S. pension funds led to historically large in?ows from these investors to
the asset class. To this day, pension funds continue to supply nearly half of all the
money for VC in the United States.
5
PricewaterhouseCoopers, Global Private Equity Report 2008, p. 44.
1.3 THE HISTORY OF VENTURE CAPITAL 11
The participation by pension funds hastened the participation by other
institutional investors, and the modern era of venture capital began. Exhibit 1-3
displays the total amount of venture capital invested by year from 1980 to 1994.
Investing activity rose sharply to $3B in 1983 and remained remarkably
stable through the 1980s. After a slight drop in 1990À1991, VC investment began a
steady climb; from $2.2B in 1991, it rose gradually to $4.1B in 1994. We refer to
these ?rst 15 years of the modern VC industry as the preboom period. As shown in
Exhibit 1-4, it was in 1995 that investment really began to grow quickly.
EXHIBIT 1-3
VC INVESTMENT, PREBOOM (IN $B)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Source: National Venture Capital Association Yearbooks.
EXHIBIT 1-4
VC INVESTMENT, BOOM AND POSTBOOM (IN $B)
0
20
40
60
80
100
120
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Source: 2009 NVCA Yearbook, NVCA website.
12 CHAPTER 1 THE VC INDUSTRY
Exhibit 1-4 shows investment nearly doubling to $7.9B in 1995 (from $4.1B
in 1994) at the beginning of an incredible growth period. This was the dawn of the
Internet era, and some of the VC investments made in 1995 and 1996 had
spectacular returns. This caused institutional investors to rush for a piece of the
asset class, and investments rose to $11.0B in 1996, $14.7B in 1997, and $20.9B
in 1998—before exploding to the previously unimaginable levels of $53.4B in
1999 and $104.0B in 2000. For obvious reasons, we refer to 1995 to 2000 as the
boom period.
As the euphoria faded in the early 21st century, VCs still had large com-
mitments from their investors, and many portfolio companies—funded in the late
1990s and 2000—were hungry for follow-on investments. Still, spending fell to
$40.3B in 2001 before leveling off at between $20B and $30B in the subsequent
years. We refer to the years after 2000 as the postboom period. Indeed, the boom
period ended abruptly at the end of 2000, as investment fell by nearly half from the
fourth quarter of 2000 to the ?rst quarter of 2001.
Although the postboom numbers are well below the peak of 2000, they still
represent a considerable increase on investment prior to 1995. This can be seen by
looking at VC investment as a fraction of GDP, where VC investment hit a new
peak of 0.084 percent in 1983 and fell steadily to its modern all-time low of 0.036
percent in 1991 before rising to 0.058 percent at the end of the preboom period in
1994. The percentage jumped to 0.106 percent to mark the beginning of the boom
period in 1995, then rose steadily to hit 0.571 percent in 1999 and its maximum of
1.045 percent in 2000. In the postboom period, the percentage has leveled off to
about 0.2 percent in 2002À2008, well above the levels of the 1980s and approxi-
mately the same as the percentages in 1997 and 1998.
It is dif?cult to put these investment levels in perspective without some model
of VC’s place in the economy. How can we tell if the new levels of investment
($20À30B, or 0.2 percent of GDP) is too low, too high, or just right? One way to
approach this question is to start with the de?nition of VC at the beginning of this
chapter. There, we discussed how VCs invest in small companies that have the
potential to become large quickly through internal growth. To qualify, a company
usually needs some sort of product innovation, usually a novel item that can
penetrate a large market. Sometimes the proposed innovation is high tech, such as a
new drug or a new type of software. Alternatively, the innovation might be in a
business process, where an early mover could erect barriers to entry by competitors.
Many of the Internet startups took this route, although most of them unfortunately
ignored the requirement that there be a barrier to entry.
With this framework, we can see that it is not just an innovation that is
necessary, but rather an innovation that should be made by a small company. Tre-
mendous innovation goes on all the time in large companies, and large companies are
the optimal place for the majority of high-tech innovations. With large research
staffs, a stockpile of trade secrets, and decades of organizational learning, companies
like IBM, Microsoft, Intel, P?zer, and Merck are factories of innovation. If a small
1.3 THE HISTORY OF VENTURE CAPITAL 13
company proposed to develop, build, and sell a new microprocessor for personal
computers, it would face almost certain failure in the face of the industry giants. If,
however, a small company proposed to develop a small piece of the technology for
such microprocessors—a piece that could be patented and potentially licensed across
a wide range of products—then this might be (and has been) accomplished.
So how much innovation should occur in small companies? In general, this
will depend on the factors that drive the optimal scale of an innovative enterprise.
In the 1990s, communications technology changed radically, with development of
the Internet occurring alongside large price decreases for telecommunications. This
communications revolution was real, even if some potential pro?ts from the
revolution proved to be illusory. Lower costs of communication opened up new
opportunities for market transactions, with lower transaction costs than traditional
methods. According to the theory of the ?rm ?rst introduced by Ronald Coase in
1937, a universal reduction in transaction costs should reduce the optimal scale of
?rms and allow for greater levels of innovation by small companies.
By this reasoning, the higher levels of VC investment that we see today—
as compared to the 1980s—may indeed represent an optimal reaction to structural
changes in the economy. Even the massive investments of 1999 and 2000, although
clearly excessive in some respects, also appear to be at least in part a response to
rapid changes in transaction costs. Prior to the Internet era, national retail brands
required massive infrastructure and logistics support. With the Internet, retailers
could operate from a single location, and consumers could ?nd them from any-
where in the world.
The organizational constraints of large enterprises seemed to prevent the
rapid competitive reactions that could have sti?ed some of these innovations. For
example, large booksellers such as Barnes and Noble already possessed the brand
name, the infrastructure, and the inventory to compete effectively as online
booksellers. Nevertheless, Amazon.com, a venture-backed startup, managed to out-
innovate and out-compete them, to the point that Amazon’s business became far
more valuable than that of its older competitor. Amazon, although among the most
successful, is one of many examples of successful entrants that relied on the new
communications technology.
1.4 PATTERNS OF VC INVESTMENT
IN THE UNITED STATES
In this section, we provide evidence about VC investing by stage, industry, and
region.
1.4.1 Investments by Stage
There are many steps, or stages, to building a new VC-backed business. In Section 1.1,
we introduced the terminology for the three broad stages: early-stage, mid-stage, and
14 CHAPTER 1 THE VC INDUSTRY
late-stage. A more complete description of these stages, along with some sub-
categories, is found in Exhibit 1-5.
EXHIBIT 1-5
STAGES OF GROWTH
6
Seed/Startup Stage Financing
This stage is a relatively small amount of capital provided to an inventor or
entrepreneur to prove a concept. If the initial steps are successful, this may involve
product development, market research, building a management team, and deve-
loping a business plan. This is a pre-marketing stage.
Early Stage Financing
This stage provides ?nancing to companies completing development where pro-
ducts are mostly in testing or pilot production. In some cases, products may have
just been made commercially available. Companies may be in the process of
organizing, or they may already be in business for three years or less. Usually such
?rms will have made market studies, assembled the key management, developed a
business plan, and are ready to or have already started conducting business. This
involves the ?rst round of ?nancing following startup, which includes an institu-
tional venture capital fund. Seed and startup ?nancing tend to involve angel
investors more than institutional investors. The networking capabilities of the
venture capitalists are used more here than in more advanced stages.
Expansion (Mid) Stage Financing
This stage involves applying working capital to the initial expansion of a company.
The company is now producing and shipping and has growing accounts receivable
and inventories. It may or may not be showing a pro?t. Some of the uses of capital
may include further plant expansion, marketing, or development of an improved
product. More institutional investors are likely to be included along with initial
investors from previous rounds. The VC’s role in this stage involves a switch from
a support role to a more strategic role.
Later Stage
Capital in this stage is provided for companies that have reached a fairly stable
growth rate—that is, companies that are not growing as fast as the rates attained in
the expansion stages. Again, these companies may or may not be pro?table, but are
more likely to be pro?table than in previous stages of development. Other ?nancial
characteristics of these companies include positive cash ?ow. This also includes
companies considering IPOs.
6
These descriptions are nearly verbatim from the 2009 National Venture Capital Association Yearbook,
p. 87.
1.4 PATTERNS OF VC INVESTMENT IN THE UNITED STATES 15
The main theme of next exhibit is the steady trend toward later-stage investing.
In the early 1980s, the three categories of “seed/startup”, “early”, and “expansion”
were approximately equal, and “later stage” was the smallest. This pattern re?ects
VC’s focus on true startups in the early years of the industry. Gradually, new VC
?rms were created to focus on later stages, and some of the original ?rms grew so
large from their successes that they needed to ?nd larger investments to put all their
capital to work. By the mid-1990s, expansion stage investments were larger than all
early-stage investments (seed/startup plus other early-stage), and later-stage invest-
ments exceeded those in seed/startup. By the late 1990s, angel investors had largely
replaced VCs at the seed/startup stage, and expansion investments comprised more
than half of all VC investments. More recently, there are modest reversals in this
trend, with the share of startup/seed investments exceeding 5 percent of total for the
?rst time since 1999, while the share of expansion investments declined to less than
40 percent in 2008.
The de?nition of the company stage should not be confused with the de?-
nition of the ?nancing round. The negotiation of a VC investment is a time-
consuming and economically costly process for all parties. Because of these costs,
neither the VCs nor the portfolio ?rms want to repeat the process very often.
Typically, a VC will try to provide suf?cient ?nancing for a company to reach
some natural milestone, such as the development of a prototype product, the
acquisition of a major customer, or a cash-?ow breakeven point. Each ?nancing
event is known as a round, so the ?rst time a company receives ?nancing is
known as the ?rst round (or Series A), the next time is the second round (or
Series B), and so on. With each well-de?ned milestone, the parties can return to
the negotiating table with some new information. These milestones differ across
industries and depend on market conditions; a company might receive several
rounds of investment at any stage, or it might receive suf?cient investment in one
round to bypass multiple stages.
With these de?nitions in hand, we are now ready to examine the investment
patterns by stage. Exhibit 1-6 illustrates these patterns by plotting the percentage of
investment each year by stage.
1.4.2 Investments by Industry
Traditionally, VC investments have been concentrated in two broad sectors: health
care and information technology (IT), where the latter sector is de?ned to include
the communications, semiconductor, software, and hardware industries. This con-
centration is no accident: because VCs invest in small companies with the potential
to quickly grow large, they need to look for businesses with large, addressable
markets. To make headway in such markets, a business usually needs a technological
advantage of some kind—hence the VC focus on the high-tech industries of health
care and IT. Of course, other industries can also provide these opportunities,
16 CHAPTER 1 THE VC INDUSTRY
particularly during times of disruptive economic change. The communications
revolution of the late 1990s provided such an opportunity for Internet-based retail
businesses, and periodic oil shocks have provided the impetus for energy
investments.
Exhibit 1-7 illustrates the industry concentration of VC investment for
three periods: the preboom period of 1980À1994, the boom period of
1995À2000, and the postboom period of 2001À2009. The data show the dom-
inance of IT (including communications, software, hardware, and semi-
conductors/electronics) and health care (including biotech and medical devices)
for VC investment; together, these two sectors comprise about 75 and 80 percent
of all investments in the preboom and postboom period, respectively. During the
boom, media/retail investment had a brief (and expensive) rise, but even then
the main story was the enormous increase in IT relative to health care. Within the
EXHIBIT 1-6
VC INVESTMENT BY STAGE
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1
9
8
0
1
9
8
2
1
9
8
4
1
9
8
6
1
9
8
8
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
8
2
0
0
0
2
0
0
2
2
0
0
4
2
0
0
6
2
0
0
8
Later Expansion Early Seed/Startup
Source: 2009 NVCA Yearbook, NVCA website.
1.4 PATTERNS OF VC INVESTMENT IN THE UNITED STATES 17
broad IT sector, the two most important industries in the boom and post-
boom periods were communications and software, followed by semiconductors/
electronics and hardware. Within health care, the story has been a gradual
emergence of biotechnology as the dominant industry, receiving almost 60
percent of total health care investment in recent years.
1.4.3 Investments by U.S. Region
With all the evidence of globalization in manufacturing and IT services, the U.S.
regional concentration of VC investment is particularly striking. Since the begin-
nings of the industry, the Silicon Valley area of northern California has remained the
epicenter of VC activity, with a consistent share of about one-third of total U.S. VC
investments per year. The area surrounding Boston has remained a secondary center
for most of this time, with between 10 and 15 percent share of the total. Exhibit 1-8
illustrates the distribution of VC investment for these centers and other U.S. regions
for 2008.
The dominance of Silicon Valley and New England (mainly Boston) hides
some important globalizing forces. Although companies headquartered in these
two regions receive almost half of all VC dollars, much of these funds are then
reinvested in foreign operations, particularly in India, by IT companies. This is a
21st-century phenomenon that has taken the industry by storm. Although it is
EXHIBIT 1-7
VC INVESTMENT BY INDUSTRY
Business/Financial Services
Media/Retail
Industrial/Energy
Medical Devices and Equipment
Biotechnology
Hardware
Semiconductors/Electronics
Software
Communications
0% 5% 10% 15% 20% 25% 30%
Postboom
Boom
Preboom
Source: Various years, NVCA Yearbooks.
18 CHAPTER 1 THE VC INDUSTRY
dif?cult to ?nd hard numbers to document this trend, such outsourcing is a common
topic of conversation among VCs.
SUMMARY
Venture capitalists (VCs) primarily invest in young, high-technology companies that have a
capacity for rapid growth. VCs are a type of ?nancial intermediary that perform three main
functions, which are (1) screening potential investments and deciding on companies to invest in,
(2) monitoring these companies and providing value-added services for them, and (3) exiting
their investments in these companies by selling their stake to public markets or to another buyer.
Venture capital is a form of private equity, which is an investment that cannot be traded in
public markets. Without the information ?ow and liquidity of public markets, VC investing
offers greater opportunities for both huge gains and terrible losses.
The modern VC industry effectively began in 1946 and grew slowly for its ?rst
35 years. Beginning in the early 1980s, new sources of capital from pension funds led to
EXHIBIT 1-8
REGIONAL DISTRIBUTION OF VC INVESTMENT
Silicon valley;
38.8%
Philadelphia; 2.7%
Colorado; 2.9%
DC/Metroplex; 3.5%
Northwest; 4.1%
San Diego;
4.3%
Southeast;
4.4%
Texas; 4.5%
Midwest;
4.8%
NY Metro;
6.6%
LA Orange
County;
7.0%
New England;
11.6%
Other;
4.8%
Source: 2009 NVCA Yearbook.
SUMMARY 19
rapid growth. This period of rapid growth leveled off in the mid-1980s and resumed in the
mid-1990s, culminating in a boom and crash at the turn of the century. The United States is
the world leader in VC, with about 40 percent of the worldwide investment and industry-
leading practices. Within the United States, information technology and health care are the
dominant sectors for VC investment, and Silicon Valley and the area around Boston,
Massachusetts, garner roughly half of all the domestic venture capital.
KEY TERMS
Venture capital (VC) and
venture capitalists (VCs)
Screen
Monitor
Exit
Financial intermediary
Limited partnership, limited
partner, general partner
Portfolio companies
Small Business Investment
Companies (SBICs)
Initial public offering
(IPO)
Angel investors = angels
Alternative investments
Private equity
Strategic investing
Corporate venture capital
Preboom, boom, postboom
periods
Early-stage, mid-stage
(expansion), late-stage
Mezzanine
Growth capital
Leveraged buyouts
(LBOs)
Distress investing5special
situations
Hedge funds
Term sheet
Due diligence
Management fees
Carried interest
Seed stage, Startup stage
Financing Round, First
round (Series A),
Second round (Series B)
REFERENCES
Coase, Ronald, 1937, “The Nature of the Firm”, Economica.
Fenn, George, Nellie Liang, and Stephen Prowse, 1998, “The Private Equity Market: An Overview”,
Financial Markets, Institutions & Instruments 6(4).
National Venture Capital Association, The NVCA Yearbooks, various years.
20 CHAPTER 1 THE VC INDUSTRY
CHAPTER 2
VC PLAYERS
THIS CHAPTER introduces the key players in the VC industry. In Section
2.1, we discuss the relationships among VC ?rms, VC funds, and the VCs who
work at them. In Section 2.2, we provide statistics on the investors in VC funds and
discuss the importance of various investor types. Section 2.3 analyzes the con-
tractual structure and compensation arrangements between VCs and their investors.
2.1 FIRMS AND FUNDS
About 80 percent of the organized VC market is controlled by independent VC ?rms.
VC ?rms are small organizations, averaging about 10 professionals, who serve as the
general partner (GP) for VC funds. A VC fund is a limited partnership with a ?nite
lifetime (usually 10 years plus optional extensions of a few years). The limited
partners (LPs) of VC funds are mostly institutional investors, such as pension funds,
university endowments, and large corporations. When a fund is ?rst raised, the LPs
promise to provide a certain amount of capital, which will be provided either on a set
schedule or at the discretion of the GP. These periodic capital provisions are known
as capital calls, drawdowns, or takedowns. The total amount of capital promised by
the LPs over the lifetime of the fund is called the committed capital of the fund.
1
Once the GP has raised the full amount of committed capital and is ready to start
investing, we say that the fund has been closed. The typical fund will invest in
portfolio companies and draw down capital over its ?rst ?ve years. These years are
known as the investment period or commitment period. After the investment
period is over, the VC can only make follow-on investments in current portfolio
companies. A successful VC ?rm will raise a new fund every few years so that there
is always at least one fund in the investment period at all times.
Most VC ?rms specialize their funds by stage, industry, and/or geography. For
example, an early-stage fund would make initial investments in early-stage compa-
nies, with some capital reserved to make follow-on investments in these companies in
their later stages. A late-stage fund would typically avoid all early-stage companies,
1
Typically, about 1% of the committed capital is provided by the GP itself. Throughout this textbook, we
will ignore this small GP contribution and pretend as if all committed capital is coming from the LPs.
21
focusing on expansion and later-stage investments. Most VC ?rms keep the same stage
focus for all their funds, but some will change focus over time or mix the two strategies
at once in a multistage fund. A few ?rms raise separate early-stage and late-stage
funds for overlapping periods and assign different professionals to each fund.
There is a wide dispersion in the levels of industry focus, with many generalists
(a fund that is willing to invest in both IT and health care is effectively a generalist)
and others with a relatively narrow focus on sectors like energy or ?nancial services.
As for geographic focus, it is important to recognize that much of the activity
experienced by VCs is local, and as a result the location of the VC’s of?ce will
usually be highly correlated with the location of most of their portfolio companies.
Not surprisingly, the geography of VC of?ces is very similar to the geography of VC
investment shown in Exhibit 1-8. Because funds tend to be geographically focused
wherever their of?ces are, the main way to attain reliable geographic diversity is to
have multiple of?ces.
Throughout this book, we will use a few prototype VC funds as example
investors. Because the compensation structures and partnership agreements of VCs
are an important driver of their investment incentives, it is useful to write down
some key terms from these agreements for our prototype funds. We do this in the
appendices to this chapter: Appendix 2.A shows some key terms for EarlyBird
Ventures Fund I, which is a $100M initial fund raised for an early-stage investor;
Appendix 2.B shows some key terms for Talltree Ventures IV, the $250M fourth
fund raised by a multistage ?rm; and Appendix 2.C shows some key terms for Owl
Ventures IX, a $500M ninth fund raised by a late-stage ?rm with a stellar reputation
and excellent track record. We will refer to these appendices several times in this
chapter and later on in the text.
Exhibit 2-1 gives a timeline for several funds for one of our prototype VC
?rms, EarlyBird Ventures (EBV).
2
A ?rm will usually number its successive funds,
so EarlyBird Ventures I is known to be the ?rst fund raised by EBV, EarlyBird
Ventures II was the second fund, and so on. In this example, EBV raises its ?rst
fund, EBV I, in 1994 with $100M in committed capital. (Think of EBV I as
the fund described in Appendix 2.A.) In future years, the performance of EBV I will
be compared to other funds raised in 1994; in industry parlance, all such funds
will have 1994 as their vintage year. This borrowed terminology from the wine
industry is appropriate: just as the weather conditions of certain years are better for
growing grapes, the economic conditions of certain years are better for growing
companies. By comparing the performance of EBV I with other funds of the same
vintage year, future investors can make a fair evaluation of EBV’s performance
as a GP.
3
2
All of our prototype funds are ?ctitious. Any resemblance to real funds, living or dead, are purely
coincidental. In case some readers are wondering, we were not aware at the time of writing this textbook
that there exists an actual early technology investment ?rm called Earlybird in Germany.
3
However, please note that some ?rms keep us on our toes by giving their funds a completely different
name from their ?rm name.
22 CHAPTER 2 VC PLAYERS
By 1998, most of EBV I has been invested. We assume here that EBV I look
good relative to other funds with a 1994 vintage year, so it is able to raise a larger
fund, EBV II, in 1998. It invests this fund rapidly in the boom years of 1999
and 2000 and returns to raise an even larger fund, EBV III, of $1 billion in 2000. By
2000, in addition to EBV III, it has two funds, EBV I and II, which are no longer
making any new investments but still have some investments outstanding. When
the market loses steam, it invests this fund slowly and with much less success than
its earlier funds. Nevertheless, its earlier reputation allows the ?rm to return to the
market, somewhat chastened, and raise a $300M fund, EBV IV, in 2005. By this
point, it has closed out all its investments from EBV I and is still trying to exit a
few investments from EBV II. As for EBV III, most of the portfolio companies
have gone out of business, but it still has modest hopes for some of the survivors.
Four years later, in 2009, EBV raises another $300M fund, EBV V, which is a
respectable size given the generally dif?cult fundraising conditions in the market.
EBV I and II are fully liquidated by then; EBV III is almost mature, but many of its
portfolio companies are still illiquid.
The experience of EBV is typical for top VC ?rms since the mid-1990s. Great
success for investments at the beginningof the boom, combinedwith seemingly endless
opportunities, led many ?rms to raise “megafunds” in 1999 and 2000. Whereas billion
dollar funds were unheardof before, theybecame almost commonplace duringthis time
period. With few exceptions, these funds performed terribly, and the surviving ?rms
have returned to raise much smaller funds in recent years.
We can gain a more detailed picture of these trends by looking at some data
from the National Venture Capital Association. Exhibit 2-2 gives its estimates on
the total number of ?rms, funds, and VC professionals since 1980.
This data echoes the industry cycles discussed in Chapter 1. Between 1997 and
2001, there was a doubling or near doubling of the total number of VC funds, the
total number of VC ?rms, and the size (capital divided by funds or ?rms) of these VC
funds and VC ?rms. The size of the industry hit a plateau in 2001 and stayed steady
between 2002 and 2006. The industry size started to decline in 2007, and between
EXHIBIT 2-1
EARLYBIRD VENTURES TIMELINE
Fund Name Vintage Year Committed Capital
Early Bird Ventures I 1994 $100M
Early Bird Ventures II 1998 $250M
Early Bird Ventures III 2000 $1B
Early Bird Ventures IV 2005 $300M
Early Bird Ventures V 2009 $300M
2.1 FIRMS AND FUNDS 23
2007 and 2008 the capital under management fell 24 percent, while the number of
?rms and the number of principals declined by 13 percent and 16 percent, respec-
tively. The contraction occurred because large funds raised in 2000 were largely
rolled out of the industry’s managed capital and were replaced by much smaller funds
EXHIBIT 2-2
VC INDUSTRY SIZE SINCE 1980
Year
New
Funds
New
Committed
Capital ($B)
Total
Funds
Total
Firms
Total
Committed
Capital ($B)
Total
Principals
(Estimate)
Principals
Per Firm
1980 52 2.0 129 92 4.1 1,435 15.6
1981 75 1.5 188 127 6.1 1,805 14.2
1982 87 1.7 248 162 7.8 2,138 13.2
1983 143 3.9 355 208 11.4 2,600 12.5
1984 116 3.0 459 260 14.6 3,224 12.4
1985 121 4.0 541 297 17.9 3,641 12.3
1986 103 3.8 603 332 21.5 4,038 12.2
1987 116 4.4 681 362 24.2 4,368 12.1
1988 104 4.4 715 377 25.5 4,550 12.1
1989 105 4.9 746 392 28.6 4,770 12.2
1990 87 3.2 734 393 29.2 4,834 12.3
1991 42 2.0 660 373 27.8 4,588 12.3
1992 80 5.2 620 365 28.4 4,563 12.5
1993 88 3.9 625 376 29.8 4,675 12.4
1994 140 8.9 651 389 34.7 4,824 12.4
1995 172 9.9 707 429 40.6 5,320 12.4
1996 162 11.8 773 469 48.9 5,769 12.3
1997 244 19.8 903 548 63.7 6,753 12.3
1998 288 29.7 1,085 624 92 7,550 12.1
1999 451 55.8 1,394 752 145.3 9,123 12.1
2000 653 105.0 1,737 881 225.2 10,684 12.1
2001 321 39.1 1,883 943 253.1 11,340 12.0
2002 206 9.3 1,852 938 253.1 11,186 11.9
2003 163 11.6 1,800 968 254.2 11,112 11.5
2004 219 19.8 1,823 1,003 262.9 10,896 10.9
2005 235 28.7 1,778 1,024 271.4 10,680 10.4
2006 241 31.8 1,722 1,027 278.1 10,260 10.0
2007 247 35.4 1,593 1,019 258.3 8,892 8.7
2008 210 27.9 1,366 882 197.3 7,497 8.5
Source: 2008 and 2009 NVCA Yearbooks.
24 CHAPTER 2 VC PLAYERS
raised in more recent years. Many ?rms that raised funds at the height of the bubble
are winding down their portfolios and exiting the industry, which also contributes to
the decline in the number of ?rms and principals. This trend is likely to continue for
some time to come. Note also that, even with two years of sharp declines, the capital
under management is still higher than the 1999 level.
In most years, the total number of funds is about twice as large as the number of
?rms, indicating that the average ?rm has two funds alive at any given time. Because of
differences in the data collection methods and sample selection, the committed-capital
amounts in Exhibit 2-2 are not directly comparable to the investment totals given in
Exhibits 1-3 and 1-4. Nevertheless, the general trends are very similar.
One striking aspect of these numbers is that there has been a steady rise in the
size of the capital managed per ?rm and per principal up until 2006À2007, while
the number of principals per ?rm itself held steady at around 12 between the mid
1980s and 2002 and even declined to 8.5 by 2008. Thus, the main trend has been a
gradual scaling up of the dollar amount managed per personnel, while the VC ?rms
themselves stayed relatively lean as organizations.
Relative to other investment and professional service ?rms, VC ?rms are quite
top-heavy and rarely showmuch of a pyramid structure. Althoughsome VCs enteredthe
industry directly out of school, most came to VC as a second career and entered
the profession at a fairly senior level, so there are not as many junior people ?oating
around. Although many people would like to know the best way to prepare for a VC
career, there is no “typical” path. Nevertheless, the analysis of hand-collected data on
125 partners from 15 VC ?rms in Wieland (2009) offers some interesting insights.
In this sample, 60 percent of VC partners hold a bachelor’s, master’s, or doc-
torate degree in science or engineering. Particularly common is a bachelor’s degree in
engineering, which 44 percent of the VCs hold. While 25 percent of VCs hold a
master’s degree and 9 percent hold a Ph.D. in engineering or science, the most
common postgraduate degree held by VCs are MBA degrees—62 percent hold them.
A signi?cant minority—16 percent—also hold a bachelor’s degree in business or
economics. As for their professional experience, most of the work experience of
individual VCs comes in the form of having worked in the IT or health care sector
(78%), having startup experience as either entrepreneur (37%) or managing executive
at a startup ?rm (32%), holding experience as line manager at a listed ?rm (38%),
having worked as industrial engineer (31%) or professional scientist (5%), having
worked for another VC ?rm as investment professional (32%), and holding experience
working as strategy consultant (23%) or in ?nance (14%).
4
Although an advanced
degree is not a necessary requirement, the most notable exceptions are second-career
VCs whose ?rst career was as a successful entrepreneur. Indeed, most VCs are in their
second career because few jobs are available to new graduates. These ?rst careers
might be decades long and consist of top management experience, or they might be
4
Zarutskie (2009) studies educational and professional backgrounds of ?rst-time VC funds and report
similar educational backgrounds: 39% of individual VCs hold a degree in either engineering or science
and 58% hold an MBA.
2.1 FIRMS AND FUNDS 25
just a few years long, consisting of a few years of experience at a consulting ?rm or at
an investment bank. Consulting and investment banking are not particularly good
ways to prepare for a VC career; it is just that many top MBA graduates start there, so
that is where the talent is. Many VCs will say that the best preparation for a VC career
is to combine technical expertise with industry experience, particularly if that
experience is at a startup ?rm. Many VC hopefuls are understandably reluctant to
follow this advice, because the VC industry has cyclical and somewhat ?ckle pre-
ferences about exactly what kind of technical experience is useful, and an unlucky
choice of specialization can render a candidate’s expertise to be super?uous.
As for the career progression, it does not have many levels. The top level is
“partner”, with modi?ers in front of that title to indicate experience, past success,
and compensation level (e.g., “Managing General Partner” or “Senior Partner”).
Although some professionals begin their VC careers as partners—either by raising
their own fund or by joining another fund after a very successful ?rst career—most
VCs have to work their way up. There are essentially two tracks to make partner.
One track, typically followed by younger professionals with a few years of pre-VC
experience, is to start as a junior VC with a title like associate, senior associate, or
principal. These professionals are not expected to lead transactions or sit on boards
in their ?rst few years, but rather spend most of their time screening investments,
performing due diligence, and generally helping out the partners. They are expected
to learn the business as apprentices, and if they are successful, their responsibilities
will be gradually increased. Depending on their past experience, the time path to
partnership can vary tremendously. With good timing and good performance, some
junior professionals can make partner in as little as two years. At the other extreme,
some ?rms do not treat these junior positions as being on the partner track, sending
even their most talented associates back out into the world to gain more experience.
Similarly, some ?rms employ recent college graduates as analysts, with tasks
similar to other junior VCs. Although these positions are generally not considered
to be on the partner track, analysts who go on to get advanced degrees have great
positioning to land a partner-track job in the future.
The second track, typically followed by successful entrepreneurs or senior
managers with many years of experience, is to enter with the title of venture
partner. This title does not mean that the new VC is a partner in the sense of sharing
the pro?ts, but rather it is a way to bring in someone trying out VC as a second
career without subjecting them to the same grind or title as a junior professional.
Venture partners would typically be expected to take a lead role on investments and
to use their industry contacts to bring in new business right from the beginning. In
this respect, venture partner is very much a provisional position, with many can-
didates ?nding out that the business is not really for them. With one or two suc-
cessful investments, a venture partner can expect to be admitted into a true partner
role. Indeed, venture partners are often paid only small salaries—the idea being that
if they are successful, they will quickly earn a partnership.
GPs receive their income from two sources—management fees and carried
interest—andthese sources must supply all the compensationfor the VCs. Base salaries
26 CHAPTER 2 VC PLAYERS
can be paid frommanagement fees, and the biggest slice of variable pay comes fromthe
carry. In most funds, the total carry percentage will be divided in advance, with partners
knowing what share of the overall carry they are due to receive. Exhibit 2-3 shows
compensationlevels for salary, bonus, andcarriedinterest for several different jobtitles.
These ?gures are from the annual Private Equity Analyst-Holt Compensation Survey,
which in 2008 received data from46 independent venture capital ?rms for 16 job titles.
Note that salaries are as of April 1st of the survey year, and bonus and carry are earned
the year before. Thus, these compensation levels re?ect fund performance in the year
prior to payment.
The levels are shown for 2008 and for 2009, so one can see the large role
played by market conditions. While the bonus levels are largely unchanged, bonus
and carry declined in 2009 due to dif?cult economic times and tough exit condi-
tions for VC-backed companies.
2.2 THE LIMITED PARTNERS
As mentioned in Chapter 1, the ?rst major burst of VC activity was driven by the
entry of pension funds as limited partners. Since 1980, pension plans—including
those of government entities, private companies, and nonpro?t organizations—have
provided 44 percent of the committed capital in the VC industry. In addition to
pension funds, several other investor groups have played an important role in the
EXHIBIT 2-3
VC COMPENSATION (IN $ THOUSANDS)
2008 2009
Title Salary Bonus Carry Total Salary Bonus Carry Total
Managing GP 688 633 192 1,513 700 350 101 1,151
Senior Partner 595 350 155 1,100 600 200 50 850
Partner 375 150 35 560 350 130 20 500
Principal/VP 240 78 2 320 206 75 6 287
Senior Associate 155 46 0 201 156 44 1 201
Associate 105 33 0 138 105 35 0 140
Analyst 101 15 0 116 100 10 0 110
Venture Partner 250 0 43 293 185 40 12 237
NOTE: 2008 data are April 1, 2008, salaries and bonus and carry earned in 2007. 2009 data are April 1,
2009, salaries and bonus and carry earned in 2008. The ?gures are based on annual compensaton surveys
of VC professionals and samples are not matched across years.
Source: Mike Holt, Founder and Managing Director of Holt Private Equity Consultants and coauthor of
Private Equity Analyst—Holt Compensation Survey.
2.2 THE LIMITED PARTNERS 27
development of VC. Exhibit 2-4 shows the fraction of newly committed capital
from these groups.
5
After pension funds, the next largest investor class is ?nancial institutions,
which includes commercial banks, investment banks, and insurance companies.
Taken together, this group has provided about 18 percent of the committed capital
since 1980. Endowments and foundations are next with 17 percent of the total. This
group is dominated by large private universities and charitable foundations. In
addition to their large supply of capital, these organizations are also the most
successful of the investor classes, with returns that far exceed those of the other
investors.
6
Part of the reason for their success is that they have been active and
consistent investors since the earliest partnerships were formed in the late 1960s
and early 1970s. However, evidence also shows that access to these older funds
EXHIBIT 2-4
COMMITTED CAPITAL BY LIMITED PARTNER TYPE
Pension Funds
Endowments &
Foundations
Individual and Family
Corporations
Financial & Insurance
70%
60%
50%
40%
30%
20%
10%
0%
Year 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
Source: National Venture Capital Association Yearbooks.
5
NVCA stopped reporting this type of data in recent years, but it appears that the fractions among the
groups have not changed signi?cantly. In 2004, the last year the data is publicly available, the breakdown
was pension funds (42%), ?nancial and insurance (25%), Endowments and foundations (21%), Indivi-
dual and family (10%), and Corporations (2%).
6
Lerner, Schoar, and Wongsunwai (2007) document this performance.
28 CHAPTER 2 VC PLAYERS
explains only part of their superior returns, and that the endowments have in fact
also done very well with their recent partnerships.
Since 1980, individuals and families have contributed about 11 percent of total
committed capital, with this fraction falling slightly in recent years. As compared to
other investment classes, this participation by individuals is low. Part of the reason
for this low participation is that the long horizon of VC investment is comparatively
more palatable to institutions than it is to individuals.
Finally, with only 9 percent of the total commitments since 1980, corpora-
tions have played a relatively small role as limited partners as compared to the
important role of their corporate pension plans. Note also that corporate partici-
pation is more variable than it is for other investors, and the importance of cor-
porate LPs has fallen dramatically in recent years. This type of indirect corporate
investment as an LP should not be confused with direct corporate investment in
portfolio companies, a practice that is known as corporate venture capital. Direct
corporate investment is not included in Exhibit 2-4, unless the corporation is
included as an LP in its own ?nite-life corporate VC fund. Because most corporate
VC funds are not organized as ?nite-life limited partnerships, the majority of direct
corporate investment is not included in this exhibit.
Exhibit 2-4 de?nes the fund ?ow by the ultimate source of capital, but in some
cases additional intermediaries stand between the capital provider and the VC. One
group of intermediaries deserves special mention: the fund-of-funds (FOF). An FOF
is typically organized as a limited partnership, with many of the same rules as other
private equity funds, except that, instead of investing directly in companies, the FOF
invests in other private-equity funds. For example, FLAG Venture Management is a
?rmthat invests exclusively in other VC?rms through FOFs. These FOFs can be quite
large: the 2000 Flag Venture Partners Fund IV has committed capital of $650M; other
boom-time FOFs raised multibillion dollar funds. FOFs appeal mostly to wealthy
individuals and small institutions that are not large enough to support a diversi?ed
portfolio of LP commitments. By pooling their resources in a FOF, a group of smaller
investors can gain access to a diversi?ed portfolio of funds and take advantage of the
contacts and skills of the specialized FOF intermediary. During the boom period,
FOFs intermediated about 5 percent of all commitments to VCfunds. FOF ?rms act as
both a GP (to their investors) and an LP (to the funds they invest in). As a GP, they also
charge management fees and (sometimes) carried interest, although these charges are
always considerably lower than those charged by direct investment ?rms.
It is important to note that LPs are not just investors, but also really are
partners in the fund. Although the day-to-day involvement of LPs is limited by law
(otherwise they can lose their limited-liability status), certain LPs are prized as
long-run partners, because they have the industry experience and patience to ride
out industry cycles and stick with their GPs. Such LPs make the fundraising task
much easier for GPs, yielding time savings that can be used to help portfolio
companies and to ?nd new investments.
For this reason, it is no accident that endowments and foundations held their
positions in the top VC funds even as other LPs were beating down the door. It is
2.2 THE LIMITED PARTNERS 29
true that during the boom many top GPs did raise their compensation; but it should
be noted that they did not raise it to market-clearing levels, instead choosing to keep
the same long-term LPs and exclude some newer money. In particular, families and
corporations are seen—perhaps justly—as ?ckle investors and are often shunned by
top GPs. In recent years, there has also been pressure on public pension funds and
public universities to reveal information about the performance of VCs in their
portfolio. A few of these LPs have been forced to reveal performance information,
and this disclosure is the source of some of the data analyzed in later chapters. For a
variety of reasons, most VCs abhor any kind of public disclosure, so a few of the
top GPs have started to bar public LPs from their funds.
2.3 VC PARTNERSHIP AGREEMENTS
Before we are able to understand VC investment decisions, we must ?rst have a
working knowledge of VC partnerships. The VC ?rm serves as the GP of the part-
nership and is compensated by management fees (discussed in Section 2.3.1) and
carried interest (discussed in Section 2.3.2). This compensation structure creates
some differences between the incentives of the GP and the LPs, and many partnership
agreements include several restrictive covenants to mitigate these differences (dis-
cussed in Section 2.3.3). Metrick and Yasuda (2010) analyze terms of fund part-
nership agreements for 94 VC funds and 144 buyout funds, which they obtained from
a large, anonymous LP (the “Investor”); all statistics in Sections 2.3.1 and 2.3.2 are
derived from this paper, and we will refer to this data as the “Investor” data.
2.3.1 Management Fees
VC investing is a long-run business, and investors must often wait many years
before enjoying any return of capital. Nevertheless, the expenses of VC investing
start immediately: salaries must be paid, the lights must stay on, and due diligence
must be performed. Thus, a baseline management fee is necessary. The typical
arrangement is for limited partners to start paying a set percentage of committed
capital every year, most commonly 2.0 percent. Sometimes this fee remains con-
stant for the full 10-year life of the fund, but in most cases the fee drops somewhat
after the ?ve-year investment period is over.
For any given VC fund, we de?ne the lifetime fees as the sum of the annual
management fees for the life of that fund. We de?ne the investment capital of the fund
as being equal to the committed capital of the fund minus the lifetime fees. For example,
Appendix 2.A shows that EBV is a $100M fund with a 10-year life and an annual
management fee of 2 percent for all 10 years. Thus, the fund has lifetime fees of $20M
(5 2% Ã $100M Ã 10 years) and investment capital of $80M (5 $100M2 $20M). As
is typical, in this case the lifetime fees are a nontrivial fraction of committed capital.
EBV will need to earn a 25 percent lifetime return on its investments ($20M on $80M
investment capital) just to earn back the fees and get to breakeven for its investors.
30 CHAPTER 2 VC PLAYERS
Our next example uses a more complex fee schedule.
EXAMPLE 2.1
Owl Ventures has raised their $500 M fund, Owl Ventures IX, with terms as given in
Appendix 2.C. The management fees given in this appendix are as follows.
Management Fees All management fees are computed based on committed capital.
These fees are 2 percent in years 1 and 2, 2.25 percent in years 3 and 4, 2 percent in year 5,
1.75 percent in year 6, 1.50 percent in year 7, 1.25 percent in year 8, 1 percent in year 9, and
0.75 percent in year 10. These fees will be paid quarterly, with equal installments within each
year.
Problem Given this description, what are the lifetime fees and investment capital for this
fund?
Solution This example uses a fee schedule that starts at 2 percent, and then increases to
2.25 percent in years 3 and 4 before falling by 0.25 percent in each subsequent year. Such
“increasing then decreasing” schedules are not unusual, with the logic that fund expenses
often reach their maximum in the middle years of the investment period. To compute the
lifetime fees, we just add up the fees in each year. Thus,
Lifetime fees ¼ committed capital à ð0:02 þ0:02 þ0:0225 þ0:0225 þ0:02 þ0:0175
10:015 þ0:0125 þ0:01 þ0:0075Þ
¼ committed capital à 0:1675 ¼ $500Mà 0:1675 ¼ $83:75M
ð2:1Þ
Then,
Investment capital ¼ committed capital 2lifetime fees ¼ $500M2$83:75M
¼ $416:25M
ð2:2Þ
’
This example follows the industry’s standard practice of computing man-
agement fees on committed capital. At ?rst glance, this method might seem strange,
because other parts of the money management industry have management fees that
are computed based on the market value of the portfolio. Why are VC funds
different?
There are several reasons. First, if management fees were to be based on
portfolio values, then these fees would be low in the ?rst few years (before all the
capital was invested), and the VCs might be unable to cover their ?xed costs.
Second, management fees based on portfolio value would create an incentive for
VCs to invest quickly—and this would result in an inevitable sacri?ce in quality.
Third, because “market” values for the portfolio are hard to calculate for nontraded
companies, the level of fees would be somewhat arbitrary.
Although the computation of management fees on committed capital is the
most standard arrangement, there are other methods. To understand these other
2.3 VC PARTNERSHIP AGREEMENTS 31
methods, we introduce a few new de?nitions. First, realized investments are those
investments that have been exited or those in companies that have been shut down,
and unrealized investments are those investments that have not yet been exited in
companies that still exist. Next, we de?ne the cost basis of an investment as being
equal to the dollar amount of the original investment. Finally, we de?ne invested
capital as the cost basis for the investment capital of the fund that has already been
deployed, and net invested capital is equal to invested capital minus the cost basis
of realized and written-off investments. It is this ?nal de?nition that is most
important for alternative fee structures, for it is common (about 43% of VC funds in
the Investor data employ this rule) to see the management fee base change from
committed to net invested capital after the ?ve-year investment period is over. This
hybrid system minimizes the incentive for ?rms to overinvest in early years,
because the fee is still ?xed for that time period. Also, because it relies on the cost
basis of the investments, it does not require the estimation of market values. In
Exercise 2.2, at the end of this chapter, you are asked to solve for the lifetime fees
for a fund that uses this hybrid system.
There are two other points worth mentioning. First, although management
fees cover most operating expenses, they do not usually cover all of them, and the
LPs will still ?nd that some of their investment capital is going to uses other than
investments. These other operating expenses charged to the fund might include the
organizational costs of setting up the fund, costs of unconsummated transactions,
and certain kinds of professional service expenses. Second, our calculations
assumed that exit proceeds cannot be reinvested into new portfolio companies. In
theory, however, most contracts allow GPs limited reinvestment rights, subject to
certain requirements being met. (The most common requirement would be that the
original investment was exited quickly, such as within one year.) In practice, these
requirements are stringent enough that signi?cant reinvestment is rare. When
reinvestment does occur, the sum of investment capital and lifetime fees would be
greater than committed capital. However, because reinvestment does not incur any
additional management fees, the economics of the reinvestment decision are a bit
different from the economics of the original investment. We will address this
possibility in Exercise 10.1 in Chapter 10.
2.3.2 Carried Interest
The other form of VC compensation is the carried interest, often referred to
simply as the carry. Carried interest enables GPs to participate in the pro?ts of the
fund, and historically it has provided the largest portion of GP compensation.
The basic idea is simple: if the investors commit $100 million to the fund, and total
exit proceeds are $200 million, then the total pro?t is $200M 2 $100M 5 $100M.
If such is the case, then a GP with 20 percent carried interest would receive $20
million of this pro?t. Indeed, this simple example tells a lot of what we need to
know about carried interest. Nevertheless, there are many variations of this basic
story, and these variations are often important and contentious points of
32 CHAPTER 2 VC PLAYERS
negotiation. Variations occur in the percentage level of the carried interest, the
carried interest basis (5 carry basis), the timing of the carried interest, priority
returns, and clawbacks. These terms are de?ned in the following paragraphs.
The most important variation concerns the percentage level of carried
interest. The vast majority of all VC ?rms receive a 20 percent carry. The Investor
data indicates that 95 percent of VC funds had a 20 percent carry, and this per-
centage was equally high if not higher in the past.
7
Indeed, 20 percent is the focal
point for the entire private equity industry and for many other partnership structures
in the investment industry. There is no consensus on the origins of 20 percent as the
focal point for risk-capital pro?t sharing; some industry analysts point to practices
in the oil and gas industry earlier in the 20th century, and others trace the roots back
to Venetian merchants in the late Middle Ages.
8
An 80À20 split even appears in the
book of Genesis.
9
Despite these historical ties, a few successful VCs have managed to buck the
trend, particularly for partnerships raised during the boom period. The Private
Equity Analyst reports that over two dozen GPs of VC funds receive carried interest
of 25 or 30 percent.
10
Some of these high-charging VCs will be discussed in
Chapter 5, along with some of their famous investments and the astronomical
returns they have earned. The remainder of the non-20 percent crowd earns a carry
between 20 and 25 percent, or receives carry on a sliding scale, with 20 percent
earned at ?rst, and some higher number (typically 25%) if certain performance
targets are met.
There is also variation in the carried interest basis, which is the threshold that
must be exceeded before the GPs can claim a pro?t. The majority of ?rms compute
pro?ts as the difference between exit proceeds and committed capital. Committed
capital is used as the basis by 94 percent of VC funds (and 83% of the buyout
funds) in the Investor data, and this has become more of an industry standard over
time. The other 6 percent of funds have the more GP-friendly basis of investment
capital, which enables pro?ts to be de?ned without consideration for fees. For a
pro?table fund with 20 percent carried interest, $100M in committed capital, $20M
in lifetime fees, and $80 million in investment capital, the $20M basis difference
between committed and investment capital would yield a difference in $20M Ã
0.20 5 $4M in carried interest over the life of the fund.
7
See Metrick and Yasuda (2010) and Gompers and Lerner (1999). Most commentators believe that the
percentage will be heading up again as terms become more LP friendly in the postboom period.
8
See Metrick and Yasuda (2010) and also Kaplan (1999).
9
Gen. 47:23-24: “Joseph said to the people, ‘Now that I have bought you and your land today for
Pharaoh, here is seed for you so you can plant the ground. But when the crop comes in, give a ?fth of it to
Pharaoh. The other four-?fths you may keep as seed for the ?elds and as food for yourselves and your
households and your children.’ ” If you read the rest of this Genesis chapter, you will see that Joseph was
acting more as a distress investor than as a VC.
10
Private Equity Analyst, September 1999.
2.3 VC PARTNERSHIP AGREEMENTS 33
EXAMPLE 2.2
A VC ?rm is considering two different structures for its new $100 M fund. Both structures
would have management fees of 2.5 percent per year (on committed capital) for all 10 years.
Under Structure I, the fund would receive a 25 percent carry with a basis of all committed
capital. Under Structure II, the fund would receive a 20 percent carry with a basis of all
investment capital.
Problems
(a) Suppose that total exit proceeds from all investments are $150M over the entire life of
the fund. How much carried interest would be earned under each of these two structures?
(b) For what amount of exit proceeds would these two structures yield the same amount of
carried interest?
Solutions
(a) Under Structure I, the GPs would receive 25 percent of the pro?ts, where pro?ts are de?ned
as the proceeds above committed capital. Therefore, the carried interest under Structure I would
be 0.25 Ã (150 À100) 5 $12.5 M. Under Structure II, the GPs would receive 20 percent of the
pro?ts, where pro?ts are de?ned as the proceeds above investment capital. Given a 2.5 percent
management fee for all 10 years, the lifetime fees are 2.5% Ã 100 M Ã 10 years 5 $25 M, so
investment capital is $100 M2 $25 M5 $75 M. Therefore, the carried interest under Structure
II would be 0.20 Ã (150 2 75) 5 $15 M.
(b) Let Z be de?ned as the total proceeds from all investments. Then, using the solution to
part (a), we can see that the formulas for carried interest under Structures I and II are
Total carried interest under Structure I ¼ 0:25 Ã ðZ2100Þ ð2:3Þ
and
Total carried interest under Structure II ¼ 0:20 Ã ðZ275Þ ð2:4Þ
We next solve for the Z that equates the carried interest under both structures:
0:25 Ã ðZ2100Þ ¼ 0:20 Ã ðZ275Þ -0:05 Ã Z ¼ 10 -Z ¼ 200 ð2:5Þ
When total exit proceeds 5Z 5200, then both structures would provide 0.25 Ã (200 2100) 5
0.20 Ã (200 2 75) 5 $25 M in carried interest.
’
The level and basis of carried interest are the main determinants for the total
dollar amount of GP carried interest. These terms determine how the “pie” of
proceeds is split between the GPs and the LPs. In addition, there are also several
possible methods for the timing of carried interest. Although these methods do not
usually affect the share of the total pie earned by the GP, they do affect how quickly
that pie can be eaten. Because a basic tenet of ?nance is that money now is worth
more than money later, GPs prefer methods that enable them to receive their carried
interest portion as soon as possible.
34 CHAPTER 2 VC PLAYERS
The most LP-friendly method is to require that the whole basis be returned to
LPs before any carried interest is paid. This method is used by about 25 percent of
the funds in the Investor data. To see how timing matters, imagine that this method
was in place for Example 2.2. In that example, we considered two possible
structures for carried interest: Structure I with 25 percent carry and a basis of
committed capital, and Structure II with 20 percent carry and a basis of investment
capital. In part (b) of that example, we found that total exit proceeds of $200M
would lead to $25M of carried interest under both of the proposed structures, with
the remaining $175M going to LPs. Although the $200M pie is shared the same in
both cases, the timing is not. Under structure I, the LPs receive their whole basis of
$100M before all proceeds above $100M are split 75/25. Under structure II, the LPs
also receive their whole basis (only $75M in this case) before all proceeds above
$75M are split 80/20. Thus, GPs get their ?rst dollar more quickly under structure
II, and at any time in the distribution of $200M of total proceeds, structure II will
always have paid at least as much carried interest as structure I.
To understand the alternative methods of carry timing, we make use of the
de?nition of invested capital (introduced in Section 2.3.1) and the related concept of
contributed capital, with the latter being de?ned as the portion of committed capital
that has already been transferred from the LPs to the GPs. Thus, contributed capital is
equal to invested capital plus any management fees paid to date. Analogous to net
invested capital, net contributed capital is equal to contributed capital minus the
cost basis of any realized and written-off investments. According to the Investor data,
another 75 percent of VC funds allow some form of early carry distribution. One such
method only requires the return of either invested capital or contributed capital before
any carried interest can be earned. Clearly, this timing method is more GP-friendly
than requiring the return of the whole basis. Another method, which lies somewhere
between the “return the whole basis” and “return only the invested/contributed
capital” methods, requires the return of invested or contributed capital plus priority
returns. This is fairly common and is found in about 45 percent of VC funds in the
Investor data.
Priority returns—also called preferred returns or hurdle returns—are
another factor affecting the timing of carried interest. With a priority return, the
GP promises some preset rate of return to the LPs before the GPs can collect any
carry. The Investor data indicates that 45 percent of VCs promise some kind of
priority return. Among these funds, 8 percent (per year) return is the most
common, with 71 percent of all funds with priority returns choosing 8 percent;
others range from 5 percent to 10 percent. Priority returns are relatively rare in
funds that focus on early-stage investing, and relatively common in funds that
focus on late-stage investing. It is important to note, however, that the priority
return usually affects the timing and not the total amount of carried interest.
Most priority returns also have a catch-up provision, which provides the GPs
with a greater share of the pro?ts once the priority return has been paid. With a
catch-up, the GP receives this greater share until the preset carry percentage has
been reached.
2.3 VC PARTNERSHIP AGREEMENTS 35
As an illustration of priority returns with a catch-up, consider a $100M fund
with a carry percentage of 20 percent, a carry basis of all committed capital, a
priority return of 8 percent, and a 100 percent catch-up. We’ll keep things simple
and imagine that all committed capital is drawn down on the ?rst day of the
fund, and that there are total exit proceeds of $120M, with $108M of these proceeds
coming exactly one year after the ?rst investment, $2M coming one year later, and
$10M coming the year after that. Under these rules, all $108M of the original
proceeds would go to the LPs. This distribution satis?es the 8 percent hurdle rate
requirement for the $100M in committed capital. One year later, the catch-up
provision implies that the whole $2M would go to the GPs; after that distribution
they would have received 20 percent ($2M) out of the total $10M in pro?ts. For the
?nal distribution, the $10M would be split $8M for the LPs and $2M for the GPs.
Beyond this simple example, the calculations quickly become unwieldy to
handle without a spreadsheet. The key takeaway is that even with a priority return,
the GPs still receive the same fraction of the pro?ts as long as the fund is suf?-
ciently pro?table. In this example, the fund made $20M of pro?ts ($120M of
proceeds on $100M of committed capital), and the GPs received 20 percent ($4M)
of these pro?ts. If, however, the fund had only earned $8M or less of pro?ts over
this time period, then all these pro?ts would have gone to the LPs.
In all but two of all funds with a priority return, there is some catch-up pro-
vision for the GPs. In the two exceptions, there is no catch-up, and thus the GP only
earns carried interest on the portion of pro?ts above the priority return. The absence
of a catch-up affects the share of the pie for the GP, not just the timing of that share.
In the preceding example, having no catch-up would have meant that the GP would
have received only 0.20 Ã ($120M 2 $108M) 5$2.4M of total carried interest.
Finally, some funds require the return of only a portion of contributed (or
invested) capital. For example, one common method is to require the return of the
cost basis of all realized investments, plus all management fees to date and any
write downs (partial losses) known to exist among the unrealized investments. In
most cases, this method is combined with a so-called fair-value test. This test
requires that the estimated values of remaining portfolio investments exceed a
preset percent (e.g., 120%) of the cost basis of these investments. The fair-value test
is found in 14 percent of the Investor data.
The early payment of carried interest can cause complications if the fund starts
off strong but weakens later in life. For example, suppose that a $100M fund has a 20
percent carried interest with a basis of all committed capital, but allows carried
interest to be paid as long as contributed capital has been returned. Then, consider
what happens if the fund is three years into its life, contributed capital is $50M, and it
receives $60M as the proceeds from its ?rst exit. Given the carried interest rules, the
fund would return the ?rst $50M to its LPs, and the remaining $10M would be split
as $8M for the LPs and $2M for the GPs. Now, fast forward ahead to the end of the
fund seven years later, and assume that there were no more exits. Contributed capital
is now the full $100M of committed capital, but the LPs have only received back the
$58M from the ?rst and only exit. According to the rules of carried interest basis,
36 CHAPTER 2 VC PLAYERS
the LPs are entitled to all the exit proceeds up to $100M. This means they need some
way to get the carried interest back from the GPs.
This refund of carried interest is accomplished with a contractual provision
evocatively known as a clawback. There are a variety of ways that clawbacks can
be designed. In practice, however, this implementation can be complicated by many
factors—for example, what if the GPs do not have the money when it comes time to
pay?—so LPs often insist (and receive) contractual guarantees to be paid back from
the individual GPs. The contract also needs to specify whether the clawback will be
net or gross of taxes that the GPs have already paid. Clawbacks become even more
of an issue when there is a priority return—it is easy to imagine how the priority
return might be exceeded in early years but missed in later years. The details here
are too messy for a simple numerical example, so we will use a spreadsheet
example to demonstrate. This exercise also allows us to see how management fees
and carried interest are computed in a more realistic setup.
EXAMPLE 2.3
Owl Ventures has raised their $500 M fund, Owl Ventures III, with terms as given in
Appendix C of this chapter. The terms for carried interest and for the general partner
clawback are
Distributions Distributions in respect of any partnership investment will be made in
the following order of priority:
(i) 100% to the limited partners until they have received an amount equal to their
contributed capital:
(ii) 75% to the limited partners and 25% to the general partners.
General Partner Clawback Obligation Upon the liquidation of the fund, the general
partner will be required to restore funds to the partnership to the extent that it has received
cumulative distributions in excess of amounts otherwise distributable pursuant to the
distribution formula set forth above, applied on an aggregate basis covering all partnership
investments, but in no event more than the cumulative distributions received by the general
partner solely in respect of its carried interest.
Problem Construct an example of fund performance where the clawback provision
would be triggered. In this example, compute the carried interest paid in each year and show
the total amount that must be paid back by the GPs on the liquidation of the ?rm.
Solution Cutting through the legal language, these terms mean that Owl is getting 25
percent carried interest, the carry basis is committed capital, the timing method uses contributed
capital, and there is a clawback at the end of the fund if too much carry has been paid. Exhibit 2-5
shows the spreadsheet output for an example with the clawback provision triggered. ’
In this example, we assume that the investment capital is distributed evenly in
each of the ?rst ?ve years. The returns in year 1 are fantastic, with investments
tripling in value and exited at the end of year 2. These realizations can be seen in the
2.3 VC PARTNERSHIP AGREEMENTS 37
row labeled “distributions” in Exhibit 2-5 and are equal to $250M in year 2. Because
only $186.5M has been contributed by this time (see the “contributed capital” row for
year 2), the GPs are entitled to 25 percent carried interest on the “pro?ts” of $250M
less $186.5M. This carried interest, shown in the “distributions to GPs” row, is equal
to $15.9M.
Following this great year, the investments perform terribly. The spreadsheet
assumes that all investments lose half their value each year, and later distributions are
low to re?ect this poor performance. The formula in the spreadsheet has 10 percent of
portfolio value being distributed in years 3 and 4, with 40 percent (of whatever
remains in each year) being distributed in the remaining years. There are no further
distributions to GPs during the remaining life of the fund.
Upon liquidation of the fund after year 10, we see that contributed capital has
reached the committed capital level of $500M, but that the cumulative distribution to
the LPs is only $344.0M. The clawback provision is thus triggered, and the GPs are
obligated to return all $20.9M of carried interest. In practice, it probably would have
been clear much earlier to all parties that the clawback would be necessary—and to
EXHIBIT 2-5
HYPOTHETICAL CLAWBACK EXAMPLE FOR OWL VENTURES
Year 1 2 3 4 5 6 7 8 9 10 close
Investments 83.3 83.3 83.3 83.3 83.3 0.0 0.0 0.0 0.0 0.0 0.0
Estimated
portfolio value
83.3 333.3 124.9 139.4 146.0 43.8 13.1 3.9 1.2 0.4 0.1
Distributions 0.0 250.0 12.5 13.9 58.4 17.5 5.3 1.6 0.5 0.1 0.1
Cumulative
distributions
0.0 250.0 262.5 276.4 334.8 352.4 357.6 359.2 359.7 359.8 359.9
Distributions to
GPs
0.0 15.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Cumulative
distributions to
GPs
0.0 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9
Distributions
to LPs
0.0 234.1 12.5 13.9 58.4 17.5 5.3 1.6 0.5 0.1 0.1
Cumulative
distributions to
LPs
0.0 234.1 246.6 260.6 319 336.5 341.7 343.3 343.8 343.9 344
Port value after
capital returned
83.3 83.3 112.4 125.5 87.6 26.3 7.9 2.4 0.7 0.2 0.0
Management fee 10.0 10.0 11.3 11.3 10.0 8.8 7.5 6.3 5.0 3.8 0.0
Contributed capital 93.3 186.5 281.0 375.5 468.8 477.5 485.0 491.3 496.3 500.0 500.0
Invested capital 83.3 166.5 249.8 333.0 416.3 416.3 416.3 416.3 416.3 416.3 416.3
Clawback 15.9
38 CHAPTER 2 VC PLAYERS
solve this problem, the GPs could give the money back earlier or just reduce the
management fees to zero for the last few years.
2.3.3 Restrictive Covenants
A VC fund is a long-term commitment. LPs tie up capital with no promise of a
return and little control over the investment activities of the GP. Although the
compensation of the GPs does go some distance toward aligning the incentives of
all parties, several potential problems still exist. Over time, LPs have used a variety
of restrictive covenants in an attempt to mitigate these problems.
Gompers and Lerner (1996) wrote the only academic study of restrictive cove-
nants. Exhibit 2-6 reproduces part of a table from their analysis. They divide covenants
into three broad categories: (1) restrictions on management of the fund, (2) restrictions
on the activities of the GP, and (3) restrictions on the types of investment.
Examples from the ?rst broad category can be seen in each of the sample
agreements in the appendices to this chapter. For example, EBVand Talltree both have
EXHIBIT 2-6
RESTRICTIVE COVENANTS FOR VC FUNDS
Description % of Contracts
Covenants relating to the management of the fund:
Restrictions on size of investment in any one ?rm 77.8
Restrictions on use of debt by partnership 95.6
Restrictions on coinvestment by organization’s earlier or later funds 62.2
Restrictions on reinvestment of partnership’s capital gains 35.6
Covenants relating to the activities of the general partners:
Restrictions on coinvestment by general partners 77.8
Restrictions on sale of partnership interests by general partners 51.1
Restrictions on fund-raising by general partners 84.4
Restrictions on other actions by general partners 13.3
Restrictions on addition of general partners 26.7
Covenants relating to the types of investment:
Restrictions on investments in other venture funds 62.2
Restrictions on investment in public securities 66.7
Restrictions on investments in leveraged buyouts 60.0
Restrictions on investments in foreign securities 44.4
Restrictions on investments in other asset classes 31.1
Total number of partnership agreements in sample 45
Average number of covenant classes 7.9
Average number of covenant classes (weighted by fund size) 8.4
Source: Gompers and Lerner (1996).
2.3 VC PARTNERSHIP AGREEMENTS 39
restrictions for the maximumpercentage of the fundto be invested in any one company.
Exhibit 2-6 shows that similar restrictions were in place in 78 percent of all
sample funds. Why would LPs insist on this restriction? An obvious answer to
this question is “to put a limit on risk”, but this answer is unsatisfying. The
typical investor in VC funds is a large institutional investor who is allocating
only a small portfolio fraction to any particular VC fund; the difference between
25 percent or 50 percent of that allocation going to one speci?c company would
barely affect the risk exposure for their broad portfolio. Instead, the main justi-
?cation for investment limits is related to the incentives of the GPs, speci?cally
the incentives induced by carried interest.
To illustrate the incentive problem, consider the ?ctitious case of Derby
Ventures. The GP of Derby Ventures makes “investments” by placing bets on
horses at a racetrack. This GP has an excellent track record from past bets, and his
LPs expect him to make dozens of small bets so that the law of large numbers
allows his superior skill to show through. The LPs expect this behavior, but it is not
written into the partnership agreement. Now assume that besides being very
knowledgeable about horses, this GP is also a savvy gambler. He realizes that his
superior knowledge would probably be able to produce 20 percent returns on
capital over the next year, giving him a few percentage points in carried interest,
but perhaps not enough to make it worth his while to quit his regular job as a
professor. Alternatively, he can put all his money on one horse, perhaps a ten-to-
one “long shot”. If the horse wins, then the carried interest earned in one day would
be enormous. If the horse loses—well, he can just go back to teaching his classes.
This example captures the main incentive problem for carried interest: it
provides an upside to the GP without the corresponding downside. In option-pricing
language, the GPs effectively hold a call option on the fund portfolio. Readers
familiar with options will know that call options are more valuable when the
underlying security has higher volatility. Thus GPs, as holder of the carried interest
“call option”, have an incentive to increase volatility by betting a lot on one horse,
or investing a lot in one company. (For readers unfamiliar with options, fear not: we
will beat that horse to death starting in Chapter 13.)
The same insight can help us understand the common restriction against funds
taking on debt (96 percent of sample funds). By taking on debt, a fund can amplify the
returns on its portfolio, an ampli?cation that increases risk and, correspondingly,
increases the value of the carried-interest call option. LPs can rein in these adverse
incentives through the use of covenants, but a formal restriction is not always neces-
sary. An alternative approach is to rely on the GPs’ unwillingness to risk their
“reputational capital”. For GPs with a long history and lucrative future—as we assume
exists for Owl Ventures, now on their ninth fund—it may no longer be necessary to
formally restrict their risk-taking behavior. If Derby Ventures fails, its GP can just go
back to teaching. If Owl Ventures fails, then a valuable franchise has been lost.
With 62 percent of sample funds, restrictions on coinvestment with earlier or
later funds by the same partnership are also common. LPs may decide to restrict such
coinvestment to avoid one fund propping up the performance of another. This can be
40 CHAPTER 2 VC PLAYERS
of particular concern around the time that a GP is fundraising for a new fund. For
example, suppose that EBV is trying to raise EBV III, and it is three years into its
investment period on Fund II and seven years into the life of Fund I. Now, when it goes
on the fund-raising trail, potential LPs will scrutinize the performance of Fund I, but
not expect much of the still young Fund II. If Fund II can help Fund I by giving some
newmoney to an otherwise failing company, then the interimreturns of Fund I would
be helped, at the expense of Fund II’s investors.
Our second category of covenants is one that involves restrictions on the
activities of the GP. In general, the covenants in this class are designed to ensure
that the GP’s attention stays focused on the whole portfolio of fund investments.
For example, restrictions on coinvestment by general partners (78 percent of
sample funds) might seem to be counterproductive—shouldn’t LPs be happy to see
GPs with their own money at stake? The problem here is that GPs may focus
excessively on the few investments with a personal stake while ignoring the other
investments. In this case, the GPs may use the fund simply as an opportunity to
cherry-pick a few great investments for themselves. One way to restrict this
practice is for LPs to insist that any personal investments by GPs be proportional
across all fund investments.
Another way to keep the GPs’ attention is to restrict them from raising
another fund before they have invested the present one (84 percent of sample
funds). This is of particular concern for debut funds like EBV, where the GPs may
want to make a quick return to the market to raise larger funds and achieve critical
mass for the management fee.
The third category of covenants includes restrictions designed to keep GPs
focused on the type of investing that they have been hired to do. LPs do not like to
see a GP who was hired to be a VC suddenly turn into an investor in LBOs, public
equities, distressed debt, or other VC funds. This motivation to switch focus can be
surprisingly strong during times of market upheaval. For example, venture perfor-
mance was poor and LBOs were hot in the mid-1980s. Many VCs wanted to try their
hand at this new activity, but the skill set was quite different, and anecdotal evidence
suggests that VCs’ performance in LBOs was terrible. A similar motivation occurred
in the postboom period. As with the other categories of covenants, a strong reputation
and franchise value can reduce the need for formal covenants. However, here even
some of the most famous names in private equity can be tempted to lose their focus,
as was seen many times during the boom and postboom periods.
SUMMARY
The VC fund, organized as a limited partnership, is the main vehicle for VC investing. The
general partner (GP) of a VC fund is a VC ?rm, and the limited partners (LPs) are usually
institutional investors, with pension funds supplying just under half of the total committed
capital in the industry. In the postboom period, there were about 900 active VC ?rms and
1,800 active VC funds.
SUMMARY 41
GPs are compensated with management fees and carried interest. Management fees
are usually about 2.0 percent per year, calculated on the basis of committed capital. Carried
interest—the pro?t participation—is most commonly set at 20 percent of all fund pro?ts.
This compensation structure is designed to help align the incentives of GPs and LPs. To get a
better alignment of incentives, LPs often restrict GP behavior with covenants written into the
partnership agreement.
KEY TERMS
VC firm
General partner (GP)
VC fund
Limited partner (LP)
Capital call
5 Drawdown
5 Takedown
Committed capital
Investment period
5 Commitment period
Follow-on investments
Early-stage fund, late-stage
fund, multistage fund
Raised, closed
Vintage year
Fund-of-funds (FOF)
Management fees
Lifetime fees
Investment capital
Invested capital, net
invested capital
Carried interest
5 Carry
Carried interest basis
5 Carry basis
Contributed capital, net
contributed capital
Priority returns
5 Preferred returns
5 Hurdle returns
Realized returns, unrealized
returns
Catch-up provision
Clawback
Restrictive covenants
Call option
REFERENCES
Gompers, Paul A. and Joshua Lerner, 1996, “The Use of Covenants: An Empirical Analysis of Venture
Partnership Agreements”, Journal of Law and Economics 39(2), 463À498.
Gompers, Paul A. and Joshua Lerner, 1999, “An analysis of compensation in the U.S. venture capital
partnership”, Journal of Financial Economics 51, 3À44.
Kaplan, Steven N., 1999, “Accel VII”, Unpublished case study, available online at http://gsbwww.
uchicago.edu/fac/steven.kaplan/teaching/accel7.pdf.
Lerner, Joshua, Antoinette Schoar, and Wan Wong, 2007, “Smart Institutions, Foolish Choices? The
Limited Partner Performance Puzzle”, Journal of Finance 62(2), 731À764.
Metrick, Andrew and Ayako Yasuda, 2010, “The Economics of Private Equity Funds”, Review of
Financial Studies 23, 2303À2341.
Venture Economics, National Venture Capital Association Yearbook, various years.
EXERCISES
2.1 Suppose that a $200M VC fund has a management fee of 2.5 percent per year for the ?rst
?ve years, with a reduction of 0.25 percent (25 basis points) in each year thereafter. All fees
are paid on committed capital, and the fund has a 10-year life. What are the lifetime fees and
investment capital for this fund?
42 CHAPTER 2 VC PLAYERS
2.2 (This is a little bit tricky.) Suppose that a $1B VC fund has fees of 2.0 percent per year in
all years, with these fees paid on committed capital in the ?rst ?ve years and on net invested
capital for years 6 through 10. You can assume the fund is fully invested by the beginning of
year 6, then realizes 20 percent of its investment capital in each of the following ?ve years.
What are the lifetime fees and investment capital for this fund? (Make assumptions for any
information that you think is still missing from the problem.)
2.3 A VC ?rm is considering two different structures for its new $250M fund. Both struc-
tures would have management fees of 2 percent per year (on committed capital) for all 10
years. Under Structure I, the fund would receive an X percent carry with a basis of all
committed capital. Under Structure II, the fund would receive a Y percent carry with a basis
of all investment capital. For a given amount of (total) exit proceeds 5 $Z, solve for the
amount of carried interest under both structures.
2.4 Talltree Ventures has raised their $250M fund, Talltree Ventures IV, with terms as given in
Appendix 2.B of this chapter. Construct an example of fund performance where the clawback
provision would be triggered. In this example, compute the carried interest paid in each year, and
show the total amount that must be paid back by the GPs upon the liquidation of the fund.
APPENDICES: KEY TERMS AND CONDITIONS
FOR THREE VC FUNDS
These appendices give excerpts from the private placement memoranda for three
(?ctional) VC funds: EarlyBird Ventures I (EBV I) [Appendix 2.A], Talltree
Ventures IV [Appendix 2.B], and Owl Ventures IX [Appendix 2.C]. We will refer
to these appendices throughout the book. All these excerpts are derived from a
more complete memorandum given in Kaplan (1999).
Appendix 2.A: EarlyBird Ventures I
Fund Size $100 million
Term Following the tenth anniversary of the initial closing, the term of the
partnership will expire on December 31st unless extended for up to two consecutive
one-year periods at the discretion of the general partner. This is to permit orderly
dissolution, and no management fees will be charged during any such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st, except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees The annual contributions will equal 2 percent of committed
capital for the ?rst 10 years of the fund. These contributions will be paid quarterly.
APPENDICES: KEY TERMS AND CONDITIONS FOR THREE VC FUNDS 43
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital.
(ii) 80 percent to the limited partners and 20 percent to the general partners.
Diversi?cation and Investment Limits The Fund may not invest more
than 25 percent of aggregate commitments in any single portfolio company.
Appendix 2.B: Talltree Ventures IV
Fund Size $250 million
Term Following the tenth anniversary of the initial closing, the term of the
partnership will expire on December 31st, unless it is extended for up to two
consecutive one-year periods at the discretion of the general partner. This is to
permit orderly dissolution, and no management fees will be charged during any
such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees The annual contributions will equal 2 percent of com-
mitted capital for the ?rst 10 years of the fund. These contributions will be paid
quarterly.
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital, plus a priority return equal to 8 percent (compounded
annually).
(ii) 100 percent to the general partner until the general partner has received catch-
up distributions equal to 20 percent of the sum of such distributions and the
preference distributions in part (i).
(iii) 80 percent to the limited partners and 20 percent to the general partner.
General Partner Clawback Obligation Upon liquidation of the fund, the
general partner will be required to restore funds to the partnership to the extent that it
has received cumulative distributions in excess of amounts otherwise distributable
44 CHAPTER 2 VC PLAYERS
pursuant to the distribution formula set forth above, applied on an aggregate basis
covering all partnership investments, but in no event more than the cumulative dis-
tributions received by the general partner solely in respect of its carried interest.
Diversi?cation and Investment Limits The fund may not invest more
than 20 percent of aggregate commitments in any single portfolio company.
Appendix 2.C: Owl Ventures IX
Fund Size $500 million
Term Following the 10th anniversary of the initial closing, the term of the
partnership will expire on December 31st unless extended for up to two consecutive
one-year periods at the discretion of the general partner. This is to permit orderly
dissolution, and no management fees will be charged during any such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees All management fees are computed based on committed
capital. These fees are 2 percent in years 1 and 2, 2.25 percent in years 3 and 4, 2
percent in year 5, 1.75 percent in year 6, 1.50 percent in year 7, 1.25 percent in year
8, 1 percent in year 9, and 0.75 percent in year 10. These fees will be paid quarterly,
with equal installments within each year.
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital.
(ii) 75 percent to the limited partners and 25 percent to the general partners.
General Partner Clawback Obligation Upon the liquidation of the fund,
the general partner will be required to restore funds to the partnership to the extent that
it has received cumulative distributions in excess of amounts otherwise distributable
pursuant to the distribution formula set forth above, applied on an aggregate basis
covering all partnership investments, but in no event more than the cumulative dis-
tributions received by the general partner solely in respect of its carried interest.
APPENDICES: KEY TERMS AND CONDITIONS FOR THREE VC FUNDS 45
CHAPTER 3
VC RETURNS
VCS SPEND their time very differently from mutual-fund managers, but
ultimately both groups are measured by their investment returns. If you open the
business section of the newspaper, you can readily see information about mutual-
fund returns, but one must search hard to ?nd any information about VC returns.
Even when such returns are revealed, they are often reported in ways that are not
comparable to standard benchmarks.
In this chapter, we learn how VC returns are measured and take our ?rst glimpse
into the returns data. In Section 3.1, we analyze two main sources of industry level
returns and compare these returns with public market benchmarks. In Section 3.2,
we show how to compute returns at the fund level and discuss several new sources
of fund level data.
3.1 INDUSTRY RETURNS
In this section, we analyze the returns for the entire VC industry. We begin with
some de?nitions.
3.1.1 De?nitions
A periodic return is de?ned as
Periodic return 5R
t
5ðP
t
1D
t
Þ=P
t21
21 ð3:1Þ
where R
t
is the return for period t, P
t
is the value (price) of the portfolio at the end
of period t, D
t
is the dividends (distributions) earned by the portfolio during period
t, and P
t 21
is the value (price) of the portfolio at the end of period t 2 1. The time
period t can be any length, and the return would correspondingly be a “monthly
return”, “quarterly return”, “annual return”, or likewise. For multi-period returns,
we multiply the periodic returns to arrive at the compound return:
Compound return 5ð1 1R
1
Þ Ã ð1 1R
2
Þ Ã . . . Ã ð1 1R
N
Þ 21 ð3:2Þ
46
Because we will often be interested in returns at the annual time horizon, we
can translate T years of multi-period returns into annualized returns as follows:
Annualized return 5ð1 1compound returnÞ
ð1=TÞ
21 ð3:3Þ
For managed portfolios, returns can be expressed either as gross returns
(before subtracting fees and carried interest) or as net returns (after subtracting
fees and carried interest).
EXAMPLE 3.1
The Largeco pension plan has invested in dozens of VC funds. The director of the pension
plan is preparing his annual report to the Largeco board of directors. Summary information
for Largeco’s VC portfolio is given in Exhibit 3-1:
Problem The board has asked for a ?ve-year report of net returns and gross returns by
year, plus the compound returns and annualized returns for all ?ve years. You can assume
that all new investments and management fees are paid at the beginning of the year, and all
distributions were paid at the end of the year.
Solution The gross returns are calculated by comparing the value at the beginning of each
year with the value at the end of each year. (Note that the beginning value in year t is equal to the
ending value in year t 2 1 minus distributions to LPs and GPs. The management fee is paid
separately by the LPs.) Thus, gross returns are 7,200/(4,000 1 2,000) 2 1 5 20 percent for
2004, 8,340/(5,950 1 1,000) 2 1 5 20 percent for 2005, and so on. For net returns, we must
subtract the distributions to GPs (carried interest) fromthe numerator and add the management
fees to the denominator: (7,200 2 250)/(4,000 1 2,000 1 100) 2 1 5 13.9 percent for 2004,
(8,340 2250)/(5,950 11,000 1100) 21 514.8 percent for 2005, and so on. The answers for
all years are given in Exhibit 3-2.
EXHIBIT 3-1
LARGECO PENSION PLAN, VC PORTFOLIO
Year 2004 2005 2006 2007 2008
Beginning Value 4,000 5,950 7,090 9,267 3,884
New Investments 2,000 1,000 1,000 1,000 1,000
Ending Value (before distributions) 7,200 8,340 10,517 5,134 7,814
Distributions to LPs 1,000 1,000 1,000 1,000 1,000
Distributions to GPs 250 250 250 250 250
Management Fees 100 100 100 100 100
3.1 INDUSTRY RETURNS 47
The compound returns are as follows:
Gross compound return51:20
Ã
1:20
Ã
1:30
Ã
0:50
Ã
1:60 21 549:8% ð3:4Þ
and
Net compound return 51:139
Ã
1:148
Ã
1:254
Ã
0:471
Ã
1:518 21 517:2% ð3:5Þ
The gross annualized return is 1.498
(1/5)
2 1 5 8.4 percent, and the net annualized return is
1.172
(1/5)
2 1 5 3.2 percent. ’
It will prove useful to give one ?nal set of return de?nitions. Returns that
have been earned in the past are known as realized returns or historical returns.
Returns that are forecast for the future are known as expected returns. We could
use the modi?er of “realized” or “expected” in front of any of the other return
de?nitions in this chapter. In a well-behaved universe, we would ?nd that average
realized returns would be equal to expected returns for all assets. Our universe is
not so well behaved, which is why so many advertisements tell us that “past per-
formance is no guarantee of future returns”.
3.1.2 A Gross-Return Index
Given current data limitations, a gross-return index is best created from the bottom
up. To construct a bottom-up index, we build a database of all VC investments, do
our best to update the values of these investments over time (including distribu-
tions), and then track the value of the whole set of investments, thus creating a
rolling portfolio for the whole VC industry. This is a herculean task, but luckily all
the work has already been done by Susan Woodward and her company, Sand Hill
Econometrics (SHE).
1
SHE began by combining the databases of the two main industry trackers,
VentureSource (a division of Dow Jones) and Venture Economics (a division of
Thomson Financial). From here, SHE added information from other industry
EXHIBIT 3-2
LARGECO PENSION PLAN, VC PORTFOLIO
Year 2004 2005 2006 2007 2008
Net Return 13.9% 14.8% 25.4% 252.9% 51.8%
Gross Return 20.0% 20.0% 30.0% 250.0% 60.0%
1
Construction of the Sand Hill Index is described in Hall and Woodward (2003).
48 CHAPTER 3 VC RETURNS
sources, from its own base of consulting clients (LPs in VC funds), and from
exhaustive searching of Web resources. The ?nal database includes over 17,000
companies and more than 60,000 ?nancing rounds. It also allows for monthly
updating. The resulting Sand Hill Index
s
is plotted in Exhibit 3-3, using the
available sample period through December 2008.
2
For comparison, we have also
plotted an index for the NASDAQ stock market. The two indices are both nor-
malized to be 100 in December 1988, the month the Sand Hill Econometrics
Venture Index started. The normalized indices are presented in log scale.
Since the inception of the SHE index, the index reached a peak of 2,302 in
August 2000, fell to a postboom low of 915 in February 2003, and recovered to
1,364 by October 2007. Meanwhile, the NASDAQ index peaked at its all-time high
at 1,306 in February 2000, fell to a postboom low of 328 in September 2002, and
reached its post-bubble high at 827 in October 2007. Since October 2007, the SHE
index slid, largely in tandem with the NASDAQ, amid the ?nancial crisis that
EXHIBIT 3-3
SAND HILL INDEX
s
VERSUS NASDAQ
2500
2000
1500
1000
500
400
300
200
100
50
J
a
n
u
a
r
y
-
8
8
J
a
n
u
a
r
y
-
8
9
J
a
n
u
a
r
y
-
9
0
J
a
n
u
a
r
y
-
9
1
J
a
n
u
a
r
y
-
9
2
J
a
n
u
a
r
y
-
9
3
J
a
n
u
a
r
y
-
9
4
J
a
n
u
a
r
y
-
9
5
J
a
n
u
a
r
y
-
9
6
J
a
n
u
a
r
y
-
9
7
J
a
n
u
a
r
y
-
9
8
J
a
n
u
a
r
y
-
9
9
J
a
n
u
a
r
y
-
9
9
J
a
n
u
a
r
y
-
0
0
J
a
n
u
a
r
y
-
0
1
J
a
n
u
a
r
y
-
0
2
J
a
n
u
a
r
y
-
0
3
J
a
n
u
a
r
y
-
0
4
J
a
n
u
a
r
y
-
0
5
J
a
n
u
a
r
y
-
0
6
J
a
n
u
a
r
y
-
0
7
J
a
n
u
a
r
y
-
0
8
Sand Hill Index
NASDAQ
NOTE: The two indices are both normalized to be 100 in December 1988. The normalized indices are
presented in log scale.
Sources: Sand Hill Econometrics (SHE), the Center for Research in Security Prices (CRSP).
2
Sand Hill Econometrics discontinued the index in December 2008 after it reached a licensing agreement
with Dow Jones. A new index called the DowJones Index of Venture Capital (comprising VentureSource
and Sand Hill Econometrics’ proprietary data) will be launched in 2010.
3.1 INDUSTRY RETURNS 49
unfolded in 2008. In December 2008 (the last month the index was calculated), it
stood at 1,110, while the NASDAQ was at 456. The annualized return over the
20-year life of the index is 12.8 percent. In comparison, the NASDAQ index—a
value-weighted index of all NASDAQ stocks, including dividends—had the
annualized return over the same 20-year time period of 7.9 percent. Although
the Sand Hill Index
s
is more than double the NASDAQ index by the end of the
sample period, the former only passes the latter in June 1996, close to the beginning
of the boom period.
3.1.3 A Net-Return Index
The Sand Hill Index
s
is built from a database of portfolio companies. An alter-
native approach is to build a database of funds and combine the returns of these
funds to form an overall industry index. This has been attempted by several groups,
the most comprehensive of which is the Cambridge Associates U.S. Venture
Capital Index
s
, which includes more than 75 percent of the dollars raised by VC
funds since 1981.
3
Cambridge Associates (CA), an investment consultant to
endowments, foundations, and wealthy families, serves as a gatekeeper for
potential LPs. It essentially acts as a paid service that puts CA between the LP and
GP for both the initiation and management of the partnership relationship. This
function gives CA access to information, which it has astutely chosen to aggregate
and analyze.
To construct its index, CA starts with the quarterly reports that GPs provide to
LPs. These reports give “current” valuations for the unrealized portfolio companies
and also summarize the cash ?ows in and out of the fund.
4
CA then aggregates the
total value (realized and unrealized) from each fund in each quarter. By combining
these totals across quarters, it is able to compute an aggregate return and build an
index. Note that CA is using cash ?ows to LPs as the basic unit. Because these cash
?ows include management fees (as negative cash ?ows) and carried interest (as a
reduction of the positive cash ?ows from realized investments), the CA index is
based on net returns and, in principle, should be lower than the corresponding gross
return index constructed by SHE.
The quarterly CA index is available from the ?rst quarter of 1981 through the
last quarter of 2008. To facilitate comparisons with the Sand Hill Index
s
, we set
the CA index value to 100 for the fourth quarter of 1988. Exhibit 3-4 plots the CA
Index versus the NASDAQ index (also normalized to be 100 in the fourth quarter of
1988) in log scale.
3
The Cambridge Associates data can be freely downloaded from https://www.cambridgeassociates.com/
pdf/Venture%20Capital%20Index.pdf.
4
We put “current” between quotes because the valuations are often quite old. In Chapter 4, we discuss
this valuation practice and its implications for performance measurement and for the estimation of the
cost of venture capital.
50 CHAPTER 3 VC RETURNS
The exhibit demonstrates that the CA index has the highest amplitude of all
three series, reaching a maximum of 4,300 in the third quarter of 2000, a postboom
low of 1,386 in the ?rst quarter of 2003, and recovering to its postbubble high of
2,412 in the fourth quarter of 2007. Since then it went down, as expected, and stood
at 2,022 in the fourth quarter of 2008. For the complete, nearly 28-year sample
period of 1981 to 2008, the CA index earned an annualized return of 13.0 percent
versus a 9.0 percent return for the NASDAQ. During the 20-year subperiod from
1988 to 2008—when we also have data for the Sand Hill Index
s
—the CA index
earned annualized returns of 16.2 percent versus 12.8 percent for the Sand Hill
Index
s
and 7.9 percent for the NASDAQ.
The relationship between the Sand Hill Index
s
and the CA Index seems
backward: the net-return index (CA)—which is computed after fees and carried
interest are subtracted out—should be lower than the gross-return index (SHE).
However, here the opposite is true, with the CA index exceeding the Sand Hill
Index
s
by 3.4 percentage points over the common subperiod.
Clearly, something is wrong with at least one of these indices. In fact, both
indices have some weaknesses; but when taken together, they can provide us with
upper and lower bounds for VCperformance. First, consider the CAindex. CAadds to
its database in several ways. One way is by tracking funds for which a CA client is a
current LP. This formof adding data does not induce any bias. However, CAdoes not
have clients in every ?rst-time fund. Suppose that ABC Fund I does not include any
EXHIBIT 3-4
CA INDEX
s
VERSUS NASDAQ
1
9
8
1
Q
1
1
9
8
2
Q
1
1
9
8
3
Q
1
1
9
8
4
Q
1
1
9
8
5
Q
1
1
9
8
6
Q
1
1
9
8
7
Q
1
1
9
8
8
Q
1
1
9
8
9
Q
1
1
9
9
0
Q
1
1
9
9
1
Q
1
1
9
9
2
Q
1
1
9
9
3
Q
1
1
9
9
4
Q
1
1
9
9
5
Q
1
1
9
9
6
Q
1
1
9
9
7
Q
1
1
9
9
8
Q
1
1
9
9
9
Q
1
2
0
0
0
Q
1
2
0
0
1
Q
1
2
0
0
2
Q
1
2
0
0
3
Q
1
2
0
0
4
Q
1
2
0
0
5
Q
1
2
0
0
6
Q
1
2
0
0
7
Q
1
2
0
0
8
Q
1
2
0
0
9
Q
1
100
50
25
500
250
1000
5000
2500
CA index
NASDAQ
NOTE: The two indices are both normalized to be 100 in the fourth quarter of 1988, to make it comparable
to the Sand Hill Econometrics Venture Index, which started in December 1988. The normalized indices
are presented in log scale.
Sources: Cambridge Associates (CA), the Center for Research in Security Prices (CRSP).
3.1 INDUSTRY RETURNS 51
CA clients as LPs. If ABC Fund I performs poorly, it is unlikely there will ever be an
ABCFund II, and CAwill never get to see the returns fromFund I. On the other hand,
if Fund I is successful, then it is more likely that ABC will be able to raise Fund II. If
ABC solicits a CA client for Fund II, then CA will request information on the per-
formance of Fund I, and then add it to its database. This method of data collection
induces a survivor bias—“survivors” have a better chance of showing up in the data,
and this bias causes an overestimate of industry returns. Thus, we think of the CA
index as representing an upper bound on the net returns to VC.
Next, consider the Sand Hill Index
s
. In principle, this index could also suffer
from survivor bias, because we might think that SHE is more likely to learn of the
existence of companies only if they have been successful. Furthermore, additional
biases are possible because valuation information might be missing for nonrandom
reasons (e.g., if the portfolio companies performed poorly). In practice, SHE has
been able to signi?cantly limit these biases through the combination of several
databases and the use of sophisticated statistical techniques designed to handle
missing data. It also has made arduous efforts to track down the exit status of
companies which existing databases list as “private” long after they were ?rst
funded, thus tackling the “zombie company” problem. It is, however, likely that this
index is a bit conservative (bias would be too strong a word here) in the way it
computes VC returns. To understand how conservatism could occur, we must go a
little deeper into the SHE methodology.
Each month, SHE takes a snapshot of all portfolio companies for all VCs. As
discussed earlier, there are several challenges in estimating the value of nontraded
companies, and SHE handles these problems with several careful methods. Because
VCs do not own 100 percent of these companies, the next step is to estimate the
value of the VCs’ portion of each company. This is tricky—indeed, the calculations
to do this estimation will take up the six chapters of Part III in this book—and the
task is made more dif?cult because SHE does not have access to the details of each
transaction. Thus, it is necessary to make an assumption about the form of VC
ownership, and SHE assumes that VCs have proportional (common-stock) own-
ership of these ?rms. This assumption is conservative, because virtually all VCs
own some form of preferred stock, which has valuation advantages over common
stock. A discussion of these advantages will be introduced in Chapter 9 and
extensively analyzed in Part III. For now, it will suf?ce to say that if SHE were to
have assumed some form of preferred stock, then the returns on the Sand Hill
Index
s
would have been a little bit higher. Thus, the Sand Hill Index
s
provides us
with a lower bound on the gross returns to VC.
Taken together, the returns data gives us an upper bound for net returns (the
CA index), and a lower bound for gross returns (the Sand Hill Index
s
). How far
apart are these bounds? The CA Index had an annualized return of 16.2 percent
from the end of 1988 to the end of 2008; the Sand Hill Index
s
had a return of 12.8
percent over the same time period. If we make a back-of-the-envelope estimate of
management fees costs of about 2 percent and carried-interest costs of about
2 percent, then we get a total of 4 percent for fees and carry, yielding an estimated
52 CHAPTER 3 VC RETURNS
net return of 12.8 2 4.0 5 8.8 percent for the Sand Hill Index
s
. This means that
the difference between the upper and lower bounds for VC net returns from 1989 to
2008 is 16.2 2 8.8 5 7.4 percent.
At ?rst glance, these returns demonstrate some advantage for VCover the most
comparable index. Of course, this is not the end of the story, because we have not said
anything about the relative risk of VC versus the NASDAQ; but at this point, a
detailed discussion of risk would take us too far off topic. In Chapter 4, we analyze the
risk of VC in the context of estimating the cost of capital for VC investments. With
that background, we will then be able to analyze the risk-adjusted performance of VC
based on the CAand SHEindices. For now, it will suf?ce to say that this analysis ?nds
that both the net risk-adjusted return (upper bound, from CA) and gross risk-adjusted
return (lower bound, from SHE) are very close to zero.
3.2 FUND RETURNS
In Chapter 4, we will show that the upper bound is zero for the net risk-adjusted
returns to the VC industry. If this is true, then investment in VC only makes sense if
one can identify managers that consistently outperform the rest of the industry.
Luckily for LPs, there is some evidence that such consistent outperformance does
exist. To understand the sources of such performance, we must ?rst learn how fund
level returns are measured.
3.2.1 De?nitions
The industry returns calculated in Section 3.1 started with periodic returns for each
month (Sand Hill) or quarter (CA), and then multiplied these returns to arrive at a
compound return for the whole time period. This is a standard procedure for com-
puting asset returns. It is used for stocks, bonds, and bank deposits, as well as for the
return measurements of mutual funds, hedge funds, and other portfolio managers.
Although this calculation is reasonable for the whole VC industry, it does not seem
reasonable when applied to a single VCfund. The main problemis that VCfunds may
have vastly different amounts of capital invested in different years of the fund, and it
can be misleading to treat all these years equally when computing returns.
To illustrate this problem, imagine that you are an LP in the ABCfund. Suppose
that you have committed $11M to the fund. For simplicity, assume fees and carry are
both zero (so gross returns are equal to net returns). On January 1, 2007, ABC calls
$1M of your investment. On December 31, 2007, it exits this investment and returns
$2M to you. On January 1, 2008, it calls the remaining $10M for another investment.
On December 31, 2008, it exits this second investment for $6M. Given these facts,
what is your annualized return from investing in ABC?
If we follow the same steps as in Section 3.1, then we would calculate the
return for 2007 as (2/1) 2 1 5 100 percent, and for 2008 as (6/10) 2 1 5 240
percent. The compound returns would then be (1 11)Ã (1 20.4) 21 520 percent,
3.2 FUND RETURNS 53
and the annualized returns would be (1.2)
(1/2)
2 1 5 9.5 percent. Although this is
mathematically correct, it is economically misleading. After all, if we ignore the
timing of these cash ?ows, we can see that you gave ABC a total of $11M when it
really only returned $2M1$6M5$8M to you. It just does not seem right to credit
them with a positive return of 9.5 percent.
The problem is that annualized returns weigh each year equally in the calcu-
lation. To get an answer consistent with our intuition, we need to compute an internal
rate of return (IRR), which effectively weighs each dollar equally. To compute the
IRR, we start with the whole streamof cash ?ows. In this case, we have a negative cash
?owof $1Mon January 1, 2007 (the original investment); a positive cash ?owof $2M
on December 31, 2007; a negative cash ?ow of $10M on January 1, 2008; and then a
positive cash ?owof $6M on December 31, 2008 (the ?nal value of the portfolio). To
simplify our calculations, we combine the cash ?ows on December 31, 2007 and
January 1, 2008 to obtain a single negative cash ?ow of $8M for the end of 2007.
We are now ready to move on and answer the following question. Suppose
that the negative cash ?ows were the deposits in a bank, and the positive cash ?ow
was the ?nal bank balance. If such is the case, then what interest rate must this bank
be paying on deposits?
Under this logic, a bank paying an interest rate equal to the IRR would give
us 1M Ã (1 1 IRR)
2
for a two-year deposit of $1M, and 8M Ã (1 1 IRR) for a one-
year deposit of $8M. If we have $6M total from these deposits, then the IRR is the
solution to
6M51M Ã ð11IRRÞ
2
18M Ã ð11IRRÞ ð3:6Þ
We can solve this quadratic equation to obtain a feasible annual IRR 5 231
percent. This negative return seems more consistent with the idea that ABC lost
money overall than the answer given by our previous procedure.
For cash ?ow streams more complex than this example, we would use a com-
puter to calculate the IRR. The IRR plays an important role in VC performance
reporting, but it is not a panacea—and careful observers must be aware of several
weaknesses in the IRR measure. First, one should never forget that the IRRcannot be
directly compared to periodic returns. In the example we just solved, the annualized
returns were about 9.5 percent, whereas the IRR was negative 31 percent. Although
not all differences will be this extreme, such differences are not uncommon. Because
most of the investment world speaks in terms of annualized returns, it is tempting to
compare these returns to IRRs. This temptation should be avoided.
Second, some standard practices of IRR calculation can lead to confusion.
Typically, VC funds will compute a monthly or quarterly IRR from all its cash ?ows,
and then annualize this periodic IRR using Equation (3.3). However, in times of high
returns, an annualized version of a monthly or quarterly IRR will be misleading,
because this exercise implicitly assumes reinvestment even when such reinvestment
has explicitly not occurred. For example, consider a $1M investment that returns
$80,000 every month for one year and then returns $1M at the end of the year. This
cash ?owstreamhas a monthly IRRof 8 percent. So far, so good—the investment has
54 CHAPTER 3 VC RETURNS
clearly returned 8 percent in every month. However, if we annualize this IRR to
(1.08)
12
21, we get an annualized IRR of 151 percent, which is similar to assuming
that all the distributions were reinvested (none were!) and also earned 8 percent per
month. Atrue “annual IRR” of 151 percent should be leaving the investor with $1MÃ
(1 11.51) 5$2.51Mat the end of the year, but the investment strategy followed here
would not do that without some extra help from excellent outside investments.
A third weakness of standard IRR reporting is that it does not usually make a
distinction between realized and unrealized investments. For VC funds that still
have unrealized investments, the IRR takes the value of these unrealized invest-
ments and treats them as a positive cash ?ow in the ?nal period. If a signi?cant
component of the portfolio is unrealized, then the IRR calculation will essentially
just re?ect the subjective valuation of these unrealized investments. In general, the
IRR becomes more informative as the fund realizes more investments.
For this last reason, the IRR is particularly misleading in the ?rst few years of a
fund. Remember that management fees are usually based on committed capital; so
LPs of a $100M fund with 2 percent annual fees would be paying out $2M in fees
each year and would have $80M left for investment capital. Suppose the fund invests
$20M of this investment capital in the ?rst year. Because one year is rarely long
enough to have any exits, it is possible that all this investment capital would still
be kept on the books at cost. The fund would then appear to have earned no gross
returns while still collecting $2Min fees. An IRRcalculation fromthese cash ?ows is
going to give a negative return. If these investments turn out well in the long run, then
the fund will look ?ne by the time of these exits. In the early years, however, it will
appear to charge very high fees compared to invested capital ($2M on $20M of
investments 510 percent in this case) and with little appreciation of the assets. Even
for funds that eventually have high IRRs, a plot of the fund IRR over time will
be negative for the ?rst few years, and then increase rapidly in the later years. The
shape of this plot, shown in Exhibit 3-5, is called a J-curve or a hockey stick.
The IRR is an answer to the question, “How well did you do with my money
while you had it?” Many investors would like to get the answer to a different
question, which asks, “Overall, how much money did you make for me?” The
IRR’s inability to answer this second question is a ?nal weakness. For example,
consider the following two funds. Fund ABC takes a $1M investment at the
beginning of year 1 and then returns $2M at the end of year 1. Fund XYZ takes a
$1M investment at the beginning of year 1 and then returns $32M at the end of year
5. Both funds have an (annual) IRR of 100 percent. Clearly, however, assuming a
normal investment and in?ation environment, fund XYZ will be preferred by all
investors. It would be nice to have a measure of this superior performance. The VC
industry indeed has such a measure, which goes by many names—value multiple,
investment multiple, realization ratio, absolute return, multiple of money,
times money. They all mean the same thing: “For every dollar I gave you, how
much did I get back?” Each of these expressions can be divided into realized and
unrealized investments. For instance, a value multiple is the sum of the realized
value multiple and unrealized value multiple.
3.2 FUND RETURNS 55
EXAMPLE 3.2
The $200M ABC Fund is seven years into its 10-year life. Its annual investments, fees,
distributions, and portfolio value are given in Exhibit 3-6.
EXHIBIT 3-5
THE J-CURVE/HOCKEY STICK PATTERN OF RETURNS
IRR
60%
50%
40%
30%
20%
–20%
10%
–10%
0%
I
R
R
0 1 2
Years since closing
3 4
EXHIBIT 3-6
CASH FLOWS FOR THE ABC FUND
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
Investments 20.0 30.0 40.0 40.0 30.0 0.0 0.0
Portfolio value 20.0 56.0 112.8 186.6 188.1 195.7 203.5
Total distributions 0.0 0.0 0.0 65.0 37.6 39.1 40.7
Carried interest 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Distributions to LPs 0.0 0.0 0.0 65.0 37.6 39.1 40.7
Cumulative distributions to LPs 0.0 0.0 0.0 65.0 102.6 141.8 182.5
Port value after capital returned 20.0 56.0 112.8 121.6 150.5 156.5 162.8
Management fee 4.0 4.0 4.0 4.0 4.0 4.0 4.0
NOTE: All entries are in $millions.
56 CHAPTER 3 VC RETURNS
Problem Compute the IRR, value multiple, realized value multiple, and unrealized value
multiple for ABC at the end of year 7.
Solution To compute the IRR, we ?rst need to aggregate the investments, fees, and
distributions into a single cash ?ow to LPs as
Cash Flow to LPs 5Distributions to LPs 2new investments
2management fees
ð3:7Þ
These cash ?ows are 2$24M for year 1, 2$34Mfor year 2, 2$44M for year 3, $21Mfor
year 4, $3.6Mfor year 5, $35.1Mfor year 6, and $36.7Mfor year 7. The portfolio value at the end
of year 7 is $162.8M. This value is counted as a positive cash?owfor the IRRcalculation. We can
use a spreadsheet or calculator to compute the IRR of this cash ?ow stream as 23.8 percent.
The value multiple is as follows:
Value Multiple 5ðTotal Distributions to LPs ½all years?
1value of unrealized investmentsÞ=ðInvested Capital
1Management FeesÞ
ð3:8Þ
Total distributions to LPs through year 7 are $182.5M. The value of unrealized invest-
ments 5the portfoliovalue after year 7 5$162.8M. Invested capital is the sumof newinvestments
over all years 5$160M. The total management fees through year 7 5$28M. Thus, the value
multiple 5 ($182.5M 1 $162.8M)/($160M 1 $28M) 5 1.84.
The realized value multiple is as follows:
Realized Value Multiple 5ðTotal Distributions to LPs½all years?Þ
=ðInvested Capital 1Management FeesÞ
5$182:5M=ð$160M1$28MÞ 50:97
ð3:9Þ
The unrealized value multiple is as follows:
Unrealized Value Multiple 5ðValue of unrealized investmentsÞ
=ðInvested Capital 1Management FeesÞ
5$162:8M=ð$160M1$28MÞ 50:87
ð3:10Þ
’
Most LPs compute value multiples on a net basis, with fees and carry already
subtracted; if you read “value multiple” in this book or in the trade press, youcanassume
that it refers to a net value multiple. In some cases, ?rms may report value multiples on a
gross basis, perhaps because the GP team wants to discuss a performance record for a
time periodwhentheywerenot explicitlychargingfees or carry. This canoccur whenthe
GPs’ prior investingexperience tookplace outsidethestandardpartnershipstructure. For
many GPteams raising their ?rst fund, such experience may represent the only evidence
of their past performance. This gross value multiple (GVM) is computed as follows:
GVM5ðTotal distributions to LPs ½all years?
1value of unrealized investments
1carried interestÞ=invested capital
ð3:11Þ
3.2 FUND RETURNS 57
Gross value multiples are also helpful for quickly communicating the raw
investment performance of a GP and for calculating shortcut estimates for carried
interest. Also, we can go back and forth between GVMs and value multiples by
making a few extra calculations. For example, consider a fully invested fund at the
end of its life, so investment capital 5 invested capital, and all investments have
been realized. Then, we can rewrite Equation (3.11) as follows:
GVM5total distributions=investment capital ð3:12Þ
where total distributions include both carried interest plus all LP distributions. We
can then compute its carried interest as
Carried interest 5carry% Ã ðtotal distributions 2carry basisÞ
5carry% Ã ðGVM Ã investment capital 2carry basisÞ
ð3:13Þ
where carry% represents the percentage level of carried interest and the carry basis
is either committed capital or investment capital as speci?ed by the fund partner-
ship agreement. We can now express the (net) value multiple of a completed fund
by rewriting Equation 3.(3.8) in terms of the GVM and other inputs as follows:
Value multiple 5ðtotal distributions to LPsÞ=ðinvestment capital
1management feesÞ
5ðtotal distributions 2carried interestÞ=committed capital
5½GVM Ã investment capital 2carry% Ã ðGVM
à investment capital2carry basisÞ?=committed capital:
ð3:14Þ
Finally, there is one more de?nition that will be useful in later chapters. For
many of our valuation analyses, we will need to estimate the fraction of the
investment that we expect to be paid to the GP as carried interest. For a completed
fund, we de?ne this GP% as
GP%5carried interest=total distributions 5carry%Ã
ðGVM Ã investment capital 2carry basisÞ=
ðGVM Ã investment capitalÞ:
ð3:15Þ
Note that GP% will never be higher than carry%, because carry% is paid on
all pro?ts, whereas GP% is a percentage of total distributions. Since pro?ts will
always be lower than total distributions, GP% will always be lower than carry%.
Also, remember that carry% is a contractual number in the partnership agreement,
whereas GP% is an estimated percentage that depends on the eventual GVM of
the fund.
The following example allows us to practice with these de?nitions.
58 CHAPTER 3 VC RETURNS
EXAMPLE 3.3
XYZ Partners is raising their ?rst fund, XYZ Partners Fund I, with $100M in committed
capital, annual management fees of 2 percent, carried interest of 20 percent, and a carried
interest basis of committed capital. The four individuals on the XYZ team have previously
managed the captive VC portfolio for the Goldenbucks family. During the 10 years of
managing the Goldenbucks’ VC portfolio, the partners did not charge management fees or
carried interest, and they achieved a GVM of 2.5.
Problem
(a) Suppose that XYZ Fund I earns the same GVM as the partners earned for Goldenbucks.
What would be the value multiple be for the fund?
(b) What would be the GP% of the fund?
Solution
(a) To see how this formula would translate into XYZ Fund I, we must make adjustments
for management fees and carried interest. For a $100M fund with 2 percent annual fees,
lifetime fees would be $20M, and investment capital would be $80M. Then, we can sub-
stitute these quantities and GVM 5 2.5 into Equation (3.14) to obtain the following:
Value multiple 5ð2:5 Ã $80MÞ20:20 Ã ðð2:5 Ã $80MÞ2$100MÞ=$100M
5½$200M20:20 Ã ð$100MÞ?=$100M51:8:
ð3:16Þ
(b) From Equation (3.15), we can compute the GP% as
GP%50:20 Ã ð2:5 Ã $80M2$100MÞ=ð2:5 Ã $80MÞ
5$20M=$200M50:10:
ð3:17Þ
’
3.2.2 Evidence
LPs get access to fund level return data through their own databases or through
gatekeepers. Well-known gatekeepers include Cambridge Associates (who release
the aggregate VC index discussed in Section 3.2), Hamilton Lane Advisors, State
Street (who launched its own venture capital and related private equity indices in
2007), and Paci?c Corporate Group. For those of us outside the LP community,
data is harder to ?nd.
The longest-standing source of fund level return data is Venture Economics
(VE). Both GPs and LPs report returns to VE under a strict rule of secrecy, in which
VE promises not to disclose any identifying information about speci?c funds.
Although VE does not provide information about speci?c funds, its summary data
has been an industry standard since the 1980s. The publicly available source for this
data is its annual publication, Investment Benchmarks Report (IBR). In each year of
the IBR, VE gives summary statistics for the vintage year. VE claims to have data
on 25 percent of all funds, and overrepresentation of the largest funds allows this
25 percent to cover over 50 percent of all industry dollars.
3.2 FUND RETURNS 59
Each annual IBR dedicates several pages to each vintage year, with summary
information about IRRs and value multiples during the complete evolution of that
vintage year. Perhaps its most closely watched statistics are the cutoffs for the
median and top-quartile fund for each vintage year. Because VE is the only public
provider of this information, these cutoffs have become the de facto benchmarks.
Because it is very dif?cult to measure risk for individual funds, the dominant
performance measures in the industry are these vintage year comparisons. Exhibit
3-7 displays the median IRR and top-quartile IRRs for all vintages since 1980.
The IBR data shows that median performance peaked for vintage year 1996, and
that the mid-1990s were extremely fortunate years to be raising VCfunds. The median
IRRs of funds raisedin2004and2005are still negative—that is expectedandconsistent
with the J-curve—whereas the poor medianperformance of 1999and 2000funds after a
decade cannot be attributed to the J-curve and seems likely to be with us for good.
Although the detailed VE data is not available to the public, subsets of the data
have been released to academic researchers. These subsets are cleansed of identifying
information, but do include codes that allow researchers to link funds from the same
GP without actually knowing who that GP is. Kaplan and Schoar (2005) use this data
to answer the crucial question posed at the beginning of this section, which asks, “Is
GP performance persistent across funds?” Using several measures of performance,
the authors ?nd that the answer is a clear “yes”. For example, let N 5 the sequence
EXHIBIT 3-7
VE MEDIANS AND TOP-QUARTILE BY VINTAGE YEAR
120.00
100.00
80.00
60.00
40.00
20.00
0.00
?20.00
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Top quartile IRR
Median IRR
I
R
R
(
%
)
Source: Thomson VentureXpert.
60 CHAPTER 3 VC RETURNS
number for funds of a speci?c GP. Kaplan and Schoar found that the IRRof Fund Nis
a signi?cant predictor for the IRR of Fund N 11 and for the IRR of Fund N 12, and
the authors also demonstrate that their results are robust to using other measures of
fund performance and to several differences in fund style.
In recent years, some newdata sources on fund level returns have appeared. This
appearance was driven mostly by media requests to public LPs under the Freedom of
Information Act (FOIA). Public LPs, such as public-pension funds and the endowments
of public universities, fought hard to avoid disclosing the returns on their private equity
portfolios, but ultimately some disclosure was required. FOIA requests uncovered the
returns of several large and experienced LPs, including the University of California,
California Public Employee Retirement System (CALPERS), the University of
Michigan, and the Universityof Texas. These disclosures gave the public its ?rst lookat
the performance of some of the most famous names in VC.
These FOIA disclosures inspired a new entrant into the VC performance
market. Private Equity International (PEI) began by gathering all the information
from FOIA requests and then combining this information with proprietary data
from LPs and GPs. They now offer several products to the general public, including
an annual publication, The Private Equity Performance Monitor (PEPM). This
publication gives performance data for hundreds of funds; we will discuss this
evidence extensively in our listing of the “best VC funds” in Chapter 5.
To give you just a ?avor of the data, Exhibit 3-8 shows the returns and
multiples of Kleiner, Perkins, Cau?eld, & Byers (KPCB), taken from the dis-
closures of the University of California and included in the 2005 PEPM.
Exhibit 3-8 shows why KPCB is so famous. By comparing these results to the
benchmarks in Exhibit 3-7, we can see that every fund from 1980 through 1996 was
above the median IRR. Truly spectacular results were obtained by KPCB VII (1994
vintage) and KPCB VIII (1996 vintage), which achieved value multiples of 32.0 and
17.0, respectively. Furthermore, the 1999 vintage KPCBIXfund, which had a net IRR
of À23.3 percent as of March 2004 and thus looked like the ?rm’s ?rst “loser”, turned
out to be the very best of hundreds of funds raised that year. Why? Because KPCBIX
had about 20M shares of Google, which went public on August 19, 2004, and
regulatory ?lings show that these shares were distributed at about $200 per share.
Assuming that about 14Mof these shares went to LPs (KPCBhas a 30 percent carried
interest), that would mean about $2.8 billion was distributed to LPs. Thus, even if
KPCB gets no other realizations from the entire fund, they would still give their
investors a value multiple of at least 5 (,2800/500) from fund IX.
5
5
While we cannot of?cially verify our assertion that KPCBIXwas a homerun fund, we take comfort fromthe
disclosure that another famous fund that invested in Google, Sequoia Capital III, has a value multiple of 14.84
and a net IRR of 106% as of September 2007 (2008 Private Equity Performance Monitor). This $250M fund
reported a value multiple of 0.44 as of March 2004, prior to the Google IPO; thus an increase of 14.4X(14.84-
0.4) in the value multiple was likely due to the Google exit. The back-of-the-envelope calculation using 30%
carryand20Mshares distributedat $200per shareyields 11.2X(2800/250) incremental contributionof Sequoia’s
Google investment toits fundperformance. The numbers (14.4and11.2) roughlymatch, andif anythingtells us
that our assumptions understate the true exit value of the Google investment for its VC backers.
3.2 FUND RETURNS 61
SUMMARY
VC is a form of private equity, and for many years the returns to VC funds have indeed
been very private. In recent years, however, several new data sources have been made
available so that it is now possible to do some analysis of industry level and fund level
returns. In this chapter, we analyzed two sources of industry level returns: the Cambridge
Associates VC Index
s
(providing an upper bound for the net returns to the industry) and
the Sand Hill Index
s
(providing a lower bound for the gross returns to the industry).
Although both of these indices have superior performance to the NASDAQ, the risk-
adjusted returns (to be studied in detail in Chapter 4) are close to zero. Although the
industry as a whole does not offer superior risk-adjusted performance, the evidence on fund
level returns suggests that top ?rms can consistently outperform their peers. To analyze
fund level performance, it is necessary to use different measures of returns from the
methods used at the industry level. The two main measures of fund level returns are
the IRR and the value multiple, the latter also known by many other names. Fund level data
is available in summary form from Venture Economics and in detailed form from Private
Equity Intelligence.
EXHIBIT 3-8
KLEINER PERKINS CAUFIELD & BYERS FUNDS
Fund Vintage Year
Committed
Capital ($M) Net IRR Value Multiple Date Reported
II 1980 65 50.6% 4.3 Mar-04
III 1982 150 10.2% 1.7 Dec-04
IV 1986 150 11.0% 1.8 Dec-04
V 1989 150 35.7% 4.0 Dec-04
VI 1992 173 39.2% 3.3 Mar-04
VII 1994 225
1
121.7% 32.0 Mar-04
VIII 1996 299 286.6% 17.0 Mar-04
IX 1999 550 223.3% See text Mar-04
X 2000 625 217.5% 0.6 Mar-04
XI 2004 400 NA NA NA
XII 2006 600 NA NA NA
XIII 2008 700 NA NA NA
1
Only $170M of Fund VII was drawn down.
NOTE: There have been no publicly available updates of KPCB funds since December 2004.
Source: Dow Jones LP Galante, 2005 Private Equity Performance Monitor.
62 CHAPTER 3 VC RETURNS
KEY TERMS
Periodic return
Compound return
Annualized return
Gross return
Net return
Realized return
5 historical return
Expected return
Gatekeeper
Survivor bias
Internal rate of return (IRR)
J-curve
5 hockey stick
Value multiple
5 investment multiple
5 realization ratio
5 absolute return
5 multiple of money
5 times money
Realized value multiple,
unrealized value multiple
Gross value multiple
5 gross investment
multiple, etc.
Carry%
GP%
Top-quartile fund
REFERENCES
Hall, Robert E., and Susan Woodward, 2003, “Benchmarking the Returns to Venture”, National Bureau
of Economic Research working paper #10202.
Kaplan, Steven N., and Antoinette Schoar, 2005, “Private Equity Performance: Returns, Persistence, and
Capital Flows”, Journal of Finance 60(4), 1791À1824.
Private Equity Intelligence, The 2005 Private Equity Performance Monitor.
Private Equity Intelligence, The 2008 Private Equity Performance Monitor.
EXERCISES
3.1 The Bigco pension plan has invested in dozens of VC funds. The director of the pension
plan is preparing his annual report to the Bigco board of directors. Summary information for
Bigco’s VC portfolio is given in Exhibit 3-9.
The board has asked for a ?ve-year report of net returns and gross returns by year, plus
the compound returns and annualized returns for all ?ve years. You can assume that all new
investments and management fees were paid for at the beginning of the year, and all dis-
tributions were paid at the end of the year.
3.2 Consider the case of XYZ Partners from Example 3.3. Now, instead of using a GVM of
2.5 (as in the example), assume that this GVM is unknown and equal to K.
(a) For any given K, solve for the carried interest, value multiple, and GP%.
(b) How large must K be for the value multiple to be greater than 3?
(c) How would your answer to parts (a) and (b) change if the carry basis were equal to
investment capital? (In the original example, the carry basis is equal to committed capital.)
3.3 True, False, or Uncertain: If both EBV and Owl have the same GVM, then the value
multiple of Owl will be lower than the value multiple of EBV. (See Appendices 2.A and 2.C
for more information on EBV and Owl.)
EXERCISES 63
3.4 The $600M XYZ Fund has completed its 10-year life. Its annual investments, fees,
distributions, and portfolio value are given in Exhibit 3-10.
(a) Compute the value multiple, realized value multiple, unrealized value multiple, and IRR
for XYZ after every year of its life.
(b) Are these returns an example of the J-curve, or are they an exception?
EXHIBIT 3-10
CASH FLOWS FOR THE XYZ FUND
Year
1
Year
2
Year
3
Year
4
Year
5
Year
6
Year
7
Year
8
Year
9
Year
10
Investments 50.0 100.0 100.0 150.0 100.0 0.0 0.0 0.0 0.0 0.0
Portfolio value 50.0 167.5 326.1 387.8 353.5 381.8 412.3 445.3 480.9 519.4
Carried interest 0.0 0.0 0.0 0.0 0.0 0.0 15.9 17.8 19.2 103.9
Distributions to LPs 0.0 0.0 150.0 200.0 70.7 76.4 66.6 71.2 76.9 415.5
Cumulative
distributions to LPs
0.0 0.0 150.0 350.0 420.7 497.1 563.6 634.9 711.8 1127.3
Port value after
capital returned
50.0 167.5 176.1 187.8 282.8 305.4 329.8 356.2 384.7 0.0
Management fee 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
EXHIBIT 3-9
BIGCO PENSION PLAN, VC PORTFOLIO
Year 2010 2011 2012 2013 2014
Beginning value 10,000 10,300 13,105 5,563 6,332
New investments 2,000 2,000 2,000 2,000 2,000
Ending value (before distributions) 13,800 16,605 9,063 9,832 12,498
Distributions to LPs 3,000 3,000 3,000 3,000 3,000
Distributions to GPs 500 500 500 500 500
Management fees 200 200 200 200 200
64 CHAPTER 3 VC RETURNS
CHAPTER 4
THE COST OF CAPITAL FOR VC
VCS SHOULD make an investment if the expected return on the investment
is higher than the cost of capital. We dedicated part of Chapter 3 to an empirical
analysis of the returns to VC investment. In this chapter, we empirically analyze the
other side of this equation: the cost of capital. The main driver of the cost of capital
is the trade-off between risk and return. This analysis of the risk-return trade-off is
probably the biggest research topic in ?nancial economics. This chapter provides an
introduction to this important topic, with a focus on the implications for the cost of
venture capital.
In Section 4.1 we introduce the capital asset pricing model (CAPM). More than
40 years after its ?rst development, the CAPM remains a workhorse model for
computing the cost of capital. Although the CAPM is widely used, it remains
poorly understood by many practitioners. Indeed, the ideas behind the model are
often counterintuitive, and many people just apply the formulas without knowing
why. In Section 4.2 we tell an economic fairy tale to discuss the CAPM intuition
without all the mathematical details. This same intuition can be applied to more
complicated multifactor models of the cost of capital. In Section 4.3 we introduce
some multifactor models to directly estimate the cost of venture capital.
4.1 THE CAPITAL ASSET PRICING MODEL
Consider two investments: The ?rst investment is a manufacturer of cardboard
boxes (Boxco), an item always in some demand because of its use in transporting
goods around the world. Although the fortunes of this company rise and fall with the
economy, the peaks and valleys are not very extreme. As a ?rst approximation,
the earnings of the company are proportional to world GDP, and world GDP rarely
moves by more than a few percentage points in any given year. Next, consider an
investment in a drug company, currently searching for the cure to some rare disease
(Drugco). The research for this disease has made some progress, but still there is
only a 20 percent chance that the drug will succeed, and we won’t know about this
success for a few years. If it does succeed, then the company will have the exclusive
65
right to market the drug for about 10 years, and it would expect to plow back some
of these earnings into similar R&D efforts in the future. If the drug does not succeed,
then the company will go out of business and be worth nothing. Neither the success of
the project nor the pro?ts from this (or future) projects are at all related to the state
of the world economy. Now, consider two related questions. First, which of these
two companies is “riskier”? Second, which of these companies will have a higher
cost of capital?
If we equate risk with the statistical measure of variance, then Drugco is
riskier.
1
There is an 80 percent chance of complete failure, and even success on the
?rst drug does not guarantee success for the future. Boxco, on the other hand, does not
have a high variance. A wary reader might suspect a trick, and of course there is one.
The performance of Drugco is not related to the global economy. If we split the
ownership of Drugco into thousands of little pieces (shares of stock), and if we ?nd
thousands of companies similar to Drugco, then a portfolio of such investments would
be well diversi?ed and could actually have close to a zero variance. Thus, in this
example, Drugco has only idiosyncratic risk, also called diversi?able risk. On the
other hand, Boxco, despite having a relatively low variance, is perfectly correlated
with the economy. If we break Boxco into thousands of pieces and ?nd thousands of
similar companies, we will still be left with the same variance in our portfolio.
If we accept this discussion of risk, then which of these two companies will
have a higher cost of capital? The classic model used to answer this question is the
Capital Asset Pricing Model (CAPM):
r
i
5R
i
5R
f
1?ðR
m
2R
f
Þ ð4:1Þ
where r
i
is the cost of capital for asset i, R
i
is the expected return for asset i, R
f
represents the risk-free rate for borrowing and lending, R
m
is the return on the
whole market portfolio, and ? (pronounced “beta”) is the level of risk for asset i.
The difference (R
m
2R
f
) is called the market premium. For this model to hold, the
?nancial market needs to be in equilibrium, so that the cost of capital for any
investment is equal to the expected return on that investment. Thus, for the
remainder of this discussion, we refer interchangeably to the “cost of capital” and
“expected return”. Although this might be a boring world to be an investor—
because all assets would trade at “fair” value—it is a very useful world if we are
trying to understand the trade-off between risk and return.
In our well-behaved equilibrium world, the CAPM applies to individual
companies like Drugco or Boxco, but asset i could also represent many other things.
For example:
1. Speci?c capital projects within companies, such as a factory to manufacture
boxes or drugs;
1
If you are unfamiliar with the de?nition of variance, then you are going to be very confused by this
chapter. Sorry.
66 CHAPTER 4 THE COST OF CAPITAL FOR VC
2. An entire industry or asset class, such as “all drug companies”, “small
stocks”, or “venture capital”;
3. The portfolio of a speci?c investment manager, such as a mutual fund or a
venture capital fund.
The key idea of the CAPM is that beta re?ects the covariance of an asset’s
returns with the returns on the overall market. The higher the beta, the higher the
expected return. Beta risk is also called market risk, nondiversi?able risk, or
systematic risk. The mathematics and intuition behind the CAPM implies that beta
risk is the only kind of risk that affects the expected return of an asset. As discussed
earlier for the Drugco example, risks that are uncorrelated with the market are
called diversi?able risk or idiosyncratic risk, and such risks are not compensated by
any extra return.
To make the CAPM operational, we need some way to estimate the variables
of (4.1). For R
i
, we can use the realized returns on asset i. For R
m
, we can use the
realized returns on a portfolio of all publicly traded stocks. For R
f
, we can use
the realized returns on short-term U.S. treasury bills. (Recall from Chapter 3 that
realized returns are the same thing as historical returns.) Then, using these realized
returns, the statistical method of least-squares regression can be used to estimate
beta. The standard approach is to modify Equation (4.1) to
R
it
2R
ft
5?1?ðR
mt
2R
ft
Þ 1e
it
ð4:2Þ
where ?, R
it
, R
mt
, and R
ft
are de?ned similarly to Equation (4.1)—except that in
(4.1) the return variables represented expected returns, whereas in (4.2) they
represent realized returns for period t. The new elements in (4.2) are ? (pronounced
“alpha”), the regression constant; and e
it
, the regression error term.
2
Once we have estimated Equation (4.2), we can use the results to compute a cost
of capital for asset i. The cost of capital is still given by Equation (4.1). To actually
compute this cost, we can substitute the regression estimate of beta into (4.1), but we
still need estimates for the risk-free rate, R
f
, and for the market premium (R
m
2R
f
). For
R
f
, most analysts recommend using the current treasury yield for a horizon that matches
the expected holding period of the investment. Thus, an investment with a ?ve-year
horizon would use the yield on the ?ve-year treasury bond. In this chapter we use a risk-
free rate of 4percent. For (R
m
2R
f
), one possibilityis touse the realizedmarket premium
over some historical period in some country or set of countries. For example, from1926
to 2008, the average market premium in the United States was approximately
7 percent.
3
Also, Welch (2000) ?nds that 7 percent is the average market premium
forecast by a sample of 226 academic ?nancial economists. Based on these two pieces
of evidence, we will use 7 percent as our estimated premiumin this book. Readers with
strong views about the premium should certainly experiment with other numbers.
2
An excellent introduction to regression techniques is Kennedy (2003). This book includes discussions at
several levels of technical detail and succeeds admirably on every level.
3
Ibbotson Associates (2009).
4.1 THE CAPITAL ASSET PRICING MODEL 67
With these estimates for the risk-free rate and the market premium, we can
compute the cost of capital as follows:
r
i
50:04 1
^
? Ã 0:07 ð4:3Þ
where
^
? is the regression estimate for beta. Thus, with a beta of 1, the typical stock
would have an 11 percent cost of capital.
By allowing the possibility of a regression constant (alpha) in Equation (4.2),
we are permitting realized returns on asset i to be higher than its cost of capital,
because the cost of capital is still given by the expected return of Equation (4.1). If
asset i is a managed asset such as a mutual fund or a VC fund, then alpha can be
interpreted as an abnormal return: if alpha is positive, then the manager has
earned a return higher than the cost of capital—a “positive abnormal return”; if
alpha is negative, then the manager has earned a return lower than the cost of
capital—a “negative abnormal return”. This interpretation of alpha as abnormal
returns means that we can use the regression in Equation (4.2) to measure the
investment performance of an asset class or asset manager. For this reason,
Equation (4.2) is sometimes called a performance evaluation regression.
EXAMPLE 4.1
The Largeco pension fund aggregates its entire portfolio every month across all asset classes
and computes its net returns, R
i
. Exhibit 4-1 displays these monthly returns for one year,
along with the market returns and the risk-free treasury bill rates for those months.
EXHIBIT 4-1
LARGEO RETURNS
Month R
i
R
m
R
f
January 1.51% 2.24% 0.07%
February 1.34% 1.49% 0.06%
March 20.39% 21.16% 0.09%
April 22.45% 22.50% 0.08%
May 1.74% 1.35% 0.06%
June 2.33% 2.08% 0.08%
July 23.81% 23.87% 0.10%
August 0.32% 0.16% 0.11%
September 2.25% 1.95% 0.11%
October 2.01% 1.67% 0.11%
November 3.76% 4.68% 0.15%
December 2.43% 3.36% 0.16%
68 CHAPTER 4 THE COST OF CAPITAL FOR VC
Problem Use Equations (4.1) and (4.2) to estimate the beta, alpha, and cost of capital for
the Largeco portfolio. How do you evaluate its investment performance?
Solution Before estimating the regression, we subtract R
f
, the risk-free rate given in the last
column, from both the R
i
and the R
m
columns. We can then estimate Equation (4.2) using a
spreadsheet or other statistical package. The estimates are beta 50.88 and (monthly) alpha 50.07
percent. The alpha estimate is not statistically signi?cant, but it does indicate a positive abnormal
performance of 0.07 percent per month, which we can translate into an annualized alpha of
approximately 0.8 percent. To compute the cost of capital for the Largeco portfolio, we combine
our estimate of beta 50.88 with a market premium of 7 percent and risk-free rate of 4 percent:
r
i
50:04 10:88 Ã 0:07 510:16 percent ð4:4Þ
’
By using Equation (4.2) and allowing for the possibility of abnormal returns, we are
engaging in some seemingly paradoxical mental gymnastics. Equation (4.1)
requires that abnormal returns are zero in the future; that is, the cost of capital must
be exactly equal to the expected return, because there is no alpha in Equation (4.1).
However, once we estimate a nonzero alpha in Equation (4.2), we are willing to
allow some abnormal returns in the past. Presence of a nonzero alpha or abnormal
returns does not contradict Equation (4.1), however, as long as Equation (4.1) holds
on average across all assets. Among ?nancial economists, it is a bit of a cottage
industry to devise statistical tests to measure whether Equation (4.1) does indeed
hold “on average”. Overall, the CAPM held up very well in the 1970s; but
anomalous evidence started to accumulate in the 1980s, and by the 1990s most
researchers came to believe that the model needed some extensions. Nevertheless,
all these extensions are based on the same underlying concepts. In Section 4.2, we
provide some intuition for these concepts; and in Section 4.3, we develop the
extended models and apply them to the estimation of the cost of venture capital.
4.2 BETA AND THE BANANA BIRDS
To gain more intuition about the CAPM, let’s lose all touch with reality and enter
the fantasy world of ?nance professors. Imagine that our entire world is populated
by 100 people, all of whom live on their own island. Travel and trade between
islands is easy and free. Each island has 100 banana trees; these trees will last
forever, and no other trees can ever be planted. Bananas are all that anybody
consumes or ever wants to consume. On average, every year, a tree will produce
200 bananas, so that the whole world produces 200 bananas à 100 trees à 100
islands 52M bananas per year. There is no limit on how many bananas a person
can eat. Although never completely sated, each additional banana provides a little
less happiness than the last one: the 100th banana of the month does not bring as
much pleasure as the 99th. Bananas cannot be stored (they go brown fast, as we
know), so everything produced by the trees must be eaten each year.
4.2 BETA AND THE BANANA BIRDS 69
Of course, the world is not a total paradise—there is some risk. One risk comes
from a ?ock of wild banana birds that settle down onto half the islands every year, and
proceedtoeat all the bananas onthose islands (while theyare still green) sothat the trees
on that island produce no ripe bananas for the entire year. These banana birds seem to
choose their islands randomly, witheachislandhavinga 50percent chance ineachyear.
Thus, the overall number of ripe bananas available to all the islanders is 50%Ã
2M51M, with the other 1M (green) bananas consumed by the birds.
The bird risk is serious, because without any bananas for the year, the islander
will be very hungry. (Being hardy folk, islanders can survive without eating for
many years, but they are not happy about it.) For each individual islander, bird risk
has a high variance: the expected number of bananas is 100 per tree, but this
represents a 50 percent chance of getting 200 bananas per tree and a 50 percent
chance of getting zero bananas per tree. How does this bird risk affect the happiness
of the islanders? We assumed at the beginning of this story that the 100th banana
does not provide as much happiness as the 99th banana, giving us a “banana utility”
function shaped like Exhibit 4-2. An islander with a 50 percent chance at 20,000
bananas and 50 percent chance at 0 bananas would have an expected utility lying at
point B, the midpoint of line AD. She would be better off if she could get to point
C, which is the utility of getting 10,000 bananas for sure. All islanders feel this way,
so they try to construct some diversi?cation strategy to get there.
EXHIBIT 4-2
BANANA UTILITY WITH BIRD RISK
C
B
D
A 10K
Bananas
20K
U
t
i
l
i
t
y
70 CHAPTER 4 THE COST OF CAPITAL FOR VC
One islander hits upon a solution: she takes all her trees and forms a company
and then sells shares in her company to all the other islanders. Each tree on her
island has an expected production of 100 ripe bananas, so the total expected pro-
duction of her island company is 100 Ã 100 510,000 bananas. She divides up 100
shares in her company (1 percent of her company 5one tree for each share), keeps
one share for herself, and offers the other 99 shares to the other islanders. She sets
the price of a share to be one tree; that is, any other islander can buy 1 percent of
her Banana Company by giving up the future rights to one tree from his own island.
How does this deal look for the other islanders? First, note that the expected
return of the deal is zero; each islander expects to get back exactly what she puts in.
By investing one tree from her own island (expected production 5100 ripe
bananas), each islander receives in return 1 percent (5 one tree) of another island
(expected production 5100 ripe bananas). Second, note that the deal will be useful
diversi?cation for the buyer: before the deal, she had a 50 percent chance of getting
20,000 bananas for the year, but also a 50 percent chance of losing everything to the
birds and getting zero. After the deal, the buyer has reduced the chance of getting
zero, with an offsetting reduction in the chance of getting 20,000. A graphical
illustration of this change is shown in Exhibit 4-3. The diversi?cation effectively
moves the extreme outcomes toward the center (from points A and D toward points
A’ and D’). The new expected utility lies at B’, the midpoint of A’D’. Because B’ is
higher than B, the buyer has succeeded in increasing her expected utility.
EXHIBIT 4-3
BANANA UTILITY AFTER DIVERSIFICATION
B'
A'
B
C
D
D'
A 10K
Bananas
20K
U
t
i
l
i
t
y
4.2 BETA AND THE BANANA BIRDS 71
Once one islander gets the idea, all the others can follow. Each islander is
driven by the narrow pursuit of her own diversi?cation. Before long, every islander
has sold shares in her island to every other islander. With each purchase, the buying
islander moves her expected utility line further up, until the extreme points have
converged on point C. When the process is complete, every islander will own one
tree on every island, and they will all be perfectly diversi?ed, with a known con-
sumption of 10,000 bananas, independent of which islands the banana birds land
on. This is the way things work in a well-functioning ?nancial system. The risk of
birds landing on an island is idiosyncratic risk, also called a diversi?able risk: if
everyone tries to run away from this risk, they can successfully do so.
Next, let’s consider a different kind of risk: the weather. Consider again our
banana economy where each banana tree is expected to grow 100 bananas per year,
and nowassume that there are no birds to worry about. In this example, the total of 100
is the average of two possibilities: In a sunny year (50 percent chance), the trees grow
150 bananas each. In a rainy year (50 percent chance), they only grow 50 bananas
each. Thus, each island would grow 100 trees à 150 bananas 515,000 bananas in a
sunny year and 100 Ã 50 55,000 bananas in a rainy year.
How does this weather risk affect the happiness of the islanders? Recall the
banana-utility function (Exhibit 4-4). An islander with a 50 percent chance at
15,000 bananas (sunny year) and a 50 percent chance at 5,000 bananas (rainy year)
EXHIBIT 4-4
BANANA UTILITY WITH WEATHER RISK
C
Y
X
Z
10K 5K
Bananas
15K
U
t
i
l
i
t
y
72 CHAPTER 4 THE COST OF CAPITAL FOR VC
would have an expected utility lying at point Y, the midpoint of line XZ. As in the
case of bird risk, the islanders would like to diversify this risk and get to point C,
which gives them 10,000 bananas for sure.
Diversi?cation worked for bird risk, but it does not work here. The funda-
mental difference is that here, the total production in the world is affected by the
weather. For the population as a whole, there is no way that the islanders can run
away from the weather: if the weather is rainy, then the combined banana con-
sumption in the whole world will still only be 5KÃ 100 5500K, no matter how they
eventually share the bananas. For example, if the islanders try the same trick that
worked for the bird risk—each islander owns one tree on every island—then it will
have no effect on anyone’s banana consumption.
Despite the overall constraint, individual islanders will still have an incentive
to diversify. Imagine that an islander offers a contract to give up 100 bananas when
it is sunny in return for 100 bananas when it is rainy. Would anyone take the other
side of this deal? As in the bird example, the expected return is zero: Because each
outcome has a 50 percent chance, the expected value of the trade is zero bananas.
Here, however, we are asking someone to give up 100 bananas when they feel
relatively hungry (the rainy year) in return for 100 bananas when they feel rela-
tively sated (the sunny year). That is not a fair trade, and nobody is going to take it.
That 5,000th banana is worth more than the 15,000th; thus it will be necessary for
the ?rst islander to offer better terms.
Suppose that some “hardy islanders” are a little less bothered than other
“hungry islanders” when they must go without bananas. Then, while all islanders
are assumed to have a banana utility function shaped something like Exhibit 4-4,
the relative slopes of these utility functions would differ between hardy and hungry
types. In this case, there will be some trades in the banana tree market, with hardy
islanders giving up some bananas in rainy years in return for extra bananas in the
sunny years. Although we would need more information about the precise utility
functions to say exactly what prices will clear this market, we can be con?dent that
an even trade of bananas is not going to do it. Using only the information we have
so far, we know that the hardy islanders would demand a positive expected return to
do any trades from sunny to rainy. This is a feature of market risk, also called
nondiversi?able risk. For example, suppose the hardy and hungry islanders could
agree to a trade of one tree in the sunny season (5 150 bananas) for one tree in the
rainy season (5 50 bananas). In this case, the hardy islanders would be trading an
expected value of 50 Ã 50%525 bananas to get an expected value of 150 Ã 50%5
75 bananas, for an expected return of 75/25 21 5200%.
The reasoning used earlier can be extended to any additional risk in this banana
economy. If this risk is diversi?able, then islanders as a group will be able to run
away from it, and nobody would earn any additional return by agreeing to bear it. On
the other hand, if the risk is nondiversi?able, then the whole economy will not able to
run away from it, and anyone who agrees to bear it will demand an extra return.
These conclusions are not driven by the variance of the underlying risk.
Indeed, the bird risk has a higher variance than the weather risk, as can be seen by
4.2 BETA AND THE BANANA BIRDS 73
comparing Exhibits 4-2 and 4-4. Instead, the main driver of ?nancial risk is co-
variance. With weather risk, the output of each tree perfectly covaries with the
output of the entire economy. Anyone who takes on the risk of another tree is
committing to eat fewer bananas precisely when she (and everyone else) is hungry.
If you don’t pay someone an extra return to accept this risk from you, then she will
not accept it. This is the intuition behind measuring risk with the CAPM beta.
4.3 ESTIMATING THE COST OF CAPITAL FOR VC
Now, we travel back from our fantasy word of banana birds and return to the slightly
more real world of VC. What do you think is the beta of a typical VC investment?
A typical public stock will have a beta of one—do you think the beta on VC will be
higher or lower than one? Usually, most people think of VC as being very “risky”,
but this natural intuition tends to be driven by variance, not by covariance. Because
much of VC risk is diversi?able across many different investments—for example,
the risk that various new technologies will actually “work”—it would be premature
to conclude that the beta risk of VC is higher than it is for public equity.
To evaluate the performance of the whole VC industry, we estimate the
regressioninEquation (4.2) for boththe SandHill Index
s
andthe CAIndex. In the ?rst
case, we use monthly data for all the variables; in the second case, we use quarterly
data. The results are summarized in Exhibit 4-5, with alphas converted to annualized
percentage points in both cases.
The results of the standard CAPM model suggest that VC is less risky than the
market (beta ,1) and that it earns abnormal returns (alpha .0), although this
alpha is only signi?cant in the Sand Hill regression. The alphas are economically
large, giving us an estimated lower bound for abnormal gross returns (Sand Hill)
of 5.7 percent points per year and an estimated upper bound for abnormal net
returns of 6.1 percent per year (CA). If these numbers are correct, then they should
EXHIBIT 4-5
CAPM ESTIMATIONS FOR VC INDICES
Coefficient Sand Hill Index (monthly) CA Index (quarterly)
Alpha (in % per year) 4.92
ÃÃÃ
6.10
Market beta 0.76
ÃÃÃ
0.56
ÃÃÃ
Adjusted R-squared 0.72 0.19
Sample period Jan. 1989 to Dec. 2008
(240 monthly observations)
1981:q2 to 2008:q4
(111 quarterly observations)
NOTE:
ÃÃÃ
,
ÃÃ
, and
Ã
indicate statistical signi?cance at the 1, 5, and 10% level, respectively.
74 CHAPTER 4 THE COST OF CAPITAL FOR VC
have investors ?ocking to the asset class, but unfortunately for VCs, there are
three problems for the interpretation of these results: (1) style adjustments, (2)
liquidity risk, and (3) stale values. These problems are discussed and analyzed
later. The solutions to these problems induce large changes in estimated betas and
alphas.
Problem #1: Style Adjustments
In our regression in Equation (4.2), we estimated the market premium (R
m
2 R
f
)
using historical data on a market portfolio comprised of stocks traded in the
United States. In theory, the market portfolio should include all risky assets, traded
or untraded, everywhere in the world. Thus, this ideal market portfolio would
include the stocks, real estate, private equity, human capital, precious metals,
banana trees, and everything else we could think of—from every country in the
world. Clearly, it is not possible to collect all this data. In Chapter 3, we saw just
how dif?cult it was to collect this data for VC in the United States—and that is one
of the easy categories! The dif?culties of properly measuring the market portfolio
make it very dif?cult to test the CAPM because it is not possible to test the model
with the properly measured market premium. This critique, originally posed by Roll
(1977), was one of several early attacks on the underpinnings of the CAPM.
As part of the ongoing debate on the relevance of the CAPM, ?nancial
economists developed several theoretical models designed to more fully capture all
possible risks. Most of these models used logic similar to our banana economy,
where what people really care about are undiversi?able risks to their consumption.
The market portfolio, however measured, is likely to represent only some of that
risk. At the same time as these theoretical developments, empirical researchers
were demonstrating that the CAPM cannot adequately explain the returns of var-
ious investing styles, such as “small stocks” or “value stocks”. In effect, the
abnormal returns of these styles are too big to be explained by chance, so we can no
longer say that Equation (4.1) holds on average. By the early 1990s, we had
empirical and theoretical objections to the CAPM, but no good model to replace it.
Two researchers, Eugene Fama and Ken French, stepped into this breach with
a new empirical approach, and their Fama-French model (FFM) is now widely
used for estimating the cost of capital.
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1e
it
ð4:5Þ
where ?, ?, R
mt
, R
ft
, and e
it
are de?ned as in Equation (4.2), SIZE
t
and VALUE
t
are
the returns to portfolios of stocks designed to be highly correlated with their
respective investing styles, and ?
size
and ?
value
are the regression coef?cients on
these returns. These portfolios are called factors, so the FFM is a three-factor
model—a market factor, a size factor, and a value factor—and the betas are known
as factor loadings. The market factor, ?rst used in the CAPM model, is computed as
the difference between the return on the market (R
m
) and the return on treasury debt.
In effect, this is a zero-cost portfolio balanced between a 100 percent long position
4.3 ESTIMATING THE COST OF CAPITAL FOR VC 75
in stocks and a 100 percent short position in bonds. The other factors are also com-
puted as the returns to zero-cost long-short portfolios. The SIZE factor has a long
position in small-company stocks and a short position in large-company stocks. The
VALUE factor has a long position in “value” stocks (stocks with a high ratio of book
equity to market value) and a short position in “growth” stocks (stocks with a lowratio
of book equity to market value).
4
To use the results of Equation (4.5) to compute the cost of capital, we need
forecasts for the expected returns to the SIZE and VALUE factors. Over the
1926À2008 period, small stocks outperformed large stocks, and the SIZE factor
had an average return of 3 percent per year. In the last 30 years, however, this size
premium has dropped by about one-third, with an average return of 2 percent per
year in the 1979À2008 period. Based on this evidence, some researchers argue that
the return premium for small stocks has permanently changed. In this book, we will
weigh this recent evidence a bit more heavily than the older evidence and use a
forecast of 2.5 percent for the size factor.
The VALUE factor earned an average return of about 4 percent per year
over the 1926À2009 period, and this return dropped to about 3 percent over the
1979À2009 subperiod. Thus, we will use 3.5 percent as our VALUE forecast in this
book. Interestingly, the VALUE factor has fairly wide swings over some short time
periods. At the height of the boom period, technology growth stocks performed
very well: in the ?ve-year period from January 1995 to December 1999, VALUE
had a negative return of 9 percent per year, including a return of negative 33.4
percent in 1999. Conversely, in the ?ve years from January 2000 through December
2004, VALUE earned a positive return of 13 percent per year. Big difference!
With these forecasts in hand, we can compute a FFM version of the cost of
capital as follows:
r
i
50:04 1
^
? Ã 0:07 1
^
?
size
à 0:025 1
^
?
value
à 0:035 ð4:6Þ
where
^
?,
^
?
size
, and
^
?
value
are the estimated factor loadings on the market, size, and
value factors, respectively. The “typical” stock would have a factor loading of one
on the market factor, and zero on the other two factors, so the typical cost of capital
would be 11 percent, just as in the CAPM. For some stocks, however, the FFM can
give a very different estimate from the CAPM.
If we only need the cost of capital for a public company, then we might stop
right here. The choice of using the CAPM or the FFM often comes down to data
availability and time constraints. CAPM betas are available from many standard
library sources, and in recent years can even be found for free on Yahoo! Finance
4
The original reference for this model, withdetails onthe exact constructionof the factors, is Fama and French
(1993). Anontechnical discussion of the development of the Fama-French model is Fama and French (2004).
The Fama-French size and value factors, called “SMB” and “HML” in the ?nance literature, can be down-
loaded from Ken French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.
html.
76 CHAPTER 4 THE COST OF CAPITAL FOR VC
(http://?nance.yahoo.com). The long tradition of using CAPM betas on Wall Street
means that many ?rms have spreadsheets with built-in beta calculations. One must
work a bit harder to get Fama-French betas, but it is getting easier over time. For
practitioners who want to avoid having to estimate Equation (4.5) themselves, the
betas can now be obtained from several commercial sources.
Problem #2: Liquidity Risk
The Fama-French model is now almost 20 years old, and many challengers have
arrived in that time. For venture capital applications, the most important innovation
is the measurement of liquidity risk developed by Pastor and Stambaugh (2003).
Many practitioners feel that venture capital should earn a higher return because the
investments are illiquid. The Pastor-Stambaugh model (PSM) allows us to esti-
mate this premium using data on VC returns by adding a liquidity factor to the
FFM. Like the value and size factors of the FFM, the liquidity factor is based on
the returns to a zero-cost long-short portfolio—in this case, a portfolio that holds
“low-liquidity” stocks and sells short “high-liquidity” stocks.
5
The idea is that the
returns to this portfolio will re?ect the returns that investors require to hold illiquid
securities. The mathematical representation of the PSM is as follows:
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1?
liq
à LIQ
t
1e
it
ð4:7Þ
where LIQ is the new liquidity factor, ?
liq
is its factor loading, and all other
variables are de?ned as in Equation (4.5). Thus, this version of the PSM is a four-
factor model. The PSM is a young model, and it has not yet penetrated into practice
to the same degree as the FFM. Nevertheless, it is invaluable for our goal of
estimating an illiquidity premium for the cost of venture capital. To obtain a cost
of capital from this model, we need a forecast for the liquidity factor. The available
data to compute this factor only goes back to 1968. In the 1968À2008 period, the
average return to the liquidity factor was 5 percent per year, and we use an expected
return forecast of 5 percent for LIQ.
With the results of estimating Equation (4.7) and forecasts for the expected
returns to the factors, we can use the PSM to estimate a cost of capital as
r
i
50:04 1
^
? Ã 0:07 1
^
?
size
à 0:025 1
^
?
value
à 0:035 1
^
?
liq
à 0:05 ð4:8Þ
where
^
?
liq
is the estimated factor loading on the liquidity factor, and the other
variables are de?ned as in Equation (4.6). As in the case of the FFM, the “typical”
stock would have a factor loading of one on the market factor and zero on the other
factors, so the typical cost of capital would still be 11 percent.
5
The liquidity factor data can be downloaded from Lubos Pastor’s website at http://faculty.chicagobooth
.edu/lubos.pastor/research/liq_data_1962_2008.txt.
4.3 ESTIMATING THE COST OF CAPITAL FOR VC 77
Problem #3: Stale Values
The CA index relies on the quarterly reports made by the GPs. In these reports, GPs
include an estimate of the values for unrealized investments. As mentioned earlier,
these estimates are often based on very old information, leading to the phenomenon
of stale values. Indeed, many GPs simply report all valuations based on the most
recent round of ?nancing, even if a company’s outlook had changed signi?cantly
since that time. During a rising market, this practice is considered to be con-
servative; but in the postboom period, some LPs began to complain that these old
valuations signi?cantly overstated the value of the portfolios and made it dif?cult
for LPs to properly assess their holdings. In either case, it is clear that such
valuations will not re?ect the current market values of the companies.
Stale values cause problems when we estimate the regression models as in
Equations (4.2), (4.5), or (4.7). In particular, our beta estimates will be downward
biased, because the stale prices will not re?ect the full current impact of the market on
the value of VC companies. (For example, if the “true beta” in the CAPM is equal to
one, but only half the companies have updated values, then we will estimate a beta of
only 0.5.) If the beta estimates are downward biased, then all the unexplained returns
are “credited” to alpha, which would then be upward biased in most cases.
These potential biases are particularly severe for the CA index. The Sand Hill
Index
s
uses several statistical adjustments to reduce the stale value problem, but
even these methods cannot completely eliminate it. To adjust our regressions for
stale values, we include past values on the right-hand side of the regressions: two
years of past values for the market factor, and one year of past values for the other
three factors. The PSM regression equation with these past values (shown here for
the monthly return regression using Sand Hill Index
s
returns), called “lags”, is as
follows:
R
vc;t
2R
ft
5
X
23
s 50
?
s
à ðR
m;t 2s
2R
f;t 2s
Þ 1
X
11
s 50
?
size
s
à SIZE
t 2s
1
X
11
s 50
?
value
s
à VALUE
t 2s
1
X
11
s 50
?
liq
s
à LIQ
t 2s
ð4:9Þ
This equation can be estimated using the same techniques as in Exhibit 4-5, where
the effective VC beta on the market is now de?ned as
? 5
X
23
s 50
?
s
ð4:10Þ
with equivalent de?nitions for the other factor loadings, except they are summed
over 12 months instead of 24 (for CA Index returns, we sum over eight quarters for
the market premium factor and over four quarters for the other factors). Thus, the
cost of capital is still given by Equation (4.7).
With these de?nitions in hand, we are prepared to estimate the cost of venture
capital using the PSM (Exhibit 4-6).
78 CHAPTER 4 THE COST OF CAPITAL FOR VC
Our ?rst use of these results is to estimate a cost of venture capital. Substituting
these beta estimates into Equation (4.8) for the SHE index yields the following:
r
i
50:04 11:63 Ã 0:07 20:09 Ã 0:025 20:68 Ã 0:035 10:26 Ã 0:05 514:1% ð4:11Þ
Similarly, substituting the beta estimates for the CA index yields this:
r
i
50:04 1 2:04 Ã 0:07 1 1:04 Ã 0:025 2 1:46 Ã 0:035 1 0:15 Ã 0:05
516:6%
ð4:12Þ
In this book we take the midpoint of the two estimates and round off this cost
of capital for VC to 15 percent. Note that the illiquidity premium is 0.26 Ã 0.05 or
0.15 Ã 0.05, which is approximately equal to 1 percent using either estimate.
Our second use of these results is to evaluate the performance of the VC
industry. With all adjustments taken into account, the alphas for both CA and SHE
are not signi?cantly different from zero. Recall from Chapter 3 that CA represents
an upper bound on the net returns to VC, and SHE represents a lower bound on the
gross returns. Thus, these results suggest a point estimate of 113 basis points
and 26.11 percent (22.11% 24%) for the upper and lower bound of net
abnormal returns.
SUMMARY
Investors cannot do their job without ?rst estimating their cost of capital. In general, the cost
of capital depends on the nondiversi?able risk of an investment. The classic model of
nondiversi?able risk is the capital asset pricing model (CAPM), which relates the cost
of capital to the market (beta) risk of an investment. In recent years ?nancial economists have
EXHIBIT 4-6
PASTOR-STAMBAUGH MODEL ESTIMATION FOR VC INDICES
Coefficient Sand Hill Index (monthly) CA Index (quarterly)
Alpha (in % per year) 22.11 0.13
Market beta 1.63
ÃÃÃ
2.04
ÃÃÃ
Size beta 20.09 1.04
ÃÃÃ
Value beta 20.68
ÃÃÃ
21.46
ÃÃÃ
Liquidity beta 0.26
ÃÃ
0.15
Adjusted R
2
0.83 0.55
Sample period Jan. 1989 to Dec. 2008
(240 monthly observations)
1981:q2 to 2008:q4
(111 quarterly observations)
NOTE:
ÃÃÃ
,
ÃÃ
, and
Ã
indicate statistical signi?cance at the 1, 5, and 10% level, respectively.
SUMMARY 79
extended the CAPM to include other forms of nondiversi?able risk, including factors related
to company size, value/growth status, and liquidity. When estimating the cost of venture
capital, we need to take these additional factors into account, as well as make adjustments for
the slow-moving values in VC portfolios. With these modi?cations, we estimate a cost of
venture capital of 15 percent. We can also use the same models to evaluate the performance
(alpha) of the VC industry. We estimate that the upper bound for the net alpha and the lower
bound for the gross alpha are both very close to zero.
KEY TERMS
Capital asset pricing model
(CAPM)
Multifactor models,
Fama-French Model
(FFM),
Pastor-Stambaugh Model
(PSM)
Variance, covariance
Idiosyncratic risk
5 diversifiable risk
Market portfolio
Beta (?), alpha (?)
Market premium, market
portfolio
Market risk
5 nondiversifiable risk
5 systematic risk
Least-squares regression
Abnormal return
Performance-evaluation
regression
Style adjustments
Liquidity risk
Stale values
Factor loadings
Long position, short
position, zero-cost
long-short portfolio
REFERENCES
Fama, Eugene, and Kenneth French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds”,
Journal of Financial Economics 33(1), 3À56.
Fama, Eugene, and Kenneth French, 2004, “The Capital-Asset-Pricing-Model: Theory and Evidence”,
Journal of Financial Economics 18(3), 25À46.
Ibbotson Associates, 2009, Stocks, Bonds, Bills, and In?ation, Ibbotson Associates, Chicago.
Kennedy, Peter, 2003, A Guide to Econometrics, 5th Edition, MIT Press, Cambridge.
Pastor, Lubos and Robert Stambaugh, 2003, “Liquidity Risk and Expected Stock Returns”, Journal of
Political Economy 111(3), 642À685.
Roll, Richard, 1977, “A Critique of the Asset Pricing Theory’s Tests. Part I: On Past and Potential
Testability of the Theory”, Journal of Financial Economics 4(2), 129À176.
Welch, Ivo, 2000, “Views of Financial Economists on the Equity Premium and on Professional Con-
troversies”, Journal of Business 73(4), 501À538.
EXERCISES
4.1 The Largeco pension fund aggregates its entire portfolio every month across all asset
classes and computes its net returns, R
i
. Exhibit 4-7 displays these monthly returns for one
year, along with the market returns and the risk-free treasury bill rates for those months. Use
Equations (4.1) and (4.2) to estimate the beta, alpha, and cost of capital for the Largeco
portfolio. How do you evaluate its investment performance?
80 CHAPTER 4 THE COST OF CAPITAL FOR VC
4.2 True, False, or Uncertain: Early stage venture capital should earn a higher expected
return than later-stage venture capital, because early stage ventures have a higher failure rate
than later-stage ventures.
4.3 Consider the following three companies:
(i) Gasco owns and operates a chain of gas stations in the northeast United States.
(ii) Fuelco is a prerevenue company that is attempting to develop new fuel cell
technologies to replace the internal combustion engine.
(iii) Combco combines the operations of Gasco and Fuelco.
Use qualitative reasoning to order the cost of capital for these three companies from lowest to
highest. (There is more than one reasonable way to answer this question, but there are also
wrong ways to answer.)
4.4 Largeco pension plan begins investing in VC funds in 2006. They commit to a few new
funds every year. They compute returns to their VC portfolio by adding the cash ?ows they
receive and the reported company values from all their funds. In 2016, the Chief Investment
Of?cer of Largco (you!) asks for a report on Largco’s VC performance over the prior 10
years. The head of the VC team estimates the following CAPM regression:
R
t
2R
ft
5?1?ðR
mt
2R
ft
Þ 1e
it
;
where R
t
is the realized quarterly return on the VC portfolio, R
ft
represents the risk-free rate
for borrowing and lending, R
mt
is the realized return on the market portfolio, ? (beta) is the
EXHIBIT 4-7
LARGECO RETURNS
Month R
i
R
m
R
f
January 1.51% 2.24% 0.07%
February 1.34% 1.49% 0.06%
March 20.39% 21.16% 0.09%
April 22.45% 22.50% 0.08%
May 1.74% 1.35% 0.06%
June 2.33% 2.08% 0.08%
July 23.81% 23.87% 0.10%
August 0.32% 0.16% 0.11%
September 2.25% 1.95% 0.11%
October 2.01% 1.67% 0.11%
November 3.76% 4.68% 0.15%
December 2.43% 3.36% 0.16%
EXERCISES 81
regression slope coef?cient, ? (alpha) is the regression intercept, and e
it
is the regression
error term. All variables are measured quarterly with time periods given by t. The regression
produces statistically signi?cant estimates of ? 50.75 and ?57.50 (annualized), with an R
2
of 0.32. Members of your staff—Albert, Bonnie, Chris, Dave, and Ellen—raise several
concerns with these results. As the Chief Investment Of?cer, you must evaluate these con-
cerns. Which ones (if any) are valid? Which ones (if any) are invalid? For the valid concerns,
is there any possible ?x?
(a) Al thinks that the estimated alpha is too high because of survivor bias.
(b) Bonnie thinks that the estimated beta is too low because of a stale value problem.
(c) Chris thinks that this model does not properly adjust for the high probability of failure
for VC investments.
(d) Dave thinks that this model does not properly adjust for the illiquidity of VC
investments.
(e) Ellen thinks something else is wrong, but she can’t put her ?nger on it.
82 CHAPTER 4 THE COST OF CAPITAL FOR VC
CHAPTER 5
THE BEST VCs
IN THIS CHAPTER we discuss speci?c VC ?rms and their activities in more
detail. The notion that a VC ?rm’s reputation can play a direct role in its future
success is an important theme of this chapter. The empirical support for this notion is
developed in Hsu (2004), who uses a sample of startup companies that received
multiple offers from VCs. Then, using a simple measure of VC reputation, he ?nds
that high-reputation VCs are more likely to have their offers accepted than are low-
reputation VCs. Furthermore, high-reputation VCs pay between 10 and 14 percent
less for shares than do low-reputation VCs. Thus, even if reputation is worth nothing
else, it enables VCs to get cheaper prices and more acceptances for their offers.
Section 5.1 discusses some basic economics of venture capital ?rms, using a simple
model of supply and demand to gain insight into the key drivers of VC performance
and reputation. Section 5.2 provides a subjective listing of 15 “top-tier” VC ?rms.
This list provides an opportunity to discuss the history, performance, and strategies of
some top VC ?rms. In Section 5.3, we discuss how VC skills and reputation can add
value for its portfolio ?rms through monitoring activities: board representation,
corporate governance, human resources, matchmaking, and strategy. These value-
added activities of high-reputation VCs provide one justi?cation for the willingness of
portfolio companies to accept lower prices from these ?rms, as found by Hsu (2004).
5.1 THE ECONOMICS OF VC
In Chapter 3, we discussed evidence of performance persistence among VCs. In
general, performance in one fund helps predict performance in subsequent funds
raised by the same ?rm. Because LPs recognize this relationship, they react to good
performance in Fund X by increasing their demand for Fund X11. An increase in
demand can be met by some combination of an increase in price (carried interest and
management fees) and quantity (size of the fund). It is interesting, however, that VCs
rarely raise prices or quantities to a level that clears the market; there is almost always
excess demand to get into funds raised by successful ?rms. There are two main reasons
for this phenomenon: one from the “supply side” and one from the “demand side”.
83
First, we analyze the supply side. Exhibit 5-1 gives an abstract representation of
the typical dilemma facing a VC. The X-axis represents the total amount of invest-
ment made by a VC for any given time period. To decide on whether to make an
investment, the VC compares the expected return on investment (ROI) with the
appropriate cost of capital for VC(r). As a conceptual device, we imagine that the VC
has ordered his investment ideas frombest to worst, which ensures that the ROI curve
is downward sloping. Furthermore, the VC’s time is limited; so with each additional
investment, he has less time to devote to each of the others, which also counts against
the ROI of each newproject. Fromthe evidence of Chapter 4, we assume that the cost
of capital (r) is constant, equal to 15 percent for all possible projects; therefore, r can
be represented by a straight line. At the optimal investment I
Ã
, the ROI will be exactly
equal to r. Although this marginal investment does not earn any economic pro?ts, the
earlier investments do, with the total economic pro?ts given by the region above r and
below the ROI curve. Another way to compute these pro?ts is by calculating the
return on capital (R), which is de?ned as the average ROI of all investments. At the
optimal investment level, I
Ã
, we have R=R
Ã
. In the language of microeconomics, ROI
is a marginal bene?t, Ris an average bene?t, r is a marginal cost, and economic pro?ts
are given by the product of (R
Ã
2r) and I
Ã
. For any given model used to estimate r, the
difference between R and r will be the alpha for the manager.
Under the representation in Exhibit 5-1, the optimal portfolio size for any VC
is driven by the height and slope of the ROI line with respect to the cost of capital.
VC investing is hard, and we are sure that if we took a random person off the street,
his entire ROI line would lie below the cost of capital, suggesting that this person
has absolutely no ability to make pro?ts on any investments. Some moderately
talented individuals might get one good idea a year, so I
Ã
would be a few million
dollars, with all other investments earning negative economic pro?ts. In all like-
lihood, such individuals would not earn enough money to be professional VCs and
would be better off plying their trade in another profession. The evidence of Chapter 3
suggests that there are a few people with consistent top performance and I
Ã
high
enough to support a lucrative career as a VC. Nevertheless, even these VCs recognize
that most of what they do is not scalable, and there are limits on the total number of
investments that they can make. The numbers from Chapter 2 (Exhibit 2-2) give
estimates of $197B for the total committed capital in the industry, as managed by an
estimated 7,497 VC professionals. This means that the industry is managing about
$26M per investment professional (with just a couple of exceptions). Even the most
famous VCfunds—listed in Exhibit 5-2—usually only manage about $50Mto $100M
per professional. A pyramid-like structure, with junior VCs doing the work with
companies and overseen by a senior VC, has never been a successful VC model.
Thus, to increase the size of a fund, a ?rm would need to hire more senior pro-
fessionals. If these professionals donot have the same quality as the incumbent members
of the ?rm, thenthe overall fundreturns will suffer. Evenif high-qualityprofessionals are
hired, there are still organizational constraints of the VC model: Because most ?rms
allow partners to share in the majority of carried interest from all deals, a large orga-
nization will tend to weaken the incentives for individual partners. Thus, ?rms are
understandably reluctant to increase fund sizes byvery much. One apparent exception to
84 CHAPTER 5 THE BEST VCs
this reluctance occurred during the boomperiod, when capital per partner increased by a
factor of ?ve at many ?rms. The exception can be understood as a natural reaction to
increased investment sizes for each portfolio company combined with shorter holding
periods. In the postboom period, fund sizes have returned closer to historical levels.
This supply-side reasoning can explain why ?rms do not increase fund sizes
to clear the market, but it cannot explain why they do not increase prices (carried
interest) to do so. To explain the failure of prices to clear the market, we need a
demand-side explanation. Of course, some ?rms do raise their carried interest—at
the height of the boom a few dozen VCs had increased carried interest on new funds
to 25 or even 30 percent—but even these ?rms do not raise carried interest as much
as they could have. For example, Accel Partners raised carried interest to 30 percent
in 1999 for its $500M Accel VII fund, but still managed to raise the fund in a few
months and to leave many LPs desiring a higher stake.
1
As a market leader, Kleiner Perkins Cau?eld & Byers was also at a 30 percent
carry and barely had to lift the phone to raise its most recent fund. Surely it could
have raised its carried interest to 35% and still raised the same size fund. The main
EXHIBIT 5-1
RETURNS AND INVESTMENT
120%
70%
–30%
–80%
20%
Return on investment (ROI)
Cost of capital (r)
Return on capital (R)
R*
I*
Investment
R
e
t
u
r
n
r
R
ROI
1
See Kaplan (1999) for a discussion of this Accel fundraising process.
5.1 THE ECONOMICS OF VC 85
reason to avoid doing this is to preserve the long-run value of its franchise. Suppose
it did raise carried interest to 35 percent. At this price, the ?rm would lose some of
its LPs. (If it didn’t lose any, then it should raise the carry even more, right?) These
LPs would be replaced by others who had been clamoring for a place. But now,
fundraising is not so easy anymore. The KPCB partners might have to travel around
a bit and sell themselves. This takes time away from working with their portfolio
companies. Furthermore, the ?rm’s mix of LPs would be different, and some of the
long-serving LPs would be gone. The new LPs, lacking the long-standing rela-
tionship, are less likely to remain loyal if the ?rm has a poor performing fund. If
that occurs, the ?rm would need to take even more time to raise its next fund. The
KPCB partners probably decided that this extra time—and the risk to investor
loyalty—was worth more than the extra return from raising the carried interest on
one fund.
2
5.2 THE BEST VCs: A SUBJECTIVE LIST
In this section, we select the top 15 VC ?rms in the world, using our own arbitrary
and subjective criteria. We do this because it gives us a good chance to discuss the
various strategies employed by the best ?rms in the world and to provide a
springboard for discussing the value of a VC reputation in the rest of the book. Of
course, other market watchers will have different opinions, but this is our book, so
we get our list. The 15 ?rms divide naturally into two groups. The six ?rms in
Group A were the easiest to select, for reasons that will be described later. These
?rms represent our selection as the top six in the world, and we do not think that
this grouping will be very controversial. The nine ?rms in Group B were more
dif?cult to select, and many other ?rms could reasonably have been included.
We begin with a few de?nitions. Although industry participants frequently
refer to top-tier ?rms, it is never clear exactly who belongs in this group. In this
book, when we use the expression top-tier ?rm, we will always be referring to the
15 ?rms on this list. Furthermore, when we refer to a star fund, we mean a speci?c
VC fund with at least $50M in committed capital and a value multiple of ?ve or
greater. A superstar fund must have committed capital of at least $50M and a value
multiple of 10 or greater. It would be ideal if we could also use IRR as part of this
de?nition; but data on IRRs are less complete than are data on value multiples, so
we rely only on the latter for the achievement of star and superstar status.
(Remember that the use of bold italics means that these de?nitions are special to
this book, and are not industry-standard terms.)
2
Yet another bene?t of not clearing the market might be to keep the emergency option of raising annex
funds in times of severe market busts. Both in the aftermath of the dot.com bubble and in 2009, a number
of top-tier VC (and buyout) ?rms (including KPCB) raised annex funds from existing and new investors
to ensure suf?cient capital to feed their existing portfolio companies while the market recovered.
86 CHAPTER 5 THE BEST VCs
A few comments on the criteria used for selection:
1. In the last several years, the industry publication Private Equity Analyst has
reported on ?rms that have been able to raise their carried interest to 30
percent. The publication identi?es eight such VC ?rms, including all six
?rms from Group A. A seventh ?rm, New Enterprise Associates, is included
in Group B. The eighth ?rm, Bain Capital, charged a 30 percent carry on a
VC fund, but had earned its reputation (and an earlier 30 percent carry)
primarily as an LBO ?rm.
2. The Private Equity Performance Monitor, a new industry publication ?rst
discussed in Chapter 3, allows us to observe the performance for 1,193 VC
funds. From this sample of funds, 63 (about 5 percent) have achieved at least
star status. Of these 63 stars, 18 had committed capital of less than $50M, so we
drop them.
3
Of the remaining 45 stars, 14 have achieved superstar status. Only
six?rms have achieveda superstar fundwithat least $100Minsize plus another
star (or better) fund. These are the six ?rms in Group A. (Not coincidentally,
this represents six of the eight ?rms with a con?rmed 30 percent carry.)
3. Items (1) and (2) make it easy to identify the top six ?rms for Group A. To
identify the nine ?rms in Group B, the primary driver was consistency of
top-quartile and top-half performance, presence of star funds (if any),
combined with information on carried interest percentage (when available),
history of innovative VC strategy, and our own subjective view of their
reputation in the industry.
Exhibit 5-2 gives the rankings, along with a few key facts about each ?rm. We
followthe exhibit with a short discussion of each ?rm. We will then use these ?rms as a
reference as we discuss VC activities and competitive advantage in Section 5.3. Note
that four of the top-tier ?rms, including three fromGroup A, are located in Menlo Park,
California, right in the heart of Silicon Valley. Menlo Park is the center of the VC
universe, with about 60 VC?rms, more than 80%of which—including all eight on our
list—have their of?ces on one street: Sand Hill Road. This curious agglomeration of
VCactivity demonstrates a phenomenon that economists call “local network effects”,
where ?rms in the same industry co-locate to take advantage of (and thus add to) the
bene?ts of that local human capital and other shared resources. Although many Silicon
Valley startups are riding the outsourcing wave for some of their corporate functions, it
is telling that the top-management function usually remains in Silicon Valley, and
many of the most successful investors remain onone street in MenloPark. Not onlyhas
this part of VC resisted globalization, but so far it has also resisted Americanization
(most VCremains in small pockets of the United States instead of spreading to cheaper
3
Prevalence of small funds among star funds is expected, and in most cases these are the VC ?rms’ ?rst
funds that had a home run or two. It is much harder for ?rms to repeat the .5X returns with subsequent
larger funds.
5.2 THE BEST VCs: A SUBJECTIVE LIST 87
places in the country), Californization (California VC is overrepresented in Silicon
Valley), and even Menlo Parkization (Sand Hill Road rents must be among the highest
inthe city—whydon’t more VCs move?). This demonstrates that local networkeffects
remain an important brake on the geographic homogenization of economic activity.
In a cross-country echo of the local network effects on Sand Hill Road, we
see that two of the ?rms on the list are located in Waltham, Massachusetts, which
lies within the second-largest VC agglomeration in the world: the Route 128 cor-
ridor around Boston. These two ?rms, Matrix Partners and Charles River Ventures,
are not only in the same town and street (Winter Street—the Sand Hill Road of the
east), but also in the same building (1000 Winter Street). All told, there are 16 VC
?rms in the small town of Waltham, with 13 of them on Winter Street—and six of
them at the same 1000 address. Battery Ventures, another top-tier VC, is only
minutes away in the neighboring town of Wellesley.
There is an important caveat to doing this exercise: as is well known among
industry participants, no one did spectacularly well after 2000, and even the Group A
funds, if they don’t performin the next ?ve years, could be in big trouble. Also, there is
not a lot of data since ?ve years ago to update the list; so the ranking is still largely
EXHIBIT 5-2
TOP-TIER VENTURE CAPITALISTS
Group Name Location Founded
$ under
management
A Accel Partners Palo Alto, CA 1983 $6.0B
Benchmark Capital Menlo Park, CA 1985 $2.9B
Charles River Ventures Waltham, MA 1970 $2.4B
Kleiner Perkins Cau?eld and Byers Menlo Park, CA 1972 $3.3B
Matrix Partners Waltham, MA 1982 $4.1B
Sequoia Capital Menlo Park, CA 1971 $4.0B
B Battery Ventures Wellesley, MA 1983 $3.2B
Doll Capital Management (DCM) Menlo Park, CA 1996 $2.0B
Draper Fisher Jurvetson Menlo Park, CA 1986 $4.4B
Institutional Venture Partners Menlo Park, CA 1974 $2.2B
InterWest Partners Menlo Park, CA 1979 $2.8B
Menlo Ventures Menlo Park, CA 1976 $4.0B
New Enterprise Associates Baltimore, MD 1978 $10.7B
Summit Partners Boston, MA 1984 $11.2B
Technology Crossover Ventures Palo Alto, CA 1995 $7.7B
NOTE: Firms are listed alphabetically within each group.
Source: Dow Jones LP Source Galante, Firm websites.
88 CHAPTER 5 THE BEST VCs
based on the performance from the 1990s and the inferences made from the fact that
these funds are still easily raising funds from LPs (who know the true performance).
Now, let’s go to the list. We begin with the Group A ?rms, in alphabe-
tical order.
Group A
Accel Partners is a ?rmthat rode the boom, had a bumpy ride in the postboomperiod,
and seems to have survived with its stellar reputation bruised but alive. In business
since 1983, it has raised 10 general funds; the most recent, Accel X, closed with
$520M in 2007. In addition to these general funds, Accel was the ?rst major VC to
raise a dedicated “Internet fund”, with the $20M Accel Internet Fund I raised in 1996
and three subsequent Internet funds raised over the next four years. Accel has also
been an innovator in other ways, with geographic expansion (the $500M Accel
Europe fund raised in 2001, second European fund raised with $450Min 2005, and the
$60M Accel India Venture Fund raised in 2008), and a unique partnership with
the most famous name in LBO investing—Kohlberg Kravis Roberts & Co.,
with whom it raised the joint Accel-KKR fund, with $500M in 2000, and two sub-
sequent funds in 2006 and 2008 at $400M and $600M, respectively.
4
Accel’s ?rst star fund was the $135M Accel IV raised in 1993, and it sealed its
reputation with the superstar $150M Accel V fund raised in 1996.
5
By the time of the
$500M Accel VII fund raised in 1999, it had joined the elite with a 30 percent carry.
The ?rmhit rough times with its 2001 Accel VIII fund. Originally, this fund had $1.6B
in committed capital. In the postboom period, it became apparent to Accel and to
many other GPs that the available opportunities were insuf?cient to sustain these
boomtime megafunds, and it subsequently reduced the size of this fund to $680M, but
not before some controversial attempts to extend its investment period on the full
amount. The LP community appears to have forgiven this episode, however, because
it effortlessly raised Accel IX with a 30 percent carry and almost certainly kept its
carry level for Accel X, judging from the LP demand. As of March 2007, Accel VIII
has returned 37 percent of committed capital and has a net IRR of 2.6 percent, which
puts it in the second quartile of its vintage year peers. Its best-known recent invest-
ment is Facebook, which it has yet to exit as of the writing of this book.
Benchmark Capital is the new kid on the block among the Group A ?rms.
Its ?rst fund, the $113M Benchmark Capital Partners Fund raised in 1995, had a
spectacular investment in eBay, which netted the fund (LPs 1GPs) $2.5B on a $5M
investment. eBay was not the only successful exit for this fund, as the fund is
reported to have earned a value multiple of 42X, giving it the highest reported
4
Unless otherwise noted, all citations to fund sizes, vintage years, and carried interest levels, are drawn
from Dow Jones Financial Information Services.
5
Unless otherwise noted, all performance data and citations to star funds or superstar funds are derived
from data from The 2005 and 2008 Private Equity Performance Monitor.
5.2 THE BEST VCs: A SUBJECTIVE LIST 89
multiple of all time. Benchmark II, a $250M fund raised in 1997, reached star status
to give the partners two great successes in a row. With this performance, it was able to
raise its carried interest to a ?at 30 percent by the time of the $1.1B Benchmark IV
fund in 1999. (Its previous funds had used a performance-based sliding scale for the
carry.) Like several other top-tier ?rms, Benchmark has expanded internationally,
with a $500M Europe fund raised in 2000 and a $260M Israel fund raised in 2002.
After successfully raising three Europe funds, Benchmark Europe was spun off in
2007 and changed its name to Balderton Capital; Benchmark Israel raised its second
fund ($250M) in 2005. As of March 2007, the 1999 Benchmark IV has returned 41
percent and has a net IRR of 0.2 percent, putting it in the second quartile among its
vintage year peers. The LPs have stayed loyal in return, and the $400MBenchmark V
fund was raised in 2004, followed by its latest, the $500M Benchmark VI raised in
2008. Its notable recent exits include OpenTable, which went public in May 2009 and
traded up 72% on its ?rst day of trading.
Charles River Ventures is one of the two Group A ?rms from 1000 Winter
Street in Waltham. The ?rm also maintains a smaller of?ce on Sand Hill Road,
giving it a presence in both VC centers. Like many of the other top-tier ?rms, it had
solid performance for many years, performed spectacularly in the boom, faltered in
the postboom period, and has regained its focus and reduced the size of its most
recent fund. Its ?rst star was the $85M 1995 Charles River VII fund. It gained
superstar status with its $100M 1997 VIII fund. Following this fund, it was able to
raise its carried interest to 30 percent, a level it has maintained ever since, most
recently with its $320M Charles River XIV fund raised in 2009. As of December
2006, its 2000 fund (CRV XI) has a net IRR of 0.9 percent, which puts it in the
second quartile of the 2000 vintage funds.
Charles River runs a seed program called QuickStart, which it launched in
2006 after recognizing that advances in technology had enabled Internet startups to
operate with much less cash than traditionally required. In this program, Charles
River invests $250K in the form of a loan to a promising new startup. Startups
accepting loans give Charles River the right to join a ?rst-round syndicate, with the
loan converting to equity at that point.
Our next fund, Kleiner Perkins Cau?eld & Byers (KPCB) was ?rst dis-
cussed in Chapter 3, where we saw evidence of two superstar funds (the $225M
KPCB VII and the $299M VIII), and we deduced that KPCB IX, a $550M fund
raised in 1999, de?ed the gravity of the worst vintage year in VC history and
reached star status with its Google exit. Perhaps even more impressive than these
returns is the list of famous KPCB investments: AOL, Amazon.com, Compaq,
Electronic Arts, Genentech, Google, Idec, Intuit, Juniper Networks, Netscape, Sun,
andSymantec. It is a “who’s who” of successful technologybusinesses, reachingacross
industry lines to leaders in life science, software, hardware, communications, and the
Internet. This performance has been sustained through multiple generations of ?rm
leadershipand seems innodanger of abating. That said, it is a bit troubling that KPCB’s
most recent funds’ (KPCBXÀKPCBXIII) performances are not publicly available as
of the writing of this book.
90 CHAPTER 5 THE BEST VCs
KPCB has recently made big bets in two directions: Asia and green tech-
nology. It closed the $360M China Fund in 2007 and now has two satellite of?ces
in Beijing and Shanghai. It also raised the Green Growth Fund in 2008, which
targets large clean-technology companies.
Matrix Partners shares a building in Waltham with Charles River Ventures
and also maintains a smaller of?ce on Sand Hill Road. Matrix had four straight top-
quartile funds from 1985 to 1997, including one star and two superstar funds: the
$80M 1990 Matrix III fund (star), the $125M 1995 Matrix IV fund (superstar), and
the $200M 1997 Matrix V fund (superstar). Indeed, Matrix came very close to
having two funds with value multiples above 20 (double-superstar?), which has not
even been accomplished by its famous peers from Sand Hill Road. Its investment
record includes several famous names and spans across software, hardware, and
communications, including Apple Computer, Veritas, and Sycamore Networks. Its
2000 Matrix VI has returned only 12 percent of committed capital and has little
chance of ever breaking even, as the remaining portfolio is held at 54 percent of
fund size. In contrast, its 2002 fund (Matrix VII) is doing much better, and has a net
IRR of 12.4 percent, putting it in the top quartile among its peers. In addition to its
latest general fund, the $450M (plus $150M optional fund) Matrix IX, raised in
2009, it also raised a China fund and an India fund in 2008 and 2006, respectively,
thus making inroads to two more fast-growing markets.
Sequoia Capital is certainly KPCB’s strongest competition for the title of
“most famous VC ?rm in the world”. Its investment list is almost as impressive as
KPCB’s—Apple, Cisco, Google, Electronic Arts, Symantec, Yahoo, YouTube—
missing only the life sciences breadth of its neighbor on Sand Hill Road. Note also the
overlap in investments between these two top ?rms. This is the most salient example
of the pervasive syndication of investments among ?rms of similar rank. In a VC
syndicate, a lead investor takes primary responsibility for the investment, usually
making the largest investment and taking the board seat. (In some cases, such as the
Google investment, this role can be shared by co-leads.) The other investors take
smaller stakes and may or may not get a board seat. Syndication helps to spread risk
and gain the bene?ts of larger networks. The prevalence of syndication varies over
time, often depending on the relative supply of capital. In the preboom period, syn-
dication was the norm. During the boom, it was comparatively rare.
Sequoia’s performance has been remarkable. It is the only ?rm in the world
with four con?rmed star funds (three of which were superstars): The $64M 1989
Sequoia V fund (star), the $100M 1993 Sequoia VI fund (superstar), the $150M
1996 Sequoia VII fund (superstar), and the $250M 1998 Sequoia VIII (superstar).
No other ?rm, not even KPCB, can match that record. KPCB’s main claim for the
top spot is that it has earned similar returns with funds about twice the size.
Group B
Battery Ventures is our third ?rm from the Route 128 corridor around Boston.
Relatively young for ?rms on this list (founded in 1983), Battery made up for lost
5.2 THE BEST VCs: A SUBJECTIVE LIST 91
time with six top-quartile funds in its ?rst six attempts, including the star $200M
1997 Battery Ventures IV. It charged a 25 percent carry on its seventh and eighth
funds (raised in 2004 and 2008). Re?ecting the tough economic conditions of
2009À2010, for its latest fundraising efforts for its ninth fund, targeted at $750M,
Battery plans to use a performance-based sliding scale, charging a base carry of 20
percent, which will climb to 30 percent once it returns three times capital to LPs.
Battery has a broad focus—both by stage and industry—and has made headlines by
teaming up with the Blackstone Group, a major LBO ?rm, on several deals.
DCM (Doll Capital Management) is the youngest ?rm in this list of top-tier
VCs—it was founded only in 1996. Though there are many other ?rms with much
longer track records, we pick this ?rm for two reasons. One is its relatively strong
track record in the non-U.S. markets, notably Asia, where we have seen the fastest
growth in recent years. It has had of?ces in Menlo Park, CA, and Beijing, China,
and recently opened a satellite of?ce in Tokyo as well. While many U.S. VC ?rms
have recently started investing in China, few can claim exits yet; in contrast, DCM
invested in the region as early as 2000, and has had a string of successful exits. Its
notable Asia investment exits include 51job (NASDAQ IPO in 2004), VanceInfo
(NYSE IPO in 2007), and Fortinet (NASDAQ IPO in 2009). Its notable domestic
U.S. investment exits include Foundry Networks (1999 IPO), About.com (1999
IPO; then acquired by New York Times; its Japanese af?liate also went public on
JASDAQ), and Neutral Tandem (NASDAQ IPO in 2007). According to the Wall
Street Journal, Fortinet was one of the best-performing VC-backed IPOs in 2009.
Another reason is the premium carry it charges. According to Private Equity
Analyst, its ?fth fund (the 2006 $505M DCM V) and its latest fund (DCM VI,
which is being raised amid the toughest economic conditions in decades) charge a
25 percent carry. We interpret this to be an indication of LPs’ enthusiasm about the
?rm’s international reach and recent successes.
Draper Fisher Jurvetson (DFJ) is an innovative ?rm that has experimented
with several different organizational forms and strategies. Its inclusion on this list
was a dif?cult decision, because not much performance information is available.
The $50M 1995 DFJ III fund reached star status, but we know very little about its
11 subsequent funds, save for the 1999 DFJ ePlanet Ventures (returned 136 percent
and is in the top quartile as of March 2007) and the 2000 DFJ VII (in the second
quartile as of September 2007). We include DFJ as a top-tier ?rm because of its
string of notable successful investments in companies including Skype, Athena-
Health, and Baidu, and because of its reputation as market leaders in extending its
VC brand. The DFJ “af?liate network” includes 17 ?rms across 13 locations on
three continents. Many of these ?rms are cobranded with the DFJ name, such as
Draper Triangle Ventures (Pennsylvania and Ohio), DFJ DragonFund (China), and
DFJ VTB Aurora (Russia).
It charged above-market carried interest of 25 percent from 1999 to 2007. In
its current efforts to raise the $250M DFJ X, it is offering a performance-based
sliding scale, charging a 20 percent base carry until the fund returns 2.5 times the
committed capital, at which point GPs will catch up to 25 percent.
92 CHAPTER 5 THE BEST VCs
Institutional Venture Partners would have made the Group B list in the ?rst
edition of this book, were it not for some uncertainty about its future given sig-
ni?cant personnel turnover at the time. The ?rm has apparently weathered the
transition well, and including it in the Group B list this time was an easy decision
for us, given its remarkable track record. It is a consistent performer with seven out
of its eight funds from 1985 to 2004 in the top half category. Three of them are
in the top quartile, including the 1994 $141M Institutional Venture Partners VI and
the 1996 $187M Fund VII, which were both star funds.
It has two of?ces, one in Menlo Park (on, you guessed it, Sand Hill Road) and
another north of San Francisco in Mill Valley, CA. It invests in late-stage private
technology companies in communications and wireless technology, enterprise IT,
and Internet and digital media. Its famous investments include TiVo, Juniper
Networks, Net?ix, MySQL, and more recently Twitter.
InterWest Partners is an early-stage VC ?rm founded in 1979. It is another
consistent performer, with six out of its seven funds from 1985 to 2005 in the top half
category. Three of them are in the top quartile. Commensurate with its long history
(its ?rst fund was raised in 1980), it boasts a long list of successful exits, with more
than 60 IPOs and nearly 60 upside acquisitions. Its early successes include Silicon
Graphics and Copper Mountain Inc., and its investments are about evenly split
between life sciences and IT areas. Its investments on the IT side are fairly con-
centrated in the San Francisco Bay Area, while its life science investments—which
are often originated in university research centers and in collaborations with bio-
pharmaceutical companies—are geographically more diverse, with locations as
varied as the Rocky Mountain states, San Diego, Northeast, and Florida.
Aside from the public record about its performance, another deciding factor
for including the ?rm on our list was its carried interest level; according to the Wall
Street Journal, it has charged 25 percent carry in the last decade.
Menlo Ventures, together with InterWest Partners, were honorable mentions
in the ?rst edition of this book. Menlo Ventures is an IT shop, meaning it does not
make any investments in life science ?rms, while it is open to investing in early to
late-stage rounds. It has one star fund, which is the 1988 $111M Menlo Ventures
IV; in addition, its 1997 $253M Menlo Ventures VII was almost a star fund, with
4.8X value multiple and a net IRR of 135.6 percent as of September 2007. Its 2001
$1.5B Menlo Ventures IX has a net IRR of 5.4 percent as of September 2007, which
puts it in the second quartile category. It invested in earlier Internet and commu-
nications companies such as Hotmail, Infoseek, and UUNET, and more recently
had successes with Acme Packet (2006 IPO) and Cavium Networks (2007 IPO). Its
slogan, “Big Ideas. Realized”, is quintessential Silicon Valley VC, and the ?rm
states it only targets “large” emerging markets that can support a $100M-per-year
revenue after achieving realistic market shares. Likewise, it has so far stuck to its
U.S.-centric model, with its focus on U.S.-headquartered companies only.
New Enterprise Associates (NEA) holds the distinction of raising the largest
dedicated VC fund in history. Unlike most other megafunds of the boom period, its
$2.3B 2000 NEA X fund was never reduced, and current performance places it
5.2 THE BEST VCs: A SUBJECTIVE LIST 93
among the top-quartile performers for its vintage. It later raised two more $2B1
funds, NEA XII ($2.5B, closed in 2006), and XIII ($2.5B, just closed as of January
2010). NEA’s history includes a remarkable six top-quartile performers, including
star status for the $230M 1993 NEA VI fund. Its famous investments include
Silicon Graphics and Immunex, and it has maintained a strong record across all
parts of the information technology and life sciences sectors, with a recent third
focus on energy investments. Though it still maintains its operations in Baltimore,
most of its investment professionals are located in either Silicon Valley or Chevy
Chase, MD, in the metropolitan DC area.
Like many of its peers, NEA has made efforts to globalize. In 2007, it con-
tributed $30Mfromits twelfth fund to $189MNEA-IndoUS Funds, which will invest
in early-stage IT companies in India. It has also made direct late-stage and growth
equity investments in companies outside of the United States using its core fund. As a
result, its twelfth fund investments consist of about 84 percent North America,
7 percent China, 4 percent India, and 5 percent the rest of the world. NEA is the only
?rm in Group B to have obtained a 30 percent carry, but it has done so while effec-
tively reducing its management fee percentage. Although this demonstrates a com-
mendable willingness to accept nearly exclusively performance-based compensation,
it also suggests slightly less pricing power than is enjoyed by Group A ?rms.
Summit Partners follows a resource-intensive, but very successful, strategy.
To generate investment opportunities, Summit has developed a proprietary database
of small to midsize companies. To maintain this database, Summit employs a
relatively large number of junior professionals to periodically communicate with
representative ?rms. Like many other ?rms, Summit also maintains a signi?cant
presence at technology industry events; but unlike most other ?rms, it takes a
systematic approach to its data gathering at these events, constantly adding to and
re?ning its database. The resulting database is the envy of the industry and often
allows Summit to obtain the holy grail of all private equity investors: proprietary
deal ?ow. Although some of its investments could be classi?ed as mezzanine or
even buyout, the majority remains at the late-stage VC and growth equity level. Its
main competitor in this strategy is TA Associates, but TA’s strategy tilts toward
somewhat larger investments and is typically not classi?ed as a VC. The compe-
tition and ties between these ?rms are quite extensive: Summit was founded when
some TA professionals broke away and formed a new ?rm.
Summit’s performance has been remarkably consistent. All seven core funds
raised since its 1984 founding have IRRs above the median for their vintage years,
and ?ve of these seven are in the top quartile, with the $610 million 1995 Summit
Ventures IV fund achieving star status. Its consistent performance allows it to
charge a 25 percent carried interest. It raised a $1B European growth equity fund in
2008, which is its ?rst non-U.S. fund.
Technology Crossover Ventures (TCV) is true to its name, engaging in
crossover investing that spans late-stage VC and young public companies. This
eclectic strategy has served TCV well, with ?ve straight top-half funds from 1995
to 2004. Its $1.7B 2000 TCV IV returned 79 percent of its capital, has a net IRR of
94 CHAPTER 5 THE BEST VCs
4.4 percent as of September 2007, and is in the second quartile among its vintage
year peers. It wrapped its largest-ever $3B TCV VII in 2007. It previously was
reported to be charging 30 percent for its ?fth fund, raised in 2004, but whether it
continued to charge a premium carry for its latest fund could not be con?rmed as of
the writing of this book.
Unlike many of its peers, TCV has stuck it out with its focus on U.S. domestic
deals—especially those away from the crowded hubs of Menlo Park, CA, and
Waltham, MA. Its portfolio company locations range from Suwanee, GA, to
Melville, NY, as well as Palo Alto and Boston.
This completes our list. Many other highly respected ?rms could reasonably
have displaced some ?rms in Group B. In alphabetical order, these “honorable
mention” ?rms include Columbia Capital (Alexandria, VA), Lightspeed Venture
Partners (Menlo Park, CA), May?eld Fund (Menlo Park, CA), Mohr Davidow
Ventures (Menlo Park), North Bridge Venture Partners (Waltham, MA), Polaris
Venture Partners (Waltham, MA), Sierra Ventures (Menlo Park, CA), TL Ventures
(Wayne, PA), Trinity Ventures (Menlo Park, CA), US Venture Partners (Menlo
Park, CA), and VantagePoint Ventures (San Bruno, CA). Three more ?rms, Bes-
semer Venture Partners (Wellesley Hills, MA), Greylock Partners (Waltham, MA),
and Venrock Associates (NY, NY), have high-pro?le reputations but do not have
suf?cient information in the public domain about past performance or carried
interest, so it is not possible to judge whether they belong in the top tier.
5.3 VC VALUE ADDED AND THE MONITORING
OF PORTFOLIO FIRMS
After studying the list of top-tier VCs, it is natural to wonder how they got there.
What value-added activities do VCs perform, and how does one acquire the skills to
do them well? In Chapter 1, we categorized VC activities into three groups:
investing, monitoring, and exiting. In each of these three groups, there is a potential
for VCs to add value. The investing and exiting groups include many activities that
require ?nancial analysis; Parts II, III, and IV of this book cover these activities in
detail. In contrast, the monitoring of portfolio ?rms, although certainly a crucial
area for VC value added, does not lend itself well to quantitative analysis. Thus, we
restrict our discussion to a brief summary of ?ve main monitoring activities, with
references to the relevant academic literature. In many of these activities, it is the
VC reputation itself that provides a main source of added value.
Board Representation A seat on the board of directors is a key mechanism
for VC monitoring. With a position on the board, a VC has explicit power to
participate in and in?uence corporate activities. The level of board representation
can be a highly contentious negotiation. VCs often want multiple board seats,
whereas entrepreneurs are understandably reluctant to cede much control. In early
round investments, a lead investor will virtually always get at least one board seat
5.3 VC VALUE ADDED AND THE MONITORING OF PORTFOLIO FIRMS 95
and other members of a syndicate will often get seats as well. In later rounds, board
seats are not universal, and some investors will settle for board observer status,
which does not have voting rights.
A VC spends a substantial fraction of his time as a board member. Many of
the other monitoring activities are accomplished in the context of the board role.
Notwithstanding the importance of this role and an enormous academic interest in
studying the workings of corporate boards, we still know very little about how an
individual person can become an effective board member. For obvious reasons,
researchers are rarely invited into boardrooms, so most of what we do know about
boards comes from quantitative studies of the relationship between company per-
formance and various board characteristics.
This academic literature is mostly focused on board structure in public com-
panies, rather than the dynamics within the boardroom. Some of the ?ndings have
some interest for VCs. For example, Yermack (1996) ?nds an inverse relationship
between ?rm market value (per dollar of book assets) and board size. Although the
causality of this ?nding is hotly debated, it is consistent with a tendency for VCs to
favor small boards, sometimes at the cost of offending members of the management
team who expected to be included. In a more cautionary result for VCs, Fich and
Shivdasani (2006) ?nd that public companies with “busy boards”—those where a
majority of outside directors hold three or more directorships—have inferior per-
formance to other companies for a variety of measures. The relevance of this ?nding
for VCs is uncertain, because the outside directors of public companies, unlike VCs,
usually do not consider their directorships to be their full-time job. Nevertheless, the
results suggest that board member effectiveness cannot be scaled inde?nitely.
In a related study, Tian and Wang (2010) develop a measure of VCs’ failure
tolerance and ?nd that IPO ?rms backed by more failure-tolerant VCs are sig-
ni?cantly more innovative, even long after VCs exit the IPO ?rms. Their measure
of failure tolerance is a function of how many rounds (and how long) VCs invested
in a ?rm before its ultimate failure. Since new rounds of ?nancing typically require
board approvals, this measure re?ects existing VCs’ exercise of their voting powers
as board members. The persistence suggests that VCs’ attitudes toward failure have
likely been internalized by the startup ?rms and become part of the ?rm’s culture.
Corporate Governance Corporate governance rules de?ne the power-
sharing relationship between shareholders and managers. In recent years, a large
body of academic research has demonstrated the relationship between corporate
governance rules and corporate performance. The best time to set good rules is
while a company is still small and before it goes public. VCs can and do have
signi?cant input into this process. Hochberg (2005) studies the ?rst proxy state-
ments ?led by public ?rms to determine the in?uence of VC-backing on various
corporate governance rules. She ?nds that VC-backed companies are (1) less likely
to engage in aggressive accounting prior to their IPO, (2) more likely to have
independent boards and board subcommittees, and (3) more likely to separate
the role of chairman and CEO. Although it is always dif?cult to prove causality in
96 CHAPTER 5 THE BEST VCs
these kinds of studies, the analysis does show that these governance differences do
not occur in the presence of large, non-VC shareholders.
Human Resources VCs also spend a large fraction of their time working on
human resource issues at their portfolio companies. This work requires the same set
of skills used to evaluate management during the investment phase, plus the ability
to recruit new managers and replace underperforming ones. In all these activities, a
VC’s reputation can make a huge difference, and the name of a VC investor is often
invoked as a reason to join a company. (We have heard many MBA students, when
describing their prior experience at a startup, say the name of the top-tier VC that
invested in the company even before they said the name and business of the
company!) Hellmann and Puri (2002) studied the human resource practices for a
sample of VC-backed and non-VC-backed companies in Silicon Valley. They
found that VC backing accelerates the hiring of senior executives (such as a VP of
marketing), the adoption of stock option plans, and the turnover of the CEO. As in
the Hochberg study, it is dif?cult to prove causality, but the authors do a good job
of trying. One notable ?nding is that CEO turnover often occurs long after the
original VC ?nancing, suggesting that the ?nancing and the turnover were separate
events. Furthermore, the authors ?nd that the replaced CEOs often stay with
the company in another capacity. This last result suggests that the VCs managed to
keep the skills of a founder-CEO while simultaneously getting a more experienced
CEO to run a larger company.
Matchmaking VCs will often use their contacts and reputation to make
introductions that can lead to new partnerships, customers, and suppliers. As in the
human resource function, the reputation of the VC can often lead to relationships that
would not otherwise be possible. One straightforward method is for VCs to make
connections among their past and current portfolio companies. Academic research on
the ef?cacy of VC matchmaking suggests that VCs do indeed facilitate alliances
among their portfolio ?rms (Lindsey 2008). In this case, a potential portfolio com-
pany should care about the average quality of the other companies in the VC’s
portfolio, because these companies are more likely to be potential partners.
Strategy As advisors to the CEO, VCs have the opportunity to participate in
strategic decisions. This opportunity must be used wisely, as many generalist VCs
are not quali?ed to give strategic advice across all sectors. Indeed, it is in the area of
strategy that it makes the most sense for individual VCs to focus on a speci?c sector
so that they can build the knowledge and experience to add value. For VC ?rms as
whole, the focus on one or two industries can enable the entire organization to
participate as specialists in strategic discussions with the ?rm.
It would be silly to cite any academic literature here. “Strategy” is a large
academic subject unto itself, and to do it justice would require at least a separate
book and certainly a different author. What we can say here is that there is no
existing academic evidence on the strategic contribution of VCs to the success of
their portfolio companies. To the extent that the VCs can make such contributions,
they can certainly be an important source of value added.
5.3 VC VALUE ADDED AND THE MONITORING OF PORTFOLIO FIRMS 97
SUMMARY
A VC’s reputation is a valuable asset. A high-reputation VC is more likely to have its term
sheets accepted and can pay lower prices for shares than do low-reputation VCs. Top-tier
VCs earn their reputations with superior investment performance, and many of these top-tier
?rms raise their carried interest to 25 or even 30 percent. Nevertheless, there is excess
demand by potential LPs to invest in such top-tier VCs, even at these higher prices. VCs
allow this excess demand so that they can maintain long-run relationships with LPs, mini-
mize the time needed for fundraising, and maximize the chance of maintaining their high
reputation. This reputation is valuable not only for striking better deals with portfolio
companies, but also for increasing the value added to these companies. This value is added
through monitoring activities such as board membership, corporate governance, human
resources, matchmaking, and strategy.
KEY TERMS
Return on investment (ROI)
Return on capital (R)
Cost of capital (r)
Top-tier firm
Star fund
Superstar fund
Sand Hill Road
Syndication
Lead investor
Proprietary deal flow
Crossover investing
REFERENCES
Asset Alternatives, 2005, Galante’s Venture Capital & Private Equity Directory. Asset Alternatives,
Private Equity Analyst, various issues.
Fich, Eliezer and Anil Shivdasani, 2006, “Are Busy Boards Effective Monitors?” Journal of Finance
61(2), 689À724.
Hellmann, Thomas, and Manju Puri, 2002, “Venture Capital and Professionalization of Start-up Firms”,
Journal of Finance 57(1), 167À197.
Hochberg, Yael V., 2005, “Venture Capital and Corporate Governance in the Newly Public Firm”,
working paper available at http://www.kellogg.northwestern.edu/faculty/hochberg/htm/.
Hsu, David H., 2004, “What Do Entrepreneurs Pay for Venture Capital Af?liation?” Journal of Finance
59(4), 1805À1844.
Kaplan, Steven N., 1999, “Accel VII”, Unpublished case study, available online at http://faculty
.chicagobooth.edu/steven.kaplan/teaching/accel7.pdf.
Lindsey, Laura, 2008, “Blurring Firm Boundaries: The Role of Venture Capital in Strategic Alliances”,
Journal of Finance 63(3), 1137À1168.
Private Equity Intelligence, 2005, Private Equity Performance Monitor.
Private Equity Intelligence, 2008, Private Equity Performance Monitor.
Tian, Xuan, and Tracy Wang, 2010, “Tolerance for Failure and Corporate Innovation”, available at
http://papers.ssrn.com/sol3/papers.cfm?abstract_id51399707.
Yermack, David, 1996, “Higher Market Valuation of Companies with a Smaller Board of Directors”,
Journal of Financial Economics 40(2), 185À212.
98 CHAPTER 5 THE BEST VCs
CHAPTER 6
VC AROUND THE WORLD
THE MODERN VC industry was born in the United States, but the rest of
the world is catching up. Although the United States still comprises about one-half
of the worldwide VC investment, markets are starting to mature in Europe—
especially the United Kingdom—and in Asia, with exciting developments in the
emerging economies of India and China. Nevertheless, many countries in con-
tinental Europe, Latin America, and Africa continue to lag behind the rest of the
world in VC activity, both in absolute terms and relative to GDP. In Section 6.1, we
document the global distribution of VC activity and discuss several reasons why
this pattern exists. In Section 6.2, we extend our risk-and-return analysis of Chapter
4 to an international setting and suggest several approaches for the estimation of the
cost of capital for international VC.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING
To study the global pattern of VC investing, we face a challenge in de?ning a
consistent set of data across different types of economies. Currently, the best avail-
able data is compiled by the global accounting ?rm PricewaterhouseCoopers in their
Global Private Equity Report (GPER). The GPER combines data from the Money-
Tree survey in the United States (?rst seen in Chapter 1) with similar data from
separate surveys of Europe, Asia, and a few countries in Africa, Latin America, and
Oceania. Because the data is pulled from disparate sources, they have varying levels
of reliability and comparability. All the surveys attempt to measure private equity
investment activity, but the categorization of private equity into “venture capital”,
“buyout”, and other classes are not always consistent. Rather than attempt to stan-
dardize these de?nitions, the GPER uses its consistent industry de?nitions to divide
private equity into “high technology” and “low technology”, with the former group
likely to contain mostly venture capital, and the latter group mostly buyout. Exhibit 6-1
shows the historical pattern of global high-technology private equity investment.
The exhibit shows that worldwide investment displays the same boom and
postboom pattern as found in the United States. (This should not be too surprising,
as the United States represented most of worldwide investment during the boom,
99
and about half during the postboom.) Investment grew in the 1990s and peaked in
2000. It has started to grow again—this time the bulk of the growth coming from
outside the U.S., with $84B of investment in 2008. Exhibit 6-2 shows the national
distribution of high-technology private equity in that year.
With $35.49B, the United States had about 40 percent of the global total of
$84B and about 60 percent more than all Western Europe combined.
1
Furthermore,
the United Kingdom, with less than one-quarter of European GDP, has almost half
the high-tech private equity investment. Still, the gap between the United States and
Europe is at an all-time low, with the difference larger in prior years. The Asia-
Paci?c region (which includes Australia and New Zealand) has grown the fastest in
recent years, and its total investment amount is now for the ?rst time almost equal
to that in Western Europe. A note of caution is warranted in interpreting these
numbers, however: On the one hand, the numbers are likely in?ated by high-tech
buyout transactions in developed countries such as Australia and Japan. On the
other hand, they likely miss low-tech VC activities, notably in China.
2
On a GDP-adjusted basis, Israel, Sweden, and United Kingdom have con-
sistently exhibited high investment intensity over the years, with Israel’s exceeding
EXHIBIT 6-1
GLOBAL HIGH-TECH PRIVATE-EQUITY INVESTMENT (IN $BILLIONS)
140
120
100
80
60
40
20
0
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
(
$
B
)
29
59
119
58
39
42
46
50
82
84
Source: PriceWaterhouseCoopers Global Private Equity Report 2008.
1
The entries in the table do not sum to $84B because some continents are not included in the table.
2
Re?ecting this gap, in 2008 new commitments to Chinese VC funds exceeded $8B (GEM Global Report
2009).
100 CHAPTER 6 VC AROUND THE WORLD
even that of the United States. In Asia, Japan is far behind the United States and the
United Kingdom in investment intensity when adjusted for GDP, whereas Korea
shows a much higher intensity in recent years.
Why is it that VC activity in continental Europe and Asia has historically
lagged behind that of the United States and the United Kingdom? And what has
changed in the recent years? Industry experts have been thinking about this
question for many years and have proposed many possible reasons. Next, we will
discuss ?ve of the main explanations.
Reason #1—Exits Without a doubt, the most important driver of VC
investment is the existence of a lucrative market to exit these investments. Among
VC practitioners, the absence of such a market is often the ?rst explanation as to
why VC activity is lower in some countries than in others. The most pro?table exits
are achieved through initial public offerings (IPOs). If the IPO market is not active,
then VCs are forced to exit through sales to large companies. Although such sales
EXHIBIT 6-2
THE GLOBAL DISTRIBUTION OF HIGH-TECH PRIVATE EQUITY IN
2007, SELECTED COUNTRIES, IN $BILLIONS
North America World Rank Asia
USA 35.49 (1) India 5.17 (3)
Canada 1.18 (15) Korea 3.18 (4)
NA Total 36.67 Singapore 2.89 (6)
New Zealand 2.13 (9)
Western Europe World Rank Japan 1.93 (10)
UK 10.5 (2) China 1.41 (11)
France 3.11 (5) Hong Kong 1.24 (12)
Sweden 2.52 (7) Australia 1.07 (16)
Germany 2.18 (8) Asia-Paci?c
Total (top 20 only)
19.02
Spain 1.20 (14)
Netherlands 1.03 (17)
Switzerland 0.71 (18)
Denmark 0.64 (19) Middle East & Africa
Finland 0.59 (20) Israel 1.20 (13)
W. Europe Total (top 20 only) 22.48
Source: PriceWaterhouseCoopers, Global Private Equity Report 2008.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 101
can sometimes be lucrative, such high-value sales only occur when companies have
the outside opportunity of an IPO.
Exhibit 6-3 shows the ratio of capital raised by IPOs (in $thousands) to GDP
(in $millions) for a select group of countries over the 1996À2000 time period.
EXHIBIT 6-3
RATIO OF CAPITAL RAISED IN IPOS (IN $THOUSANDS) TO GDP (IN
$MILLIONS), 1996 TO 2000
United Kingdom
Hong Kong
Greece
Australia
Canada
Sweden
Italy
Singapore
United States
Korea
Germany
Spain
Japan
France
Egypt
Indonesia
Venezuela
South Africa
India
Argentina
Chile
Israel
Mexico
Brazil
0 2 4 6 8 10 12
Source: Djankov et al. (2008).
102 CHAPTER 6 VC AROUND THE WORLD
There are two main themes in this exhibit. First, the ratio of IPOs to GDP is
relatively low in “low-income” countries. These countries, with low GDP to begin
with, also have low levels of ?nancial development relative to GDP. Note, for
example, the almost nonexistent IPO levels in many Latin American countries. The
second theme is that many of the countries with high VC activity also have high
IPO activity. (The low IPO total for Israel is misleading, as it does not include the
large number of Israeli IPOs sold in the United Kingdom and the United States.)
It is natural to wonder whether the IPO markets induce more VC activity, or
vice versa. There is substantial evidence that the causation indeed runs from vibrant
IPO markets to higher VC activity. In the United States, the historical record
demonstrates a persistent pattern of hot IPO markets leading VCs to raise and invest
more capital. The ?rst such pattern occurred in the late 1960s, when an excellent
IPO market led to successful exits for the ?rst wave of VC limited partnerships,
leading to a record number of VC funds raised in the following years. The next
example came in 1979À1980, driven by regulatory changes that allowed pension
funds to invest in small companies for the ?rst time. This pattern repeated itself in
the mid 1990s, leading up to the massive IPO boom of 1999À2000, which was
followed quickly by record-breaking fundraising by VCs.
This, then, partly explains the rapid growth of high-tech private equity invest-
ment activities in Asia, following strong recent IPO market performances of Chinese
?rms (including those based in Taiwan or Hong Kong) either listing locally or directly
accessing the U.S. stock markets. In fact, after Israel, Chinese companies are the
second group of foreign ?rms who have successfully tapped the U.S. IPO markets in
the recent years. India, in the meantime, has also enjoyed booming domestic equity
markets, which have buoyed the high-tech private equity activities there.
Reason #2—The Entrepreneurial Ecosystem If you are an entrepre-
neur and you could start your company anywhere, where would you go? For the sake of
answeringthis question, assume that youcanspeakall languages andlive anywhere that
you want. Faced with this problem, many entrepreneurs would think about the ease of
setting up their business, ?nding capital and quali?ed employees, and generally
avoiding all hassles so they could focus on their business. Venture capitalists refer
to this set of requirements as an entrepreneurial ecosystem. In a well-functioning
ecosystem, you do not need to train your bankers, lawyers, or accountants to structure a
high-growth business; you do not need to look far to ?nd quali?ed scientists, engineers,
and experienced managers; you do not need to spend hours dealing with (or bribing)
government of?cials. Also, it’s nice if your friends andneighbors don’t thinkthat you’re
crazy just because you’re starting your own business.
Taken together, these requirements seem almost tautological: It is good to
start a business where many other people have started a business. (In other words,
“we do it this way because it has always been done this way”.) We discussed a
similar phenomenon in previous chapters, when we learned of VC clusters within
the United States in Silicon Valley and around Boston.
Although it is dif?cult to identify cause and effect for most aspects of the
entrepreneurial ecosystem, there are some illuminating data points. One interesting
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 103
project (Djankov et al., 2002) analyzed the direct and indirect costs of starting a
company in 85 different countries. For each country, the authors counted the
number of regulatory procedures necessary to start a company. These procedures
include activities necessary in most countries such as checking the uniqueness of
the company’s name, ?ling a certi?cate of incorporation, and opening a bank
account. There are also less common procedures such as proving that the com-
pany’s of?cers do not have a criminal record, designating a bondsman, and pub-
lishing a notice with the business’s location. After counting the procedures in each
country, the authors estimated the number of business days needed to complete all
procedures. Exhibit 6-4 shows their results for a selected group of countries.
As in the IPO/GDP ratio shown in Exhibit 6-3, we see that Canada, Australia,
the United States, and the United Kingdom all perform well by this measure. In each
of those countries, the authors estimate that it takes between two and four business
days to comply with regulations to open a business. In contrast, the corresponding
estimates are 26 days in Japan, 42 days in Germany, 53 days in France, and 62 days
in Italy. Many emerging economies raise even higher hurdles, with estimates of 92
days in China, 104 days in Venezuela, and 149 days in Mozambique.
Although this evidence does not prove a relationship between entry costs and
entrepreneurial activity, it is hard to imagine that high costs of entry are conducive
to start-up activity. If it takes 10 times as long to start a company in continental
Europe than it does in its EU neighbor of the United Kingdom, one can imagine
where entrepreneurs would prefer to locate. With even small differences at one
point in the chain, local network effects can amplify the location incentives, so that
the entrepreneurial ecosystem moves to one place and stays there.
Reason #3—Lawand Corporate Governance Emerging economies in
Asia, Latin America, and Africa have relatively cheap labor supplies and often
underserved local markets. Such conditions would seem ripe for high-growth
business opportunities. We have already spoken about the high costs of entry and
the dif?culty of exiting such investments, but these barriers may have been over-
come were it not for concerns about law, corporate governance, and the enforce-
ment of contracts. Although these issues are of secondary importance in developed
countries, they loom large everywhere else.
The relationship between legal systems and ?nancial development has been a
subject of great academic interest and progress in the last 10 years. Some recent
work on this topic by Simon Djankov, Rafael LaPorta, Florencio Lopez-de-Silanes,
and Andrei Shleifer (DLLS, for short) provides striking evidence about the relation-
ship between law and ?nance. In their paper, the authors worked with lawyers to
quantify the legal protections against self-dealing behavior in 102 different
countries. Self-dealing, also called tunneling or investor expropriation, is a major
concern of VCs in all countries. As de?ned by DLLS, self-dealing occurs when
“those who control a corporation, whether they are managers, controlling share-
holders, or both, can use their power to divert corporate wealth to themselves,
without sharing it with other investors” (Djankov et al., 2008, p. 1).
104 CHAPTER 6 VC AROUND THE WORLD
EXHIBIT 6-4
TIME TO START A BUSINESS, IN DAYS
Canada
Australia
United States
United Kingdom
Sweden
Hong Kong
Singapore
South Africa
Korea
Chile
Israel
Greece
Germany
France
Russia
Poland
Italy
Brazil
Mexico
India
Spain
Bolivia
China
Venezuela
Indonesia
0 20 60 80 100 120 140 40
Egypt
Argentina
Japan
Source: Djankov et al. (2002).
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 105
The authors considered the following prototypical self-dealing transaction:
Mr. James owns 90 percent of Company A (“Seller”) and 60 percent of Company B
(“Buyer”). Buyer proposes to purchase some assets from Seller. Because Mr. James
controls (.50 percent ownership) both companies, he can make this transaction
happen. Because Mr. James owns more of the Seller than he does of the Buyer, he
has an incentive for the Buyer to overpay for the Seller’s assets. What protections
do the minority investors in the Buyer have against this transaction?
The authors considered several different classes of protections. First, what
details of the transaction must be disclosed to minority investors? Second, what rights
do minority (disinterested) investors have to approve the transaction? Third, what
rights do minority investors have to sue Mr. James after the transaction goes through?
For each class of protections, the authors gathered data for a variety of different legal
rights. They combined all these rights into an index of self-dealing. The index goes
from 0 (no protections for minority investors) to 1 (maximum protection). Exhibit 6-5
gives this index for a selection of the 102 countries analyzed in the paper.
It should come as no surprise that law-and-order Singapore tops the list, with
a maximum score of 1.00. Once again, we see above-average scores by the English-
speaking quartet of Canada, Australia, the United States, and the United Kingdom.
With a score of 0.85, France also lies above this average, but many of its con-
tinental European neighbors do not: Germany at 0.28, Spain at 0.37, and Italy at
0.39. Among developing nations in the bottom GDP quartile, the average score is
0.43, with Latin American countries often having the lowest scores.
The table also has some surprises: for example, China’s score of 0.78 and
Indonesia’s score of 0.68 would seem contrary to venture capitalists’ governance
concerns in these two large countries. It is important to remember, however, that
this self-dealing index does not attempt to measure whether the self-dealing laws
are actually enforced. Rather, the index purports to measure whether the self-
dealing laws exist at all. Thus, we can think of the index as measuring Mr. James’s
ability to “steal without breaking the law”.
The main conclusion of the DLLS research is that the index of self-dealing is
correlated with many measures of ?nancial development. For example, the authors
?nd that the ratio of total stock market capitalization to GDP is strongly related to
all the major components of the self-dealing index. Also, comparison of the highest
and lowest countries in Exhibits 6-3, 6-4, and 6-5 will uncover many similarities.
Our focus on the English-speaking countries of Canada, Australia, the United States,
and the United Kingdom was no accident: In addition to the English language, all
four of those countries also share legal origins of English common law.
3
In the DLLS
research, the 21 countries with English common-law systems—including Singapore,
India, Israel, Hong Kong, and South Africa from Exhibit 6-5—have an average self-
dealing index of 0.67. Outside these 21 countries, all other nations in the DLLS study
3
Common-law systems derive a signi?cant amount of their rules from custom and judicial precedent. In
contrast, civil-law systems rely more heavily on legislatures to write laws.
106 CHAPTER 6 VC AROUND THE WORLD
EXHIBIT 6-5
INDEX OF PROTECTIONS AGAINST SELF-DEALING (HIGHER 5
MORE PROTECTIONS)
Singapore
Hong Kong
United Kingdom
France
South Africa
Australia
China
Israel
Indonesia
United States
Canada
Chile
India
Egypt
Japan
Russia
Korea
Argentina
Poland
Italy
Spain
Sweden
Brazil
Germany
Greece
Mexico
Venezuela
Bolivia
0 0.2 0.4 0.6 0.8 1.2 1
Source: Djankov et al. (2008).
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 107
can trace their legal origins to the civil codes of ancient Rome. Such civil codes tend
to provide less protection to minority investors, and the average self-dealing index in
these civil-law countries is 0.37.
Reason #4—Country Risk In emerging markets, many investors are con-
cerned about national-level political and economic risks: corporate assets can be
directly seized, capital controls can keep foreign investors from repatriating pro?ts
or proceeds of a sale, and ?nancial crises can lead to political and social upheaval.
In any of these cases, a VC can lose virtually all his investment, even if the business
was performing well. Collectively, these concerns are called country risk.
Economists have been trying to quantify country risk for many years.
Unfortunately for investors, there is no standard way to do this. Every country—
and every investment within that country—carries a unique set of risks. Companies
with a high level of tangible assets have a greater risk of asset seizures than do
human-capitalÀintensive businesses, and companies related to national interests
can run into dif?culties even in developed countries. The problem is so dif?cult that
many ?rms have carved out a business as “country risk calculators”, performing
estimates for any given project—and charging a tidy sum to do it. The only
component of country risk that lends itself to an easy estimate is the risk of a
government default on its foreign debt. This risk can be measured using the
sovereign spread, usually de?ned as the difference in yield between dollar-
denominated government debt and U.S. government debt of the same duration. For
example, suppose that 10-year Mexican debt, with interest and principal paid in
dollars, has a current yield of 8 percent. If 10-year U.S. government bonds have a
yield of 5 percent, then the sovereign spread for Mexico would be 825 53 percent.
Exhibit 6-6 shows the sovereign spread for 12 developing countries that have
dollar-denominated government debt.
The exhibit shows that most Latin American countries have sovereign
spreads between 1 and 3 percent. Like all reported bond yields, these are not
expected returns, but instead represent the yield-to-maturity on the assumption
that all principal and interest is actually paid back. Thus, the spread represents
the additional amount that must be paid to compensate investors for the risk that
some of these payments will not be made. Indeed, if the beta for a bond is zero, then
the expected return on the bond would be the same as the risk-free rate, with the
entire sovereign spread needed to compensate for expected losses. We discuss these
issues further in Section 6.2. In any case, the sovereign spread can represent only
one component of country risk—the component that is correlated with government
default—and cannot measure risks that exist even when the government itself pays
back its debt. Overall, these different forms of country risk make many VCs wary
of investment in emerging markets.
Reason #5—Cultural Differences When all else fails, we can always
blame “cultural differences” for the global pattern of VC activity. Many observers
have posited that differences in attitudes toward risk, the stigma of failure,
108 CHAPTER 6 VC AROUND THE WORLD
individual expression, and self-con?dence may explain the patterns of entrepre-
neurship across countries. Because VCs cannot invest unless entrepreneurs are
willing to start companies, a dearth of the latter can sti?e a VC industry. For hard
evidence on the relationship between entrepreneurship and cultural attitudes, we
turn to the Global Entrepreneurship Monitor, a project managed at Babson College.
This project documents the entrepreneurship landscape across many countries,
using individual questionnaires as the key survey instrument. Researchers perform
thousands of face-to-face and telephone interviews to measure the extent of
entrepreneurial activity and estimate the determinants of individual participation.
4
Detailed analysis by Arenius and Minniti (2005) and Koellinger et al. (2007) has
demonstrated the important role of cultural factors and personal attitudes on an
individual’s decision to become an entrepreneur, with wide differences across
countries. Exhibit 6-7 illustrates some of these differences. In this exhibit from
Koellinger et al. (2007), we see the percentage of respondents in 18 countries who
answered “yes” to the question: “Do you have the knowledge, skill, and experience
to start a new business?”
The most striking entries in the table are the extraordinary self-con?dence
levels of New Zealanders and the extraordinary lack of self-con?dence among
EXHIBIT 6-6
SOVEREIGN SPREAD OF DOLLAR-DENOMINATED BONDS
R
u
s
s
i
a
S
o
u
t
h
A
f
r
i
c
a
M
e
x
i
c
o
T
u
r
k
e
y
U
k
r
a
i
n
e
B
r
a
z
i
l
V
e
n
e
z
u
e
l
a
C
o
l
o
m
b
i
a
P
h
i
l
i
p
p
i
n
e
s
P
e
r
u
A
r
g
e
n
t
i
n
a
E
c
u
a
d
o
r
6%
5%
4%
3%
2%
1%
0%
Source: Financial Times, April 7, 2006.
4
For a full description of the results and methodology, see The 2009 Global Entrepreneurship Monitor 2009
Global Report, online at http://www3.babson.edu/ESHIP/research-publications/upload/GEM_2009_
Global_Report.pdf.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 109
the Japanese. In general, we see that many English-speaking countries are above
average (38 percent), and most continental European countries are below average.
The authors ?nd a strong correlation between self-con?dence and entrepreneurship
across these 18 countries. Anecdotally, we can see this relationship by comparing
EXHIBIT 6-7
ENTREPRENEURIAL SELF-CONFIDENCE IN 18 COUNTRIES
New Zealand
Hungary
United States
Agentina
Canada
India
Singapore
Poland
Germany
Portugal
Denmark
Italy
Finland
Russia
Israel
Sweden
Korea
Japan
AVERAGE
0% 10% 20% 30% 40% 50% 60% 70%
Source: Koellinger et al. (2007).
110 CHAPTER 6 VC AROUND THE WORLD
the fraction of entrepreneurs in New Zealand—the second-highest in the sample
at 22.5 percent—and Japan—the third-lowest in the sample at 8.3 percent. Note
that these differences in entrepreneurship, although large, are considerably smaller
than the differences in self-con?dence that are reported in Exhibit 6-7. Thus, it is
not just the entrepreneurs who are answering “yes” to the survey question.
Of course, it is possible that residents of all countries have the same under-
lying levels of self-con?dence and differ only in the cultural acceptability of
admitting such self-con?dence to an interviewer. Even in this case, however, such
cultural differences could affect the willingness of individuals to become entre-
preneurs. After all, starting a company is a fairly public way to state one’s self-
con?dence.
The Global Entrepreneurship Monitor has followed up by including a wide
variety of cultural and attitudinal questions in their annual entrepreneurship sur-
veys. We cannot do justice to the richness of the results they report, given the
limited space here, but one interesting indicator that varies quite considerably
across “innovation-driven” (5 developed) countries, according to their report, is
whether the respondents feel that successful entrepreneurs receive a high status in
their society. The percentage of respondents who answer “yes” is 73 percent and 75
percent in the United Kingdom and the United States, respectively, while it is only
49 percent and 50 percent in Belgium and Japan, respectively. Not coincidentally,
these latter countries also scored quite low on the question, “Do you perceive
entrepreneurship as a good career choice?” Forty-six percent in Belgium and 28
percent in Japan said “yes”.
5
6.2 THE COST OF CAPITAL FOR INTERNATIONALVC
In Chapter 4, we estimated the cost of capital for VC in the United States as 15
percent per year. Should this estimate be different for VC investments in other
countries? To gain insight into this question, we need to step into the thorny issues
involved in estimating the cost of capital for international investments. This is a
broad and important topic, and we will not be able to do it full justice here. Instead,
we take a three-step whirlwind tour of the key concepts. In Section 6.2.1 we
introduce a baseline model for the international cost of capital. This model is
similar to the CAPM, but is extended to consider global investments. The key
assumption of this model is that international capital markets are fully integrated,
so that there is a single worldwide price of risk. In Section 6.2.2 we discuss several
objections and extensions to this baseline model to account for currency risk,
country risk, style factors, and the possibility of segmented markets. In Section
6.2.3 we suggest a method to estimate the cost of international VC.
5
GEM (2009).
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 111
6.2.1 Baseline Model: The Global CAPM
In Chapter 4, we introduced the CAPM as our ?rst model of risk and return:
r
i
5R
i
5R
f
1?ðR
m
2R
f
Þ ð6:1Þ
where r
i
is the cost of capital for asset i, R
i
is the expected return for asset i, R
f
represents the risk-free rate for borrowing and lending, R
m
is the return on the
whole market portfolio, and ? (beta) is the level of risk for asset i. In imple-
mentations of this model in the United States, the market premium is typically
estimated on a market portfolio of U.S. stocks. This implementation should pro-
perly be called a domestic CAPM. As ?rst discussed in Chapter 4, the proper
theoretical interpretation of the CAPM requires that this market portfolio must
comprise all assets, traded and untraded, from everywhere in the world. Although
such universal coverage is not possible, it is relatively easy to construct the market
portfolio as a value-weighted portfolio of all traded equities in all world markets.
With a market premium, (R
m
2 R
f
), de?ned as the expected premium on all global
stocks, then we can de?ne Equation (6.1) as the global CAPM.
In the global CAPM, the betas are driven by correlations between asset i and
the global market portfolio. If the ?nancial markets of the world are perfectly
integrated, so that all investors are diversifying among all assets in all countries,
then the global CAPM is a more appropriate model than any domestic CAPM.
Historically, most U.S.-based investors relied on a domestic CAPM because of
limitations on data for global returns. These days, with global returns easily
available, U.S. investors rely on the domestic CAPM either because of inertia or
because of a belief that markets are not perfectly integrated. We discuss the inte-
gration issue further in Section 6.2.2.
For now, we maintain the assumption of perfectly integrated markets, and we
analyze the expected return of investments made outside the United States. To
estimate the model, we need a time series of returns for the global market premium,
for risk-free rates, and for asset i. The historical premium on global stocks is
between 6 and 7 percent. For consistency with our earlier analysis in the United
States, we will use an expected global premium of 7 percent. For now, we will
measure risk-free rates with U.S. government bonds, leaving a discussion of cur-
rency risk for Section 6.2.2. Last, we need a time-series of returns for VC. Now, we
have a major problem because we have no international equivalents for either the
Cambridge Associates or the Sand Hill Econometrics data in the United States.
Furthermore, even if such time series did exist, the small size of the VC markets in
most countries would render these returns to be highly unreliable as predictors of
future performance.
Luckily for us, this problem is quite common in other settings, and analysts
have devised a procedure for making estimates when data is sparse. For example,
consider the investment decision of Telco, a multinational telecommunications
company based in the United States and considering a $100M investment in a
telecom services project in Brazil. To estimate the cost of capital for this
112 CHAPTER 6 VC AROUND THE WORLD
investment, Telco would like to know the average global beta for a telecom
company in Brazil. Although data on global returns is readily available from many
sources, data on individual companies in emerging markets is somewhat harder to
obtain. Furthermore, there may not be very many publicly traded telecom com-
panies in Brazil. In an extreme case, there might be no publicly traded companies in
a country that belong to the same industry.
For this example, Telco can use a three-step procedure to estimate the beta of
their investment. The key assumption behind this procedure is that the domestic beta
of a telecom industry is identical across all countries: that is, the beta of a telecom
company in Brazil relative to the Brazilian stock market is the same as the beta of a
telecom investment in the United States relative to the U.S. market. In the ?rst step of
the procedure, Telco estimates the domestic beta for a similar telecom investment
in the United States; we refer to this estimate as ?
d
. We can obtain this estimate by
regressing the historical returns for the telecom industry in the United States on the
market premium in the United States. Next, Telco estimates the country beta for
the whole Brazilian equity market; we refer to this estimate as ?
c
. We make this
estimate by regressing the historical returns for the Brazilian stock market on the
returns on global market premium. Finally, using the assumption that domestic betas
for telecom are the same across all countries, we have
?
d
5beta of U:S: telecom investment relative to the U:S: stock market
5beta of the Brazilian telecom investment relative to the Brazilian
market; and
?
c
5beta of the Brazilian market relative to the global market
-?
d
à ?
c
5beta of the Brazilian telecom investment relative to the
global market
ð6:2Þ
The Excel ?le betas.xls simpli?es this procedure by providing a wide range of
domestic betas (for industries in the United States) and country betas.
6
In the
industry worksheet of the betas spreadsheet, we can see that the beta for the tele-
com industry in the United States is 1.43. In the countries worksheet, we can see
that the country beta for Brazil is 1.46. Thus, the estimated beta for Telco’s
investment in Brazil is 1.43 Ã 1.46 = 2.08.
EXAMPLE 6.1
Bankco, a multinational ?nancial services company based in the United States, is considering
a consumer-banking investment in Thailand.
6
The industry beta data are from Professor Damodaran’s website; the country beta data are from Reyent
(2009), at http://seekingalpha.com/article/110434-calculating-country-risk-observed-by-betas.
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 113
Problems
(a) Use the betas.xls ?le to estimate the beta for this investment.
(b) With a risk-free rate of 4 percent and a global risk premium of 7 percent, what is the
estimated cost of capital for this investment?
Solution
(a) In the industry worksheet of betas, we can look up the beta for the banking industry
in the United States as 0.71. In the countries worksheet, we can look up the country beta
for Thailand as 0.50. Thus, the estimated beta for Bankco’s investment in Thailand is
0.71 Ã 0.50 = 0.36.
(b) By substituting a global beta of 0.36, a risk-free rate of 4 percent, and a global risk premium
of 7 percent into the global CAPM of Equation (6.1), we obtain a cost of capital of
R
i
50:04 10:36 Ã ð0:07Þ 56:5% ð6:3Þ
’
6.2.2 Objective and Extensions to the Global CAPM
Most objections to the global CAPM are rooted in the belief that the estimated dis-
count rates are “too low”. Example 6-1 provides a typical illustration: the estimated
cost of capital is 6.5 percent, lower than the cost of capital would be for an equivalent
investment in the United States. This lower estimate occurs because the country beta
for Thailand is less than 1. Many analysts are bothered by this, because Thailand
“seems” to be much riskier than the United States. Indeed, the volatility of the Thai
market is almost twice the volatility of the U.S. market. However, it is important to
remember that beta is driven by covariance, not variance. The correlation of the Thai
market with the world market is relatively low: From the perspective of a globally
diversi?ed investor, most of the variance in Thailand is idiosyncratic.
Thailand is not unique. Many developing countries have country betas less
than 1. Exhibit 6-8 shows the volatilities (expressed as a ratio to U.S. market
volatility) and country betas (relative to the global market premium) for select
economies. The exhibit shows that many of these markets have country betas below
1, with both Thailand and India close to 0.5. Do we really think that these countries
should have a lower cost of capital than the United States? For many analysts, this
result is simply too counterintuitive to accept, and several extensions have been
proposed to this baseline model. Next, we will discuss four of these extensions.
Extension #1—Style Adjustments In Chapter 4 we learned that many
economists no longer consider the CAPM to be the best model of expected returns,
with multifactor models such as the Fama-French model (which extends the CAPM
to include size and value/growth factors) and the Pastor-Stambaugh model (which
extends the Fama-French model to include a liquidity factor) doing a better job of
114 CHAPTER 6 VC AROUND THE WORLD
explaining the pattern of realized returns in the United States. The international
evidence for these models is also compelling, and thus it is probably wise to extend
the global CAPM to include these additional factors. In Section 6.2.3, we provide a
suggested method for doing this for the estimation of the cost of capital for
international VC. Nevertheless, the low correlation of the Thai market with the
global premium will still be the main driver of low expected returns for all Thai
investments. Thus, multifactor models, although sensible, do not solve the main
concern that some of these cost-of-capital estimates are “too low”.
Extension #2—Currency Risk The global CAPM ignores differences in
currency across countries. If a U.S.-based investor makes an investment in Thailand,
then revenues from domestic sales will come in Thai currency. If the U.S. company
needs to pay its own investors back in dollars, then they can either hedge the foreign
exchange risk or absorb it—in either case, the potential costs may be large.
To handle currency risk in the context of a factor model, we must ask our-
selves whether such risks are diversi?able. If so, then there is no reason that such
risks should affect expected returns. There is a long history of academic literature
on this question, well beyond the scope of this chapter.
7
The incredibly concise
EXHIBIT 6-8
COUNTRY BETAS AND VOLATILITY RATIOS, SELECTED COUNTRIES
Country Country Beta Volatility Ratio
Brazil 1.46 2.35
Finland 1.29 2.26
Mexico 1.23 1.75
Sweden 1.21 1.17
South Africa 0.91 1.67
Poland 0.84 1.82
Israel 0.78 1.54
China 0.68 1.91
India 0.57 1.80
Thailand 0.50 1.86
Japan 0.46 1.43
Egypt 0.16 1.78
NOTE: Calculated based on daily index stock returns from 1998 to 2008.
Source: http://seekingalpha.com/article/110434-calculating-country-risk-
observed-by-betas.
7
For a longer discussion of this literature, see Solnik and McLeavey (2004), Chapter 4, or Bodnar,
Dumas, and Marston (2004).
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 115
summary of this literature is that, in the long run, currency risks probably have an
expected return of 0, because gains for one currency are exactly offset by losses for
another. In the context of our banana economy of Chapter 4, it should not matter if
some people quote banana prices in euros while others do so in dollars, because
these currency differences have no effect on the overall production of bananas and
thus have no effect on the average level of hunger in the economy. In the short run,
however, it is possible that this long-run relationship breaks down. In our banana
economy, this can occur if, for example, the dollar-currency islanders are more
risk-averse than the euro-currency islanders. In this scenario, the two groups may
bear different amounts of risk in equilibrium, so short-run shocks to the weather
affect the hunger (and currencies) of the two groups disproportionately.
In practice, analysts adjust for short-run differences in currency risk by
adding currency factors to the right-hand side of Equation (6.1). These currency
factors are typically constructed as a historical premium for holding any given
currency, perhaps adjusted for short-run differences in expectations. Solnik and
McLeavey (2004) give an example of such a model. For the applications in this
book, we take the long-run view that the average risk premium is 0, so there is no
adjustment to the cost of capital.
Extension #3—Country Risk In Section 6.2 we discussed “country risk”
as one reason that investors avoid VC in emerging markets. To quantify this
country risk, Exhibit 6-6 displayed the sovereign spread for several developing
countries. It is common practice on Wall Street for analysts to add this sovereign
spread as an additional term on the right-hand side of Equation (6.1). In that case,
an augmented version of the global CAPM is the risk-free rate (from U.S. bonds),
plus beta times the global market premium, plus the sovereign spread. The idea
behind this augmentation is that the sovereign spread, which represents the risk of
government default on its foreign debt, might also be the best available proxy for
the country risk in private investments.
Unfortunately, there are serious problems with this augmented model. The
?rst problem is straightforward: there is no reason to equate the risk of government
default with the risk of private project failure. The second problem is deeper and
concerns the difference between a government bond yield and an expected return.
As we ?rst discussed in Section 6.1, the sovereign spread represents the additional
yield under the assumption that all interest and principal payments are actually
made. This yield is not an expected return, because it assumes no default. It is
entirely possible that expected return on Thai bonds is the same as the expected
return on U.S. bonds. In an equilibrium model like the CAPM, expected returns are
equated with discount rates and the cost of capital. By adding the sovereign spread
to the global CAPM, we can no longer claim to be estimating expected returns,
discount rates, or the cost of capital.
To illustrate this second problem, assume that we knew that the probability of
a government default was exactly 10 percent per year, and all private companies
116 CHAPTER 6 VC AROUND THE WORLD
would go bankrupt in the case of a government default. Furthermore, assume that
this default is independent of the global equity market. Now, in this case, the
sovereign spread would re?ect the yield in the 90 percent of the cases without
default. The spread would be positive to compensate investors for the negative 100
percent return in the case of default. Nevertheless, the expected return on
government debt would be equal to the risk-free rate because, by assumption,
default is uncorrelated with the global market premium.
In this example, the correct way to handle the 10 percent default probability is
not in the discount rate, but in the expected cash ?ows. Indeed, this kind of problem
occurs for every VC investment, foreign or domestic. In Chapter 7, we will show
that a substantial fraction of all VC investments provide no returns to the investors.
In Chapter 10, we will show that this “probability of success” does not affect the
expected return, but rather should be used as a separate input into the valuation
decision.
Extension #4—Segmented Markets So far, we have described three
possible extensions to the global CAPM, but we have argued that none of these
three extensions are likely to explain why estimates seem “too low”. Extension #4
drops the assumption of perfect integration of international ?nancial market.
Without this assumption, we can sometimes estimate a much higher cost of capital.
To see how this works, consider the opposite extreme to perfectly integrated
markets: perfectly segmented markets. Under this extreme assumption, investors
are only permitted to invest in their own countries. Then, there would be no such
thing as the global CAPM. Instead, we would have a different domestic CAPM for
every country. For each country, we would estimate a version of Equation (6.1)
using the market premium from that country. Of course, in this world of perfect
segmentation, it would not make any sense to consider an investment by a U.S.
investor in Thailand—we have assumed that this is impossible. Thus, analysts
sometimes consider a hybrid CAPM, shown in Equation (6.4), which allows for
separate betas and market premia for the global and domestic markets.
r
i
5R
i
5R
f
1?
1
ðR
g
2R
f
Þ 1?
2
ðR
d
2R
f
Þ ð6:4Þ
where r
i
, R
i
, and R
f
are de?ned as in Equation (6.1), R
g
is the return on the global
market portfolio, R
d
is the return on the domestic market portfolio corresponding to
the country of investment i, and ?
1
and ?
2
are the betas on the global premium and
domestic premium, respectively. Equation (6.4) can generate a high cost of capital
because some countries have very high historical premia. Nevertheless, the hybrid
CAPM rests on shaky theoretical foundations. It is very dif?cult to write down a
rigorous model of “partially segmented” markets that would give rise to Equation
(6.4). Furthermore, most limited partners in VC funds are large institutions with the
capability of investing anywhere in the world. Thus, although a hybrid CAPM
might satisfy a craving to obtain a higher estimate for the cost of capital, this
satisfaction would come with some sacri?ce to logical consistency.
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 117
6.2.3 A Global Multifactor Model for Venture Capital
So, with all these possible extensions, how should an honest analyst estimate the
cost of capital for international VC? In this book, we suggest an approach that is
internally consistent with the domestic estimate done in Chapter 4. The starting
point is the Pastor-Stambaugh model (PSM) cost-of-capital estimate for the United
States. In Chapter 4, we introduced the PSM model as
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1
?
liq
à LIQ
t
1e
it
ð6:5Þ
where ?, ?, R
mt
, R
ft
, and e
it
are de?ned similarly as in Equation (6.1), SIZE
t
,
VALUE
t
, and LIQ
t
are the factor premia for their respective investing styles, and
?
size
, ?
value
, and ?
liq
are the regression coef?cients on these factors. In Chapter 4,
we discussed the historical evidence for each of these factor premia and suggested
estimates of 7 percent (for the market), 2.5 percent (for size), 3.5 percent (for
value), and 5 percent (for liquidity). We then estimated Equation (6.5) for the Sand
Hill Econometrics index and Cambridge Associates index (each with lags) and
obtained estimated coef?cients, as shown in Exhibit 4-6. By substituting these
coef?cients and premia into Equation (6.5), we obtain a cost-of-capital equation of
15 percent.
Now, to estimate the cost of capital for VC in a country other than the United
States, we multiply all the PSMbetas—?, ?
size
, ?
value
, and ?
liq
fromEquation (6.5)—
by the country beta, ?
c
, from the betas.xls ?le. Using the rounded estimate of 15
percent and subtracting the historic average risk-free rate of 4 percent, we obtain
11 percent for the sum of all factor loadings times the historic average factor returns
(? Ã 0.07 1?
size
à 0.025 1?
value
à 0.035 1?
liq
à 0.05). Thus, for an investment in
Thailand, we would multiply all factor loadings by 0.50 (see betas.xls), so we have:
r
i
ðThailandÞ 50:04 10:50 Ã ð0:15 À 0:04Þ 59:5% ð6:7Þ
Some readers might see this estimate, 5.5 percent lower than the corre-
sponding estimate in the United States, and express disbelief. Remember, however,
that we must not confuse a higher probability of failure with a higher cost of capital.
If you believe that investments in Thailand have a higher probably of outright
failure than do similar investments in the United States, then you can take account
of this higher probability in a different part of your valuation calculation. In
Chapter 10, we show exactly how such probabilities can be incorporated into an
investment decision, separate from the cost of capital.
EXAMPLE 6.2
EBV is considering an investment in South Africa.
Problem What is the cost of VC for this investment?
118 CHAPTER 6 VC AROUND THE WORLD
Solution We can see in the betas.xls spreadsheet (and in Exhibit 6-8), that the country
beta for South Africa is 0.91. Thus, the cost of VC for a South African investment can be
estimated by
r
i
ðSouthAfricaÞ 50:04 10:91 Ã ð0:15 À 0:04Þ 514:01% ð6:8Þ
’
SUMMARY
VC is a worldwide industry, but some countries have been more successful than others in
developing a thriving culture of entrepreneurship and VC investment. The United States
continues to lead the world with about half of all high-tech private equity investment—and a
ratio of investment to GDP nearly double that of Western Europe. Within Western Europe,
nearly half of all investment is concentrated in the United Kingdom. We discussed ?ve factors
that help drive VC activity in a country. First, the IPO markets should be active to provide the
possibility of high-value exits. Second, there should be an entrepreneurial ecosystemthat eases
the tasks of setting up new companies and recruiting necessary talent. Third, the legal system
should protect minority investors from self-dealing by owners and managers. Fourth, the level
of political risk should not be so high as to scare VCs away. Fifth, the culture should be sup-
portive of entrepreneurs starting (and sometimes failing) in their ventures.
In Chapter 4, we estimated the cost of capital for VC in the United States to be 15
percent. This estimation is different in every country. In theory, the main driver of these
differences is the country beta, which measures the extent to which a county’s asset markets
are correlated with the global market. Multifactor models like the Pastor-Stambaugh model
can be combined with country betas to provide an estimate of the cost of capital for VC for
any country.
KEY TERMS
Entrepreneurial ecosystem
Self-dealing
5 tunneling
5 investor expropriation
Country risk
Global CAPM, global beta
Domestic CAPM, domestic
beta
Country beta
Integrated markets,
segmented markets
REFERENCES
Arenius, Pia, and Maria Minniti, 2005, “Perceptual Variables and Nascent Entrepreneurship”, Small
Business Economics 24(3), 233À247.
Bodnar, Gordon, Bernard Dumas, and Richard Marston, 2004, “Cross-Border Valuation: The Interna-
tional Cost of Equity Capital”, in The INSEAD-Wharton Alliance on Globalizing: Strategies for
REFERENCES 119
Building Successful Global Businesses, R. Gunther, H. Gatignon, and J. Kimberly, eds., Cambridge
University Press, New York.
Djankov, Simon, Rafael LaPorta, Florencio Lopez-de-Silanes, and Andrei Shleifer, 2002, “The Reg-
ulation of Entry”, Quarterly Journal of Economics 117(1), 1À37.
Djankov, Simon, Rafael LaPorta, Florencio Lopez-de-Silanes, and Andrei Shleifer, 2008, “The Law and
Economics of Self-Dealing”, Journal of Financial Economics 88(3), 430À465.
Global Entrepreneurship Monitor 2009 Global Report, http://www3.babson.edu/ESHIP/research-
publications/upload/GEM_2009_Global_Report.pdf.
Koellinger, Phillip, Maria Minniti, and Christian Schade, 2007, “I Think I Can, I Think I Can: Over-
con?dence and Entrepreneurial Behavior”, Journal of Economic Psychology 28(4), 502À527.
PricewaterhouseCoopers, Global Private Equity Report 2008, http://www.pwc.com/en_GX/gx/investment-
management-real-estate/pdf/2008_global_private_equity_report.pdf.
Reyent, Suna, 2009, “Calculating Country Risk Observed by Betas”, http://seekingalpha.com/article/
110434-calculating-country-risk-observed-by-betas.
Solnik, Bruno and Dennis W. McLeavy, 2004, International Investments, 5th Edition, Addison-Wesley,
Reading, MA.
EXERCISES
6.1 True, False, or Uncertain: Private equity is a substitute for public equity (i.e., if a
country has a relatively active public-equity market, then private-equity activity will be
relatively low).
6.2 True, False, or Uncertain: Countries with common-law based legal systems have
relatively weak protections against investor expropriation.
6.3 Softco, a multinational software company based in the United States, is considering an
investment to produce and sell business software in Mexico. Use the betas.xls ?le to estimate
the beta for this investment.
6.4 Talltree is considering an investment in India. What is the cost of VC for this
investment?
120 CHAPTER 6 VC AROUND THE WORLD
PART II
TOTAL VALUATION
121
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CHAPTER 7
THE ANALYSIS OF VC
INVESTMENTS
IN THIS CHAPTER we introduce the main topic for Parts II and III of this
book: the analysis of VC investments. In the past decade, the data on VC invest-
ments has become much more complete. In Section 7.1 we study this data and
provide key statistics about the distribution of returns to individual VC investments.
In Section 7.2 we turn our attention from data to methodology, and we sketch the
key steps in the investment decision-making process.
7.1 VC INVESTMENTS: THE HISTORICAL
EVIDENCE
For a long time the VC industry existed in a data vacuum. VCs invested billions of
dollars in startup companies with little more than intuition and rules of thumb to
guide them. Ten years ago there was no way to reliably answer basic questions like,
“What fraction of all VC investments goes out of business?” and, “What fraction of
VC investments eventually has IPOs?” To make decisions without this information
is like playing poker without knowing how many aces and kings are in the deck.
Yes, you can do it, but it makes the luck factor loom even larger.
The good news is that this data vacuum has been steadily ?lling over the
past 10 years. The ?rst entrant on the scene was VentureExpert, a product of
Venture Economics (a unit of Thomson Financial), soon to be followed by
VentureSource, a product of Dow Jones. Venture Economics, the producers of
much of the data used in Chapters 1 and 2, began its data collection in the 1970s
but did not track much data on valuations until recent years. VentureSource
(formerly VentureOne) has always been much more comprehensive with valua-
tion data, but its industry coverage was not very broad until the early 1990s. The
next leap forward came from Sand Hill Econometrics (SHE), whom we ?rst met
in Chapter 3 through its VC return index. SHE initially combined data from
Venture Economics and VentureSource, added some information from some
newer providers, and performed some detailed investigations of its own. The SHE
123
database is state of the art and serves as the basis for the statistics presented in this
chapter.
1
To build a VC database requires three main steps. First, one must learn about
investments as they occur. Second, one must track these investments over time. Third,
one must get accurate information about exits. At each of these steps, it is not enough to
knowthat anevent occurred; one must alsoget valuationdata. Without valuationdata, it
is impossible to compute the returns to the VC investors. At each step, there are chal-
lenges. For example, if you miss some companies at their initial investment, but then
pick themup later if they make it to a second or third round, then you run the danger of
introducing survivor bias into the data. (We ?rst saw survivor bias in Chapter 3, when
discussing the Cambridge Associates return index.) Furthermore, even if you gather all
information about the rounds of investment, it is still a big challenge to ?nd out when
companies have gone out of business. Neither VCs nor their companies are eager to
publicize their failures, and SHE expends considerable effort to track these down.
Finally, the valuation data for exits is not always available. IPO exits are always
available, and large-value acquisitions are virtually always disclosed. Nevertheless, in a
signi?cant fraction of small acquisitions, the purchase price is never disclosed.
For any investment, there are four possible outcomes at any point: (1) exited
through an IPO (IPO), (2) exited through an acquisition (ACQ), (3) out of business
before any exit (DEF, for “defunct”), and (4) still a private company in a VC’s
portfolio (PRI). Exhibit 7-1 shows the likelihood for these outcomes as a function
of time since the ?rst round of VC investment, using data from all VC-backed
companies in the SHE database that received their ?rst ?nancing before 2001.
The exhibit shows that by ?ve years after the initial investment, 12.7 percent of
all companies have had an IPO, 24.1 percent have been acquired, 26.1 percent
are defunct (out of business), and 37.1 percent are still private. By 10 years after the
initial investment, the respective percentages are 15.4 percent for IPO, 35.5 percent
for an acquisition, 33.4 percent for defunct, and 15.7 percent for still private.
The largest remaining unresolved issue is the identi?cation of out-of-business
dates. Even with SHE’s efforts, 16 percent of all companies are listed as “still
private” 10 years after their initial investment, and only about one-third are listed as
defunct. Because VC funds ordinarily must exit all their investments within
10 years, the still-private percentage seems too high. It is likely that the vast
majority of these companies has either gone out of business or been “acquired” for
some nominal price.
2
SHE has chosen a reasonable and conservative path of listing
these companies as “still private” when no other information is available. An
alternative assumption would be that these companies have gone out of business,
1
Sand Hill Econometrics entered into a licensing agreement with DowJones (the provider of VentureSource)
in 2009. As a result, it stopped using Venture Economics as a raw data source. The results presented in this
chapter are based on the new version of their database, which excludes data from Venture Economics.
2
VentureSource has two separate categories for asset acquisitions (where a company is liquidated and sells
some of its assets, such as computers, ergonomic chairs, foosball tables, etc.) and other acquisitions. When a
deal is classi?ed as an asset acquisition by VentureSource, Sand Hill classi?es it as “defunct”. That said, it is
possible that some asset acquisitions are classi?ed as “acquired” with an undisclosed price.
124 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
with the exit rate (over the previous 10 years) assumed to be the same as that for the
companies withknownout-of-business dates. Exhibit 7-2is ananalogue toExhibit 7-1,
but now with this more aggressive assumption:
In Exhibit 7-2, the IPO and acquisition percentages are the same as in Exhibit
7-1, but the still-private and out-of-business lines are different. In Exhibit 7-2, by
assumption, no companies are still private after 10 years, with the defunct per-
centage increasing to 49.1 percent.
Both of the prior exhibits show that about 51 percent of all VC investments
end in an IPO or an acquisition, but this does not mean that all these investments
could be labeled as “successes”. For the original (early stage) investors, an IPO is
almost always a pro?table exit, but we cannot say the same thing about all
acquisitions. Exhibit 7-3 shows the likelihood for various ranges of gross value
multiples (GVMs) for both IPOs and acquisitions.
3
The exhibit shows that 53.6 percent of all IPOexits yield value multiples in excess
of ?ve times the original investment (the ?ve highest categories) and 3.3 percent yield
EXHIBIT 7-1
PORTFOLIO COMPANY STATUS OVER TIME: FIRST ROUND
INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since First Venture Round Investment
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
3
Because the SHE data is before fees and carry, the value multiples are “gross” and not “net”.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 125
multiples in excess of 50 times the original investment (the two highest categories). It is
important to note, however, that these multiples represent only the time period fromthe
initial investment by the VC to the IPO date. Because VCs usually do not distribute
stocks to their LPs for at least six months after the IPO, the actual returns to LPs will
differ fromthose inthe SHEdatabase. This six-monthreturnis unlikelytochange the big
picture of Exhibit 7-3, but it can make a huge difference for speci?c investments. For
example, the most successful VC investment of all time is Benchmark Capital $6.7M
investment in eBay. At the time of the eBay IPO in September 1998, eBay’s stock was
pricedat $18per share. The?rst trade onSeptember 24occurredat $54per share, andthe
Benchmark investment was valued at $416M. By the time Benchmark started to dis-
tribute this stock to its LPs six months later, eBay had risen to a (split-adjusted) price
above $600 per share, and the value of the overall stake (GPs 1LPs) was $5.1B.
4
EXHIBIT 7-2
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER 10 YEARS, ALL FIRST-ROUND INVESTMENTS
0 12 24 36 48 60 72 84 96 108
Months Since First Venture Round Investment
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
4
These ?gures are cited in Stross (2000), p. 216, who had the good timing to be writing a book about
Benchmark Capital and following the ?rm from the inside while the eBay investment was happening.
126 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Exhibit 7-3 also shows that the multiples for acquisitions are much lower.
First, note that 37.9 percent of all acquisitions result in a loss (the three lowest
categories). This number is likely to be signi?cantly understated because we are
missing the acquisition price for about one-third of all acquisitions, and these
missing values are almost surely tilted toward lower-return cases. (As mentioned
earlier, missing acquisition values often indicate a going-out-of-business sale. In
contrast, we always know the value of the IPO exit.) Among the cases where we do
know the acquisition value, 20.9 percent yield multiples of ?ve times or greater,
and 0.9 percent yield multiples of 50 times or greater.
We turn next to an analysis of all ?rst-round investments, including defunct
companies. As in Exhibit 7-2, we assume that all private, unexited companies are
defunct after 10 years.
5
For exited companies for which we are missing the exit value,
we impute exit values based on observable investment characteristics such as amount
raised to date, time elapsed since last round, last known value if there is one, whether
acquirer was public or private, and whether the deal was for stock or cash. Exhibit 7-4
shows the wide distribution of multiples for ?rst-round investments. Once we include
EXHIBIT 7-3
GVMs FOR FIRST-ROUND INVESTMENTS: IPOs AND ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.7% 15.1%
0.25 to ,0.50 1.6% 9.3%
0.50 to ,1.00 3.9% 13.6%
1.00 to ,1.50 6.5% 10.7%
1.50 to ,2.00 6.6% 8.2%
2 to ,3 12.1% 10.8%
3 to ,5 15.0% 11.4%
5 to ,10 24.3% 11.4%
10 to ,20 15.6% 5.6%
20 to ,50 10.5% 3.0%
50 to ,100 2.4% 0.6%
.5100 0.8% 0.3%
NOTE: Data includes all ?rst-round investments with
known exit values.
Source: Sand Hill Econometrics.
5
Some of these “still private” companies (as many as one in ?ve) eventually do exit, so to the extent that
we force all of them to have a multiple of 0, our results are conservative.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 127
our conservative assumptions for “still private” companies and for the returns in
acquisitions with unknown prices, we ?nd that 74.22 percent of all ?rst-round
investments lead to a negative return (value multiple below1). On the other end of the
spectrum, 12.0 percent of all ?rst-round investments yield multiples of 5 or greater,
and 0.7 percent yield multiples of 50 or greater.
One caveat to this exercise is that, given the end of the sample period at the end of
2000, the results are disproportionately in?uenced by the record number of investments
made in the tech bubble years of 1999 and 2000. According to the 2009 NVCA
Yearbook, out of 9,052 early stage investments during 1990À2000, 4,553 (about 50%
of all deals) were made in 1999 and 2000. It is all too well-known that many of these
investments, made at the height of the market exuberance about Internet stocks, should
never havebeenmade—andsubsequentlyfailed. Ina sense these wereanomalyyears of
VC investing, probably never to be repeated. If we excluded these two anomaly years
from the analysis, the results would have probably looked a lot different, with a
lower percentage of failures and near failures, and a higher percentage of exits at
multiples of 5 or higher. It will be interesting to update these ?gures in ?ve years, when
we have more information about ?nal outcomes of investments made post-2000.
EXHIBIT 7-4
GVMs FOR ALL FIRST-ROUND INVESTMENTS
Value Multiple Percentage
0 49.10%
.0 to ,0.25 10.68%
0.25 to ,0.50 7.69%
0.50 to ,1.00 6.74%
1.00 to ,1.50 3.53%
1.50 to ,2.00 2.62%
2 to ,3 3.65%
3 to ,5 3.99%
5 to ,10 5.66%
10 to ,20 3.41%
20 to ,50 2.24%
50 to ,100 0.49%
.5100 0.19%
NOTE: These return distributions are estimated using
the information on Exhibits 7-2 and 7-3, with some
additional assumptions (described in the text) to
handle missing exit values. The “still private”
companies after 10 years are assumed to have failed.
Source: Sand Hill Econometrics.
128 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Exhibit 7-5 uses second-round investments and repeats the survival analysis
of Exhibit 7-2. As in Exhibit 7-2, we assume that all companies reported as “still
private” after 10 years by SHE have actually gone out of business at the same rate
as those companies observed to be defunct.
After ?ve years, 27.3 percent of second-round investments have been
acquired, 16.9 percent have had an IPO, 36.3 percent are defunct, and 19.5 percent
are still private. After 10 years, 37.3 percent have been acquired, 19.3 percent have
had an IPO, 43.4 percent are defunct, and, by assumption, none are still private. By
comparing these percentages to their analogues in Exhibit 7-2, we can start to see
some differences between ?rst-round and second-round investments. For the
second-round investments, IPO and ACQ percentages are both higher in all periods,
and the DEF and PRI percentages are lower in all periods (until 10 years, when PRI
is 0 for both.) These differences make sense because later-round investments should
have demonstrated a greater capacity for survival than ?rst-round investments.
Because these higher survival probabilities are well understood by all parties, they
will be factored into the share prices, and hence we cannot infer anything about
EXHIBIT 7-5
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER TEN YEARS, ALL SECOND-ROUND
INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since Second Venture Round
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 129
GVMs or returns from Exhibit 7-5. Instead, we must repeat the analysis of ?rst-
round investments and look directly at the GVMs. Exhibit 7-6 displays ranges of
GVMs for second-round investments with IPO or acquisition exits.
By comparing Exhibits 7-6 and 7-3, we can see that the frequency of very high
returns is signi?cantly reduced in second rounds. For ?rst-round investments, 3.3
percent of all IPOs led to GVMs of 50 or greater. For second rounds, only 0.6 percent
of IPOs led to such extreme outcomes. Similarly, while more than half (53.6%) of all
IPOs had GVMs of 5 or greater for ?rst-round investments, the portion of IPOs with
GVMs of 5 or greater is just over one-third (36.6%) for second-round investments. Of
course, GVMs do not tell the whole story, as they make no allowance for differences
in average holding periods. Exhibits 7-5 and 7-2 demonstrated that average holding
periods are shorter (fewer private ?rms at each point) for second-round investments
than for ?rst-round investments. This shortening of holding periods would tend to
make GVMs look less extreme for second-round investments, even if there were no
difference in annualized returns. Nevertheless, the overall pattern of more extreme
returns for ?rst-round investments still holds, even if we focus on annualized returns.
Exhibit 7-7 gives the GVMs for all second-round investments.
By comparing Exhibits 7-4 and 7-7, we can see that extreme multiples are less
frequent for second-round investments compared to the ?rst-round investments. This
EXHIBIT 7-6
GVMs FOR SECOND-ROUND INVESTMENTS: IPOs AND
ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.8% 20.2%
0.25 to ,0.50 1.1% 11.2%
0.50 to ,1.00 6.4% 14.5%
1.00 to ,1.50 9.9% 9.0%
1.50 to ,2.00 9.9% 8.9%
2 to ,3 15.4% 10.2%
3 to ,5 19.8% 13.1%
5 to ,10 22.0% 8.3%
10 to ,20 10.4% 3.0%
20 to ,50 3.6% 1.1%
50 to ,100 0.5% 0.3%
.5100 0.1% 0.1%
NOTE: Data includes all second-round investments with
known exit values.
Source: Sand Hill Econometrics.
130 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
result is consistent with our ?ndings about IPOs and acquisitions discussed for the
previous exhibit. Among all second-round investments, 0.2 percent had GVMs of 50
or greater, compared to 0.7 percent among all ?rst-round investments. This lower
frequency for great investments is somewhat counterbalanced by a lower frequency
for write-offs, which occur for 46.6 percent of second-round investments compared to
49.1 percent of ?rst-round investments.
Exhibit 7-8 uses third-round investments and repeats the survival analysis of
Exhibits 7-2 and 7-5. As in those previous exhibits, we assume that all companies
reported as “still private” after 10 years have actually gone out of business at the
same rate as those companies observed to be defunct. After ?ve years, 27.10
percent of third-round investments have been acquired, 19.90 percent have had an
IPO, 36.97 percent are defunct, and 16.03 percent are still private. After 10 years,
34.73 percent have been acquired, 21.99 percent have had an IPO, 43.28 percent are
defunct, and, by assumption, none are still private. As compared to second-round
(Exhibit 7-5) investments, we see that failure rates for third round investments are
slightly higher than those for second round investments in the initial months fol-
lowing investments, while after 10 years they are both at about 43%. As for IPO
EXHIBIT 7-7
GVMs FOR ALL SECOND-ROUND INVESTMENTS
Value Multiple Percentage
0 46.56%
.0 to ,0.25 13.34%
0.25 to ,0.50 7.95%
0.50 to ,1.00 6.54%
1.00 to ,1.50 3.69%
1.50 to ,2.00 3.31%
2 to ,3 4.39%
3 to ,5 5.46%
5 to ,10 5.35%
10 to ,20 2.43%
20 to ,50 0.82%
50 to ,100 0.14%
.5100 0.03%
NOTE: These return distributions are estimated using
the information on Exhibits 7-5 and 7-6, with some
additional assumptions to handle missing exit
values. The “still private” companies after 10 years
are assumed to have failed.
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 131
versus ACQ outcomes, third-round investments have slightly higher IPO rates and
lower ACQ rates than second-round investments.
Exhibit 7-9 reports GVMs for IPOs and acquisitions for all investments made
in the third rounds.
6
The evidence of Exhibit 7-9 continues the pattern of later
rounds showing less extreme GVMs than earlier rounds. Only 0.1 percent of IPOs
have GVMs of 50 or greater, and only 20.3 percent have GVMs of 5 or greater. In
comparison, 3.3 percent of ?rst-round investments had GVMs of 50 or greater, and
53.6 percent were 5 or greater. Although some of these differences can be ascribed
to shorter holding periods of third-round investments, the difference still remains if
we examine annualized returns. These patterns are reinforced when we examine the
returns to all third-round investments.
Among third-round investments, only 44.7 percent are writeoffs, as compared to
46.6 percent of second rounds and 49.1 percent of ?rst rounds. On the high end, only 5.6
percent hada valuemultiple of 5or greater, comparedto8.8percent above this threshold
EXHIBIT 7-8
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER 10 YEARS, ALL THIRD-ROUND INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since Third Round
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
6
Analysis of fourth-round investments shows that they are similar to third-round investments, with an
even higher concentration of multiples in the range of above 0 and below 5.
132 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
in the second round and 12.0 percent in the ?rst round. The relatively lowfrequency on
the extremes means that 49.7 percent of all third-round investments had multiples in the
range above 0 and below5, compared to 44.7 percent of second rounds and 38.9 percent
of ?rst rounds. It is in this middle range above 0 and below5 that the return advantage of
preferred stock becomes apparent. The GVMs in this chapter are all based on the
baseline SHE assumption that all investments are made in common stock. These
exhibits would look different if we made more realistic assumptions about the security
types in each round. We discuss and value these differences in Part III of the book.
The evidence fromExhibits 7-1 and 7-2 shows that IPO exits occurred for about
15.4 percent of all ?rst-round investments made before 2001, and these investments
were often quite pro?table for the investors. As mentioned before, it is important to note
that these results are disproportionately in?uenced by the unprecedented number of
investments made during the 1999À2000 boomperiod. So in several more years, when
more investments fromthe post-2000 period are included in the completed-investment
sample, wouldthe IPOexit rate start increasingagain?This does not seemlikely, at least
not in the immediate future. The reason is that while the number of VCinvestments has
declined to a more sustainable level in the post-2000 period, the number of VC-backed
IPOs has plummeted even more drastically. Exhibit 7-11 shows this trend.
In particular, the exhibit shows the 10-year, rolling-window averages for the
number of new VC investments and the number of VC-backed IPOs. For 1990, for
example, the average number of new VC investments for the previous 10 years
EXHIBIT 7-9
GVMs FOR THIRD-ROUND INVESTMENTS: IPOs AND ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.5% 21.6%
0.25 to ,0.50 1.4% 13.2%
0.50 to ,1.00 8.2% 15.2%
1.00 to ,1.50 14.1% 10.2%
1.50 to ,2.00 13.0% 8.7%
2 to ,3 19.2% 11.3%
3 to ,5 23.5% 11.1%
5 to ,10 14.5% 6.6%
10 to ,20 4.6% 1.2%
20 to ,50 1.1% 0.9%
50 to ,100 0.1% 0.1%
.5100 0.0% 0.0%
NOTE: Data includes all third-round investments with
known exit values.
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 133
(1981À1990) is 508, and the average number of VC-backed IPOs in the previous
10 years is 95. The ratio of the two numbers (shown on the right-hand axis in %) is
a back-of-the-envelope measure of the IPO rate of VC investments. In the ?rst half
of the 1990s, as the number of VC ?nancings stayed low and the IPO market
boomed, this ratio climbed up and peaked at 31 percent in 1994. Near the end of
the decade, however, the number of VC ?nancings ballooned much faster than the
number of VC-backed IPOs, and the ratio rapidly started to decline. By 2000,
the ratio of the two 10-year average numbers is down to 16 percent, which is almost
exactly the same as the IPO rate in Exhibit 7-2 (15%).
Post-2000, the number of investments declined—but never declined to the
level last seen in the early 1990s. Even in 2009, at the depth of the recession, 725
new ?nancings took place, compared to just 417 in 1994. Meanwhile, the number of
VC-backed IPOs continued to stagnate at the level last seen in the late 1980s—less
than 50 a year on average—throughout the ?rst decade of the new century. Thus,
the ratio of the 10-year averages of IPOs and new VC ?nancing keeps going down,
and as of 2009, it is just 5 percent—that is, on average there were only 67 IPOs for
1,260 investments per year.
EXHIBIT 7-10
GVMs FOR ALL THIRD-ROUND INVESTMENTS
Value Multiple Percentage
0 44.71%
.0 to ,0.25 13.54%
0.25 to ,0.50 7.88%
0.50 to ,1.00 6.92%
1.00 to ,1.50 4.94%
1.50 to ,2.00 4.11%
2 to ,3 5.73%
3 to ,5 6.57%
5 to ,10 3.98%
10 to ,20 1.14%
20 to ,50 0.43%
50 to ,100 0.05%
.5100 0.00%
NOTE: These return distributions are estimated using
the information on Exhibits 7-8 and 7-9, with some
additional assumptions to handle missing exit
values. The “still private” companies after 10 years
are assumed to have failed.
Source: Sand Hill Econometrics.
134 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
For this rate to start going back up again, one or both of two things needs to
happen. First, there will have to be more VC-backed IPOs and more IPOs in
general. Second, the number of VC ?nancings will need to go down further. While
some argue precisely both of these things need to take place for the VC model to
start working again, others assert that VC investments need not rely on IPO exits
alone. It will be interesting to revisit this data in several years and ?nd out if
the patterns of VC investment exits evolve further away from IPOs or return to the
long-term historical levels of IPO rates.
7.2 THE INVESTMENT PROCESS
In Chapter 1, we listed several stages a potential VC investment goes though before
any money changes hands. These stages included screening, the term sheet, due
diligence, and closing. Exhibit 7-12 gives an example of the number of investments
that reach each stage of this process for a “typical” VC:
7
EXHIBIT 7-11
10-YEAR AVERAGE VC FINANCINGS AND IPO EXITS, BY ENDING
YEAR
1600
35%
30%
25%
20%
15%
10%
5%
0%
1400
1200
1000
800
600
400
200
0
1
9
8
9
1
9
9
0
1
9
9
1
1
9
9
2
1
9
9
3
1
9
9
4
1
9
9
5
1
9
9
6
1
9
9
7
1
9
9
8
1
9
9
9
2
0
0
0
2
0
0
1
2
0
0
2
2
0
0
3
2
0
0
4
2
0
0
5
2
0
0
6
2
0
0
7
2
0
0
8
2
0
0
9
# of initial VC financings, 10-yr. ave.
# of VC-backed IPOs, 10-yr. ave.
IPO/investments,10-yr. ave.
Source: 2009 NVCA Yearbook, press releases on NVCA website.
7
There is no academic research to back up Exhibit 7-12. These numbers are estimates gleaned from
conversations with VCs and researchers.
7.2 THE INVESTMENT PROCESS 135
The ?rst entry in the exhibit has a wide range, from 100 to 1,000, because the
?rst screening stage is somewhat amorphously de?ned. If we include every busi-
ness idea ever seen by the VC, then the number would be closer to 1,000. If we
include only those ideas that receive any formal attention, then the number would
be closer to 100. In any case, the odds are long to reach the next stage. The exhibit
shows that for every 100 to 1,000 opportunities that cross a VC’s desk, only about
10 will reach the more intensive screening stage that we are calling “preliminary
due diligence”. Of these 10, about 3 will justify a term sheet. Term sheets are
preliminary contracts designed as a starting point for the more detailed negotiations
required for the contract. In Chapter 8 we cover term sheets in detail.
The acceptance of a term sheet by the entrepreneur leads to a more complete
due diligence and contract negotiation. There are many ways that an agreement can
break down between the term sheet and the ?nal investment. Although hard data are
dif?cult to ?nd, some VCs report that only about half of all accepted term sheets
lead to an investment. Thus, the typical VC would need to screen at least 100
companies to make one investment.
As we move down Exhibit 7-12, each successive stage takes progressively more
work. The exact process for each stage varies considerably across ?rms. There is no
consensus on the best practices for each stage, and it is doubtful that such a consensus
will ever occur. Nevertheless, a fewthemes are apparent. First, the existence of a formal
process is highly correlated with the size of the VC?rm. Firms with just a fewpartners
are likely to make decisions as a group, with all partners somewhat informed and
involved in all stages of due diligence and in the investment decision. For midsize ?rms
larger than ?ve or six partners, this group decision making becomes unwieldy, and we
are more likely to see a deal driven by one or two partners, with the full partnership
investing on the basis of a written memo and an oral presentation by the lead partner for
the deal. Such midsize ?rms often attempt to make their investment decisions at reg-
ularly scheduled weekly meetings, where all partners try to participate in person or by
telephone. For the larger ?rms, regular meetings of the entire partnership are not fea-
sible, and commitment decisions are usually made by a committee of senior partners. If
there is an investment committee, then a written memo becomes an important way for
EXHIBIT 7-12
THE INVESTMENT PROCESS
Screening [100À1,000]
Preliminary Due Diligence [10]
Term Sheet [3]
Final Due Diligence [2]
Closing [1]
136 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
other principals to communicate with the committee. Also, large ?rms are the only
place where we ?nd a signi?cant number of junior VCs who do not take the lead on
investments, but whose main role is to screen potential investments, perform due
diligence, and take on various other detail work.
A big component of VC success is the quality of prospects at the screening
stage, also called the deal ?ow. The generation of high-quality deal ?ow, also
called “sourcing”, is a major challenge and takes a big chunk of VC time and
energy. The VCs use a variety of sourcing strategies. In general, the better the
reputation of the VC ?rm, the better the deal ?ow, and the less work the VCs have
to do to get it. In our discussion of Summit Partners in Chapter 5, we mentioned
how its extensive database of private companies often provides it with proprietary
deal ?ow, the holy grail of all private equity investors. Other top-tier VCs will often
garner proprietary deal ?ow through the sheer force of their reputation, as entre-
preneurs will want the famous VC brand attached to their company. These top-tier
VCs receive most of their deal ?ow either from repeat entrepreneurs or as direct
referrals from close contacts. Younger and less-prestigious ?rms also rely on direct
referrals—often from professional service providers such as accountants, lawyers,
and consultants—but also must be more proactive about attending trade shows,
accessing third-party databases, and even cold-calling new ?rms.
Once the deal ?ow is generated, VCs must perform the initial screen. Although
some investments may be screened through informal conversation or fromthird-party
information sources, the majority of investments are screened using a business plan
prepared by the entrepreneur. The business plan gives a summary of all crucial
information about the company; it includes a detailed description of the strategic plan
for the company, the current and potential competitors, and the background of the
management team. Although ?nancial projections are also included, the detail in
these projections varies widely. For early stage companies, the projections usually
focus on the uses of funds; for later-stage companies, the projections should be more
complete ?nancial statements. In general, the VCs (correctly) take all such forecasts
with a grain of salt.
Many academics have studied the screening phase, but lack of access to a broad
database prevents any strong quantitative conclusions. These studies, in addition to
published interviews with famous VCs, do allow for some qualitative conclusions
about the most important elements of the initial screen. These two elements also
remain the key focus of the next phases of diligence. We will call them the market
test and the management test. They can both be phrased as questions:
1. Does this venture have a large and addressable market? (Market test)
2. Does the current management have the capabilities to make this business
work? (Management test)
The market test focuses on whether the company could conceivably lead to a
large exit. For most VCs, a “large” market is one that could sustain a public
company, with a plausible valuation of several hundred million dollars within about
7.2 THE INVESTMENT PROCESS 137
?ve years. A company developing a novel drug to treat breast cancer is going after a
big market; a company developing a novel drug to treat a disease with only 1,000
sufferers worldwide is not. An “addressable” market is one that can conceivably be
entered by a new company. If a company has a new operating system for personal
computers, the potential market is certainly large, but it is quite unlikely that the
product will make any progress against the Microsoft juggernaut.
The market test requires both art and science. The science component is most
important when you are looking at a business with established markets (e.g., breast
cancer), even if the product is novel (e.g., a new drug). The market test is much
more of an art when the VC is evaluating new markets, either because there are
currently no products in that space, or because the products in that space have not
yet found any path to pro?tability. eBay is an example of a company that addressed
a completely new market. Many VCs scoffed at eBay when it ?rst began, and it is
hard to blame them.
8
Even Benchmark Capital, the eventual investor, did not invest
until the company was already pro?table, although one must still admire its ability
to spot the huge market potential that eventually led to a return of nearly 1,000
times the VC investment. Yahoo! and Netscape are other examples of such new
markets from the early Internet era. On the health care side, the investment in
Genentech, the ?rst company based on the new science of DNA replication, also
required high artistry of market vision.
Google is an example of a company that addressed an existing market, but
one without a clear path to pro?tability. In 1999, at the time of Google’s ?rst (and
only) round of institutional VC investment, Internet search was already old news.
All the major Internet portals had search technology, and search was viewed as
something of a commodity tool on these portals, and not one that could garner huge
pro?t by itself. The bet on Google was essentially a bet that its superior search
technology would eventually lead to a shift in consumer practices, allowing a pure
search site to develop its own revenue stream. This kind of investment requires
business vision that is certainly more art than science, and more than one famous
VC has publicly admitted that his vision failed in this case.
9
8
Bessemer Venture Partners, a VC ?rm with many famous successes, humorously admits their oversights
on the website of their “antiportfolio”: http://www.bvp.com/port/anti.asp. In honest moments, many
other VCs would sympathize with Bessemer’s reaction to eBay: “Stamps? Coins? Comic books? You’ve
GOT to be kidding.” Just as good was the reaction of a Bessemer partner upon learning that the student
founders of Google were renting the garage (yes, the garage) of a college friend: “Students? A new
search engine? How can I get out of this house without going anywhere near your garage?”
9
See the previous footnote for Bessemer Venture Partner’s admission. A second admission comes from
Tim Draper of Draper Fisher Jurvetson, one of our top-tier ?rms from Chapter 5. The April 2005 issue of
the Venture Capital Journal summarizes an interview Draper gave to the San Francisco Chronicle, in
which he says he passed on Google because his ?rm had already backed “some 20 other companies
featuring search engine technology.” The same article also states that another top VC admitted—off the
record—to passing on Google.
138 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Both eBay and Google—the two most successful VC investments of all
time—demonstrate the importance of both sourcing and the initial screen for the
long-term competitive advantage of VCs. In both cases, the opportunities were only
made available to some of the top VCs; “no-name” ?rms never got the chance to
demonstrate their investing vision. Nevertheless, in both cases some of these top
VCs passed on the opportunity, because the large, addressable market was not at all
obvious.
The evaluation of the management team—the management test—is most
qualitative part of screening and due diligence. Many VCs argue that the evaluation
of people is the most important part of their job and believe that success or failure is
driven primarily by the strength of the management team. In evaluating the man-
agement of a start-up company, the VC must form a judgment about both
the individuals and the team. In evaluating individuals, VCs carefully study the
backgrounds and personalities to determine whether the individual has the ability to
carry out her assigned role in the company. The easy cases occur when the indi-
vidual has previous experience in a similar role, which is the main reason that
repeat entrepreneurs are the most prized—particularly the successful ones. Besides
the obvious resume analysis, VCs must use their judgment to decide whether
speci?c individuals have the right temperament to thrive in an entrepreneurial
company. Although many studies have attempted to analyze the characteristics of
successful entrepreneurs, it is fair to say that there is no clear consensus. Instead,
VCs must rely on intuition and experience.
In the evaluation of the entire management team, VCs must make sure that all
the key functions are covered, and that the team dynamics allow all the managers to
play to their strengths. For example, a visionary CEO can act as a great motivator
and salesman for the company, but such CEOs will usually need a strong manager
to handle the details. It is ideal if both roles can coexist, but many times the
visionary will be unwilling to yield operational control, or the detail manager will
be unable to work with a visionary CEO. In many cases VCs may feel that man-
agement teams have most of the necessary skills but lack one crucial component.
This missing piece could be in some speci?c function such as sales or ?nance, or it
could lie in the CEO position. Indeed, many startups are lead by a visionary and
?lled with talent in science and engineering, but lack any managers with entre-
preneurial business experience. In this case, the VC must be able to judge whether
this preexisting team will be able to work with newly recruited players, perhaps
drawn from the VC’s own Rolodex.
The focus on strong management is virtually universal among VCs. An oft-
spoken mantra at VC conferences is, “I would rather invest in strong management
with an average business plan than in average management with a strong business
plan”. This notion is supported by the claims that it is easier for a great management
teamto switch into a newline of business than it is for an average management teamto
execute a good idea. Indeed, claims like this are spoken so often that one might expect
mountains of evidence to support them, but in fact the evidence that does exist points
in the opposite direction. Kaplan, Sensoy, and Stromberg (2005) studied 49 successful
7.2 THE INVESTMENT PROCESS 139
VCinvestments fromtheir early business plans (birth) through their IPOs (exit). They
discovered, to much surprise, that core business lines are remarkably stable frombirth
to exit. On the other hand, management changes are quite common. These results, the
only rigorous evidence that exists on this question, suggest that conventional wisdom
is wrong.
Screening is a crucial step, and poor performance here can ruin the best deal
?ow. There are a variety of approaches to this step. Some ?rms hire junior profes-
sionals to handle much of this task, while the senior VCs focus on later stages of the
investment decision and on the active monitoring of the portfolio companies.
The advantage of this division of labor is that much more time can be dedicated to the
initial screen; the disadvantage is that inexperienced VCs might not do the job as
well. Other ?rms eschewthe use of junior professionals completely, and all screening
is handled by experienced VCs. One can ?nd these ?rms on both ends of the reputation
spectrum, from low-reputation ?rms, who do not have suf?cient deal ?ow and
management fees to justify hiring junior VCs, to high-reputation ?rms, who rely
mostly on referrals froma superior network, thus getting some of the initial screening
for free.
Investments that make it through the screening phase are then subjected to a
preliminary level of due diligence. The screening phase is about identifying
opportunities that meet the market test and the management test; it is a phase
dominated by optimism and happy thoughts. In contrast, due diligence is all about
hard questions and thinking about what can go wrong. The ?rst part of this due
diligence is the meeting of VCs with the company management. This pitch
meeting is a famous touchstone of the VC-entrepreneur relationship. For many
companies, the process ends right there. The pitch meeting is an ideal place to see if
an investment meets the management test, and successful VCs often have a well-
developed sixth sense for sizing up managerial capabilities.
For companies that pass the pitch meeting, the next phase of due diligence
can take many forms. Exhibit 7-12 breaks up the due diligence steps into a pre-
term-sheet step (preliminary diligence) and a post-term-sheet step (?nal diligence).
The fraction of diligence done before the term sheet varies across ?rms, and even
across deals within the same ?rm. In general, the more competitive the deal, the
quicker the ?rm will want to deliver a term sheet, and the more of the diligence that
will be left until afterward. Many term sheets include a period of exclusivity, giving
the VC some time to complete diligence while the company is restricted from
negotiating with other potential investors. In recent years, with less competition and
more wary investors, there has been an increase in the level of diligence done prior
to the term sheet.
Given this variation in the level of diligence in each of these steps, it is not
possible to say what steps belong in the preliminary part and what steps belong in
the ?nal part, so we will just treat both together. Overall, in due diligence the VC
aims to check every part of the company’s story. This is an important part of the
investing process, but one for which we have little hard evidence or academic
research. Thus, given the quantitative focus of this book, it is beyond our scope to
140 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
treat due diligence in detail.
10
Instead we brie?y discuss 12 main topics for a due
diligence investigation: management, market, customers, product, technology,
competition, projections, channels, partners, money, transaction terms, and a ?nal
catchall category of “terrible things”. The ?rst two topics—management and
market—are the two most important, just as they were in the screening phase.
Management
The management test was a key hurdle for the screening stage, and it remains (with the
market test) the most important part of due diligence. At the screening stage,
the management test was about upside, asking whether the present management team
appeared to have the capabilities to execute the company’s business plan. These
questions become much more detailed at the due-diligence stage, with careful eva-
luations of weaknesses on the management team. Often, these evaluations will lead to
VC demands that seasoned executives be hired to ?ll new roles such as CFO or VP of
marketing. This process is only the ?rst step in hands-on recruiting and management
support that VCs provide to their portfolio companies.
In addition to the continued evaluation of managerial capabilities, the due-
diligence stage also includes a detailed level of management vetting. At some ?rms, the
process is just as rigorous as an FBI background check, with job histories, educational
backgrounds, and even personal relationships checked. This vetting function is often
outsourced to specialized agencies.
Market
At the screening stage, the market test required large, addressable markets. In the
due-diligence phase, the ?rst impressions of such markets must be carefully ana-
lyzed. What might have been a quick and dirty estimate now must be backed up by
hard data. Many of the remaining items on this list cover some component of
market due diligence. When all these items are put together, the VC should criti-
cally examine his initial impressions of the overall market and convince himself
(and his partners) that a large, addressable market exists.
Customers
Who are (or will be) the customers for this company? Does the company rely on
just a few key customers? If so, the stability of these relationships must be assessed.
Some VCs will even tag along on a sales call to judge the reaction of potential
customers and to simultaneously evaluate the sales capabilities of the company.
10
Readers interested in a more detailed treatment of due diligence should consult Camp (2002) and
Gladstone and Gladstone (2004).
7.2 THE INVESTMENT PROCESS 141
Product
If the product is already available, how good is it? For certain kinds of products, the
VC can try it out himself. If this is not practical, then at least he can speak with
potential customers to understand the advantages and disadvantages of the product.
In some cases, it is useful to conduct focus groups and surveys. (This last item is
often outsourced.)
Technology
In evaluating technology, it is almost always necessary to consult experts in the
?eld, and access to the right experts is crucial for VCs. One bene?t of high repu-
tation for a VC is the ability to attract a high-quality set of scienti?c advisors for
formal and informal consultations. In addition to the scienti?c evaluation of the
technology, it is also crucial to perform diligence on the legal protection provided
by patents or trade secrets. The best time to ?nd out that a company’s technology
infringes on someone else’s patent is before you make an investment.
Competition
Who is the competition? How will the portfolio company build a sustainable
competitive advantage to compete in this market? Note: If a company claims it has
no competitors or potential competitors, then it is probably wrong. Virtually all
products developed for large, addressable markets will have competition. Under-
estimating the competition is a red ?ag about managerial capabilities.
Projections
All business plans have projections, and of course they are always grossly in?a-
ted.
11
Although such in?ation is expected, it is still important that management
understands how it will grow. If management projects revenue growth of 100
percent over the next year, then at the very least it should have a sales force,
manufacturing plan, and other costs that are consistent with such an increase. Of
course, VCs will make their own projections, but management projections are still a
great window to make sure that the managers really understand their business.
Channels
How does the product actually get sold? A focus on sales channels forces the VC to
understand all the players in the business, both upstream and downstream. In
11
One VC at a top-tier ?rm con?ded a humorous anecdote about one of his ?rm’s portfolio companies.
This particular company received an award from a national magazine as the “fastest growing private
company for the last three years”. Nevertheless, even over this time period the company did not achieve
the management projections from its business plan.
142 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
principle, channel analysis should be an important component of the customer and
projection categories (see earlier discussion). Many potential markets are char-
acterized by standards battles, powerful wholesale players, and relationship-driven
sales at several points in the value chain. Indeed, the analysis of channels is the most
important step in understanding whether a large market is indeed “addressable.”
Partners
Many startup companies are particularly reliant on a few partners. We use the term
“partners” loosely here to mean anything from key suppliers, development partners,
and ?rms with any kind of cooperative agreement. VCs should certainly speak with
any partners and con?rm that the relationships are healthy and stable. A high-
reputation VC can be particularly in?uential in attracting and retaining partners, a
strategy that has particular value in businesses where potential partners and cus-
tomers need to see some evidence of credibility.
Money
How has the company been ?nanced up to this point? How well does it take care of
its cash? What exactly does it intend to do with the investment? VCs should insist
on a high level of ?nancial controls (hence the common requirement to add a CFO)
and should make sure they understand the cash situation of their portfolio com-
panies at all times. Many startups begin on shoestring budget and do not have the
discipline to handle the large new sums from a VC investment. Furthermore, this
analysis must include a reasonable estimate of the total amount of ?nancing that
would be required to reach a successful exit. It is not uncommon for VCs to ?nd
investments that meet the market and management tests but nevertheless are not
viable investments, because their cash needs are so great. The classic example here
is in early stage drug development. To bring a drug through the approval process
has become such an expensive proposition that only a few early stage companies
can qualify for VC ?nancing. Companies with high cash needs are said to have a
high burn rate, meaning that they “burn through cash at a high rate”. The burn rate
can also be used to calculate how long a company can last between rounds of
investment.
Transaction Terms
Although VCs should certainly rely on lawyers for the careful checking of legal
language in the ?nal contracts, there is still work for VCs to do in crafting economic
terms speci?c to each transaction. Many of these terms will be introduced in
Chapter 8 and then discussed in Part III of the book. Transaction terms are a due-
diligence subject, because it is the information uncovered by due diligence that
should lead VCs to ask for (or, in some cases, demand) certain terms in the ?nal
contract. Furthermore, the negotiation of these speci?c terms will often provide
insights into speci?c concerns and private information of management.
7.2 THE INVESTMENT PROCESS 143
Terrible Things
Lots of terrible things can be lurking in the shadows ready to pounce on an
unsuspecting investor. This category encompasses “legal” due diligence (is there
an active or potential lawsuit against the company? Are the ?rms’ incorporation
documents in good order? And so on.). It also includes environmental due diligence
(is the property on a toxic site? Don’t laugh that one off.). Finally, this category is
also a good catchall for anything else that might seem ?shy and require more
digging.
As mentioned earlier, some of this due diligence would be completed before a
term sheet is offered, and some would be completed afterward. Frequently, the ?nal
due diligence will uncover issues that require amending some elements of the term
sheet. Almost always, such amendments improve the terms for the VCs at the
expense of the company. Nevertheless, VCs should resist the temptation to use this
post-due-diligence negotiation as a way to extract extra concessions from their
portfolio companies. Tough negotiation during a period of exclusivity can breed ill
will that lasts for the remainder of the VC’s association with the company. If a poor
relationship begins at this stage, it is often dif?cult for the VC to add value later.
Furthermore, the entrepreneurial community is small enough that bad reputations
can be quickly built, and good reputations can be quickly lost.
Following the acceptance of the term sheet by both parties, the completion of
due diligence, and the negotiation and signing of the ?nal contract, the transaction
closes, often with an anticlimactic wire transfer.
SUMMARY
Before making an investment, a VC must assess the probability of success and potential returns.
The historical evidence can provide a useful benchmark. The extensive database built by Sand
Hill Econometrics tells us that 23.3 percent of all ?rst-round investments eventually had an IPO.
This percentage rises to 28.2 percent for second-round investments and 30.3 percent for third-
round investments. The lower percentage of IPOs in earlier rounds is counterbalanced by higher
returns for these IPOs. Overall, 19.1 percent of all ?rst-round investments earna value multiple of
?ve or more, whereas 43.7 percent return nothing. For second-round investments, we estimate
that 13.7 percent earn a value multiple of ?ve or more, and 38.8 percent return nothing. For later-
round investments, the corresponding percentages are 7.4 percent and 33.7 percent.
Once VCs make an initial screening of an investment, they proceed to a more detailed
level of due diligence. The most important parts of both screening and due diligence are the
assessments of the potential market (“Is it large and addressable?”) and the quality of
management (“Is it good enough to execute the business plan?”). These major questions are
supplemented by analyses in 10 major areas: customers, product, technology, competition,
projections, channels, partners, money, transaction terms, and terrible things.
144 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
KEY TERMS
Screening
Term sheet
Due diligence
Closing
Deal flow, sourcing, pro-
prietary deal flow
Business plan
The market test
The management test
Pitch meeting
Burn rate
REFERENCES
Camp, Justin J., 2002, Venture Capital Due Diligence, Wiley, New York.
Gladstone, David, and Laura Gladstone, 2004, Venture Capital Investing, Prentice Hall, Upper Saddle
River, New Jersey.
Kaplan, Steven N., Berk Sensoy, and Per Stromberg, 2009, “Should Investors Bet on the Jockey or
the Horse? Evidence from the Evolution of Firms from Early Business Plans to Public Companies”,
Journal of Finance 64(1), 75À115.
Stross, Randall E., 2000, eBoys, Crown Publishers, New York.
Venture Capital Journal, 2005, April.
REFERENCES 145
CHAPTER 8
TERM SHEETS
IN THIS CHAPTER, we step through a sample term sheet for a $5M invest-
ment. This sample term sheet is a simpli?ed version of the Model Term Sheet
produced by the National Venture Capital Association (NVCA) and is available in
the most up-to-date version on its website.
1
The complete Model Term Sheet, as
last updated April 2009, is given in Appendix A at the back of this book.
A VC typically signals its intention to invest by offering a term sheet to the potential
portfolio company. The company responds by signing the term sheet, rejecting it
completely, or negotiating changes to some of the provisions. If the parties can agree
on a term sheet, then it is signed, and the VC proceeds to a detailed level of due
diligence, usually with a period of exclusivity spelled out in the term sheet. Term
sheets can be thought of as starting points for a good-faith negotiation. Although few
term sheet provisions have binding consequences if they are not followed, the
document still serves as an anchor for all future negotiations between the parties.
Term sheets are broken into sections, with each section providing a summary
for a longer legal document that will be executed at closing. In Section 8.1 we give the
basic opening information of our sample term sheet, including the size of
the investment, the parties involved, and the proposed capitalization for the company.
In Section 8.2 we discuss the Charter section of the termsheet, which includes many
of the most hotly negotiated provisions. In Section 8.3 we cover the Investor Rights
Agreement, a relatively long and technical section of the termsheet. Finally, Section
8.4 covers the remaining portions of the term sheet under the label of “Other Items”.
In most sections of this chapter, we begin with a verbatim reproduction of a
section in the term sheet. This is followed by a discussion of several (but not all) of
the provisions. During this discussion, we often reference the survey ?ndings from the
sixth Edition of the DowJones Venture Capital Deal Terms Report, which is referred to
as the “Dow Jones Report”. This report gives the ?ndings from a recent survey of
completed deals while allowing us to see the relative popularity of different provisions.
1
Check http://www.nvca.org/index.php?option5com_content&view5article&id5108&Itemid5136 for
the most recent version.
146
This chapter contains a good deal of legal jargon and technical terminology.
However, to master the concepts of VC, there is no escaping some of this detail—
but it is helpful to remember the big picture. VCs are usually minority investors in
high-risk businesses, and the investment they provide is at the mercy of a small
number of managers. VC contracts are designed to protect this investment from
expropriation, which can occur either through negligence (low effort by managers)
or malice (stealing or self-dealing). Thus the big picture is that a term sheet
describes the basic structure of a transaction and provides a set of protections
against expropriation.
8.1 THE BASICS
The search for VC funding is time-consuming and economically costly. These costs
make it inef?cient for companies to constantly be looking for new investors.
Instead, as ?rst discussed in Chapter 1, VCs make lumpy investments organized
into sequential rounds. A ?rst-round investment is designated as Series A, a
second-round investment as Series B, and so on. The sample term sheet that fol-
lows describes a Series A investment.
TERM SHEET FOR SERIES A PREFERRED STOCK FINANCING OF
Newco Inc. January 1, 2010
This Term Sheet summarizes the principal terms of the Series A Preferred Stock Financing of
[___________], Inc., a [Delaware] corporation (the “Company”). In consideration of the
time and expense devoted and to be devoted by the Investors with respect to this investment,
the No Shop/Con?dentiality [and Counsel and Expenses] provisions of this Term Sheet shall
be binding obligations of the Company, whether or not the ?nancing is consummated. No
other legally binding obligations will be created until de?nitive agreements are executed and
delivered by all parties. This Term Sheet is not a commitment to invest, and is conditioned on
the completion of due diligence, legal review, and documentation that is satisfactory to the
Investors. This Term Sheet shall be governed in all respects by the laws of the [State of
Delaware], and does not constitute an offer to sell or a solicitation of an offer to buy
securities in any state where the offer or sale is not permitted.
Offering Terms
Closing Date: As soon as practicable following the Company’s acceptance of this Term
Sheet and satisfaction of the Conditions to Closing (the “Closing”).
Investors: Early Bird Ventures I (“EBV”): 5,000,000 shares (33.33%), $5,000,000
Amount Raised: $5,000,000
Price Per Share: $1 per share (based on the capitalization of the Company set forth below)
(the “Original Purchase Price”).
(Continued)
8.1 THE BASICS 147
Pre-Money
Valuation:
The Original Purchase Price is based upon a fully-diluted pre-money
valuation of $10,000,000 and a fully-diluted post-money valuation of
$15,000,000 (including an employee pool representing 15% of the fully-
diluted post-money capitalization).
Capitalization: The Company’s capital structure before and after the Closing is set forth
below:
Pre-Financing Post-Financing
Security # of Shares % # of Shares %
Common—Founders 7,750,000 77.5 7,750,000 51.7
Common—Employee Stock Pool 2,250,000 22.5 2,250,000 15.0
Issued 300,000 3.0 300,000 2.0
Unissued 1,950,000 19.5 1,950,000 13.0
Series A Preferred 0 0.0 5,000,000 33.3
Total 10,000,000 100 15,000,000 100
8.1.1 Investors
This section of the term sheet lists all investors, the dollar amount of their investment
(which we will call the $investment), and the number of shares they receive for this
amount. In this case, the investment implies ownership of 33.33 percent of the
company on a fully diluted basis (which assumes that all preferred stock is converted
and that all options are exercised). The details of the fully diluted share count are
given in the capitalization table immediately preceding this paragraph. We refer to
the 33.33 percent represented by the Series Aas the proposed ownership percentage,
a number that will play an important role in our analysis.
In this term sheet, all of the $investment is paid at one time. In some cases,
the $investment is spread across multiple payments, known as tranches, which
may be contingent on the ?rm reaching some prespeci?ed milestones, such as the
development of a working prototype for a product, the ?rst major customer, or
some speci?c level of sales. The Dow Jones Report tells us that about 19 percent of
all rounds had such tranches in the July 2007ÀJune 2008 period, with this fre-
quency higher in ?rst rounds (Series A) than in later rounds. Anecdotal evidence
suggests that such tranching is more common in weak VC markets (such as the
postboom) than it is in strong markets (such as the boom period).
2
Most analysis in
this book is appropriate only for one-time investments without additional tranches.
The analysis of tranched investments requires speci?c modeling of each milestone.
2
Consistent with this view, the rounds with tranches were 16.5% of total in the July 2006ÀJune 2007
period, according to the Dow Jones Report.
148 CHAPTER 8 TERM SHEETS
The real-options analysis of Chapter 21 can provide some direction for this
modeling, but in general it is not possible to build a general framework that can
handle all possible cases.
8.1.2 Price Per Share
The price per share, also called the original purchase price (OPP), serves as the
basis for many other calculations in VC transactions. In this example, the OPP is
straight forward to compute, because there is only one type of security, and it has a
set number of shares. However, in cases with multiple security types, the OPP
computation can be more arbitrary. We will give an example of such a computation
in Chapter 9.
In this book, we will also use the term aggregate purchase price (APP) to
refer to the price paid for all shares of a security, where APP 5OPP Ã shares
purchased. When there is only one security type, the APP is equal to $investment.
When there are multiple security types, then the exact division of $investment into
the APP for each security is important.
8.1.3 Pre-Money and Post-Money Valuation
Pre-money valuation and post-money valuation are heavily used terms in the VC
industry. In principle, post-money valuation is an analogue to market capitalization
for public companies. To compute (equity) market capitalization for a public
company, we multiply the price per share times the number of shares outstanding.
Post-money valuation is calculated the same way:
Post-money valuation 5price per share à fully diluted share count: ð8:1Þ
For our example, this calculation gives us $1 Ã 15M5$15M. An alternative
way to calculate post-money valuation is as follows:
Post-money valuation 5 $investment=proposed ownership percentage: ð8:2Þ
This method also gives us $15M, this time as $5M/0.3333. Equations (8.1)
and (8.2) are completely equivalent and are used interchangeably in practice.
Pre-money valuation is the market capitalization of the company before the
VC investment. We can compute it by simply subtracting the investment from the
post-money valuation:
Pre-money valuation5post-money valuation2$investment: ð8:3Þ
For our example, we get a pre-money valuation of $15M2$5M5$10M. An
alternative method to compute the pre-money valuation is to multiply the price per
share by the pretransaction shares outstanding:
Pre-money valuation
5price per share à pretransaction ðfully dilutedÞ share count: ð8:4Þ
8.1 THE BASICS 149
The pretransaction share count of 10M includes everything except the VC
shares. We can observe this share count in the ?rst set of columns in the capita-
lization table. Like equation (8.3), this alternative calculation gives us a pre-money
valuation of $1 Ã 10M5$10M.
3
In many VC transactions, the pre-money and post-money valuations are the
key terms discussed by the parties. Although these terms are certainly useful for
quickly communicating some basic aspects of a transaction, it is important to note
that they can be misleading about certain details. Speci?cally, the analogy to
market capitalization breaks down once we acknowledge that preferred stock
(which VCs usually buy) can be quite different from common stock (which
founders usually own). Because the post-money and pre-money calculations do not
distinguish between preferred and common stock, the results of these calculations
do not necessarily re?ect anything about the market value of the company. To
accurately compute the implied market value of a company, we will need the
option-pricing tools developed in Part III of this book. Once these tools have been
developed, we dedicate all of Chapter 17 to this computation.
8.1.4 Capitalization
The ?nal part of this introductory section is the capitalization table. In addition
to the categories used here, a capitalization table might also include shares owned
by previous investors (including angel investors and VCs from earlier rounds) or
additional security types purchased in this round. Some possible security types will
be discussed at length in Chapter 9. For now, we will note without comment that, in
contrast to the common stock held by founders and employees, VCs typically
purchase some form of preferred stock.
The capitalization table will always include a section for the employee stock
pool, which contains shares set aside as incentive compensation for employees. The
employees are usually issued call options on common stock, and the stock pool is used
to provide shares onthe exercise of these options. Because VC-backed companies rely
heavily on options for compensation, VCs typically insist that the expected option
compensation be included in the capitalization table at the time of ?nancing. In our
example, we include a pool that represents 15 percent of the fully diluted share count.
This choice is consistent with historical industry practice according to the DowJones
Report, though there seems to be a downward trend in the most recent two survey
years (2007 and 2008). Also note that this number is lower for later rounds, as they
have more shares issued to investors. Fifteen percent has become a focal point for
stock pools and is both the median and mode in the Dow Jones Report.
3
Equation (8.4) can yield an incorrect answer for pre-money valuation in cases where antidilution
protections have been triggered. Chapter 9 gives an example and a discussion of this point. For safety, an
analyst can always use Equation (8.3) to compute pre-money valuation.
150 CHAPTER 8 TERM SHEETS
8.2 THE CHARTER
The Charter, also known as the Certi?cate of Incorporation, is a public document
?led with the state in which the company is incorporated. In the majority of VC
transactions, this state is Delaware, which has the best-developed and best-understood
corporate law. Among other things, the Charter establishes the rights, preferences,
privileges, and restrictions of each class and series of the company’s stock.
Charter
Dividends: Dividends will be paid on the Series A Preferred on an as-converted basis
when, as, and if paid on the Common Stock.
Liquidation
Preference:
In the event of any liquidation, dissolution, or winding up of the
Company, the proceeds shall be paid as follows:
First pay one times the Original Purchase Price on each share of Series A
Preferred. The balance of any proceeds shall be distributed to holders of
Common Stock.
A merger or consolidation (other than one in which stockholders of the
Company own a majority by voting power of the outstanding shares of
the surviving or acquiring corporation) and a sale, lease, transfer, or other
disposition of all or substantially all of the assets of the Company will be
treated as a liquidation event (a “Deemed Liquidation Event”), thereby
triggering payment of the liquidation preferences described above.
[Investors’ entitlement to their liquidation preference shall not be
abrogated or diminished in the event part of consideration is subject to
escrow in connection with a Deemed Liquidation Event.]
Voting Rights: The Series A Preferred Stock shall vote together with the Common Stock
on an as-converted basis, and not as a separate class, except (i) the Series A
Preferred as a class shall be entitled to elect two members of the Board (the
“Series A Directors”), and (ii) as required by law. The Company’s
Certificate of Incorporation will provide that the number of authorized
shares of Common Stock may be increased or decreased with the approval
of a majority of the Preferred and Common Stock, voting together as a
single class, and without a separate class vote by the Common Stock.
Protective
Provisions:
So long as any shares of Series A Preferred are outstanding, in
addition to any other vote or approval required under the Company’s
Charter or By-laws, the Company will not, without the written consent
of the holders of at least 50% of the Company’s Series A Preferred,
either directly or by amendment, merger, consolidation, or otherwise:
(i) liquidate, dissolve, or wind-up the affairs of the Company, or effect any
Deemed Liquidation Event; (ii) amend, alter, or repeal any provision of the
Certificate of Incorporation or Bylaws; (iii) create or authorize the creation
of or issue any other security convertible into or exercisable for any equity
(Continued)
8.2 THE CHARTER 151
security, having rights, preferences, or privileges senior to or on parity with
the Series A Preferred, or increase the authorized number of shares of
Series APreferred; (iv) reclassify, alter, or amend any existing security that
is junior to or on parity with the Series APreferred, if such reclassification,
alteration, or amendment would render such other security senior to or on
parity with the Series A Preferred; (v) purchase or redeem or pay any
dividend on any capital stock prior to the Series A Preferred; or (vi) create
or authorize the creation of any debt security; (vii) create or hold capital
stock in any subsidiary that is not a wholly owned subsidiary, or dispose of
any subsidiary stock or all or substantially all of any subsidiary assets; or
(viii) increase or decrease the size of the Board of Directors.
Optional
Conversion:
The Series A Preferred initially converts 1:1 to Common Stock at any
time at option of holder, subject to adjustments for stock dividends, splits,
combinations, and similar events and as described below under “Anti-
dilution Provisions”.
Anti-dilution
Provisions:
In the event that the Company issues additional securities at a purchase
price less than the current Series A Preferred conversion price, such
conversion price shall be reduced to the price at which the new shares are
issued.
The following issuances shall not trigger anti-dilution adjustment:
(i) securities issuable upon conversion of any of the Series A Preferred, or
as a dividend or distribution on the Series APreferred; (ii) securities issued
upon the conversion of any debenture, warrant, option, or other convertible
security; (iii) Common Stock issuable upon a stock split, stock dividend, or
any subdivision of shares of Common Stock; and (iv) shares of Common
Stock (or options to purchase such shares of Common Stock) issued or
issuable to employees or directors of, or consultants to, the Company
pursuant to any plan approved by the Company’s Board of Directors.
Mandatory
Conversion:
Each share of Series A Preferred will automatically be converted into
Common Stock at the then-applicable conversion rate (i) in the event of
the closing of an underwritten public offering with a price of 5 times the
Original Purchase Price (subject to adjustments for stock dividends,
splits, combinations and similar events) and net proceeds to the Company
of not less than $15,000,000 (a “Qualified Public Offering” 5“QPO”), or
(ii) upon the written consent of the holders of 75% of the Series A
Preferred.
Redemption
Rights:
The Series A Preferred shall be redeemable from funds legally
available for distribution at the option of holders of at least 50% of
the Series A Preferred commencing any time after the fifth anniversary
of the Closing at a price equal to the Original Purchase Price plus all
accrued but unpaid dividends. Redemption shall occur in three equal
annual portions. Upon a redemption request from the holders of the
required percentage of the Series A Preferred, all Series A Preferred
shares shall be redeemed (except for any Series A holders who
affirmatively optout).
152 CHAPTER 8 TERM SHEETS
8.2.1 Dividends
In public companies, preferred stock is usually issued with the promise of cash
dividends. However, preferred stock in VC transactions rarely promises cash divi-
dends, because portfolio companies are usually cash poor, and these dividends would
accelerate the need for more ?nancing. Instead, some term sheets—like our exam-
ple—will give a dividend preference to preferred stock, meaning that you cannot
pay any dividends to common stock unless you ?rst pay dividends to the preferred.
This is essentially a way to prevent the management of the company from sneaking
cash out to common shareholders. Alternatively, the preferred stock might receive
accrued cash dividends to be paid in cash only upon a deemed liquidation event (see
the Liquidation Preference topic of the Charter for a de?nition).
Finally, the preferred stock might receive stock dividends, which adds the
total holdings of preferred. Such stock is called payment-in-kind (“PIK”) preferred.
Dividend rights may be cumulative or noncumulative—the difference being that
cumulative dividends accrue even if not paid, whereas noncumulative dividends only
accrue during the ?nal period before they are paid. Cumulative dividends can accrue
by simple interest (the same ?at percentage every year on the OPP) or by com-
pound interest (which includes dividends paid on previous dividends.) Overall,
dividends may be either for cash (accrued cash dividends) or stock (PIK dividends),
each type of dividends may be cumulative or noncumulative, and cumulative divi-
dends may be by simple or compound interest. See the NVCA model term sheet in
Appendix A for the example language for several of these cases.
8.2.2 Liquidation Preference
When a company is sold, merged, or shut down—a deemed liquidation event—the
proceeds are distributed to bondholders, preferred stockholders, and common
stockholders, in that order. A liquidation preference tells an investor where she
stands in the capital structure hierarchy. In our example, there is no debt and only
one round of VC investment, so the Series A preferred is getting the ?rst dollar from
any liquidation. When there have been multiple rounds of investment, it is common
for the latest-round investors to get their money back ?rst. Thus, Series D investors
would have liquidation preference to Series C investors, Series C investors would
be preferred relative to Series B, and so on. An alternative to this ordering, known
as “pari passu”, is for all (or some) preferred investors to be paid back at the same
time. The Dow Jones Report ?nds that about two-thirds of deals give the latest-
round investors priority over all other (earlier) classes of preferred stock.
In some cases, investors insist on liquidation preferences in excess of their
original investment. For example, a 2X or 3X liquidation preference requires that the
investor be paid back double or triple, respectively, their original investment before
any of the other (junior) equity claims are paid off. In the term sheet, we would write
a 2X liquidation preference by replacing the second section of the liquidation pre-
ference section with “First pay two times the Original Purchase Price”. The Dow
8.2 THE CHARTER 153
Jones Report ?nds that about one-quarter of all deals contain an excess liquidation
preference, with about 70 percent of these preferences being 2X or less.
8.2.3 Voting Rights and Other Protective Provisions
As discussed earlier, most of what we see in term sheets can be understood as VCs
(the minority shareholders) protecting themselves from expropriation by the majority
shareholders. Several of these methods of protection are contained in the voting
rights and protective provisions part of the term sheet. In our example, the Series A
investors are guaranteed two spots on the board and are also given the power to block
some corporate actions with a separate vote. In the Investor Rights Agreement part
of the term sheet (addressed in Section 8.3), we are told that the board will contain
?ve members in total, with two members selected by Series A, two by the founders,
and one that is acceptable to all parties. Thus in our example, EBV will control
approximately half of the board while only having one-third of the fully diluted
shares. Such shared control is typical following Series A investments, including
more than half of all cases in the Dow Jones Report. In contrast, after receiving
Series B and later rounds of VC ?nancing, boards of ventures are increasingly
controlled collectively by the investors.
The Dow Jones Report ?nds that about three-quarters of all deals contain
some form of antidilution protection. In principle, these provisions protect inves-
tors’ stakes if future investments are done at a lower price per share; such investments
are known in the industry as a down round. The details of antidilution provisions
can quickly get quite messy; we will cover this topic in detail in Chapter 9.
8.2.4 Mandatory Conversion
Convertible preferred stock usually converts to common stock at the discretion of
the investor. Some events, however, may trigger an automatic conversion, such as a
quali?ed public offering (QPO), which is a public offering that meets certain
thresholds (for example, dollars raised or price per share). In our example, the QPO
would require an offering of at least $15M and a price per share of ?ve times the
OPP 5$5 per share.
8.2.5 Redemption Rights
For situations other than liquidation, redemption rights give conditions under which
investors can demand that the company redeem (pay back) their initial investment.
Examples of such conditions include a prespeci?ed length of time or failure to meet
certain milestones. In our example, these rights would commence ?ve years after the
original investment—but in practice, redemption rights are rarely exercised, in part
because the legal status of preferred stock as “equity” restricts the power of preferred
holders to demand repayment of their investment. Although the language of
redemption rights tries to get around these restrictions—for example, “the Series
154 CHAPTER 8 TERM SHEETS
A Preferred shall be redeemable from funds legally available for distribution”—the
reality is that redemption rights don’t provide much leverage unless the company is
cash rich and can easily pay the investors back.
8.3 INVESTOR RIGHTS AGREEMENT
Investor Rights Agreement
Registration Rights:
Registrable Securities: All shares of Common Stock issuable upon conversion of the
Series A Preferred and any other Common Stock held by
the Investors will be deemed “Registrable Securities”.
Demand Registration: Upon earliest of (i) five years after the Closing; or (ii) six months
following an initial public offering (“IPO”), persons holding 25%
of the Registrable Securities may request one (consummated)
registrationbythe Company of their shares. The aggregate offering
price for such registration may not be less than $10 million. A
registration will count for this purpose only if (i) all Registrable
Securities requested to be registered are registered and (ii) it is
closed, or withdrawn at the request of the Investors (other than as a
result of a material adverse change to the Company).
Registration on Form S-3: The holders of 10% of the Registrable Securities will have the
right to require the Company to register on Form S-3, if
available for use by the Company, Registrable Securities for
an aggregate offering price of at least $1 million. There will be
no limit on the aggregate number of such Form S-3 registra-
tions, provided that there are no more than two per year.
Piggyback Registration: The holders of Registrable Securities will be entitled to “piggy-
back” registration rights on all registration statements of the
Company, subject to the right, however, of the Company and its
underwriters to reduce the number of shares proposed to be
registered to a minimumof 30%on a pro rata basis and to complete
reduction on an IPO at the underwriter’s discretion. In all events,
the shares to be registered by holders of Registrable Securities will
be reduced only after all other stockholders’ shares are reduced.
Expenses: The registration expenses (exclusive of stock transfer taxes, under-
writingdiscounts, andcommissions) will be borne bythe Company.
The Company will also pay the reasonable fees and expenses.
Lockup: Investors shall agree in connection with the IPO, if requested by
the managing underwriter, not to sell or transfer any shares of
(Continued)
8.3 INVESTOR RIGHTS AGREEMENT 155
Common Stock of the Company for a period of up to 180 days
following the IPO subject to extension to facilitate compliance
with FINRA rule (provided all directors and officers of the
Company and 5% stockholders agree to the same lockup). Such
lockup agreement shall provide that any discretionary waiver or
termination of the restrictions of such agreements by the
Company or representatives of the underwriters shall apply to
Investors, prorata, based on the number of shares held.
Management and
Information Rights:
A Management Rights letter from the Company, in a form
reasonably acceptable to the Major Investors, will be delivered
prior to Closing to each Investor that requests one.
Any Major Investor will be granted access to Company facilities
and personnel during normal business hours and with reasonable
advance notification. The Company will deliver to the Investor
(i) annual and quarterly financial statements, and other informa-
tion as determined by the Board; (ii) thirty days prior to the end
of each fiscal year, a comprehensive operating budget forecast-
ing the Company’s revenues, expenses, and cash position on a
month-to-month basis for the upcoming fiscal year; and (iii)
promptly following the end of each quarter an up-to-date
capitalization table. A “Major Investor” means any Investor
who purchases at least $1 million of Series A Preferred.
Right to Maintain
Proportionate Ownership:
All Major Investors shall have a pro rata right, based on their
percentage equity ownership in the Company (assuming the
conversion of all outstanding Preferred Stock into Common
Stock and the exercise of all options outstanding under the
Company’s stock plans), to participate in subsequent issuances
of equity securities of the Company (excluding those issuances
listed at the end of the “Anti-dilution Provisions” section of this
Term Sheet). In addition, should any Major Investor choose not
to purchase its full pro rata share, the remaining Major Investors
shall have the right to purchase the remaining pro rata shares.
Matters Requiring
Investor Director
Approval:
So long as the holders of Series A Preferred are entitled to elect
a Series A Director, the Company will not, without Board
approval, which approval must include the affirmative vote of
100% of the Series A Director(s):
(i) make any loan or advance to, or own any stock or other
securities of, any subsidiary or other corporation, partnership, or
other entity, unless it is wholly owned by the Company; (ii) make
any loan or advance to any person, including any employee or
director, except advances and similar expenditures in the ordinary
course of business or under the terms of a employee stock or
option plan approved by the Board of Directors; (iii) guarantee
any indebtedness except for trade accounts of the Company or any
subsidiary arising in the ordinary course of business; (iv) make
any investment inconsistent with any investment policy approved
156 CHAPTER 8 TERM SHEETS
by the Board; (v) incur any aggregate indebtedness in excess of $1
million that is not already included in a Board-approved budget,
other than trade credit incurred in the ordinary course of business;
(vi) enter into orbea party to any transaction with any director,
officer, or employee of the Company or any “associate”
(as defined in Rule 12b-2 promulgated under the Exchange Act)
of any such person except transactions resulting in payments to
or by the Company in an amount less than $60,000 per year [or
transactions made in the ordinary course of business and pursuant
to reasonable requirements of the Company’s business and upon
fair and reasonable terms that are approved by a majority of the
Board of Directors]; (vii) hire, fire, or change the compensation of
the executive officers, including approving any option plans;
(viii) change the principal business of the Company, enter new
lines of business, or exit the current line of business; or (ix) sell,
transfer, license, pledge, or encumber technology or intellectual
property, other than licenses granted in the ordinary course of
business; or (x) enter into any corporate strategic relationship
involving the payment contribution or assignment by the Com-
pany or to the Company of assets greater than $100,000.00.
Non-Competition and
Non-Solicitation
and Agreements:
Each Founder and key employee will enter into a one-year non-
competition and non-solicitation agreement in a form reason-
ably acceptable to the Investors.
Non-Disclosure and
Developments Agreement:
Each current and former Founder, employee, and consultant will
enter into a non-disclosure and proprietary rights assignment
agreement in a form reasonably acceptable to the Investors.
Board Matters: Each non-employee director shall be entitled in such person’s
discretion to be a member of any Board committee.
The Board of Directors shall meet at least quarterly, unless
otherwise agreed by a vote of the majority of Directors.
The Company will bind D&O insurance with a carrier and in an
amount satisfactorytotheBoardof Directors. Companyshall agree
that its indemnification obligations to Series A Directors are
primary, and obligations of affiliated Investors are secondary. In
the event the Company merges with another entity and is not the
surviving corporation, or transfers all of its assets, proper provi-
sions shall be made so that successors of the Company assume
Company’s obligations with respect to indemnification of
Directors.
Employee Stock Options: All employee options to vest as follows: 25%after one year, with
remaining vesting monthly over next 36 months.
Key Person Insurance: Company to acquire life insurance on Founders in an amount
satisfactory to the Board. Proceeds payable to the Company.
8.3 INVESTOR RIGHTS AGREEMENT 157
8.3.1 Registration Rights
Stock purchased in private transactions is restricted. This means that the stock
cannot be sold in a public offering. To lose this restriction, a transaction must be
registered. Registration means ?ling legal documents and disclosing data about
the ?rm to the SEC. This is a costly activity that ?rms like to avoid.
Even if no other shares are being sold, demand registration rights allow
investors to force the company to register a transaction for their shares. Term sheets
spell out exactly how often such rights can be exercised and for how many shares.
S-3 registration rights are weaker than demand rights, because they are only
useful if the company is already reporting to the SEC. Piggyback registration
rights are even weaker than S-3 rights; they allow investors to go along with a
registered transaction already being prepared for other shares. These are much less
costly to a company than demand rights.
Rule 144 is an exception to the registration rules, allowing shares to be sold to
the public after they have been held for a certain period of time (as long as the
company has some other public shares or follows ?ling requirements with the SEC).
As of 2010, the rule allows unlimited sales by non-insiders of otherwise restricted
stock after it has been held for at least one year; such sales can often be made by LPs
after in-kind distributions of stock by the GP. In addition, the rule allows for
unlimited sales by non-insiders after the stock has been held for at least six months
but less than one year, as long as adequate current information about the Company
is publicly available. In contrast, sales by insiders (such as GPs who sit on the board
of the Company) are subject to additional volume and ?ling restrictions. Rule 144A
is another exception that allows resale of stock or debt to Quali?ed Institutional
Buyers (QIBs) outside the registration process; QIBs are institutions with more
than $100 million in investment assets under management. All insider stock tends to
be subject to an additional lockup—often 180 days—after an IPO. This lockup is
contractually imposed by the underwriter and is independent of the SEC restrictions.
8.3.2 Matters Requiring Investor-Director Approval
This category of investor rights attempts to give minority investors protection
against a laundry list of possible expropriation by managers and other investors.
The standardized list in the Newco termsheet contains 10 items. While these lists
can run much longer, the danger of a very long list is that the company will be
hamstrung in its ability to operate the business. Overall, VCs must walk a ?ne line
between protecting their investment and encouraging corporate growth.
8.3.3 Employee Stock Options
When key employees are hired, they are typically given shares or options to buy
shares in the company as part of their compensation. If such shares are promised,
they are usually earned over time, or vested. Step vesting often occurs at annual,
158 CHAPTER 8 TERM SHEETS
quarterly, or monthly increments, usually over periods of three to ?ve years. Cliff
vesting takes place all at one time. Some contracts—like this Newco termsheet—
use step vesting for part of the shares and cliff vesting for the rest. In this case, we
see cliff vesting of 25 percent after one year, with monthly step vesting for the next
36 months. Vesting is sometimes also used for founders’ shares at the time of the
?rst venture capital investment, meaning that a founder who previously “owned”
the whole company must now temporarily hand back his ownership stake and stay
for a few years before he gets it back.
8.4 OTHER ITEMS
Stock Purchase Agreement
Representations and
Warranties:
Standard representations and warranties by the Company.
Conditions to Closing: Standard conditions to Closing, which shall include,among other
things, satisfactory completion of financial and legal due dili-
gence, qualification of the shares under applicable Blue Sky laws,
the filing of a Certificate of Incorporation establishing the rights
and preferences of the Series A Preferred, and an opinion of
counsel to the Company.
Counsel and Expenses: Investor counsel to draft closing documents. Company to pay all
legal and administrative costs of the financing at Closing,
including reasonable fees and expenses of Investor counsel.
Right of First Refusal/Co-Sale Agreement and Voting Agreement
Right of first Refusal/
Right of Co-Sale
(Take-me-Along):
Company first and Investors second (to the extent assigned by the
Board of Directors) have a right of first refusal with respect to any
shares of capital stock of the Company proposed to be sold by
Founders and employees holding greater than 1% of Company
Common Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of options), with a
right of oversubscription for Investors of shares unsubscribed by
the other Investors. Before any such person may sell Common
Stock, he will give the Investors an opportunity to participate in
such sale on a basis proportionate to the amount of securities held
by the seller and those held by the participating Investors.
Lockup: Founders will not transfer, hedge, or otherwise dispose of any
capital stock following an IPO for a period specified by the
Company and the managing underwriter (not to exceed 180 days).
(Continued)
8.4 OTHER ITEMS 159
Board of Directors: At the initial Closing, the Board shall consist of five members
comprised of (i) Joe Veesee, as a representative designated by
EBV, (ii) Jane Vencap as a representative designated by EBV, (iii)
Jim Goodfriend as a representative designated by the Founders, (iv)
Neel Onterpraynoor, the Chief Executive Officer of the Company,
and (v) one person who is not employed by the Company and who
is mutually acceptable to the Founders and Investors.
Other Matters
Founders’ Stock: All Founders to own stock outright, subject to Company’s right to
buyback at cost. Buyback right for 50% for first 12 months after
Closing; thereafter, right lapses in equal monthly increments over
following 36 months.
No Shop/Confidentiality: The Company agrees to work in good faith expeditiously towards a
closing. The Company and the Founders agree that theywill not, for a
period of six weeks from the date these terms are accepted, take any
action to solicit, initiate, encourage, or assist the submission of any
proposal, negotiation, or offer fromany person or entity other than the
Investors relating to the sale or issuance, of any of the capital stock of
the Company or the acquisition, sale, lease, license, or other disposi-
tion of the Company, or any material part of the stock or assets of
the Company, and shall notifythe Investors promptlyof any inquiries
by any thirdparties in regards to the foregoing. The Company will not
disclosethe terms of this TermSheet toanypersonother thanofficers,
members of the Board of Directors, the Company’s accountants and
attorneys, and other potential Investors acceptable to EBV, as lead
Investor, without the written consent of the Investors.
Expiration: This Term Sheet expires on January 8, 2010 if not accepted by the
Company by that date.
8.4.1 Rights and Restrictions
Investors want key personnel in their portfolio ?rms to have ?nancial incentives to
stay and work hard. They also want to prevent founders from exiting in “sweet-
heart” transactions. To achieve these goals, transfer restrictions may be placed on
a founder’s (or an investor’s) shares. Such restrictions may prevent all sales of
founders’ stock without express permission from later investors, or may allow later
investors to participate in such sales (called take-me-along or tag-along rights), or
be offered the shares before anyone else (right of ?rst offer), or have the option to
participate at the price that has been offered by other parties (right of ?rst refusal).
Another type of transfer provision not seen in this term sheet is a drag-along right,
which provides a selling investor with the ability to force other investors to sell
their stakes at the same price. Drag-along rights can be useful for investors who
need to force a sale of the whole ?rm.
160 CHAPTER 8 TERM SHEETS
8.4.2 Founders’ Stock
The buyback right on founders’ stock is usually valid only when founders have been
dismissed from the ?rm “for cause”. The de?nition of “for cause” is often a sticking
point in the ?nal negotiations. Note that this buyback right means that founder
shares are effectively vested at a similar rate to employee options. Although this
might seem unfair—after all, the founders may have been committed to the ?rm for
many years already—the founders are often so crucial to the company that the VC
needs to make sure that they have strong incentives to stick around.
SUMMARY
The term sheet is a preliminary agreement used to anchor the key contractual provisions for a
VC investment. The term sheet begins with the basic information of the investment and
includes a summary for many of the contractual documents needed for the ?nal closing. Most
term sheet provisions can be understood as attempts by minority shareholders (VCs) to
protect themselves from expropriation by managers and majority shareholders. For valuation
purposes, the most important portion of the term sheet is the information about investment
size, price per share, and security type. Most VC securities are preferred stock: the rights of
these preferred shares are described in the company’s Charter. Additional restrictions on
corporate activities and the reporting requirements to the investors are described in the
Investor Rights Agreement.
KEY TERMS
Term Sheet, Charter, Inves-
tor Rights Agreement
Expropriation
Rounds
Series A investment
$investment
Original purchase price
(OPP), Aggregate
purchase price (APP)
Fully diluted basis, fully
diluted share count
Capitalization table
Proposed ownership
percentage
Tranch
Pre-money valuation,
post-money valuation
Deemed liquidation event
Dividend preference
Stock dividends
5 payment-in-kind
(PIK) dividends
Accrued cash dividend
Cumulative dividends,
noncumulative dividends
Simple interest, compound
interest
Liquidation preference, 2X
(3X, 4X, etc.) excess
liquidation preference
Down round
Qualified public offering
(QPO)
Redemption rights
Restricted stock
Registration rights, demand
registration rights, S-3
registration rights,
piggyback registration
rights
Rule 144, Rule 144A
In-kind distributions
Qualified Institutional
Buyers (QIBs)
Lockup
Step vesting, cliff vesting
Transfer restrictions,
take-me-along
5 tag-along, right of first
offer, right of first refu-
sal, drag-along
KEY TERMS 161
REFERENCES
Dow Jones, 2009, Deal Terms Report, 6th Edition, Jersey City, NJ.
National Venture Capital Association, 2009, Model Term Sheet, available at http://www.nvca.org/index.
php?option=com_content&view=article&id=108&Itemid=136.
EXERCISES
8.1 True, False, or Uncertain: After a portfolio company has an IPO, the VCs are free to sell
their stock in this company in the public market.
8.2 EBV is considering a $6M Series A investment for 6M shares of CP at $1 per share. The
proposed capitalization table for Newco is as follows:
(a) What are the OPP and APP for the Series A?
(b) What is the fully diluted share count?
(c) What is the proposed ownership percentage?
(d) What is the post-money valuation?
(e) What is the pre-money valuation?
EXHIBIT 8-1
CAPITALIZATION TABLE FOR NEWCO
Prefinancing Postfinancing
Security # of Shares % # of Shares %
Common—Founders 15,000,000 83.3 15,000,000 62.5
Common—Employee Stock Pool 3,000,000 16.7 3,000,000 12.5
Issued 600,000 3.3 600,000 2.5
Unissued 2,400,000 13.4 2,400,000 10.0
Series A Preferred 0 0.0 6,000,000 25.0
Total 18,000,000 100 24,000,000 100
162 CHAPTER 8 TERM SHEETS
CHAPTER 9
PREFERRED STOCK
IN THE UNITED STATES, VCs almost always use preferred stock in their
transactions. This preferred stock comes in many ?avors. In Section 9.1 of this
chapter, we analyze the main types of preferred stock and learn how to graphically
represent them. Most types of preferred stock are convertible into common stock,
either at the discretion of the investor (voluntary conversion) or when some preset
threshold is reached (automatic conversion). These conversion conditions are
sometimes adjusted due to antidilution protections, as ?rst mentioned in Chapter 8.
In Section 9.2 of this chapter, we provide mathematical formulas and examples to
illustrate the impact of antidilution protections.
9.1 TYPES OF PREFERRED STOCK
In public markets, the vast majority of equity investments are made with common
stock. However, for VC transactions in the United States, nearly all the investments
are made with preferred stock. The key characteristic of preferred stock is that it
has a liquidation preference to common stock. This is seen in the Newco charter of
Chapter 8, where the preferred stock has a liquidation preference (for $5M APP)
and an optional conversion (for 5M shares, representing one-third of the fully
diluted share count). These two features de?ne the Series A Newco stock as con-
vertible preferred (CP). With CP, EBV must decide at the time of exit whether to
redeem (and receive all proceeds up to $5M, but nothing else) or to convert to 5M
shares and receive one-third of all proceeds.
The key step here is the determination of the conversion condition, an
inequality de?ning the level of proceeds where conversion is more valuable than
redemption. We call this level the conversion point. The conversion point for a
Series A investment is written as W
A
. We will need to make this calculation
numerous times in the chapters to follow, thus it will be useful to go through the
procedure carefully this ?rst time.
If EBV chooses to convert, then this conversion would give it 5M shares.
Because the founders have 10M shares, this would give EBV one-third of the ?rm.
For total exit proceeds 5$W, we have
CP ðconversion valueÞ 51=3 Ã $W: ð9:1Þ
163
For proceeds $W, if EBV chooses to redeem the CP, it would receive
CP ðredemption valueÞ 5Minð$5M; $WÞ: ð9:2Þ
To make the conversion decision, EBV compares the value of Equations (9.1) and
(9.2) for any given W. The conversion condition holds when Equation (9.1) is
greater than Equation (9.2). This condition is illustrated in Exhibit 9-1.
The dotted line in Exhibit 9-1 represents conversion (Equation 9.1).The solid
line in Exhibit 9-1 represents redemption (Equation 9.2). EBV’s choice between
conversion and redemption can be made by answering the question, “Do I want to
be on the dotted line or the solid line?” For low values of W, the solid line is above
the dotted line, so the investor is better off redeeming for cash—but for high values
of W, the dotted line is above the solid line, so the investor is better off converting
to common shares. The conversion point occurs when conversion and redemption
are equal, which is found at the intersection of the two lines. The conversion
condition holds for all W above that point.
Conversion Condition: 1=3 Ã W.5-W
A
515 ð9:3Þ
If the proceeds of the liquidation are $15M, then EBV will receive $5 million for
either redeeming or converting. Below $15 million, EBV is better off redeeming.
Above $15 million, it is better off converting. Exhibit 9-2 redraws Exhibit 9-1 to
re?ect this conversion condition and include only the higher of the two lines in
Exhibit 9-1.
We refer to Exhibit 9-2 as an exit diagram because it plots the value of a
security against the value of the whole ?rm at the time of the exit of the investment.
EXHIBIT 9-1
CONVERSION CONDITION FOR CP
5
5
15
W
A
$W
C
P
164 CHAPTER 9 PREFERRED STOCK
We will use exit diagrams extensively when we do valuation of preferred stock in
Part III.
CP is not the only ?avor of preferred stock. Redeemable preferred (RP)
stock has the same liquidation preference as given in the Newco charter, but omits
the conversion features. Thus RP offers no possibility of conversion—and thus no
upside. Although a VC would never accept RP by itself, some transactions will
combine RP with common stock or with CP.
The Model Term Sheet (Appendix A) gives three alternatives for the liqui-
dation preference. The Newco charter from Chapter 8 uses Alternative 1, which is
called CP.
Alternative 1
In the event of any liquidation, dissolution, or winding up of the Company, the
proceeds shall be paid as follows:
First pay one times the Original Purchase Price on each share of Series A
Preferred. The balance of any proceeds shall be distributed to holders of
Common Stock.
A merger or consolidation (other than one in which stockholders of
the Company own a majority by voting power of the outstanding shares of the
surviving or acquiring corporation) and a sale, lease, transfer, or other dis-
position of all or substantially all of the assets of the Company will be treated
as a liquidation event (a “Deemed Liquidation Event”), thereby triggering
payment of the liquidation preferences described above.
The language of Alternative 2 leads to a security called participating con-
vertible preferred (PCP). The text of Alternative 2, which follows, would replace
the second paragraph of Alternative 1 from the preceding.
EXHIBIT 9-2
EXIT DIAGRAM FOR CP
5
5
$W
C
P
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 165
Alternative 2
First pay one times the Original Purchase Price on each share of Series A
Preferred. Thereafter, the Series A Preferred participates with the Common
Stock on an as-converted basis.
By itself, this language implies that the PCP holders would get back the OPP
and then also receive any additional proceeds that would have been garnered if it
had also converted to common stock. In this respect, we could say that PCP is like
having RP plus common stock. It is important to remember, however, that this
liquidation preference only applies in the case of a deemed liquidation event. If the
PCP is converted—perhaps because of a mandatory conversion—then it becomes
just like common stock.
The language of Alternative 3 in the Model Term Sheet is very similar to
Alternative 2, except that there is a cap on the liquidation preference. Thus we refer
to this security as participating convertible preferred with cap (PCPC). The text
of Alternative 3 is given as follows:
Alternative 3
First pay one times the Original Purchase Price on each share of Series
A Preferred. Thereafter, Series A Preferred participates with Common Stock
on an as-converted basis until the holders of Series A Preferred receive an
aggregate of [______] times the Original Purchase Price
The cap is driven by ?lling in the blank space in the last sentence. The language in
these alternatives determines whether the security is common stock, RP, CP, PCP,
or PCPC. In practice, it is much easier to refer to securities with these acronyms
than to write out the liquidation preference; therefore, we will follow that practice
in this book.
To illustrate the differences among these different ?avors of preferred stock,
we draw exit diagrams for each of them in Example 9.1.
EXAMPLE 9.1
EBV is considering a $5M Series A investment in Newco. The founders and employees of
Newco have claims on 10M shares of common (including the stock pool). Thus, we are
adopting the same setup as in the Newco charter in Chapter 8. Now, however, in addition to
the CP structure considered there, EBV is considering six alternative structures for their
investment:
Structure I: 5M shares of common
Structure II: RP ($5M APP)
Structure III: RP 15M shares of common
Structure IV: PCP with participation as if 5M shares of common
Structure V: PCPC with participation as if 5M shares of common, with liquidation return
capped at four times OPP
Structure VI: RP ($4M APP) 15M shares of CP ($1M APP)
166 CHAPTER 9 PREFERRED STOCK
Structures IV and V have mandatory conversion upon a QPO, where a QPO is any
offering of at least $5 per common share and $15M of proceeds. For the purpose of solving
this problem, assume that any exit above $5 per share will qualify as a QPO (i.e., acquisitions
for at least $5 per common share would also be considered to be QPOs).
Problems
(a) Draw an exit diagram for each structure.
(b) Compare the ?ve structures for exit proceeds of $3M, $8M, $32M, $72M, and $96M.
Also include a comparison for the original CP structure from the Newco charter.
Solutions
(a) Structure I is for 5M shares of common, that there would be 15M shares total (10M for
founders and 5M for EBV.) Thus, under this structure EBV would get exactly one-third of all
proceeds for any exit, with an exit diagram as shown in Exhibit 9-3.
As mentioned earlier, it is rare for a VC in the United States to accept common stock
by itself. Outside the United States, this is not unusual.
Structure II would never happen anywhere in the world: no VCs would limit their
upside completely by taking only RP. We include this case only as a building block for the
other structures. With only RP, EBV would receive all proceeds up to $5M, and then nothing
after that. This implies an exit diagram as shown in Exhibit 9-4.
Structure III is the combination of Structures I and II, but we cannot just add the lines
in Exhibits 9-3 and 9-4, because when RP and common coexist, the RP must be paid back
?rst. This raises the question: how much of the $5M investment was used to buy the RP,
and how much was used to buy the common? Although the allocation of value between RP
and common is arbitrary, it does determine the payoff to the Series A as a whole. In different
cases, the allocation of purchase price can determine conversion rates and antidilution
protections. We will return to these issues in Part III. For now, we assume that the whole
EXHIBIT 9-3
EXIT DIAGRAM FOR COMMON STOCK
$W
C
o
m
m
o
n
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 167
$5M purchase price is allocated to the RP (APP 5$5M), with the common “free”.
This assumption eases comparisons of Structure III with the other structures. With this
assumption, under Structure III, EBV would receive all proceeds until $5M, and then one-
third of whatever is left over. This gives us an exit diagram as shown in Exhibit 9-5.
Structure IV is a hybrid of Structures I and III with a cutoff at the QPO threshold. For
exits below the QPO threshold, Structure IV looks like the RP plus common of Structure III,
because EBV would be allowed to both redeem (for $5M) and to participate in the upside as
though it also had 5M of common stock. Above the QPO threshold, there would be automatic
conversion, thus making the PCP look like the common stock of Structure I. The partici-
pation threshold here is ?ve times the original investment, which occurs when the Series A is
worth at least $25M:
1=3 Ã W 5$25M-W5$75M5QPO threshold ð9:4Þ
This implies an exit diagram as shown in Exhibit 9-6. Note that Exhibit 9-6 is just a hybrid of
Exhibit 9-5 (below the W5$75M threshold) and Exhibit 9-3 (above the W5$75M
threshold). At the W5$75 threshold, at the instant before conversion, this structure has a
total value of $5M11/3 Ã ($75M2$5M) 5$28 1/3M. Immediately after conversion, the
value drops to $25M. Hence, the diagram shows a drop of $28 1/3M2$25M5$10/3M.
Structure V may seem similar to Structure IV, but in fact they are quite different. For
Structure IV, automatic conversion occurs at the QPO of $5 per share, which implies that
W
A
5$75M. Although this automatic conversion might still be binding for Structure V, it is
also possible that EBV would choose to convert the PCPC for a lower value of W. To analyze
this voluntary conversion decision, we set up a conversion condition using a redemption
value equal to the PCPC cap at four times the APP (5$20M). We can visualize this con-
version decision as an analogue of Exhibit 9-1.
We can write the corresponding conversion condition as
ðVoluntaryÞ Conversion Condition: 1=3 Ã W.20-W
A
560 ð9:5Þ
EXHIBIT 9-4
EXIT DIAGRAM FOR RP
5
5
$W
R
P
168 CHAPTER 9 PREFERRED STOCK
Because voluntary conversion would occur at W5$60M, the automatic conversion at $75M
is a redundant and nonbinding constraint.
For PCPC, the last step is to determine the level of proceeds W where the redemption
value is capped, which we refer to as the cap point, and write as W
A
(cap). At any exit above
$5M, Structure V would receive back the APP (5$5M) plus one-third of any remaining
proceeds. The cap occurs when this total reaches four times APP 5$20M:
1=3 Ã ðW25MÞ 15M520M-W
A
ðcapÞ 5$50M ð9:6Þ
EXHIBIT 9-5
EXIT DIAGRAM FOR RP + COMMON
$W
S
e
r
i
e
s
A
5
5
S
lo
p
e
=
1
/3
EXHIBIT 9-6
EXIT DIAGRAM FOR PCP
P
C
P
28 1/3
25
5
5 75
$W
Drop
= 10/3
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 169
The careful reader may have noticed this cap point labeled on the YÀaxis of Exhibit 9-7. For
exit proceeds above the cap at W5$50M, the value line is ?at until the conversion point at
W5$60M. Exhibit 9-8 gives the exit diagram.
In this example, the computation of the QPO threshold for PCP and PCPC is relatively
straightforward. The computation becomes more complex when there are multiple rounds of
investment. Readers do not have to worry about this until Chapter 16, but should consider
themselves warned in advance!
EXHIBIT 9-7
VOLUNTARY CONVERSION FOR THE PCPC
$W
20
5
5 50 60
P
C
P
C
Conversion Point
S
lo
p
e
=
1
/
3
P
C
P
C
(
R
e
d
e
m
p
t
io
n
V
a
lu
e
)
P
C
P
C
(
C
o
n
v
e
r
s
io
n
V
a
lu
e
)
EXHIBIT 9-8
EXIT DIAGRAM FOR PCPC
P
C
P
C
S
lo
p
e
=
1
/
3
S
lo
p
e
=
1
/
3
5 50 60
$W
20
5
170 CHAPTER 9 PREFERRED STOCK
Structure VI combines features of Structure II (RP) with the baseline CP from the
Newco term sheet. In this example, there are two types of preferred stock, CP and RP, and
there is no statement about which version would be paid ?rst in a liquidation (term sheets
often omit such information). Because EBV owns all of both the CP and the RP, this liquidity
preference between the two is not relevant for the aggregate value of the Series A; for
simplicity of exposition, we treat the RP as superior to the CP.
To draw the exit diagram, we will ?rst draw the RP and CP separately. Because we
have assumed that the RP has a liquidation preference to the CP, we can draw the exit
diagram for the RP as shown in Exhibit 9-9.
Next, we look at the CP. The CP here is similar to the CP in baseline case, with some
added twists. First, because the RP is paid ?rst, the CP has no value unless the proceeds are
above $4M. Second, because the APP of the 5M shares is only $1M, the conversion con-
dition will come sooner. This conversion condition is as follows:
1=3 Ã ðW 24Þ .1-W
A
57: ð9:7Þ
Next, the exit diagram for the CP is shown in Exhibit 9-10.
The exit diagram for Structure VI is the combination of Exhibits 9-9 and 9-10.
(b) We next solve for the exit value of each structure for all six structures plus the
original CP structure from the Newco charter in Chapter 8. We use the following cases: $3M,
$8M, $32M, $72M, and $96M. Using the diagrams and reasoning from part (a) and Exhibit
9-2, we have the results shown in Exhibit 9-12.
Structure I always receives one-third of all proceeds. Structure II gets all proceeds up
to $5M but nothing more. Structure III does at least as well as other structures in all cases,
receiving all proceeds up to $5M and then one-third of everything that is left over. Structure
IV and Structure V are identical except for the W572 case, where Structure IV (PCP) still
looks like Structure III (RP 1common), but Structure V has converted and looks like
EXHIBIT 9-9
EXIT DIAGRAM FOR THE SERIES A RP
$W
R
P
i
n
S
e
r
i
e
s
A
4
4
9.1 TYPES OF PREFERRED STOCK 171
Structure I. At ?rst glance, one might think that Structure VI would provide a higher payoff
than the RP 1common combination of Structure III, but the exhibit shows this is not the
case. The reason is that once the CP converts, there is only $4M of APP paid for the RP (not
$5M as in Structure III). Finally, the original CP structure from the charter is a hybrid
EXHIBIT 9-11
EXIT DIAGRAM FOR RP + CP
$W
S
e
r
i
e
s
A
5
5
7
S
lo
p
e
=
1
/3
EXHIBIT 9-10
EXIT DIAGRAM FOR THE SERIES A CP
$W
C
P
i
n
S
e
r
i
e
s
A
5 7 4
1
S
l
o
p
e
=
1
/
3
172 CHAPTER 9 PREFERRED STOCK
between structures I and II: it looks like Structure II (RP) for W53 and W58, but looks like
Structure I (common stock) in all other cases. ’
9.2 ANTIDILUTION PROVISIONS
The Newco charter of Chapter 8 gave EBV a form of antidilution protection that
applies in the case of a down round. The two forms of antidilution protection are
full-ratchet and weighted-average. The language in the Newco term sheet of
Chapter 8 is
In the event that the Company issues additional securities at a purchase price
less than the current Series A Preferred conversion price, such conversion
price shall be reduced to the price at which the new shares are issued.
This language corresponds with full-ratchet protection, which the Dow Jones
Report ?nds for 20 percent of all deals that have any antidilution protection. With
full-ratchet adjustment, the Series A adjusted conversion price would be set to the
lowest conversion price of any later stock sale, and the adjusted conversion
rate would then be calculated as OPP divided by adjusted conversion price. To
illustrate how this would work, consider our Series A round of $5 million of
convertible preferred stock at an OPP of $1 per share. Now, assume that one year
later there is a Series B round for $5 million with a price of $0.50 per share, for
10M shares. Given full-ratchet protection, the Series B price of $0.50 would cause
an adjusted conversion price of $0.50 for Series A. The adjusted conversion rate of
the Series A stock would then be $1/$0.50 52. In fact, this same calculation would
occur even if the down round were only for a single share.
Alternatively, in a weighted-average antidilution protection, the Series A
investors would obtain an adjusted conversion price that depends on the size of the
current and past rounds. The exact adjustments depend on whether the formula is
EXHIBIT 9-12
EXIT PROCEEDS UNDER ALL STRUCTURES
Structure (charter)
I II III IV V VI CP
W 5 3 1 3 3 3 3 3 3
W 5 8 2.7 5 6 6 6 5.3 5
Exit W 5 32 10.7 5 14 14 14 13.3 10.7
W 5 72 24 5 27.3 27.3 24 26.7 24
W 5 96 32 5 35.3 32 32 34.7 32
9.2 ANTIDILUTION PROVISIONS 173
broad-base or narrow-base. The NVCA model term sheet in Appendix A gives
the formula for the broad-base weighted average as
CP
2
5adjusted conversion price 5CP
1
à ðA 1BÞ=ðA1CÞ ð9:8Þ
where
CP
2
5 Series A Conversion Price in effect immediately after new issue
CP
1
5 Series A Conversion Price in effect immediately prior to new issue
A 5 Number of shares of Common Stock deemed to be outstanding immediately
prior to new issue (includes all shares of outstanding common stock, all
shares of outstanding preferred stock on an as-converted basis, and all
outstanding options on an as-exercised basis; does not include any con-
vertible securities from this round of financing)
B 5 Aggregate consideration received by the Corporation with respect to the
new issue divided by CP
1
C 5 Number of shares of stock issued in the subject transaction
For our example, we have CP
1
5$1, A515M, B5$5M/$1 55M, and C510M.
Thus, we have
CP
2
ðbroad baseÞ 5$1 Ã ð15M15MÞ=ð15M110MÞ 5$0:80 ð9:9Þ
In a narrow-base weighted-average formula, everything is the same except for the
de?nition of A:
A (narrow-base) 5 Number of shares of Common Stock deemed to be outstanding
immediately prior to new issue (including all shares of out-
standing preferred stock on an as-converted basis, but excluding
all shares of outstanding common stock and all outstanding
options on an as-exercised basis; does not include any con-
vertible securities from this round of ?nancing).
With this change, the narrow-base case for our example gives A55M, so
CP
2
ðnarrow baseÞ 5$1 Ã ð5M15MÞ=ð5M110MÞ 5$0:67 ð9:10Þ
The Dow Jones Report tells us that a weighted-average formula is used in 80
percent of all antidilution provisions; of these weighted-average cases, broad-based
formulas are common, and narrow-based formulas are rarely used.
EXAMPLE 9.2
Suppose EBV makes a $6M Series A investment in Newco for 1M shares at $6 per share.
One year later, Newco has fallen on hard times and receives a $6M Series B ?nancing from
Talltree for 6M shares at $1 per share. The founders and the stock pool have claims on 3M
shares of common stock. Going forward, for brevity we will use the term “employees” to
mean “founders and the stock pool”.
174 CHAPTER 9 PREFERRED STOCK
Problems
Consider the following cases:
Case I: Series A has no antidilution protection.
Case II: Series A has full-ratchet antidilution protection.
Case III: Series A has broad-base weighted-average antidilution protection.
Case IV: Series A has narrow-base weighted-average antidilution protection.
For each of these cases, what percentage of Newco (fully diluted) would be controlled
by EBV following the Series B investment? What would be the post-money and pre-money
valuations?
Solutions Case I: Without any antidilution protection, EBV has 1M shares out of a fully
diluted share count of 1M16M (Series B) 13M employees 510M. Thus, they would
control 10 percent. The Series B investors paid $1 per share, so the post-money valuation
would be 10MÃ $1 5$10M, and the pre-money valuation would be $10M2$6M5$4M.
Case II: With full-ratchet antidilution protection, the Series A adjusted conversion
price would become $1 (the price of the Series B), and EBV would control 6M shares of a
fully diluted share count of 6M16M13M515M for 40 percent. The postmoney valuation
would be 15MÃ $1 5$15M, and the premoney valuation would be $15M2$6M5$9M.
Case III: With broad-base weighted-average antidilution protection, we can use
Equation (9.8) to compute the adjusted conversion price. Using the de?nitions for this equation,
we have A51M13M54M, B5$6M/$6 51M, and C56M. Substituting into (9.8) yields
CP
2
ðbroad baseÞ 5$6 Ã ð4M11MÞ=ð4M16MÞ 5$3: ð9:11Þ
Therefore, EBV would control $6M/ $3 52M shares of a total of 2M16M13M5
11M for 22.2 percent of the company. The postmoney valuation would be 11MÃ $1 5$11M,
and the premoney valuation would be $11M2$6M5$5M.
Case IV: With narrow-base, weighted-average antidilution protection, we must adjust
our de?nition of A in Equation (9.8) to omit the 3M shares held by employees, so A51M.
We then substitute this new A into Equation (9.8) to obtain
CP
2
ðnarrow baseÞ 5$6 Ã ð1M11MÞ=ð1M16MÞ 5$1:71: ð9:12Þ
With this conversion price, EBV obtains approximately 6M/$1.71 53.5M shares,
yielding it 28 percent of the 3.5M16M13M512.5M total shares. The postmoney valuation
would be 12.5M Ã $1 5$12.5M, and the premoney valuation would be $12.5M 2$6M5
$6.5M. ’
In the cases with antidilution protection, if we were to build a cap table, the
number of premoney shares is ambiguous. Some VCs might write the table with
the premoney shares given before the antidilution correction, while others would
write these shares after the correction. Either way is reasonable. However, it would
de?nitely be incorrect in Cases II, III, and IV to compute the premoney valuation as
$1 Ã 6M premoney shares 5$6M. In these cases, the only correct way to compute
premoney valuation is postmoney valuation minus $investment, as shown in the
solution.
9.2 ANTIDILUTION PROVISIONS 175
REALITY CHECK: Antidilution protection provides more protection on
paper than in practice. According to an earlier edition of the Dow Jones Report
(where they ask this question), VCs are forced to waive their antidilution protection
in about 64 percent of the applicable down rounds. Furthermore, it is likely that in
the remaining 36 percent of cases, the protections do not work nearly as strongly
as the contractual language would suggest. What is going on here?
Basically, antidilution protections are useful only when the protected party is
willing to walk away from the deal. If a company is performing poorly and a VC
wants to liquidate but the majority shareholders want to do another round of
?nancing, then the antidilution protection can prove useful. In the majority of cases,
however, the VC wants the new ?nancing and has little leverage to maintain
the protections. If a company needs ?nancing to survive, and the real value of the
company has fallen since the previous round, then most new investors will
insist that the previous investors waive their antidilution rights. Additionally,
triggering the protection would further dilute the incentives of founders and
employees, which the VC also has to take into account.
Consider the full-ratchet case (Case II) from Example 9.2. If this provision is
allowed to stand, then the new investor (Talltree) would receive only 40 percent of
Newco for its $6M. If Talltree expects to get 60 percent of the ?rm for its $6M and
EBV refuses to waive its antidilution rights, then Talltree can simply walk away.
Thus, the antidilution rights do give EBV a seat at the negotiation table, and it may
be able to extract some value—perhaps a small adjustment to its conversion price—
but antidilution rights are simply one of many bargaining chips that EBV can use to
try to get a better deal.
SUMMARY
VCs use preferred stock in most transactions. There are four main types of preferred stock.
Redeemable preferred (RP) stock is a bondlike security that is senior to common stock but
cannot be converted to common stock. No VC would ever accept RP by itself, but would
instead combine it with common stock or another type of preferred stock. Convertible preferred
(CP) stock provides the same downside protection as RP with the additional option of con-
verting to common stock. Participating convertible preferred (PCP) stock provides its holder
with a combination of the downside protection of RP and the upside potential of CP, with the
caveat that the redeemable rights go away upon a quali?ed public offering. Sometimes
the liquidation return to PCP is capped at some preset multiple of the purchase price: We refer
to such securities as participating convertible preferred with cap (PCPC) stock.
VCs often receive antidilution protection on their preferred stock. Such protection
provides the holder with the right to adjust the conversion price of their preferred in the event
of a down round. In theory, such protection gives a VC claims on additional shares in the
event of a down round. In practice, investors in struggling companies are usually forced to
give up these rights to secure a new round of investment. Nevertheless, it is important
to learn how these protections work, if only to know the relative bargaining positions for
various investors.
176 CHAPTER 9 PREFERRED STOCK
KEY TERMS
Conversion condition,
Conversion point 5W
A
Common stock, preferred
stock
Convertible preferred (CP)
Redeemable preferred (RP)
Participating convertible
preferred (PCP)
Participating convertible
preferred with cap
(PCPC)
Cap point 5W
A
(cap)
Exit diagram
Full-ratchet antidilution,
weighted-average
antidilution
Adjusted conversion price,
adjusted conversion rate
Broad-base formula,
narrow-base formula
REFERENCE
Dow Jones, 2009, Venture Capital Deal Terms Report, 6th Edition, Dow Jones, Jersey City, NJ.
EXERCISES
9.1 Suppose that it is one year after EBV’s investment in Newco (using the CP structure
from Exercise 8.2), and Talltree makes a Series B investment for 6M shares of Newco at $0.2
per share. Following the Series B investment, what percentage of Newco (fully diluted)
would be controlled by EBV? Consider the following cases:
Case I: Series A has no antidilution protection.
Case II: Series A has full-ratchet antidilution protection.
Case III: Series A has broad-base weighted-average antidilution protection.
Case IV: Series A has narrow-base weighted-average antidilution protection.
9.2 Suppose that EBV decides to consider six possible structures for the Series A stock in
Exercise 8.2:
Structure I: The original structure considered in Exercise 8.2: 6M shares of CP.
Structure II: 6M shares of common.
Structure III: RP + 6M shares of common.
Structure IV: PCP with participation as-if 6M shares of common.
Structure V: PCPC with participation as-if 6M shares of common, with liquidation return
capped at 5 times OPP.
Structure VI: RP ($4M APP) 15M shares of CP ($2M APP).
Structures IV and V have mandatory conversion upon a QPO, where a QPO is any offering of
at least $5 per common share and $15M of proceeds. For the purpose of solving this problem,
assume that any exit above $5 per share will qualify as a QPO (i.e., acquisitions for at least $5
per common share would also be considered to be QPOs).
Draw an exit diagram for each structure.
EXERCISES 177
CHAPTER 10
THE VC METHOD
THIS CHAPTER INTRODUCES concepts and mechanics for the VC method,
the most common valuation strategy used by venture capitalists. What we call “the
VC method” refers to a wide range of different implementations, all of which share
four common elements. These four elements are discussed in Section 10.1. In
Section 10.2 we discuss and illustrate one speci?c implementation, which we call
the standard VC method. This standard method does not account for management
fees or carried interest, so in Section 10.3 we introduce a modi?ed VC method to
handle these costs.
10.1 THE VC METHOD: INTRODUCTION
There are many different ways to implement the VC method. All these imple-
mentations share four main elements, and the main differences among implemen-
tations are the exact set of steps and ordering of steps. These four main elements are as
follows:
1. An estimate of an exit valuation for the company. The exit valuation is
forward-looking and represents the expected value of the company at the
time of a successful exit, where a successful exit is considered to be an IPO
or equivalent valued sale. This part of the VC method is discussed in Section
10.1.1, with more detail in Chapters 11 and 12.
2. An estimate of the VC’s target multiple of money in a successful exit. Such
multiples may be stated directly (“we look for investments that can earn 5
times our money in ?ve years”) or may be built up from an annual target
return for the IRR of a successful exit. This part of the VC method is dis-
cussed in Section 10.1.2 and is based in part on the analysis from Chapter 4.
3. An estimate of the expected retention percentage between the current
investment and a successful exit. New shares must be issued when the
current investment plus the future cash ?ows of the company are insuf?cient
to fund the growth necessary for a successful exit. Although the current VC
may participate in the future rounds of investment, we still want to know
178
about the reduction to the proposed ownership percentage for the current
investment. For the purposes of the VC method, we view each round as a
stand-alone investment. Retention is discussed in Section 10.1.3.
4. The investment recommendation, where the required investment is com-
pared to the proposed ownership percentage of the total valuation. Total
valuation is de?ned as the exit valuation, multiplied by the expected
retention percentage and divided by the target multiple of money. In most
implementations of the VC method, the investor does not explicitly account
for management fees and carried interest when making the investment
recommendation. An example of this standard approach is given in Section
10.2. In Section 10.3, we show how to modify the standard method to
include management fees and carried interest.
10.1.1 Exit Valuation
A wide range of techniques is employed for the estimation of exit value. In each
case, the focus is on the value of company at the time of a successful exit. The
reason to focus on a successful exit is obvious—that is where the vast majority of
the pro?ts will be made. The de?nition of a successful exit is less obvious. It is
perhaps easiest to talk about what a successful exit does not mean. It does not mean
“everything went perfectly, growth hit the entrepreneur’s most optimistic projec-
tions, and we are all going to be rich beyond our wildest dreams”. It would be
wrong to focus attention on such rare outcomes, because a lot of the expected value
of the company is contained in more modest successes—and because by ignoring
such cases, we would not end up with a good estimate for the total valuation.
Conversely, successful exit does not mean “anything except liquidation”. Many
VC-backed companies end up being acquired with very little money going to the
shareholders. A central idea of the VC method is to ignore these lesser payoffs and
focus attention on the places where the payoffs are signi?cant.
What does “successful exit” mean? The best working de?nition is probably
“an IPO or competitive sale”, where a competitive sale means “we could have done
an IPO, but the sale was better”. For companies where an IPO is unrealistic from
the outset—perhaps because the potential market is more limited—then a compe-
titive sale should mean “acquisition with more than one interested party, in a
situation where we did not have to sell”. In general, we are trying to work through
the case where the business has achieved some major milestones.
Once we have a notion of success in mind, we need to estimate the value of the
company conditional on this success. The two main approaches are relative valua-
tion and absolute valuation. In relative valuation, we ?nd a set of current companies
that are comparable to our company at the time of its (hypothetical) successful exit.
Comparability is usually established based on similarities in industry and growth
potential. We then compute various valuation ratios for these companies, usually
based on multiples of market value to some accounting measure. There is no hard rule
10.1 THE VC METHOD: INTRODUCTION 179
about the best multiple to use—choices are usually governed by industry standards,
where the guiding principle is to use multiples that are the most consistent across
companies. Relative valuation methods are covered in Chapter 12.
Although relative valuation uses the market’s opinion of comparable com-
panies to value the baseline company, absolute valuation re?ects the analyst’s
opinion by using a discounted cash ?ow (DCF) model. This DCF analysis can use a
variety of speci?c techniques, but the underlying idea is to determine the value of
the company by forecasting future cash ?ows and discounting them back at some
appropriate discount rate. Absolute valuation methods are neither better nor worse
than relative valuation methods; both have their strengths and weaknesses, and
careful analysts should do both. Although we will focus (in Chapter 11) on the use
of DCF models for exit valuation, they can also be used as the main method of total
valuation, particularly for later-stage investments.
In addition to the two main methods of relative valuation and absolute
valuation, a third shortcut method may be used to obtain quick inputs for the VC
method. In this shortcut—which we use in the following examples—the analyst
simply uses the average valuation for successful exits in the same industry. For
example, for an investment in the telecommunications industry, suppose that IPOs
in the previous few years have had an average valuation of $300M. Then the
analyst could assume $300M as the exit valuation, and the main valuation task
becomes to estimate the probability of an IPO.
10.1.2 Target Returns
Exit valuations are estimates of company value at some time in the future. To
convert this value to today’s dollars, we need an appropriate discount rate, which
we call the target return. In Chapter 4, we showed how to estimate the cost of VC
by using historical data and a factor model regression. It is important to note,
however, that the target return is not the same thing as the cost of VC. Our estimate
of 15 percent for the cost of VC is appropriate for the typical VC investment. When
VCs discuss target returns, they are referring to successful investments. In a VC
method valuation, only the successful cases are considered, with unsuccessful
failure cases given an effective value of 0. Let p represent the probability of suc-
cess. Then, the expected value at exit is
Expected value at exit 5exit valuation à p: ð10:1Þ
If this exit is expected in T years with no further rounds of investment, then
the present discounted value for this exit is
Present discounted value of exit 5exit valuation à p=ð1 1r
vc
Þ
T
ð10:2Þ
where r
vc
is the cost of venture capital. In Equation 10.2, the expression p/(1 1r
vc
)
T
represents the effective discount factor for the exit valuation; we call the inverse of
this discount factor the target multiple of money and denote it as M. We can also
180 CHAPTER 10 THE VC METHOD
convert the target multiple of money to an annual target return, which is implicitly
computed as:
p=ð1 1r
vc
Þ
T
51=M51=ð1 1Target ReturnÞ
T
ð10:3Þ
Exhibit 10-1 shows output from the worksheet, TARGET, from the VC_
method.xls spreadsheet. The worksheet uses Equations (10.2) and (10.3) to relate
inputs for the cost of venture capital into a matrix of outputs relating the target
return and target multiple of money with the probability of success and the time to
successful exit. For example, if time to exit is ?ve years and the probability of a
successful exit is 20 percent, then we can look in the corresponding cell and ?nd a
target multiple of money of 10.1 (calculated from Equation (10.2), and a target
return of 59 percent per year (calculated from Equation (10.3)).
It might seem as though all these steps require signi?cant guesswork.
Although guesses are certainly required, there are many ways to provide structure
for these guesses using personal experience and historical data. In the exercises at
the end of this chapter, you are asked to use the data from Chapter 7 to evaluate
some speci?c probability assumptions. More generally, however, the estimate of p
is where a VC must use his experience and judgment. What appears to be a wild
guess to the untrained eye can in fact be the exercise of hard-won intuition. For
EXHIBIT 10-1
TARGET RETURNS AND TARGET MULTIPLES OF MONEY
Cost of capital for VC 15.0%
Table of “Target Return” (top cell) and “Target Multiple-of-Money” [M]
(bottom cell)
Probability of successful exit (p)
10.0% 20.0% 25.0% 30.0% 35.0% 40.0% 50.0%
2 264% 157% 130% 110% 94% 82% 63%
13.2 6.6 5.3 4.4 3.8 3.3 2.6
3 148% 97% 83% 72% 63% 56% 45%
15.2 7.6 6.1 5.1 4.3 3.8 3.0
Years To 4 105% 72% 63% 55% 50% 45% 37%
Exit 5 T 17.5 8.7 7.0 5.8 5.0 4.4 3.5
5 82% 59% 52% 46% 42% 38% 32%
20.1 10.1 8.0 6.7 5.7 5.0 4.0
6 69% 50% 45% 41% 37% 34% 29%
23.1 11.6 9.3 7.7 6.6 5.8 4.6
7 60% 45% 40% 37% 34% 31% 27%
26.6 13.3 10.6 8.9 7.6 6.7 5.3
10.1 THE VC METHOD: INTRODUCTION 181
example, many basketball players can correctly assess whether their shots will go in
the basket from the instant the shot leaves their hands. (And for shots that miss, they
have a pretty good idea of where the rebound will go.) Talented scientists are adept
at judging the success probability of an untried experiment. Champion poker
players can estimate not only the mathematical odds of receiving any given card
(that part is easy) but also whether other players are bluf?ng. All these skills
combine some natural intuition with “data”, where the data may be drawn from
daily experience or from past experiments.
10.1.3 Expected Retention
In the valuation of mature companies, a DCF analysis usually includes positive
cash ?ows before the terminal date. In the VC method, the opposite is true: we
must usually account for negative cash ?ows, which then require further rounds of
investment and a reduction in the ownership percentage for previous investors. For
example, if a VC purchases 5M of Newco’s 20M shares in a Series A investment,
then a 5M Series B round will reduce the Series A stake from 25 percent to
20 percent. In that case, we would say that the Series A investors have a retention
percentage of 0.20/0.25 580 percent. Even if the same VC participates by pur-
chasing 1.25M shares of the Series B—thus maintaining a 25 percent stake over
the two rounds—the impact on the 5M share Series A investment remains the
same. If we expect all future rounds to be made at a fair market price, then
the identity of the Series B investor is irrelevant to the Series A investment
decision, and it is necessary to account for future reductions when analyzing the
Series A investment.
The mathematics of retention is straightforward, but the underlying
assumptions—as always—require some educated guesswork. We start with the
number of shares outstanding after the current round of investment. This share total
should include all founders’ shares (including those not yet vested) and all
employee options (including those not yet issued or vested). The reason to include
nonvested and even nonissued options and shares is that we are focused on the
valuation at a successful exit, and all these shares will certainly be issued, vested,
and valuable at such a time. Here we follow the same rule as used for pre-money
valuation (Chapter 8) and include the option pool in the computation of current
shares outstanding.
The next step is to estimate the number of shares necessary to achieve a
successful exit. This estimate should include all new shares issued at an IPO,
assuming that a post-IPO valuation is used as a successful exit. The ratio of current
shares to ?nal (new1current) shares becomes our estimate of the expected
retention. This estimation can be done by appealing to past experience, data on
successful exits, and formal modeling.
We can make a ?rst approximation for retention percentages by examining
data in the Sand Hill Econometrics database. When we analyze the experience for
all IPOs—a simple measure of “success”—we ?nd that the average retention
182 CHAPTER 10 THE VC METHOD
for all ?rst-round investments was about 50 percent, meaning that for every 10
percent of the company owned by a ?rst-round investor, an average of 5 percent
of the company was still owned by that investor after the IPO. Using the same
data, we also ?nd a retention percentage of about 60 percent for second-round
investments, 67 percent for third-round investments, and 70 percent for invest-
ments in the fourth round or later. In this chapter, we will use these estimated
percentages as our retention estimates. In practice, a VC can use specialized
knowledge to adjust these averages for differences in industry, company stage,
and market conditions.
10.1.4 The Investment Recommendation
The ?nal step in any VC method is to make an investment recommendation. The
investment recommendation is always based on a comparison of the investor’s
costs to his bene?ts. In the standard VC method (Section 10.2), the investor’s costs
are just the dollars invested, referred to simply as the required investment. To ?gure
the investor’s bene?ts (the value of his stake in the company), we ?rst need to
calculate the total valuation of the company. This total valuation is effectively the
present discounted value of the exit valuation, with an additional adjustment for the
retention percentage.
The total valuation gives us a valuation for the whole ?rm today, but of
course the investor does not own the whole ?rm. Instead, we need to know the
partial valuation for the fraction of the company claimed by the investor. In Part
III we develop option-pricing tools that allow us to compute this partial valuation
for a range of possible securities and contractual provisions. In this part of the book,
we focus our attention on total valuation and make a simple approximation that
partial valuation is equal to total valuation multiplied by the proposed ownership
percentage. In the standard VC method (Section 10.2), the investment recom-
mendation is based on a comparison of investor costs (the required investment)
with investor bene?ts (partial valuation). In the modi?ed VC method (Section
10.3), we ?rst add management fees to the investor’s costs and then subtract
expected carried interest from the investor’s bene?ts before making the investment
recommendation.
We refer to this ?nal element in the VC method as an “investment recom-
mendation” rather than “investment decision” to emphasize that the calculations are
best used as an input into decision making, and not as a ?nal answer. Valuation is
not an exact science even in the best of conditions; therefore we do not want to rely
too heavily on the conclusions. Nevertheless, the investment recommendation step
is a crucial reality check, and it should not be ignored. Great investments often look
great from all angles, whereas poor investments will give themselves away
somewhere. The prudent investor must be alert to the warning signs. A complete
VC method provides outputs based on a range of possible input values so that the
investor can understand the sensitivity of the recommendations to different
assumptions.
10.1 THE VC METHOD: INTRODUCTION 183
10.2 THE STANDARD VC METHOD
In this section we discuss the most common VC method, which we call the
standard VC method. There are many different ways this standard method can
be implemented—our version is just one example. After we do an example using
this method, we will discuss several possible variations that can be seen in
practice. For all examples in this chapter, we will assume that the VC is pur-
chasing convertible preferred stock, and all statements about ownership per-
centages will be under the assumption that all preferred stock has been converted
to common shares.
Our standard VC method has eight steps:
Step 1: What is the required investment today? (5$I)
Step 2: What is the exit valuation for this company? ($ exit valuation)
Step 3: What is the target multiple of money on our investment? (M)
Step 4: What is the expected retention percentage? (retention)
Step 5: Estimate the total valuation for the company today:
Total valuation 5$ exit valuation à retention=M ð10:4Þ
Step 6: What is the proposed ownership percentage today? ( proposed %)
Step 7: Estimate the partial valuation for this investment:
Partial valuation 5proposed %Ã total valuation: ð10:5Þ
Step 8: Investment Recommendation: Compare partial valuation to required
investment.
EXAMPLE 10.1
EBV is considering a $6M Series A investment in Newco. EBV proposes to structure the
investment as 5M shares of convertible preferred stock. The founders of Newco, who will
continue with the ?rm, currently hold 10M shares of common stock. Thus, following the
Series A investment, Newco will have 10M common shares outstanding and would have
15M shares outstanding upon conversion of the CP. EBV estimates a 30 percent probability
for a successful exit, with an expected exit time in ?ve years.
Problem What is your investment recommendation?
Solution To answer this question, we perform each step of the standard VC method:
Step 1: The required investment 5$I 5$6M.
Step 2: For the exit valuation, we will just do a basic estimate for this example. Let’s suppose
that the 30 percent success probability refers to an IPO exit, and that the average IPO
exit in Newco’s industry is at a valuation of $300M. For now, we will use $300M as
184 CHAPTER 10 THE VC METHOD
our estimate of the exit valuation. (In Chapters 11 and 12, we study exit valuations in
more detail.)
Step 3: With a cost of venture capital of 15 percent (as found in Chapter 4), a successful
exit probability of 30 percent, and a successful exit time of ?ve years, we can
calculate the required multiple of money as
Required multiple of money 5M5ð1 1r
vc
Þ
T
=p 51:15
5
=0:30 56:7: ð10:6Þ
Step 4: For expected retention, we use 50 percent, the average estimate from the SHE
database for successful ?rst rounds.
Step 5: Using the answers to Steps 2 to 4, we can estimate the total valuation as
Total valuation 5exit valuation à retention=M
5$300M Ã 0:50=6:7 5$22:39M:
ð10:7Þ
Step 6: The proposed ownership percentage today is 5M/15M533.3%.
Step 7: The partial valuation is
Partial valuation5proposed %Ã total valuation
50:333 Ã $22:39M5$7:46M
ð10:8Þ
Step 8: Because partial valuation ($7.46M) is greater than the required investment ($6M),
the investment recommendation is positive. ’
This section has discussed one speci?c implementation of the VC method.
There are many other ways that practitioners combine the four main elements of
Section 10.1 into a VC method of valuation. In general, the main differences among
implementations are in the ordering of the steps. For example, one popular
implementation of the VC method is to leave the computation of the proposed
ownership percentage until the last step.
1
This proposed ownership percentage then
becomes a cutoff value for a good investment. Another variation is to leave the exit
valuation until the last step—then the VC method produces a cutoff exit valuation
for a good investment. All these alternative implementations will lead to the same
investment recommendations if the same inputs are used.
10.3 THE MODIFIED VC METHOD
The modi?ed VC method differs from the standard method in the explicit recog-
nition of the costs of VC investing: management fees and carried interest. As
discussed earlier in Section 10.1.2, the standard approach assumes (implicitly) that
such costs are included in the target multiple of money. This assumption is not ideal
1
Lerner (2002) demonstrates an example of this implementation.
10.3 THE MODIFIED VC METHOD 185
for two reasons. First, it mixes costs into the valuation step so that the total
valuation may not be the same across different investors, even if these investors
have the same expectations and value-added for the company. Second, it makes it
dif?cult to be precise about target rates, because many different concepts are being
included in one number. In this section we explain the mechanics for some simple
adjustments for fees and carried interest.
In Chapter 2, we de?ned the lifetime fees as the sum of the annual management
fees for the life of that fund, then the investment capital of the fund as equal to the
committed capital of the fund minus the lifetime fees. For EBV, Appendix 2.A tells
us that the fund has $100M of committed capital, with 2 percent fees charged on this
capital in each year. This implies lifetime fees of $20M and investment capital of
$80M. Next, we add another de?nition: the LP cost of an investment represents the
gross cost (including fees) of an investment to the LPs of the fund. We compute
the LP cost for any investment as
LP cost 5ðcommitted capital=investment capitalÞ Ã $I ð10:9Þ
Thus, for the example of EBV, committed capital is $100M and investment
capital is $80M, so the LP cost is (100/80 Ã $6M) 5$7.5M. The idea behind this
calculation is for the GPs to explicitly consider the true cost of each investment.
Because a $6M investment represents 7.5 percent of the $80M of investment capital,
the GP is effectively “spending” 7.5 percent of the lifetime fees on this investment as
well. After all, if the GP fails to ?nd enough good investments, he can always release
the LPs from their commitments and proportionally reduce the management fees of
the fund. In the postboom period, many VC ?rms did exactly that.
Some VCs object to the modeling of LP cost in this way. Often it seems
that this objection is based on a belief that the management fees should be
considered as “reasonable compensation” for the GP’s time and effort, and the
GP should not make different investments just because of these fees. It is
important to emphasize that our model of LP cost does not mean anything about
the “reasonableness” of management fees. Rather, it just puts GPs on par with
any other honest agent who is providing a service. For example, consumers
frequently must decide whether to repair a broken item or to buy a new one. The
cost of repairing that item is an important input into this decision; to estimate the
cost of repair, one should certainly include the labor costs as one component.
From an economic perspective, these labor costs are no different than the man-
agement fees paid to a GP.
A second modi?cation to the standard VC method is a deduction for carried
interest. The partial valuation of the investment does not belong entirely to the
limited partners. If the overall VC fund is pro?table, some of the proceeds from
the investment will belong to the GPs of the VC fund, and the remainder will go to
the LPs. Thus, in this step, we divide the partial valuation into two components, the
GP valuation (5expected carried interest) and the LP valuation (5partial
valuation2GP valuation). Then the investment recommendation is made by com-
paring LP valuation to LP cost.
186 CHAPTER 10 THE VC METHOD
Conceptually, it is straightforward to think of the GP valuation as repre-
senting the component of partial valuation that belongs to the GP. Mechanically, it
is not so easy to estimate this component. The main problem is that carried interest
in any one investment will depend on the pro?ts (and losses) of all other invest-
ments made by the fund. Because some of these fund investments have not been
made yet, it is not possible to get an exact solution for this problem. Instead, we
attempt only a rough approximation for an entire fund, using the (expected) gross
value multiple (GVM) of the fund as the key input. As ?rst de?ned in Chapter 3
(Equation (3.15)), the GP% for a completed fund is
GP%5carried interest=total distributions
5Carry%Ã ðGVM Ã Investment Capital 2Carry BasisÞ
=ðGVM Ã Investment CapitalÞ
ð10:10Þ
To make Equation (10.10) operational for living funds, we replace the GVM
in the equation with our best guess for the GVM for the fund. We call this guess the
“expected” GVM. If an analyst has special information about any speci?c fund,
then he can use this information in estimating the expected GVM for that fund. For
the general cases studied in this book, we will use an expected GVM of 2.5, which
is the approximate GVM found for the full set of investments in the SHE database.
This GVM tends to differ by round (as shown in the exhibits in Chapter 7), but to
keep things simple we will ignore these differences and just use 2.5 for all examples
in this chapter.
The formula for GP% tells us what part of any investment effectively
“belongs” to the GP. We can then use this GP% to estimate the GP valuation for
any speci?c investment as
GP valuation 5GP%Ã partial valuation ð10:11Þ
and the LP valuation as
LP valuation5Partial valuation 2GP valuation
5ð1 2GP%Þ Ã partial valuation
ð10:12Þ
With these de?nitions, we are ready to list the 11 steps in the modi?ed VC
method. The ?rst 7 steps are the same as in the standard VC method. Steps 8, 9, and
10 are new steps where we calculate LP cost, GP valuation, and LP valuation,
respectively. Step 11 is a revised version of the investment recommendation step.
Modi?ed VC Method: 11 Steps
Step 1: What is the required investment today? (5$I)
Step 2: What is the exit valuation for this company? ($ exit valuation)
Step 3: What is the target multiple of money on our investment? (M)
Step 4: What is the expected retention percentage? (retention)
10.3 THE MODIFIED VC METHOD 187
Step 5: Estimate the total valuation for the company today:
Total valuation 5$ exit valuation à retention=M
Step 6: What is the proposed ownership percentage today? ( proposed %)
Step 7: Estimate the partial valuation for this investment:
Partial valuation 5proposed %Ã total valuation
Step 8: Estimate the LP cost for the investment:
LP cost 5ðcommitted capital=investment capitalÞ Ã $I
Step 9: What is the expected GP% for this investment?
GP%5Carry%Ã ðGVM Ã Investment Capital 2Carry BasisÞ
=ðGVM Ã Investment CapitalÞ
Step 10: Estimate the LP valuation from this investment:
LP valuation 5ð1 2GP%Þ Ã partial valuation
Step 11: Investment Recommendation: Compare LP valuation to LP cost.
EXAMPLE 10.2
Assume the same setup as Example 10.1, except now we will also perform the new Steps 8,
9, and 10 before making an investment recommendation in Step 11.
Problem What is your investment recommendation?
Solution Our starting points are the answers to Steps (1) through (7) in Example 10.1.
Picking up where we left off, we go to Step 8 in the modi?ed VC method:
Step 8: As discussed earlier, annual fees of 2% for 10 years imply lifetime fees of $20M
and investment capital of $80M for this $100M fund. Thus, we can compute the
LP cost as
LP Cost 5ð100=80Þ Ã $6M5$7:5M ð10:13Þ
Step 9: Using a baseline estimate of 2.5 for the GVM, we have
GP%50:20 Ã ð2:5 Ã 80 2100Þ=ð2:5 Ã 80Þ 50:10 ð10:14Þ
188 CHAPTER 10 THE VC METHOD
Step 10: In Example 10.1, we estimated a partial valuation of $7.46M. Thus, the LP
valuation is
LP valuation 5ð1 20:10Þ Ã 7:46M5$6:71M: ð10:15Þ
Step 11: The investment recommendation is based on the comparison between LP
valuation ($6.71M) and LP cost ($7.5M). We can see that the modi?cations
made a big difference: The cost side went up by $1.5M and the bene?ts (to LPs)
fell by $0.75M. Together, these two changes alter our baseline recommendation.
Exhibit 10-2 shows the output for the VC_METHOD worksheet, with results for
both the standard and modi?ed VC method for this example.
We should never rely on a single set of assumptions. In particular, the investment
recommendation will often be sensitive to assumptions about the exit valuation and the success
probability. A sensitivity analysis for these assumptions is given in Exhibit 10-3.
EXHIBIT 10-2
VC METHOD SPREADSHEET
Standard and Modi?ed VC Method
Required Investment $6.00
Exit Valuation $300.00
Target Multiple of Money 6.7
Expected Retention 50.00%
Proposed Ownership Percentage 33.33%
Committed Capital $100
Lifetime Fees $20
Carry% 20.00%
Expected Gross Value Multiple 2.5
GP% 10.00%
Total Valuation $22.39
Partial Valuation $7.46
LP Cost $7.50
GP Valuation $0.75
LP Valuation $6.71
Standard VC Method Recommendation Invest
Modi?ed VC Method Recommendation Do Not Invest
NOTE: All $ in millions.
10.3 THE MODIFIED VC METHOD 189
’
Let’s do one more example of the modi?ed method, this time from the beginning.
EXAMPLE 10.3
Assume that EBV invested in Newco at the terms in Example 10.1, and it is now one year
later. Talltree is considering an $8M Series B investment in Newco. Talltree proposes to
structure the investment as 5M shares of CP. The employees of Newco have claims on 10M
shares of common stock, and the previous venture investors (EBV) hold 5M shares of Series
A CP. Thus, following the Series B investment, Newco will have 10M common shares
outstanding and would have 20M shares outstanding upon conversion of all the CP. Talltree
estimates a 50 percent probability for a successful exit, with an expected exit time in four
years. The $250M Talltree fund has annual fees of 2 percent for each of its 10 years of life
and earns 20 percent carried interest on all pro?ts.
Problem What is your investment recommendation?
Solution To answer this question, we perform each step of the modi?ed VC method:
Step 1: The required investment 5$I 5$8M.
Step 2: We will use the same basic approach as we did in Example 10.1 and use $300M as
our estimate of the exit valuation.
Step 3: With a cost of venture capital of 15%, a successful exit probability of 50%, and a
successful exit time of 4 years, we can calculate the required multiple of money as
Required multiple of money 5M51:154=0:50 53:5 ð10:16Þ
EXHIBIT 10-3
SENSITIVITY ANALYSIS
Sensitivity of LP Valuation
(LP Cost 5 $7.5M for all cases)
Positive investment recommendations given in bold
probability of success (p)
0.2 0.3 0.4
200 2.98 4.47 5.97
Exit valuation 300 4.47 6.71 8.95
400 5.97 8.95 11.93
190 CHAPTER 10 THE VC METHOD
Step 4: For this example, we assume the sample average from the Sand Hill Econometrics
data set for second round investments: retention 560%.
Step 5: Using the answers to Steps 2 to 4, we can estimate the total valuation as
Total valuation 5$300M Ã 0:60=3:5 5$51:43M ð10:17Þ
Step 6: The proposed ownership percentage today is 5M / 20M525%
Step 7: The partial valuation is
Partial valuation 551:43 Ã 0:25 5$12:86M ð10:18Þ
Step 8: Annual fees of 2% for 10 years imply lifetime fees of $50M for this $250M fund.
Thus, the investment capital is $250M2$50M5$200M, and we can compute the
LP cost as
LP Cost 5ð250=200Þ Ã $8M5$10M: ð10:19Þ
Step 9: Using a baseline estimate of 2.5 for the GVM, we have
GP%50:20 Ã ð2:5 Ã 200 2250Þ=ð2:5 Ã 200Þ 50:10 ð10:20Þ
Step 10: The LP valuation is
LP valuation 5ð1 20:10Þ Ã 12:86M5$11:58M: ð10:21Þ
Step 11: The investment recommendation is based on the comparison between LP valuation
($11.58M) and LP cost ($10.00M). Thus, the baseline recommendation is to invest.
A sensitivity analysis for this recommendation is given in Exhibit 10-4.
’
EXHIBIT 10-4
SENSITIVITY ANALYSIS
Sensitivity of LP Valuation
(LP Cost = $10M for all cases)
Positive investment recommendations given in bold
probability of success
0.4 0.5 0.6
200 6.17 7.72 9.26
Exit Valuation 300 9.26 11.58 13.89
400 12.35 15.44 18.52
10.3 THE MODIFIED VC METHOD 191
SUMMARY
The VC method is the most popular valuation technique used by practicing venture capi-
talists. The key elements of this technique are (1) focusing on the value of the company at the
time of a successful exit, (2) using of a high target return re?ecting the signi?cant probability
of failure, (3) accounting for a reduction in the current ownership percentage because of later
rounds of investment, and (4) an investment recommendation. There are many ways that
these elements can be combined—the actual implementation of the VC method is often a
matter of taste. In this chapter, we showed two possibilities. The standard VC method is an
example of the most popular approach; the modi?ed VC method adjusts the standard method
to explicitly account for management fees and carried interest.
KEY TERMS
Exit valuation
Successful exit
Target multiple of money,
Target return
Expected retention
percentage
Required investment
Total valuation
Relative valuation,
Absolute valuation
Standard VC method
Modified VC method
LP cost
Partial valuation
GP valuation
LP valuation
REFERENCES
Lerner, Josh and John Willinge, 2002, A Note on Valuation in Private Equity Settings, HBS Background
Note 297À050.
EXERCISES
10.1 Suppose that the following four funds—all with committed capital of $100M—have
combined to form a syndicate to invest in Newco:
(I) ABC Fund, management fees of 2.5 percent per year of committed capital for all
10 years.
(II) DEF Fund, management fees of 2.5 percent per year for the ?rst 5 years, then decreasing
by 25 basis points per year in each year from 6 to 10. All fees calculated based on committed
capital.
(III) UVW fund, management fees of 2.0 percent per year. During the ?rst 5 years of the
fund, these fees are charged based on committed capital. Beginning in year 6, the fees are
charged based on net invested capital. UVW expects to be fully invested by the beginning of
year 6, and also to have realized 25 percent of all investment capital by this time. In each of
the subsequent 5 years, UVW expects to realize about 15 percent of all investment capital.
(IV) XYZ fund, management fees of 2.0 percent per year of committed capital for all 10
years. The XYZ fund expects to make all exits very quickly and to reinvest capital back into
new investments. The total amount of investments is limited to $100M.
192 CHAPTER 10 THE VC METHOD
(a) Suppose that each fund in the syndicate invests $5M in Newco. What is the LP cost for
each fund?
(b) It is possible that all four funds could agree on all the assumptions to the VC method, but
still disagree about the wisdom of making this investment. Explain the economic logic
behind this possibility.
10.2 EBV is considering a $5M Series A investment in Newco. EBV proposes to structure the
investment as 6M shares of convertible preferred stock. The employees of Newco have claims
on 10M shares of common stock. Thus, following the Series A investment, Newco will have
10M common shares outstanding and would have 16M shares outstanding on conversion of the
CP. EBV estimates a 25 percent probability for a successful exit, with an expected exit time in
5 years and an exit valuation of $500M. The $100M EBV fund has annual fees of 2 percent for
each of its 10 years of life and earns 20 percent carried interest on all pro?ts.
(a) What is your investment recommendation for EBV? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 25 percent is an aggressive
assumption about the probability of success for a ?rst-round investment?
10.3 Assume that EBV invested in Newco at the terms in Exercise 10.2, and it is now one
year later. Talltree is considering a $10M Series B investment in Newco. Talltree proposes to
structure the investment as 8M shares of convertible preferred stock. The employees of
Newco have claims on 10M shares of common stock, and the previous venture investors
(EBV) hold 6M shares of Series A convertible preferred. Thus, following the Series B
investment, Newco will have 10M common shares outstanding, and would have 24M shares
outstanding on conversion of the CP. Talltree estimates a 40 percent probability for a suc-
cessful exit, with an expected exit time in 4 years and an exit valuation of $500M. The
$250M Talltree fund has annual fees of 2 percent for each of its 10 years of life and earns 20
percent carried interest on all pro?ts.
(a) What is your investment recommendation for Talltree? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 40 percent is an aggressive
assumption about the probability of success for a second-round investment?
10.4 Assume that EBV and Talltree invested in Newco at the terms in Exercises 10.2 and
10.3, and it is now one year later. Owl is considering a $20M Series C investment in Newco.
Talltree proposes to structure the investment as 12M shares of convertible preferred stock.
The employees of Newco have claims on 10M shares of common stock, and the previous
venture investors hold 6M shares of Series A convertible preferred (EBV) and 8M shares of
Series B Convertible Preferred (Talltree). Thus, following the Series C investment, Newco
will have 10M common shares outstanding and would have 36M shares outstanding on
conversion of the CP. Owl estimates a 50 percent probability for a successful exit, with an
EXERCISES 193
expected exit time in three years, and an exit valuation of $500M. The $500M Owl fund has
fees as given in Appendix 2.C in Chapter 2.
(a) What is your investment recommendation for Owl? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 50 percent is an aggressive
assumption about the probability of success for a third-round investment?
194 CHAPTER 10 THE VC METHOD
CHAPTER 11
DCF ANALYSIS OF GROWTH
COMPANIES
THE EXIT VALUE is the most important input into the VC method. How
should we estimate this value? There are two types of approaches: discounted cash
?ow (DCF) analysis (absolute valuation) and comparables analysis (relative
valuation). The key idea of absolute valuation is to “make up your own mind” about
the company. You can use all kinds of evidence to inform your decision, but
ultimately you must take a stand on the various inputs necessary to value the
business at a successful exit.
In Section 11.1, we provide a framework for our DCF analysis, breaking down
the valuation problem into three distinct periods in the life cycle of a company: the
venture period (which ends with the exit), a rapid-growth period (which immediately
follows the exit), and a stable-growth period. Cash ?ow analysis is introduced in
Section 11.2 with an explanation of the key formulas and an example DCF calcu-
lation. In Section 11.3, we focus on the transition from rapid to stable growth and the
estimation of the value of the company at the time of this transition. This value,
which we call a “graduation value”, is of particular importance for growth compa-
nies. In Section 11.4, we do a full DCF model for two companies and demonstrate
how to use market data to inform the key drivers of the model. Many of the examples
in this chapter use data from the DCF.xls spreadsheet included with the book.
The topics covered in Chapters 11 and 12 are worthy of an entire book. With
these two chapters, we focus on key valuation concepts and their application to
young growth companies. The general topics of absolute and relative valuation are
covered in more depth in many other books, two of which stand out. The ?rst,
Valuation (Koller et al., 2005), is the most recent valuation book from McKinsey
and Company. This book takes a managerial view toward valuation and value
creation and develops the useful framework for the valuation of growth discussed in
Section 11.3. The second book, The Dark Side of Valuation (Damodaran, 2009), is
a specialized treatment of the valuation of growth companies (and other hard-to-
value assets), written by a ?nance professor who is a proli?c author of valuation
195
books. Professor Damodaran’s website, http://pages.stern.nyu.edu/Badamodar/, is
an excellent source for current data that can be used as inputs and comparisons for
valuation problems.
11.1 DCF ANALYSIS: CONCEPTS
VC-backed companies go through many stages of development. In earlier chapters,
we focused on the stages corresponding to rounds of VC investment; all these
stages effectively occur during the “childhood” of a company. We refer to this
childhood as the venture period. For a successful VC-backed company, an IPO exit
marks the beginning of its adolescence, with a rapid-growth period still to come.
Usually, it is only after many more years that the company will reach maturity and
settle down to a stable-growth period. Exhibit 11-1 gives a schematic example of
these periods, with some appropriate milestones. One of these milestones, which we
call graduation, marks the transition from the rapid-growth period to the stable-
growth period.
At time zero—the initial VC investment—we need to estimate an exit value
for the end of the venture period. The venture period is T years long, where T
typically varies between three and seven years. The exit value will be based on
forecasts for the rapid-growth and stable-growth periods. Thus, in estimating the
exit value, we are imagining the company T years into the future and trying to
EXHIBIT 11-1
PHASES OF GROWTH
S T 0
Rapid-
Growth
Period
Stable-
Growth
Period
graduation exit Venture
Period
Initial VC investment
3 to 7 years long:
ends with IPO or
acquisition
3 to 10 years long:
ends when company
enters period of stable growth
and return on capital and
operating margin approach
industry averages
In perpetuity
return on new
investment close
to the cost
of capital
196 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
?gure out how long rapid growth will be sustained from that point. Although this
may seem to be a daunting exercise, even a cursory treatment can provide useful
insights into the determinants of long-run success for the business and can also help
investors to better understand the dynamics of a company’s industry.
How can we estimate the typical length of a rapid-growth period? We can get
some hints by looking at historical data. Exhibit 11-2 compares the revenue growth
of newly listed public companies to that of their respective industries in the years
following their IPOs.
The key variable in Exhibit 11-2 is the industry-adjusted revenue growth
rate. To obtain this rate, we start by computing the revenue growth rate for each
industry. Then, for each ?rm, we subtract the appropriate industry rate from the ?rm’s
growth rate.
1
We compute the “years since IPO” as the total number of years since the
company ?rst appeared in the S&P database, a comprehensive source of all ?rms
that ?led ?nancial statements with the SEC. The middle line of Exhibit 11-2
shows the median industry-adjusted growth rate, the top line gives the 75th percentile,
and the bottom line gives the 25th percentile. In the ?rst full year after their IPO, ?rms
EXHIBIT 11-2
REVENUE GROWTH COMPARED TO INDUSTRY AVERAGES,
PLOTTED AS A FUNCTION OF “YEARS SINCE IPO”
1 2 3 4
Years since IPO
5 6 7
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
–20.0%
10.0%
–10.0%
0.0%
R
e
v
e
n
u
e
G
r
o
w
t
h
-
I
n
d
u
s
t
r
y
A
v
e
r
a
g
e
75th percentile
25th percentile
median
Source: Wharton Research Data Systems (WRDS), S&P Compustat.
1
Industries are de?ned by the ?rst three digits of the Standard Industrial Classi?cation (SIC) code. These
codes can be viewed at http://www.osha.gov/pls/imis/sic_manual.html.
11.1 DCF ANALYSIS: CONCEPTS 197
grow much faster than their industry: in year 1, the median industry-adjusted growth
rate is 14.7 percent, and the 75th percentile is 57.1 percent. By the ?fth year after the
IPO, however, this median is almost exactly 0; thus, as measured by revenue growth,
we can say that the typical ?rm reaches “maturity” within ?ve years after the IPO.
Also, although some ?rms continue to grow faster than their industry average beyond
year 5, the overall distribution of industry-adjusted growth rates is nearly symmetric
around zero. This symmetry demonstrates that the ?ve-year-old public ?rms are fairly
representative of their industries.
Revenue growth at the industry average is not the only signal that a company
has entered a stable-growth period. A good analyst should also consider the
company’s return on capital (R) and operating margins. During the rapid-growth
phase, we would expect a company to be earning R above the cost of capital (r),
even if these returns are not expected to be realized until several years in the future.
Furthermore, the rapid-growth phase is often characterized by operating margins
lower than industry averages, as companies scale up their production and price
aggressively to gain market share. In the stable-growth phase, both R and operating
margins should settle down to industry averages.
11.2 DCF ANALYSIS: MECHANICS
DCF analysis is the gold standard of valuation. If done properly with accurate
inputs—a big “if ”—a DCF model will produce the “correct” valuation of a ?rm.
For this reason, most investment bankers, ?nancial analysts, and academics make
DCF analysis a centerpiece of their valuation work. Although there are many
different types of DCF models, the simple capital structure of most VC portfolio
companies renders moot many of these differences, so we will be able to con-
centrate on the key concepts common to all types.
All DCF models have two key inputs: Discount rates (the “D” part) and cash
?ows (the “CF” part). Discount rates for venture capital were discussed at length in
Chapter 4. In this chapter, we need discount rates for public companies, so the cost
of venture capital is not directly applicable. There are several options for estimating
discount rates for public companies. The simplest option—used in this chapter—is
to just use the average cost of capital for the company’s industry. The Industry
Statistics worksheet of the DCF.xls spreadsheet provides this data for 100 different
industries. A more complex alternative is to use a smaller group of comparable
companies. This alternative will be discussed in Chapter 12.
We focus most of this section on the computation of cash ?ow. The concept
of cash ?ow is designed to pierce the accounting veil used for ?nancial reporting
and taxes so that we are left with the cash that is actually generated by the business.
Also, we want to compute the cash ?ows generated by all the assets of the ?rm,
irrespective of the types of claims (equity, debt, preferred stock), on those assets.
198 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
To do this, we abstract from the actual capital structure and assume that the ?rm is
all-equity ?nanced. Indeed, the assumption of all-equity ?nancing is very reason-
able for VC-backed companies. Exhibit 11-3 shows the mean and median per-
centage of debt in the capital structure of VC-backed companies in each of the 15
years subsequent to their IPOs. For each ?rm, we compute the enterprise value as
the market value of equity plus the book value of debt and then compute the
percentage of debt in this enterprise value:
We see from these data that even 15 years after their IPOs, VC-backed ?rms
still have only a mean debt percentage of 11.0 and a median percentage of 6.4.
During the rapid-growth phase in the ?rst few years after the IPOs of these ?rms,
their percentages are even lower. Thus, we conclude that the simplifying assumption
of all-equity ?nancing is close to the truth for the vast majority of VC-backed ?rms.
Throughout our analysis, we analyze only operating assets, income, and
expenses. Nonoperating assets would include excess cash, marketable securities, or
EXHIBIT 11-3
LEVERAGE OF VC-BACKED FIRMS
Years Since IPO Mean Median
0 4.7% 1.2%
1 4.0% 1.9%
2 5.7% 2.8%
3 6.8% 3.8%
4 7.2% 3.9%
5 8.1% 4.4%
6 8.2% 5.1%
7 11.1% 6.0%
8 8.7% 5.6%
9 10.6% 6.2%
10 11.0% 6.0%
11 11.8% 6.4%
12 12.4% 8.9%
13 11.0% 7.8%
14 7.7% 4.8%
15 11.0% 6.4%
Source: Michael Roberts, Wharton.
11.2 DCF ANALYSIS: MECHANICS 199
anything else that is unrelated to the revenue-producing business of the company.
Nonoperating assets can comprise a signi?cant fraction of the asset base of mature
companies, and disentangling operating from nonoperating assets can require deep
analysis of accounting statements. In this instance, we are fortunate to be analyzing
companies with short histories, so both the capital structure and asset base are rela-
tively simple, and we can focus our attention on the operating side of the business.
For a company with only operating assets, the standard de?nition of cash
?ow is
CF 5EBITð1 2tÞ 1depreciation 1amortization
2capital expenditures 2NWC
ð11:1Þ
where
CF 5 cash ?ow,
EBIT 5 earnings before interest and taxes,
t 5 the corporate tax rate, and
?NWC 5 ?net working capital 5?net current assets À ? net current liabilities.
Let’s examine each of the terms in Equation (11.1). The ?rst term, EBIT, is the
accounting measure that forms the base for all cash ?ow calculations. For an all-
equity ?rm without nonoperating income or expenses, EBIT is equivalent to pretax
net income. In this case, EBIT (1 2 t) represents the total after-tax income that is
produced by all the assets of the ?rm. This is an accounting measure of income that
includes some noncash expenses and also excludes some cash expenditures. The
included noncash expenses are depreciation and amortization, which reduce EBIT
on the income statement but do not require any direct cash outlays by the ?rm.
Thus, we add both these items back in Equation (11.1). In contrast, capital
expenditures—investments by the company in plant and equipment—are not
treated as an expense on the income statement, but do require a cash outlay. Thus,
we subtract capital expenditures in Equation (11.1). For growing ?rms, it will
usually be the case that capital expenditures exceed depreciation. The remaining
item is ?NWC, the change in net working capital. As a business grows, its working
capital needs will usually grow as well. If working capital goes up, then some extra
cash must be kept in the business, and this will reduce cash ?ow. Thus, we subtract
?NWC in Equation (11.1).
Using Equation (11.1), cash ?ow calculations are straightforward for past
years, when all the inputs are easily available. In DCF valuation, however, we need
inputs for future years; therefore it is necessary to make forecasts, most often for
the next ?ve or ten years. This is not as dif?cult as it sounds because many of the
forecasts will be driven by a few common assumptions. We will demonstrate how
this works in Section 11.3. For now, we focus on the mechanics of Equation (11.1),
with a few additional simpli?cations. First, because we have already assumed an
all-equity ?rm, there will be no interest expense, and EBIT (1 2t) will just be equal
to earnings (E). Second, we assume that amortization—which is most often related to
200 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
the acquisition of assets from other companies—is zero. Finally, we de?ne net
investment (NI) as
NI 5capital expenditures 1?NWC 2depreciation: ð11:2Þ
For some applications, it is helpful to write NI as a fraction of earnings, with
this fraction known as the investment rate (IR):
NI 5IR Ã E: ð11:3Þ
Some authors refer to the investment rate as the plowback ratio (because it
is the fraction of earnings that is “plowed back” into investment) or the rein-
vestment rate.
By substituting Equation (11.2) and Equation (11.3) into Equation (11.1), we
can rewrite cash ?ow as
CF5E2NI 5E2IR Ã E5ð1 2IRÞ Ã E: ð11:4Þ
To complete a DCF calculation, we add the discounted values for each annual
cash ?ow. In principle, one must estimate cash ?ows for every year until the end of
time. At this point, the timing of Exhibit 11-1 comes to rescue us. At graduation,
instead of building a model with forecasts for each year, we exploit the assumptions
of stable growth and compute graduation value as a perpetuity: the NPV of a
perpetual income stream with a constant growth rate and constant discount rate.
The present value of a perpetuity with an initial annual payment (starting in one
year) of X growing at rate g and discounted at rate r is
NPV of perpetuity 5X=ðr 2gÞ: ð11:5Þ
Thus, the graduation value in our DCF can be written as
Graduation Value 5GV5CF
S 11
=ðr 2gÞ 2E
s
à ðg=RðnewÞÞ
2
: ð11:6Þ
With these quantities and de?nitions, we can compute the NPV of the ?rm as
NPV of firm at exit 5
CF
T 11
1 1r
1
CF
T 12
ð1 1rÞ
2
1
. . .
1
CF
T 1n
ð1 1rÞ
n
1
. . .
1
CF
S
1GV
ð1 1rÞ
S 2T
ð11:7Þ
where CF
n
is the cash ?ow in year n. Note that we will use both the growth rate g
and the discount rate r in real terms—that is, they are nominal rates minus the
in?ation rate. The model is thus invariant to in?ation, because it uses real forecasts
and real discount rates. Equation (11.7) implicitly assumes that all cash ?ows occur
2
Note that the second term in Equation (11.6) is a necessary adjustment to make the model invariant to
changes in g when the ?rm’s investment return (in the stable growth period) equals exactly its cost of
capital.
11.2 DCF ANALYSIS: MECHANICS 201
at the end of the year. Because it is more realistic to assume that annual cash ?ows
are spread evenly through the year, many analysts perform a midyear correction
on Equation (11.7) by bringing every cash ?ow forward by six months. Mathe-
matically, this correction is done by multiplying the answer from Equation (11.7)
by the square root of (1 1r). We will use this correction on all the computations in
this chapter.
EXAMPLE 11.1
The projections for Newco’s rapid-growth period are given in Exhibit 11-4. The nominal
discount rate is 11 percent, the stable nominal growth rate is 5 percent, and the in?ation rate
is 3 percent. Thus the real discount rate and stable growth rate are 8 percent and 2 percent,
respectively. We will express everything in real dollars.
Problems
(a) Compute the NI in each period.
(b) Compute CF in each period.
(c) Compute the graduation value.
(d) Compute the NPV of Newco.
(e) Do a sensitivity analysis of this NPV using (real) stable growth rates of 0 percent and 4
percent.
Solutions (a) and (b) The computations for NI and CF are given in Exhibit 11-5 and are
discussed below.
Several assumptions have been made to reach these forecasts. In Section 11.3, we
discuss these assumptions at length; for now, we take these forecasts as given and just work
through the computations of cash ?ow and NPV. The graduation revenue and margin (year 7)
EXHIBIT 11-4
NEWCO CASH FLOW FORECASTS
Year 0 1 2 3 4 5 6 7 8
Revenue 80.0 127.4 175.2 224.7 276.1 332.7 395.6 462.5 471.7
Operating Margin 10.0% 10.7% 11.4% 12.1% 12.9% 13.6% 14.3% 15.0% 15.0%
EBIT 8.0 13.6 20.0 27.3 35.5 45.2 56.5 69.4 70.8
Taxes 3.2 5.5 8.0 10.9 14.2 18.1 22.6 27.7 28.3
E 4.8 8.2 12.0 16.4 21.3 27.1 33.9 41.6 42.5
Depreciation 5.0 7.8 10.6 13.3 16.1 18.9 21.7 24.5 27.3
Gross Investment
(Capex 1 Net
New WC)
32.8 35.6 38.4 41.2 44.0 46.7 49.5 52.3 37.9
202 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
are $462.5M and 15 percent, respectively, and rapid growth rates (matched to historical
average of high growth ?rms) have been assumed between exit and graduation. To achieve
this growth, gross investment increases each year, but as can be seen in Exhibit 11-5, the NI
is constant across years. Then, to compute the cash ?ow, we can use Equation (11.1) for
each year.
(c) The graduation value will be a large part of the value of Newco. Using the assumption of
2 percent annual growth and a stable operating margin of 15 percent, the year 8 forecasts give
an estimated revenue of $471.7M, EBIT of $70.8M, and earnings of $42.5M. The tricky part
here is the forecast of NI. Although we can estimate depreciation using some fraction of the
capital base, the gross investment estimate is not so straightforward. It might seem logical to
forecast NI growth of 2 percent from year 7 to year 8, but this forecast would be a mistake.
NI is needed to fund growth. During the rapid-growth period, the investment rate is almost
always higher than it will be during the stable growth phase. To correctly forecast the
investment rate necessary for stable growth, we need some assumption about the return on
new investment. In these forecasts there is an assumption lurking behind the scenes; this
assumption will be discussed in Section 11.3.
Once we have a forecast for NI in year 8, we can calculate the CF in year 8 as $31.8M.
Then we can use a growth rate of 2 percent in Equation (11.6) to compute GV as
GV531:8=ð0:08 20:02Þ 241:6 Ã ð0:02=0:08Þ 5$520:3M: ð11:8Þ
(d) To compute the NPV, we use Equation (11.7), with a discount rate of 8 percent, GV as
given by Equation (11.8), and annual cash ?ows as given Exhibit 11-5. This yields an NPV of
$279.85M.
(e) To perform a sensitivity analysis using different growth rates, it is tempting to just
substitute these different rates into Equation (11.6). For example, for a growth rate of 3
percent, we would have
GV531:8=ð0:08 20:00Þ 241:6 Ã ð0:00=0:08Þ 5$398M; ð11:9Þ
and for a growth rate of 7 percent we would have
GV531:8=ð0:08 20:04Þ 241:6 Ã ð0:04=0:08Þ 5$775:2M: ð11:10Þ
With these estimates of GV, the NPV would change signi?cantly. Note, however, that
neither of these estimates takes into account any change in investment during the stable
growth period. As discussed earlier in part (c), growth is supported by new investment, and
different levels of growth require different investment rates. Thus, the GVs given in Equa-
tions (11.9) and (11.10) are not correct. To see why this is true, we need to do a little more
work, which we do in Section 11.3. ’
EXHIBIT 11-5
NI AND CF CALCULATIONS
NI 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 10.6
Cash Flow 223.0 219.6 215.8 211.5 26.5 20.7 6.1 13.8 31.8
11.2 DCF ANALYSIS: MECHANICS 203
11.3 GRADUATION VALUE
Equations (11.9) and (11.10) demonstrate that GV can be very sensitive to the
speci?c assumption about growth rates—especially if we are not careful about
adjusting for the correct level of investment. Indeed, this sensitivity is often criti-
cized as the main shortcoming of DCF models, particularly for VC transactions. To
deal with this sensitivity, some analysts use valuation ratios from comparable
companies to estimate graduation values. This book strongly recommends against
using comparable companies to compute graduation values in DCF models. In
Chapter 12, we use comparable companies to estimate exit values as an exercise in
relative valuation. There is nothing wrong with using comparables for relative
valuation. In this chapter, however, we are attempting an absolute valuation using a
DCF. The whole point of a DCF model is to make up your own mind about the
valuation of the company. By using valuation information from comparable com-
panies, you will never form your own opinion, and you will be missing the
opportunity for valuable insight into your investment.
To gain this insight, we begin by analyzing the determinants of growth. Con-
sidering some time period N, where Newco invests NI and earns a return on this new
capital of R. Thus, the new investment provides incremental earnings of NI Ã R. If we
assume that the period N earnings can be sustained inde?nitely without any new
investment (i.e., by simply replacing the old capital as it depreciates), then earnings in
period N11 can be written as
E
N 11
5E
N
1NI Ã R: ð11:11Þ
So the growth rate g is given by
g 5ðE
N 11
2E
N
Þ=E
N
5ðNI Ã RÞ=E
N
5IR Ã R: ð11:12Þ
Thus, growth is the product of the investment rate (IR) with the return on
capital (R). Holding R constant, if a company wants to increase growth, then it must
increase its investment rate. An increase in the investment rate, however, will
decrease cash ?ow (5(1 2 IR) Ã E), so there will always be a tradeoff. If the
investment NI earns a return of R every year in perpetuity, then the NPV of this
investment will be NI Ã R/r. With this equation, it is easy to see that the NPV of
this new investment will be positive if and only if R is greater than r. In other
words, new investment will only increase the value of a company when the return
on capital is greater than the discount rate.
We can gain further insight into the NPV of growth by substituting Equations
(11.4) and (11.12) into Equation (11.6) to obtain the following:
GV 5ð1 2IRÞ Ã E=ðr 2ðIR Ã RÞÞ: ð11:13Þ
Note that if R5r, then Equation (11.13) reduces to GV5E/r, so that gra-
duation value is independent of the investment rate and growth. By using Equation
(11.12), one can also rewrite Equation (11.13) in terms of g instead of IR:
204 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
GV 5ð1 2g=RÞ Ã E=ðr 2gÞ: ð11:14Þ
Koller, Goedhart, and Wessels (2005) refer to Equation (11.14) as “the Zen
of corporate ?nance”, and we agree with them that it is an equation worthy of
some contemplation. In particular, Equations (11.13) and (11.14) remind us that
a company cannot control both g and IR at the same time, and one cannot become
attached to any particular level of growth without recognizing that current cash ?ow
will suffer. Indeed, the relationship between g and IR is even deeper than suggested
by Equations (11.13) and (11.14), because the return on capital should also be a
function of IR.
Exhibit 11-6 is similar to Exhibit 5-1. The optimal NI
Ã
occurs when the (mar-
ginal) return on investment (ROI) is equal to r. By increasing NI further, the com-
pany could increase growth, but only at the cost of reduction in R. Similarly, the
company could increase R by cutting back on NI, but this would reduce growth.
To make Exhibit 11-6 operational, we need some intuition on how to estimate
NI
Ã
and R
Ã
. In general, ROI can only exceed r for investments where the company
has some competitive advantage (e.g., a patent on a key piece of technology, a
period of market exclusivity on a drug, or a powerful brand name). Most forms of
competitive advantage can be sustained only as long as there are barriers to entry.
EXHIBIT 11-6
RETURN ON CAPITAL AS A FUNCTION OF NI
10.0%
9.5%
9.0%
8.5%
8.0%
7.5%
7.0%
6.5%
6.0%
5.5%
5.0%
NI*
ROI
R
r
Return on investment (ROI)
Cost of capital (r)
Return on capital (R)
11.3 GRADUATION VALUE 205
Without barriers to entry, other companies will enter the market and put downward
pressure on ROI. In Section 11.4, we propose a baseline DCF model where R is set
to r for all levels of NI. Then, from this starting point, the analyst can experiment
with various levels of R
Ã
.r.
To illustrate a more complete model, we return to the Newco forecasts from
Example 11.1. The forecasts in this example were generated from a small-scale
model of growth, as shown in Exhibit 11-7. In building this model, we make a
distinction between capital in place at the time of graduation—“old capital”—and
capital created by new investments after graduation—“new capital”. The returns to
old capital are given by R(old), and the returns to new capital are given by R(new).
Unless otherwise noted, all general comments about return on capital refer to
R(new).
The inputs to the model are given in bold type. These inputs then drive the
cash?ow calculations in each year of the model (Exhibit 11-4), with graduation
values implied by the graduation inputs, and intermediate values pinned down by
EXHIBIT 11-7
MODEL ASSUMPTIONS FOR EXAMPLE 11.1
Exit (T) Graduation (S)
Years until Graduation (S-T) 7
Expected In?ation 3.0%
Industry Growth (average, nominal) 5.0%
Extra Growth (above 75th percentile) 0.0%
Revenue 80.0 462.5
Operating Margin 10.0% 15.0%
Tax Rate 40.0% 40.0%
Assets 50.0 244.8
Stable Growth (nominal) 5.0%
Stable Growth (real) 2.0%
Discount Rate (nominal) 11.0% 11.0%
Discount Rate (real) 8.0% 8.0%
R(old) (nominal) 20.0%
R(old) (real) 17.0%
R(new) (real) 8.0%
IR 25.0%
Depreciation % of Assets 10.0%
NPV $279.85
GV $520.27
206 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
matching the ?rm’s revenue growth rates to those of newly-public, rapid-growth
companies in the respective industry. Note that several entries in the table for
the graduation period are not given in bold: revenue, assets, and IR (as well as the
in?ation-adjusted values for r, g, and R(old)). These entries are all determined by
other inputs: the graduation revenue is determined by the exit year revenue and
rapid-growth assumptions; the graduation assets are determined by the graduation
earnings combined with R(old); and the IR is determined by the assumptions about
growth and R(new). This model is given in the Example 11.1 worksheet of the DCF
spreadsheet, and readers are encouraged to experiment with the inputs. This
spreadsheet also contains the investment function worksheet that was used to
generate Exhibit 11-6 (see “exhibit 11.6” tab). By using this function, readers can
input the correct level of R (average return on capital) for any corresponding level
of g or IR.
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL
With this background, we are prepared to sketch a baseline DCF model that can be
used as a starting point for exit valuation. We call this model the reality-check
DCF model.
11.4.1 Baseline Assumptions for the Reality-Check DCF
(I) On the exit date:
(a) Revenue is forecast for the average success case.
(b) Other accounting ratios (not valuation ratios) are estimated using
comparable companies or rule-of-thumb estimates.
(c) The discount rate is estimated from industry averages or comparable
companies (see Chapter 12).
(II) On the graduation date:
(a) The stable nominal growth rate is equal to expected in?ation; thus, the
real growth rate is zero.
(b) The return on new capital—R(new)—is equal to the cost of capital (r).
(c) The return on old capital—R(old)—is equal to the industry-average
return on capital (ROC).
(d) The operating margin is equal to the industry average.
(e) The cost of capital (r) is equal to the industry average cost of capital.
(III) During the rapid-growth period:
(a) The length of the rapid-growth period is between ?ve and seven years.
(b) Average revenue growth is set to the 75th percentile of growth for new
IPO ?rms in the same industry in respective years and is constructed
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 207
from data contained in Growth and Industry Statistics worksheets of
the DCF spreadsheet. Thus, as a baseline assumption, extra growth
(above 75th percentile) in Cell B8 is set to 0%.
(c) Margins, tax rates, and the cost-of-capital all change in equal incre-
ments across years so that exit values reach graduation values in the
graduation year.
These assumptions should be considered as a starting point of analysis; they
are not intended to be de?nitive. For example, Assumption II(b)—that the return
on new capital is equal to the cost of capital—would only be consistent with
optimal investment behavior if the ROI line in Exhibit 11-6 was identical to the
cost of capital line. This is clearly an extreme assumption, which can be relaxed
as the analyst experiments with different inputs necessary to produce any given
valuation. Then, once this experimentation is complete, the analyst can ask
whether these relaxed assumptions are reasonable. For example, we can assume
that R(new) is greater than the cost of capital. This modi?ed assumption could
re?ect an adjustment from the base case based on an investment function like
Exhibit 11-6.
The next two examples illustrate the application of the reality-check model.
EXAMPLE 11.2
EBV is considering an investment in Semico, an early-stage semiconductor company. If
Semico can execute on its business plan, then EBV estimates it would be ?ve years until a
successful exit, when Semico would have about $50M in revenue, a 10 percent operating
margin, a tax rate of 40 percent, and approximately $50M in capital (5assets). Subsequent to
a successful exit, EBV believes that Semico could enjoy seven more years of rapid growth.
Problem To make the transaction work, EBV believes that the exit value must be at least
$300M. How does this compare with the reality-check DCF? How much must the baseline
assumptions change to jeopardize this valuation?
Solutions To get the inputs of the model, we consult the industry statistics worksheet in
DCF.xls. The semiconductor industry is listed in row 86 of this worksheet, which gives us
inputs of R(old) 528.67%, operating margin 527.73%, and r 515.55%. Also, the worksheet
gives the average revenue growth in the industry as 8.70 percent. To ?nd the 75th percentile
for rapid growth, we look in the Growth worksheet of DCF.xls and ?nd the respective annual
growth rate and adjust for the industry and for the in?ation. For example, the 75th percentile
rapid growth phase is 57.20%18.70% 2 3.0%562.9%.
3
Exhibit 11-8 summarizes the results of the reality-check model. The exhibit shows a
baseline reality-check estimate of $206.70M for the NPV. The problem asks us to test
3
Another way to relax the baseline assumptions here is to play with extra growth above the 75th per-
centile. You can experiment with adding an extra 5 percent, say, by entering the value in Cell B8 of the
worksheet. This cell is set to zero as a baseline assumption.
208 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
the sensitivity of this estimate to changes in the inputs and to see what changes would be
necessary to obtain an NPV of $300M. If we experiment with different inputs, we can
quickly see that the model is not sensitive to the stable growth (g) assumptions as long as
R(new) 5r. This is due to the second term in the Graduation Value formula, which
essentially “charges” the ?rm extra NI in year S for additional growth in year S11. So any
increase in g (which increases future CF) is exactly offset by a decline in current CF. If
R(new) .r, then increase g will result in a larger GV and thus also larger NPV. For
example, with g 510% and R(new) 520%, GV increases by $247.79M, and NPV rises to
$321.63. These would be very aggressive assumptions because it would imply a perpetual
return on capital near the same rate as the return earned in the rapid growth phase.
4
EXHIBIT 11-8
REALITY-CHECK DCF MODEL FOR SEMICO
Exit (T) Graduation (S)
Years until Graduation (S2T) 7
Expected In?ation 3.0%
Industry Growth (average, nominal) 8.7%
Extra Growth (above 75th percentile) 0.0%
Revenue 50.0 353.0
Operating Margin 10.0% 27.7%
Tax Rate 40.0% 40.0%
Assets 50.0 228.8
Stable Growth (nominal) 3.0%
Stable Growth (real) 0.0%
Discount Rate (nominal) 15.5% 15.5%
Discount Rate (real) 12.5% 12.5%
R(old) (nominal) 28.7%
R(old) (real) 25.7%
R(new) (real) 12.5%
IR 23.9%
Depreciation % of Assets 10.0%
NPV (with mid-year corrections) $206.70
GV $468.06
4
If R(new) , r, however, increasing g actually has a negative effect on NPV. Why? Because IR 5 g/R
(new), excessive investments when return on investments is low would hurt CF at S 11, and thus GV
shrinks. This is akin to setting NI . NI
Ã
in Exhibit 11-6.
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 209
Similarly, we could get the NPV to almost $300M ($295.87M) by adding extra 10 percent to
the rapid-growth rates from year 1 to year 7 (by entering “10%” to cell B8). Although this
change might seem arbitrary, we can anchor ourselves in the industry data to see just how
extreme this assumption would be. Furthermore, an extra 10 percent growth rate implies that
graduation revenue would be $589.3M, or 70 percent higher than the baseline level. To decide
whether this level is reasonable, we need to rethink our assumptions about market size, pricing,
and market penetration. Of course, we do not have enough data about Semico to make informed
judgments, so all we can do here is experiment with numbers. Next, we consider a more con-
crete example. ’
EXAMPLE 11.3
For the 12 months ended on September 30, 2009, Amgen, a publicly traded biotechnology
company (NASDAQ: AMGN), had $14.6B in revenue, an operating margin of 38.31 percent,
and $29.6B in assets (net of goodwill). Amgen’s enterprise value (on January 30, 2010) was
approximately $55B. It had no signi?cant net debt or interest costs.
Problem Perform a reality-check DCF for Amgen. What assumptions would be neces-
sary to justify Amgen’s current valuation?
Solutions To apply the reality-check DCF, we need to make some forecasts for Amgen’s
stable growth period. In the industry statistics worksheet, Amgen could be included in two
different industries, “biotechnology” and “drugs”, because the company enjoys both the
high growth potential of the biotech industry and the high current pro?tability of drug
companies.
The industry data worksheet shows more favorable averages for the drug industry, so
we give Amgen the bene?t of the doubt and use these estimates: r 511.55 percent,
R(old) 522.57 percent, and margin 530.15 percent.
5
In the past ?ve years, Amgen has
enjoyed growth of about 14 percent per year; for the next ?ve years, the consensus analysts’
forecast is 9 percent per year.
6
For our baseline model, we extend these forecasts for a seven-
year rapid growth period at 9 percent per year. As in all baseline reality-check models, we
assume only in?ationary growth ((real)g 50 percent, in this case) and R(new) 5r. Using
these assumptions, the reality-check DCF is summarized in Exhibit 11-9. The NPV com-
puted there, $56.09B, is almost exactly the actual market value. It turns out that no additional
assumptions are necessary to justify Amgen’s current market valuation. Exhibit 11-10 shows
the sensitivity of this NPV to some changes in the baseline assumptions.
5
Under current accounting rules, R&D is treated as an expense and not as a capital expenditure. Although
this accounting treatment does not affect cash ?ow calculations, it can lead to misleading calculations
about return on capital. For a detailed study of value creation, it makes more sense to treat R&D the same
way as other capital expenditures. This correction is beyond the scope of our treatment of DCF models.
Please see Koller et al. (2005) for a discussion.
6
Source: Yahoo Finance, http://?nance.yahoo.com/q/ae?s=AMGN, January 30, 2010.
210 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
Exhibit 11-10 shows a series of changes that would either positively or negatively
affect NPV. Moving down the rows in Exhibit 11-10 shows the combined impact of all
changes above and including that row. If we assume that Amgen maintains the 14 percent
nominal growth rate for the next seven years, its NPV will go up to $64.97B; further
assuming that R(new) 520 percent (second row) and g 55 percent (third row) raises the
NPV further to $72.59B. Finally, assuming that the operating margin perpetually stays at
38.3 percent pushes up the NPV to $82.93B. These together are very aggressive assumptions
indeed, and do not look very sustainable.
Now what changes to our baseline assumptions could lower the NPV? Recall that we
used industry estimates of the drug industry, since they were more favorable than those of the
biotechnology industry. If the operating margin matches that for the biotechnology industry
(26.9 percent), the NPV declines to $53.61B; increasing the cost of capital (r) to 12.3 percent
lowers NPV to $49.93B; decreasing the return on old capital to 14.8 percent further pushes
NPV down to $40.41B; ?nally, assuming a very conservative growth rate of 5 percent for the
next seven years lowers the NPV to $38.15B.
EXHIBIT 11-9
REALITY-CHECK DCF FOR AMGEN
Exit (T) Graduation (S)
Years until Graduation (S-T) 7
Expected In?ation 3.0%
Analysts’ Estimate (consensus, nominal) 9.0%
Analysts’ Estimate (consensus, real) 6.0%
Revenue 15.6 23.4
Operating Margin 38.3% 30.1%
Tax Rate 40.0% 40.0%
Assets 29.6 21.7
Stable Growth (nominal) 3.0%
Stable Growth (real) 0.0%
Discount Rate (nominal) 11.5% 11.5%
Discount Rate (real) 8.5% 8.5%
R(old) (nominal) 22.6%
R(old) (real) 19.6%
R(new) (real) 8.5%
IR 0.0%
Depreciation % of Assets 10.0%
NPV $56.09
GV $49.58
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 211
Of course, an in?nite number of combinations could obtain this result, but Exhibit 11-10
gives the ?avor of what is necessary. Based on these calculations, it appears that Amgen can
justify its January 2010 valuation. ’
SUMMARY
The exit value is the most important input in a VC valuation. To estimate exit values, we
have two main methods: absolute valuation (in this chapter) and relative valuation (in
Chapter 12). All types of absolute valuation can be reduced to some form of discounted cash
?ow (DCF) analysis. To perform a DCF analysis for a venture-backed company, we divide
the company’s life cycle into three parts: the venture period (while the company is still being
funded by VCs), the rapid-growth period (which immediately follows the VC exit), and the
stable-growth period (when growth, margins, and return on capital have settled down to
industry averages). Our reality-check DCF model uses inputs from the beginning of the
rapid-growth and stable-growth periods to determine the key cash ?ows and then computes
the NPV of these cash ?ows using industry average cost of capital.
KEY TERMS
Absolute valuation, relative
valuation
Discounted cash flow
(DCF) analysis
Venture period
Rapid-growth period
Graduation
Stable-growth period
Operating assets
Cash Flow (CF)
Earnings before interest and
taxes (EBIT)
EXHIBIT 11-10
NPV OF AMGEN UNDER DIFFERENT ASSUMPTIONS
Positive Changes to NPV
rapid growth (real) 11.0% $64.97
and R(new) 20.0% $64.97
and g 5.0% $72.59
and operating margin 38% $82.93
Negative Changes to NPV
operating margin 26.9% $53.61
and Cost of capital 12.3% $49.93
and R(old) 14.8% $40.41
and rapid growth (real) 5% $38.15
NOTE: All dollars in billions.
212 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
Earnings 5Net Income
Net investment (NI)
Investment rate (IR)
5plowback ratio
5reinvestment rate
Perpetuity
Graduation value
Midyear correction
Competitive advantage,
barriers to entry
Reality-check DCF
REFERENCES
Damodaran, Aswath, 2009, The Dark Side of Valuation, Prentice Hall, Upper Saddle River, NJ.
Koller, Tim, Marc Goedhart, and David Wessels, 2005, Valuation: Measuring and Managing the Value
of Companies, Wiley, Hoboken, NJ.
EXERCISES
11.1 EBV is considering an investment in Softco, an early-stage software company. If
Softco can execute on its business plan, then EBV estimates it would be ?ve years until a
successful exit, when Softco would have about $75M in revenue, a 20 percent operating
margin, a tax rate of 40 percent, and approximately $75M in capital. Subsequent to a suc-
cessful exit, EBV believes that Softco could enjoy seven more years of rapid growth. To
make the transaction work, EBV believes that the exit value must be at least $400M. How
does this compare with the reality-check DCF? How much must the baseline assumptions
change to justify this valuation?
11.2 True, False, or Uncertain: Firm value is maximized when the return on capital is
exactly equal to the cost of capital.
11.3 True, False, or Uncertain: If two ?rms have exactly the same balance sheet and income
statement on their respective graduation dates, then the ?rm with the higher growth rate will
also have the higher graduation value.
11.4 Perform a reality-check DCF for a publicly traded company of your choice.
EXERCISES 213
CHAPTER 12
COMPARABLES ANALYSIS
IN THIS CHAPTER we analyze exit values using comparables analysis,
sometimes abbreviated as comps and also known as multiples analysis, method of
multiples, and relative valuation. In the DCF analysis of Chapter 11, we valued
a company based on its cash ?ow and discount rates. DCF analysis is a form
of absolute valuation because it does not use information from relative values of
similar companies. In contrast, in comparables analysis the main idea is to get the
market’s opinion about a company. To do this we ?rst identify a set of similar
companies, and then we analyze a variety of valuation ratios for these companies.
We then use other market information to choose among and combine these various
ratios to arrive at our estimate of the exit valuation.
Suppose we are trying to estimate an exit valuation for Newco. After some
re?ection, we estimate that a success case for Newco would be $50M of revenue in
six years. We also observe that the public companies in Newco’s industry have
enterprise valuations of about 5 times revenue. By applying this same multiple to
Newco, we estimate an exit valuation of $250M. That is a quick-and-dirty example
of comparables analysis. In many cases, VCs will not take this analysis any further.
Sometimes this quick analysis is justi?ed, because a bundle of uncertainties pre-
vents any additional accuracy. In other cases, however, a careful analysis that
combines DCF and comparables can yield insights into valuation anomalies. In this
section we learn the steps necessary to perform a more careful comparables ana-
lysis. These steps expand on the quick-and-dirty analysis in two ways:
1. The choice of valuation measures (Section 12.1)
2. The choice of comparable companies (Section 12.2)
Among VCs, comparables analysis is by far the most popular method of exit
valuation. There is some empirical support for this popularity, as IPO valuation
seems to be driven more by comparables than by DCF analysis. Nevertheless, a
prudent investor should perform both DCF analysis (absolute valuation) and
comparables analysis (relative valuation) before making any investment decision.
In other words, form your own opinion, and then test it against the market.
214
It is important to remember that the valuation methods studied in Chapters 11
and 12 are only providing an analytical framework. By itself, this framework does
not answer the most dif?cult questions of valuation; for example, how do we
forecast “success case” revenue at exit? In the quick-and-dirty example given
above, we used a success-case revenue of $50M for Newco. Where does this
estimate come from? It does not come from ?nancial analysis, but rather from more
general business analysis that must occur during due diligence and investment
screening. There is no magic formula for making these estimates—if there were
such a formula, then venture capital would be an easy profession.
12.1 INTRODUCTION TO COMPARABLES
ANALYSIS
Suppose that we have been asked to estimate an exit valuation for Newco, the
same company analyzed in Example 11.1. In a successful exit, we estimate that the
company will have about 100 employees and generate $80M in revenue, $8M in
EBIT, $13M in EBITDA (5 earnings before interest, taxes, depreciation, and
amortization), $4.8M in earnings, and have $50M in book value of equity. We use
the same ?nancial estimates here as we did for the starting point of our DCF model.
If we attempt to value this company using the tools of DCF analysis, we would
begin at the exit date and forecast the cash ?ows, estimate a cost of capital, and then
compute an NPV for the company. Alternatively, we could ignore our own opinion
and look at how the public market values some similar companies today.
Exhibit 12-1 gives summary ?nancial and market data for four comparable
companies in Newco’s industry. For now, we will ignore the question of how we
identi?ed these speci?c companies, leaving that topic for Section 12.2. To form a
valuation multiple we need both numerators and denominators. The two numerators
most often used in comparables analysis are enterprise value (EV) and equity
market capitalization (5 market cap or equity market value). The former mea-
sures the market value of all the securities of the company, whereas the latter
measures the market value of just the common stock. Next, we need some
denominators. The most intuitive denominators are proxies for cash ?ow. Indeed, all
multiples have some deep connection to a cash ?ow ratio, even if the connection is
not apparent. In the end, however, all that really matters is that investors perceive
some usefulness in a multiple. If a multiple is perceived as useful, then it can be
predictive for the valuation of a comparable company.
For the analysis and exercises in this chapter, we will use six different
multiples:
1. EV/EBIT: EV is the total market value of all securities of the company,
including common stock, long-term debt, preferred stock, and so on.
12.1 INTRODUCTION TO COMPARABLES ANALYSIS 215
In practice, most of EV for public companies is in common stock and long-
term debt. The denominator, EBIT, is often viewed as proportional to a
steady-state cash ?ow measure, in which case the EV/EBIT ratio has an
intuitive interpretation as the ratio of ?rm value to cash ?ow.
2. EV/EBITDA: This is another popular measure, particularly among leveraged-
buyout investors. Like EBIT, some analysts view EBITDA as a cash ?ow
measure. Although this is true in the short run (where capital expenditures to
replace depreciated equipment can be delayed), it is de?nitely not true in the
long run. Nevertheless, even if EV/EBITDA does not have the same cash ?ow
interpretation as EV/EBIT, it can be particularly useful for evaluating
industries that have wide variation in their depreciation practices.
3. EV/Revenue: This is the multiple used in the quick-and-dirty analysis in the
introduction to this chapter. At ?rst glance, this multiple appears completely
divorced from any cash ?ow rationale because no measure of pro?tability is
included in the denominator. Nevertheless, this measure often provides the
most useful valuation ratio, particularly for high-growth industries favored
by VCs. In these industries, many companies have negative EBIT and
EBITDA, thus making it impossible to form reasonable multiples for those
measures. Because revenue is never negative, the EV/Revenue multiple is
always available.
4. Price/Earnings: The ratio of price to earnings, “P/E”, is probably the most
widely known valuation measure. In this context, “price” refers to the price
of a single share of stock, and “earnings” refers to earnings per share. With
company level data, we can compute the P/E ratio by dividing net income
(5 earnings) into market cap. Because earnings accrue only to shareholders
EXHIBIT 12-1
SUMMARY FINANCIAL INFORMATION FOR NEWCO COMPARABLES
ABC DEF GHI JKL
Revenue 80 70 40 55
EBIT 30 5 10 10
EBITDA 50 10 20 20
Net income 17 3 4 6
LTD 10 0 20 10
BV of equity 100 20 50 50
Market cap (Price) 300 280 150 200
EV 310 280 170 210
Employees 300 120 200 50
216 CHAPTER 12 COMPARABLES ANALYSIS
(not bondholders), the P/E numerator uses only the market cap, not the
whole enterprise value.
5. Price/Book: This measure is also popular among Wall Street professionals.
As with the P/E ratio, it is often referred to by the share level term of “price”,
which is then divided by book value per share. With company level data, we
can compute the P/B ratio by dividing book value of common equity into
market cap. As in the case of the P/E ratio, the P/B numerator uses only the
market cap, not the whole enterprise value. An enterprise level equivalent of
P/B would divide the book value of all assets into the EV. This enterprise
measure is popular among academics, but has not caught on much with
practitioners. The P/Bratio is motivated not by cash ?ow, but also by breakup
value. The idea here is that—if we believe the accounting statements—a P/B
ratio below 1 would indicate that the equity holders would be best off by
selling the company, repaying the debt, and pocketing the difference.
6. EV/Employees: Like the EV/Revenue ratio, the EV/Employees ratio would
appear to have no clear connection to either cash ?owor breakup value. As will
be seen below, a connection can indeed be established, but the best reason to
follow this ratio is that it can provide surprising insights in some cases.
Essentially, the logic is that the number of employees is the fastest-moving
measure of potential ?rm size, so even if all other accounting-based ratios are
lagging, the EV/Employee ratio might still provide some insight. Furthermore,
like the EV/Revenue ratio, the EV/Employee ratio will never be negative.
Although we focus attention on these six ratios, there is virtually no limit on
the ratios that are used in practice. In general, when forming a ratio, one starts with
a denominator of interest and then applies either EV or equity market value as the
numerator. One cannot use these numerators interchangeably—for any given
denominator, only one of these numerators would be correct. If the denominator is
an enterprise level quantity (e.g., EBIT, EBITDA, revenue, or employees), then EV
is the correct numerator. If the denominator represents some quantity that only
accrues to equity holders (e.g., earnings or book value of equity), then equity
market value is the correct numerator.
EXAMPLE 12.1
Problem Given the information on comparables in Exhibit 12-1, what is your best
estimate for the relative valuation of Newco?
Solution Exhibit 12-2 gives these valuation multiples for our four comparable compa-
nies, along with the average and median for each multiple:
1
1
In a sample of four companies, the median is the average of the two middle estimates.
12.1 INTRODUCTION TO COMPARABLES ANALYSIS 217
For each multiple and each comparable company, we can compute a comparable
valuation for Newco. For example, our exit revenue estimate (from Chapter 11) is $80M.
Then, using the ABC EV/Revenue multiple of 310/80 5 3.88, we can compute a comparable
valuation of 3.88 Ã $80M 5 $310M for Newco. Using the same procedure, we provide the
complete set of comparable valuations in Exhibit 12-3.
OVERALL AVERAGE5$254:2M
Notice that the medians are never larger than the averages. This is a typical situation for
these multiples, as outliers on the high end can easily skew the averages. For this reason, some
analysts prefer to use the median values when making their ?nal estimates. Other methods to
reduce the in?uence of outliers is to compute the geometric mean (multiply the ratios for all N
?rms and then take the Nth root (e.g., if there are two comparable companies with
EV/EBIT of 12 and 3, then the geometric mean is the square root of 12 Ã 3 and is equal to 6) or
the harmonic mean (take the reciprocal of the mean of the reciprocals, e.g., if there are two
comparable companies with EV/EBIT of 12 and 3, then the harmonic mean is 1 divided by the
arithmetic average of 1/12 and 1/3, and is equal to 4.8).
To decide on our best estimate, we need to go beyond a simple analysis of the averages.
Although the individual implied valuations are all over the map—a high-estimate com-
parable valuation of $700M using the price/book of DEF, down to a low-estimate comparable
EXHIBIT 12-3
IMPLIED VALUATIONS FOR NEWCO USING COMPARABLES
Multiples ABC DEF GHI JKL Average Median
EV/EBIT 83 448 136 168 199.6 152.0
EV/EBITDA 81 364 111 137 172.9 123.5
EV/Revenue 310 320 340 305 318.9 315.0
Price/Book 150 700 150 200 300.0 175.0
Price/Earnings 85 448 180 160 218.2 170.0
EV/Employees 155 350 128 630 315.6 252.5
EXHIBIT 12-2
VALUATION MULTIPLES
Multiples ABC DEF GHI JKL Average Median
EV/EBIT 10.3 56.0 17.0 21.0 26.1 19.0
EV/EBITDA 6.2 28.0 8.5 10.5 13.3 9.5
EV/Revenue 3.9 4.0 4.3 3.8 4.0 3.9
Price/Book 3.0 14.0 3.0 4.0 6.0 3.5
Price/Earnings 17.6 93.3 37.5 33.3 45.5 35.4
EV/Employees 1.0 2.3 0.9 4.2 2.1 1.7
218 CHAPTER 12 COMPARABLES ANALYSIS
valuation of $81M for the EV/EBITDA ratio of ABC—the average comparable valuations are
quite stable across different ratios. Nevertheless, the range of average estimates does vary
from a high of 318.9 for EV/Revenue to a low of 172.9 for EV/EBITDA. Although it would be
prudent to check both the high and low in any sensitivity analysis, one could make a
strong argument that the EV/Revenue estimate is the most realistic. The main support for this
argument is the relative variation of these valuation ratios. We don’t need any fancy math to
see that the EV/Revenue ratio provides by far the most consistent valuations across the dif-
ferent comparable companies. The stability of the EV/Revenue ratio can be seen by inspecting
the columns of Exhibit 12-3, and simple statistics can con?rm this casual inference. The
standard deviations of each row in Exhibit 12-3 are, in order, $163M, $129M, $15M, $268M,
$159M, and $232M. The EV/Revenue comparable has the lowest standard deviation by far.
Even if we were to eliminate all the data from DEF—the company that appears to provide the
most anomalous valuations—it still appears that EV/Revenue provides the most stable
answer.
In summary, if we need to pick one number for an exit valuation, the EV/Revenue
comparable of $318.9M is the most defensible. One can make an argument for adjusting this
number slightly to re?ect the lower comparable valuations from the other ratios, but choosing
the overall average of $254.2M seems too conservative. ’
Exhibits 12-1 and 12-2 use historical data. Many academics and practitioners
argue that valuation ratios are more accurate when using forecast data. For example,
instead of using EBIT or earnings from the most recent ?scal year, the analyst would
substitute forecasts for the next ?scal year or even for the following ?scal year. The
evidence for the superiority of forecasts is compelling, but in this book we still
recommend using the historical estimates as a baseline case. Why? Because the
main purpose of comparables analysis is to get the market’s opinion about valuation.
Once we introduce forecasts into this analysis, we run the risk of con?ating expert
predictions with the market’s opinion. Indeed, many forecasters logically take
market prices into account when making their forecasts, and companies with high
multiples for historical earnings are given higher forecasts for future earnings.
We made a similar argument in Chapter 11 against the use of comparable
company multiples to estimate the graduation value in DCF models. If an analyst
uses forecast multiples in the comparables analysis and then uses similar multiples
as the graduation value in a DCF, then it is possible that lots of work has been done
on two models based on the same set of information. There is nothing wrong with
using forecasts in a comparables analysis as an additional check on your work, but
you should not rely exclusively on these forecasts.
12.2 CHOOSING COMPARABLE COMPANIES
To choose comparable companies, it is important to ?rst understand the connection
between comparables analysis and DCF analysis. Most valuation ratios have some
connection to DCF formulas. Consider a ?rm in a zero-in?ation environment with
12.2 CHOOSING COMPARABLE COMPANIES 219
steady-state growth. Then, the present discounted enterprise value of this ?rm
would be
EV 5CF=r 2g 5CF=ðr 2R Ã IRÞ; ð12:1Þ
where g is the perpetual growth rate of cash ?ows, r is the discount rate, IR is the
investment rate, R is the return on (new) capital, and CF is cash ?ow in the next
period. Equation (12.1) is similar to Equation (11.6), the graduation value for a
DCF model. Next, consider the basic cash ?ow formula from Chapter 11:
CF 5ð1 2IRÞ Ã E5ð1 2IRÞ Ã ð1 2tÞ Ã EBIT; ð12:2Þ
since (1 2 t) Ã EBIT 5 E for all-equity ?rms.
Substituting Equation (12.2) into Equation (12.1) and dividing both sides by
E (or EBIT) yields
EV=E5Market Cap=E5P=E5ð1 2IRÞ=ðr 2R Ã IRÞ; ð12:3Þ
or,
EV=EBIT 5ð1 2tÞ Ã ð1 2IRÞ=ðr 2R Ã IRÞ: ð12:4Þ
We can continue this approach by substituting EBIT 5 Revenue à Margin
into Equation (12.4) and rearranging terms to yield
EV=Revenue 5margin à ð1 2tÞ Ã ð1 2IRÞ=ðr 2R à IRÞ: ð12:5Þ
Then we can disaggregate revenue to be Employees à Revenue per employee,
substitute into Equation (12.5), and rearrange to yield
EV=Employees 5Revenue per employee à Margin
à ð1 2tÞ Ã ð1 2IRÞ=ðr 2R à IRÞ:
ð12:6Þ
Thus, to ?nd comparable companies for P/E or EBIT ratios, we must search
for companies with similar steady-state levels for investment opportunities (for R
and IR), discount rates, and (for EBIT) tax rates. If current operating margins are
not yet at their steady levels, then we might be better off using an EV/Revenue
margin and identifying comparable companies with stable operating margins.
Finally, if revenue is not yet at its steady state (but employees are), then we can use
Equation (12.6). Overall, these equations provide some guidance to analysts as they
search for comparable ?rms. The analysis suggests that we look to ?rms in the same
industry, facing similar investment opportunities, with similar long-run margins
and productivity.
EXAMPLE 12.2
EBV is considering an investment in Semico, an early-stage semiconductor company. (This
is the same company analyzed in Example 11.2.) If Semico can execute on its business plan,
then EBV estimates it would be ?ve years until a successful exit. At that time Semico would
220 CHAPTER 12 COMPARABLES ANALYSIS
have about $50M in revenue, 150 employees, a 10 percent operating margin, a tax rate of 40
percent, and approximately $50M in capital (5 assets). Semico’s business is to design and
manufacture analog and mixed-signal integrated circuits (ICs) for the servers, storage sys-
tems, game consoles, and networking and communication markets. It also plans to expand
into providing customized manufacturing services to customers that outsource manufacturing
but not the design function. It expects to sell its product predominantly to electronic
equipment manufacturers.
Problems
(a) Identify comparable companies for Semico.
(b) Use accounting and market information from these companies to estimate a relative
valuation for Semico.
Solutions
(a) To identify comparable companies, we begin by screening similar-sized companies in
Semico’s industry. Our goal is to ?nd the subset of such companies that are the closest match
for Semico using the variables in Equations (12.3) through (12.6). Many possible databases
can be used for this exercise. A VC with experience in semiconductors might have access to
specialized industry databases. Even without such access, the experienced VC would not
need to start fresh for the analysis, as he would likely be able to make an educated guess
about the identity of the most comparable companies. Because we are starting from relative
ignorance, we will need to cast a wide net in our search.
At the time of this writing, the Yahoo! Finance portal is an excellent (and free) source
of all the necessary data. Using the “Stock Screener” tool,
2
we restrict our search to the
“Semiconductors: Integrated Circuits” industry, which is the closest match to the description
of Semico. The problem states that our success case revenue estimate is $100M. Because we
want companies with similar investment opportunities (which will then imply IR and R), we
don’t want to stray too far from this size, so we look for companies in this industry that have
between $25M and $125M in projected revenue. Using the most recent four quarters of data
(at the time of this analysis, this data usually goes through September 30, 2009), the stock
screener ?nds 13 such companies. Note that we have chosen to screen by revenue rather than
other accounting variables—we do this because revenue will be the best measure of ?rm size,
and ?rm size is probably our best measure of investment opportunities. Enterprise value,
which would also be a measure of ?rm size, would be an incorrect way to screen for
comparable companies. If we were to use EV (or market cap) to choose comparable com-
panies, then we would be implicitly placing restrictions on the valuation ratios.
Once we have identi?ed these 13 candidates, we need to study the descriptions of these
businesses to ?nd those most comparable to Semico. Once again, we are guided by the
variables in Equations (12.3) to (12.6). To ?nd companies with similar investment oppor-
tunities (IR and R), we want companies facing the most similar economic environments—
ideally, companies selling to original equipment manufacturers for ultimate sale into con-
sumer and home of?ce markets. The underlying growth (or decline) of these channels and
markets would then have a similar impact on Semico and its comparable companies. Next,
2
http://screen.yahoo.com/stocks.html.
12.2 CHOOSING COMPARABLE COMPANIES 221
we want as much as possible to match companies based on stable operating margins and
revenue per employee. To do this, we look for companies at a similar point in the supply
chain. In general, companies at similar points in the supply chain (e.g., manufacturer,
wholesaler, or retailer) have similar margins and productivity measures.
After studying the list of 13 companies, we ?nd three that satisfy our criteria for the
closest matches.
3
These companies are: PLX Technology Inc. (NASDAQ GM: PLXT),
Supertex Inc. (NASDAQ GS: SUPX), and Volterra Semiconductor Corporation (NASDAQ
GS: VLTR). Summary ?nancial information for these companies is given in Exhibit 12-4.
(b) This information is much messier than the fantasy case of Example 12.1. One of the
three companies has negative EBIT, EBITDA, and earnings. Furthermore, we note that the
EVs are lower than the market caps for all of the three companies (i.e., these companies have
more cash than debt) so net debt is negative. Based on this data, we construct valuation
multiples and display them in Exhibit 12-5.
The negative multiples in Exhibit 12-5 are problematic. Consider what happens to the
multiple as a company moves from a positive EBIT, to zero, to negative. As EBIT falls close
to zero, the EV/EBIT multiple rises to in?nity, only to change abruptly to a large (absolute)
negative number as EBIT turns negative. As mentioned in Section 12.1, these negative
multiples are a common occurrence for growth companies, hence the reliance on the more
robust multiples of EV/Revenue, Price/Book, and even EV/Employees (though, in this case,
the number of employees is available for only one of the three companies). Exhibit 12-6
gives the implied valuations for these multiples.
Overall Average : $204:6 Overall Median : $193:9
3
For readers who would like to try this analysis on their own, the list of 13 companies is given in
Appendix 12.A.
EXHIBIT 12-4
SUMMARY FINANCIAL INFORMATION FOR SEMICO COMPARABLES
Supertex PLX Volterra Semico Exit Estimates
Revenue 61.17 82.83 104.94 50
EBIT 5.02 280.04 5.61 5
EBITDA 5.55 25.88 18.19 10
Net income 4.91 218.80 10.94 3
LTD 0.00 0.86 0.00 0
BV of equity 179.12 69.32 83.50 50
Market cap (Price) 317.32 180.25 503.03 ??
EV 235.10 128.41 406.92 ??
Employees 352 N/A N/A 150
Source: Yahoo! Finance, January 2010.
222 CHAPTER 12 COMPARABLES ANALYSIS
To put these valuations in perspective, recall from Example 11.2 that the reality-check
DCF provided a baseline estimate of $206.7M. Thus, both the average and median com-
parables are fairly close to the DCF valuation, while the estimates have a wide range.
Overall, the EV/Revenue, Price/Book, and Price/Earnings multiples provide lower estimates
than EV/EBIT and EV/EBITDA multiples. EV/Employees (usually a reliable multiple
because of its relative stability across similar companies) is of little use in this example,
because we do not have the data for two of the three companies.
To go beyond this analysis, we would need to take an even closer look at these com-
parable companies and try to decide whether any of themprovides a particularly close match to
the success case of Semico. This example does not provide enough information about Semico
to allow for this analysis, and it would be rare for this additional precision to be available in a
real-world investment. ’
Example 12.2 is typical for this kind of analysis. With negative EBIT,
EBITDA, and earnings, and non-availability of employee ?gures, we are forced to
rely on revenue and book multiples. Luckily, these multiples provide similar
answers, but we are still left with a signi?cant range of valuation multiples. If, as in
Example 11.2, EBV requires an exit valuation of $300M to justify the investment,
EXHIBIT 12-5
VALUATION MULTIPLES
Multiples Supertex PLX Volterra Average Median
EV/EBIT 46.9 (1.6) 72.6 59.7 NA
EV/EBITDA 42.4 (21.8) 22.4 32.4 NA
EV/Revenue 3.8 1.6 3.9 3.1 3.8
Price/Book 1.8 2.6 6.0 3.5 2.6
Price/Earnings 64.6 (9.6) 46.0 55.3 NA
EV/Employees 0.7 NA NA NA NA
EXHIBIT 12-6
IMPLIED VALUATIONS FOR SEMICO USING COMPARABLES
Multiples Supertex PLX Volterra Average Median
EV/EBIT 234.4 NA 362.9 298.6 NA
EV/EBITDA 423.6 NA 223.7 323.7 NA
EV/Revenue 192.2 77.5 193.9 154.5 192.2
Price/Book 88.6 130.0 301.2 173.3 130.0
Price/Earnings 193.9 NA 137.9 165.9 NA
EV/Employees 100.2 NA NA NA NA
12.2 CHOOSING COMPARABLE COMPANIES 223
then this analysis suggests noninvestment unless EBV believes Semico to have
prospects signi?cantly better than these companies.
We must end this section with one big caveat: comparables analysis is dangerous
for VCinvestors—so be careful! One obvious problemis that an excessive reliance on
comparables analysis can make a VC prone to market fads, with current valuation
ratios taken as long-run predictions. Alas, valuation ratios can change dramatically in
?ve years. Indeed, when the ?rst edition of this book was published four years ago, the
comp valuations tended to be much higher than the reality-check DCF model valua-
tion, re?ecting the market conditions. Today, in 2010, the general pattern is the
opposite. In addition, Equations (12.3) to (12.6) all emphasize the importance of
?nding comparable companies with similar investment opportunities, but the time
difference between the current investment and a successful exit means that we need to
identify public companies today that have investment opportunities similar to those
available for our portfolio company at exit. In the rapidly changing markets frequented
by VCs, this exercise requires a heroic leap of faith. Many VCs rely exclusively on
comparables analysis—this reliance is very dangerous! Although the companies in
Exhibit 12-4 may be in the same business as Semico, the growth prospects for this
business are likely to be very different today from?ve years down the road. Of course,
these challenges are a main reason that VC investing is so dif?cult in the ?rst place.
12.3 USING COMPARABLE COMPANIES TO
ESTIMATE THE COST OF CAPITAL
In Chapter 11, we used the industry-average cost of capital in our DCF calculations.
Although an industry average makes sense for companies in the stable-growth
phase, it may be an underestimate for companies in the rapid-growth phase. In
general, the cost of capital will tend to fall as a company gets older. Thus, for some
applications we might want to estimate the cost of capital at exit by using com-
parable companies. This estimation requires ?ve steps:
1. Identify a set of comparable companies (as in Example 12.2).
2. Estimate a performance evaluation regression (as in Chapter 4) for each of
these companies.
3. Compute the unlevered betas for these companies (described below).
4. Compute the average of these unlevered betas.
5. Use the corresponding cost of capital formula (as in Chapter 4) to estimate
the cost of capital.
Of these ?ve steps, only step (3) is completely new. In our discussion in Chapter 4,
we didnot distinguishbetweenunleveredbetas andleveredbetas, but insteadreferredto
all factor loadings simply as “betas”. In Chapter 11, we also did not consider this dis-
tinction, as we were analyzing all-equity ?rms. Here, however, we must consider the
224 CHAPTER 12 COMPARABLES ANALYSIS
possibility that some of the comparable ?rms will have some debt in their capital
structures, and thus the estimated betas will re?ect both the “unlevered” cost of equity
and the “leverage” costs of debt. In computing the proper cost of capital for exit
valuations, it is necessary to unlever these betas. We illustrate this procedure in Example
12.3. In this example, we use the CAPM (as in Chapter 4) as our model for the cost of
capital. Following the example, we discuss how the computations can be adjusted for
multifactor cases such as the Fama-French model or the Pastor-Stambaugh model.
EXAMPLE 12.2
EBV is considering an investment in Newco—the same company from Examples 11.1 and
12.1. Newco’s comparable companies are given in Exhibit 12.1. In addition to the information
given in that exhibit, EBV estimates that the CAPM betas for these companies are 1.5 for
ABC, 1.0 for DEF, 2.0 for GHI, and 2.0 for JKL.
Problem Use these comparable companies to estimate a discount rate (cost of capital) for
Newco.
Solutions Step 1 is provided for us in Exhibit 12-1, and Step 2 (the CAPM betas) is given
by assumption. If we did not have this assumption, then we could use data on realized returns to
estimate betas as in Chapter 4. Because these regressions use realized stock returns, they
provide estimates of levered betas, also called equity betas. For an all-equity company (or
industry), leverage is zero and the levered beta is the same thing as the unlevered beta. If there
are other assets in the capital structure, then the levered beta will be different from the
unlevered beta. Because our DCF analysis assumes an all-equity company, we may need to
unlever the betas of the comparable companies. This unlevering procedure is the task of Step 3.
In theory, the unlevering process is very complex. The exact formulas for unlevering
depend on the analyst’s assumption about each company’s capital structure policy, and these
formulas can vary across companies and even across time for the same company. Luckily for
us, our focus on high-growth companies means that most of the comparable companies will
have little or no debt. (Indeed, if a comparable company does have a lot of debt, then perhaps
we should rethink whether that company is truly “comparable”.) When debt is small, it does
not matter very much which formula is used, so we choose the simplest one. Also, we assume
that the debt—and any other component of the capital structure—has a beta of zero. In that
case, the relationship between unlevered beta and levered beta can be written as
?
u
5
MC
EV
à ?
l
ð12:7Þ
where ?
u
is the unlevered (CAPM) beta, ?
l
is the levered beta, MC is the market capitali-
zation of equity, and EV is the enterprise value.
4
4
As discussed earlier, this is only one possible variant of the unlevering formula. Speci?cally, this variant
applies when tax shields are discounted at the unlevered cost of equity, and when all other parts of the
capital structure have betas of zero. To read about other variants of this formula, and to learn the
conditions under which they are applicable, see Holthausen and Zmijewski (2010).
12.3 USING COMPARABLE COMPANIES TO ESTIMATE THE COST OF CAPITAL 225
Using Equation (12.7), we can compute the unlevered betas for the comparable
companies. Exhibit 12-1 shows that DEF has no debt, so its ?
u
5 ?
l
5 1.0. For ABC, we
have MC5300 and EV5310, so ?
u
5300/310 Ã 1.5 51.45. For GHI, we have MC5150
and EV5170, so ?
u
5150/170 Ã 2.0 51.76. For JKL we have MC5200 and EV5210, so
?
u
5200/210 Ã 2.0 51.90.
Once we have computed the unlevered betas for all the comparable companies, we
move to Step 4 of the procedure and calculate the average of these betas as (1.0 11.45
11.76 11.90)/4 11.53. Then, for Step 5, we follow the same procedure as in Chapter 4 and
use a risk-free rate of 4 percent and an estimated market premium of 7 percent to estimate the
cost of capital as
r 50:04 11:53 Ã 0:07 514:71 percent: ð12:8Þ
’
In Example 12.3, we used the CAPM to estimate the cost of capital. If we
want to use a multifactor model such as the FFM or PSM, then all we need to do is
compute a separate version of Equation (12.7) for each of the factor loadings, and
then substitute the average of these loadings into the appropriate cost of capital
equation, analogous to Equation (12.8).
Because the unlevering step takes account of the difference between MC and
EV, how should we handle cases like Example 12.2, where companies have excess
cash and negative net debt? In theory, there is no difference in the way we handle
companies with negative debt. Using Equation (12.7), these companies will typi-
cally have unlevered betas higher than their levered betas. In practice, we need to
take special care that the excess cash situation existed during the estimation period
for beta. If the excess cash is a temporary phenomenon, then the estimated betas
may not require any adjustment.
SUMMARY
In this chapter, we showed how to perform a relative valuation analysis using comparable
companies. The ?rst step in this analysis is to choose comparable companies. To ?nd these
companies, we look at all companies in the same industry with revenue close to the forecast
successful-exit case. We then choose the subset of these companies with the closest match for
predicted investment opportunities, operating margins, and discount rates. Once these com-
panies have been chosen, we compute valuation multiples using a variety of measures and
then examine the implied valuations for each company and multiple. Although all multiples
provide some information, we pay particular attention to the multiples that provide the most
stable estimates (lowest standard deviation) across companies. Comparable companies can
also be used to estimate the cost of capital used in DCF analysis. To make these estimates, it is
sometimes necessary to unlever the beta estimates for the comparable companies.
226 CHAPTER 12 COMPARABLES ANALYSIS
KEY TERMS
Comparables analysis
5multiples analysis
5method of multiples
5relative valuation
Market capitalization
5market cap
5equity market value
Enterprise value (EV)
Earnings before interest,
taxes, depreciation, and
amortization (EBITDA)
Geometric mean, harmonic
mean
Unlevered betas, levered
betas
REFERENCES
Holthausen, Robert W., and Mark E., Zmijewski, 2010, Corporate Valuation: Theory, Practice, and
Evidence, forthcoming.
EXERCISES
12.1 Softco, the company valued in Exercise 11.1, is expected to have the following busi-
ness at exit:
Softco provides business process integration software and services for corporations across a
broad range of enterprise markets. Its main product is the Softco business process inte-
gration software platform together with packaged applications and content, where it expects
to derive 75 percent of its revenue. In addition, the company expects to earn the remainder of
its revenue from mainframe outsourcing and midrange systems management.
Use whatever resources you want to identify at least two comparable companies for Softco
and to estimate a relative valuation.
12.2 Consider the following “denominators” suggested as part of a comparables analysis:
(a) Number of unique visitors to a website
(b) Number of patents held by the company
(c) Level of dividends paid to common shareholders
(d) Number of demo software programs downloaded per month
For each of these four denominators, choose the numerator that is most appropriate for doing
comparables analysis.
12.3 True, False, or Uncertain: The harmonic mean will always provide a lower valuation
than the geometric mean, which in turn will always provide a lower valuation than the
median.
12.4 True, False, or Uncertain: The levered beta for a company is always greater than or
equal to the unlevered beta for the same company.
EXERCISES 227
APPENDIX 12.A: POTENTIAL COMPARABLES
FOR SEMICO
(Includes all companies in Yahoo! Finance, in the Semiconductors: Integrated
Circuits industry, with between $25M and $125M in revenue for the 12 months
ending closest to September 30, 2009. All these companies traded on the NASDAQ
as of January 2010, unless otherwise noted below.)
EXHIBIT 12-A
POTENTIAL COMPARABLES FOR SEMICO
API ADVANCED PHOT A (Amex)
WYNX.OB WAYTRONX INC (OTC BB)
AXTI AXT Inc
SATC SatCon Technology Corporation
TXCC TranSwitch Corporation
PXLW Pixelworks, Inc.
SUPX Supertex, Inc.
TUNE Microtune, Inc.
PLXT PLX Technology, Inc.
VLTR Volterra Semiconductor Corporation
EXAR Exar Corporation
OIIM O2Micro International Limited
PSEM Pericom Semiconductor Corporation
228 CHAPTER 12 COMPARABLES ANALYSIS
PART III
PARTIAL VALUATION
229
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CHAPTER 13
OPTION PRICING
PART III PRESENTS an investment framework that demonstrates how
option pricing concepts can be ef?ciently incorporated into VCs’ investment
decisions.
This chapter provides the crucial building blocks for this framework. Option
pricing theory and technology have made considerable progress in the last 35 years,
and we are now at a point where most of the complicated mathematical tasks can be
automated. Indeed, the main purpose of the model accompanying this book is to
provide the automation so that these powerful tools can be used in a fast-moving
VC transaction. Nevertheless, to apply these tools properly it is necessary to have at
least some exposure to the underlying equations. The exposition in this chapter
focuses on the intuition behind these equations with minimum technical detail.
Readers interested in these technical details—or in a more comprehensive survey of
option pricing—are encouraged to look at Hull (2008).
Throughout Part III, we will make many references to the VCV model. Links
to updated versions of this model, with documentation, are available at http://
VCVtools.com. Appendix B of this textbook provides brief descriptions for all the
spreadsheets and models used in this book, with particular attention to VCV.
Nevertheless, readers are encouraged to refer to the most recent version of the
model maintained on the websites, as updates and patches are likely.
In Section 13.1 we discuss European options: options that can only be
exercised on a preset expiration date.
1
In Section 13.2 we demonstrate how to value
a European option using replication techniques. These techniques—with some extra
mathematics—form the basis of the famous Black-Scholes equation. In Section
13.3, we examine this equation—derived under the assumption of liquid markets—
and discuss its applicability to illiquid private companies. In Section 13.4, we
discuss American options, which can be exercised on many possible dates, and in
1
The de?nitions of European options, their exercises, and expiration dates will be provided in Section
13.1. Other option pricing terms used in this introduction are given in the corresponding sections of the
chapter.
231
Section 13.5 we discuss random-expiration options, where the expiration date is
unknown to the option holder. Such random-expiration options are typical for VC,
where exit dates for investments are unknown. In Section 13.6 we show how to
translate exit diagrams (as ?rst introduced in Chapter 9) as a portfolio of options. In
Section 13.7 we reinterpret carried interest as a call option held by GPs on the value
of all fund investments.
13.1 EUROPEAN OPTIONS
Financial options are derivative assets, with their value derived from an
underlying asset. The prototypical ?nancial option is the European call, which
gives the holder the right to buy an underlying asset at a preset strike price on an
expiration date.
For example, consider a European call option to purchase a share of Bigco
stock (the underlying asset) in exactly one year for a strike price of $100 per share.
If Bigco is worth less than $100 per share on the expiration date, then the option
holder will choose not to exercise, and the option will expire worthless. If Bigco is
worth more than $100 per share on the expiration date, then the option holder
would exercise the option, pay $100, and earn a pro?t equal to the difference
between the stock price and $100.
Exhibit 13-1 shows the value of the option as a function of the value of Bigco
on the expiration date. We see from the exhibit that there is a direct relationship
between the value of the call option and the underlying Bigco stock. We refer to
EXHIBIT 13-1
CALL OPTION
C
a
l
l
O
p
t
i
o
n
(
S
t
r
i
k
e
?
1
0
0
)
Bigco's Stock Price
100
232 CHAPTER 13 OPTION PRICING
Exhibit 13-1 as an expiration diagram—a concept related to the exit diagrams
studied in Chapter 9. In an expiration diagram, the date of expiration is known with
certainty. In an exit diagram, the date of exit is unknown and random. In Section 13.6,
we demonstrate the relationship between these two types of diagrams; for now, we
focus on the expiration type.
We can write an equation corresponding to Exhibit 13-1 as
Value of Call with Strike of 100 on its expiration date
5C
1
ð100;1Þ 5MaxðV
1
2100; 0Þ;
ð13:1Þ
where V
1
is the value of Bigco on the expiration date. The value of the call option
will either be zero (if V
1
is less than or equal to 100) or it will be the difference
between V
1
and 100 (if V
1
is greater than 100). We use the operator Max (for
“maximum”) to capture this relationship.
In general, the expiration value of a call option with strike price X and
expiration date T is written as
C
T
ðX;TÞ 5MaxðV
T
2X; 0Þ: ð13:2Þ
Another standard option is the European put, which gives the holder the
right to sell an underlying asset at a preset strike price on an expiration date. For
example, consider a European put option to sell one share of Bigco stock (the
underlying asset) in exactly one year for a strike price of $100 per share. On
the expiration date, if Bigco is worth more than $100 per share, then the option
holder will choose not to exercise, and the option will expire worthless. If Bigco is
worth less than $100 on the expiration date, then the option holder would exercise
the option, receive $100 of proceeds, and earn a pro?t equal to the difference
between the stock price and $100. The expiration diagram for this put option is as
shown in Exhibit 13-2.
The corresponding equation is
Value of Put with Strike of 100 on its expiration date
5P
1
ð100;1Þ 5Maxð100 2V
1
; 0Þ:
ð13:3Þ
The general equation for the expiration value of a European put option with a
strike of X and an expiration of T is
P
T
ðX; TÞ 5MaxðX 2V
T
; 0Þ: ð13:4Þ
Although call options (and their variations) are frequently included in VC
transactions, the explicit use of put options is rare, except for their almost standard
inclusion as part of the VC’s redemption rights. Recall from Chapter 8 that
redemption rights give the investor the option to resell shares back to the ?rm after
some prespeci?ed time period (usually ?ve to seven years) or upon some triggering
event. This type of option is a put option, because the strike price is the resale price.
Notwithstanding this theoretical interpretation, it is very dif?cult to exercise this
redemption right in practical situations, so we will not attempt to value it.
13.1 EUROPEAN OPTIONS 233
13.2 PRICING OPTIONS USING A REPLICATING
PORTFOLIO
The expiration diagrams show the value of an option on the expiration date, T.
Although it is helpful to solve for this date T value (C
T
), we also want to know the
current (date 0) value of the option (C
0
).
EXAMPLE 13.1
Suppose that Bigco is currently trading for $100 per share. We are offered a European call
option to purchase one share with an expiration date in one year. We know that on the
expiration date Bigco stock will sell for either $120 per share (a “good day”) or for $80 per
share (a “bad day”). No other prices are possible. The stock will not pay any dividends during
the year. Risk-free interest rates are zero, so a bond can be purchased (or sold) for a face
value of $100 and have a certain payoff of $100 in one year. Stocks, bonds, and options can
all be bought or sold, long and short, without any transaction costs.
Problem What is the value of the call option today?
Solution This problem may appear to be impossible on ?rst glance: although we know
that there are two possible prices for the stock in one year, we are not told the probabilities of
these two prices. It would seem that the answer must depend on these probabilities, but
surprisingly it does not. This is the strange reality of option pricing. Instead of using
probabilities, we solve for the option price by building a replicating portfolio (a combi-
nation of the stock and the bond that yields the same exact payoffs as the call option).
First, we draw some pictures. For an example with only two possible outcomes, we
can dispense with expiration diagrams and use simple diagrams instead. Because the bond is
riskless, it is worth $100 on both a good day and a bad day.
EXHIBIT 13-2
PUT OPTION
P
u
t
O
p
t
i
o
n
(
S
t
r
i
k
e
?
1
0
0
)
Bigco's Stock Price
100
234 CHAPTER 13 OPTION PRICING
The stock is worth $120 on a good day and $80 on a bad day:
When the stock is worth $120, the call option would be exercised for a pro?t of C
1
(good day) 5$120 2$100 5$20. When the stock is worth $80, the call option would not be
exercised, C
1
(bad day) 5 0.
EXHIBIT 13-4
STOCK VALUES ON GOOD DAY AND BAD DAY
S
0
? 100
S
1
(good day) ? 120
S
1
(bad day) ? 80
EXHIBIT 13-3
BOND VALUES ON GOOD DAY AND BAD DAY
B
0
? 100
B
1
(good day) ? 100
B
1
(bad day) ? 100
13.2 PRICING OPTIONS USING A REPLICATING PORTFOLIO 235
We summarize these outcomes with the equation
C
1
ð100;1Þ 5MaxðS
1
2100; 0Þ: ð13:5Þ
Next, we use some algebra to ?nd the combination of stocks and bonds that provides
exactly the same payoff as the option on both possible days. We write an equation for each
outcome, good or bad, that takes the form
Option Value at Expiration ðgood day or bad dayÞ
5ðShares of StockÞ Ã ðStock ValueÞ 1ðShares of BondÞ Ã ðBond ValueÞ:
ð13:6Þ
Denoting shares of stock as y and shares of the bond as z, we write the equations as
C
1
ðgood dayÞ 520 5120y 1100z; ð13:7Þ
and
C
1
ðbad dayÞ 50 580y 1100z: ð13:8Þ
Equations (13.7) and (13.8) give us two equations and two unknowns (y and z), which
we can then solve to ?nd that y 5 0.5 and z 5 20.4. To check and interpret this solution, we
return to the logic of replication: if we purchase 0.5 shares of the stock and sell (“purchase a
negative amount”) 0.4 shares of the bond, then we exactly replicate the payoffs to the call
option. On a good day, 0.5 shares of stock are worth $120/2 5 $60, and 0.4 shares of the
bond, $40, needs to be paid back. That transaction will net $60 2 $40 5 $20, the same
amount that the call option is worth on the good day. On a bad day, 0.5 shares of stock are
worth $80/2 5 $40, which is exactly the amount needed to pay back 0.4 shares of the bond.
This strategy nets $40 2 $40 5 $0 on the bad day, the same amount as the call option.
These calculations should convince you that the call option provides exactly the
same payoffs as 0.5 shares of stock minus 0.4 shares of the bond. Thus, we should expect
EXHIBIT 13-5
OPTION VALUES ON GOOD DAY AND BAD DAY
C
0
? ??
C
1
(good day) ? 20
C
1
(bad day) ? 0
236 CHAPTER 13 OPTION PRICING
that the value of the call option, at time 0, must be exactly the same as the cost of this
combination:
C
0
50:5 Ã S
0
20:4 Ã B
0
: ð13:9Þ
Equation (13.9) is an option-pricing formula: it expresses the value of the option today
(C
0
) in terms of the observable market prices of the underlying stock (S
0
) and bond (B
0
). We
can substitute these prices to ?nd the dollar value of the option as
C
0
50:5 Ã 100 20:4 Ã 100 5$10: ð13:10Þ
Thus, the value of the call option today is $10. ’
Upon?rst seeingthis answer, manypeople express disbelief. Our solutionmade no
use of any probabilities for the outcomes, nor did we use beta or any other risk measure.
How can it be possible to compute the value of the option without accounting for risk?
It is possible because risk should already be incorporated into the stock price.
The underlying probabilities of good and bad days, and the correlation of the stock
with these good and bad days, should be the main determinant of the stock price.
Because we have already shown that the option is effectively just a combination of
the stock and bond, there is no additional information to be considered.
Option pricing solutions like this rely on arbitrage. Arbitrage is the act of
simultaneously buying and selling the same set of cash ?ows for different prices. In
our example, with no transaction costs, let’s see how arbitrage would work to keep
the price of the option at $10.
First, suppose that someone was willing to buy the option for $11. We could
arbitrage this buyer by selling her an option for $11 and then replicating the option
payoffs by purchasing 0.5 shares of stock and selling 0.4 shares of the bond. As we
showed earlier, this replication strategy costs $10 and gives the same payoffs as the
option on both good and bad days. Thus, today we will pocket the difference
($11 2 $10 5 $1), and tomorrow we will break even for sure. With this strategy,
we could earn $1 on every option without taking on any risk. We will continue to
sell options until the price is driven down to $10.
The same reasoning in reverse demonstrates that the price cannot be less than
$10. For example, suppose that someone is willing to sell the option for $9. We
could then arbitrage this seller by buying the option from him for $9 and then
replicating this (short) option by selling 0.5 shares of stock and buying 0.4 shares of
the bond. This replication strategy will put $10 in our pocket today, enough to pay
$9 for the option and earn a $1 pro?t. As before, the whole transaction will wash
out tomorrow. Again, we would be happy to do this transaction until there is
nobody left willing to sell the option for less than $10.
In this example, the interest rate was set to zero for computational con-
venience. The intuition for the solution is the same for any interest rate. To see this is
true, pick some arbitrary riskless rate, r, replace B
0
5100 in Exhibit 13-3 with B
0
5
100/(1 1r) and then work through the same calculations as we used in the example.
13.2 PRICING OPTIONS USING A REPLICATING PORTFOLIO 237
13.3 THE BLACK-SCHOLES SOLUTION
Example 13.1 assumes only one discrete point where the stock price could change
and only two possible outcomes for this price. This is a great simpli?cation. In
principle, the same replication strategy can be used for any number of price
changes. In Chapter 22, we will show how to build and solve binomial trees for any
?nite number of price changes. Things become particularly interesting when we
take this process to the limit and allow prices to change continuously. In this case, it
is no longer feasible to write a diagram for the in?nity of possible outcomes, but the
insight of Black and Scholes is that a solution can still be obtained by combining a
replication strategy with some clever math. The technical details of their solution
are given in option pricing textbooks such as Hull (2008). For our purposes here, it
suf?ces to sketch the assumptions, give the famous formula, and then discuss the
intuition behind it.
The Black-Scholes solution requires two sets of assumptions. The ?rst set of
assumptions relates to “perfect markets”—markets that are open all the time, allow
assets to be traded in any quantity, have no taxes or transaction costs, and have no
remaining arbitrage possibilities. All these perfect-market assumptions are neces-
sary to obtain a unique price for the option. The second set of assumptions includes
technical restrictions on the statistical properties of stock and bond returns; these
restrictions can be relaxed, if necessary, for more general option pricing solutions.
It is obvious that the assumption of perfect markets does not even hold for
actively traded public stocks. Thus, it is natural to be skeptical of its relevance
for the private markets of VCs. In the “reality check” discussion later, we discuss
the implications of these assumptions for private markets. For now, let us suspend
our skepticism and assume that the assumptions hold.
Under these assumptions, the Black-Scholes formula for the value of a
European call option is
C
0
5Nðd
1
ÞS
0
2Nðd
2
ÞXe
2rT
; ð13:11Þ
where N(.) is the Normal distribution function and
d
1
5½lnðS
0
=XÞ 1ðr 1?
2
=2ÞTÞ?=ð?OTÞ; ð13:12Þ
d
2
5½lnðS
0
=XÞ 1ðr 2?
2
=2ÞT?=ð?OTÞ 5d
1
2?OT; ð13:13Þ
where
T 5years until the expiration date,
? 5the annual volatility of returns, and
r 5the annual riskless rate.
All stock returns and interest rates in the Black-Scholes framework are
expressed as continuously compounded returns, also known as log returns,
because these returns can be calculated as natural log of one plus the periodic
return: log return 5 ln(1 1 periodic return).
238 CHAPTER 13 OPTION PRICING
The Black-Scholes formula may look complex, but is almost an exact ana-
logue of the simple solution for Example 13.1 given in Equation (13.9). The ?rst
terms in these two equations are 0.5 Ã S
0
for Equation (13.9) and N(d
1
)S
0
for
Equation (13.11). In both cases, this is a number between 0 and 1 (N(d
1
) is the
normal distribution function, so it will always give us a probability, which must be
a number between 0 and 1) multiplied by the current stock price.
The interpretation of this multiplier is the answer to the question “How much
stock would I have to purchase today to replicate the option position?” In Example
13.1, the option could either be worth $20 (on a good day) or $0 (on a bad day). The
stock could be worth $120 (on a good day) or $80 (on a bad day). Thus, the option
has a spread of $20 between good and bad days, and the stock has a spread of $40
between good and bad days. This means that after we ?nish the algebra exercise for
replication, we end up with one-half of a share of stock ($40 spread à 1/2) needed to
replicate the $20 spread for the option. In the Black-Scholes case, the math is more
complicated but the idea is the same: after plugging in the inputs to obtain N(d
1
),
we obtain the fraction of stock needed to replicate a single option.
Next, consider the second term in Equations (13.9) and (13.11). These
terms are 0.4B
0
and N(d
2
)Xe
2rT
, respectively. Again, these terms are analogues
of each other. The Xe
2rT
term in Equation (13.10) represents the present dis-
counted value of the strike price. In Example 13.1, we used a riskless bond with a
payoff (or strike price) of B
1
5 $100. Given this, B
0
turns out to be the price of
this bond in period 1, which is also the same thing as the present discounted value
of the strike price.
How about N(d
2
)? This is a number between 0 and 1 that can almost (but not
exactly) be thought of as “the probability that we will exercise the option”. Then,
the whole term N(d
2
) Xe
2rT
can be interpreted as “the probability that we will
exercise the option multiplied by the amount of money that we will need for the
strike price if we do actually exercise”. In Equation (13.11), the 0.4 multiplier in
front of B
0
serves the same purpose. Of course we have not solved for any actual
probabilities, but it is helpful to interpret the multipliers in this way, because it
allows us to see the role that they are playing in the more complex Black-Scholes
formula.
We are nowready to apply the Black-Scholes formula in an example. In this and
all future examples, we will assume that all the Black-Scholes assumptions hold.
EXAMPLE 13.2
Suppose that Bigco is currently trading for $100 per share. We are offered a European call
option to purchase one share with an expiration date in ?ve years. We know that the volatility
of Bigco’s stock is 90 percent per year, and that the stock will not pay any dividends during
the year. The riskless interest rate is 5 percent.
Problem What is the value of the call option today?
13.3 THE BLACK-SCHOLES SOLUTION 239
Solution Because Black and Scholes have done all the hard work for us, the solution here is
just a matter of plugging numbers into the Black-Scholes formula. We have r 55%, ? 590%,
X 5 100, S0 5 100, and T 5 5. We can also use the European Call Option Calculator at
VCVtools.com to calculate the answer as $72.38. Output from this Calculator is shown in
Exhibit 13-6. ’
REALITY CHECK: Is the Black-Scholes solution reasonable for private
companies? The solution requires several assumptions about perfect markets. These
include assumptions that markets are open for trading at all times, that there are no
taxes or transactions costs, and that there are no remaining arbitrage possibilities.
Furthermore, there are additional assumptions about stock and bond returns,
including the assumption that the logarithm of stock returns has a normal dis-
tribution. Many of these assumptions do not even hold for stocks traded on the New
York Stock Exchange, so they will de?nitely not hold for unlisted private com-
panies. Research has shown that when the perfect market assumptions are dropped,
there are many possible option prices that can hold in equilibrium, and without lots
of additional information, it is not possible to predict what the exact solution will
be. Given these concerns, how should we interpret the Black-Scholes solution for
private companies?
Before answering this question, it is important to remember the reason why
we do option valuation for private companies in the ?rst place. For public com-
panies, option pricing is often a serious and exact business, because mistakes can
lead to arbitrage possibilities for other traders—and those on the wrong side of
arbitrage trades can lose money in a hurry. However, the VC problem is different.
Here, our goal is to break a complex transaction down into digestible parts to
provide guidance to an investor about the relative merits of different deal structures.
Having an exact answer would be ideal but it is not crucial. We can live with an
approximate answer, as long as the approximation is unbiased. An unbiased
approximation is sometimes too high and sometimes too low, but the average error
EXHIBIT 13-6
EUROPEAN CALL
European Call
Stock Price 100
Strike Price 100
Volatility (%) 90
Risk Free Rate (%) 5
Time to Expiration 5
Call Option Value 72.38
240 CHAPTER 13 OPTION PRICING
is zero. An unbiased approximation can aid decision making, whereas a biased
approximation would be misleading. Thus, the key question is: “Is the Black-
Scholes solution an unbiased approximation for private companies?” Concerns
about bias fall into two main groups: (1) the need for a “nontradability discount” on
the option and (2) the understatement of volatility when using lognormal returns.
We address these two concerns next.
Some people argue that there should be a nontradability discount subtracted
from the option price. This argument asserts that because standard options can be
traded and hedged, and because no investor would prefer to have a restriction on
trading, the standard options as priced by Black-Scholes should be worth more than
a nontradable option. This argument seems compelling, but we would argue that,
for private companies, it is the nontradable options that can be approximately
priced by Black-Scholes, whereas the tradable options would be biased. Why?
Because the underlying asset here is itself not traded, and any discount for non-
tradability should already be built into the value of this asset. (Recall the discussion
of the liquidity factor in Chapter 4.)
The second main concern about bias comes from the assumption of log-
normal returns. The argument is this: “VC investments do not have returns like
public companies. Instead, a VC investment often returns absolutely nothing, and
occasionally returns a huge amount. This binary type of outcome is not consistent
with a lognormal distribution”. There are two responses to this concern. First, it is
not true that VC returns are binary. We saw in Chapter 7 that many VC outcomes
end up somewhere in the middle. Second, periodic returns that are often very low
(and only sometimes very high) are consistent with lognormality—and in fact, this
is exactly what lognormal returns do look like. Exhibit 13-7 gives an example
EXHIBIT 13-7
FIVE-YEAR COMPOUND RETURNS FOR A LOGNORMAL
DISTRIBUTION
150%
Return
?99% 400%
.198
.009
P
r
o
b
o
f
R
e
t
u
r
n
13.3 THE BLACK-SCHOLES SOLUTION 241
distribution of ?ve-year compound periodic returns using a lognormal distribution
with an annual standard deviation of 90 percent.
This exhibit does not appear to be a bell curve; the low outcomes are much
more prevalent than the high outcomes, and the high outcomes can be very high.
The objection here is usually caused by confusion about the difference between
normal distributions (which look like a bell curve when drawn in periodic returns)
and lognormal distributions (which look like a bell curve if drawn in log returns,
but look like Exhibit 13-7 if drawn in periodic returns.)
This discussion does not attempt to exhaust the possible objections and
responses to the use of the Black-Scholes formula to value options on private
companies, and no doubt this debate will continue. Nevertheless, it does not yet
appear that there is any clear bias in the use of Black-Scholes for these applications,
so we will make use of it in the examples in this book.
13.4 AMERICAN OPTIONS
Thus far, we have worked with European options, where exercise is restricted to the
expiration date. However, most VC options in practice are American options,
which allow for exercise at any time until the expiration date. For example, an
American call option gives the holder the right to buy an underlying asset at a
preset strike price on or before an expiration date, and an American put option
gives the holder the right to sell an underlying asset at a preset strike price on or
before an expiration date.
In discussing these options, it is useful to introduce a few more de?nitions.
First, if the strike price is higher than the current stock price, then a call option is
out of the money. Similarly, if the strike price is lower than the current stock price,
then a call option is in the money. If the strike price is equal to the current
price, then a call option is at the money. For put options, we reverse the out of
the money and in the money de?nitions: puts are out of the money when the strike
price is below the current price and are in the money when the strike price is above
the current price. The at the money de?nition is the same for puts and calls.
For stocks with no dividends, and for diversi?ed investors without immediate
risk management or liquidity concerns, an American call is equivalent to a Eur-
opean call. This is because it is never optimal under these conditions to exercise an
American call early. To see why, consider what might occur before expiration.
First, if the option is out of the money or at the money, then the investor should
certainly not exercise early, because she might as well just buy the (cheaper) stock
instead. Second, if the option is in the money, the investor can continue to earn
interest on the cash needed for the strike price while still effectively enjoying any
price appreciation by waiting to exercise until the expiration date. In this case,
waiting has the extra bene?t that, if the stock price falls below the exercise price
before expiration, the investor will be especially happy that she did not exercise. In
these aspects American calls are equivalent to European calls; thus we can use the
242 CHAPTER 13 OPTION PRICING
same Black-Scholes formula to price both of them. Note that this argument does not
apply if the stock pays dividends, because the investor would forego these divi-
dends in exchange for waiting to exercise.
The same logic does not work for put options, because there are some cases
where exercising early can be optimal. The reason here is that stock prices cannot
fall below zero, so if the price gets very close to zero, it can make sense to exercise
a put early and collect the proceeds. Unfortunately, there is no analytical solution
leading to a single equation to price American puts, and numerical methods must be
used. Lucky for us, put pricing is much less important than call pricing for VC
transactions.
13.5 RANDOM-EXPIRATION OPTIONS
Up to this point, all the options we have discussed have had a ?xed expiration date.
This date might be the only possible time for exercise (European options) or the last
possible time (American options), but in either case there is some end point. In VC
transactions there are often some special conditions that supersede these rules. For
example, as we will show in Chapter 14, convertible preferred stock can be
modeled as a bond plus an embedded call option. However, unlike standard call
options, this embedded option will have a forced exercise in the case of an IPO or
sale of the company, and would expire worthless if the company goes out of
business. In general, many liquidity events for the underlying company will force a
contemporaneous expiration of the embedded option, and in this situation the
investor will face an immediate exercise decision.
The possibility of forced expiration adds another complication to option
pricing, but under some reasonable assumptions, it can be handled without much
dif?culty. For example, take a case where an option has a 50 percent chance of
forced expiration in exactly 5 years, with the remaining 50 percent being the chance
of forced expiration in exactly 10 years. If this is the case, then we can think of this
complex option as the combination of two standard European options: a 50 percent
chance of a European call option with expiration in ?ve years plus a 50 percent chance
of a European call option with expiration in ten years. Because both of these European
call options can be valued using the Black-Scholes formula, then under the
assumptions, the combination option can be priced as the expected value of the two
standard call options.
The same logic can be used when the option has any number of dates for its
possible forced expiration. Suppose that the company’s board of directors sits down
every month and considers whether the time has come to sell the company, have an
IPO, or shut down. If each month is equally probable for exit over a 10-year period,
then any options on this company would have 120 possible expiration dates, each
with a 1/120 chance of happening, and the option could be priced at the expected
value of 120 European call options with expirations of 1 month, 2 months, and so
on, all the way up to 10 years. This calculation is easy for a computer, because all
13.5 RANDOM-EXPIRATION OPTIONS 243
we need is to repeat the same Black-Scholes formula 120 times with a different
input for the expiration date. If we take this process to the limit, then the option
would have a continuous-time probability of forced expiration, an in?nite number
of possible expiration dates, and the expected value of the option would be cal-
culated as an integral of the probability of expiration for any given date multiplied
by the Black-Scholes value of the call option with that expiration.
These options with unknown expiration are important for VC valuation
problems, so we will develop some new terminology for them. We de?ne a random-
expiration (RE) option to have a continuous-time probability, q, of forced
expiration. This forced expiration is random and is uncorrelated with the perfor-
mance of the ?rm or the overall market. RE options do not have ?xed expiration
dates, but for any q we can compute an expected holding period, H. Conveniently,
the math works so that H51/q. Because “expected holding periods” are more
intuitive objects than are “continuous-time probabilities”, we will work through
the book with the former. Appendix 13.A gives more details for the derivation of
the pricing formula for RE options.
The numerical valuation of RE call options is hard for humans, but easy for a
computer; and a template for valuation is available at VCVtools.com (Random
Expiration Call Option Calculator). The only difference in the inputs between a
standard European call and a RE call is that the former gives a time to expiration, T,
whereas the latter gives an expected holding period H. The following example is
identical to Example 13.2 except for the portion in italics.
EXAMPLE 13.3
Suppose that Bigco is currently trading for $100 per share. We are offered a random-
expiration call option to purchase one share with an expected holding period of ?ve years.
We know that the volatility of Bigco’s stock is 90 percent per year, and that the stock will not
pay any dividends during the year. The riskless interest rate is 5 percent.
EXHIBIT 13-8
RANDOM-EXPIRATION CALL
Random Expiration Call
Stock price 100
Strike price 100
Volatility (%) 90
Risk Free Rate (%) 5
Expected Holding period 5
Call Option Value 60.70
244 CHAPTER 13 OPTION PRICING
Problem What is the value of the RE call option today?
Solution As in the previous example, the computer does the hard work. We have r 5
5%, ? 5 90%, X 5 100, S
0
5 100, and H 5 5. The Random Expiration Call Option Cal-
culator at VCVtools.com calculates the answer as $60.70, as shown in Exhibit 13-8. ’
13.6 READING EXIT DIAGRAMS
VCs must often analyze investments with complex payoff structures. In these
structures, VCs do not receive explicit call options, but rather have options
embedded into other securities, such as convertible preferred stock. Because VCs
can make many different rounds of investment, their exit payoffs can look quite
complicated, and it can seem at ?rst glance that no sense can be made of the
investment. However, we will see that it is often possible to translate these complex
investments into a portfolio of options with different strike prices. To do this, we
draw exit diagrams where the x-axis shows the value of the whole company, and the
y-axis gives the fraction of the company represented by a speci?c investment.
These are exit diagrams, not expiration diagrams, because the date of exit (5
expiration of the options) is unknown. Under the assumption that this unknown exit
date follows the statistical distribution discussed in Section 13.5, we can read the
exit diagrams as a portfolio of random-expiration options.
For example, suppose that EBV invests in Newco across several venture
rounds. Exhibit 13-9 represents the value of EBV’s investment as a function of the
proceeds ($W) from selling the whole company.
EXHIBIT 13-9
EXIT DIAGRAM FOR EBV’S STAKE IN NEWCO
S
lo
p
e
?
1
/
4
10 20
$W
V
a
l
u
e
o
f
E
B
V
'
s
S
t
a
k
e
40
13.6 READING EXIT DIAGRAMS 245
In all exit diagrams in this book, we label the x-axis for all in?ection points. We also
label all slopes, except for slopes of zero or one, which will always be left unlabeled.
As the ?gure shows, EBV does not receive anything unless there are proceeds of at
least $10M. Between $10M and $20M, EBV receives all the proceeds, but it receives
none of the proceeds between $20M and $40M, and it receives one-quarter of all
proceeds above $40M. It turns out that it is relatively straightforward to interpret this
exit diagram into a portfolio of options, which we call an exit equation. We call
this process reading the exit diagram. To do so, we start at the origin of the diagram
and read from left to right. At every point that the slope changes, we add (or subtract)
a fraction of a call option, with strike price equal to the corresponding point on the
x-axis, and the fraction equal to the change in slope at that point.
The ?rst slope change occurs at $10M, where the slope goes from 0 to 1. We
write this as the purchase of a full call option with a strike price of 10: C(10). At $20M,
the slope falls by one, represented by the sale of a full call option: 2C(20). Finally, at
$40M, the slope rises to one-quarter: 1/4 C (40). Putting this all together yields
Exit equation5Cð10Þ 2Cð20Þ 11=4 Ã Cð40Þ: ð13:14Þ
Equation (13.14) is the output of reading Exhibit 13-9 as a portfolio of (random-
expiration) call options. Note that we have not put time subscripts on the value of the
call options in Equation (13.14). This is because there is no need for time subscripts on
the call option values, for even though we use exit diagrams for the reading, the
equation holds at all times. In most applications, we will value the options at time zero.
EXAMPLE 13.4
Suppose that Talltree invests in Newco across several venture rounds. After one of these
rounds of investments, Talltree draws an exit diagram as shown in Exhibit 13-10.
EXHIBIT 13-10
EXIT DIAGRAM FOR TALLTREE’S STAKE IN NEWCO
S
l
o
p
e
?
1
/
2
S
lo
p
e
?
1
/4
S
lo
p
e
?
3
/
8
20 30 50
$W
80
V
a
l
u
e
o
f
T
a
l
l
t
r
e
e
'
s
S
t
a
k
e
246 CHAPTER 13 OPTION PRICING
Problem What is the exit equation corresponding to this exhibit?
Solution To answer the question, we read the exit diagram. Talltree will receive one-half
of the ?rst $20M in exit proceeds, all the next $10M (up to $30M total), none of the next
$20M (up to $50M total), one-quarter of the next $30M (up to $80M total), and three-eighths
of everything after that. In this example, we start with a slope of one-half beginning at the
origin. This gives us half of a call option with a strike price of 0: 1/2 C (0). A call option with
strike price of zero is the same thing as owning the asset outright, so we can also write 1/2 C
(0) 5 1/2V, where V is the value of the whole company. At $20M the slope rises to one, an
increase of 1/2 of a unit: 1/2 C (20). At $30M the slope falls to zero, a reduction of one unit:
2C (30). At $50M the slope rises to one-quarter: 1/4 C (50). At $80M the slope rises to 3/8,
an increase of 1/8: 1/8 C (80). Putting this all together yields
Exit equation 51=2 Ã V 11=2 Ã Cð20Þ 2Cð30Þ 11=4 Ã Cð50Þ 11=8 Ã Cð80Þ: ð13:15Þ
’
13.7 CARRIED INTEREST AS AN OPTION
In Chapter 3, we showed how to estimate the carried interest for a fund by using an
estimate for the gross investment multiple combined with knowledge about lifetime
fees and the carry%. This approach gave us a simple formula for GP% (Equation
(3.15)), which we later used in the modi?ed VC method of Chapter 10. With our
new option-pricing tools, we might be tempted to do something fancier. For
example, if a GP has 20 percent carried interest with a committed capital basis, then
we can draw an exit diagram for carried interest as shown in Exhibit 13-11.
EXHIBIT 13-11
EXIT DIAGRAM FOR CARRIED INTEREST
Committed Capital
$W
C
a
r
r
i
e
d
I
n
t
e
r
e
s
t
13.7 CARRIED INTEREST AS AN OPTION 247
We can read this diagram as
Carried Interest 51=5 Ã CðCommitted CapitalÞ: ð13:16Þ
The underlying asset of this call option is the “portfolio of all fund invest-
ments”. For a fund with only one investment, this call option would be easy to
compute, because we could use the volatility of that one investment as an input for
a single random-expiration option. In general, however, the problem is more
complicated because there are multiple investments, each with a different exit date.
Furthermore, if the GP loses money on one investment, it will need to make up
these losses on other investments before any carried interest is earned.
To a ?rst approximation, these complexities can be modeled by changing the
volatility of the underlying option in Equation (13.16). At one extreme, we have
the case mentioned earlier: a VC makes only one investment (or many investments,
all perfectly correlated). In that case, the volatility of the underlying portfolio
would be the same as the volatility of a speci?c investment. At the other extreme,
we can imagine that a single VC fund makes hundreds of investments, with these
investments correlated only through their betas in some factor model. In that case,
the volatility of the whole portfolio would be approximately the same as the
volatility of the underlying factors, as multiplied by their betas. Because a portfolio
with hundreds of investments gains the bene?t of diversi?cation, the volatility
estimate for such a portfolio would be much lower than the corresponding estimate
for a single investment. With a lower volatility estimate, we would obtain a cor-
respondingly lower option value in Equation (13.16).
In reality, the volatility of the VC’s portfolio is likely to be somewhere
between these two extremes. A typical VC fund makes dozens of investments (not
hundreds), and these investments are more correlated than would be implied by
factor models. To ?nd the appropriate volatility for this complex portfolio, we will
need to use mathematical tools beyond the scope of this textbook. Furthermore, to
accurately capture all the variations of carried interest, we need to set up a model
that allows for separate treatment of each investment in the fund’s portfolio. In an
academic paper, Metrick and Yasuda (2010) perform this exercise and estimate GP
% for a wide variety of fee and carry structures. The good news is that these
estimates show that the simple formula of Equation (3.15) does a good job of
approximating the GP% for the most common carry structures. Thus, for this book,
we will use this simple formula in all applications.
SUMMARY
Options often appear in VC transactions, and it is important for investors to learn to spot
these options and to obtain approximate values for them. The fundamental option-pricing
formula is the Black-Scholes equation. The intuition for this equation comes from building a
replicating portfolio from the underlying stock and a riskless bond. By modifying the Black-
Scholes formula to account for random expiration, we can make it more applicable to VC
248 CHAPTER 13 OPTION PRICING
investments. Although the assumptions of the Black-Scholes approach do not hold for private
companies, the Black-Scholes solution still seems to be an unbiased approximation for the
value of options in these companies.
KEY TERMS
Derivative assets, under-
lying assets
Financial options
European call, European put
Strike price
Expiration date
Expiration diagram
European put
Replicating portfolio
Black-Scholes formula
Continuously-compounded
returns
5 log returns
American option
Out of the money
In the money
At the money
Random-expiration (RE)
option
Expected holding period
Reading the exit diagram
Exit equation
REFERENCES
Black, Fischer, and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities”, Journal of
Political Economy 81(3), 637À654.
Hull, John, 2008, Options, Futures, and Other Derivatives, 7th Edition, Prentice Hall, Upper Saddle
River, NJ.
Metrick, Andrew, and Ayako Yasuda, 2010, “The Economics of Private Equity Funds”, Review of
Financial Studies 23, 2302-2341.
EXERCISES
13.1 Suppose that Bigco is currently trading for $100 per share. We know that in one year
Bigco stock will sell for either $150 per share (“good day”) or for $75 per share (“bad day”).
No other prices are possible, and the stock does not pay any dividends. The riskless interest
rate is 5 percent, so a bond worth B
1
next year sells for B
0
5B
1
/(1 1r) today. Stocks, bonds,
and options can all be bought or sold, long and short, without any transaction costs.
(a) What is the value of a European call option with a strike price of $100 and expiration in
one year?
(b) What is the value of a European put option with a strike price of $100 and expiration in
one year?
13.2 Suppose that Bigco is currently trading for $100 per share. The stock has an annual
volatility of 90 percent and does not pay any dividends. The riskless interest rate is 5 percent.
(a) What is the value of a European call option with a strike price of $100 and expiration in
10 years?
(b) What is the value of a RE call option with a strike price of $100 and an expected
holding period of 10 years?
EXERCISES 249
13.3 True, False, or Uncertain: Other things equal, an increase in the volatility of the
underlying asset will increase the value of call options on that asset.
13.4 Suppose that Owl invests in Newco across several venture rounds. After one of these
rounds of investments, Owl draws an exit diagram as shown in Exhibit 13-12.
(a) What is the portfolio of options corresponding to this exhibit?
(b) Suppose the founders of Newco own one-half of everything not owned by Owl. What is
the portfolio of options corresponding to the founder’s ownership?
APPENDIX 13.A
RE OPTIONS: TECHNICAL DETAILS
For RE options, the probability q works much like the continuous compounding of
a discount rate. The probability that an option remains alive (does not yet have a
forced expiration) on any given date T can be calculated as e
2qT
, which can be
interpreted as a discount factor at T. A plot of this probability for various levels of q
is shown in Exhibit 13-13.
To determine the probability of a forced expiration at any time T, we multiply
the instantaneous probability of expiration, q, by the probability the option is still
alive at that time, e
2qT
, yielding a probability of qe
2qT
, which is also the probability
distribution function for the exponential distribution. Then, the value of a RE call
option is
Value of RE call option 5
Z
N
0
½SNðd
1
Þ 2Xe
2rT
Nðd
2
Þ?qe
2qT
dT; ð13:17Þ
EXHIBIT 13-12
EXIT DIAGRAM FOR OWL’S STAKE IN NEWCO
20 40 80
S
lo
p
e
?
1
/
2
S
lo
p
e
?
1
/3
S
lope ?
1/6
$W
S
e
r
i
e
s
X
250 CHAPTER 13 OPTION PRICING
where the ?rst part of the integrand is de?ned as in the Black-Scholes formula of
Equation (13.11). This integral is solved numerically in the Random Expiration
Call Option Calculator. Because qe
2qT
is the probability distribution function for
the exponential distribution, we know the mean of this distribution is 1/q (the
expected holding period). We write this mean value throughout the book as H.
EXHIBIT 13-13
SURVIVAL PLOT FOR RE OPTION
P
r
o
b
a
b
i
l
i
t
y
o
p
t
i
o
n
i
s
s
t
i
l
l
a
l
i
v
e
1
.75
.25
1 2 3
q
?
.
1
q
?
.
2
q
?
.
3
T
4
.5
APPENDIX 13.A RE OPTIONS: TECHNICAL DETAILS 251
CHAPTER 14
THE VALUATION OF
PREFERRED STOCK
ALMOST ALL VC investments include some form of preferred stock. In
Chapter 9 we introduced four types of preferred stock: redeemable preferred (RP),
convertible preferred (CP), participating convertible preferred (PCP), and partici-
pating convertible preferred with cap (PCPC). In Chapter 9 we also demonstrated
how to draw exit diagrams for all these types of preferred stock. With the intro-
duction of option-pricing methods in Chapter 13, we are now ready to estimate the
partial valuation of preferred stock structures. In this chapter we learn how to value
Series A investments with RP and CP structures. We will leave the valuation of
later rounds for Chapter 15 and the valuation of PCP and PCPC for Chapter 16. In
all these chapters, we make heavy use of term sheet de?nitions ?rst introduced
in Chapters 8 and 9. If your memory of these earlier chapters is hazy, now would be
a good time to review.
We begin our analysis in Section 14.1 with a discussion of base-case option
pricing assumptions for interest rates, expected holding periods, and volatility. In
Section 14.2 we use these assumptions to analyze a Series A structure of RP and
common stock. This is the most basic of all structures, and it allows us to introduce
some new steps for making investment recommendations. The ?rst step in this
valuation is to determine the redemption value (RV) of the RP. For RP without
dividends or excess liquidation preferences, RV is the same as the aggregate pur-
chase price (APP). Once we have determined the RV, we can draw an exit diagram
for the structure and then read this diagram to obtain an exit equation. Then we
adjust this exit equation for carried interest to obtain an LP valuation equation.
At this point, if we already have an estimate for the total valuation, then we can use
this estimate in the VCV model to compute the LP valuation. Alternatively, if we do
not have an estimate for the total valuation, then we can use the VCV model to
compute the breakeven valuation that equates LP valuation and LP cost. This
breakeven valuation can then be used to inform our investment decision.
252
In Section 14.3, we show how to extend the analysis for excess liquidation
preferences (which make RV greater than APP), and in Section 14.4 we do the
same for dividends (which make RV change over time.) In Section 14.5, we ana-
lyze CP, and in Section 14.6 we extend the CP analysis for excess liquidation
preferences and dividends. Once these building blocks are in place, we can do
partial valuations for structures that combine RP and CP (Section 14.7). We can
also compare investments with different structures (Section 14.8).
14.1 BASE-CASE OPTION-PRICING
ASSUMPTIONS
Before solving any examples, it is helpful to de?ne some base-case option-pricing
assumptions. Unless otherwise noted, for Series A investments we will assume a
riskless interest rate (r) of 5 percent, an expected holding period (H) of 5 years, and
a volatility (?) of 90 percent. For Series B investments we adjust the expected
holding period to be 4 years; for Series C and beyond we adjust it to be 3 years. Of
these assumptions, the riskless interest rate is the easiest to establish. Although we
use 5 percent for the option-pricing examples in Parts III and IV of this book, readers
should adjust this number to re?ect the prevailing riskless (treasury) interest rate at
any time. For the expected holding periods, we rely on (approximate) averages from
the Sand Hill Econometrics database, as seen in Exhibits 7-2, 7-5, and 7-8.
The most dif?cult input is the volatility. For publicly traded stocks, analysts
can estimate volatility by looking at historical returns. Of course, this estimation is
not possible for nontraded private companies. Instead, we rely on a clever technique
developed by Cochrane (2005). In this article, the author begins with a CAPM
model of expected (log) returns, similar to Equation (4.2). He then uses the Ven-
tureSource database to estimate the parameters of Equation (4.2) for the typical
VC-backed company. In Chapter 4, we applied this approach to the analysis of
returns for the entire VC industry. To extend this analysis to speci?c companies, we
have a sample-selection problem: we only observe returns for a company upon
some ?nancing or liquidation event. To solve this problem, Cochrane simulta-
neously estimated thresholds for IPOs and bankruptcy liquidations. With these
thresholds in place, the parameters of the CAPM equation can be estimated, and
these parameters then imply means and standard deviations for returns.
Cochrane’s procedure can be compared to a physics experiment, where a
researcher attempts to infer the motion of particles in a room by using data about
how often these particles strike the walls of the room. Using these methods,
Cochrane estimates an annualized volatility (standard deviation of continuously
compounded returns) of 89 percent. We round this up to 90 percent for the
examples in this book. Although he also attempts to estimate different volatilities
for different industries and for different rounds of investment, these differences are
14.1 BASE-CASE OPTION-PRICING ASSUMPTIONS 253
usually not statistically signi?cant, so we use the same estimate for all examples.
Readers who want to make use of these differences are encouraged to look at
Cochrane’s article.
14.2 RP VALUATION
In the early years of the VC industry, it was popular for investors to receive both RP
and common stock. This combination is useful because the investors are paid back
in the event of a deemed liquidation event, but also have upside potential. Since the
1980s, this structure has been rarely used, but it remains a useful building block for
understanding the valuation of more popular structures.
In a transaction with RP and common stock, the contract must specify what
portion of the investment is being allocated to the RP and what portion is being
allocated to the common stock. This allocation is explicit in the APP used for the
redemption of the RP. Although this allocation might seem arbitrary, it does matter
for valuation, because the RV of the RP is driven by its APP.
EXAMPLE 14.1
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco at $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) From Chapter 10, the formula for LP cost is
LP cost ¼ ðcommitted capital=investment capitalÞ Ã $I: ð14:1Þ
From Appendix 2.A, we can compute that lifetime fees are $20M, so investment
capital is $100M 2 $20M5$80M, and LP cost is 5 (100/80) Ã $6M5$7.5M.
EBV receives the ?rst $5M in proceeds for the RP. Following this redemption, EBV
owns one-third of the common stock (5M out of 15M shares). Thus, the exit diagram for the
Series A is as shown in Exhibit 14-1.
254 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
We can read this exit diagram as
Partial valuation of Series A ¼ V 22=3 Ã Cð5Þ: ð14:2Þ
To solve for LP valuation, we must subtract carried interest from Equation (14.2).
Following the same procedures as in the modi?ed VC method of Chapter 10, we estimate LP
and GP valuation as
LP valuation ¼ partial valuation 2GP valuation; ð14:3Þ
where
GP valuation ¼ GP% Ã partial valuation: ð14:4Þ
As in Chapter 10, we estimate GP% using an expected GVM of 2.5 and the formula
GP% ¼ Carry% Ã ðGVM Ã Investment Capital 2Carry BasisÞ=ðGVM
à Investment CapitalÞ: ð14:5Þ
For EBV, we have a GP% of 0.20 Ã (2.5 Ã 80 2 100)/(2.5 Ã 80) 50.10, which implies
an LP valuation equation of
LP Valuation ¼ 0:9 Ã ½V 22=3 Ã Cð5Þ?: ð14:6Þ
(c) Equation (14.6) expresses the LP valuation of the Series A as a portfolio of options. These
options can be valued using techniques similar to those described in Chapter 13. For example,
the FLEX Calculator at VCVtools.com enables the simultaneous valuation of several options.
The user inputs each component of Equation (14.6), and the calculator values these compo-
nents and adds them together. Using this calculator with base-case option-pricing assumptions
and a total valuation assumption of $18M, we can compute a partial valuation of $7.92M, of
which the LP valuation is $7.13M and the GP valuation is $0.79M.
For most of the examples used in this textbook, the FLEX Calculator will not be
necessary, and we can use built-in valuation functions in the AUTO Calculator at VCVtools.
com. In the AUTOCalculator, users need only to input the properties of the preferred stock and
EXHIBIT 14-1
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
=
1
/3
5
$W
S
e
r
i
e
s
A
14.2 RP VALUATION 255
do not need to solve for the LP valuation equation. The Calculator does this solution auto-
matically and also calculates the speci?c LP valuation for any set of option-pricing assump-
tions. Readers are referred to Appendix B for the documentation of AUTO and FLEX.
(d) The breakeven valuation is the total valuation such that LP valuation 5LP cost. In this
example, we are solving for the total valuation (V) such that
0:9 Ã ½V 22=3 Ã Cð5Þ? ¼ $7:5M: ð14:7Þ
Because V is contained in this equation and also appears indirectly as the underlying asset in
C(5), we must use iterative methods to solve for V. This iterative process is automated in the
AUTO Calculator, where the breakeven valuation is given as standard output. Under base-case
assumptions, the breakeven valuation is $19.19M. Thus, if EBV believes that the total valuation
is $19.19M or greater, then the model would produce a positive investment recommendation.
Although it may be tempting to minimize work and just use the AUTO Calculator to
answer these questions, readers are encouraged to experiment with the FLEX Calculator
to better understand the workings of the model. At some point, every VC will be faced by a
complex problem that does not ?t into the preprogrammed functions in AUTO; when that
happens—as in Chapter 18—he will need to understand how to use FLEX.
(e) As a general rule, the common stock acts like a call option in transactions with RP. The
value of the common stock also increases when volatility or expected holding period
increases. Because the Series A holds all the RP and only a portion of the common stock,
increases in the common stock—at the expense of the RP—will tend to reduce the partial
valuation of the Series A. We can see this effect if we experiment with different option-
pricing assumptions. Other things equal, a volatility of 120 percent implies a breakeven
valuation of $20.39M, which is $1.2M higher than the breakeven valuation under base-case
assumptions (i.e., to obtain a positive investment recommendation, EBV would require a
higher total valuation by $1.2M). Similarly, if we use all base-case assumptions but set the
expected holding period to be seven years, then the breakeven valuation becomes $20.01M,
which is $0.82M higher than the base case.
Although increases in volatility or in the expected holding period will tend to increase
the breakeven valuation, reductions in these inputs will tend to reduce it. For example, if we
start from the base case but change volatility to 60 percent, then the breakeven valuation
becomes $17.90M. Similarly, if we start from the base case but change the expected holding
period to be three years, then the breakeven valuation becomes $17.99M. Exhibit 14-2
displays several combinations of these changes. ’
EXHIBIT 14-2
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 16.93 17.99 19.10
Holding 5 17.90 19.19 20.39
Period 7 18.63 20.01 21.18
256 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
14.3 EXCESS LIQUIDATION PREFERENCES
As ?rst discussed in Chapter 8, a liquidation preference provides superiority in
capital structure in the event that the ?rm is sold or shut down. Preferred stock has a
liquidation preference to common stock, and some classes of preferred stock can
be contractually given a liquidation preference to other classes of preferred
stock. Excess liquidations preferences of 2X or 3X can provide additional value.
For example, suppose a company has 10M shares of common stock and RP with
$10M APP, where the RP has a 2X liquidation preference and thus an RV of $20M.
If the company is then sold, the ?rst $20M of proceeds (two times the original
$10M) will go to the RP holders, and the remainder will be split among the
common shareholders.
EXAMPLE 14.2
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco as $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding. This is the same setup as in Example 14.1, except that now we also add a 2X
excess liquidation preference on the RP.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) With a 2X liquidation preference, the RV is 2 Ã APP 5$10M, so EBV receives the ?rst
$10M in proceeds for the RP. Following this redemption, EBV owns one-third of the
common stock (5M out of 15M shares). Thus, the exit diagram for the Series A is the same as
in Example 14.1, except that the slope does not change until W5$10M.
We can read the exit diagram in Exhibit 14-3 as
Partial Valuation of Series A ¼ V 22=3 Ã Cð10Þ: ð14:8Þ
With GP% 5 0.10 (the same as in Example 14.1), we have
LP Valuation ¼ 0:9 Ã ½V 22=3 Ã Cð10Þ?: ð14:9Þ
14.3 EXCESS LIQUIDATION PREFERENCES 257
(c) Using base-case assumptions with a total valuation of $18M, we can use the AUTO or
FLEX Calculators to compute LP valuation as $8.34M. Thus, in contrast to the base case in
part (c) of Example 14.1, this computation implies a positive investment recommendation
(LP valuation .LP cost).
(d) The VCV model gives a breakeven valuation of $15.64M (i.e., for total valuations above
this cutoff, there is a positive investment recommendation).
(e) The option-pricing assumptions have the same effects as in Example 14.1. Increases in
volatility or expected holding period would decrease the LP valuation and, thus, increase the
breakeven valuation. Exhibit 14-4 demonstrates the sensitivity of the breakeven valuation to
changes in the volatility of the expected holding period. ’
EXHIBIT 14-3
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/3
10
$W
S
e
r
i
e
s
A
EXHIBIT 14-4
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 11.78 13.77 15.59
Holding 5 13.30 15.64 17.58
Period 7 14.47 16.93 18.84
258 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
Reality Check: The preceding analysis assumed that liquidation preferences are
honored in all outcomes, but it can be a lot messier in reality. In many cases,
investors in down rounds of ?nancing will insist that all prior liquidation pre-
ferences be wiped out. Thus, we may be overstating the valuation of the liquidation
preferences as well as the preferred stock itself.
This is a valid objection that can be addressed in several ways. First, analysts
should recognize that the option-pricing valuation of liquidation preferences is
essentially providing an upper bound for their value. It would be nice to compute
exactly how close this bound is to the “true value”, but given current data and
methods, it is not possible to do so. Second, one should not interpret the preceding
objection to mean that liquidation preferences are worth nothing. In most successful
investments, there are no down rounds, so liquidation preferences can be paid
without objection. Even in down rounds, the preferences do provide prior investors
with some protections in the form of additional leverage in the negotiation, thus
functioning as yet another bargaining chip that investors can put on the table.
14.4 DIVIDENDS
As ?rst discussed in Chapter 8, preferred stock can include a cumulative dividend.
This dividend does not pay in cash; instead, it adds to the RV of the preferred and is
paid on exit. These dividends can either be a constant amount paid on the APP
(simple interest) or can compound on past dividends (compound interest). Including
dividends in our analysis is more complex than the inclusion of a liquidation
preference because the RV is changing over time. For RP, it does not matter
whether the dividend is an accrued cash dividend (5liquidation dividend) or a
stock dividend (5PIK dividend). In Example 14.3 we analyze the former case.
EXAMPLE 14.3
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco as $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding. This is the same setup as in Example 14.1, except now we also add a cumulative
simple dividend of 1 percent per month on the RP, to be paid only if dividends are paid to the
common stock or on the liquidation of the company.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
14.4 DIVIDENDS 259
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) For computational convenience, it is simplest to express the dividend rate as a con-
tinuous annual rate, which is approximately equal to 12% (51.00% Ã 12) of the APP. Let T
equal the time, in years, between investment and exit for proceeds of $W. Given this case,
the RV of the RP at time T is equal to RV (T) 5$5M (1 10.12T) and the exit diagram for the
Series A is
1
shown in Exhibit 14-5.
The corresponding exit equation for the Series A is
Partial valuation of the Series A ¼ V 22=3 Ã CðRVðTÞÞ: ð14:10Þ
As in the previous examples, GP% is 0.1, so we can write the LP valuation
equation thus:
LP valuation of the Series A ¼ 0:9 Ã ½V 22=3 Ã CðRVðTÞÞ?: ð14:11Þ
1
For compound dividends of 12 percent, the corresponding formula would be RV(T) 5 $5 MÃ e
0.12T
.
EXHIBIT 14-5
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/3
RV(T)
$W
S
e
r
i
e
s
A
260 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
(c) Although these equations are more complex than the analogues from Examples 14.1
and 14.2, it is not a problem for the all-powerful computer. The strike prices for the call
options change over time, but because the RE option already requires us to effectively
compute a separate Black-Scholes formula at every point in time, the computer doesn’t care
if the strike price is different in each of these formulas. Using base-case assumptions with a
total valuation of $18M, we can use the AUTO Calculator to compute the LP valuation as
$7.89M.
(d) The VCV model gives a breakeven valuation of $16.82M.
(e) The option-pricing assumptions have the same effects as in Examples 14.1 and 14.2.
Increases in volatility or expected holding period would decrease the LP valuation and, thus,
increase the breakeven valuation. Exhibit 14-6 demonstrates the sensitivity of the breakeven
valuation to changes in the volatility of the expected holding period.
’
14.5 CP VALUATION
As ?rst discussed in Chapter 9, the key step in the valuation of CP is the deter-
mination of the conversion condition, an inequality de?ning the level of proceeds
where conversion is more valuable than redemption. We call this level of proceeds the
conversion point, and we write the conversion point for a Series Ainvestment as W
A
.
The conversion condition is calculated in the partial valuation step. In other
respects, the valuation of CP is similar to that for RP and common.
EXAMPLE 14.4
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees of
Newco have claims on 10M shares of common stock. Following the Series A investment,
EXHIBIT 14-6
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 14.59 16.14 17.61
Holding 5 14.77 16.82 18.52
Period 7 14.97 17.34 19.16
14.5 CP VALUATION 261
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) We can calculate the conversion condition as
1=3 Ã W .6-W
A
¼ 18: ð14:12Þ
If the proceeds of the liquidation are exactly $18M, then the investor will receive $6M
for either redeeming or converting. However, if the proceeds are below $18M, he is better off
redeeming. Above $18M the investor is better off converting. Exhibit 14-7 gives the exit
diagram:
We can read this exit diagram as
Partial valuation of Series A ¼ V 2Cð6Þ 11=3 Ã Cð18Þ: ð14:13Þ
Thus, the LP valuation is
LP valuation of Series A ¼ 0:9 Ã ½V 2Cð6Þ 11=3 Ã Cð18Þ?: ð14:14Þ
(c) With base-case assumptions, we can use the VCV model to solve for a breakeven
valuation of $22.38M.
EXHIBIT 14-7
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/
3
6 18
$W
C
P
262 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
(d)
Note that these option-pricing sensitivities are smaller than those found for RP
structures. The reason for this difference is that CP is harmed less than RP from increases in
volatility and holding period because there is no redemption value at extreme levels. In the
limit, as either of these inputs approaches in?nity, CP looks just like common stock. Indeed,
it is possible for an increase in expected holding period (or volatility) to lead to a decrease in
the breakeven valuation. This can only happen when these inputs start at low levels, as we
see when volatility is at 60 percent, and the expected holding period increases from three to
?ve years. To see how this is possible, consider an extreme case where expected holding
period (or volatility) is zero. Then the CP would convert for sure for any total valuation
above 18M, and thus would be worth exactly the same as the common stock. CP only has
some advantage if there is at least some chance that the redemption feature will be used,
which requires at least some volatility. For “too much” volatility, the redemption feature
becomes relatively worthless (because most redemptions are for close to zero), and the value
of the CP once again is close to common stock.
’
14.6 CP WITH EXCESS LIQUIDATION
PREFERENCES OR DIVIDENDS
Earlier in this chapter we gave extended examples for liquidation preferences and
cumulative dividends for an RP investment. We will not repeat those whole
examples here, but instead will focus only on the parts of the valuation problem that
differ from Example 14.4. As in the earlier example, we analyze accrued cash
dividends, leaving the more complex analysis of stock dividends for Chapter 15.
EXAMPLE 14.5
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees of
EXHIBIT 14-8
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 22.50 22.03 22.18
Holding 5 22.47 22.38 22.73
Period 7 22.59 22.68 23.09
14.6 CP WITH EXCESS LIQUIDATION PREFERENCES OR DIVIDENDS 263
Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP. This is the same setup as in Example 14.4, except that we now add a
2X liquidation preference on the CP.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) The crucial difference between this example and the previous one is that the RV of the
CP is now 2 Ã $6M5$12M. Thus, the new conversion condition is
1=3 Ã W.12-W
A
¼ 36: ð14:15Þ
The exit diagram for the CP with a 2X liquidation preference is shown in Exhi-
bit 14-9
We can read Exhibit 14-9 as
Partial valuation of the CP ¼ V 2Cð12Þ 11=3 Ã Cð36Þ: ð14:16Þ
Thus, the LP valuation is
LP valuation of the CP ¼ 0:9 à ½ðV 2Cð12Þ 11=3 à Cð36Þ?: ð14:17Þ
(b) We can use base-case option-pricing assumptions in the VCV model to solve for the
breakeven valuation as $17.67M.
’
EXHIBIT 14-9
EXIT DIAGRAM FOR SERIES A
S
lo
p
e
?
1
/3
12 36
$W
C
P
264 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
EXAMPLE 14.6
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees
of Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP. This is the same setup as in Example 14.4, except that we now add a
cumulative simple dividend of 1 percent per month. This dividend will be paid only if
dividends are paid to the common stock or upon the liquidation of the company.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) We use the same approach to dividends here as we did in Example 14.3, using a con-
tinuous approximation for the dividends and obtaining a redemption value of
RVðTÞ ¼ $6M Ã ð1 10:12TÞ: ð14:18Þ
The conversion condition is
1=3 Ã W .RVðTÞ-W .3 Ã RVðTÞ; ð14:19Þ
which implies an exit diagram as shown in Exhibit 14-10.
This exit diagram looks exactly like Exhibits 14-8 and 14-9, except that the conversion
point is at 3 Ã RV(T) 5$18M Ã (1 10.12T). We can read this diagram as
Partial valuation of the CP ¼ V 2CðRVðTÞÞ 11=3 Ã Cð3 Ã RVðTÞÞ: ð14:20Þ
EXHIBIT 14-10
EXIT DIAGRAM FOR SERIES A
RV(T) 3*RV(T)
$W
C
P
14.6 CP WITH EXCESS LIQUIDATION PREFERENCES OR DIVIDENDS 265
So the LP valuation equation is
LP valuation of the CP ¼ 0:9 Ã ½V 2CðRVðTÞÞ 11=3 Ã Cð3 Ã RVðTÞÞ?: ð14:21Þ
(b) The VCV model gives a breakeven valuation of $19.54M.
’
14.7 COMBINING RP AND CP
In Examples 14.1, 14.2, and 14.3, EBV received a combination of RP and common
stock in the Series A investment. A similar payoff structure can be obtained through
the combination of RP and CP.
EXAMPLE 14.7
Suppose EBV is considering a $10M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of CP ($6M APP) plus RP ($4M APP). The employees
of Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) In this example, there are two types of preferred stock, CP and RP, and there is no
statement about which version would be paid ?rst in a liquidation. This structure is very
similar to the RP 1CP structure that was analyzed as part of Example 9.1. Because EBV
owns all of both the CP and the RP, this liquidity preference between the two is not relevant
for the aggregate value of the Series A; following Example 9.1, we treat the RP as superior
to the CP.
To estimate the partial valuation, we ?rst examine the RP component. Because we
have assumed that the RP has a liquidation preference to the CP, we can draw the exit
diagram for the RP as Exhibit 14-11.
We can read Exhibit 14-11 as
RP in Series A ¼ V 2Cð4Þ: ð14:22Þ
The CP here is similar to the CP in Example 14.4, except that the CP has no value
unless the proceeds are above $4M. The conversion condition for this CP is
1=3 Ã ðW 24Þ . 6-W
A
¼ 22: ð14:23Þ
To draw an exit diagram for the CP, it is as though we take Exhibit 14-7 and shift the
line $4M to the right:
266 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
We can read Exhibit 14-12 as
CP in Series A ¼ Cð4Þ 2Cð10Þ 11=3 Ã Cð22Þ: ð14:24Þ
Then, the partial value of Series A is RP 1CP:
Partial valuation of Series A ¼ V 2Cð10Þ 11=3 Ã Cð22Þ: ð14:25Þ
and the LP valuation is
LP valuation of Series A ¼ 0:9 Ã ½V 2Cð10Þ 11=3 Ã Cð22Þ?: ð14:26Þ
EXHIBIT 14-11
EXIT DIAGRAM FOR SERIES A, RP
4
$W
R
P
i
n
S
e
r
i
e
s
A
EXHIBIT 14-12
EXIT DIAGRAM FOR SERIES A
S
lo
p
e
?
1
/3
4 10 22
$W
C
P
i
n
S
e
r
i
e
s
A
14.7 COMBINING RP AND CP 267
(b) The LP cost is $10M Ã (100/80) 5$12.5M. The AUTO Calculator solves for a breakeven
valuation of $34.90M, where LP valuation 5LP cost.
’
14.8 COMPARING RP AND CP
Now that we have done examples with both RP and CP, we are prepared to analyze
comparisons between these two structures and the implications of these compari-
sons for deal structure negotiation.
EXAMPLE 14.8
Suppose that EBV makes an initial offer to Newco as given in Example 14.1, with the offer
providing $6M for RP (APP5$5M) as well as 5M shares of common stock. The only
difference here is that we assume that the total valuation of the company is $25M. The
entrepreneurs counteroffer with a CP structure. In principle, EBV is not opposed to a CP
structure, but they would like to get the same expected value as they would under the RP
structure. Thus, they are considering two possibilities for their $6M investment:
Structure 1 5RP($5M APP) 15M shares of common stock($1M APP);
Structure 2 5Z shares of CP($6M APP)
Problem For what number of shares Z should EBV be indifferent between Structures 1
and 2?
Solution We will answer this question from the perspective of a limited partner in EBV,
so the key comparison will be between the LP valuations of the two possible structures. Our
goal is to solve for the unknown quantity of shares Z, which would equate the LP valuations
of the two structures. We have already solved for the LP valuation of Structure 1 in Example
14.1. That valuation was given in Equation (14.6). Using the VCV model, we can compute
the LP valuation as $9.32M (when the total valuation is $25M).
In Example 14.4 we did most of the work to solve for the LP valuation in Structure 2.
The only difference here is that instead of receiving 5M shares on conversion (one-third
of the ?rm), EBV would receive Z shares. These Z shares will convert to a fraction of the ?rm
equal to
CP fraction ¼ Z=ð10 1ZÞ: ð14:27Þ
We can then write the general conversion condition as
Z=ð10 1ZÞ Ã W .6-W
A
¼ 6 Ã ð10 1ZÞ=Z: ð14:28Þ
This conversion condition implies an exit diagram for the CP as shown in
Exhibit 14-13.
We can read Exhibit 14-13 as
Partial valuation ðStructure 2Þ ¼ V 2Cð6Þ 1Z=ð10 1ZÞ Ã Cð6 Ã ð10 1ZÞ=ZÞ; ð14:29Þ
268 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
so we have
LP valuation ðStructure 2Þ 50:9 Ã ½V 2Cð6Þ 1Z=ð10 1ZÞ
à Cð6 à ð10 1ZÞ=ZÞ?:
ð14:30Þ
Now we are ready to answer the initial question: What value of Z will equate the LP
valuations for Structure 1 and Structure 2? This can be answered through trial and error by
trying different values for Z, solving for the implied values for the CP fraction and the
conversion point, and then using the VCV model to compute the LP valuation with these
inputs. We can continue this process by trial and error until we obtain an LP valuation answer
of $9.32M, which is the value we found for Structure 1. It is useful to try this brute-force
approach a few times to get a feel for how the valuations change when Z changes. Using this
method, we can obtain a solution of Z56.29M, yielding a CP fraction of 38.6 percent and a
conversion point of $15.39M. ’
SUMMARY
Venture capitalists typically receive preferred stock for their investments. In one structure,
redeemable preferred stock (RP) is combined with common stock to provide both downside
protection and upside potential. This combination of securities can be valued using option-
pricing techniques. Sometimes the RP component includes additional liquidation preferences
that provide the holder with an additional return on a sale or liquidation. Cumulative divi-
dends can also provide the same bene?t, and both of these enhancements can be priced using
small modi?cations to our standard techniques.
EXHIBIT 14-13
EXIT DIAGRAM FOR SERIES A, STRUCTURE 2
S
l
o
p
e
?
1
S
lo
p
e
?
Z
/1
0
?
Z
6 6(10 ? Z)/Z
$W
C
P
SUMMARY 269
Convertible preferred (CP) stock is the most prevalent security in VCtransactions. CP is
a hybrid between RP and common stock, acting like the former when proceeds are lowand like
the latter when proceeds are high. CP can be valued as a bond plus an embedded call option. The
key step in CP valuation is to determine the conversion condition (the level of exit proceeds
necessary to induce the CP holder to convert rather than to redeem the stock). Once we have
mastered the valuation techniques for CP, we can compare transactions with different types of
preferred stock (RP or CP) or with combinations of preferred stock (RP plus CP).
KEY TERMS
Redemption value (RV) LP valuation equation Breakeven valuation
REFERENCES
Cochrane, John, 2005, “The Risk and Return of Venture Capital”, Journal of Financial Economics
75(1), 3À52.
EXERCISES
14.1 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as RP with APP of $4M plus 5M shares of common stock. (We refer
to this basket of RP plus common as “Series A”.) The employees of Newco have claims on
15M shares of common stock. Following the Series A investment, Newco will have 20M
common shares outstanding.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $30M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
14.2 Same setup as Exercise 14.1, except that now EBV is considering two additional
structures:
Alternative I: A 2X liquidation preference on the RP; or
Alternative II: A cumulative compound dividend of 0.75 percent per month, to be paid only if
dividends are paid to the common stock or on the liquidation of the company.
(a) Find the LP valuation equation for both alternatives.
(b) Compute the LP valuation for both alternatives under the assumption that total valua-
tion 5$30M. Which alternative should EBV prefer?
(c) Perform a sensitivity analysis of this preference.
270 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
14.3 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of CP. The employees of Newco have claims on
15M shares of common stock. Following the Series A investment, Newco will have 15M
common shares outstanding, with another 5M shares on conversion of the Series A.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $30M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
14.4 Same setup as Exercise 14.3, except that now EBV is considering two additional
structures:
Alternative I: A 2X liquidation preference on the CP; or
Alternative II: A cumulative compound dividend of 0.75 percent per month, to be paid only if
dividends are paid to the common stock or on the liquidation of the company.
(a) Find the LP valuation equation for both alternatives.
(b) Compute the LP valuation for both alternatives under the assumption that total valua-
tion 5$30M. Which alternative should EBV prefer?
(c) Perform a sensitivity analysis of this preference.
EXERCISES 271
CHAPTER 15
LATER-ROUND INVESTMENTS
THUS FAR WE have analyzed preferred structures only for Series A (?rst-
round) investments. Although Series A is the simplest setting for learning partial
valuation techniques, it is also the least applicable. This is because Series A
investments are made in early stage companies, often without any revenue, where it
is dif?cult to perform total valuations. Thus, the partial valuations—which require
additional assumptions—are even less reliable.
For more mature companies, valuation analysis can be more precise. In later-
round investments, companies often have revenues and sometimes have pro?ts, so
there is a stronger basis for the estimation of total valuations. In addition, the path
to exit can be clearer, so it is easier to estimate exit values and future dilution.
Finally, the required investments often are larger, and the possible investment
structures are more complex, so there is a greater importance of getting the numbers
right. For these reasons, it is important that we extend our methods to later rounds.
In this chapter, we show how to extend our investment framework to Series B and
beyond. We will do three examples: Series B (Section 15.1), Series C (Section
15.2), and then, as an example of a very late round, Series F (Section 15.3).
15.1 SERIES B
EXAMPLE 15.1
Talltree is considering a $12M Series B investment in Newco. Two possible structures are
being considered. Structure 1 is 5M shares of common plus RP with $10M APP and a 2X
liquidation preference. Structure 2 is 10M shares of CP. The other investors are the
employees, who have claims on 10M shares of common, and the Series A investors, EBV,
who have 10M shares of CP with $6M APP. In both of these structures, Series B has a
liquidation preference to Series A. Both Talltree and EBV receive carried interest of 20
percent and charge management fees of 2 percent per year for all 10 years (as shown in the
appendices to Chapter 2).
272
Problems
(a) What is the LP valuation equation and breakeven valuation for Structure 1?
(b) What is the LP valuation equation and breakeven valuation for Structure 2?
(c) Plot the LP valuation for both structures for a range of possible total valuations. For
what total valuation should Talltree be indifferent between the two structures?
Solutions (a) The ?rst step is to compute LP cost. Talltree’s partnership agreement has
the same fee schedule as EBV. On the $250M Talltree fund, this implies lifetime fees of
$50M and investment capital of $200M. Thus, the LP cost for a $12M investment is
LP cost 5ð$250M=$200MÞ Ã 12M5$15M: ð15:1Þ
Next, we estimate partial valuation under Structure 1. With an APP of $10M on the RP
and a 2X liquidation preference, Talltree would receive the ?rst $20M of the proceeds from
any liquidation. After the ?rst $20M, the next $6M would go to EBV to cover the RV5APP
of their Series A CP. Beyond this point ($26M), things get trickier. The next dollar of
proceeds beyond $26M would be shared by the common stockholders, but how many shares
of common stock are outstanding? The founders have 10M, Talltree has 5M, and because
EBV has not yet converted, they have 0. Thus, Talltree has one-third of the outstanding
shares, and the founders have two-thirds. These fractions hold unless the proceeds are high
enough for EBV to convert, at which point there would be 25M shares outstanding and
Talltree would have 5/25. This means that we cannot draw an exit diagram for Talltree until
we solve for EBV’s conversion point.
To determine EBV’s optimal conversion point, we use the same inequality discussed
for the conversion of CP in Chapters 9 and 14. On the left-hand side of the inequality, we put
the amount earned by EBV if they choose to convert. Under conversion, EBV would have
10M shares, for 10/25(52/5) of the total shares outstanding. They would then be entitled to
two-?fths of the proceeds after $20M had been paid back to Talltree: 2/5 Ã (W220). On the
right-hand side of the inequality, we put the amount earned by EBV if they choose to redeem:
$6M. We then solve for the level of proceeds, $W, that leads to conversion.
Series A conversion condition:
2=5 Ã ðW 220Þ .6-W
A
5$35: ð15:2Þ
This inequality completes the picture for all parties. For proceeds of $35M or more,
EBV converts and owns 2/5 of the outstanding shares, Talltree owns 5/25 (51/5), and the
founders own the remaining two-?fths. With this ?nal piece, we are prepared to draw an exit
diagram for the Series B.
Exhibit 15-1 shows Talltree receiving the ?rst $20M of proceeds to pay for their 2X
liquidation preference, nothing of the next $6M, one-third of the next $9M (until W5$35M),
and then one-?fth thereafter. We can read this diagram as
Partial valuation of Series B ðStructure 1Þ 5V 2Cð20Þ 11=3 Ã Cð26Þ
22=15 Ã Cð35Þ:
ð15:3Þ
Because Talltree has carried interest of 20 percent (see Appendix 2.B), the compu-
tation of GP% (when the expected gross value multiple is 2.5) gives the same answer as it did
for EBV (50.10) and we have
15.1 SERIES B 273
LP valuation of Series B ðStructure 1Þ 50:9 Ã ½V 2Cð20Þ
11=3 Ã Cð26Þ 22=15 Ã Cð35Þ?:
ð15:4Þ
Using the VCV model, we can compute the breakeven valuation as $39.32.
(b) We begin again with the LP cost, which is $15M, the same as in part (a). Next, we need to
compute the partial valuation for Structure 2. For low levels of proceeds, the exit diagram is
easy to draw. Talltree receives the ?rst $12M of proceeds to cover redemption of Series B,
and EBV receives the next $6M of proceeds to cover redemption of Series A. Proceeds
above $18M are shared by the common stock holders, but how many of these shares are
outstanding?
Both Series Aand Series Bare CP. The ?rst step in this case—and in all cases with more
than one round of CP—is to determine the order of conversion. This step is tricky, because each
investor’s conversion decision depends on whether the other investor has already converted.
To determine the order of conversion, we ?rst compute the conversion point for each
investor under the assumption that the other investor has not converted. Consider Talltree’s
decision. Assume that proceeds are above $18M, because no investor would convert before
the APPs have been paid back at $18M. After that point, if EBV does not convert the Series
A, then Talltree could either receive $12M for redemption or 1/2Ã(W26M) for conversion.
(After conversion, Talltree would have 10M shares, and the employees would have 10M
shares, while $6M would be paid to redeem the Series A.) Thus, if EBV does not convert,
Talltree’s conversion condition would be
Series B conversion conditionÀSeries A not converted:
1=2 Ã ðW 26MÞ .12M-W
B
5$30M: ð15:5Þ
For EBV, if Talltree does not convert the Series B, then EBV would receive $6M if they
redeem the Series A, and 1/2 Ã (W2 12) if they convert. This implies a conversion condition of
Series A conversion conditionÀSeries B not converted:
1=2 Ã ðW 212MÞ .6M-W
A
5$24M: ð15:6Þ
EXHIBIT 15-1
EXIT DIAGRAM FOR SERIES B, STRUCTURE 1
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274 CHAPTER 15 LATER-ROUND INVESTMENTS
A comparison of Equations (15.5) and (15.6) shows that EBV (Series A) would
convert “?rst”, with a conversion point of W
A
5$24M.
Now that we know that Series A converts ?rst, we revisit Talltree’s conversion
decision. Equation (15.5) is no longer relevant, because it was derived under the assumption
that the Series A did not convert. If the Series A does convert, then the Series B is still worth
$12M on redemption. If the Series B converts, however, it would be worth 1/3 Ã W, because
10M shares would now be one-third of the total. This implies a new conversion condition of
Series B conversion condition—Series A converted:
1=3 Ã W .12M-W
B
5$36M: ð15:7Þ
With the conversions solved, we are ready to draw an exit diagram for the Series B
under Structure 2:
This exhibit shows that Talltree receives everything from the ?rst $12M. After that,
they will receive nothing until they convert for one-third of the common stock at $36M. The
corresponding exit equation for Exhibit 15-2 is
Partial valuation of the Series B ðStructure 2Þ 5V 2Cð12Þ 11=3 Ã Cð36Þ: ð15:8Þ
The LP valuation equation is
LP valuation of the Series BðStructure 2Þ 50:9 Ã ½V 2Cð12Þ 11=3 Ã Cð36Þ?: ð15:9Þ
Using the VCV model, we can compute the breakeven valuation as $44.36M.
(c) Now, for each LP valuation Equations [(15.4) and (15.9)], we can use the VCV model and
base-case option pricing assumptions to compute an LP valuation for any given level of total
valuation. Because this is a Series B investment, our base-case assumption is an expected
holding period of four years. Exhibit 15-3 plots LP valuation for each structure. The crossing
point occurs at a total valuation of $61.25M, where both structures yield LP valuations of
EXHIBIT 15-2
EXIT DIAGRAM FOR SERIES B, STRUCTURE 2
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15.1 SERIES B 275
$19.80M. That is, for a total valuation below $61.25M, Talltree should prefer Structure 1; for
a total valuation above $61.25M, Talltree should prefer Structure 2. ’
After analyzing Series B structures, many students wonder why we don’t try
to account for later investments when we ?rst analyze the Series A. Put another
way, why is it all right to just ignore future rounds when we draw exit diagrams?
Because these future rounds will change the exit diagrams of the earlier rounds,
how can these early round diagrams be correct?
To answer these questions, it is helpful to put ourselves in the shoes of a Series
A investor like EBV. At the time of a Series A investment in Newco, EBV fully
expects more investments to be made. Although other investors may lead these later
rounds, EBV may invest in these rounds as well. In either case, as an investor in the
company, EBV has the incentive to drive the best possible bargain for the company
in later rounds. Indeed, the board of directors of Newco has a legal duty to get the
best deal. If the VC market is competitive—and all evidence says that it is—then
these later-round investments should be priced at “fair” levels. In this case, even
through the Series A exit diagrams will change, they should change in a way that
preserves the pre-transaction value of the Series A stake. We can draw an analogy
here to the DCF analysis of Chapter 11. There, if some future investment earns
exactly the cost of capital, this investment has no effect on valuation today. It is the
same thing here: if future rounds are sold at a fair price that re?ects the cost of
venture capital, then these rounds have no effect on the valuation of any stake today.
EXHIBIT 15-3
LP VALUATION OF SERIES B, STRUCTURES 1 AND 2
25 50 75
Total Valuation of Newco
100
35
25
15
5
30
20
10
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Structure 1
Structure 2
276 CHAPTER 15 LATER-ROUND INVESTMENTS
15.2 A CONVERSION SHORTCUT
To determine the conversion order in Structure 2 of Example 15.1, we derived a
conversion condition for each investor under the assumption that the other investor
did not convert. When there are only two investors, this does not take much time.
However, this procedure can become unwieldy when there are three or more
investors; because in addition to determining which investor converts ?rst, we must
then repeat the process to determine which investor converts second, third, and so on.
Luckily, a shortcut greatly simpli?es the task of determining conversion
order. Recall the ?rst conversion condition tried for the Series B in Example 15.1:
Series B conversion conditionÀSeries A not converted:
1=2 Ã ðW 26MÞ .12M-W
B
5$30M: ð15:5Þ
This condition means that if EBV does not convert the Series A, then Talltree
would convert the Series B as long as total proceeds are at least $30M. Now, let’s
interpret this equation another way. If, for proceeds of $30M, Talltree decides to
convert and EBV does not, then there would be 20M total shares outstanding, and
the total amount available for the common stock holders would be $30M2$6M
5$24M, because $6M would be needed to pay back EBV when they redeem the
Series A. Thus, the value of each common share would be $24M/20M5$1.20 per
share. This means that, in this case, we can say that Talltree will convert if they
receive at least $1.20 per share.
The $1.20 number is the redemption value per share (RVPS) of the CP: the
RVPS of preferred stock is equal to the total redemption value of the preferred
divided by the number of common shares received on conversion. In this case, the
CP has 12M APP and could convert to 10M shares, $12M/10M5$1.20 per share.
We will get the same RVPS of $1.20 no matter how many other investors have
already converted. To illustrate this point, consider Equation (15.7), the conversion
condition for the Series B when the Series A has already converted:
Series B conversion conditionÀSeries A converted:
1=3 Ã W .12M-W
B
5$36M: ð15:7Þ
With Series A already converted, there will be 30M shares outstanding on
conversion of Series B. Thus, $36M available to the common stock holders is
equivalent to an RVPS of $36M/30M5$1.20 per share.
It is also helpful to review Equation (15.6), EBV’s conversion condition for
the Series A in the case where the Series B has not converted:
Series A conversion condition—Series B not converted:
1=2 Ã ðW 212MÞ .6-W
A
5$24M: ð15:6Þ
For proceeds of $24M, if Series A converts and Series B does not, then there
would be 20M total shares outstanding, and the total amount available for the common
stock holders would be $24M2$12M5$12M, because $12M would be needed to
15.2 A CONVERSION SHORTCUT 277
pay back Talltree when they redeem the Series A. Thus, the value of each common
share would be $12M/20M5$0.60 per share. It is easy to verify that this number is
exactly the same as the RVPS of the Series A ($6M/10M5$0.60).
For Structure 2 in Example 15.1, we found that the Series A converted before
the Series B. We also ?nd that the Series A has a lower redemption value per share
than does the Series B ($0.60 versus $1.20). These two results are logically con-
nected through the conversion-order shortcut: the order of CP investors by their
RVPS, from lowest to highest. The investors will convert in the order of their RVPS
(i.e., the lowest RVPS will convert ?rst, the second-lowest RVPS will convert
second, and so on, and the highest RVPS will convert last). To demonstrate the
application of this shortcut, we do an example of a Series C investment.
15.3 SERIES C
In computing valuations for Series C, we follow the same steps as for Series B. The
analysis is more complicated because of the large range of possible structures
across three rounds. Despite this added complexity, the building blocks of any
partial valuation analysis remain the same no matter how many rounds of invest-
ment have already occurred.
EXAMPLE 15.2
Begin with the same setup as in Example 15.1. Assume that Talltree chose Structure 2 and
invested $12M in a Series B round for CP. It is now one year later, and Owl is considering a
$10M Series C investment in Newco. Structure 1 is 5M shares of common plus RP with $8M
APP and a 3X liquidation preference. Structure 2 is 10M shares of CP. The other investors
are (1) the employees, who have claims on 10M shares of common, (2) the Series A
investors, EBV, who have 10M shares of CP for $6M APP, and (3) the Series B investors,
Talltree, who have 10M shares of CP for $12M APP. In both structures, Series C has a
liquidation preference to Series B, which in turn has a liquidation preference to Series A.
Neither of the previous investors is covered by antidilution protection. As shown in Chapter 2,
the $500M Owl fund has a 25 percent carry and $83.75M in lifetime fees.
Problems
(a) What is the LP valuation equation and breakeven valuation for Structure 1?
(b) What is the LP valuation equation and breakeven valuation for Structure 2?
(c) Plot the LP valuation for both structures for a range of possible total valuations. For
what total valuation should Owl be indifferent between the two structures?
Solutions (a) The ?rst step is to compute LP cost. The $500M Owl fund has lifetime
fees of $83.75M and investment capital of $416.25M. Thus, the LP cost is
LP cost 5ð500=416:25Þ Ã 10M5$12M: ð15:10Þ
278 CHAPTER 15 LATER-ROUND INVESTMENTS
Next, we estimate partial valuation under Structure 1. With an APP of $8M on the RP
and a 3X liquidation preference, Owl would receive the ?rst $24M of the proceeds from any
liquidation. After the ?rst $24M, the next $12M would go to Talltree to cover the RV of their
Series B CP, and the next $6M would go to EBV for RV of the Series A CP. Beyond this
point ($42M), we have to ?gure out the order of conversion for Series A and Series B. In
the previous section, we computed the RVPS for the Series B as $1.20 per share and for the
Series A as $0.60 per share. The Series A is lower, so it converts ?rst.
When EBV converts the Series A, they will own two-?fths (10M/25M) of the
remaining proceeds (W236M). We obtain their conversion condition by comparing this
value to the $6M RV for redemption. Thus, EBV converts the Series A when
Series A conversion conditionÀSeries B not converted:
2=5 Ã ðW 236MÞ .6M-W
A
5$51M: ð15:11Þ
Once EBV converts, then Talltree would own two-sevenths (10M/35M) of the
remaining proceeds (W224M) when they convert, or $12M if they redeem. Thus, Talltree’s
conversion condition is
Series B conversion conditionÀSeries A converted:
2=7 Ã ðW 224MÞ .12M-W
B
566M: ð15:12Þ
With this information, we are prepared to draw an exit diagram for Series C (Structure 1),
as shown in Exhibit 15-4.
For the Series C, Owl gets all of the ?rst $24M in proceeds, nothing for the next $18M
while Series A and B are being paid back, and then one-third of all proceeds (because they
will own 5M out of 15M shares of common) until the Series A is converted at W5$51M.
For proceeds between $51M and $66M, Owl owns one-?fth of the common stock (5M/25M).
After the Series B is converted at W5$66M, Owl owns one-seventh of the common
(5M/35M). We can read Exhibit 15-4 as
EXHIBIT 15-4
EXIT DIAGRAM FOR SERIES C, STRUCTURE 1
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15.3 SERIES C 279
Partial valuation of Series C ðStructure 1Þ 5V 2Cð24Þ 11=3 Ã Cð42Þ
22=15 Ã Cð51Þ 22=35 Ã Cð66Þ:
ð15:13Þ
Owl has carried interest of 25 percent, which is higher than the industry-standard 20
percent carried interest charged by EBV and Talltree. With an expected gross value multiple
of 2.5, Owl has GP% of 0.25 Ã (2.5 Ã 416.25 2 500)/(2.5 Ã 416.25) 50.13. Thus, the GPs
receive an expectation of 13 percent of the partial valuation, and the LPs receive an
expectation of 87 percent.
LP valuation of Series C ðStructure 1Þ 50:87 Ã ½V 2Cð24Þ 11=3 Ã Cð42Þ
22=15 Ã Cð51Þ 22=35 Ã Cð66Þ?:
ð15:14Þ
Using the VCV model, we can compute the breakeven valuation as $25.32.
(b) For Structure 2, we have the same LP cost as in Structure 1: $12M. To complete the next
step, the partial valuation of the Series C, we must ?rst determine the conversion order.
Things look more dif?cult than in earlier examples because we now have three different
rounds of CP, but we can apply the conversion-order shortcut to keep things from getting too
messy. We already know the RVPS for Series A and B to be $0.60 and $1.20, respectively.
For Series C, we can compute the RVPS as $10M/10M5$1.00 per share. Thus, the con-
version order is Series A, then Series C, then Series B. With this ordering determined, we can
compute each conversion point.
EBV (Series A) converts ?rst. Series B and C have not yet converted. When EBV
converts, they receive 10Mshares and get half (10M/20M) of all proceeds after the Series Band
Chave been redeemed (W222M). To obtain their conversion condition we compare this value
to the redemption proceeds of $6M:
Series A conversion conditionÀB and C not converted:
1=2 Ã ðW 222Þ .6-W
A
5$34M: ð15:15Þ
Next to convert is Owl (Series C). Series A has converted and Series B has not. When
Owl converts, they receive 10M shares, the founders will have 10M shares, and EBV will have
10M shares, for a total of 30M shares outstanding. Thus, Owl will receive 10M/30M5one-
third of any proceeds after the Series B has been redeemed (W 2 12M). To obtain their
conversion condition, we compare this value to the redemption proceeds of $10M:
Series C conversion condition—A converted, B not converted:
1=3 Ã ðW 212Þ .10-W
c
5$42M: ð15:16Þ
Series A and C have already converted, so last to convert is Talltree (Series B). Upon
conversion, Talltree receives 10M shares for a total of 40M shares outstanding. Thus,
Talltree would be entitled to one-fourth of the total proceeds, $W, because there are no other
preferred shares outstanding to be redeemed before the common stock. A redemption value
of $12M implies a conversion condition of
Series B conversion condition—Both A and C already converted:
1=4 Ã W .12-W
B
5$48M: ð15:17Þ
We are now ready to draw an exit diagram for the Series C. As holders of the Series C,
Owl would receive the ?rst $10M of proceeds, and then would not receive anything else until
they choose to convert at W5$42M. Upon conversion, Owl would own one-third of the
280 CHAPTER 15 LATER-ROUND INVESTMENTS
common. When Talltree converts the Series B at W5$48M, Owl would then own 10M/
40M51/4 of the common.
We can read Exhibit 15-5 as
Partial valuation of Series C ðStructure 2Þ 5V 2Cð10Þ 11=3 Ã Cð42Þ
21=12 Ã Cð48Þ:
ð15:18Þ
EXHIBIT 15-6
LP VALUATION OF SERIES C, STRUCTURES 1 AND 2
100 125 150 175
Total Valuation of Newco
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EXHIBIT 15-5
EXIT DIAGRAM FOR SERIES C, STRUCTURE 2
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15.3 SERIES C 281
Then, the LP valuation equation is
LP valuation of Series C ðStructure 2Þ 50:87 Ã ½V 2Cð10Þ 11=3 Ã Cð42Þ
21=12 Ã Cð48Þ?:
ð15:19Þ
Using the VCV model, we can compute the breakeven valuation as $47.37.
(c) Now, for each LP valuation Equation (15.14) and (15.19), we can use the VCV model and
base-case option-pricing assumptions to compute an LP valuation for any given level of total
valuation. Because this is a Series C investment, our base-case assumption is an expected
holding period of three years. Exhibit 15-6 plots LP valuation for each structure.
The crossing point occurs at a total valuation of $130.5M, where both structures yield
LP valuations of $29.28M. That is, for a total valuation below $130.5M, Owl should prefer
Structure 1; for a total valuation above $130.5M, Owl should prefer Structure 2. ’
15.4 DIVIDENDS IN LATER ROUNDS
Many VC investors receive dividends on their preferred shares. In Chapter 14 we
showed how to incorporate accrued cash dividends into the valuation of Series A
investments. For later-round investments, we must carefully analyze how dividends
can affect the conversion order and conversion conditions for each round. In
Section 15.4.1., we show how to do this for accrued cash dividends. In Section
15.4.2, we consider the case of stock dividends (5PIK dividends).
15.4.1 Accrued Cash Dividends
EXAMPLE 15.3
We begin with the same setup as in Example 15.2. We assume that Owl chose Structure 2: a
$10M investment for 10M shares of CP (APP 5$10M). The other investors are (1) the
employees, who have claims on 10M shares of common; (2) the Series A investors, EBV,
who have 10M shares of CP for $6M APP; and (3) the Series B investors, Talltree, who have
10M shares of CP for $12M APP. Series C has a liquidation preference to Series B, which in
turn has a liquidation preference to Series A. The new wrinkle we introduce here is that all
preferred investors—Series A, B, and C—have cumulative accrued cash dividends of 1.00%
per month, to be paid only on a deemed liquidation event.
Problem Find the conversion order and conversion conditions for all investors.
Solution We ?rst solve for the conversion order. First, let T be the time elapsed since the
latest round (Series C in this example). We differentiate this from T
X
, the time elapsed since
the time Series X took place. In this case, Series A was two years ago and Series B was one
year ago, so T
A
5T 12, T
B
5T 11, and T
C
5T.
To obtain the RVPS for each series, we can write the RV at time T as
RV
X
ðTÞ 5RV
X
ðat issue of Series XÞ Ã ð1 10:12T
X
Þ ð15:20Þ
282 CHAPTER 15 LATER-ROUND INVESTMENTS
where the subscript “X” represents Series A, B, or C. Then, the RVPS for each Series will
also be a function of T and can be written as
RVPS
A
ðTÞ 5ð1 10:12T
A
Þ Ã $6M=10M5
1 10:12 Ã ðT 12Þ
à $0:6
5 $0:74 10:072 T
ð15:21Þ
RVPS
B
ðTÞ 5ð1 10:12T
B
Þ Ã $12M=10M5
1 10:12 Ã ðT 11Þ
à $1:2
5 $1:34 10:144 T
ð15:22Þ
RVPS
C
ðTÞ 5ð1 10:12TÞ Ã $10M=10M5ð1 10:12TÞ Ã $1:0 5$1 10:12 T ð15:23Þ
The ?rst term (e.g., $0.74 for Series A) for each series represents the amount of
RVPS that it gets if they had a liquidation event today (the day of Series C investment). Note
that this is greater than RVPS at the time of original investments for Series A and B, because
they have accumulated dividends for two years and one year, respectively. The conversion
order when T 50 is therefore A-C-B. The second term represents how RVPS grows for
each series over time as a function of T. Note that A has the lowest slope and B has the
highest slope. Thus, the original conversion order will always be preserved.
The conversion conditions are
Series A conversion condition:
1=2 Ã ½W 2RV
B
ðTÞ 2RV
C
ðTÞ? . RV
A
ðTÞ-W
A
52 Ã RV
A
ðTÞ
1RV
B
ðTÞ 1RV
C
ðTÞ
ð15:24Þ
Series C conversion condition:
1=3 Ã ½W 2RV
B
ðTÞ? . RV
C
ðTÞ-W
C
53 Ã RV
C
ðTÞ 1RV
B
ðTÞ ð15:25Þ
Series B conversion condition:
1=4 Ã W . RV
B
ðTÞ-W
B
54 Ã RV
B
ðTÞ: ð15:26Þ
If we wanted to take next logical step in this solution, we could draw an exit diagram
for the Series C. This diagram would be identical to Exhibit 15-5, except that the relevant
conversion points would be a function of T and use Equations (15.25) and (15.26). These
conversion points would then serve as strike prices for the underlying random-expiration
options. As in the dividend examples of Chapter 14, the VCV model can handle these
changing strike prices without any dif?culty.
The valuation gets trickier if the dividends vary across the different series. For
example, consider the same setup as Example 15.3, except that Series A has cumulative
accrued cash dividends of 2 percent per month, to be paid only on a deemed liquidation
event, Series B has no dividends, and Series C has cumulative accrued cash dividends
of 1.00% per month. How could we ?nd the conversion order now? The RV would a function
of T for Series A and Series C, but not for Series B. Then, the RVPS for each Series would be
RVPS
A
ðTÞ 5ð1 10:24T
A
Þ Ã $0:6 5
1 10:12 Ã ðT 12Þ
à $0:6
5$0:888 10:144T
ð15:27Þ
RVPS
B
ðTÞ 5$1:2 ð15:28Þ
RVPS
C
ðTÞ 5ð1 10:12TÞ Ã $1:0 5$1 10:12T ð15:29Þ
’
15.4 DIVIDENDS IN LATER ROUNDS 283
Now, because these RVPS for each series change with time at differing rates,
the conversion order will not be constant over time. At T 50, RVPS for Series
AÀC are $0.888, $1.20, and $1.00, so we have the same conversion order as in the
Example 15.3: A, C, B. But note that Series A has the highest slope (0.144) and
Series B has the lowest (0). Thus, RVPS for A and C will eventually surpass that for
B as time passes, and moreover RVPS for A will eventually overtake that for C.
Speci?cally, when T.1.67, the Series C RVPS would be above $1.20, so B would
convert before C. When T .2.17, the Series A RVPS would be above $1.20, so B
would convert before A. Finally, when T.4.67, the Series A RVPS would be
above the Series C RVPS, so C would convert before A. From this point forward,
the conversion order would be B, C, A—a complete reversal of the order when
T50. With conversion order changing, we would need different exit diagrams and
exit equations for different ranges of T. At this point, it is no longer very helpful to
draw these diagrams, but the VCV model can still compute the valuations.
15.4.2 PIK Dividends
PIK (payment-in-kind) dividends are paid in stock. Each PIK dividend adds to
the number of shares held by the investor, which will increase both the RV of the
shares (using the same OPP as the investment) and the fraction of the company to
be owned on conversion. These two changes combine to make the conversion
conditions and exit diagrams a bit more complex than they are for accrued cash
dividends.
EXAMPLE 15.4
We begin with the same setup as in Example 15.3. Owl invests $10M in Series C for 10M
shares of CP (APP 5$10M). The other investors are (1) the employees, who have claims on
10M shares of common; (2) the Series A investors, EBV, who have 10M shares of CP for
$6M APP; and (3) the Series B investors, Talltree, who have 10M shares of CP for $12M
APP. The Series C has a liquidation preference to Series B, which in turn has a liquidation
preference to Series A. The difference between this case and Example 15.3 is in the divi-
dends: here, all preferred investors—Series A, B, and C—have cumulative PIK dividends of
1 percent per month.
Problem Find the conversion order and conversion conditions for all investors.
Solution We ?rst solve for the conversion order. As in Example 15.3, we can write the
RVPS for each Series “X” as
RV
X
ðTÞ 5RV
X
ðat issue of Series XÞ Ã ð1 10:12T
X
Þ: ð15:30Þ
Unlike Example 15.3, in this case we must also take account of a change in the number
of shares, which are also growing (through PIK dividends) at a rate of 0.12 per year. The
good news is that the increase in the number of shares will exactly cancel out the increase in
RV, so that the RVPS for each series will not be a function of T:
284 CHAPTER 15 LATER-ROUND INVESTMENTS
Series ARVPSðTÞ 5ð1 10:12T
A
Þ Ã $6M=½ð1 10:12T
A
Þ Ã 10M? 5$0:60 ð15:31Þ
Series B RVPSðTÞ 5ð1 10:12T
B
Þ Ã $12M=½ð1 10:12T
B
Þ Ã 10M? 5$1:20 ð15:32Þ
Series CRVPSðTÞ 5ð1 10:12TÞ Ã $10M=½ð1 10:12TÞ Ã 10M? 5$1:00: ð15:33Þ
Because these are the same RVPS found in Example 15.2, the conversion order will
not be affected and will always be A, C, B. The conversion conditions will change, however,
because ownership fractions (slopes) will change over time, as will the RVs. Denote the
fraction of the ?rm to be held on conversion by Series X as F
X
(T). Then, we can write the
conversion conditions as
Series A conversion condition:
F
A
ðTÞ Ã ½W 2RV
B
ðTÞ 2RV
C
ðTÞ? .RV
A
ðTÞ-
W
A
5RV
A
ðTÞ=F
A
ðTÞ 1RV
B
ðTÞ 1RV
C
ðTÞ;
ð15:34Þ
Series C conversion condition:
F
C
ðTÞ Ã ½W 2RV
B
ðTÞ? .RV
C
ðTÞ-W
C
5RV
C
ðTÞ=F
C
ðTÞ 1RV
B
ðTÞ; ð15:35Þ
Series B conversion condition:
F
B
ðTÞ Ã W .RV
B
ðTÞ-W
B
5RV
B
ðTÞ=F
B
ðTÞ: ð15:36Þ
’
If we were to take this solution to the next logical step, we could draw an exit
diagram for the Series C. This diagram would be identical to Exhibit 15-5, except
now the conversion points and the slopes would be a function of T and use
Equations (15.35), and (15.36). These conversion points then serve as strike prices
for the underlying random-expiration options, with the fractions of these options
determined by the time-varying slopes. Again, although this might look dif?cult to
solve, the VCV model does not mind. As in the earlier example, things get messier
if the investors have different PIK dividends, or if there is a mixture of PIK divi-
dends with accrued cash dividends. Although these complex structures do not yield
helpful exit diagrams, we can still use the VCV model to value them.
15.5 BEYOND SERIES C
From a theoretical perspective, there is nothing new in later round transactions. We
can follow the same steps as used to compute LP valuation in Series A, B, and C. In
this section, we review these steps in the context of a Series F round.
EXAMPLE 15.5
Begin with the same setup as in Example 15.2. Assume that Owl chose Structure 2 and
invested $10M in a Series C round for CP. Following Series C, there were three more rounds
of investment, each for CP, and each made by a separate VC. The details of all rounds are
given below. Liquidation preferences are in reverse order of investment, with F before E
before D, and so on. Assume that Series D, E, and F investors all have committed capital of
$100M investment capital of $80M and carried interest of 20 percent. None of the investors
have any dividends.
15.5 BEYOND SERIES C 285
Series A: $6M for 10M shares (EBV)
Series B: $12M for 10M shares (Talltree)
Series C: $10M for 10M shares (Owl)
Series D: $10M for 10M shares (2X liquidation preference) (Series D investors)
Series E: $10M for 10M shares (3X liquidation preference) (Series E investors)
Series F: $25M for 10M shares (Series F investors)
Problems
(a) What is the conversion order for these investors?
(b) What is formula for the partial valuation of the Series A?
(c) Suppose that the total valuation is $100M. Use the VCV model to compute the LP
valuation for each series.
Solution
(a) For a company with six rounds of investment, we are very happy to have the conversion-
order shortcut. To compute the RVPS for Series D and E, we must not forget the excess
liquidation preferences, which imply redemption values of $20M for Series D and $30M for
Series E. Otherwise, the calculations are similar to those in earlier examples. The RVPS for
each Series is
Series A : $6M=10M5$0:60 ð15:37Þ
Series B : $12M=10M5$1:20 ð15:38Þ
Series C : $10M=10M5$1:00 ð15:39Þ
Series D : $20M=10M5$2:00 ð15:40Þ
Series E : $30M=10M5$3:00 ð15:41Þ
Series F : $25M=10M5$2:50 ð15:42Þ
This implies an order of conversion of A, C, B, D, F, E.
(b) Series A converts ?rst, so as each series converts after it, EBV’s share of the common
stock changes. Because the founders own 10M shares and all series also convert to 10M
shares, EBV’s share will be one-half upon conversion and then will fall to one-third, one-
fourth, one-?fth, one-sixth, and one-seventh with each successive conversion. This will lead
to an exit diagram with many slope changes. To determine the points of these slope changes,
we must compute the conversion conditions for each series. For each series Z, the conversion
condition is computed as
ðFraction of firm owned by Series Z on conversionÞ
à ð$W2total redemption value for all series that convert after Series ZÞ
.total redemption value for Series Z:
ð15:43Þ
These conversion conditions are given following for each series, in the conversion
order as determined by the RVPS:
Series A conversion condition : 1=2 Ã ðW 297Þ .6-W
A
5$109 M ð15:44Þ
286 CHAPTER 15 LATER-ROUND INVESTMENTS
Series C conversion condition : 1=3 Ã ðW 287Þ .10-W
C
5$117 M ð15:45Þ
Series B conversion condition : 1=4 Ã ðW 275Þ .12-W
B
5$123 M ð15:46Þ
Series D conversion condition : 1=5 Ã ðW 255Þ .20-W
D
5$155 M ð15:47Þ
Series F conversion condition : 1=6 Ã ðW 230Þ .25-W
F
5$180 M ð15:48Þ
Series E conversion condition : 1=7 Ã W .30-W
E
5$210M ð15:49Þ
Under these conditions, the exit diagram for Series A is as shown in Exhibit 15-7.
EXHIBIT 15-7
EXIT DIAGRAM FOR SERIES A, AFTER SERIES F
S
l
o
p
e
?
1
/
2
S
l
o
p
e
?
1
/
3
S
lo
p
e
?
1
/4
S
lo
p
e
?
1
/5
Slope ? 1/6
Slope ? 1/7
97 103 109 117 123
$W
155 180 210
S
e
r
i
e
s
A
EXHIBIT 15-8
LP VALUATIONS FROM AUTO CALCULATOR
A B C D E F Founders
Security Type CP CP CP CP CP CP C
Investment ($M) $6.00 $12.00 $10.00 $10.00 $10.00 $25.00
Shares (M) 10 10 10 10 10 10 10
Liquidation Pref (X) 1 1 1 2 3 1
APP ($M) $6.00 $12.00 $10.00 $10.00 $10.00 $25.00
LP Cost ($M) $7.50 $15.00 $12.01 $12.50 $12.50 $31.25
Partial Valuation ($M) $10.07 $10.79 $11.04 $14.07 $20.77 $23.33
GP Valuation ($M) $1.01 $1.08 $1.43 $1.41 $2.08 $2.33
LP Valuation ($M) $9.06 $9.71 $9.60 $12.66 $18.69 $21.00
15.5 BEYOND SERIES C 287
We can read Exhibit 15-7 to obtain the partial valuation of the Series A as follows.
Partial valuation of the Series A
5Cð97Þ 2Cð103Þ 11=2 Ã Cð109Þ 21=6 Ã Cð117Þ 21=12 Ã Cð123Þ
21=20 Ã Cð155Þ 21=30 Ã Cð180Þ 21=42 Ã Cð210Þ:
ð15:50Þ
(c) The LP valuations for all series are given in the (partial) output from the VCV model in
Exhibit 15-8. ’
SUMMARY
Later-round investments provide the most important and interesting environment for our
valuation techniques. To extend our analysis to these later rounds, it is necessary to ?rst
determine the conversion order for the various classes of preferred stock. In this chapter, we
learned how to do this by using the redemption value per share (RVPS) for each class. Once
the conversion order is established, we can compute the conversion conditions for each class
and then use these conditions to draw and read exit diagrams. Dividends can introduce
complications for the drawing of exit diagrams, but these complications are easily handled by
the VCV model.
KEY TERMS
Redemption Value per Share
(RVPS)
Conversion-order
shortcut
EXERCISES
15.1 Consider the following four CP investors:
(1) Series A: $5M APP (and 2X liquidation preference) or converts to 5M shares;
(2) Series B: $10M APP or converts to 8M shares;
(3) Series C: $10M APP or converts to 5M shares;
(4) Series D: $5M APP or converts to 10M shares.
In addition to these investors, the founders hold 10M shares of common.
(a) Find the conversion order for these investors.
(b) Find the conversion conditions for these investors.
(c) Draw and read the exit diagrams following the Series D investment.
(d) Assume that total valuation is $50M. Compute the LP valuation for each series.
15.2 Using the same setup as Example 15.1, compute the LP valuation equation for the
Series A investors (EBV) under Structures 1 and 2 for Series B. For the same range of total
288 CHAPTER 15 LATER-ROUND INVESTMENTS
valuations considered in Exhibit 15-3, which structure would EBV prefer that Talltree
choose?
15.3 Using the same setup as Example 15.2,
(a) Compute the LP valuation for the Series B investors (Talltree) under Structures 1 and 2
for Series C. For the same range of total valuations considered in Exhibit 15-6, which
structure would Talltree prefer that Owl choose?
(b) Compute the LP valuation for the Series A investors (EBV) under Structures 1 and 2 for
Series C. For the same range of total valuations considered in Exhibit 15-6, which
structure would EBV prefer that Owl choose?
15.4 Draw the exit diagrams for Series B-F for Example 15.5.
EXERCISES 289
CHAPTER 16
PARTICIPATING CONVERTIBLE
PREFERRED STOCK
AS FIRST SEEN in Chapter 9, participating convertible preferred stock
(PCP) is a hybrid between an RP plus common structure and a plain common-stock
structure. In a PCP transaction, the investor is allowed to redeem his stock and also
to “participate” in the proceeds paid to the common stock as though he had con-
verted. If the proceeds of any exit reach some preset threshold, then the redemption
component of the PCP goes away, and the investor is forced to convert all the
shares to common. Thus, above this threshold, PCP is just like common stock.
Typically, such thresholds will be stated as a “quali?ed IPO” or as a “quali?ed IPO
or sale”, with a speci?c numerical share price. Sometimes, the threshold may be set
explicitly as a 5X or 10X return, or as a compounded annualized return so that the
threshold changes with the length of the holding period. Furthermore, there may
be an upper limit on the liquidation return, giving rise to the participating con-
vertible preferred with cap (PCPC) structure.
Although simpler CP structures are the norm in rising markets, PCP struc-
tures become more popular in falling markets. For example, during the VC
downturn in the postboom period, PCP structures became very popular, as did
many other investor-favorable terms such as liquidation preferences and antidilu-
tion rights.
1
In general, in falling markets entrepreneurs are often slow to accept the
lower value in their companies, and VCs employ a variety of structures—including
PCP—to maximize as-converted per-share prices while still receiving enough value
to justify the investment.
The de?nition of PCP used here is historically accurate, but some VCs use
“PCP” to mean the same thing as “RP 1 common”. For this usage, we can just
think of the PCP threshold as being set to in?nity, thus making it equivalent to RP
1 common. In this chapter, we use the more ?exible de?nition of PCP that allows
1
See Kaplan and Stromberg (2003) and Asset Alternatives (2005).
290
for a ?nite threshold. To solve for the partial valuation of PCP structures, we
include binary options in the valuation equations. These binary options are intro-
duced in Section 16.1. Section 16.2 demonstrates an investment recommendation
for a Series A PCP investment, Section 16.3 does the same for a PCPC structure,
and Section 16.4 shows how to extend the analysis to later rounds.
16.1 BINARY OPTIONS
To value PCP, we ?rst need to discuss the valuation of binary options. Binary
options pay some ?xed amount (K) if the stock price (S) is above the exercise
price (X) on the expiration date (T). Thus, an exit diagram for a binary option looks
like Exhibit 16-1.
The formula for the pricing of binary options looks similar to the second part
of the Black-Scholes formula 5 KÃ e
2rT
à N(d2), where N(d2) is de?ned the same
way as in Equation (13.13).
In our applications, we will use random-expiration binary calls. Like the
random expiration calls introduced in Chapter 13, we can price an RE binary call by
integrating a regular binary call over time. The formula for an RE binary call,
which we write as K Ã BC(X), is
K Ã BC ðXÞ 5
Z
N
0
Ke
2rT
Nðd
2
Þ Ã qe
2qT
dT ð16:1Þ
where q 5 1/H is the continuous-time probability of expiration, and H is the
expected holding period.
EXHIBIT 16-1
EXIT DIAGRAM FOR A BINARY OPTION
X
K
$W
B
i
n
a
r
y
C
a
l
l
a
t
E
x
p
i
r
a
t
i
o
n
16.1 BINARY OPTIONS 291
EXAMPLE 16.1
Suppose EBV makes a Series A investment in Newco and simultaneously offers the
employees a bonus pool of $5M on any exit where ?rm value exceeds $200M. Currently, the
?rm value of Newco is $40M, and base-case option-pricing assumptions apply.
Problem What is the current value of this bonus incentive?
Solution Under the assumption that the exit date remains independent of the ?rm value,
then we can value this incentive as an RE binary call, with K set to $5M. The FLEX Cal-
culator can be used for this computation. We ?nd a value of $0.12M. ’
16.2 THE VALUATION OF PCP
EXAMPLE 16.2
Suppose that EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCP, with a threshold ?ve times APP (5 $6 per
common share upon conversion). The employees of Newco hold 10M shares of common
stock. Thus, following the Series A investment, Newco will have 10M common shares
outstanding and would have 15M shares outstanding on conversion of the PCP.
Problems
(a) Solve for the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) As we have now seen many times in previous chapters, the LP cost for EBV on a $6M
investment is (100/80) Ã $6M 5 $7.5M.
(b) The threshold requires a price of $6 per share (as converted). This implies value of 15M
à $6 5$90M for the whole ?rm. Below the threshold, PCP looks like RP plus common. EBV
receives the ?rst $6M in proceeds for the RP. Following this redemption, EBV owns one-
third of the common stock (5M out of 15M shares).
The only difference between PCP and RP 1 common is that there is a drop in value at
the threshold. Below the threshold, the Series A would receive $6M for redemption plus one-
third of the remaining proceeds: 1/3 Ã (W 2 6). At W 5 90, this total value is
Value of PCP at W 590ðbefore dropÞ 56 11=3 Ã ð90 26Þ 5$34M: ð16:2Þ
Immediately above the threshold, the Series A would no longer receive any redemp-
tion value and would instead be forced to convert and to receive exactly one-third of the
292 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
proceeds. At W 5 90, this share would be worth 1/3 Ã 90 5 $30M. Thus, there is a 34M 2
30M 5 $4M drop at the threshold.
We are now prepared to draw the exit diagram for the Series A, as in Exhibit 16-2.
We can read this diagram as
Partial valuation of Series A5V 22=3 Ã Cð6Þ 24 Ã BCð90Þ: ð16:3Þ
With our now-standard estimate of GP% 5 0.10 for EBV, we have
LP valuation of Series A50:9 Ã ðV 22=3 Ã Cð6Þ 24 Ã BCð90ÞÞ: ð16:4Þ
(c) We can use the VCV model to compute the breakeven valuation as $18.60M.
(d) Exhibit 16-3 shows the sensitivity of the breakeven valuation to various assumptions for
volatility and the expected holding period.
EXHIBIT 16-2
EXIT DIAGRAM FOR THE SERIES A PCP
6 90
30
34
$W
S
e
r
i
e
s
A
P
C
P
S
lo
p
e
=
1
/3
S
lo
p
e
=
1
/3
4
EXHIBIT 16-3
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60% 90% 120%
Expected 3 15.73 17.14 18.49
Holding 5 16.96 18.60 19.98
Period (years) 7 17.90 19.57 20.89
16.2 THE VALUATION OF PCP 293
These sensitivities are similar to those in the RP 1 common structure analyzed in
Example 14.1. The only thing that keeps PCP from being identical to an RP 1 common
structure is the inclusion of the threshold, priced as a binary option in Equation (16.3).
For a total valuation of $20M and base-case option-pricing assumptions, the value of
this binary option, 4 Ã BC(90), is about $0.11M. Whereas standard options increase in value
when volatility increases, binary options do the reverse. For higher levels of volatility, the
value of the binary option decreases, and the PCP structure converges to an RP 1 common
structure. Indeed, as volatility goes to in?nity, all structures will look the same as plain
common stock. Readers are encouraged to experiment with the FLEX Calculator to con?rm
these relationships.
’
16.3 THE VALUATION OF PCPC
PCPC structures include a cap for the liquidation return. In most cases, this cap is
low enough so that conversion occurs by choice at or below the QPO. When
conversion is by choice and occurs at levels below the QPO, the exit diagram will
be smooth, and no binary options need be included in the exit equation. The fol-
lowing example illustrates this case.
EXAMPLE 16.3
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCPC, with a threshold at ?ve times APP (5 $6 per
common share on conversion). Furthermore, the liquidation value of the PCPC is capped at
four times the APP (5 $24M). The employees of Newco hold 10M shares of common stock.
Thus, following the Series A investment, Newco will have 10M common shares outstanding
and would have 15M shares outstanding on conversion of the PCP. (Note that this is the same
setup as Example 16.2, with the additional cap at four times APP.)
Problems
(a) Solve for the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
Solutions
(a) As in Example 16.2, the LP cost is $7.5M.
(b) With PCPC, EBV faces a similar decision—redeem or convert—as it would with plain
CP. When we ?rst analyzed PCPCstructures in Chapter 9, we demonstrated that the ?rst step is
to check whether conversion will be mandatory (at the QPO) or voluntary (using a conversion
condition). In this case, mandatory conversion would occur at $6 per share. With 15M shares
outstanding, this QPO would occur when W 5 15M Ã $6 5 $90M.
294 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
The (voluntary) conversion condition for the PCPC is
1=3 Ã W .24-W
A
572: ð16:5Þ
Because Equation (16.5) yields a conversion point ($72M) lower than the mandatory
QPO conversion ($90M), the latter is a redundant and nonbinding constraint: only the
voluntary conversion will matter.
Our next step is to determine the cap point. Because EBV receives the ?rst $6M plus
one-third of the remaining proceeds, the 4X (5 $24M) cap point is
6 11=3ðW 26Þ 524-W
A
ðcapÞ 560M: ð16:6Þ
Using this conversion condition and cap, we can drawthe exit diagramas in Exhibit 16-4.
We can read Exhibit 16-4 as
Partial valuation of Series A5V 22=3 Ã Cð6Þ 21=3 Ã Cð60Þ 11=3 Ã Cð72Þ: ð16:7Þ
Thus, the LP valuation equation for EBV is
LP valuation of Series A50:9 Ã ½V 22=3 Ã Cð6Þ 21=3 Ã Cð60Þ 11=3 Ã Cð72Þ?: ð16:8Þ
(c) We can use the VCV model to compute the breakeven valuation as $18.75M. This is only
$0.15M more than the cutoff without the cap found in Example 16.2.
’
For some applications, it is helpful to express the conversion condition in per-
share terms. Once we do this, we can insert the PCPC into a conversion order.
Although that is not necessary for a Series A investment, it can be useful in later
rounds. In Example 16.3, we could do this by computing
RVPS of Series A PCPC ðat capÞ 5$24M=5M5$4:80 per share: ð16:9Þ
EXHIBIT 16-4
EXIT DIAGRAM FOR SERIES A PCPC
6 60 72
$W
S
e
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i
e
s
A
P
C
P
C
S
lo
p
e
=
1
/3
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lo
p
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=
1
/3
16.3 THE VALUATION OF PCPC 295
Similarly, we could express the per-share value of the common stock at the cap
by subtracting the APP from the cap and dividing by the number of common shares:
Per-share cap5ð$24M2$6MÞ=5M5$3:60 per share: ð16:10Þ
In words, Equation (16.10) means “the Series A PCPC hits its liquidation cap
when the value of common stock is $3.60 per share”.
Notice that we were able to solve Example 16.3 without using binary options
because voluntary conversion at (W 5 72M) occurred before the QPO (at $90M, as
computed in Example 16.2). If, instead, mandatory conversion at the QPO occurred
at a lower point than voluntary conversion, then binary options will be included. In
those cases, we still must ?nd the cap point because it is possible (but unusual)
for the cap to occur at a point below the QPO. In Example 16.3, this could only
occur if the cap was between 5 and 5.67 times APP. For example, with a cap of 5.5
times APP, the liquidation return would be capped at 5.5 Ã 6M5$33M. The RVPS
for voluntary conversion would be at $33M/5M 5 $6.60 per share, which is higher
than the QPO threshold. Then, the QPO threshold would be the binding constraint.
Nevertheless, we would also have a cap point at
33 56 11=3 Ã ðW 26Þ-W
A
ðcapÞ 587: ð16:11Þ
Thus, at W 5 87, the exit line would go ?at until the QPO at W 5 90, when it
would drop in value from $33M (the cap) to $30M (after conversion).
16.4 SERIES B AND BEYOND
To value PCP in later rounds, we follow the same steps as shown in Chapter 15. If
there are multiple rounds of PCP, then one must be careful to consider the impli-
cations of different QPO thresholds.
EXAMPLE 16.4
Suppose EBV made the transaction as described in Example 16.2. It is now one year later, and
Talltree is considering a $12M Series B investment in Newco. Talltree is considering two
possible structures for the Series B. In Structure 1, Talltree would receive RP ($10M APP) plus
5M shares of common stock. In Structure 2, Talltree would receive 5M shares of PCP with a
threshold of $12 per share. The founders of Newco, who will continue with the ?rm, currently
hold 10Mshares of common stock, and EBVholds 5Mshares of PCP (as-if converted). Talltree
has carried interest of 20 percent, committed capital of $250M, and lifetime fees of $50M.
Problems
(a) Compute the LP cost for the Series B.
(b) What is the LP valuation equation and breakeven valuation for Structure 1?
(c) What is the LP valuation equation and breakeven valuation for Structure 2?
296 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
(d) Plot the LP valuation for both structures for a range of total valuations. For what total
valuation should Talltree be indifferent between the two structures?
Solutions
(a) Because Talltree has committed capital of $250M and lifetime fees of $50M, its
investment capital is $200M and we can compute LP cost as
LP cost 5ð250=200Þ Ã $12M5$15M: ð16:12Þ
(b) To compute LP valuation, we ?rst draw an exit diagram for the Series B. With the RP 1
common structure, Talltree would receive the ?rst $10M of proceeds to redeem the RP, and
EBV (Series A) would receive the next $6M to redeem the PCP. Following these redemp-
tions, there would be 20M shares of common stock, with 5M held by Talltree. Thus, Talltree
would receive one-fourth of the proceeds beyond $16M. The only complication occurs on a
QPO, when EBV must return $6M to the ?rm. This Series A threshold is set at $6 per
common share. With 20M common shares and a $10M redemption for the Series B, total
proceeds at this QPO must be at least 20M Ã $6 1 $10M 5 $130M. Because the $6M
windfall will be shared by all common holders, it provides a jump of $6M Ã 1/4 5 $1.5M for
the Series B.
We can draw the exit diagram for the Series B, Structure 1 as in Exhibit 16-5.
We can read Exhibit 16-5 as
Partial valuation of Series B ðStructure 1Þ
5V 2Cð10Þ 11=4 Ã Cð16Þ 13=2 Ã BCð130Þ:
ð16:13Þ
The LP valuation equation is
LP valuation of Series B ðStructure 1Þ 50:9 Ã ½V 2Cð10Þ 11=4 Ã Cð16Þ
13=2 Ã BCð130Þ?:
ð16:14Þ
We can use the VCV model to compute the breakeven valuation as $49.63M.
EXHIBIT 16-5
EXIT DIAGRAM FOR SERIES B, STRUCTURE 1
10 16 130
$W
S
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s
B
,
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u
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1
3/2
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?
1
/4
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lo
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?
1
/4
16.4 SERIES B AND BEYOND 297
(c) To compute LP valuation, we ?rst draw an exit diagram for the PCP. For the Series B, a
quali?ed IPO or sale requires a price of $12 per share (as-if converted). This implies a value
of 20M Ã $12 5 $240M for the whole ?rm. We refer to $240M as the “Series B threshold”.
Below the Series B threshold, Structure 2 looks similar to Structure 1, except that that RV of
the Series B is $12M here, as compared to $10M in Structure 1. This yields a $2M difference
in the strike price of all the options (as compared to Structure 1), including a change in the
Series A threshold from $130M in Structure 1 to $132M in Structure 2. The other difference
between Structures 1 and 2 is that there is a drop in value above the Series B threshold.
Below the Series B threshold, the Series B PCP would receive $12M for redemption plus
one-fourth of the remaining proceeds: 1/4 Ã (W 2 12). At W 5 240, this total value is
Value of Structure 2 at W 5240 ðbefore dropÞ 512 11=4 Ã ð240 212Þ
569M:
ð16:15Þ
Immediately above the Series B threshold, the PCP would no longer receive any
redemption value and would instead be forced to convert and to receive exactly one-fourth of
the proceeds.
At W 5 240, this share would be worth 1/4 Ã 240 5 $60M. Thus, there is a 69M 2
60M 5 $9M drop at the threshold.
We are nowprepared to drawthe exit diagramfor the Series B, Structure 2 (Exhibit 16-6).
We can read Exhibit 16-6 as
Partial Valuation of Series B ðStructure 2Þ
5V 2Cð12Þ 11=4 Ã Cð18Þ 13=2 Ã BCð132Þ 29 Ã BCð240Þ:
ð16:16Þ
This implies an LP valuation equation of
LP valuation of Series B ðStructure 2Þ
50:9 Ã ½V 2Cð12Þ 11=4 Ã Cð18Þ 13=2 Ã BCð132Þ 29 Ã BCð240Þ?:
ð16:17Þ
EXHIBIT 16-6
EXIT DIAGRAM FOR SERIES B, STRUCTURE 2
12 18 132 240
9
3/2
$W
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B
,
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2
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1
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298 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
We can use the VCV model to compute the breakeven valuation as $47.11M.
(d) Exhibit 16-7 shows the sensitivity of LP valuation to different total valuations. Notice
that the values of the two structures are very similar.
We begin the sensitivity diagram for a total valuation close to the cutoff level for both
structures. Above this level, although it is dif?cult to tell the two lines apart, the numbers
indicate the Structure 2 has a slightly higher LP valuation than Structure 1 for virtually all the
range. It is not until the very end—for total valuations close to $148M, that Structure 1 has a
slight advantage. This situation is ideal for the VC because he can con?dently accept
whichever of these structures is more preferred by the entrepreneur.
’
This example illustrates a general rule that can be used in analyzing all PCP
structures. Any Series X PCP that hits its threshold will return the RV of that Series
X (5 RV
X
) to be split among all the common stock holders. If the holder of a
Series Y holds some fraction y of the common stock, then the Series Y will receive
a one-time jump of y à RV
X
at the Series X threshold. For Series X itself, there will
be a drop of RV
X
, but this drop will be reduced by the increase of x à RV
X
, where x
is the fraction of the common stock held by Series X. Thus, the total drop for Series
X at the Series X threshold will be equal to (1 2x) Ã RV
X
.
We next consider a multiround example with both PCP and PCPC along with
several rounds of CP. To solve this example, we must merge the conversion order
EXHIBIT 16-7
LP VALUATION AND COST OF SERIES B, STRUCTURES 1 & 2
Structure 1
Structure 2
LP cost
45
35
25
15
40
30
20
10
5
0
L
P
v
a
l
u
a
t
i
o
n
a
n
d
c
o
s
t
o
f
S
e
r
i
e
s
B
50 75 100
Total valuation of Newco
125 150
16.4 SERIES B AND BEYOND 299
shortcut of Chapter 15 (using RVPS) with the complexities of participation
thresholds and caps.
EXAMPLE 16.5
Talltree is considering a $20M Series F investment in Newco for 10M shares of PCP with a
QPO threshold of $6 per share. The details of the prior rounds are
Series A: 10M shares of CP ($6M APP)
Series B: 10M shares of CP ($10M APP)
Series C: 10M shares of CP ($4M APP and a 3X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 3X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($10M APP).
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. None of these investors are covered by any antidilution
protections. In the event of a liquidation, the preferred stock is redeemed in reverse order of
investment (i.e., the Series F has a preference to the Series E, which has a preference to the
Series D, and so on). In addition to these investors, the employees have claims on 20M shares
of common stock.
Problems
(a) Draw and read the exit diagram for the Series D PCPC.
(b) Compute the breakeven valuation for the Series F under base-case assumptions.
Solutions
(a) First, we ?nd the conversion order for the CP. In order of the RVPS of the CP, we have
Series A: $6M/10M 5 $0.60
Series B: $10M/10M 5 $1.00
Series C: $12M/10M 5 $1.20
Series E: $10M/10M 5 $1.00.
We next add the PCP and PCPC to the ordering. For the Series F PCP, automatic
conversion occurs at a QPO of $6 per share. Because the highest RVPS is $1.20 per share, this
threshold is higher than all conversion points for the CP.
For the Series D PCPC, we ?rst determine if conversion is voluntary or automatic.
Voluntary conversion occurs at the RVPS, with the cap used as the redemption value. Auto-
matic conversion occurs at the QPOof $5. This yields a Series Dconversion at the lesser of the
voluntary conversion at $30M/10M5$3.00 or the automatic conversion at the QPO 5$5.00.
Thus, the QPO threshold is redundant, and conversion will occur voluntarily at $3 per
share, after all the CP has converted (the highest RVPS is $1.20 per share), but before the
Series F PCP at $6 per share.
Finally, we compute the cap point. To make comparisons with the conversion order, it
is helpful to compute this point on a per-share basis. When the PCPC is liquidated, the
holders receive $10M for the liquidation, plus value from the common stock of 10M Ã per-
share value. The cap is reached when
300 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
Series D cap point 5W
D
ðcapÞ 5$10M110M Ã per-share cap 5$30M: ð16:18Þ
Solving for the per-share cap yields
ð$30M2$10MÞ=10M5per-share cap 5$2:00: ð16:19Þ
Thus, the cap will be reached after all the CP has converted, because $2.00 is higher
than the RVPS for each CP series. Taken together, these calculations imply a conversion and
cap order of A ($0.60), B and E together ($1.00), C ($1.20), D (cap) ($2.00), D (conversion)
($3.00), and F ($6.00).
When Series A converts, there will be 50M shares outstanding: 20M from the
employees, 10M each from Series D and Series F (as-if conversion), and the 10M for Series A.
Thus, we can compute the Series A conversion conditions as
Series A conversion condition :1=5 Ã ðW 262Þ .6 -W
A
5$92M: ð16:20Þ
Series B and E convert at the same time, followed by Series C:
Series B conversion condition : 1=7 Ã ðW 242Þ .10-W
B
5$112M; ð16:21Þ
Series E conversion condition : 1=7 Ã ðW 242Þ .10-W
E
5$112M; ð16:22Þ
Series C conversion condition : 1=8 Ã ðW 230Þ .12-W
C
5$126M: ð16:23Þ
Next in order is the Series D cap, followed by the Series D voluntary conversion.
Series D cap : 10 11=8 Ã ðW 230Þ 530 -W
D
ðcapÞ 5$190M; ð16:24Þ
Series D conversion condition : 1=8 Ã ðW 220Þ .30-W
D
5$260M: ð16:25Þ
EXHIBIT 16-8
EXIT DIAGRAM FOR THE SERIES D
30 40 68 92 112 126 190 260 480
$W
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s
D
S
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1
/
4
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/
5
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1
/7
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2.5
16.4 SERIES B AND BEYOND 301
For the PCP, the QPO of $6 per share occurs at
Series F conversion condition ðQPOÞ: 80M Ã $6 5W
F
5$480M: ð16:26Þ
At this QPO, Series F will return $20M to the other shareholders and recapture 1/8 Ã
$20M 5 $2.5M for themselves, for a net drop of $20M 2 $2.5M 5 $17.5M. With these
calculations in hand, we are almost ready to draw the exit diagram for the Series D. Because
Series D is paid after Series E and F, they receive no proceeds until W 5 $30M, then they
receive the next $10M, and then nothing until the common stock begins to pay off after all
liquidations are complete at W 5 $68M. From that point, Series D has as-if claims on 10M
shares for one-fourth of the proceeds (employees have 20M shares and Series F has 10M as-if
shares). This fraction then falls off as other series convert. At W 5 $190M, the Series D line
goes ?at, only increase again after voluntary conversion at W 5 $260. Finally, at W 5
$480M, the Series D investors receive $2.5M from the returned redemption value of the
Series F. We can read this diagram as
Partial valuation of the Series D
5Cð30Þ 2Cð40Þ 11=4 Ã Cð68Þ 21=20 Ã Cð92Þ 22=35 Ã Cð112Þ
21=56 Ã Cð126Þ 21=8 Ã Cð190Þ 11=8 Ã Cð260Þ 12:5 Ã BCð480Þ:
ð16:27Þ
(b) Note that over the range of 190 , W , 260, the PCPC is capped so the exit line is ?at.
Over this ?at range for the Series D, all the other common stock holders will receive pro-
ceeds as if the Series D shares did not exist, so their slopes will increase. This can be seen in
the exit diagram for the Series F in Exhibit 16-9.
EXHIBIT 16-9
EXIT DIAGRAM FOR THE SERIES F
20 68 92 112 126 190 260 480
$W
S
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s
F
S
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/
4
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1
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17.5
302 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
We can read this diagram as
Partial valuation of the Series F
5V 2Cð20Þ 11=4 Ã Cð68Þ 21=20 Ã Cð92Þ 22=35 Ã Cð112Þ 21=56 Ã Cð126Þ
11=56 Ã Cð190Þ 21=56 Ã Cð260Þ 217:5 Ã BCð480Þ:
ð16:28Þ
The LP valuation of the Series F is 90 percent of Equation (16.28). The LP cost is (250/
200) Ã $20M 5 $25M. Finally, we can use the VCV model to compute the breakeven
valuation under base-case assumptions as $132.81M.
’
SUMMARY
Participating convertible preferred stock (PCP) is frequently used in VC transactions. PCP is
similar to structures that combine RP and common stock, with the main difference that the
RP component disappears for exits above some preset threshold. PCPC is a further re?ne-
ment of PCP, where there is a cap on the liquidation return. PCP can be valued by including
binary call options at the threshold points. For transactions where the threshold is far away
from the current valuation, there is little difference between PCP structures and RP plus
common structures. For transactions where the cap is close to the threshold, there is little
difference between PCPC and PCP.
KEY TERMS
Binary call option Random-Expiration
binary call option (BC(X))
REFERENCES
Asset Alternatives, 2005, Deal Terms Report, 2nd Edition, Dow Jones, Jersey City, NJ.
Kaplan, Steven N., and Per Stromberg, 2003, “Financial Contracting Theory Meets the Real World:
Evidence from Venture Capital Contracts”, Review of Economic Studies, April, 281À316.
EXERCISES
16.1 True, False, or Uncertain: Other things equal, the value of a binary call option
decreases as volatility increases.
16.2 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCP with a threshold at $3 per share. The employees
of Newco have claims on 15M shares of common stock. Thus, following the Series A
EXERCISES 303
investment, Newco will have 15M common shares outstanding, with another 5M shares on
conversion of the Series A.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
16.3 Consider the same setup as in Example 16.4, except that now there is an additional
possibility, Structure 3, where Talltree would receive 6M shares of CP with $12M APP.
(a) Perform a sensitivity analysis for the LP valuation of Structure 3 versus Structure 2 as a
function of total valuation.
(b) Suppose that total valuation is $100M. For what number of shares, Z, in Structure 3,
should Talltree be indifferent between Structures 2 and 3?
16.4 Consider the following four investors in Newco:
Series A: CP: $5M APP (and 2X liquidation preference) or converts to 5M shares
Series B: RP: $10M APP plus 5M shares of common
Series C: PCP: $10M APP and as-if conversion to 5M shares, with a threshold at
$10 per share
Series D: PCP: $20M APP and converts to 5M shares, with a threshold at $15 per share
In addition to these investors, the employees have claims on 10M shares of common.
All four VC investors have 20 percent carry, committed capital of $250M, and lifetime fees
of $50M. Following the Series D investment, all investors agree that the total valuation of the
?rm is $100M. Base-case option-pricing assumptions apply.
(a) Find the LP valuation equation for each Series.
(b) Compute the LP valuation for each Series.
304 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
CHAPTER 17
IMPLIED VALUATION
IN CHAPTER 8, we showed how to calculate post-money valuation, which is
typically interpreted as “the market value of the company implied by the purchase
price in the current round”. For example, if a VC pays $5M to purchase CP
that would convert to one-third of the common stock, then the post-money
valuation would be $15M. From the post-money valuation, we can then compute
the pre-money valuation as the difference between the post-money valuation
and the new investment, which in this case would be $10M.
These simple calculations, although useful for the quick communication of some
critical terms, do not in fact provide an accurate market valuation for the com-
pany. The problem is that these calculations do not account for the special features
of preferred stock, and instead treat all investments as though they were common
stock. Furthermore, standard post-money valuation calculations ignore the extra
costs of management fees and carried interest. In Chapters 13 through 16 we
developed a framework for the valuation of preferred stock. As part of this frame-
work, we computed the breakeven valuation necessary to equate LP valuation and
LP cost. In this chapter, we reinterpret the breakeven valuation as the implied post-
valuation (IV
post
) of the company based on the actual transaction structure. This
implied post-valuation can then be used to estimate the market valuation—which we
call the implied valuation—for any investor’s stake.
Section 17.1 discusses the relationship between IV
post
and post-money
valuation and argues that the former is a more accurate measurement of market
value. This additional accuracy is useful for three reasons. First, strong voices in
the LP community are demanding more accurate interim valuation of companies
from their GPs. Because many of these valuations are inferred from recent
transactions, it is better to use implied post-valuation than post-money valuation.
An application to interim valuation is given in Section 17.2. Second, implied
valuations may also be necessary in contractual disputes, particularly those
focused on the de?nition of a down round. Section 17.3 shows how the concept of
implied valuation can be used to adjudicate such disputes. Third, recent changes in
tax and accounting standards have forced companies to set values for their com-
mon shares for the reporting of executive compensation. The methods introduced in
305
this chapter can be used to provide a rigorous method for estimating the “implied”
market value of this common stock, and can provide an input into the valuation of
executive stock options.
At this point in the book, we have introduced many different terms with
“valuation” as part of their name. In Section 17.4 we review these different terms
and provide some tips on their correct usage.
17.1 POST-MONEY VALUATION REVISITED
The post-money valuation of private companies is often interpreted analogously
to the enterprise value of public companies. For public companies, enterprise value
is computed by adding the market values of all outstanding securities of the com-
pany: common stock, preferred stock, and long-term debt. For many public
companies, it is possible to observe market values for all these securities, so
the computation is easy. For other companies, analysts must use nonmarket infor-
mation to estimate market values for nontraded components of the capital structure.
In any case, no analyst would ever assume that all the securities are equivalent to
common stock, and then just use common stock prices for everything. Nevertheless,
this is exactly what we do for private companies when we calculate post-money
valuation. If a VC pays $5M for CP that would convert to one-third of the common
stock, then we can only interpret post-money valuation as an enterprise value if
we think that each share of CP has the same value as each share of common. As we
know from the previous chapters, this is not correct.
To compute a more accurate version of enterprise value for VC-backed
companies, we use information from the most recent transaction to estimate the
market prices for each security in the capital structure. For example, consider
the value components for Newco after a Series A investment by EBV. Exhibit 17-1
gives a general depiction of the division of value among the LPs of EBV, the GPs
of EBV, and the employees of Newco. The partial valuation of the Series A is
the GP valuation plus the LP valuation. We learned in Chapter 14 how to ?nd the
values of any of these components, assuming that we knew the value of the whole
pie (total valuation). Here we want to answer a different question: Assuming that
EBV paid a fair price for its stake, what is the implied market value for the whole
pie? We write this implied market value as IV
post
Then, using IV
post
as the total
valuation, we can use three steps to solve for the implied valuation of any other
shareholders: (1) draw their exit diagram, (2) read their exit diagram into an exit
equation, and (3) solve their exit equation using IV
post
as the total valuation input
in the VCV model. In many applications, we can use shortcuts to make this pro-
cedure go much faster. Before describing these shortcuts, we do one example the
hard way.
306 CHAPTER 17 IMPLIED VALUATION
EXAMPLE 17.1
Newco has 10 million shares of common stock outstanding. The founder-employees claim
8M of these shares, and angel investors own the other 2M, which they bought for $1 per
share a year ago. Newco management believes that the time is right for a major expansion.
The expansion will require several million dollars over the following two years, but pre-
liminary conversations with VCs have reached an impasse over valuation and dilution of
the current owners. The founders are concerned about control and are thus reluctant to sell
more than 6M shares because doing so would leave them with less than 50 percent of the
business.
Furthermore, the founders also believe that the company has performed well over the
last year and should not have to drop from the $10M post-money valuation after the angel
investment ($1 per share and 10M shares outstanding). Other VCs have disagreed, believing
that the angel investors overpaid, because although the company is pro?table, the upside is
limited. After many failed negotiations with other VCs, Newco ?nally seems close to a deal
with EBV. EBV has offered $6M for RP ($5M APP) plus 6M shares of common stock. Base-
case option-pricing assumptions apply.
Problems Assuming this transaction goes through,
(a) What are the pre- and post-money valuations for Newco?
(b) What is the implied valuation of Newco (5IV
post
)?
(c) What is the implied valuation of the GP stake in Newco?
(d) What is the implied valuation of the angel shares? Has this value fallen since their
purchase one year ago?
(e) What is the implied valuation of the employee shares?
EXHIBIT 17-1
VALUE DIVISION AFTER SERIES A INVESTMENT
Employees
Series A LP
Valuation
Series A GP
Valuation
17.1 POST-MONEY VALUATION REVISITED 307
Solutions
(a) EBV is investing $6M for three-eighths of the common stock of Newco (6M/16M), so
the post-money valuation is $6M/(3/8) 5$16M. The pre-money valuation is $16 2
$6 5$10M.
(b) To ?nd the implied valuation of Newco, we must ?rst compute the formulas for the LP
cost and valuation. Because EBV has $100M of committed capital and $80M of investment
capital, the LP cost is (100/80) Ã $6M5$7.5M. The exit diagram for the Series A is given by
Exhibit 17-2.
We can read this diagram as
Partial valuation of the Series A5V 25=8 Ã Cð5Þ:
ð17:1Þ
Thus, the LP valuation is
LP valuation50:9 Ã ½V 25=8 Ã Cð5Þ?:
ð17:2Þ
Because EBV has “paid” LP cost for this stake, the implied valuation of Newco will be
the V in Equation (17.2) that equates LP valuation and LP cost:
$7:5M50:9 Ã ½IV
post
25=8 Ã Cð5Þ?:
ð17:3Þ
This is exactly the same procedure we use to ?nd the breakeven valuation. Thus, we
can use the VCV model to compute IV
post
5breakeven valuation 5$17.46M.
EXHIBIT 17-2
EXIT DIAGRAM FOR THE SERIES A
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308 CHAPTER 17 IMPLIED VALUATION
(c) The GP valuation is
GP valuation 5Partial valuation 2LP valuation 50:1 Ã ½V 25=8 Ã Cð5Þ?:
ð17:4Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of GP stake as $0.83M. Note that we could also just use a shortcut to compute the
GP valuation as (0.1/0.9) Ã LP valuation, where LP valuation 5LP cost 5$7.50M.
(d) To ?nd the implied valuation of the angel shares, we solve for the partial valuation of the
angel shares and then use IV
post
as the total valuation. Because the angels own 2M shares out
of 16M total, the exit diagram for these shares is shown in Exhibit 17-3.
We can read this diagram as
Partial valuation of the angel shares 51=8 Ã Cð5Þ:
ð17:5Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of the angel shares as $1.83M. Because the angels purchased 2M shares for $2M
one year ago, this implied valuation represents a decrease in the value of the shares.
(e) To ?nd the implied valuation of the employee shares, we follow the same procedure as
in part (d). Because the employees have claims on 8M out of 16M shares, their exit diagram
is shown in Exhibit 17-4.
We can read this diagram as
Partial valuation of the employees’ shares 51=2 Ã Cð5Þ:
ð17:6Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of the employee shares as $7.30M.
EXHIBIT 17-3
EXIT DIAGRAM FOR THE ANGEL SHARES
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17.1 POST-MONEY VALUATION REVISITED 309
’
After completing this example, it is easy to verify that the whole pie is the
sum of the slices: IV
post
5$7.50M1$0.83M1$1.83M1$7.30M5$17.46M.
Given that the whole must be the sum of the parts, we could have solved steps (c)
through (e) without using the VCV model—that is, we could solve these parts using
two additional equations: (1) GP valuation 50.1/0.9 Ã LP valuation; and (2) IV of
employee shares 54 Ã IV of angel shares.
17.2 MEASUREMENT OF PORTFOLIO VALUE
In the United States, there is no binding rule for the interim valuation of VC
investments. In practice, many GPs report all investments at cost for the quarterly
reporting to LPs unless there has been a new round of (outside) investment.
However, this practice has come under considerable criticism from the LP com-
munity in the past few years, with most of the criticism focused on the stale values
reported between rounds of ?nancing. The updates based on the actual ?nancing
events have garnered much less attention, as these events would appear to place a
“market” value on the companies. These market values, however, are usually based
on the post-money valuations, which, as we have seen, can be quite misleading as
measures of market value.
Although post-money valuation remains an important concept for quickly
communicating the basics of a transaction, it is simply not an appropriate market
EXHIBIT 17-4
EXIT DIAGRAM FOR THE EMPLOYEES’ SHARES
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310 CHAPTER 17 IMPLIED VALUATION
valuation measure for an honest analyst. Instead, the best estimate is the implied
valuation of the LP stake. Exhibit 17-5 displays the components of total value
following a Series B investment.
If we set the Series B LP valuation 5Series B LP cost, then we can use VCV
to solve for the breakeven valuation 5IV
post
. Then we can follow the same pro-
cedure as in Example 17.1 to compute the implied valuations for any other slice of
the pie. With all these new pieces ?oating around, it is helpful to introduce some
new terminology: after a Series Y investment, the implied LP valuation for
the Series X investment (X # Y) is the LP valuation for the Series X investment,
where the total valuation used for the calculation is set equal to the implied
valuation (IV
post
) after Series Y. Similarly, the implied GP valuation for the Series
X investment (X # Y) is the GP valuation for the Series X investment, where the
total valuation used for the calculation is set equal to the implied valuation (IV
post
)
after Series Y. Finally, the implied partial valuation for the Series X investment (X
# Y) is the partial valuation for the Series X investment, where the total valuation
used for the calculation is set equal to the implied valuation (IV
post
) after Series Y.
We can also write the implied partial valuation for Series X as implied LP
valuation 1implied GP valuation.
With these de?nitions in hand, we can also de?ne IV
pre
, the implied pre-
valuation, as representing the part of IV
post
that is owned by the previous investors.
For a Series Y investment, we can write IV
pre
as
IV
pre
5IV
post
2Series Y implied partial valuation
5IV
post
2Series Y implied LP valuation2Series Y implied GP valuation
EXHIBIT 17-5
VALUE DIVISION AFTER SERIES B INVESTMENT
Employees
Series A LP
Valuation
Series A GP
Valuation
Series B LP
Valuation
Series B GP
Valuation
17.2 MEASUREMENT OF PORTFOLIO VALUE 311
5IV
post
2Series Y LP cost 2Series Y implied GP valuation
5IV
post
2Series Y LP cost 2ðGP%=ð1 2GP%ÞÞ Ã Series Y LP cost
5IV
post
2Series Y LP cost=ð1 2GP%Þ: ð17:7Þ
We could also build IV
pre
from the bottom up. Suppose there has just been a
Series C investment. In this scenario,
IV
pre
5Series A implied partial valuation 1Series B implied partial valuation
1Employee stock implied partial valuation: ð17:8Þ
Let’s do another example.
EXAMPLE 17.2
Same setup as in Example 17.1, but now it is one year later, and Newco needs another
infusion of capital. Talltree is considering a $10M Series B investment for 8M shares of CP.
The option-pricing assumptions remain the same as in Example 17.1, except that now we
assume an expected holding period of four years. Talltree has 20 percent carried interest,
$250M of committed capital, and $50M of lifetime fees.
Problems
(a) After this round with Talltree, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) After this round by Talltree, what is the Series A implied LP valuation?
Solutions
(a) If Talltree pays $10M to purchase 8M shares, they would be purchasing 1/3 of the 24M
common shares outstanding (as-converted), making the post-money valuation $10M/
(1/3) 5$30M. Thus, the pre-money valuation is $30M 2 $10M5$20M.
(b) To compute the implied valuations, we must ?rst compute the formulas for the LP cost
and valuation. LP cost is (250/(250 250)) Ã $10M5$12.5M. Next, we need to ?nd the
conversion condition for Talltree. Because the Series B is the only CP in the capital structure,
we do not need to worry about conversion order. Talltree would receive 1/3 Ã (W25) if it
converts (the $5M is needed to redeem the Series A RP), and $10M if it redeems. Thus,
Talltree’s conversion condition for the Series B is
1=3 Ã ðW 25Þ.10-W
B
5$35M:
ð17:9Þ
The exit diagram for the Series B is given in Exhibit 17-6. We can read this diagram as
Partial valuation of the Series B5V 2Cð10Þ 11=3 Ã Cð35Þ:
ð17:10Þ
Thus, the LP valuation is
LP valuation 50:9 Ã ðV 2Cð10Þ 11=3 Ã Cð35ÞÞ:
ð17:11Þ
312 CHAPTER 17 IMPLIED VALUATION
Now, the ?nal step is to compute the implied post-valuation (5breakeven valuation).
We set LP cost 5LP valuation and solve for IV
post
:
$12:5M5ð0:9Þ Ã ðIV
post
2Cð10Þ 11=3 Ã Cð35ÞÞ:
ð17:12Þ
The VCV model yields a breakeven valuation 5IV
post
5$38.48M. To solve for IV
pre
,
we use Equation (17.7):
IV
pre
5IV
post
2Series B LP Cost=ð1 2GP%Þ
5$38:48M2$12:5M=0:9 5$24:59M:
ð17:13Þ
(c) The easy way to ?nd the implied LP valuation for Series A is to substitute a total
valuation of $38.48M into the AUTO Calculator, and then just look at the answer for the LP
valuation of Series A. Here we will do this calculation the hard way, by ?nding the equation
for this LP valuation and then solving this equation in the FLEX Calculator. We begin by
drawing the exit diagram for the Series A (Exhibit 17-7).
We can read this diagram as
Partial valuation of the Series A ðafter Series BÞ 5Cð10Þ 25=8 Cð15Þ 21=8 Ã Cð35Þ:
ð17:14Þ
This makes the LP valuation
LP valuation ðSeries A after Series BÞ 50:9 Ã ðCð10Þ 25=8 Cð15Þ 21=8 Ã Cð35ÞÞ:
ð17:15Þ
Using a total valuation 5IV
post
, we can use the FLEX Calculator to calculate this
implied LP valuation as $9.70.
EXHIBIT 17-6
EXIT DIAGRAM FOR SERIES B
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17.2 MEASUREMENT OF PORTFOLIO VALUE 313
’
17.3 DOWN ROUNDS?
Another important application of implied valuation occurs in the identi?cation of
down rounds. Although it can sometimes be in the economic or emotional interest
for some parties to pretend that a down round has not occurred, there are other times
when the determination of a down round is crucial for negotiation or contractual
reasons.
EXAMPLE 17.3
Consider the setup given in Example 17.2. It is now one year later, and Newco needs another
infusion of capital. Owl is considering a $12M Series C investment for RP, with APP of
$2M, with a 5X liquidation preference and 8M shares of common. The option-pricing
assumptions remain the same as in Example 17.1, except that now the expected holding
period is three years. Owl has carried interest of 25 percent, committed capital of $500M, and
lifetime fees of $83.75M.
Talltree, the Series B investor, is covered by full-ratchet antidilution protection. The
other investors (particularly the founders and EBV) are denying that this is a down round
and claim that the antidilution protection does not apply. They have two arguments. First,
they claim that the RP should be ignored in these calculations, and thus $12M is being paid
for 8M shares of common, a higher price than paid by Talltree for their CP. Second, they say
that if Talltree insists on counting the RP, it should only count for $2M (its APP), with the
other $10M allocated to the common. Even in this case, they claim that the price is the same
as paid by Talltree. Talltree, in its defense, believes that these arguments greatly understate
EXHIBIT 17-7
EXIT DIAGRAM FOR SERIES A (AFTER SERIES B)
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314 CHAPTER 17 IMPLIED VALUATION
the value of the RP component, and that the implied valuation of the Series B shares will be
lower than its original LP cost. Owl wants the issue resolved before it invests.
Problems
(a) After this round with Owl, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) Is Talltree correct in their assertion that the investment by Owl lowers the implied
valuation of the Series B below its original LP cost?
Solutions
(a) If Owl pays $12M to purchase 8M common shares (ignoring the RP component), it
would be purchasing one-fourth of the of 32M common shares outstanding (as-converted).
This makes the post-money valuation $12M/(1/4) 5$48M, and the pre-money valuation is
$48M 2 $12M5$36M.
(b) To compute the implied valuations, we must ?rst compute the formulas for the LP cost
and valuation. LP cost is 500/(500 283.75) Ã $12M5$14.4M. Next, we need to ?nd the
conversion condition for the Series B, which is still the only CP in the capital structure.
Talltree would receive 1/4 Ã (W215) if it converts ($5M to redeem the Series A RP and
$10M to redeem the Series C RP), and $10M if it redeems. Thus, Talltree’s conversion
condition for the Series B is
1=4 Ã ðW 215Þ .10-W
B
5$55M:
ð17:16Þ
With this information about Series B conversion, we are ready to draw the exit dia-
gram for the Series C as shown in Exhibit 17-8.
EXHIBIT 17-8
EXIT DIAGRAM FOR THE SERIES C
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17.3 DOWN ROUNDS? 315
We can read this diagram as
Partial valuation of the Series C5V 2Cð10Þ 11=3 Ã Cð25Þ 21=12 Ã Cð55Þ:
ð17:17Þ
The terms of the Owl fund differ fromthose of EBVand Talltree. With an expected gross
value multiple of 2.5, Owl has GP% of 0.25 Ã (2.5 Ã 416.25 2 500)/(2.5 Ã 416.25) 50.13.
Thus, the LP valuation is
LP valuation of the Series C50:87 Ã ðV 2Cð10Þ 11=3 Ã Cð25Þ
21=12 Ã Cð55ÞÞ:
ð17:18Þ
Now, the ?nal step is to compute the implied post-valuation, we set LP cost 5LP
valuation and solve for IV
post
.
$14:4M50:87 Ã ðIV
post
2Cð10Þ 11=3 Ã Cð25Þ 21=12 Ã Cð55ÞÞ:
ð17:19Þ
We can use the VCV model to solve for a breakeven valuation 5IV
post
5$49.19M.
Then, we have
IV
pre
549:19 214:40=0:87 5$32:64M:
ð17:20Þ
(c) To determine if there has been a down round, we need to compute the implied LP
valuation for Series B (after Series C) and compare it to the dollars invested by Talltree in
Series B. Again, the easy way is to read the answer out of AUTO Calculator. To do this the
hard way, we ?rst ?nd the formula for the LP valuation. Note that this formula will be
slightly different from what we found in Example 17.2, because now there is a new investor
(Series C) in the capital structure. The LP cost for the Series B is $12.5M (same as in
Example 17.2). The new exit diagram for the Series B is shown in Exhibit 17-9.
EXHIBIT 17-9
EXIT DIAGRAM FOR THE SERIES B (AFTER SERIES C)
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316 CHAPTER 17 IMPLIED VALUATION
We can read this diagram as
Partial valuation of the Series B ðafter Series CÞ
5Cð10Þ 2Cð20Þ 11=4 Ã Cð55Þ:
ð17:21Þ
The LP valuation is
LP valuation ðSeries B after Series CÞ 50:9 Ã ðCð10Þ 2Cð20Þ 11=4 Ã Cð55ÞÞ:
ð17:22Þ
We can solve for the implied LP valuation in the FLEX Calculator by substituting in
total valuation 5IV
post
549.19. This yields an answer of $10.53M.
The ?nal step is to compare this implied LP valuation ($10.53M) to the “price” 5LP
cost originally paid for these Series B shares ($12.50M). As the latter is higher than the
former, we conclude that Talltree is correct in its claim that the Series C is a down round.
’
REALITY CHECK: Although this example gives Talltree some ammuni-
tion in a debate about down rounds, in most real-world transactions the contractual
provisions are worded tightly enough so that the legal de?nition of “down round”
may have nothing to do with the actual economic values computed by implied
valuation. For example, if a down round is explicitly considered as a “lower con-
version price”, then the economic value of all other features may be irrelevant from
a legal perspective. Furthermore, even if all parties were willing to agree that a
down round occurred in Example 17.3, it is not clear how antidilution adjustments
would be computed, because such adjustments usually rely on preset formulas that
can only take account of conversion prices. In practical situations, down-round
computations such as Example 17.3 are more likely to show up in cases where
contracts have not been carefully drafted.
17.4 HOW TO AVOID VALUATION CONFUSION
We have been throwing so many valuation terms around that some readers may be
confused. This short section is intended to review some of the most important
valuation de?nitions. In this section, we use bold type for valuation terms, and bold
italic for valuation terms that are not standard industry usage.
When we “do a valuation” or “value a company”, this is usually referring to
our own opinion about what something is worth. We arrive at this valuation using
DCF, comparables, VC method, or some other valuation technique. You can think
of this as your personal valuation of the company. The total valuation computed in
the VC method is an example of a personal valuation.
Personal valuation has nothing to do with the actual market valuation implied
by a transaction. In fact, the whole challenge of being a successful investor is to ?nd
companies where your personal valuation is higher than the market valuation (and to
be right about it!). Instead, the structure of the actual transaction implies a speci?c
17.4 HOW TO AVOID VALUATION CONFUSION 317
market valuation. The industry-standard approach to the computation of market
valuation is to pretend that the whole purchase price was for common stock, and then
divide this purchase price by the fraction of the company that has been purchased.
This de?nition of the market valuation is called post-money valuation. Post-money
valuation is sometimes a fair approximation for market valuation (such as when
convertible stock is purchased in a high-volatility venture) and sometimes a bad
approximation (such as when common stock is combined with redeemable preferred
stock in a low-volatility venture). In many cases, it is often helpful for a careful
investor or owner to compute a more accurate measure of the market valuation,
which we call the implied post-valuation and write as IV
post
. We compute the
implied post-valuation by ?rst ?nding the LP valuation and then recursively solving
for the total valuation that equates LP valuation and LP cost.
Important points to remember:
1. Do not use your personal valuation when you mean market valuation. If
somebody asks about the post-money valuation of a company, don’t ever
look at your models for the answer. Absolute and relative valuation models
cannot answer this question.
2. Do not use market valuation when you should be using your personal
valuation. If you doing a partial valuation of your stake in a company, the
correct “stock price” to put into option-pricing models is your personal
valuation of the whole company (5total valuation), not the market valuation.
3. It’s ?ne to use post-money valuation if you want to communicate with people,
but don’t forget that, as a proxy for the market valuation of the company, it is
often misleading or just plain wrong. When it is important to knowwhat price
is really being implied by the transaction, you should compute the implied
valuation.
SUMMARY
Pre-money valuation and post-money valuation are used by VCs for many purposes, including
communication, interim valuation for reporting, and as starting points in contractual disputes.
In this chapter, we demonstrated that pre- and post-money valuation are not accurate measures
of value—and in their place we developed alternative measures called implied pre-valuation
and implied post-valuation that are more accurate re?ections of market value.
KEY TERMS
Implied valuation
Market valuation
Implied post-valuation
(IV
post
), implied
pre-valuation (IV
pre
)
Implied LP valuation,
implied GP valuation,
implied partial valuation
Personal valuation
318 CHAPTER 17 IMPLIED VALUATION
EXERCISES
17.1 True, False, or Uncertain: If an investor believes that the total valuation of a company
is higher than the implied post-valuation for the transaction, then he should invest.
17.2 Suppose that EBV is considering a $10M Series A investment in Newco. EBV proposes
to structure the investment as 6M shares of convertible preferred stock (CP) plus RP with
$4M APP. The employees of Newco have claims on 10M shares of common stock. Fol-
lowing the Series A investment, Newco will have 10M common shares outstanding and
would have 16M shares outstanding on conversion of the CP.
(a) After this round, what are the pre- and post-money valuations for Newco?
(b) Find IV
post
and IV
pre
.
17.3 Talltree is considering a $12M Series B investment in Newco for 5M shares of CP with
$12M APP. The other investors are (1) the employees, who have claims on 10M shares of
common; and (2) EBV, the Series A investors, who have 5M shares of CP with $6M APP. In
both of these structures, the Series B has a liquidation preference to Series A. All the parties
agree on an estimate of $30M for the total valuation of Newco.
(a) After this round with Talltree, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) After this round by Talltree, what is the implied LP valuation for the Series A
investment made by EBV?
17.4 Consider the situation given in Example 17.3. After the Series C investment by Owl, is
the Series A implied LP valuation lower than its original LP cost?
EXERCISES 319
CHAPTER 18
COMPLEX STRUCTURES
IN PART III, we have developed a framework for the partial valuation of
many different types of VC structures. Because most VC transactions use standard
security types such as RP, CP, PCP, and PCPC, we are able to automate many of
these techniques in the AUTO calculator of the VCV model. Some transactions,
however, use complex structures that are not easily reduced to a one-size-?ts-all
methodology. In this chapter, we give a few examples of such transactions and
show how to break them down into the same pieces used in the previous chapters.
With practice, analysts can learn to analyze many nonstandard securities using
these techniques. As a general rule, if all securities are paid off only at exit, then
you can write an exit diagram. If you can write an exit diagram, then you can read
the diagram and value the underlying securities. Of course, not all transactions can
be handled within this framework. In particular, if there are intermediate cash
payments (before exit), then the exit diagrams won’t tell the whole story, and the
analytic formulas for RE options do not apply. To value these kinds of transactions,
we need to use techniques developed in Part IV.
18.1 MANAGEMENT CARVE-OUTS
Many times, a complex structure will arise as part of a down round. In these cases,
early expectations for the business have turned out to be too ambitious, but at least
one new investor is convinced that value can still be captured in a new transaction.
In these cases, the new investor often decides that there are insuf?cient incentives
for the management and employees to stay around, and a new employee stock pool
may not solve the problem, because of large preferences that stand before the
common stock. Then, to provide incentives for management to stay around and
work hard, a management carve-out is often made at the time of the new
investment. The simplest type of carve-out is to set aside some fraction of exit
320
proceeds to be given to management.
1
This fraction is often paid from the ?rst
dollar of exit proceeds to incent management for even the smallest exits. We
illustrate this type of carve-out in Example 18.1. More complex incentive schemes
can be provided by lump-sum payments when certain exit thresholds or perfor-
mance targets are met. We illustrate this kind of carve-out in Example 18.2.
EXAMPLE 18.1
Newco has received four rounds of investments (Series A, B, C, and D) for a total of 40M
shares of CP plus 10M shares of common claimed by the employees. After the Series D
investment, Newco falls on hard times. After searching hard for new ?nancing, the investors
?nally agree to $12M Series E investment with Vulture Ventures (VV) for 50M shares of CP
and a 3X liquidation preference. As part of this agreement, all previous investors (Series A
through Series D) give up all their preferred rights and are converted to common stock, so the
capital structure of Newco is now 50M shares of common plus the Series E CP. As part of the
investment, Vulture creates a carve-out: management will receive 10 percent of all exit
proceeds, with a value of this carve-out capped at $5M. Vulture Ventures has $250M of
committed capital, $50M of lifetime fees, and 20 percent carried interest.
Problems
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case assumptions.
Solutions
We begin by drawing the exit diagram for the carve-out in Exhibit 18-1. Management
receives 10 percent of all proceeds up to a total of $5M. This cap is reached when proceeds
are equal to $50M.
We can read this diagram as
Partial valuation of management carve-out 51=10 Ã V 21=10 Ã Cð50Þ: ð18:1Þ
With this equation in hand, we are ready to tackle the Series E stake. The trick here is
to adjust for the change in the redemption value caused by the carve-out. Without the carve-
out, Vulture Ventures would be entitled to the ?rst $36M in proceeds (5$12M APP Ã 3X
liquidation preference.) Although the total RV of Series E is still $36M after the carve-out, it
will now take a little bit longer to get there, because Series E will only receive 90 percent of
the proceeds. Thus, Vulture will receive 90 percent of all proceeds until 36M50.9 Ã W,
which occurs at W5$40M.
1
Management carve-outs in VC transactions should not be confused with the more common meaning of
“carve-out” in mature companies, where a division of a company is separated from the parent and given
an independent existence.
18.1 MANAGEMENT CARVE-OUTS 321
After receiving the RV, Vulture would choose to convert the CP when its conversion
value exceeds the redemption value of $36M. How is this conversion condition affected by
the carve-out? As long as the conversion point occurs above $40M, the only difference would
be the reduction of the maximal $5M carve-out from the exit proceeds:
Series E conversion condition
1=2 Ã ðW 25Þ .36M-W
E
5$77M: ð18:2Þ
We are now ready to draw the exit diagram for the Series E as shown in Exhibit 18-2.
EXHIBIT 18-2
EXIT DIAGRAM FOR THE SERIES E
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0
EXHIBIT 18-1
EXIT DIAGRAM FOR MANAGEMENT CARVE-OUT
50
$W
M
a
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322 CHAPTER 18 COMPLEX STRUCTURES
We can read this diagram as
Partial valuation of the Series E59=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ: ð18:3Þ
We next analyze the remaining investors—Series A through Series D plus the
employee claims—who collectively own 50 million shares of common stock. This holding
includes complex changes, which are easiest to analyze by reversing our usual order and
doing the exit equation ?rst. Because the 50 million shares held by these remaining investors
include everything not already claimed by Vulture or the carve-out, we can write the exit
equation as the difference between the whole ?rm (V) and the partial valuations given in
Equations (18.1) and (18.3):
Partial valuation of the 50 million remaining shares
5V 2½1=10 Ã V 21=10 Ã Cð50Þ? 2½9=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ?
59=10 Ã Cð40Þ 11=10 Ã Cð50Þ 11=2 Ã Cð77Þ:
ð18:4Þ
We draw this exit diagram in Exhibit 18-3.
(a) To compute the breakeven valuation for the Series E, we use the typical GP% of 0.10
(since VV has carried interest of 20 percent like EBV and Talltree) and subtract the GP
valuation from Equation (18.3) to obtain
LP valuation of Series E50:9 Ã ½9=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ?: ð18:5Þ
Next, we ?nd the LP cost as ($250M/ $200M) Ã $12M5$15M. The breakeven
valuation (5IV
post
) is found by setting LP valuation 5LP cost. Because this transaction
includes a nonstandard structure (the carve-out), it is necessary to use the FLEX Calculator of
the VCV model for this computation. Under base-case assumptions for a Series E investment,
we ?nd a breakeven valuation 5IV
post
5$24.26M.
EXHIBIT 18-3
EXIT DIAGRAM FOR THE REMAINING SHARES
40 50 77
$W
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m
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0
18.1 MANAGEMENT CARVE-OUTS 323
(b) Using the IV
post
of $24.26M and the same base-case assumptions as in part (b), we can
use FLEX Calculator to compute the partial valuation of the carve-out (Equation (18.1) as
$1.52M. ’
The previous example used a proportional carve-out. It is also possible to
have discrete payouts at preset trigger points. The next example illustrates this case.
EXAMPLE 18.2
We use the same setup as in Example 18.1, but this time with a different structure for the
management carve-out. Now, following the $12M Series E investment from Vulture Ven-
tures (50M shares of CP with a 3X liquidation preference), management is promised the
following incentives: If Newco has an exit of at least $50M, then the employees will receive
$5M from these proceeds. If Newco has an exit of at least $80M, then the employees will
receive an additional $5M from these proceeds. The earlier investors have 40M shares of
common, and the employees have claims on a further 10M shares.
Problems
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case assumptions.
(c) Compute the implied valuation for the management carve-out under base-case assumptions.
Solutions
We begin by drawing the exit diagram for the carve-out in Exhibit 18-4. Here, we have
discrete jumps in the payouts to management at $50M and $80M.
We can read this diagram as
Partial valuation of management carve-out 55 Ã BCð50Þ 15 Ã BCð80Þ: ð18:6Þ
We next turn to the Series E stake. Now the main complication is to adjust properly for
the discrete payouts. Without doing some calculations, we cannot tell whether the jumps
occur below or above the conversion point. In principle, it is possible that neither payout
occurs before conversion (if W
E
,50), that only the ?rst one does (50 ,W
E
80), or that both
do (W
E
. 80). The only way to know for sure is to compute all the cases and look for logical
contradictions. For example, Series E conversion condition, if occurs below the ?rst payout
(W
E
, 50):
1=2 Ã W .36M-W
E
5$72M: ð18:7Þ
This condition gives us a contradiction, because if W
E
is equal to $72M, we should
have to include a payout (because W
E
.50). Thus, Equation (18.7) is not a proper conversion
condition.
We next consider the possibility that $50M , W
E
, $80M.
324 CHAPTER 18 COMPLEX STRUCTURES
Series E conversion condition, if occurs above the ?rst payout (50M , W
E
, 80M)
1=2 Ã ðW 25Þ .36M-W
E
5$77M: ð18:8Þ
In this case, there is no logical inconsistency, because the condition for being between
the two payouts (50M,W
E
,80M) is consistent with W
E
5$77M. Thus, Equation (18.8) is
a proper conversion condition.
Even though we have found a conversion condition, we still check the last possibility,
W
E
. 80. As we shall see, an interesting surprise awaits us. Series E conversion condition, if
occurs above the second payout (W
E
.$80M):
1=2 Ã ðW 210Þ.36M-W
E
5$82M: ð18:9Þ
Again, there is no logical inconsistency here: W
E
5$82M is higher than the condition
for the second payout, W
E
.80M. It seems as though we have two different conversion
conditions.
How is this possible? It happens because for all exits between $77M and $80M,
Equation (18.8) applies, and it is optimal for Vulture to convert the Series E. However, for an
exit between $80M and $82M, after the second payout is made, Equation (18.9) applies, and
it is no longer optimal to convert. For exits in this range, Vulture would choose to redeem.
They would again convert for any exit above $82M. Their exit diagram is shown in Exhibit
18-5. In complex cases like this, we must take special care to label all the key points to
facilitate our reading of the diagram. For example, at W5$80M, the Series E will suffer
a drop of 3/2 (because instead of 1/2 Ã (W 2 5) 537.5 they drop back to 36) and a slope
change of one-half (because they no longer are converting and getting half of all additional
exit proceeds.)
EXHIBIT 18-4
EXIT DIAGRAM FOR MANAGEMENT CARVE-OUT
50 80
$W
M
a
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5
10
5
5
18.1 MANAGEMENT CARVE-OUTS 325
We can read this diagram as
Partial valuation of the Series E5V 2Cð36Þ 11=2 Ã Cð77Þ 21=2
à Cð80Þ 23=2 à BCð80Þ 11=2 à Cð82Þ:
ð18:10Þ
We next analyze the remaining investors—Series Athrough Series Dplus the employee
claims—who collectively own 50 million shares of common stock. As in Example 18.1, we
write this exit equation as the difference between the whole ?rm (V) and the partial valuations
of the other investors. These partial valuations are given in Equations (18.6) and (18.10):
Partial valuation of the 50 million remaining shares 5V 2½5 Ã BCð50Þ 15 Ã BCð80Þ?
2½V 2Cð36Þ 11=2 Ã Cð77Þ 21=2 Ã Cð80Þ 23=2 Ã BCð80Þ 11=2 Ã Cð82Þ?
5Cð36Þ 25 Ã BCð50Þ 21=2 Ã Cð77Þ 11=2 Ã Cð80Þ 27=2 Ã BCð80Þ 21=2 Ã Cð82Þ
ð18:11Þ
We can draw this exit diagram as shown in Exhibit 18-6.
EXHIBIT 18-5
EXIT DIAGRAM FOR THE SERIES E
36 77 80 82
$W
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3/2
EXHIBIT 18-6
EXIT DIAGRAM FOR THE REMAINING SHARES
36 50 77 80 82
$W
R
e
m
a
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n
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g
s
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7/2
5
326 CHAPTER 18 COMPLEX STRUCTURES
(b) To compute the breakeven valuation (5IV
post
) for the Series E, we ?rst subtract the GP
valuation from Equation (18.10) to obtain
LP valuation of Series E50:9 Ã ½V 2Cð36Þ 11=2 Ã Cð77Þ 21=2 Ã Cð80Þ
23=2 Ã BCð80Þ 11=2 Ã Cð82Þ?:
ð18:12Þ
As in Example 18.1, it is necessary to use the FLEX Calculator to compute the IV
post
.
Under base-case assumptions for a Series E investment, we ?nd an IV
post
of $22.82M.
(c) Using the IV
post
of $22.82M and the same base-case assumptions as in part (b), we can
use FLEX to compute the partial valuation of the carve-out (Equation (18.6)) as $0.59M.
’
18.2 DEALING WITH PARTNERS
Because VC-backed companies are cash poor, they often must give up equity as
payment in transactions with service providers or other partners. The following
example shows how we could value these transactions.
EXAMPLE 18.3
EBV makes a $10M Series A investment in Newco for 10M shares of CP. The employees
of Newco have claims on 10M shares of common stock. At the same time as this investment,
Newco enters into a transaction with Techco to obtain licenses for some Techco patents. As
consideration for providing these licenses, Techco receives an option to purchase 10M shares
of common stock for $1.50 a share, but this option can only be exercised upon an exit above
$150M. (Assume that this $150M would be adjusted for any future dilution, so that the
threshold is effective for the proceeds owed to the current shareholders.) EBV is aware of
the deal with Techco at the time that they make their Series A investment.
Problems
(a) Draw and read the exit diagrams for Techco and for the Series A.
(b) Compute the breakeven valuation for the Series A investment under base-case
assumptions.
(c) Compute the implied valuation for Techco’s stake under base-case assumptions.
Solutions
(a) We begin with Techco. Their options are valuable only for an exit above $150M. What
happens at this point? Techco exercises their options at a cost of $15M, and receives 10M
shares, which are worth 10M/30M5one-third of the ?rm5$50M. In addition, the $15M total
strike price will be shared equally among the common stock holders, so Techco will effectively
get back one-third of their strike price 5$5M. In the exit diagram, these two pieces will be
represented by a jump up (binary option) representing the pro?t they make on the option
18.2 DEALING WITH PARTNERS 327
transaction ($50M 2 $15M1$5M5$40M), plus a positive slope starting at $150M (regular
call option) representing their new ownership of one-third of the common shares.
We can read this exit diagram as
Partial valuation of Techco options 540 Ã BCð150Þ 11=3 Ã Cð150Þ: ð18:13Þ
To ?nd the value of the Series A, we must ?rst compute the conversion condition. As
in Example 18.2, we don’t know whether this conversion condition occurs before or after the
conversion of Techco’s options, and we don’t have a simple RVPS rule to help us. Thus, we
must check both possibilities.
Series A conversion condition, Techco not yet converted (W
A
, 150):
1=2 Ã W.10-W
A
520: ð18:14Þ
This condition is consistent with W
A
, 150.
Next, we look to check for a conversion condition if Techco has already converted. In
this case, we must add $15M to the proceeds to represent Techco’s exercise payments.
Series A conversion condition, Techco converted (W
A
. 150):
1=3 Ã ðW 115Þ.10-W
A
515: ð18:15Þ
Clearly, Equation (18.15) represents a contradiction with Techco’s threshold of
$150M, so Equation (18.14) is the only valid conversion condition. We can now draw the
exit diagram for the Series A stake as shown in Exhibit 18-8.
We can read this diagram as
Partial Valuation of Series A5V 2Cð10Þ 11=2 Ã Cð20Þ 220 Ã BCð150Þ
21=6 Ã Cð150Þ:
ð18:16Þ
EXHIBIT 18-7
EXIT DIAGRAM FOR THE TECHCO OPTIONS
40
150
$W
T
e
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328 CHAPTER 18 COMPLEX STRUCTURES
Usually, the part of this diagram that confuses people is the drop of $20M at W5150.
This drop is due to the combination of two effects. First, when Techco exercises their options,
they immediately receive 1/3 of the proceeds, which reduces the value of the EBV stake from
one-half of $150M (5$75M) to one-third of $150M (5$50M). This causes a drop of $25M.
This drop is somewhat cushioned by one-third of the proceeds from the exercise cost (1/3 Ã
$15M5$5M), leaving a total drop of $25M 2 $5M5$20M. Note that this kind of binary
call does not occur when “regular” preferred stock converts, because there is no windfall
pro?t or loss at the time of such conversions. In this example, however, Techco’s options are
well in-the-money before they are allowed to convert them at W5$150M. When they are
?nally able to convert, the resulting pro?ts cause the jumps in the diagrams.
(b) To compute the breakeven valuation (5implied valuation) for the Series A, we ?rst
subtract the GP valuation from Equation (18.16) to obtain
LP valuation of Series E59=10 Ã ½V 2Cð10Þ 11=2 Ã Cð20Þ
220 Ã BCð150Þ 21=6 Ã Cð150Þ?:
ð18:17Þ
The LP cost is ($100M/$80M) Ã $10M5$12.5M. As in the previous examples, it is
necessary to use the FLEX Calculator to compute the IV
post
. Under base-case assumptions for
a Series A investment, we ?nd an IV
post
of $30.52M.
(c) Using the IV
post
of $30.52M and the same base-case assumptions as in part (b), we
can use FLEX to compute the partial valuation of Techco’s options (Equation (18.13))
as $4.58M. ’
18.3 A COMPLEX EXAMPLE
Next, we try to solve a real messy problem. If we can do this, we can do (almost)
anything.
EXHIBIT 18-8
EXIT DIAGRAM FOR THE SERIES A
10 20 150
$W
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20
18.3 A COMPLEX EXAMPLE 329
EXAMPLE 18.4
We begin with the same setup as in Example 16.5. Talltree has just made a Series F
investment in Newco. The details of the Series F and all prior rounds are given below.
Series A: 10M shares of CP ($6M APP)
Series B: 10M shares of CP ($10M APP)
Series C: 10M shares of CP ($4M APP and a 3X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 3X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($10M APP).
Series F: 10M shares of PCP ($20M APP) with a QPO at $6 per share.
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. In the event of a liquidation, the preferred stock is
redeemed in reverse order of investment (i.e., the Series F has a preference to the Series E,
which has a preference to the Series D, and so on). In addition to these investors, the
employees have claims on 20M shares of common stock.
Now, we add two new features to this capital structure from Example 16.5, with both
of these new features put in place at the same time as the Series F investment. First, the
investors create a management carve-out for 20 percent of the ?rst $50M in exit proceeds.
Second, Newco acquires a smaller competitor, Subco, with the owners of Subco receiving
20M shares of common stock, with a further payment of 10M shares of common stock if the
merged company has an exit exceeding $1000M.
Problems
(a) Compute the breakeven valuation for the Series F under base-case assumptions.
(b) Given this breakeven valuation, compute the implied valuation for the management
carve-out.
(c) Given this breakeven valuation, compute the implied valuation for Subco’s stake.
Solutions
(a) We begin this solution with the same two steps as in Example 16.5. First, we compute
the conversion order for the CP. Second, we insert the PCP and PCPC into this order. In order
of the RVPS of the CP, we have
Series A: $6M/10M5$0.60
Series B: $10M/10M5$1.00
Series C: $12M/10M5$1.20
Series E: $10M/10M5$1.00
We next add the participating preferred to the ordering. For the Series F PCP, auto-
matic conversion occurs at a QPO of $6 per share, which will be after all series of CP have
converted. For the Series D PCPC, we ?rst determine if conversion is voluntary or automatic.
With voluntary conversion at $30M/10M5$3.00 and automatic conversion at the
QPO5$5.00, the QPO threshold is redundant and conversion will occur voluntarily at $3 per
share. Finally, we can compute the Series D per-share cap as
Per-share cap :ð$30M2$10MÞ=10M5$2:00:
330 CHAPTER 18 COMPLEX STRUCTURES
So far, these are exactly the same answers we found in Example 16.5. Our next step is
different, as we must ?nd the trigger point for the Subco incentive. At an exit value of $1B,
even if all shares of CP and PCP have already been converted (yielding a total of 100M
shares outstanding), the proceeds available to the common stock would be $1B 2 $10M (for
the carve-out) 5$990M, for a per-share value of $990/100M5$9.90. Thus, the Subco
trigger will not occur until after all other series have converted.
Taken together, these calculations imply a conversion and cap order of A ($0.60), B
and E together ($1.00), C ($1.20), D (cap) ($2.00), D (convert) ($3.00), F ($6.00), and Subco
incentive ($9.90). Except for the Subco incentive, this is the same answer as we found in
Example 16.5. We diverge more from Example 16.5 when we compute the actual conversion
conditions for all series. Here, we must take account of the management carve-out and of the
additional 20M shares given to Subco. The management carve-out is for the ?rst $50M of
proceeds. As there is a total of $20M1$10M1$10M1$12M1$10M1$6M5$68M
of preferences, we can be con?dent that the carve-out will be complete while preferences are
still being paid, and thus before any of the preferred would choose to convert. Thus, we can
simply add the entire value of the carve-out (50.20 Ã $50M5$10M) as a preference to the
common stock. For the Series A, these preferences total $68M À $6M (the Series A RV)
1$10M (the carve-out) 5$72M. Upon conversion, the 10M shares from Series A would
represent one-seventh of the common stock because 60M shares would already be out-
standing: 20M to the employees, 20M to the previous owners of Subco, 10M (as if) to the
Series D PCPC, and 10M (as if) to the Series F PCP. Thus, we have
Series A conversion condition : 1=7 Ã ðW 272Þ.6-W
A
5$114M: ð18:18Þ
Series B and E convert at the same time, followed by Series C:
Series B conversion condition : 1=9 Ã ðW 252Þ.10-W
B
5$142M: ð18:19Þ
Series E conversion condition : 1=9 Ã ðW 252Þ.10-W
E
5$142M: ð18:20Þ
Series C conversion condition : 1=10 Ã ðW 240Þ.12-W
C
5$160M: ð18:21Þ
Next in order is the Series D cap, followed by the Series D voluntary conversion.
Series D cap : 10 11=10 Ã ðW 240Þ 530-W
D
ðcapÞ 5$240M ð18:22Þ
Series D conversion condition : 1=10 Ã ðW 230Þ.30-W
D
5$330M: ð18:23Þ
At the QPO of $6 per share, the only preference left is the $10M carve-out, so the QPO
occurs at
Series F conversion condition ðQPOÞ: 100M Ã $6 1$10M5W
F
5610: ð18:24Þ
At this QPO, the Series F will return $20M to the other shareholders and thus
recapture 1/10 Ã $20M5$2M for themselves, for a net drop of $20M 2 $2M5$18M.
Finally, we have the contractual condition that the Subco trigger for extra shares is at W
5$1000M. At this trigger, Subco receives 10M additional shares, to raise their stake in the
company from 2/10 to 3/11. At this point, the only liquidation preference still being paid is
the $10M management carve-out, so $1000M 2 $10M5$990M remains for the common.
The additional 10M shares means that the stake of the Series F investor drops by
1=10 Ã 990 21=11 Ã 990 5$9M: ð18:25Þ
18.3 A COMPLEX EXAMPLE 331
With these calculations in hand, we are ready to draw the exit diagram for the Series F,
as shown in Exhibit 18-9.
We can read this diagram as
Partial valuation of the Series F
54=5 Ã V 24=5 Ã Cð25Þ 11=6 Ã Cð78Þ 21=42 Ã Cð114Þ 22=63 Ã Cð142Þ 21=90 Ã Cð160Þ
11=90 Ã Cð240Þ 21=90 Ã Cð330Þ 218 Ã BCð610Þ 29 Ã BCð1; 000Þ 21=110 Ã Cð1; 000Þ
ð18:26Þ
Using our standard GP% of 10 percent, the LP valuation of the Series F is 90 percent
of Equation (18.26). LP cost for Series F is (250/200) Ã $20M5$25M. Finally, we can use
the FLEX Calculator of VCV to compute the breakeven valuation under base-case assump-
tions as $171.10M.
(b) The exit diagram for the management carve-out is shown in Exhibit 18-10.
We can read this diagram as
Partial valuation of the management carve-out 51=5 Ã V 21=5 Ã Cð50Þ: ð18:27Þ
Using base-case assumptions and the breakeven valuation (5IV
post
) from part (a), we
can use FLEX to compute this valuation as $6.96M.
(c) The previous owners of Subco have 20M shares of common stock before their trigger
point at W51,000, when they receive an additional 10M shares. At this trigger point, their
value increases by
3=11 Ã ð1; 000 210Þ 22=10 Ã ð1; 000 210Þ 5$72M: ð18:28Þ
EXHIBIT 18-9
EXIT DIAGRAM FOR THE SERIES F
142 160 240 330 25 78 114 610 1000
$W
S
e
r
i
e
s
F
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/9
S
lo
p
e
=
1
/9
S
lo
p
e
=
1
/7
S
lo
p
e
=
1
/6
S
l
o
p
e
=
4
/
5
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/1
1
18
9
332 CHAPTER 18 COMPLEX STRUCTURES
We can draw the exit diagram for Subco’s stake as shown in Exhibit 18-11. We can
read this diagram as
Partial valuation for Subco’s stake
51=3 Ã Cð78Þ 21=21 Ã Cð114Þ 24=63 Ã Cð142Þ 21=45 Ã Cð160Þ 11=45 Ã Cð240Þ
21=45 Ã Cð330Þ 14 Ã BCð610Þ 172 Ã BCð1; 000Þ 14=55 Ã BCð1; 000Þ:
ð18:29Þ
EXHIBIT 18-11
EXIT DIAGRAM FOR THE SUBCO STAKE
142 160 240 330 78 114 610 1000
$W
S
u
b
c
o
72
4
S
lo
p
e
=
1
/5
S
lo
p
e
=
3
/1
1
S
lo
p
e
=
1
/5
S
lo
p
e
=
1
/5
S
lope = 2/9
S
lo
p
e
=
2
/9
S
lope =
2/7
S
lo
p
e
=
1
/3
EXHIBIT 18-10
EXIT DIAGRAM FOR THE MANAGEMENT CARVE-OUT
50
$W
M
a
n
a
g
e
m
e
n
t
c
a
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-
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/
5
18.3 A COMPLEX EXAMPLE 333
Under base-case assumptions and the IV
post
found in part (a), we can use FLEX to
compute the implied value of this stake as $31.62M.
’
SUMMARY
The option-pricing approach to partial valuation allows us to estimate valuations for virtually
all VC structures. In previous chapters, we derived solutions for structures with the standard
VC securities of RP, CP, PCP, PCPC, and common stock. These structures can be valued
using the prepackaged routines in the AUTO Calculator of VCV. In some cases, however, the
transaction structures can contain unique components that cannot easily be automated. In this
chapter, we demonstrated how to use the techniques of Part III to draw exit diagrams for
these complex structures and then to value these structures using the FLEX Calculator of
VCV. Examples of such complex securities include management carve-outs (where managers
share in exit proceeds with the preferred investors), deals with suppliers or service providers,
or incentives included as part of a merger.
KEY TERMS
Management carve-out
EXERCISES
18.1 Newco has received four rounds of investments (Series A, B, C, and D) for a total of
50M shares of CP plus 10M shares of common claimed by the employees. After the Series D
investment, Newco falls on hard times. After searching hard for new ?nancing, the investors
?nally agree to $10M Series E investment with Vulture Ventures (VV) for 40M shares of CP
and a 2X liquidation preference. As part of this agreement, all previous investors (Series A
through Series D) give up all their preferred rights and are converted to common stock, so the
capital structure of Newco is now 60M shares of common 1the Series E CP. As part of
the investment, Vulture creates a carve-out: management will receive 20 percent of all exit
proceeds, with a value of this carve-out capped at $5M. Vulture Ventures has $250M of
committed capital, $50M of lifetime fees, and 20 percent carried interest.
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case
assumptions.
334 CHAPTER 18 COMPLEX STRUCTURES
18.2 We use the same setup as in Exercise 18.1, but this time with a different structure for
the management carve-out. Now, following the $10M Series E investment from Vulcan
Ventures (40M shares of CP with a 2X liquidation preference), management is promised the
following incentives: If Newco has an exit of at least $40M, then the employees will receive
$5M from these proceeds. If Newco has an exit of at least $60M, then the employees will
receive an additional $5M from these proceeds. The earlier investors have 50M shares of
common, and the employees have claims on a further 10M shares.
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case
assumptions.
18.3 EBV makes a $5M Series A investment in Newco for 5M shares of CP. The employees
of Newco have claims on 10M shares of common stock. At the same time as this transaction,
Newco enters into a transaction with Techco to obtain licenses for some Techco patents. As
consideration for providing these licenses, Techco receives an option to purchase 10M shares
of common stock for $1.00 a share, but this option can only be exercised on an exit above
$100M. (Assume that this $100M would be adjusted for any future dilution, so that the
threshold is effective for the proceeds owed to the current shareholders.) Newco is aware of
the deal with Techco at the time that they make their Series A investment.
(a) Draw and read the exit diagrams for Techco and for the Series A.
(b) Compute the breakeven valuation for the Series A investment under base-case
assumptions.
(c) Compute the implied valuation for Techco’s stake under base-case assumptions.
18.4 Talltree has just made a Series F investment in Newco. The details of the Series F and
all prior rounds are given below.
Series A: 10M shares of CP ($5M APP)
Series B: 10M shares of CP ($8M APP)
Series C: 10M shares of CP ($10M APP and a 2X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 4X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($12M APP).
Series F: 10M shares of PCP ($20M APP) with a QPO at $6 per share.
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. In the event of a liquidation, the preferred stock is
redeemed in reverse order of investment (i.e., the Series F has a preference to the Series E,
which has a preference to the Series D, and so forth). In addition to these investors, the
employees have claims on 10M shares of common stock.
Now, we add two other features to this capital structure. First, the investors create a
management carve-out for 10 percent of the ?rst $50M in exit proceeds. Second, Newco
EXERCISES 335
acquires a smaller competitor, Subco, with the owners of Subco receiving 10M shares of
common stock, with a further payment of 20M shares of common stock if the merged
company has an exit exceeding $805M.
(a) Compute the breakeven valuation for the Series F under base-case assumptions.
(b) Given this breakeven valuation, compute the implied valuation for the management
carve-out.
(c) Given this breakeven valuation, compute the implied valuation for Subco’s stake.
336 CHAPTER 18 COMPLEX STRUCTURES
PART IV
THE FINANCE OF
INNOVATION
337
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CHAPTER 19
R&D FINANCE
RESEARCH AND development (R&D) is critical for economic growth and
improvements in human health and welfare. Indeed, human civilization owes its
existence to prehistoric R&D activity. Some early humans sacri?ced productive
labor time to tinker with toolmaking “technology”, experiment with different forms
of agricultural cultivation, and devise alphabets. All these activities would be
classi?ed today as R&D, which in its of?cial international de?nition “comprises
creative work undertaken on a systematic basis in order to increase the stock of
knowledge, including knowledge of man, culture, and society, and the use of this
stock of knowledge to devise new applications”.
1
In the United States, R&D investment is between $300B and $400B per year
and comprises approximately 2.7 percent of GDP. Because total VC investment has
averaged about $20B per year since 2002, it is clear that the majority of R&D
spending must come from other sources. In Section 19.1, we discuss these sources
and provide data on geographic and sectoral patterns of R&D investment. In this
discussion, we rely on statistics published by the National Science Foundation (NSF)
in their annual reports on worldwide and U.S. R&D. In Section 19.2, we introduce
two R&D examples—a drug development project and fuel cell development pro-
ject—that will serve as touchstones for the remaining chapters of the book. In Section
19.3, we describe the advantages and disadvantages of the various methods to ?nance
such projects. Section 19.4 describes the organization of the remaining chapters and
introduces the tools necessary for the valuation of complex R&D projects.
19.1 R&D AROUND THE WORLD
Worldwide R&D spending is concentrated in developed countries. Exhibit 19-1
shows the distribution of R&D spending for select countries tracked by the
1
This is the of?cial de?nition used by the OECD, as quoted in NSF (2005), p. 7.
339
Organization for Economic Co-operation and Development (OECD) in 2007, the
most recent year with data for all surveyed countries in the most recent NSF
publication. The 30 OECD member countries include all developed economies in
the world and some of the developing economies; Israel, Russia, and China are not
yet member countries of OECD as of the writing of this book.
As shown in the exhibit, the United States has the most R&D among these
developed countries, but the patterns are less skewed than they are for VC spending
(as seen in Chapter 6). Most of these countries spend between 1 and 3 percent of
GDP on R&D, while Japan and Israel spend higher percentages. Most developing
countries spend considerably less, both in absolute terms and as a percentage of
domestic GDP. Exhibit 19-2 tabulates R&D as a percentage of GDP for a broad
range of countries.
Exhibit 19-2 illustrates the strong emphasis on R&D in both Asian and
Nordic countries—it is no accident that these countries have their fair share of high-
technology industries. Low R&D percentages in developed countries (e.g., Spain
and Italy) do not bode well for the long-run competitiveness of these economies.
On the other hand, the low R&D percentages in many developing countries is
probably less of a problem, as these economies can still grow rapidly through
technology transfer from richer nations; inexpensive labor provides incentives for
companies to set up operations in developing countries and to bring advanced
technology with them. For example, while India and Brazil (part of BRIC) are
missing from this OECD survey, UNESCO (2007) reports that their R&D share of
GDP was between 0.5 and 1 percent.
EXHIBIT 19-1
R&D SPENDING IN SELECT COUNTRIES IN 2007
Total OECD 886.3
U.S. 368.8
Japan 147.8
Germany 71.9
France 43.2
UK 38.9
Italy 19.7
Canada
a
23.8
Russia 23.5
China 102.3
Israel 8.8
Figures in PPP $billions.
a
The Canadian statistics is from 2008.
Source: NSF (2010), p. 8.
340 CHAPTER 19 R&D FINANCE
We turn next to the distribution of R&D activity by funding source, type of
R&D organization, and industry. In these exhibits, we focus on data from the United
States, for which we have the longest time series of data. In the United States, the vast
majority of R&Dis funded by either the federal government or by industry. Fifty years
ago the federal government was the main provider of R&D funds; around 1980,
private industry became the main provider. In 2008, the latest year for which the NSF
data is available, industry provided 67 percent of all R&D funding, the federal gov-
ernment provided 26 percent, universities and colleges provided 3 percent, and other
nonpro?t sources provided the remainder. Exhibit 19-3 illustrates these trends, with
spending by source, indexed to in?ation using constant 2000 dollars.
EXHIBIT 19-2
R&D SHARE OF GDP, MOST RECENT YEAR, 2004À2008
Region/country/economy RD/GDP (%) Region/country/economy RD/GDP (%)
North America Central and Eastern Europe
United States (2007) 2.68 Russian Federation (2007) 1.12
Canada (2008) 1.82 Turkey (2007) 0.71
Latin America and Caribbean Czech Republic (2007) 1.54
Mexico (2005) 0.46 Poland (2007) 0.57
Argentina (2007) 0.51 Hungary (2007) 0.97
Western Europe Romania (2007) 0.53
Germany (2007) 2.54 Slovenia (2007) 1.53
France (2007) 2.08 Slovak Republic (2007) 0.46
United Kingdom (2007) 1.79 East, South, West Asia
Italy (2006) 1.13 Japan (2007) 3.44
Spain (2007) 1.27 China (2007) 1.49
Sweden (2007) 3.60 South Korea (2007) 3.47
Netherlands (2007) 1.70 Taiwan (2007) 2.63
Austria (2008) 2.66 Singapore (2007) 2.61
Switzerland (2004) 2.90 Paci?c
Belgium (2007) 1.87 Australia (2006) 2.01
Finland (2008) 3.46 New Zealand (2007) 1.20
Denmark (2007) 2.55 Africa and Middle East
Norway (2007) 1.64 Israel (2007) 4.68
Ireland (2008) 1.45 South Africa (2005) 0.92
Portugal (2007) 1.18 Selected country group
Greece (2007) 0.58 OECD (2007) 2.29
Luxembourg (2007) 1.63 European Union-27 (2007) 1.77
Iceland (2008) 2.76 G-7 countries (2007) 2.53
Source: NSF (2010), p. 8.
19.1 R&D AROUND THE WORLD 341
Since 1953, in?ation-adjusted R&D spending has increased more than eleven-
fold. Federal spending on R&D has been dominated by defense spending since the
beginningof the ColdWar; in 2003, the most recent year inwhichsuchdata is available,
the Department of Defense represents nearly half of the federal R&D budget. The
largest other component of the federal R&D budget is the National Institutes of
Health—a unit of the Department of Health and Human Services—which represents
about one-quarter of the total. The cycles of federal R&D can mostly be attributed to
corresponding cycles in defense spending, most recently for bioterrorism research.
Exhibit 19-3 tells us where the money came from, but not where the money was
spent. For example, in 2008, although the federal government provided 26 percent of
R&D funding, it only performed about 11 percent of this work itself. The other 15
percent was paidout touniversities andtoindustry. Exhibit 19-4illustrates the difference
between the source of funds and the actual performance of R&D. The largest bene?ciary
of federal spending is the academic sector, especially those large universities with
medical centers. Industry also receives a considerable transfer from the federal gov-
ernment, but the vast majority of that spending is for defense-related R&D projects.
Thus far, we have discussed R&D as one broad class of activities. It is also
informative to break R&D into three types: basic research, applied research, and
development. The National Science Foundation’s de?nitions for these three cate-
gories are given in Exhibit 19-5.
Of the $398B of R&D performed in the United States in 2008, approximately
17 percent was basic research, 22 percent was applied research, and 60 percent was
EXHIBIT 19-3
U.S. R&D FUNDING BY SOURCE (IN $B OF 2000 DOLLARS)
350
300
250
200
150
100
50
0
1
9
5
3
1
9
5
5
1
9
5
7
1
9
5
9
1
9
6
1
1
9
6
3
1
9
6
5
1
9
6
7
1
9
6
9
1
9
7
1
1
9
7
3
1
9
7
5
1
9
7
7
1
9
7
9
1
9
8
1
1
9
8
3
1
9
8
5
1
9
8
7
1
9
8
9
1
9
9
1
1
9
9
3
1
9
9
5
1
9
9
7
1
9
9
9
2
0
0
1
2
0
0
3
2
0
0
5
2
0
0
7
$B
Business
Federal government
Other
Total
Source: NSF (2010), p. 5.
342 CHAPTER 19 R&D FINANCE
development. In any R&D project, the basic research must be performed before the
applied research, which must be performed before development. Although some
companies will perform all three steps themselves, it is also common for each step
to take place at a different institution. For example, whereas universities performed
only 13 percent of all R&D in the United States in 2008, they focus almost
EXHIBIT 19-4
R&D EXPENDITURE BY SOURCE AND PERFORMER, 2008
Business Federal
government
Other Academic
80%
70%
60%
50%
40%
30%
20%
10%
0%
Source of funds
Performance of funds
Source: NSF (2010), p. 4.
EXHIBIT 19-5
R&D DEFINITIONS FROM THE NSF
Basic research: The objective of basic research is to gain more comprehensive knowledge or
understanding of the subject under study without speci?c applications in mind. In industry,
basic research is de?ned as research that advances scienti?c knowledge but does not have
speci?c immediate commercial objectives, although it may be performed in ?elds of present
or potential commercial interest.
Applied research: The objective of applied research is to gain the knowledge or under-
standing to meet a speci?c, recognized need. In industry, applied research includes
investigations to discover new scienti?c knowledge that has speci?c commercial objectives
with respect to products, processes, or services.
Development: Development is the systematic use of the knowledge directed toward the
production of useful materials, devices, systems, or methods, including the design and
development of prototypes and processes.
Source: National Science Foundation (2005), p. 7.
19.1 R&D AROUND THE WORLD 343
exclusively on basic research: universities performed about 56 percent of all basic
research in the United States in 2008, with the results broadly disseminated in
academic journals. These results can then provide the background for applied
research and development done by industry.
Exhibit 19-6 provides the breakdown of R&D activity across broad industry
groups.
The exhibit gives the R&D totals for all industry groups and their subgroup
industries that have at least $5B in R&D. The industry group with the highest R&D
by far is “computers and electronic products”. The other manufacturing groups with
EXHIBIT 19-6
R&D BY INDUSTRY AND INDUSTRY GROUP, 2007 IN $BILLIONS
Industry
All
R&D Federal
Company
and other
All industries 269.3 26.6 242.7
Manufacturing industries 187.5 18.2 169.3
Chemicals D D 55.3
Pharmaceuticals and medicines D D 47.6
Machinery 9.9 0.1 9.8
Computer and electronic products 58.6 8.8 49.8
Communications equipment 11.7 0.2 11.4
Semiconductor and other electronic
components
18.7 0.4 18.3
Navigational, measuring, electromedical,
and control instruments
20.4 8.2 12.3
Electrical equipment, appliances, and
components
2.7 0.1 2.6
Transportation equipment D D 31.0
Nonmanufacturing industries 81.8 8.4 73.4
Information D D 28.8
Publishing, including software 20.9 0.0 20.9
Telecommunications D D 3.1
Internet service and data processing
providers
D D 4.2
Professional, scienti?c, and technical
services
40.5 7.6 32.9
Computer systems design and related
services
14.4 0.8 13.6
Scienti?c R&D services 16.8 4.8 12.0
D 5 suppressed to avoid disclosure of con?dential information.
Source: NSF (2009), p. 3.
344 CHAPTER 19 R&D FINANCE
more than $5B in R&D are “transportation equipment”, “machinery”, “electrical
equipment”, and “chemicals”, the latter of which is dominated by the pharma-
ceutical industry.
When the NSF ?rst began gathering R&D statistics, virtually all R&D was
performed by manufacturing ?rms. Over time, with the increased role of service
industries in the U.S. economy, a substantial share of R&D has moved to non-
manufacturing companies. In particular, the high R&D in the “professional, sci-
enti?c, and technical services” group is illustrative of large outsourcing trends in
the U.S. economy—in this case, the outsourcing of R&D to specialized research
organizations. This outsourcing is particularly prominent in the pharmaceutical and
computer industries. Another nonmanufacturing group with more than $5B in R&D
is “Information”, which is dominated by the software industry, but also includes
“Telecommunications” and “Internet service and data processing providers”. These
two categories include both wired and wireless telecommunications carriers,
satellite service providers, and web search portals such as Google and Yahoo!.
19.2 TWO TOUCHSTONES
In this section, we discuss two prototypical projects: drug development (Section
19.2.1) and energy innovation (19.2.2). Because we will return to these projects
frequently in the following chapters, we call them our “touchstones”.
19.2.1 Drug Development
Our ?rst example is drug development by a pharmaceutical company. The phar-
maceutical industry is one of the largest industries in the world in terms of sales,
pro?ts, market capitalization, and R&D. For our purposes, their R&D projects are
particularly interesting, because drug development is carefully regulated by
government agencies. Because of this regulation, drug companies must take their
R&D projects through well-de?ned stages. These stages provide a framework for
modeling the investment decisions. In the United States, the principal regulator is
the Food and Drug Administration (FDA), and the stages are preclinical, Phase I,
Phase II, Phase III, and FDA approval. Here, preclinical refers to all activities
that precede testing in humans. Testing in humans—which includes Phases I, II,
and III—is collectively known as clinical trials or human trials. Once all clinical
trials have been completed, the data is submitted to the FDA, who makes the ?nal
decision allowing (or forbidding) sales to the public.
Typically, scientists work for many years before deciding on a speci?c
compound for testing. During these early years, they use a variety of techniques to
identify candidate compounds; then they screen these compounds in the laboratory,
by using computer models, and in a progression of animals with increasing simi-
larity to humans. All these activities are classi?ed as preclinical. In this preclinical
testing, the researchers are attempting to estimate the potential ef?cacy and side
19.2 TWO TOUCHSTONES 345
effects of the drug. Although all these preclinical activities are costly, the costs
increase substantially once a compound proceeds to clinical trials.
To better understand the stages of a clinical trial, we consider a prototypical
drug development project by Drugco for Newdrug, a chemical compound designed
to treat complications of diabetes. Before any human trials can begin, Drugco must
?le an Investigational New Drug (IND) application with the FDA. If the FDA
accepts the IND, then Phase I trials can begin. In Phase I trials, Newdrug is given to
a small number of healthy volunteers—those without diabetes or any other serious
medical condition. Because Phase I trials take place in healthy subjects, it is not
possible to assess the ef?cacy of the drug. Instead, the purpose of Phase I trials is to
assess the safety of the treatment and to establish some baselines of how the drug is
metabolized in humans. On average, Phase I trials cost about $15M and take one
year to complete.
2
If Phase I trials are “successful”, then Drugco may proceed to Phase II. What
determines success? Obviously, the drug must appear relatively safe. Virtually all
drugs have some side effects, but Drugco must carefully weigh the potential side
effects against its estimated ef?cacy before deciding whether to proceed. While the
FDA will sometimes approve drugs with serious side effects, this is only likely
when the drug ?lls a serious medical need. In addition to safety, Drugco may also
consider any changes in the business conditions related to Newdrug. A lot can
happen in the one year it takes to complete Phase I trials. Drugco would be par-
ticularly aware of any alternative diabetes treatments coming to market and of any
changes in the willingness of insurance companies and government agencies to pay
for diabetes drugs.
Phase II trials are the ?rst opportunity for Drugco to test the ef?cacy of
Newdrug in diabetes patients. On average, these tests use several hundred patients,
take two years, and cost $25M. During these trials, the drug is assessed for both
ef?cacy and side effects. It is important to note that these trials must conform to the
highest standards of medical testing: double-blind randomized trials. In these trials,
some patients receive the actual drug, whereas others receive either an identical-
looking but inactive placebo, or an existing standard treatment. Here, “double-
blind” means that neither the patient nor the treating physician is aware of whether
the patient has received the actual drug or a placebo or standard treatment. This is
important, as some researchers can behave differently toward patients depending on
whether they are given treatments or placebos.
After Phase II, Drugco must decide whether to proceed to Phase III. On
average, Phase III trials take three years and cost $85M. These trials typically
include thousands of patients across several different medical centers. The objec-
tive of this phase is to assess de?nitively the ef?cacy of the new drug compared
with the current “gold standard” treatment for the indication. At the end of Phase III
trials, Drugco will submit all their data to the FDA. In making an approval decision,
2
Cost estimates for clinical trials are from DiMasi et al. (2003).
346 CHAPTER 19 R&D FINANCE
the FDA relies heavily on advisory panels of specialized physicians, who weigh the
potential costs (side effects) and bene?ts (ef?cacy). The FDA would typically take
alternative treatments (or lack thereof) into account when considering the potential
bene?ts of the drug. The FDA approval process takes an average of 18 months
following the completion of Phase III.
Exhibit 19-7 gives a graphical depiction of the Newco project. The exhibit
shows three different types of risks: technical risks, business risks, and compe-
titive risks. Any or all of these risks may play a role at any point in the project.
Technical risks are the most straightforward. For Newdrug, the technical risks are
“Will this drug work?” (ef?cacy) and “Will this drug harm patients?” (side effects).
These technical risks exist at every stage—it is even possible to learn of new side
effects long after a drug has been approved. For valuation purposes, technical risks
are often the easiest to model. There are two reasons for this ease of modeling.
First, as narrowly de?ned scienti?c or engineering projects, it is often possible for
project scientists to accurately estimate the probabilities of success. Scientists, with
long experience and a familiarity with probability and statistics, can provide ana-
lysts with well-informed estimates. Second, as we ?rst studied in Chapter 4,
technical risks often have a zero beta (i.e., no correlation with the market). In this
case, we can use the risk-free rate as the discount rate and do not have to deal with
the complexities of computing a risk-adjusted discount rate. The modeling of
technical risks can often be accomplished using Monte Carlo simulation, a topic to
be covered in Chapter 20.
EXHIBIT 19-7
DRUG DEVELOPMENT
COMPETITIVE RISKS BUSINESS RISKS
Phase I
Safety tests
on healthy
volunteers
Phase II
Medium-scale
efficacy and safety
tests
Phase III
Large-scale
efficacy and safety
tests
FDA Approval?
Based on efficacy
and safety
First to market?
Better
alternative? Pricing Reimbursement
One year avg Two years avg Three years avg 18 months avg
Efficacy and safety
affect market size, share, and growth
TECHNICAL RISKS
19.2 TWO TOUCHSTONES 347
Business risks can take many forms. In general, a business risk relates to changes
in consumer preferences. For example, the demand for Newdrug would be affected by
the performance of the overall economy, because the availability of health insurance
and consumers’ willingness to pay out of pocket would both be affected by the strength
of the labor market. Also, because diabetes strikes disproportionately among older
patients, it is likely that Medicare—government-run health insurance for citizens over
the age of 65—would be a major customer. Thus, Drugco needs to worry about the
pressure of federal budgets. These types of risks would certainly have positive market
betas and would require risk-adjusted discount rates. The computationof these discount
rates requires careful modeling for the timing of various investment decisions. These
models often use decision trees and real-options analysis (to be studied in Chapter 21),
sometimes aided by the use of binomial trees (to be studied in Chapter 22).
Competitive risks relate to the behavior of other companies. For the devel-
opment of Newdrug, Drugco needs to worry about the competitive responses of
other drug companies in the diabetes business. In response to Newdrug, competitors
may accelerate (or decelerate) their own diabetes drug projects. Even if these
competitors do not develop new drugs, they may alter the pricing of existing drugs,
?le lawsuits claiming the infringement of some intellectual property, or increase
their sales efforts on existing drugs. Some of these activities depend on the state of
the economy and hence would carry positive betas and require the calculation
of risk-adjusted discount rates. In any case, competitive risks require careful
modeling using game theory, a topic covered in Chapter 23.
19.2.2 Energy Innovation
Fuelco is considering several development projects using its patented Newcell
technology. Project A is a government contract that requires competitive bidding
against other companies. Project B is a product to be sold to automotive manu-
facturers for eventual resale in consumer projects. Project C is product to be sold
directly to consumers. The technology for Project C requires a successful com-
pletion of Projects A and B as inputs. Exhibit 19-8 sketches the timeline and risks
for these projects.
In the shorthand representation of Exhibit 19-8, we see that each of the three
projects has technical risks, with Project C effectively incorporating technical risks
from Projects A and B in addition to direct risks from Project C. All three projects
may have competitive risks. These risks are clearest for Project A, which must
compete for a government contract against other companies. Business risks may be
largely absent from Project A (if we are willing to believe that the government will
follow through on the contract regardless of economic conditions), but these
business risks are present for Projects B and C. In some cases, long-term contracts
with potential customers can alleviate business risk in the short run (particularly for
Project B), but in the long run it is dif?cult for energy projects to completely
eliminate business risks. For Fuelco, the main business risk is the price of crude oil.
348 CHAPTER 19 R&D FINANCE
If oil is relatively expensive, then there is more scope for alternative energy projects
such as Newcell.
In the Newdrug example of the previous section, the regulatory hurdles
provide us with a clear framework for modeling. Here, we have no such luck. To
model Fuelco’s decisions, we will need to make some informed assumptions about
the length of time for various development steps, the probability of success for
these steps, and the potential market size for each project. Although the Newdrug
problem is relatively tidy, the Newcell problem is much messier and much more
representative of “typical” R&D projects.
19.3 HOW IS R&D FINANCED?
Return now to our ?rst touchstone, Drugco’s R&D project for Newdrug. Suppose
Drugco estimates that the Newdrug project will cost $100M to reach FDA approval.
What options does Drugco have to ?nance this project? In this section, we consider the
following options: (1) government, (2) internal corporate funds, (3) banks, (4) public
debt markets, (5) public equity markets, (6) venture capital, and (7) strategic partners.
1. Government. In the United States, the federal government funds about
25 percent of all R&D. This total funding of $104B in 2008 was performed at
federal, academic, and industrial locations. Although nearly $14B of this
$104B was used for development-stage R&D in industry, the majority of that
$14B was for defense-related projects. Thus, unless Newdrug is believed
to have some biodefense function, it is unlikely that Drugco will be able to
?nance much of their required $100M from direct government sources.
EXHIBIT 19-8
FUEL CELL PROJECT
1 Year Total
Project A
(government contract)
Technical risk A (does tech A work?)
Competitive risk A (do we win the bid?)
Project B
(sold to auto manufacturers)
Technical risk B (does tech B work?)
Business risk B (what happens to oil prices?)
Project C
(sold to consumers)
Technical risk A, B, and C (do tech A,B,C all work?)
Business risk C (what happens to oil prices?)
Competitive risk C (what do other companies do?)
Technical risk is uncorrelated across the three projects
Business risk (oil prices) is correlated across B and C
Competitive risk is uncorrelated across A and C
19.3 HOW IS R&D FINANCED? 349
Nevertheless, although the government is unlikely to be much help in
the direct ?nancing of the Newdrug project, Drugco may receive a sig-
ni?cant bene?t from the tax system. The ?rst bene?t is that, unlike other
investments, R&D spending is treated as an expense for tax purposes, so that
with an effective federal tax rate of 35 percent, (pro?table) companies can
recover more than one-third of their costs when they ?le their taxes. Fur-
thermore, the United States—like most developed countries—has an R&D
tax credit. A $1 credit is more valuable than a $1 deduction, because a $1
deduction only gives a company 35 cents. The federal Research and
Experimentation Tax Credit was ?rst introduced in 1981 and provided
companies with a credit of 25 percent of “incremental” R&D costs, where
these incremental costs are de?ned as Quali?ed Research Expenses
(QREs). Although the de?nition of QREs is complex and often contentious,
on average they comprise about two-thirds of all R&D costs.
From 1981 to 2009, the “temporary” R&D tax credit was extended 14
times, and the credit grew more complex and slightly less generous. In its
most recent form, the typical credit gives companies 20 percent of their
QREs. On December 31, 2009, the latest version of the R&D tax credit
expired. As of this writing (early 2010), a bill extending the credit through
the end of 2010 has passed the House, and is being considered at the Senate
(where, if history is any indication, it will probably pass again). In addition
to the federal tax credit, many states and municipalities have passed their
own R&D tax credits, although total expenditures for these local credits are
far lower than the federal version.
2. Internal corporate funds. A pro?table company can ?nance R&D from its
own positive cash ?ows. Although $100M for Newdrug might seem like a
lot of money, it would only buy a small portion of the R&D at the largest
pharmaceutical companies. We do not have aggregate statistics to tell us the
percentage of R&D ?nanced by internal funds, but we can still draw some
inferences from the data. Exhibit 19-9 gives the size distribution of com-
panies in the United States, along with the R&D spending for each size
group.
We see from this data that more than half of all R&D spending is
made by those companies that have more than 10,000 employees. These
companies collectively employed nearly 10 million people in the United
States alone and had domestic sales of more than 4 trillion dollars in 2007.
Because it is dif?cult to sustain such large enterprises without pro?ts, it is
likely that a large portion of that R&D could be ?nanced by internal funds.
For smaller companies, we cannot be as sure about the availability of
internal funds. For example, the vast majority of publicly traded bio-
technology ?rms has fewer than 500 employees and has a negative cash
?ow. It is safe to assume that—at least for these money-losing companies—
internal funds will not be suf?cient to pay for a $100M project like
Newdrug.
350 CHAPTER 19 R&D FINANCE
3. Banks. In the United States, banks provide the majority of external capital
for small companies. In other developed countries, banks have a near-
monopoly on small-company ?nance. Nevertheless, banks are unlikely to
provide any signi?cant funds for a $100M project like Newdrug. Banks are
?nancial institutions that specialize in making loans backed by collateral
and a demonstrated ability to repay. A typical bank loan would allow a
pro?table manufacturer to invest in plant, property, or equipment. Such
loans rely on the manufacturer’s positive cash ?ow from other operations,
combined with the ability to seize the purchased assets in foreclosure. For
riskier loans, banks often turn to various government guarantees. In the
United States, the largest such programs are run by the Small Business
Administration, which effectively subsidizes loans for “small” companies.
Although such loans are certainly helpful for some development projects,
the maximum loan size is about $1M and would provide little help for
Drugco.
4. Public debt markets. Historically, public markets for corporate debt have
been able to take on projects that are either too large or too risky for an
individual bank. For example, it was European investment in publicly traded
bonds that largely ?nanced the expansion of railroads in the United States.
Although railroads may seem a staid industry today, it was a capital-hungry
and speculative industry in the middle of the nineteenth century. More than
EXHIBIT 19-9
R&D EXPENDITURE AND COMPANY SIZE IN 2007
Size of company
(number of employees) $B
5À24 $10.9
25À49 $7.9
50À99 $10.1
100À249 $13.4
250À499 $8.3
500À999 $14.3
1,000À4,999 $41.1
5,000À9,999 $22.7
10,000À24,999 $45.9
25,000 or more $94.8
Total $269.3
Source: NSF (2009), p. 2.
19.3 HOW IS R&D FINANCED? 351
100 years later, the public bond markets ?lled a ?nancing void for mezza-
nine debt in the large leveraged buyouts of the 1980s. These so-called junk
bonds, junior to bank debt in the capital structure, allowed some LBO
investors to purchase large companies with less than 10 percent of the deal
in equity. Fifteen years later, in the latest credit boom of 2005À2007, the
rapid growth of collateralized debt obligations (CDOs) and collateralized
loan obligations (CLOs) markets helped LBO ?rms to buy even larger
companies, though the debt-to-equity ratio was considerably lower this time
around.
Would public debt markets be willing to ?nance Drugco’s $100M
Newdrug project? It is highly unlikely. Although Newdrug is risky like old-
time railroads and new-age LBOs, it is unlike those projects in its inability
to pay interest in early years. When railroads were successful, they would
have revenues within a few years at most, and most LBOs are even quicker.
Newdrug, on the other hand, is expected to take between ?ve and seven
years before FDA approval is possible. Until that point, the project would
have costs but no revenues. To ?nance such a project would require zero-
coupon bonds, which accrue all interest until their expiration date. However,
a zero-coupon bond on a risky project would require a very high interest
rate. In this case, the bond would pay off zero if the project failed and would
give a large payout, far in the future, if the project succeeded. This sounds a
lot like equity! Indeed, the ?nancial instrument just described is almost the
de?nition of “equity capital”, which we turn to next.
5. Public equity markets. Without question, public equity markets ?nance a
signi?cant fraction of R&D. For evidence, one needs to look no further than
the biotechnology industry. There are currently about 350 publicly traded
biotechnology companies, which collectively have over $40B in sales.
Approximately one-third of these sales are plowed back into R&D. This
industry loses a lot of money: only about one-sixth of all biotech ?rms are
pro?table, and the collective losses for the industry have been between $10B
and $15B per year since 2000. Overall, the industry’s losses are about equal
to its R&D spending, and that money has to come from somewhere. Since
the founding of the industry in the 1970s, biotechnology ?rms have raised
about $150B, about 60 percent of which came from the public markets.
3
From this evidence, we can conclude that public equity markets might
make a dent in the $100M Newdrug project. Indeed, public markets are
capable of funding projects of this size, and many public biotech companies
can largely ?nance their drug development by issuing stock to the public.
For nonpublic companies, however, such issuance would require an IPO.
Historically, biotech companies usually must be in Phase III trials, or at least
3
All statistics on the biotechnology industry are from Burrill (2005).
352 CHAPTER 19 R&D FINANCE
far along in Phase II, before an IPO is possible. Outside the biotech
industry—except during the boom period of the late 1990s—companies
typically need to be pro?table before they can go public. Thus, if Fuelco
(Section 19.2.2) were not already public or pro?table, then it would be
dif?cult for it to use an IPO to raise funds for the fuel cell project.
Overall, public equity markets are an important source of capital for
R&D projects. Nevertheless, even with the other main sources discussed
earlier—governments and internal funds—there are still some ?nancing
gaps that need to be ?lled. In particular, applied research and the earliest
stages of development are ?nancing challenges for negative cash ?ow
companies.
6. Venture capital. Public equity markets have ?nanced approximately 60
percent of the $150B raised by the biotech industry; the other 40 percent
came from VCs. Readers of the previous 18 chapters will already know that
VC is an obvious source to ?ll the ?nancing gap for applied research and
early development-stage projects. Unfortunately for Drugco, many biotech
VCs are wary of investing in projects in Phase I trials. The low probability
of success coupled with large capital needs has pushed most VCs toward
projects at Phase II and beyond. Although some VCs do still invest in at
Phase I, projects like Newdrug face a dif?cult task in attracting VC
investment, and few VCs would be willing (or able) to support Newdrug
through the entire approval process. At some point, Drugco will need to
raise public equity or receive an investment from a larger company.
7. Large companies. If Drugco is a small company without signi?cant internal
funds or access to public markets, then the main alternative to VC is to form
a strategic alliance with a large drug company. Here, we use the term
strategic alliance to mean any long-term agreement between companies.
The most common strategic alliance in high-tech industries is an R&D
licensing agreement, also known simply as a license. In a typical licensing
agreement, the larger company pays the costs for an R&D project performed
by a smaller company in return for receiving some rights to the technology.
In addition to the direct R&D costs, the larger company often provides an
upfront payment at the time the deal is signed and milestone payments as
the project advances. If the larger company has received the rights to sell
products based on the technology, then the agreement would typically
include royalty payments as some fraction of these sales. Finally, in some
cases the larger company will make a direct investment in the smaller
company at the time of the deal.
Suppose that Drugco enters an R&D licensing agreement with Bigco
for the Newdrug project. Drugco expects to need $100M to pay for the
R&D. Bigco agrees to pay these R&D costs, plus a $50M upfront payment
and additional milestone payments of $25M if Newdrug makes it to
Phase II, $50M for Phase III, and $100M for FDA approval. In return,
19.3 HOW IS R&D FINANCED? 353
Bigco receives exclusive worldwide marketing rights for Newdrug, with a
10 percent royalty paid to Drugco on all sales. With this license, Bigco
would expect to pay a total of $100M+ $50M+ $25M+$50M+$100M
5$325M just to get Newdrug approved, plus the royalty on all sales.
Obviously, Bigco only enters this transaction if they believe that the NPV
for their share of the sales is worth this investment. Many deals of this size
or larger are signed every year in the pharmaceutical industry. Overall,
licensing deals are the most important source of ?nance for pharmaceutical
R&D at small companies.
Licensing deals can be both lucrative and complex, with many oppor-
tunities for ?nancial analysis and the use of option-pricing techniques. For
example, consider the following deal in 2005 between Anadys Pharmaceu-
ticals Inc. (the smaller company) and Novartis AG (the larger company):
Novartis gets the exclusive worldwide development, manufacturing, and
marketing rights to Anadys’s ANA975 and other [similar compounds] for
chronic hepatitis B and C viruses and other infectious diseases . . . .
Novartis will pay a $20M up-front license fee, $550M in regulatory and
commercial milestones for the development and marketing of ANA975,
including $10M payment upon a successful IND submission (it antici-
pates a mid-2005 ?ling). Novartis will provide funding for 80.5 percent
of the expenses associated with developing the lead candidate, with
Anadys funding 19.5 percent of the costs. Anadys has a co-promotion
option to keep 35 percent of the U.S. pro?ts if it pays that percentage of
the marketing costs. If Anadys declines the option, it will get royalties on
global sales of the resulting product. No equity was exchanged. (Source:
In Vivo, July/August 2005, p. 92)
This agreement poses several interesting problems for a ?nancial ana-
lyst. In addition to valuing the product conditional on FDA approval (this is
somewhat like a success-case exit valuation), it is necessary to estimate the
probabilities for achieving each milestone and to value the Anadys option to
pay marketing costs. Novartis must make all these estimates before agreeing to
this deal. Unlike leanly staffed VC ?rms, large companies like Novartis often
have specialized groups whose sole purpose is to value these deals. Such
groups are heavy users of the tools studied in the next ?ve chapters.
19.4 WHERE DO WE GO FROM HERE?
In this chapter, we gave brief descriptions of two examples of R&D projects: a
pharmaceutical project (drug development) and an energy project (fuel cell
development). The schematic exhibits that accompanied these descriptions,
354 CHAPTER 19 R&D FINANCE
Exhibits 19-7 and 19-8, summarize the types of risks involved, but do not give us
any speci?c models to analyze. In future chapters, we provide more structure for
these (and other) examples in specialized diagrams known as trees. The following
paragraph describes various types of trees that will be analyzed in the next ?ve
chapters. This description is only intended to provide a road map for Part IV—
readers are not expected to know how to de?ne or use any of these trees until after
they have been covered in the later chapters.
The simplest tree is an event tree, which we will study in Chapter 20. Event
trees are particularly useful for handling technical risks. Once a decision on a
project has been made, event trees help us to value that project. If, instead, we want
a tool to help us decide between different options, we use a decision tree, which
we introduce in Chapter 21. Decision trees are particularly helpful in dealing with
technical risks and business risks that are intertwined with future decisions, with
the trees showing us if any of the key decisions can be delayed until after these
risks have been resolved. Such delay often gives rise to real options, which we also
study in Chapter 21. Binomial trees, studied in Chapter 22, are a special case of
decision trees. In this special case, if we restrict the way that certain risks are
modeled, we can pack a large amount of information into a model. Binomial trees
are particularly useful for the valuation of options that provide some payoffs before
the expiration (or exit) date. In Chapter 23 we introduce game theory and game
trees, which allow us to model the actions of multiple decision makers in one
diagram. Game trees are helpful for modeling competitive risks such as technology
races or competitive bidding. Finally, in Chapter 24 we pull all these tools together
and solve full-blown models for the drug-development and energy-innovation
projects.
SUMMARY
Research and development (R&D) is about 2.7 percent of the U.S. economy and is the
primary driver of long-run economic growth. In the United States, almost two-thirds of R&D
is funded by corporations, with half of that spending occurring in large corporations that have
more than 10,000 employees. R&D investment decisions share many features with VC
investment decisions, with long time horizons, high failure rates, and business risks
embedded in a rapidly changing technological landscape. In this chapter we introduced two
prototypical R&D projects—one in drug development and one in energy innovation. Drug
development takes place in a highly regulated environment, which lends itself to structured
models with well-speci?ed data and milestones. The energy-innovation project is typical of
most other R&D projects, with little regulatory structure and many modeling decisions
necessary for the analyst.
In the previous chapters, we studied the VC industry in great detail. Although VC is an
important contributor to R&D projects at small companies, most R&D is ?nanced from other
sources, including internal cash ?ow, public equity markets, and strategic alliances. R&D
licensing agreements—a type of strategic alliance—play a particularly important role in the
funding of drug development R&D.
SUMMARY 355
KEY TERMS
Research and development
(R&D)
Basic research, applied
research, development
Preclinical, Phase I, Phase
II, Phase III, FDA
approval
Clinical trials
5human trials
Technical risks, business
risks, competitive risks
R&D tax credit
Qualified Research
Expenses (QREs)
Strategic alliance
R&D licensing agreement
5license
Upfront payments, mile-
stone payments, royalty
payments
Trees, event trees, decision
trees, binomial trees,
game trees
REFERENCES
Burrill & Company, 2005, Biotech 2005, Burrill & Company LLC, San Francisco, CA.
DiMasi, Joseph A., Ronald W. Hansen, and Henry G. Grabowski, “The Price of Innovation: New
Estimates of Drug Development Costs”, Journal of Health Economics 22, 151À185.
National Science Foundation, 2005, National Patterns of Research and Development Resources: 2003,
NSF 05À308, Brandon Shackleford, Arlington, VA.
National Science Foundation, 2008, National Patterns of R&D Resources: 2007 Date Update, NSF 08-
318, Mark Boroush, Arlington, VA.
National Science Foundation, 2009, Info Brief, NSF 09À316, Raymond M. Wolfe, Arlington, VA.
National Science Foundation, 2010, Info Brief, NSF 10À312, Mark Boroush, Arlington, VA.
UNESCO Institute for Statistics, 2007, A Global Perspective on Research and Development: Fact Sheet,
UIS/FS/07/05, available at www.uis.unesco.org.
356 CHAPTER 19 R&D FINANCE
CHAPTER 20
MONTE CARLO SIMULATION
IN MANY R&D projects, several random variables can affect the outcome.
To compute the NPVs of these projects, it is necessary to multiply the probability of
each outcome by its corresponding payoff. When many different risks intersect at
one time, this computation can be dif?cult or impossible. To solve this problem,
analysts often use computers to simulate thousands (or millions) of possible out-
comes and then estimate the NPV as the average of these simulated outcomes.
Because these computational methods are reminiscent of games of chance in Monte
Carlo, the most popular method is called Monte Carlo simulation.
In this chapter, we learn the concepts and mechanics behind these simula-
tions. In Section 20.1, we show how to represent uncertainty by using event trees,
and we demonstrate how to solve for the NPV of an event tree by Monte Carlo
simulation. The problems in Section 20.1 use simple discrete random variables
with two possible outcomes: “success” or “failure”. In Section 20.2, we introduce
continuous random variables and demonstrate how to use these variables in
Monte Carlo simulation. The examples in Section 20.1 and 20.2 are relatively
simple and, in fact, could be solved without using simulation. In Section 20.3, we
model a version of the Newdrug project from Chapter 19. In this model, there are
several independent sources of uncertainty, and simulation provides the fastest
route to a solution.
20.1 EVENT TREES
Drugco has just begun Phase III trials for Newdrug. Drugco’s scientists estimate
that the R&D has a 50 percent chance of success (5FDA approval), and Drugco
management estimates an NPV of $1B at the time of approval. If the drug fails,
then it would be worth nothing. The success of the drug will be learned over
the next three years, over which the discount rate is equal to the riskfree rate of
357
5 percent per year.
1
The total cost of R&D is $100M and must be paid at the
beginning of development. Exhibit 20-1 gives a graphical representation of this
information using an event tree.
The event tree uses circles to signify a risk node in the tree. In this case, the
risk node is followed by two possible branches. The success branch has a pro-
bability of 50 percent, leading to a terminal node with a payoff of $1B. The failure
branch has a probability of 50 percent, leading to a terminal node of $0. We can use
all the information in the tree to calculate the expected value of the terminal nodes
as 0.5 Ã $1B5$500M. Using a discount rate of 5 percent for three years, we can
compute the NPV of the new drug as
NPV50:5 Ã $1B=ð1:05Þ
3
2$100M5$331:9M: ð20:1Þ
This is about as easy as a valuation can get: one source of risk, two branches, and
a constant discount rate. For the next ?ve chapters we will take problems like this and
add complications. In many cases, these complications make it dif?cult to calculate
NPVs in simple equations like (20.1). In those cases, Monte Carlo simulation is
often the most ef?cient way to compute the NPV. In Monte Carlo simulation, the
1
Why the riskfree rate? Recall the Boxco versus Drugco example from Chapter 4: if the project only has
technical risk, then this risk can be diversi?ed away and has a zero beta. We discuss discount rates in
more detail in Chapter 21.
EXHIBIT 20-1
EVENT TREE FOR NEWDRUG
Phase III
$–100M
$1B
$0
0.5
0.5
FDA Failure
FDA Approval
3 years
358 CHAPTER 20 MONTE CARLO SIMULATION
analyst generates random numbers and “simulates” thousands of possible outcomes
for the event tree. Then, the average outcome is the expected value of the tree.
In our simple Newdrug tree, the only random variable is FDA approval of the
drug, which has a simple yes/no probability distribution. To simulate this dis-
tribution, we can imagine ?ipping a coin 10,000 times, with each “heads” ?ip
leading to FDA approval, and each “tails” ?ip leading to FDA failure. On average,
this process will give us 5,000 ?ips of heads, so the expected outcome will be the
same as Equation (20.1). To perform this randomization on a computer—a much
more ef?cient way to ?ip a coin—we can either use specialized simulation soft-
ware, or we can program the simulation ourselves using a general package like
Microsoft Excel.
For the next two examples in this chapter, we will show how to do the simu-
lation “the hard way” using Microsoft Excel. By doing some simple examples in
Excel, the reader can learn the intuition and mechanics behind the simulation
methods. For complex examples, programming everything in Excel becomes
unwieldy, and it is much more ef?cient to use a specialized package. In Appendix Cof
this book, we provide a brief users’ guide to Crystal Ball
s
, a popular simulation
program that works as an add-in to Excel. In that appendix, we also provide Crystal
Ball solutions for all the examples in this chapter.
To compute the NPV of Newdrug using Excel, we use the random number
function—the Excel command is “rand()”—to generate a random number between
0 and 1. Then, if this random number is less than or equal to 0.5, we classify
the outcome as FDA approval. If the outcome is greater than 0.5, we classify the
outcome as FDA failure.
Exhibit 20-2 displays the output for 10 draws of the simulation. In the
“Random Number” column, we type the Excel command “rand()”, which yields a
random number between 0 and 1. In the “FDA Approval” column, we use an if
EXHIBIT 20-2
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw Random number 5 rand() FDA approval? NPV
1 0.8172 0 2$100.00
2 0.8729 0 2$100.00
3 0.3396 1 $763.84
4 0.9276 0 2$100.00
5 0.0186 1 $763.84
6 0.6416 0 2$100.00
7 0.4539 1 $763.84
8 0.9188 0 2$100.00
9 0.2199 1 $763.84
10 0.3146 1 $763.84
20.1 EVENT TREES 359
statement: if (Random Number ,0.5, 1, 0), which yields the answer of one if FDA
approval occurs, and zero if it fails.
2
Finally, the NPV column computes the NPV as
FDA Approval à $1B/(105)
3
À $100M. To run multiple draws, we need only type
these formulas into the ?rst row and then copy this row down. (Thus, it is just as
easy to do 10,000 draws as it is to do 10.) The average of the “NPV” column is the
Monte Carlo estimation of the NPV. On average, we should get $331.9M, the same
answer as achieved from Equation (20.1).
Of course, real problems are rarely so simple. A slightly more complex
version of the problem would consider all three phases of the approval process. We
do this in the next example.
EXAMPLE 20.1
Drugco has just begun Phase I trials for Newdrug. Phase I takes one year and costs
$10M. Drugco’s scientists estimate that the R&D has a 50 percent chance of successfully com-
pleting Phase I and moving toPhase II. Phase II takes one year and costs $30M. If Newdrug enters
Phase II, the scientists estimate a 40 percent chance of successfully completing Phase II and
movingtoPhase III. Phase III takes three years (including the time waiting for FDAapproval) and
costs $60M. If Newdrug enters Phase III, the scientists estimate a 50 percent chance of success
(5FDAapproval). Drugco management estimates an NPVof $1B at the time of approval. If the
drug fails, then it would be worth nothing. The discount rate is equal to the risk-free rate of
5 percent per year. All development costs must be paid at the beginning of the respective phase.
Problems
(a) Draw the event tree for the Newdrug project.
(b) Find and solve the formula for the NPV of the Newdrug project.
(c) Build a Monte Carlo simulation for Newdrug and con?rm the same (average) NPV
solution as obtained in part (b).
Solutions
(a) Given the information in the example, we can drawthe event tree as shown in Exhibit 20-3.
(b) In Exhibit 20-3, there is a different probability of success for each stage. Each risk node
in the tree is given a number (1 to 3 in the tree) to help us keep track of things. At any node,
the failure branch ends the project and has a payoff of zero. Only the terminal node with $1B
has a positive payoff. To ?nd the NPV of the project, we must compute the probability of
reaching each node in the tree, and then discount the expected payoffs of those nodes by the
appropriate number of years. Thus, the NPV for Node 1 is À$10M, and
NPV of Node 2 5ð0:5 Ã 2$30MÞ=1:05 5 2$14:3M; ð20:2Þ
NPV of Node 3 5ð0:5 Ã 0:4 Ã 2$60MÞ=ð1:05Þ
2
5 2$10:9M; ð20:3Þ
NPV of terminal node of $1B5ð0:5 Ã 0:4 Ã 0:5 Ã $1BÞ=ð1:05Þ
5
5$78:4M: ð20:4Þ
2
In the actual Excel spreadsheet, we would need to use an exact cell address instead of “random vari-
able”. Similarly, other examples in this chapter will use variable names instead of cell addresses.
360 CHAPTER 20 MONTE CARLO SIMULATION
So the NPV of the whole project is
NPV of project 5$78:4M2$10M2$14:3M2$10:9M5$43:1M: ð20:5Þ
(c) To do a Monte Carlo simulation, we de?ne a random variable in Excel for each risk node
and then combine these random variables with the costs of development and terminal values,
just as in Equation (20.4). Exhibit 20-4 demonstrates an example of this simulation.
In Exhibit 20-4, Phase I success depends only on the outcome of the ?rst random
number [labeled as (1) in the top row of the table], Phase II success depends on the outcome of
EXHIBIT 20-4
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw
(1)
rand()
Phase I
success?
(2)
rand()
Phase II
success?
(3)
rand()
FDA
approval? NPV
1 0.4127 1 0.0373 1 0.7718 0 2$92.99
2 0.8501 0 0.7807 0 0.0544 0 2$10.00
3 0.9134 0 0.8742 0 0.9967 0 2$10.00
4 0.7750 0 0.6548 0 0.2297 0 2$10.00
5 0.9448 0 0.4999 0 0.5549 0 2$10.00
6 0.9625 0 0.5304 0 0.0089 0 2$10.00
7 0.0766 1 0.3117 1 0.5861 0 2$92.99
8 0.1479 1 0.7106 0 0.4112 0 2$38.57
9 0.9461 0 0.3570 0 0.0422 0 2$10.00
10 0.1802 1 0.0104 1 0.0674 1 $690.53
EXHIBIT 20-3
EVENT TREE WITH THREE RISK NODES
Phase I
$–10M
Phase II
–$30M
Phase I
success
Phase I
Failure
Phase II
Failure
FDA
Failure
Phase II
success
Phase III
$–60M
FDA Approval
Year 0 Year 1 Year 2 Year 5
0.5
0.5 0.5 0.6
0.4 0.5
$1B
$0 $0 $0
1 2 3
20.1 EVENT TREES 361
both Phase I and Phase II [labeled as (2) in the top row], and FDA approval requires Phase I
success, Phase II success, plus the outcome of Phase III [labeled as (3) in the top row].
The average estimate from this simulation is $43.1M, the same answer as we obtained
in part (b). ’
20.2 SIMULATION WITH CONTINUOUS
PROBABILITY DISTRIBUTIONS
Example 20.1 used discrete random variables, where the different outcomes can
be separated when plotted on a line, like a “1” for success and a “0” for failure. In
many applications, it is necessary to use continuous random variables, where the
different outcomes have no gaps when plotted on a line. Continuous variables
have an in?nite number of possible outcomes, where the relative likelihoods of
these outcomes is represented as a probability density function (pdf) and drawn as
two-dimensional curve.
The simplest type of continuous distribution is the uniform distribution. If a
variable x is distributed as a uniform distribution with a minimum point of a and
a maximum point of b, then we use the shorthand notation x B U [a, b], where
“B” stands for “is distributed as”. We write the pdf, f(x), as
Uða; bÞ : f ðxÞ 51=ðb 2aÞ: ð20:6Þ
Exhibit 20-5 illustrates this pdf.
For Monte Carlo simulations, we will make heavy use of the cumulative
distribution function (cdf). The cdf, written as F(x), is the area under a pdf up to
EXHIBIT 20-5
UNIFORM PDF
a b
f(x)
1
b-a
362 CHAPTER 20 MONTE CARLO SIMULATION
point x, which can be written as the integral of f(x) from the distribution mini-
mum to x.
The cdf of a uniform distribution is
FðxÞ 5
Z
x
a
1
b 2a
dz 5
x 2a
b 2a
: ð20:7Þ
By construction, all cdfs must be equal to one at the maximum of their range.
The uniform cdf is illustrated in Exhibit 20-6.
In general, the mean (5 expected value) of a continuous random variable, x,
can be written as the integral
Z
N
2N
x à f ðxÞ dx: ð20:8Þ
For a uniform distribution, we have f(x) 5 1/(b 2 a). Also, the upper and
lower bounds are not in?nity, but are given by a and b. Thus, the mean of a uniform
distribution can be solved as
Z
b
a
x Ã
1
b 2a
dx 5
b
a
x
2
2ðb 2aÞ
5
b
2
2a
2
2ðb 2aÞ
5
ðb 1aÞðb 2aÞ
2ðb 2aÞ
5
b 1a
2
: ð20:9Þ
Now, let’s use the uniform distribution in an NPV calculation.
EXHIBIT 20-6
UNIFORM CDF
a b
F(x)
1
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 363
EXAMPLE 20.2
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we are
sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy. Ef?cacy
is distributed E BU [0,1] and will be learned during three years of Phase III trials. The NPV
of the drug after 3 years is $1BÃ E
2
(i.e., even with a low ef?cacy and a high likelihood of
FDA failure, we are still allowing for some salvage value for the project). The discount rate is
equal to the riskfree rate of 5 percent per year. The total cost of R&D is $100 M and must be
paid at the beginning of development.
Problems
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) Why is the answer to part (b) different than the answer to part (c)?
Solutions
(a) We begin with the event tree, given in Exhibit 20-7.
Because the uniform distribution has an in?nity of possible outcomes, we do not bother
drawing lots of branches, but instead draw three branches connected by a curve. The notation
for the distribution— U[0,1]— is then given after an arrow on the middle branch. The top
EXHIBIT 20-7
EVENT TREE FOR NEWDRUG, WITH UNIFORM DISTRIBUTION
Phase III
$–100M
$1B
$1B *E
2
E ~ U[0, 1]
$0
Efficacy?
3 years
364 CHAPTER 20 MONTE CARLO SIMULATION
branch represents the maximum of the distribution (if applicable), and the bottom branch
represents the minimum. The main formula for the terminal nodes is given on the middle
terminal node. In the remaining chapters, we follow this same convention for representing
continuous distributions within trees.
(b) From Equation (20.9), we know that the mean (5 expected value) of a uniform dis-
tribution is equal to (b 1 a)/2. In this case, we have b 5 1 and a 5 0, so the mean is 1/2. If
we substitute E 51/2, then the expected terminal value would be $1BÃ (1/2)
2
5$250 M, and
the NPV would be $250 M/(1.05)
3
2 $100 M 5 $116.0 M.
(c) To simulate from a continuous distribution, we must invert the cdf to ?nd the ef?cacy
(E) that goes with a speci?c random draw. To provide a graphic illustration of this inversion,
consider the following three steps:
Step 1: Draw a random number between 0 and 1.
Step 2: Plot this random number on the Y-axis of the cdf.
Step 3: Find the corresponding point on the X-axis.
The answer to Step 3 is the “draw” from the continuous distribution. These three steps
are illustrated in Exhibit 20-8 for an example draw of rand() 50.748. For this case, the
sampling procedure turns out to be very easy, because the cdf of a U [0,1] distribution is just
F(E) 5E. Nevertheless, for even more complex distributions considered later, we can still
visualize the procedure using the same three steps. Of course, the actual steps are done by a
computer. With our knowledge that F(E) 5E, we build an Excel worksheet to perform the
simulation.
EXHIBIT 20-8
SAMPLE FROM A CDF FOR E B U[0, 1]
STEP 2
STEP 3
1
0, 0
STEP 1
rand()
? 0.748
F(E)
E ? 0.748 1
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 365
Exhibit 20-9 displays sample output from 10 draws.
On average, this simulation yields an estimate of $187.9M for the NPV.
(d) In part (b), we substituted the mean value of E51/2 and solved for an NPV of $116.0M. In
part (c), we used Monte Carlo simulation to estimate an expected NPV of $187.9M. The most
important thing to recognize about this difference is that Monte Carlosimulation is the correct way
to estimate the NPV. The answer in part (b) is wrong. It is wrong because when we have a non-
linear model, it is not correct to simply substitute expected values in for random variables. The
model is nonlinear because it includes a termfor E
2
, the square of ef?cacy. Once we introduce any
nonlinearity, it is nolonger correct tosubstituteexpectedvalues for randomvariables. This is a very
important point that applies to any DCF analysis that has nonlinear interactions between its inputs.
It is ?ne to replace variables by their expected values in a linear model. Suppose, for
example, that the terminal payoffs were written as $1B Ã E. Then, an analyst would get the
same (average) answer from simulation as he would by just substituting E51/2. Exercise
20.1 will ask you to con?rm this result.
’
Mathematical Interlude
Example 20.2 calculated the NPV using a simulation—this is called a “computa-
tional solution”. Alternatively, we could have just derived the formula for the
NPV—this is called an “analytical solution”. To derive an analytical solution with
continuous variables, we take an integral of each possible outcome multiplied by its
probability density. (This is similar to the way we computed the mean of an
expected value in Equations (20.8) and (20.9)). For any outcome, E, the terminal
value is E
2
à $1B. The probability density of that outcome is f(E), so the quotient
EXHIBIT 20-9
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw rand() 5 F(E) 5 E NPV
1 0.2171 2$59.29
2 0.5099 $124.58
3 0.7905 $439.80
4 0.4074 $43.37
5 0.8775 $565.21
6 0.2346 2$52.47
7 0.9779 $726.03
8 0.9250 $639.07
9 0.2250 2$56.26
10 0.5531 $164.31
366 CHAPTER 20 MONTE CARLO SIMULATION
is 5E
2
à $1B à f(E). Then, the expected terminal value is the integral of these quo-
tients for the entire [0,1] range of E. In our example, we have b51 and a 50.
Thus, f(E) 51/(b À a) 51. With this formula, we can compute the expected terminal
value as
Expected terminal value 5
Z
b
a
$1B Ã E
2
dE 5
b
a
$1B Ã
E
3
3
5$333:3M: ð20:10Þ
Then, we can solve for the NPV as
NPV5$333M=ð1:05Þ
3
2$100M5$187:9M: ð20:11Þ
We solved Example 20.2 with a computational solution to illustrate an
important point: Monte Carlo simulation is just a computational method to solve
integrals. For relatively simple problems like Example 20.2, the integral would be
easier to do than the simulation. However, in most real-world problems, it is not
possible to solve the integral. In those cases, Monte Carlo simulation is the best way
to get an answer.
End Mathematical Interlude
Next, we examine two other useful distributions: the normal and the log-normal.
Exhibit 20-10 shows the familiar “bell curve” for the pdf of a normal distribution
with a mean of µ and a standard deviation of ?.
EXHIBIT 20-10
NORMAL PDF
µ–2? µ+2? µ–? µ+? µ
0.45
0.35
0.25
0.15
0.05
0.4
0.3
0.2
0.1
0
f(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 367
The formula, f(x), for this pdf is
Nðµ; ?Þ : f ðxÞ 5
1
?
??????
2?
p exp 2
ðx 2µÞ
2
2?
2
: ð20:12Þ
There is no need to integrate Equation (20.12) to ?nd the mean of the normal
distribution: the mean is already given to us as the parameter µ.
The corresponding cdf is illustrated in Exhibit 20-11.
Log-normal distributions are often used in ?nance for distributions of asset
returns. In a log-normal distribution, the natural log of x(5ln x) is distributed with a
normal distribution (as in 20.12). This has the nice property that x can never be
negative, which is useful for many ?nance applications. We ?rst saw a picture of a
log-normal distribution in Chapter 13, when we studied the Black-Scholes formula.
If x is distributed log-normally, with x B LogN(µ, ?), then the pdf of x is
Log Nðµ; ?Þ : f ðxÞ 5
1
?x
??????
2?
p exp 2
ðln x 2µÞ
2
2?
2
; ð20:13Þ
where the notation “exp[x]” is equivalent to e
x
.
This pdf is illustrated in Exhibit 20-12. In the x BLogN[µ, ?] notation, µ is
not the mean of x, but rather is the mean of ln x. Similarly, ? is not the standard
deviation of x, but is the standard deviation of ln x. To compute the mean of x, we
would integrate x à f(x) from 0 to in?nity, where f(x) is given by Equation (20.13).
The solution to this integral is
mean of x when x BLogN½µ; ?? 5exp½µ1?
2
=2?: ð20:14Þ
EXHIBIT 20-11
NORMAL CDF
µ
F(x)
1
0.8
0.6
0.4
0.2
0
368 CHAPTER 20 MONTE CARLO SIMULATION
This “extra” term of ?
2
/2 might remind some readers of similar terms ?oating
around as part of the Black-Scholes formula (Chapter 13). This similarity is no
coincidence: the Black-Scholes formula uses assumptions about log-normal returns in
continuous time, so the means of these distributions will have the ?
2
/2 term in them.
Exhibit 20-13 illustrates a cdf for a log-normal distribution.
EXAMPLE 20.3
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we are sure
the drug has no side effects, so all that matters for FDA approval is its ef?cacy. Ef?cacy is
distributed EBLogN[0, 1] and will be revealed after three years of Phase III trials. The NPVof
the drug after three years is $1BÃ E
2
. The discount rate is equal to the risk-free rate of 5 percent
per year. The total cost of R&D is $100M and must be paid at the beginning of development.
EXHIBIT 20-12
LOG-NORMAL PDF
0.5
0.4
0.3
0.2
0.1
0
f(x)
EXHIBIT 20-13
LOG-NORMAL CDF
1
0.8
0.6
0.4
0.2
0
F(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 369
Problems
(a) Draw the event tree for this project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to estimate the NPV of the project.
Solutions
(a) The event tree is identical to Exhibit 20-7, except that we replace the uniform dis-
tribution with a log-normal distribution.
(b) From Equation (20.14), we know that the mean of Log N[0,1] is equal to exp[0 11/2 Ã
(1)
2
] 5exp[1/2] 51.65. Substituting this mean for E yields an expected terminal value of
$2.72B and
NPV5$2:72B=ð1:05Þ
3
2$100M5$2:25B: ð20:15Þ
Because this is a nonlinear model, we know that $2.25B is not the correct NPV for the
project.
(c) To solve for the correct NPV, we set up a Monte Carlo simulation as in Exhibit 20-9. To
perform this simulation, we make use of the Microsoft Excel built-in function to give the
inverse of the cdf for a log-normal distribution. The syntax for this function is loginv[(F(x),
µ, ?], so we can do simulations by substituting the random number function, rand(), for F(x).
After 1,000,000 draws, this simulation gave an average NPV of $6.24B. This is
much higher than the answer in part (b), which demonstrates the importance of using
simulation in this example. Why is this answer much higher? Because the log-normal
distribution is not symmetric—extreme outcomes are possible only in the long “right-tail”
of Exhibit 20-12. When extreme outcomes are possible, the square term exacerbates these
EXHIBIT 20-14
EVENT TREE FOR NEWDRUG, WITH LOG-NORMAL DISTRIBUTION
Phase III
$–100M
$1B
$1B *E
2
E ~ LogN[0, 1]
$0
Efficacy?
3 years
370 CHAPTER 20 MONTE CARLO SIMULATION
outcomes into extreme values for the NPV. We can see an example of such an extreme
outcome in draw #1 of Exhibit 20-15. ’
Although many other distributions are useful for analysts, in this book we will
use only the uniform, normal, log-normal, and one other—the triangular distribution.
Unlike the other distributions used in this book, triangular distributions are rarely
found “in nature”. Instead, these distributions are an invention of analysts looking for
a shorthand way to express their intuition about relative likelihoods on a ?xed range.
A triangular distribution is described by three parameters—minimum (a), maximum
(b), and mode (c)—with notation T (a, b, c), with a pdf that looks like Exhibit 20-16.
EXHIBIT 20-15
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw rand() 5 F(E) E NPV
1 0.9931 11.7513 $119,190.77
2 0.4724 0.9332 $652.31
3 0.0474 0.1882 2$69.41
4 0.8850 3.3221 $9,433.84
5 0.7578 2.0123 $3,397.88
6 0.8735 3.1363 $8,397.22
7 0.9013 3.6301 $11,283.62
8 0.9246 4.2056 $15,178.48
9 0.4581 0.9001 $599.87
10 0.3610 0.7007 $324.11
EXHIBIT 20-16
TRIANGULAR PDF
a c b
2/(b–a)
f(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 371
Because the triangular distribution is not found in most standard textbooks,
it will be useful for us to take some time to discuss a few of the key properties for
this distribution. To be a proper pdf, the total area under the f(x) curve must be
equal to a total probability of 100 percent. Because the triangular distribution is
indeed a triangle, its area is equal to 1/2 à base à height. Writing the base as 5
maximum 2 minimum 5 b 2 a, and the height at the mode (point c) as h,
we have
Area 51=2 Ã ðb 2aÞ Ã h 51-h 52=ðb 2aÞ; ð20:16Þ
which is given as the maximum height in Exhibit 20-16. Because the density begins
at zero at point a, rises linearly to its maximum height at point c, and then falls
linearly back to zero at point b, we can write the equation for the pdf as
for x ,c :
2
b 2a
Ã
x 2a
c 2a
5
2 Ã ðx 2aÞ
ðb 2aÞ Ã ðc 2aÞ
:
Tða; b; cÞ : f ðxÞ 5
For x $c :
2
b 2a
Ã
b 2x
b 2c
5
2 Ã ðb 2xÞ
ðb 2aÞ Ã ðb 2cÞ
:
ð20:17Þ
The mean of a triangular distribution is 5(a 1b 1c)/3. We will use this
mean in our solution to Example 20.4.
The cdf for this triangular distribution is illustrated in Exhibit 20-17.
EXHIBIT 20-17
TRIANGULAR CDF
a c b
1
F(x)
372 CHAPTER 20 MONTE CARLO SIMULATION
20.3 SIMULATION WITH MULTIPLE SOURCES
OF UNCERTAINTY
With the tools of the earlier sections, we are ready to tackle a more complex
problem.
EXAMPLE 20.4
Drugco has just begun Phase III trials for Newdrug at a cost of $100M. Drugco expects Phase III
trials to take two years and the FDAapproval decision to take one year, so that the FDAdecision
is expected in three years. Phase II trials were promising, with a score of 40 on the standard
medically recognized scale. (We will refer to this score as the “ef?cacy” of the drug.) Although
the best alternative drug has an ef?cacy of 50, it is not helpful for all patients. Given the side
effects of Newdrug and the risks and bene?ts of alternative treatments, Drugco believes that the
FDA will approve Newdrug if the Phase III trials ?nd an ef?cacy of 30 or greater. Based on the
results of the Phase II trials, Drugco estimates that the ef?cacy results of Phase III will be EBN
(40, 20). (It is possible for ef?cacy to be negative because some drugs can make symptoms
worse.) During the three years of Phase III trials, it is possible that the alternative treatments will
also improve from their current ef?cacy of 50. Drugco estimates a ?nal distribution for the
alternative of ABT(50, 100, 50). If Newdrug is approved by the FDA, then its market share will
depend on the relative ef?cacy of Newdrug versus the best available treatment, that is,
Newdrug market share 5E
2
=ðE
2
1A
2
Þ: ð20:18Þ
Drugco estimates market size for Newdrug in the approval year (in millions of doses) as
M B N(1000, 100), with 6 percent annual growth going forward. Each dose yields a gross
pro?t of $1. To stay in the market, Drugco must spend $300M on marketing in the ?rst year,
with this sum increasing each year by 6 percent. Upon approval, Newdrug would have 10 years
of patent life remaining. After the patent expiration, Drugco expects generic competition and
other improved alternatives to greatly erode the value of Newdrug, so for simplicity we assume
that the continuing value would be zero after the patent expires. Following earlier examples
in this chapter, we assume a discount rate equal to the riskfree rate of 5 percent.
Problems
(a) Draw the event tree for the valuation of Newdrug.
(b) What is the probability of FDA approval for Newdrug?
(c) What is the expected value in three years for A, the ef?cacy of the best alternative
treatment?
(d) Suppose that all random variables are exactly equal to their expected values. What
would be the NPV of Newdrug?
(e) Use Monte Carlo simulation to estimate the NPV of Newdrug.
Solutions
(a) The event tree is given in Exhibit 20-18.
20.3 SIMULATION WITH MULTIPLE SOURCES OF UNCERTAINTY 373
The ?rst year of pro?ts following the terminal nodes with E.30(FDA approval) 5
M Ã E
2
/(E
2
1A
2
) À $300M. For years 2 through 10, multiply pro?ts in the previous year by
1.06, then sum all years and discount by 1.05 per year to get the NPV.
(b) Ef?cacy is distributed as N[40, 20], so we can estimate the probability that E . 30 by
using the cdf for this distribution, F(E):
Probability of approval 5Prob ðE .30Þ 51 2Fð30Þ 50:69: ð20:19Þ
Thus, there is a 69 percent chance that a draw from the N[40, 20] distribution will be
greater than 30. (The normal cdf can be accessed as a built-in function of Microsoft Excel
called “normdist”.)
(c) As mentioned earlier in our discussion of triangular distributions, the mean of a triangular
distribution is equal to (a 1b 1c)/3. In this case, we have a 5 50, b 5 100, and c 5 50, so
Expected value of the alternative treatment 5ð50 1100 150Þ=3 566:7: ð20:20Þ
(d) Exhibit 20-19 provides a DCFmodel for calculating the NPVof Newdrug. The bolded cells
in the model are the randomvariables: ef?cacy, alternative ef?cacy, and starting market size. In
this model, each of the randomvariables is set at its expected value. Ef?cacy is distributed as N
[40, 20] and so is set to 40. Alternative ef?cacy is distributed T[50, 100, 50] and so is set to 66.7
(as discussed in part (c)). Starting market size is distributed as N[1000, 100] and so is set to1000.
At these expected values, Newdrug is approved by the FDA, the market share is equal to 26.5
percent (540
2
/(40
2
166.7
2
), and pro?ts in the ?rst year postapproval (5year 4 of the model)
are equal to gross pro?ts of 0.265 Ã 1000, minus marketing costs of $300M5À$35.3M. The
overall NPV (as of year 0) is then equal to 2$410.6M.
(e) To perform a Monte Carlo simulation on this model, we need to make separate draws for
each of the random variables. Because three random variables feed into a multiyear model, it
would be unwieldy (but not impossible) to build this simulation directly in Excel. Instead, we
EXHIBIT 20-18
EVENT TREE FOR NEWDRUG
Alternative:
A ~ T[50,100,50]
Market size:
M ~ N[1000,100]
Efficacy:
E ~ N[40,20]
Same
as 2
Same
as 3
Same
as 2
Same
as 3
Phase III
–$100M
1 2 3
If E ? 30
3 years
$0
See below
for payoffs
at terminal
nodes
374 CHAPTER 20 MONTE CARLO SIMULATION
EXHIBIT 20-19
DCF MODEL FOR NEWDRUG, ALL VARIABLES SET TO THEIR EXPECTED VALUES
Mean Stdev Min Mode Max
Efficacy 40 40 20
Alternative efficacy 67 50 50 100
Starting market size 1,000 1,000 100
Approval threshold 30
Gross profit per unit 1
Market share 26.5%
Market growth 6.0%
Discount rate 5.00%
approved? 1
$ in millions
Year 3 4 5 6 7 8 9 10 11 12
Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
Gross profit $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
Profit 2$35.3 2$37.4 2$39.7 2$42.0 2$44.6 2$47.2 2$50.1 2$53.1 2$56.3 2$59.6
NPV as of year 0 2$410.6
3
7
5
suggest using a specialized program like Crystal Ball. In Appendix C, we show how to use
Crystal Ball, and we discuss the implementation of Crystal Ball for the model in Exhibit 20-19.
After 1M draws, the simulation gives an average NPV of $285.9M, which is signi?cantly higher
than the NPV found in part (d). Sixty-nine percent of the draws resulted in FDA approval (as
solved in part (b)). The outcomes below À$100M occur when gross pro?ts are less than the
$300M marketing costs. An example of such an outcome is given in Exhibit 20-19. One might
think that Drugco should simply abandon the project if projected pro?ts are negative. This
reasoning is absolutely correct, but it is not yet built into this model. To allow Drugco this kind
of ?exibility, we will need to use decision trees and real options. We will learn these tools in
Chapter 21, and we will extend Example 20.4 to allow for such ?exibility in Example 21.4.
’
SUMMARY
R&D investment decisions often require the analysis of several risks at the same time. These
risks can often be modeled as random variables and represented in an event tree. If the analyst
needs to estimate the NPV of an R&D project, then she will need to posit the probability dis-
tributions of these random variables. In this chapter, we learned some basic properties of four
different continuous probability distributions: uniform, normal, log-normal, and triangular. In
some cases, a model may be simple enough to allow an analytical solution for the NPV of an
R&Dproject. In many cases, however, the analyst must ?nd a computational solution by using
Monte Carlo simulation. In Monte Carlo simulation, the computer makes draws from each
probability distribution for each draw of the simulation. The estimated answer is the average
answer over many draws. Simple simulations can be performed using Microsoft Excel. For
more complex simulations, it is helpful to use a specialized package such as Crystal Ball.
Appendix C shows how to solve all the examples from this chapter using Crystal Ball.
KEY TERMS
Monte Carlo simulation
5 Monte Carlo analysis
Discrete random variables,
continuous random
variables
Event tree
Risk node, terminal node
Branch
Probability density
function (pdf)
Cumulative distribution
function (cdf)
Mean
Nonlinear model, linear
model
EXERCISES
20.1 Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we
are sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy.
Ef?cacy is distributed E BU[0, 1] and will be learned during three years of Phase III trials.
The NPV of the drug after three years is $1B Ã E. The discount rate is equal to the riskfree
rate of 5 percent per year. The total cost of R&D is $100M and must be paid at the beginning
376 CHAPTER 20 MONTE CARLO SIMULATION
of development. (Note that this problem is identical to Example 20.2 except for the formula
for the NPV after three years.)
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) On average, will the answer to part (b) be different than the answer to part (c)?
20.2 Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we
are sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy.
Ef?cacy is distributed E B T[0, 1, 0.4] and will be learned during three years of Phase III
trials. The NPV of the drug after three years is $1BÃ E
2
. The discount rate is equal to the
risk-free rate of 5 percent per year. The total cost of R&D is $100 M and must be paid at
the beginning of development. (This is tricky, because Microsoft Excel does not have a built-
in function for the Triangular distribution. To solve this, you will either need to be creative or
use Crystal Ball.)
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) On average, will the answer to part (b) be different than the answer to part (c)?
20.3 True, False, or Uncertain: Done properly, analytical solutions and computational
solutions will give the same result every time.
20.4 Consider the same problem as in Example 20.4, except that now we add two additional
types of uncertainty. In Example 20.4, we assumed that the gross pro?t per unit was ?xed at
$1. Now, we assume that this gross pro?t is distributed as T[$0.50, $1.50, $1], with this level
learned on FDA approval and then ?xed for the life of the product. Next, if Newdrug is
approved, then there is a 10 percent chance every year that a superior product will be
introduced by a competitor. If this superior product is introduced, then Newdrug’s sales are
cut in half for all future years (relative to what they would have been without this superior
product.) Only one superior product can be introduced in each year, but it is possible for
such products to be introduced in multiple years. For example, if a superior product occurs in
year 6 and in year 8, then Newdrug would have one-half of its original (Example 20.4) sales
in years 6 and 7, and then one-quarter of its original sales in year 8 and beyond.
(a) Use Monte Carlo simulation to solve for the NPV of Newdrug.
EXERCISES 377
CHAPTER 21
REAL OPTIONS
YOU ARE stranded alone on a desert island. For the sake of argument, we
assume that you would like to get off this island. You have a ?are gun with one
charge. You see a plane ?ying overhead. The plane is not directly over the island,
so you are uncertain if your ?are will be visible. Do you ?re? If you do ?re, it will
be your only shot. If you don’t ?re, what are the chances that a plane will ever ?y
any closer?
In making this decision, you are considering a real option. Real options are
created whenever you face a decision that is costly to reverse. In the desert island
example, the ?ring of the gun is irreversible. You can delay ?ring the gun (thus
preserving the “option” to ?re), but you are uncertain about the outcome. If you do
?re, the real option is exercised, as your only ?are has been spent. It is not easy to
solve this problem. To do it right, you would need to estimate various probabilities
and make complex calculations—all in the short time before the plane goes by.
The solving of real options problems has two parts. The ?rst part is “spotting
options” and the second part is “valuing options”. To spot options, we need to have
a deep understanding of the whole decision landscape. In our desert island case, this
would only require that you realize that the gun has only one ?are. In other
situations, an analyst must be clever enough to recognize (or create) real options
where none are obvious.
In Section 21.1, we show how real options can be represented in a decision
tree. In Section 21.2, we classify different types of real options that are relevant for
R&D decisions. In Section 21.3, we show how to value these options using
replication—the same technique ?rst studied in Chapter 13. In Section 21.4, we
demonstrate another solution technique: risk-neutral valuation. Finally, in Section
21.5, we apply real-options methodology to extend our Drugco example from the
previous chapter.
378
21.1 DECISION TREES
When a decision maker is considering all possibilities, it is helpful to sketch all
possible events and decisions in a decision tree. A decision tree adds decision
nodes to an event tree (Chapter 20). Exhibit 21-1 gives a decision tree for Joe
Veesee’s drive home from work.
Upon leaving his garage, Joe has two choices: he can take the highway or he
can take “back roads”. This choice is represented with a box at the decision node.
If he takes back roads, then he will get home in 20 minutes for sure. If he takes
the highway, there is some traf?c risk. This risk is represented by a risk node
(circle) in the tree. When there is no traf?c on the highway, it is Joe’s fastest route
(15 minutes). If there is traf?c on the highway, then the same commute would
take 30 minutes. Based on past experience, Joe knows that there is a 40 percent
chance of traf?c (and a 60 percent chance of “no traf?c”), so his expected commute
time if he takes the highway is 0.6 Ã 15 1 0.4 Ã 30 5 21 minutes. If Joe cares only
about the average time of his commute, then he would compare the expected
commute times for each of his choices and then pick the faster (back roads) route.
So far, this is a straightforward problem. Joe has to make an irreversible
decision right at the beginning, and then nature takes its course. The problem gets
more interesting if we give Joe the “option” of getting off the highway. For
example, suppose that traf?c conditions can be observed once he enters the high-
way (but not before) and that after only a few minutes of such traf?c he can exit the
highway and take an alternate route. This alternate route is not as fast as the original
“back roads” option, but it is not as slow as staying on the highway with traf?c.
Exhibit 21-2 gives a decision tree for Joe’s commuting problem with this new exit
option.
EXHIBIT 21-1
COMMUTING OPTIONS
highway
back
roads
20 15
30
traffic
40%
no
traffic
60%
1
2
21.1 DECISION TREES 379
Decision trees are solved backward. Consider Joe’s decision at Node 3. If he
chooses toexit the highway, his commute will be 25minutes. If hechooses tostayonthe
highway, his commute will be 30 minutes. Thus, he should choose to exit the highway.
Conversely, at Node 4 his fastest option is to stay on the highway, for a commute time
of 15minutes. With this information, we can prune the decisiontree byreplacing Nodes
3 and 4 with their optimal decisions. This pruning yields Exhibit 21-3. Next, we
EXHIBIT 21-3
COMMUTING OPTIONS, PRUNED
highway
back
roads
20
15
4
25
3
traffic
40%
no
traffic
60%
Stay on
highway
Exit highway
1
2
EXHIBIT 21-2
COMMUTING OPTIONS, WITH EXIT
highway
back
roads
20
15
30
25
22
traffic
40%
no
traffic
60%
Stay on
highway
Stay on
highway
Exit
highway
Exit
highway 1
2 3
4
380 CHAPTER 21 REAL OPTIONS
compute the expectedvalue at Node 2 as 0.4 Ã 2510.6 Ã 15519minutes. Because this
is less than the 20 minutes for “back roads”, the optimal decision at Node 1 is to take the
highway.
21.2 REAL OPTIONS IN R&D
As mentioned in the introduction, real options occur whenever you face a decision
that is costly to reverse. Anybody who shies away from commitment with the
excuse that “I am just trying to keep my options open” is indeed doing exactly that:
commitment implies some cost for reversing the decision. Real option analysis is an
attempt to quantify the value of “?exibility”. In R&D settings, there are many
possible applications. Most of these applications can be classi?ed more naturally as
either call options or put options—but keep in mind that for a decision maker
considering whether to take “Action A” or “Action B”, it is often possible to
rede?ne a call option on Action A as a put option on Action B.
The following discussion describes six different types of real options. This is
by no means a comprehensive list.
Call Options
The Option to Delay: Drugco has possible development projects based on
the same science behind Newdrug. Drugco scientists are not sure if these new
projects will work, but they expect to learn more about the probabilities of success
after learning whether the original Newdrug project is successful. Examples 21.1
and 21.2 analyze options to delay.
The Option to Expand: Semico is considering whether to add capacity to
their microchip fabrication plant. The value of an added-capacity plant depends on
the demand for Semico’s chips. If Semico can wait and learn more about demand
before deciding whether to add capacity, then this is a type of call option.
1
The Option to Extend: Autoco currently builds its Oldcar at an aging plant
in Michigan. The assembly lines in this plant are so outdated that Autoco loses
money manufacturing Oldcar, and it looks like the brand is slowly dying. If we
know with certainty that the demand for the brand will never pick up, then it is best
to shut down the plant today. But Autoco management believes that there is
some chance that the demand will be high again in the near future, so keeping the
1
In recessions, new investments decline because many companies decide to keep their expansion options
alive and not exercise them. In recoveries, the opposite happens À ?nally companies see enough positive
signs in the economy and decide to exercise their options, so investments surge. See, for example,
“Radical Shifts Take Hold in U.S. Manufacturing”, Wall Street Journal, February 3, 2010.
21.2 REAL OPTIONS IN R&D 381
plant open gives them an option to extend the brand for a few more years at a
moderate cost.
2
Put Options
The Option to Abandon: Drugco is currently developing Newdrug to treat
diabetes. Drugco scientists believe it is likely that Newdrug will be approved by the
FDA, but this approval is still three years away. In the meantime, alternative
treatments might be improved, the expected market for Newdrug might shrink, and
pricing pressures might harm margins for the drug. Although it is possible that
Newdrug will be a blockbuster, it is also possible that it will be a money loser (after
marketing costs). Drugco would like to continue trials for the drug while preserving
the option to abandon the project later on if it proves to be unpro?table. We analyze
this case in Example 21.4.
The Option to Shrink: This is the ?ip side of the option to expand, con-
sidered earlier. If Semico needed to wait a year before deciding whether to reduce
some capacity, then it would be a type of put option.
Combinations of Options
Option to Switch: Joe Veesee’s commuting problem in Section 21.1 is an
example of a switching option. Switching options can be calls, puts, or a combi-
nation of the two. It is more natural to think of the option on the asset that has some
uncertainty. Hence, for Joe Veesee, it was a put option because he would have to
“sell” the road that he was already on. Alternatively, if Joe could start on the back
roads, listen to the traf?c report on the radio, and then switch to the highway if there
was no traf?c, then he would be “buying” a new road, and it would be a call option.
Finally, if both the back roads and the highway had uncertainty, and Joe could learn
about the traf?c on both roads and switch back and forth, then he would hold a
combination of puts and calls.
21.3 THE VALUATION OF REAL OPTIONS
The valuation of real options is essentially about solving for the correct discount
rate. The easiest problems to solve are those with no beta risk, so that all discount
rates are equal to the riskfree rate.
2
As of 2010, it looks like the Big 3 let this option expire for Saturn, Pontiac, and a few other brands.
382 CHAPTER 21 REAL OPTIONS
EXAMPLE 21.1 (Fuelco)
Fuelco is considering a development project using its patented fuel-cell technology. (This
corresponds to “Project A” as originally discussed in Chapter 19.) If Fuelco pays $200M to
start the project, then they are permitted to bid for a government contract. The objective
probability of winning the contract is 50 percent, and there is no beta risk for the govern-
ment’s decision. If Fuelco’s bid is accepted (one year later), then they can choose to ?nish the
project by accepting the contract (cost 5 $300M), when they will earn an NPV (as of one
year from now) of $600M (not including the $300M cost of ?nishing the project). If they do
not receive the contract, then they can still ?nish the development project (cost 5 $300M),
but they could only receive $200M for the project by selling it to some nongovernmental
buyer (not including the $300M cost of ?nishing the project). The riskfree rate is zero.
Problems
(a) Draw the tree for Fuelco’s problem under the assumption that it starts the project.
(b) Compute the NPV for the project. Should Fuelco start the project?
Solutions
(a) Based on the information given in the example, we draw Fuelco’s decision tree as shown
in Exhibit 21-4.
(b) To compute the NPV, we prune the tree at Nodes 2 and 3 by ?nding Fuelco’s optimal
decision at each node. At Node 2, Fuelco would receive 600M2300M5300M for ?nishing
the project, and 0 for abandoning it. Thus, the project should be ?nished if Node 2 is reached.
At Node 3, Fuelco would receive 200M 2 300M 5 2100M for ?nishing the project and 0
EXHIBIT 21-4
FUELCO’S DECISION TREE (PROJECT A)
Get contract
Don't get contract
$600M
$200M
$0
$0
2
3
1
50%
50%
?$300M
?$300M
Abandon
Abandon
Finish project
Finish project
Duration ? one year
Cost to start project ? $200M
21.3 THE VALUATION OF REAL OPTIONS 383
for abandoning it. Thus, the project should be abandoned if Node 3 is reached. To complete
the solution, we compute the expected value of receiving the contract, discount this expected
value by the riskfree rate (conveniently equal to 0), and subtract the cost to start the project
(5 $200M):
NPV of project 5ð0:5 Ã 300 10:5 Ã 0Þ 2200 5 250M ð21:1Þ
Because the NPV is negative, Fuelco should not start the project.
’
In Example 21.2, we computed the NPV for Fuelco’s project by using
backward induction, the objective probabilities of success, and a riskfree discount
rate. This riskfree discount rate was appropriate because we assumed a zero beta for
the government’s decision to award the contract. The decision problem is more
complex when there is beta risk in the underlying project.
EXAMPLE 21.2
In addition to the government contract considered in Example 21.1, Fuelco is also con-
sidering a separate investment in fuel-cell technology designed to replace oil-based energy
for some types of engines.(This corresponds to “Project B” as ?rst discussed in Chapter 19.)
By investing $100M today to start the project, Fuelco would maintain the option to ?nish the
project with a further investment (5 $200M) in one year. If oil prices are at least $60 per
barrel in one year (objective probability 5 50%), then on completion of the project, Fuelco
would have an NPV (as of one year from now) of $1,000M (not including the $200M cost of
?nishing the project). If oil prices are less than $60 a barrel in one year (objective probability 5
50%), then the project would not be economical for most applications and would have an NPV
(one year fromnow) of $300M(not including the $200Mcost of ?nishing the project). If Fuelco
decides not to ?nish the project, then they can sell the technology to a competitor for $200M,
regardless of the price of oil. The beta for the project is unknown, but we do have some
information about oil prices: the market price of a European binary call option (payoff 5$1) on
oil with a strike price of $60 per barrel and an expiration of 1 year is 25 cents.
Problems
(a) Draw the tree for Fuelco’s problem under the assumption that it starts the project.
(b) Compute the NPV for the project. Should Fuelco start the project?
Solutions
(a) We draw Fuelco’s decision tree in Exhibit 21-5.
(b) We solve backward by ?nding the optimal decisions at Nodes 2 and 3. In both
cases, abandonment would result in a payoff of $200M. At Node 2, Fuelco would receive
1,000M 2 200M 5 800M by ?nishing the project, so it should ?nish. At Node 3, Fuelco
would receive 300M 2 200M 5 100M by ?nishing the project, so they should abandon and
receive $200M. Pruning the tree to re?ect these decisions leaves us with Exhibit 21-6.
384 CHAPTER 21 REAL OPTIONS
At this point, it is easy to compute the expected future value of the project (in one
year) as 0.5 Ã 800M 1 0.5 Ã 200M 5 $500M, but what discount rate should we use to bring
this value back to today? Before proceeding to the correct answer, let’s consider two
incorrect alternatives: (1) the riskfree rate and (2) the cost of capital for the binary option
given in the problem.
EXHIBIT 21-5
FUELCO’S DECISION TREE (PROJECT B)
High oil price
Low oil price
$1,000M
$300M
$200M
$200M
2
3
1
50%
50%
?$200M
?$200M
Abandon
Abandon
Finish project
Finish project
Duration ? one year
Cost to start project ? $100M
EXHIBIT 21-6
FUELCO’S DECISION TREE (PROJECT B, PRUNED)
High oil price
Low oil price
1
50%
50%
$800M
Finish project
Duration ? one year
Cost to start project ? $100M
2
$200M
Abandon
3
21.3 THE VALUATION OF REAL OPTIONS 385
If we use a riskfree rate of zero, then the NPV of the project would be $500M 2
$100M 5 $400M. This would be correct if and only if there is no beta risk associated with
the project. In Example 21.1, we were able to use the riskfree rate for exactly this reason:
under the assumption that the government’s decision had no beta risk, the appropriate dis-
count rate was the riskfree rate. In Example 21.2, the value of the project is based on the price
of oil. Do oil prices have beta risk? Lucky for us, we do not have to answer this question in a
vacuum, as the example provides us with pricing information for a binary option on oil
prices. This option pays $1 if oil prices are high (50 percent chance), so it has an expected
future value of 50 cents. With a price today of 25 cents, the option has an expected return of
100 percent. Clearly, this return is signi?cantly higher than the riskfree rate of zero, so
there must be some beta risk in oil prices. Thus, it would not be appropriate to use the
riskfree rate to discount the returns to Project B. As our next alternative, we consider using
the same discount rate of 100 percent that applies for the binary option. In this case, the NPV
of the project would be 500M/(1 1 1) 2 100M5 $150M. Why is this wrong? Because there
is absolutely no reason to believe that Project B has the same beta risk as the binary option.
Although it is tempting to think that exposure to oil risk makes these two assets equivalent,
this equivalence is incorrect. To see why this is true, imagine a leveraged version of the binary
option where an investor combines 25 cents of capital with 75 cents of borrowed money to buy
4 options (5 25 cents à 4 5 $1 cost). In this case, the payoffs in the next period when oil
prices are high would be $4 (option payoff) 2 $0.75 (loan payback) 5 $3.25. When oil prices
are low, the payoffs would be $0 (option payoff) 2 $0.75 (loan payback) 5 2$0.75. Thus, the
expected value of this leveraged option would be 0.50 Ã 3.25 1 0.50 Ã 20.75 5 $1.25, for a
whopping expected return of 400 percent on the 25-cent investment. As in the original binary
option, these payoffs depend only on the oil price. Note, however, that the expected returns are
very different: 400 percent here versus 100 percent for the original option.
Because we cannot blindly apply the discount rate from the binary option, it is
necessary to ?nd another solution. Instead of computing a discount rate directly, we can
adopt the replicating-portfolio approach ?rst discussed in Chapter 13. Although the appli-
cations in Chapter 13 were for ?nancial options, the same approach can also be applied for
real options like Project B.
To build a replicating portfolio, we begin with two “known” assets: the binary call and
a riskfree bond. The binary call is worth 25 cents today. In one year, if oil prices are high,
the binary call is worth $1, and if oil prices are low, the binary call is worth $0. Because the
riskfree rate is zero, the price of the bond today is the same as its value in both the high-
price and low-price cases next year. For convenience, we set this value to be $1 in all cases,
but we could equally well choose any other value. (After the solution, we will demonstrate
why this is so.) The asset to be priced is the value of Project B in one year, after the oil price
is known. The value of the project is $800M in the high-price state and $200M in the low-
price state.
Next, we build a portfolio of binary options and riskfree bonds that provides exactly
the same payoff as Project B in both states. As in Chapter 13, we write an equation for each
outcome, high or low, that takes the form
Project Value at Expiration ðhigh price or low priceÞ
5ðShares of binary optionÞÃðbinary option value 5$1 if high price; $0 if low priceÞ
1ðShares of BondÞ Ã ðBond Value 5$1 in both casesÞ: ð21:2Þ
386 CHAPTER 21 REAL OPTIONS
Denoting shares of the binary option as y and shares of the bond as z, we write the
equations as
Project B ðhigh oil priceÞ 5800M5y 1z; ð21:3Þ
and
Project B ðlow oil priceÞ 5200M5z: ð21:4Þ
Equations (21.3) and (21.4) give us two equations and two unknowns (y and z), which
we can solve to ?nd that y 5 600M and z 5 200M. To check this solution, we return to the
logic of replication: if we purchase 600M binary options and 200M bonds, then we exactly
replicate the payoffs to the call option. If oil prices are high, 600M binary options would be
worth $600, and 200M bonds would be worth $200, for a total of $800M, the same value as
Project B. If oil prices are low, then the binary options are worthless, whereas the bonds are
still worth $200M, also the same value as Project B.
Now, to ?nd the present value of owning Project B (not including the $100M cost of
investment today), we compute the cost of the replicating portfolio
Value of Project B ðnot including today’s 100M investmentÞ
5600M Ã BC
0
1200M Ã B
0
5600M Ã 0:25 1200M5$350M
ð21:5Þ
This solution of $350M represents the value of Project B once the initial
$100M investment has been made. The total NPV of the project should include this $100M
investment and is equal to 350M 2 100M 5 $250M. Nevertheless, the $350M ?gure is still
an important input into our analysis, as it represents the total valuation for the project after
the investment. That is, after making the initial $100M investment, if Fuelco wanted to sell
all the rights to Project B (including the right to ?nish the project), they would use $350M as
their total valuation. One application of the total valuation is to compute the appropriate
discount rate for Project B. Earlier we computed the expected value of Project B to be
$500M. Thus, if the total valuation (after the initial investment) is $350M, then the expected
return on Project B would be 500M/350M 2 1 5 43 percent. Recall that the expected return
on the binary option was much higher (100 percent). Why the difference? Equation (21.5)
gives us the answer. Project B is just like a $350M portfolio with $200M invested in the
riskfree bond and $150M invested in the binary option. This portfolio is less risky than a 100
percent allocation in the binary option, so the expected return is lower.
When setting up this problem, we used a bond price of $1 and claimed that the exact price
does not matter. With the solution in hand, we can check that claim. If, for example, we had
chosen a bond price of $2, then Equations (21.2) and (21.3) would have included a “2 Ã z ”
term, the solution for z would have been 100M (instead of 200M), and the contribution of
the bonds to the Project B value (the 200M Ã B
0
term in Equation (21.5)) would have been
100M Ã $2 5 $200M, the same amount as we found when using $1 for the bond price. In
general, for any bond price B
0
, we would obtain a solution of z 5200/B
0
, with a contribution to
the Project B value of B
0
à 200/B
0
5 $200M. ’
21.3 THE VALUATION OF REAL OPTIONS 387
21.4 RISK-NEUTRAL PROBABILITIES
In this section, we introduce an alternate solution method based on risk-neutral
probabilities. Risk-neutral probabilities are from the world of make-believe. We
“make believe” that all investors are completely risk-neutral, and then we ask, “In
this make-believe world, what probabilities would lead to the same asset prices as
we observe in the real world?” Once we obtain these probabilities, we then use
them to price any asset in the economy. The key feature of a risk-neutral world is
that beta does not matter: in a risk-neutral world, nobody cares about any kind of
risk, and all assets have an expected return equal to the riskfree rate. An extra $1
of consumption means the same thing to a poor person as it does to a rich person. In
the banana-bird language of Chapter 4, we could say that each extra banana is
worth the same no matter how many bananas have already been eaten. The banana-
utility functions would be straight lines, with no curvature.
To make this concept more concrete, we return to Fuelco’s problem in
Example 21.2. In that example, the objective probability of a high oil price was
given as 50 percent. In the solution, we found that the expected return on a binary
option—with a price of 25 cents and paying $1 in the state with a high oil price—
was 100 percent. In a risk-neutral world, the same 25-cent binary option still exists,
but now the return on this option must be equal to the riskfree rate of zero. We can
use this information to solve for the risk-neutral probabilities. Let p
t
represent the
risk-neutral probability of a high oil price. Then, the expected value of the option in
one year in a risk-neutral world would be given by
Expected value of the option at expiration 5p
t
à $1 1ð1 2p
t
Þ Ã $0: ð21:6Þ
Because the price of the option is $0.25, the expected return on the option would be
Expected return on the option 5½p
t
à $1 1ð1 2p
t
Þ Ã $0?=0:25 21: ð21:7Þ
If we set this expected return to be equal to the riskfree rate (5 0), then we
can solve for p
t
5 0.25. Thus, in a risk-neutral world, the probability of a high oil
price must be 25 percent. Now, the nice thing about this make-believe number is
that we can use it to solve for option prices. For example, we can now write
Fuelco’s tree as shown in Exhibit 21-7.
The only difference between Exhibits 21-6 and 21-7 is that the probabilities
have shifted from 50/50 (in Exhibit 21-6) to 25/75 (in Exhibit 21-7). The key
conceptual distinction is that in the “real world” of Exhibit 21-6, we did not know
the proper discount rate, and we had to build a replicating portfolio to solve for the
NPV of the project. In the “make-believe” risk-neutral world of Exhibit 21-7,
we know that all assets must earn the riskfree rate of zero percent, so we can
compute the NPV of Project B (not including the initial $100M investment as)
Value of Project Bðnot including today’s 100M investmentÞ
5800M Ã 0:25 1200M Ã 0:75 5$350M;
ð21:8Þ
which is exactly the same solution as found by replication.
388 CHAPTER 21 REAL OPTIONS
This solution method is very powerful and is used in many ?nance applica-
tions. Nevertheless, many students ?nd the whole topic to be somewhat magical
and confusing. If you are confused, then you are not alone, as many of the smartest
?nancial economists were also puzzled by these concepts at ?rst. We can gain some
conceptual understanding by reexamining the replicating-method solution of
Example 21.2. In that example, we knew that the objective probability of a high oil
price was 50 percent, but the solution never used this information. Indeed, the
probabilities were completely extraneous. We have seen this phenomenon before:
in Chapter 13, in our very ?rst option pricing problem (Example 13.1), we solved
for an option price without ever knowing the probabilities. Instead, we used only
the market prices of the underlying assets—a stock in Example 13.1, and a binary
option in Example 21.2. Probabilities are unnecessary because the options are
derivative assets, and all the probability information is already embodied in the
underlying assets.
Once we notice that the probabilities are not used, it gives us license to make
up whatever probabilities that we want. We then use this freedom to create our
make-believe risk-neutral world. We imagine that everyone is risk neutral; this
implies that all assets earn the riskfree rate, and the riskfree return then implies
some speci?c probabilities. Then, we have bootstrapped our way to alternative
solution method, because if everyone is risk-neutral, then it is easy to price all
assets as equal to their expected values, discounted by the riskfree rate.
In the Fuelco example, we were very lucky to have information about a
binary call option. This information allowed us to easily compute the risk-neutral
EXHIBIT 21-7
FUELCO’S DECISION TREE (PROJECT B, PRUNED) RISK-NEUTRAL
WORLD
High oil price
Low oil price
1
25%
75%
$800M
Finished project
$200M
Abandon
Duration ? one year
Cost to start project ? $100M
2
3
21.4 RISK-NEUTRAL PROBABILITIES 389
probabilities. We are rarely so lucky. In the next example, we must ?gure out the
risk-neutral probabilities using a more roundabout method.
EXAMPLE 21.3
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19) They have already completed several R&D
projects with this technology, so they have eliminated the technical risk for this new project.
To begin producing and marketing to the consumer market would require a new investment
of $150M, to be paid in one year. The value of Project C depends on consumer demand. If
demand is “high” (50 percent chance), then the value of the project would be $600M (one
year from now). If demand is “low” (50 percent chance), then the value of the project would
be $200M. If Fuelco chooses not to undertake the project, then they can still sell some of the
related patents to another ?rm. If demand is “high” (50 percent chance), then the salvage
value of these patents would be $300M (one year from now). If demand is “low” (50 percent
chance), then the salvage value of these patents would be $100M. Selling the patents has no
effect on any of Fuelco’s other projects. We will use the CAPM to estimate expected returns
in this problem, where the expected market premium is 7 percent, and the riskfree rate is
5 percent.
Problems
(a) Draw Fuelco’s decision tree, where its ?rst decision (Node 1) is whether to invest in the
project immediately (at a cost of $150M), or to wait one year before making an investment
decision.
(b) Suppose that Fuelco chooses to invest at Node 1. Under this assumptions, solve for the
NPV of the project as a function of its beta. Compute this value in the special cases of ? 5 1
and ? 5 0.
(c) Suppose that Fuelco chooses to wait at Node 1. Use replication methods to solve for the
NPV of this decision.
(d) What is the value of the real option to wait at Node 1?
(e) Compute the risk-neutral probabilities of high demand and low demand under the same
cases as in part (b). Use these risk-neutral probabilities to calculate the NPV of waiting.
Verify that these NPVs are the same as found in part (c).
Solutions
(a) Fuelco’s decision tree is given in Exhibit 21-8.
(b) If Fuelco chooses to invest at Node 1, then there are no further decisions to make. If
demand is high, then the value of the project would be $600M. If demand is low, then the
value of the project would be $150M. To compute the present value of choosing invest at
node 1, we discount the expected value (5 0.5 Ã 600M 1 0.5 Ã 200M 5 400M) by the
appropriate discount rate. For now, we ignore the $150M cost to add the capacity. We can
compute the appropriate discount rate using the CAPM as
r 5R
f
1?ðR
m
2R
f
Þ 50:05 1? Ã 0:07: ð21:9Þ
390 CHAPTER 21 REAL OPTIONS
Thus, the present value of the project with commitment can be written as a function of ?, V
(?), as
Vð?Þ 5400=ð1:05 1? Ã 0:07Þ: ð21:10Þ
Then, V(0) 5 400/1.05 5 381.0, and V(1) 5 400/1.12 5 357.1.
Note that these calculations represent a “present value” for the project, but not a “net
present value”. If we want an NPV, we need to subtract the $150M cost of adding capacity.
Because this cost is committed to be paid in one year, we should discount it by the riskfree
rate, so that the NPV of the project with commitment would be
NPVð?Þ 5Vð?Þ 2150=1:05: ð21:11Þ
(c) If Fuelco chooses to wait at Node 1, we must still take account of the option to invest in
one year. If demand is strong, it would be optimal to invest (600M 2 150M . 300M). If
demand is weak, it would not be optimal to invest (200M 2 150M , 100M). Thus, the
pruned version of the tree is shown in Exhibit 21-9.
EXHIBIT 21-8
FUELCO’S DECISION TREE
Invest
Invest
Don't
Invest
Don't
Strong market
Weak market
Weak market
Strong market
Wait
?$150M
(to be paid at terminal nodes)
?$150M
$600M
$600M
$200M
$200M
$100M
$300M
?$150M
1 year
50%
50%
50%
50%
1
2
3
4
5
NOTE: The branches
after nodes 2 and 3
are perfectly correlated.
21.4 RISK-NEUTRAL PROBABILITIES 391
In part (b), we were able to solve for the present value of invest as a function of beta.
To solve for the present value of wait is a harder problem, because we do not know the beta
for the bottom half of the tree. We can solve for this NPV by building a replicating portfolio
that combines the top half of the tree (with the present value solved in part (b)) and a riskfree
bond. As we learned in Example 21.2, the exact expiration value of the bond is not important,
so we arbitrarily set it to be equal to the cost of adding capacity 5$150M. Denoting “shares”
of the added-capacity factory as y and shares of the bond as z, we write the replicating
equations as
Value of waiting ðstrong demandÞ 5450M5600y 1150z; ð21:12Þ
and
Value of waiting ðweak demandÞ 5100M5200y 1150z: ð21:13Þ
Equations (21.12) and (21.13) give us two equations and two unknowns, which we can
solve for y 5 0.875 and z 5 20.5. The cost of this replicating portfolio will be the same as
the NPV of the project with ?exibility.
NPV of project with flexibility50:875 Ã Vð?Þ 20:5 Ã B
0
50:875 Ã Vð?Þ 20:5 Ã 150=1:05;
ð21:14Þ
EXHIBIT 21-9
FUELCO’S DECISION TREE, PRUNED
Invest
Strong market
Weak market
Weak market
Strong market
Wait
?$150M
$600M
$200M
50%
50%
50%
50%
1
2
3
NOTE: The branches
after nodes 2 and 3
are perfectly correlated.
$450M
Invest
$100M
Don't
4
5
392 CHAPTER 21 REAL OPTIONS
where V(?) is given by Equation (21.10). For ? 5 0 we have V(0) 5 381.0, and thus
NPV of project with flexibility ð? 50Þ
0:875 Ã 381:0 20:5 Ã 150=1:05 5261:9:
ð21:15Þ
For ? 5 1 we have
NPV of project with flexibility ð? 51Þ
0:875 Ã 357:1 20:5 Ã 150=1:05 5241:1:
ð21:16Þ
(d) To compute the option value of waiting, we compare the NPV of project with com-
mitment to the NPV of project with ?exibility. The difference between these NPVs is the
value of the waiting “option”:
Option value of waiting 5NPV of project with flexibility
2NPV of project with commitment
ð21:17Þ
The NPV of project with commitment is given by Equation (21.11). The NPV of
project with ?exibility is given by Equation (21.14). By substituting these equations in
Equation (21.17), we obtain
Option Value of Waiting ð? 50Þ 5$261:9M2$238:1M5$23:8M ð21:18Þ
and
Option Value of Waitingð? 51Þ 5$241:1M2$214:3M5$26:8M: ð21:19Þ
(e) Let p
t
be the probability of strong demand in a risk-neutral world. Then, the present
value of investing at node 1 (5 V
t
) in the risk-neutral world would be
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05: ð21:20Þ
Now, to ?gure out the appropriate risk-neutral probabilities, we set V
t
equal to V (?).
For example, when ? 5 1, we have V (1) 5 357.1. In a risk-neutral world, p
t
is set so that the
value of the asset V
t
would also be equal to 357.1:
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05 5Vð1Þ 5357:1-p
t
50:4375: ð21:21Þ
This answer can be interpreted the following way: “If everyone was risk-neutral and
the probability of strong demand was 43.75 percent, then the Project C would be worth
$357.1M today and would have an expected return of 5 percent.” Using this risk-neutral
probability, we can rewrite Exhibit 21-9 as shown in Exhibit 21-10.
Now, we can solve for the expected terminal value of waiting as
Expected terminal value 50:4375 Ã 450 10:5625 Ã 100 5253:125: ð21:22Þ
In the risk-neutral world, all assets must earn the riskfree rate, so the NPV is
NPV5253:125=1:05 5$241:1M: ð21:23Þ
This is the same answer we found in part (c).
If we do the same steps for the case of ? 5 0, things turn out to be simpler. When ? 5
0, we have V (1) 5 381.0. In a risk-neutral world, p
t
is set so that the value of the asset V
t
would also be equal to 380.1:
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05 5Vð0Þ 5380:1-p
t
50:5: ð21:24Þ
21.4 RISK-NEUTRAL PROBABILITIES 393
Thus, when ? 5 0, the risk-neutral probability is exactly the same as the objective
probability. You should think about this result and convince yourself of its generality.
When ? 5 0, the investment already earns the riskfree rate, so risk-neutral people would
feel right at home. Because p
t
5 0.5, we can compute the NPV by using the event tree in
Exhibit 21-10. The expected terminal value of waiting is
Expected terminal value 50:5 Ã 450 10:5 Ã 100 5275: ð21:25Þ
In the risk-neutral world, all assets must earn the riskfree rate, so the NPV is
NPV5275=1:05 5$261:9M: ð21:26Þ
This is the same answer we found in part (c) for the ? 5 0 case.
’
Please note that the betas and risk do matter here: our answers in the ? 5 0
and ? 5 1 cases are different. “Risk-neutral option pricing” just means that all the
relevant information about betas is already built into the underlying asset prices,
represented here by V (?). Once we know the underlying asset prices, we can
compute option values based on these assets without ever again using betas or
expected returns.
As a special case, any time we have ? 5 0, we can just use objective
probabilities and the riskfree rate. This shortcut comes in very handy when the only
risks we face are (diversi?able) technical risks. We see an example of this shortcut
in the next section.
EXHIBIT 21-10
FUELCO’S EVENT TREE, AFTER NODE 3
4
$450M
Invest
5
$100M
Don't
p' ? 43.75%
(1–p') ? 56.25%
Weak demand
Strong demand
3
394 CHAPTER 21 REAL OPTIONS
21.5 DRUGCO, REVISITED
In this section, we take another look at the long Drugco example from the last chapter.
Our new version is identical to Example 20.4 from the previous chapter, except that
now we allow Drugco to abandon the Newdrug project even after it has been approved.
The new text in this example (as compared to Example 20.4) is given in italics.
EXAMPLE 21.4
Drugco has just begun Phase III trials for Newdrug. Drugco expects Phase III trials to take
two years and the FDA approval decision to take one year, so that the FDA decision is
expected in three years. Phase II trials were promising, with a score of 40 on the standard
medically recognized scale. (We will refer to this score as the “ef?cacy” of the drug.)
Although the best alternative drug has an ef?cacy of 50, it is not helpful for all patients.
Given the side effects of Newdrug and the risks and bene?ts of alternative treatments,
Drugco believes that the FDA will approve Newdrug if the Phase III trials ?nd an ef?cacy of
30 or greater. Based on the results of the Phase II trials, Drugco estimates that the ef?cacy
results of Phase III will be E BN (40, 20). (It is possible for ef?cacy to be negative because
some drugs can make symptoms worse.) During the three years of Phase III trials, it is
possible that the alternative treatments will also improve from their current ef?cacy of 50.
Drugco estimates a ?nal distribution for the alternative of A BT (50, 100, 50). If Newdrug is
approved by the FDA, then its market share will depend on the relative ef?cacy of Newdrug
versus the best available treatment, that is,
Newdrug market share 5E
2
=ðE
2
1A
2
Þ: ð21:27Þ
Drugco estimates market size for Newdrug in the approval year (in thousands of doses)
as M BN (1,000, 100), with 6 percent annual growth going forward. Each dose yields a gross
pro?t of $1. Following FDA approval, with all uncertainty about market size and ef?cacy
known, Drugco can decide either to enter or not to enter the market. If they do not enter, then
they can still sell the approved drug to a European company for $100M Ã E/(E 1A). If they do
enter, then to stay in the market, Drugco must spend $300M on marketing in the ?rst year, with
this sum increasing each year by 6 percent. Upon approval, Newdrug would have 10 years of
patent life remaining. After the patent expiration, Drugco expects generic competition and
other improved alternatives to greatly erode the value of Newdrug, so for simplicity we will
assume that the continuing value would be zero after the patent expires. We assume that
Newdrug faces only technical risk and that the riskless rate is 5 percent.
Problems
(a) Draw the decision tree for the valuation of Newdrug.
(b) Use Monte Carlo simulation to estimate the NPV of Newdrug.
Solutions
(a) The decision tree is given in Exhibit 21-11. This tree is identical to the event tree in
Exhibit 20-18 (from Example 20.4), except for the additional decision nodes at the end of the
21.5 DRUGCO, REVISITED 395
tree. At these decision nodes, Drugco must decide whether or not to enter the market. If
Drugco enters the market, then they earn pro?ts of M Ã E
2
/(E
2
1 A
2
) Ã $300M in the ?rst
year, with increases of 6 percent in each subsequent year up to year 10. If they choose not to
enter the market, then Drugco can sell Newdrug for $100 Ã E/(E 1 A).
(b) Exhibit 21-12 provides a DCF model for calculating the NPV of Newdrug. This model
is identical to Exhibit 20-19 (from Example 20.4) except for two additional cells used for the
decision calculation. These additional cells are given in bold type. The ?rst bolded cell is
the discounted salvage value 5$100 Ã E/ [(E1A) Ã (1.05)
3
]. This cell is set to its expected
value in the exhibit. The middle bolded cell represents the NPV with commitment. This cell
is set to its average over 1M draws, $285.9M, the same average as computed in Chapter 20,
$285.9M. The bottom bolded cell is the NPV with the option to abandon, computed in each
draw by comparing the NPVs in the previous two shaded cells. After 1M draws, the average
NPV was $473.8M, a signi?cant increase over the NPV with commitment. (This example is
also discussed in Appendix C.)
At “enter” terminal nodes, the ?rst year of pro?ts 5 M Ã E
2
/(E
2
1 A
2
) 2 $300M. For
years 2 through 10, multiply pro?ts in the previous year by 1.06, then sum all years and
discount by 1.05 per year to get the NPV.
EXHIBIT 21-11
DECISION TREE FOR NEWDRUG
Alternative:
A ~ T[50,100,50]
Market size:
M ~ N[1000,100]
Efficacy:
E ~ N[40,20]
Same
as 3
Same
as 2
Same
as 3
Same
as 2
Phase III
?$100M
Same
as 4
1 2 3 4
don't
enter
(sell Newdrug)
$100 * E/
(E ? A)
enter
See below
for payoff
E ? 30
$0
3 years
396 CHAPTER 21 REAL OPTIONS
EXHIBIT 21-12
DCF MODEL FOR NEWDRUG
Mean Stdev Min Mode Max
Ef?cacy 40 40 20
Alternative ef?cacy 67 50 50 100
Starting market size 1,000 1,000 100
Approval threshold 30
Gross pro?t per unit 1
Market share 26.5%
Market growth 6.0%
Discount rate 5.00%
approved? 1
Discounted salvage value 32.39
$ in millions
Year 4 5 6 7 8 9 10 11 12 13
Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
Gross pro?t $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
Pro?t 2$35.3 2$37.4 2$39.7 2$42.0 2$44.6 2$47.2 2$50.1 2$53.1 2$56.3 2$59.6
NPV (if enter) 285.9
NPV (with option) 473.8
’
3
9
7
SUMMARY
Real options are ?nance-speak for “?exibility”; real options are created when costly deci-
sions can be delayed. A commuter has a real option to switch from a congested highway to
back roads; a fuel company has a real option to abandon its fuel-cell project if oil prices are
low; a semiconductor company has a real option to expand its factory if demand is strong. A
good analyst must learn to spot real options by keeping an open mind and developing a deep
understanding of his business. Once spotted, real options can be represented in decision trees
and valued using two main techniques. The ?rst technique, replication, is useful for simple
problems but unwieldy for complex problems. The second technique, risk-neutral valuation,
relies on a key insight learned from replication: option-pricing formulas do not rely on risk
aversion—if everyone is highly risk-averse we still get the same answer as the one we get if
everyone is risk-neutral. With this insight, we pretend that we live in a make-believe world
where everyone is risk-neutral, and then use the probabilities from this make-believe world to
price options. This powerful method can be extended to complex examples by using binomial
trees, a topic studied in the next chapter.
KEY TERMS
Real options
Decision trees
Decision nodes
The option to delay
The option to expand
The option to extend
The option to abandon
The option to shrink
The option to switch
Risk-neutral probabilities
EXERCISES
21.1 True, False, or Uncertain : In a risk-neutral world, all assets earn a zero rate of return.
21.2 True, False, or Uncertain : To use risk-neutral valuation, we assume that the under-
lying asset only faces technical risks.
21.3 Semico is considering whether to add capacity to their microchip fabrication plant.
Adding capacity would cost $600M, to be paid in one year. The value of an added-capacity
plant depends on the demand for Semico’s chips. If demand is “high” (25 percent chance),
then the value of the added-capacity plant would be $1,600M (one year from now). If
demand is “low” (75 percent chance), then the value of the added-capacity plant would be
$400M. If Semico chooses to keep the current capacity, then there is no incremental cost. If
demand is “high” (25 percent chance), then the value of the current-capacity plant would be
$600M (one year from now). If demand is “low” (75 percent chance), then the value of the
current-capacity plant would be $400M. We will use the CAPM to estimate expected returns
in this problem, where the expected market premium is 7 percent, and the riskfree rate is
5 percent.
398 CHAPTER 21 REAL OPTIONS
(a) Draw the decision tree for Semico’s problem, where its ?rst decision (node 1) is
whether to commit today to add capacity at a cost of $600M (to be paid in one year), or to
wait one year until information about demand is revealed.
(b) Suppose that Semico chooses to commit at node 1. Solve for the NPV of the project as a
function of its beta. Compute this value in the special cases of ? 5 1 and ? 5 0.
(c) Suppose that Semico chooses to wait at node 1. Use replication methods to solve for the
NPV under the same cases as in part (b).
(d) What is the value of the real option to wait?
(e) Compute the risk-neutral probabilities of high demand and low demand under the same
cases as in part (b). Use these risk-neutral probabilities to calculate the NPV of the project
with ?exibility. Verify that these NPVs are the same as found in part (c).
21.4 (This problem takes some work. For some guidance, see the last example in Appendix
C, which solves a slightly easier version of the problem.) Begin with the same setup as in
Example 21.4, except that now it is one year earlier, and Drugco is deciding whether to
proceed with Phase II trials. Phase II trials will take one year and cost $50M. Following the
Phase II trials, Drugco will learn some information about ef?cacy, denoted as E
t
, with E
t
BT
[0, 80, 40], and about alternative ef?cacy denoted as A
t
BT[50, 80, 50]. If, after learning this
information, Drugco decides to go forward with Phase III trials, then everything is identical to
Example 21.4, except that now the ef?cacy after Phase III trials is distributed as E BN[E
t
, 20],
and alternative ef?cacy is distributed as ABT[A
t
, A
t
1 50, A
t
]. All risks are technical risks, so
all betas are zero and the appropriate discount rate is the riskfree rate of 5 percent.
(a) For what values of E
t
should Drugco continue on to Phase III trials?
(b) What is the NPV of Newdrug at the beginning of Phase II trials?
EXERCISES 399
CHAPTER 22
BINOMIAL TREES
INCHAPTER 21, we learned about risk-neutral probabilities and showed how
to use these probabilities to solve one-step option-pricing problems. In this chapter,
we extend the risk-neutral approach to multistep problems using binomial trees. In
a binomial tree, we restrict all risk nodes to have only two branches, and we set the
moves in those branches by a speci?c formula. In Section 22.1, we show how
binomial trees can be used to approximate the Black-Scholes formula for European
options. The advantage of binomial trees over analytical formulas is that the former
can be used even when underlying assets have dividends or changes in volatility, and
when the options allow for early exercise, have multiple strike prices on different
dates, and have other special features. In Section 22.2, we value an option on Drugco
with early exercise and multiple strike prices; in Section 22.3, we value a real option
for Fuelco with early exercise and dividend payments. Indeed, the main concepts
behind binomial trees allow analysts to handle virtually any complication that nature
can throw at them. For this reason, binomial trees are the main tools used to analyze
complex derivatives on Wall Street and complex real options on Main Street.
22.1 THE BLACK-SCHOLES EQUATION, REVISITED
Bigco stock currently trades for $S per share. Joe Trader holds a (European) call
option with a strike price of $X and an expiration date of one year. The riskfree rate
is r, and Bigco stock has an annualized volatility of ?. As is usual in option-pricing
problems, we assume that these are continuously compounded returns. In Chapter
13, we learned how to value this call option using the Black-Scholes formula. In
this chapter, we learn a new valuation technique based on binomial trees. The
advantage of binomial trees is that they are ?exible enough to handle many
deviations from the Black-Scholes assumptions. However, before we introduce
these deviations, we demonstrate how to build and solve binomial trees for standard
European call options.
We begin by expressing Joe’s call option as a decision tree (Exhibit 22-1).
400
Node 1 is a risk node, and Node 2 is a decision node. At node 1, we draw a
one-year stock return, R, from a log-normal distribution. This is a continuously
compounded return, so the new stock price is then equal to S Ã exp(R). Working
backward, we can see that Joe’s optimal decision at Node 2 would be to exercise if
S Ã exp(R) is greater than X, the exercise price. This gives us a terminal value of
Max[S Ã exp(R), 0] at each possible terminal node.
The hard part about this problem is ?guring out the correct discount rate to
use for the terminal values. This problem is so hard that we didn’t have a solution
until Black and Scholes. When we ?rst saw this solution in Chapter 13, we did
not have all the tools and language to properly discuss all its implications. Now, we
do have this language, so let’s take another look. The Black-Scholes equation for a
European call option is
C
0
5Nðd
1
ÞS
0
2Nðd
2
ÞXe
2rT
; ð22:1Þ
where N (.) is the Normal distribution function and
d
1
5½lnðS
0
=XÞ 1ðr 1?
2
=2ÞTÞ?=ð?OTÞ; ð22:2Þ
d
2
5½lnðS
0
=XÞ 1ðr 2?
2
=2ÞT?=ð?OTÞ 5d
1
2?OT; ð22:3Þ
where T 5 years until the expiration date, ? 5 the annual volatility of returns, and r 5
the annual riskfree rate.
When this solution was ?rst unveiled by its authors, the most surprising part
was that the expected return of the stock does not appear anywhere in the formula.
EXHIBIT 22-1
CALL OPTION IN A DECISION TREE
1 2
Same
as 2
Same
as 2
R ~ LogN[µ–?
2
/2, ?]
S* exp(R) – X
Exercise
Don't
Exercise
0
1 Year
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 401
Take a look again—there is no µ to be found. The only return that appears is the
riskfree rate, r. What is happening here? It all comes back to the logic of repli-
cation. The Black-Scholes logic is the same as the replication logic that we used to
value options in chapters 13 and 21. In replication, we match the option payoffs by
constructing portfolios of riskfree bonds plus underlying risky assets. When we do
this, all information about probabilities, risk aversion, and expected returns is
already embodied in the price of the underlying risky asset. If expected returns
change, then the stock price S
0
would change. Thus, option prices do depend on
expected returns, but only indirectly through the price of the underlying asset.
The insight about expected returns led directly to the development of risk-
neutral probabilities. The idea is that because expected returns and objective
probabilities do not appear anywhere in the formula, then any set of probabilities
that gives the same stock price should also imply the correct option price. We
demonstrated applications of risk-neutral probabilities in Chapter 21. In those
applications, the use of risk-neutral probabilities was limited to one-step trees. The
real power of the risk-neutral insight is that it can be applied to multistep trees. In
the most widely used applications, these trees have exactly two branches after every
risk node: hence, they are called binomial trees. Exhibit 22-2 gives an example of a
three-step binomial tree applied to Joe Trader’s example. In this exhibit, we break
the one-year time period into three subperiods of four months each. Then, in each
EXHIBIT 22-2
A BINOMIAL TREE
9
10
8
7
Su Su
S
S
p p
p
p
p
p
1-p
1-p
1-p
1-p
1-p
1-p
Sd
Sd
Su
3
Su
2
Sd
2
Sd
3
1
3
2
4
5
6
exercise
exercise
exercise
exercise
don't
don't
don't
don't
0
0
0
0
Su
3
– X
Sd
3
– X
Su – X
Sd – X
4 months
Step 2
4 months
Step 3
4 months
Step 1
Set u ? 1/d
402 CHAPTER 22 BINOMIAL TREES
subperiod, we allow only two possible movements for the stock price, an “up”
movement or a “down” movement.
In this tree, there are three different steps, each lasting four months. In each step,
the stock price can either go up (with a return 5 u), or down (with a return 5 d 5 1/u).
Thus, after the ?rst step (Node 1), we have two possible outcomes: a stock price of Su
(Node 2) or a stock price of Sd (Node 3). From Node 2, once again the stock can go up
or down. If the stock goes up, then the value is Su
2
(Node 4), and if it goes down, then
the value is Sdu 5 S (Node 5). The nice feature of binomial trees is that they
recombine, so that the down movement from Node 2 leads to the same stock price as
an up movement from Node 3. With our assumption that u 5 1/d, this recombination
occurs at the same price across each two time periods.
After all three risk steps, we reach the decision nodes of the tree. At each
decision node, Joe should exercise if the stock is valued higher than the exercise
price. In solving binomial trees, it is often helpful to construct two separate
binomial trees: a base tree and an option tree. The base tree gives only the values
of the underlying asset. We build a base tree forward at each node by multiplying
the previous price by either u or d. Exhibit 22-3 gives the base tree for Joe’s option.
Once the base tree is constructed, we solve the option tree backward, starting
with the decision nodes 7 through 10 at time 5 T. At each decision node, we set the
value of the call option equal to the Max (S
T
2 X, 0). Then, we compute
the expected discounted value of the call option at each prior node as
C
T 21
5 p à C
T
ðfrom up nodeÞ 1ð1 2pÞC
T
ðfrom down nodeÞ ½ ?=R
ft
; ð22:4Þ
EXHIBIT 22-3
BASE TREE
Su
S
S
u
u
u
u
d
u
d
u
d
d
d
d
Sd
Su
2
Sd
2
1
3
2
4
5
6
4 months
Step 2
4 months
Step 3
4 months
Step 1
Set u ? 1/d
7
Su
3
10
Sd
3
8
Su
9
Sd
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 403
where R
ft
is the appropriate riskfree discount rate for a time step length of t.
Exhibit 22-4 illustrates this option tree.
To understand the option tree, we must begin at the decision nodes: 7 to 10.
Each of the decision nodes, 7 to 10, contains an equation C
M
5 Max (S
M
2 X, 0),
where M is the node number and S
M
is the terminal value from that node, as taken
from the base tree. Next, we solve backward from these terminal nodes, taking the
expected discounted value at each previous node. For example, consider Node 4.
From Node 4, there will be a probability p of an up move to Node 7 and a pro-
bability (1 2 p) of a down move to Node 8. The expected value of these moves is p
à C
7
1 (1 2 p) Ã C
8
. Because this move take t units of time, we must discount this
expected value by R
ft
, which yields a discounted value of C
4
5 (p à C
7
1 (1 2 p) Ã
C
8
)/R
ft
. (R
ft
is known as the periodic growth factor of the tree.) We solve every risk
node in the tree using exactly the same formula. When we ?nally reach C
1
, we get a
solution for the starting value of the call option.
To transform the general solution of Exhibit 22-4 into a numerical solution,
we apply the same risk-neutral approach as in Chapter 21. First, we need to derive
the appropriate risk-neutral probabilities (p and 1 2 p) and the appropriate size
EXHIBIT 22-4
OPTION TREE
9
10
8
7
p p
p
p
p
p
1-p
1-p
1-p
1-p
1-p
1-p
1
3
2
4
5
6
exercise
exercise
exercise
exercise
don't
don't
don't
don't
0
0
0
0
Su
3
– X
Sd
3
– X
Su – X
Sd – X
4 months
Step 2
4 months
Step 3
4 months
Step 1
C
1
? (pC
2
+ (1 – p)C
3
)/R
ft
C
2
? (pC
4
+ (1 – p)C
5
)/R
ft
C
3
? (pC
5
+ (1 – p)C
6
)/R
ft
C
6
? (pC
9
+ (1 – p)C
10
)/R
ft
C
10
? Max (Sd
3
– X,0)
C
7
? Max (Su
3
– X,0)
C
9
? Max (Sd – X,0)
C
8
? Max (Su – X,0)
C
5
? (pC
8
+ (1 – p)C
9
)/R
ft
C
4
? (pC
7
+ (1 – p)C
8
)/R
ft
404 CHAPTER 22 BINOMIAL TREES
of the up and down movements (u and d). Thus, we have three unknown parameters,
p, u, and d. To solve for these parameters, we need three equations. Just our luck, we
have exactly three equations: one for the expected return (which must be equal to the
riskfree rate, r, in our risk-neutral world), one for the volatility (which must be equal
to ?, the “known” volatility of the stock), and a ?nal equation with our assumption
that d 5 1/u.
We begin with the expected return equation. In Exhibit 22-2, the length of the
whole tree is one year, and the length of each step on the tree is four months. For
generality, we write the length of the whole tree as T and the length of each step as
t 5T/N, where N is the number of steps in the tree. Then, the risk-free return (5
growth factor) over each step size t is R
ft
5 exp(r à t). Then, using the up and down
movements in the tree, we can write this growth factor as
R
ft
5expðr à tÞ 5p à u 1ð1 2pÞ Ã d: ð22:5Þ
We next write an equation for the variance of returns. The variance of returns
in each full year in the tree is ?
2
. Because variance is additive over time, the
variance of returns for the whole tree must be ?
2
à T, and the variance of returns in
each step in the tree must be ?
2
à t. In general, the formula for the variance of
returns, R, can be written as
Variance of returns; R5Expected value ½R
2
? 2ðExpected Value ½R?Þ
2
: ð22:6Þ
We now replace each term of Equation (22.6). As stated earlier, the left-hand
side of the equation is equal to ?
2
à t. Next, the ?rst term on the right-hand side can
be written by multiplying the probability of each branch by the square of the return
on each branch:
Expected value ½R
2
? 5p à u
2
1ð1 2pÞ Ã d
2
: ð22:7Þ
Finally, we can write the second term on the right-hand side of Equation
(22.6) by squaring the expected return from Equation (22.5)
ðExpected Value ½R?Þ
2
5ðp à u 1ð1 2pÞ Ã dÞ
2
: ð22:8Þ
Next, we substitute Equations (22.7) and (22.8) into (22.6) to obtain
Variance of returns; R5?
2
à t 5p à u
2
1ð1 2pÞ Ã d
2
2ðp à u 1ð1 2pÞ Ã dÞ
2
:
ð22:9Þ
Now Equations (22.5) and (22.9) can be combined with our assumption that
d 51/u to give us three equations and three unknowns. The hard part is over, and
the rest is algebra. We can use these equations to solve for the unknown variables as
p 5
R
ft
2d
u 2d
ð22:10Þ
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 405
where
R
ft
5expðr à tÞ;
u 5expð?
??
t
p
Þ; and
d 5expð2?
??
t
p
Þ:
ð22:11Þ
The solution in Equations (22.10) and (22.11) was ?rst proposed by Cox, Ross,
and Rubinstein (1979) and is known as the CRR model. The key assumption of the
CRR model is that d 5 1/u, which leads to a tree like Exhibit 22-2, with nodes that
recombine at the same value as previous nodes on the same row of the tree. There are
many other methods to build binomial trees, but we will exclusively use the CRR
model in this chapter. Please see Hull (2005) for a discussion of other methods.
For concreteness, let’s assume that for Joe Trader’s Bigco option, we have a
starting stock price of $100, a strike price of $50, a volatility ? 5 60 percent, and
a riskfree interest rate of r 5 5 percent. With a three-step tree (N 5 3) and a
one-year option (T 5 1), we have t 5 1/3 (four months), so that
R
ft
5expðr à tÞ 5expð0:05 à 1=3Þ 51:017 ð22:12Þ
Now, we are ready to solve for u, d, and p as
u 5expð?
??
t
p
Þ 5expð0:6 Ã
???????
1=3
p
Þ 51:414; ð22:13Þ
d 51=u 50:0707; and ð22:14Þ
p 5
R
ft
2d
u 2d
5
1:017 20:707
1:414 20:707
50:438: ð22:15Þ
To solve for the option value, we use these numbers to build the base tree, and
then we substitute the terminal values into the option tree and solve backward.
Exhibits 22-5 and 22-6 give these two trees. Readers can compare the analytical
formulas in Exhibits 22-3 and 22-4 with their numerical solutions in Exhibits 22-5
and 22-6 and see that the solutions are consistent. To make it easier to read these
trees, we put the numerical values inside in the nodes, with the node label (#1, #2,
etc.) given above the nodes.
Exhibit 22-6 gives a solution of $54.91 for C
1
(the ?rst entry in the tree). To
check this solution, we can use the European Call Option Calculator of the VCV
model, where these same inputs yield a solution of $54.52. Because we know that
the Black-Scholes solution in European Call Calculator is correct, the three-step
tree is off by $0.39, which is less than 1 percent of the true value. To achieve more
precise estimates, we need to use a larger tree with shorter time steps. There are
many commercial sources for binomial trees.
1
For this book, we use a relatively
small tree, ?xed at 60 steps, included in a spreadsheet named as bintree.xls. This
spreadsheet contains three linked worksheets: inputs, base-tree, and option-tree.
1
For inexpensive versions, see the software included with Hull (2005) and Haug (1998).
406 CHAPTER 22 BINOMIAL TREES
EXHIBIT 22-5
JOE’S PROBLEM, BASE TREE
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
1
3
5
6
4
2
4 months
Step 2
4 months
Step 3
4 months
Step 1
7
$282.70
10
$35.37
8
$141.40
9
$70.72
$100.00
$141.40
$199.93
$100.00
$50.02
$70.72
EXHIBIT 22-6
JOE’S PROBLEM, OPTION TREE
exercise
don't
exercise
don't
exercise
don't
exercise
don't
1
4
5
6
2
3
$93.04
$54.91 $100.00
$8.93
$232.70
$0
$91.40
$0
$20.72
$0
–$14.63
$0
$0
10
9
$20.72
8
$91.40
0.438
0.438
0.438
0.562
0.562
0.562
0.438
0.562
0.438
0.562
0.438
0.562
7
$232.70
$50.83
$150.96
$26.83
407
The inputs worksheet converts assumptions for interest rates, volatility, and time-
to-expiration into outputs for t, u, d, and p, and then the base-tree worksheet builds
a base tree from these outputs. The worksheet then solves a European call-option tree.
To solve more complex options, we usually need to copy and alter the option-tree
worksheet. We will describe how to do this in Examples 22.1 and 22.2.
Exhibit 22-7 shows a portion of the inputs sheet for Joe’s problem.
In Exhibit 22-7, the inputs are given on the left, and the outputs are given
on the right. With N 5 60, the time steps are 1/60 of a year, and the growth factor
(5 exp(r à t)) is 1.000834 for each step. From this inputs sheet, we build a base
tree with 60 steps in the base-tree worksheet. Of course, this whole worksheet is
much too large to display on the printed page. At step 1 there is one risk node, at
step 2 there are two risk nodes, . . ., all the way up to 60 risk nodes at step 60.
Overall, there are 1 1 2 1 3 1 ?1 60 5 1,830 risk nodes in the tree, followed
by 61 terminal nodes after Step 60. The option-tree worksheet then takes the 61
terminal nodes from the base-tree worksheet, “decides” whether to exercise based on
Max(S
60
2$50, 0), and then solves backward exactly as in Exhibits 22-4 and 22-6.
The answer of $54.53 is displayed at the base of the option-tree worksheet. This
answer is only $0.01 away from the Black-Scholes solution found in European Call
Calculator.
Note that the actual option-tree worksheet does not include branches after
the decision nodes. Instead, the decision-node cells use the “max” function in
Microsoft Excel. This is a space-saving device that is particularly useful when
we alter the sheet to value American options, where every time period includes
both a risk node and a decision node. American options will be discussed in
Section 22.3.
EXHIBIT 22-7
THE INPUTS SHEET FOR JOE’S PROBLEM
? 60% t 0.02
R 5% R
ft
1.000834
S 100 u 1.080539
T 1 d 0.925464
X 50 p 0.486021
408 CHAPTER 22 BINOMIAL TREES
22.2 MULTIPLE STRIKE PRICES AND
EARLY EXERCISE
In the previous section, we showed that binomial trees can approximate the Black-
Scholes solution. By itself, this approximation does not buy us anything because we
already had an analytical solution for European options. The real payoff of bino-
mial trees comes when we introduce complications that cannot be handled by
Black-Scholes, or by any other analytical formula. In this section, we use binomial
trees to value an option with two different strike prices on two different dates. The
options analyzed in Example 22.1 are warrants. Warrants are call options that are
issued by companies on their own stock; in contrast, regular call options are issued
by some third party. Although there are some valuation differences between call
options and warrants, we will sidestep these differences by making some subtle
assumptions in the example, so that we can just treat these warrants as regular
call options. Readers interested in exploring the differences between warrants and
options are encouraged to look at Chapter 11 of Hull (2005).
EXAMPLE 22.1
Drugco is a publicly traded biotechnology company with several drugs in development, but no
products on the market. To raise capital for the development of Newdrug, Drugco enters a
strategic alliance with Bigco. In return for marketing rights for Newdrug, Bigco will pay for
clinical trials and will give drugco up-front and milestone payments. Bigco also agrees to make
an equity investment in Drugco, purchasing 10 million shares at the market price of $10 per
share and also receiving warrants to purchase an additional 10 million shares. (The market price
of $10 includes the market reaction to the Bigco alliance.) These warrants can either be
exercised in exactly two years at a strike price of $20 per share or in exactly ?ve years, with a
strike price of $50 per share. Drugco does not pay dividends and has no plans (or cash) to do so
for at least the next ?ve years. The expected volatility of Drugco stock is 60 percent per year.
Problem What is the value of Bigco’s warrants?
Solution If not for the step up in the exercise price, this would be a straightforward
option pricing problem and could be solved by the Black-Scholes equation. With the step
up, we need to use a binomial tree to solve the problem. We start by building the base
tree, which is invariant to strike-price complications. If we use bintree.xls, then we have a
60-step tree. With T 5 5 years, then t 5 5/60 5 1/12 5 0.833 5 one month. Exhibit 22-8
shows the other inputs for the tree.
From these inputs, the base-tree worksheet builds values for the stock. Now, the tricky
part—how do we build and solve the option tree? Option trees are always solved backward.
We start at the exercise date, after all 60 steps of the tree. At that point, the exercise decision
is the “normal” one: exercise if and only if the stock price is greater than the exercise price
(5$50). Because this is the standard approach in the option tree, we do not need to make any
22.2 MULTIPLE STRIKE PRICES AND EARLY EXERCISE 409
changes. Similarly, to compute the discounted value at steps 59, 58, . . ., 25, we can just
follow the same procedure as in earlier examples. The only complication occurs at Step 24,
which is after two years of the tree. At this step, Bigco has another choice to make: it can
either exercise the option, and receive an immediate payoff of S
24
2 $20, or let the ?rst
exercise date expire and receive the present discount value of the option that would ordi-
narily be calculated for that node of the tree.
Exhibit 22-9 gives portions of Steps 24 and 25 for various trees associated with
Bigco’s two-strike problem. Column (A) gives the row number, so that we can refer to cells
in the tree as we would in a spreadsheet. Column (B) shows all possible payoffs in the upper
half of the base tree at Step 24: these payoffs are copied from the base-tree worksheet. The
next four columns, (C) through (F), show Steps 24 and 25 from two different versions of
the option-tree worksheet. The ?rst version is the standard option-tree worksheet included
in the bintree ?le. This sheet is shown in columns (C) and (D), and it is a standard European
call without allowing for the possibility of an early exercise at Step 24. The second version,
named as early-tree and shown in columns (E) and (F), modi?es the ?rst version to allow for
early exercise.
To build the early-tree worksheet, we start with a copy of option-tree. In early-tree, all
columns from Step 25 to Step 60 are identical to the corresponding columns in option-tree.
This is illustrated in part by column (F) in the exhibit, which is identical to column (D). Next,
we edit the cells in Step 24 of column (E) to re?ect the possibility of early exercise at a strike
of $20. For example, to compute the entry for cell E2, we write
E2 5Max ðB2 2$20; C2Þ: ð22:16Þ
Equation (22.16) states that, at Step 24, Bigco can either choose to exercise and
receive the stock value (cell B2) minus the strike price ($20), or it can choose to hold onto the
option and receive the expected discounted value of a one-strike option (cell C2). We then
repeat this same formula for all cells in column (E). These are the only changes that are
needed to solve the two-strike tree. By examining the exhibit, we can see that Bigco would
choose to exercise early in all cases at row 20 and above. If we then look at the solution in
Step 1 of the tree (not shown in the exhibit), we get an option value of $2.15. In contrast,
the one-strike tree yields an option value of $1.87. Thus, the possibility of early exercise
EXHIBIT 22-8
INPUTS TREE FOR BIGCO’S PROBLEM
? 60% T 0.08
r 5% R
ft
1.004175
S 10 U 1.18911
T 5 D 0.840965
X 50 P 0.4688
410 CHAPTER 22 BINOMIAL TREES
at $20 gives an incremental value of $2.15 2$1.87 5$0.28 per option, making Bigco’s 10M
options worth $2.8M. ’
22.3 DIVIDENDS
Many public companies pay periodic dividends on common stock, and these
dividends can complicate the valuation of call options. For non-dividend-paying
EXHIBIT 22-9
EXCERPTS FROM TREES FOR EARLY-STRIKE DECISION
(A) (B) (C) (D) (E) (F)
Base-tree Option-tree Early-tree
Step 24 Step 24 Step 25 Step 24 Step 25
1 716.44 716.44
2 638.75 595.92 618.75
3 494.25 494.25
4 451.74 409.21 431.74
5 337.38 337.38
6 319.48 277.55 299.48
7 226.93 226.93
8 225.94 185.09 205.94
9 149.61 149.61
10 159.79 120.66 139.79
11 96.06 96.06
12 113.01 76.38 93.01
13 59.62 59.62
14 79.92 46.60 59.92
15 35.48 35.48
16 56.52 27.19 36.52
17 20.08 20.08
18 39.97 15.04 19.97
19 10.71 10.71
20 28.27 7.83 8.27
21 5.35 5.35
22 19.99 3.81 3.81
23 2.47 2.47
24 14.14 1.71 1.71
25 1.05 1.05
26 10.00 0.71 0.71
27 0.41 0.41
22.3 DIVIDENDS 411
stocks, a diversi?ed investor that holds American call options should never exercise
early. The logic for waiting until the very end—?rst discussed in Chapter 13—is
that the option holder can earn the interest on the strike price without giving up
anything. If the stock pays dividends, then waiting to exercise until the end may no
longer be optimal. Unfortunately, analytical solutions are usually not possible for
these problems. Thus, most analysts build binomial trees to compute numerical
solutions for American options on dividend-paying stocks.
Consider Joe’s three-step problem, as ?rst illustrated in Exhibit 22-2. Now,
let’s add a dividend in the second-to-last period (eight months into the year) that is
equal to 10 percent of the stock value. Now, if Joe decides to exercise after eight
months, he would receive the whole value of the stock (including the 10 percent
dividend). If, instead, he decides to wait until the full year is over, then the 10
percent dividend gets paid out after eight months, and the stock price falls by
10 percent before making an up or down move in the last period. Exhibit 22-10
illustrates the new base tree under this assumption.
EXHIBIT 22-10
JOE’S PROBLEM, BASE TREE, WITH DIVIDENDS
$100.00
$141.40
$70.72
3
2
1
$100.00
5
$90.00
$199.93
4
$179.94
$50.02
6
$45.02
0.438
0.438
0.438
0.562
0.438
0.438
0.562
0.562
0.438
0.562
0.562
0.562
Dividend
? $19.99
Dividend
? $10.00
Dividend
? $5.00
7
$254.43
8
$127.26
9
$63.65
10
$31.84
412 CHAPTER 22 BINOMIAL TREES
In Exhibit 22-11, we show the option tree, an analogue to Exhibit 22-6 from
the no-dividend case. In this tree, we divided nodes 4, 5, and 6 into two nodes each.
For example, Node 4 is now a decision node for early exercise, and Node 4A is a
risk node that is only relevant if Joe decides to wait at Node 4. Although these
nodes would not be divided in the bintree spreadsheet, it is useful to divide them in
the exhibit to make comparisons to decision trees.
As always, we solve the option tree backward. In nodes 7 through 10, Joe
needs only to compare payoffs at the terminal nodes. If he chooses to exercise, then
the option would be worth S
T
2 $50, where S
T
is taken from the corresponding
terminal node of the base tree; if he chooses not to exercise, then the option is
worth $0. We then assign each terminal node (7 though 10) with the maximum of
S
T
2 $50 and $0.
Continuing our backward march through the tree, we next come to risk nodes
4A, 5A, and 6A. Joe will only reach these nodes if he chooses to wait at decision
EXHIBIT 22-11
JOE’S PROBLEM, OPTION TREE, WITH DIVIDENDS
1
2
$204.43
$77.26
$13.65
–$18.16
exercise
exercise
exercise
exercise
exercise
exercise
wait
wait
wait
exercise
$0
$0
$0
$0
don't
don't
don't
don't
$0
10
9
$13.65
6
5
3
$24.79
$92.22
4
8
$77.26
7
$204.43
0.438
0.438
0.438
0.438
0.438
0.438
0.562
0.562
0.562
0.562
0.562
0.562
$40.83
5A
$130.97
$149.93
$50.00
$0.02
4A
$5.88
6A
$53.43
4 months 4 months 4 months
$5.88
$50.00
$149.93
22.3 DIVIDENDS 413
Nodes 4, 5, and 6, respectively. To compute the expected value at these risk nodes,
we take 0.438 Ã the up branch 1 0.562 Ã the down branch, discounted by R
ft
5
1.017 (from Equation (22.12)). For example, at Node 4A we have
2
Value at Node 4A5ð0:438 Ã $204:43 10:562 Ã $77:26Þ=1:017 $130:97 ð22:17Þ
Now, at Node 4, Joe can either choose to wait (and receive a discounted
expected value of $130.97) or exercise immediately. If he exercises immediately,
then he will get the stock before it pays the dividend. This is the key factor
driving the possibility of early exercise. Thus, with early exercise he would get
the full value of the stock before the dividend, minus the strike price of $50:
$199.93 2 $50 5$149.93. The decision at Node 4 is to take the maximum of the
waiting value ($130.97) and the early exercise value ($149.93). We then type this
maximum into Node 4 in the tree.
With similar comparisons, we can see that early exercise is optimal at Nodes
4 and 5, but not at Node 6. We then back the expected values up through risk nodes
2 and 3, and ?nally back to the base of the tree at Node 1. This procedure yields an
option value of $53.43 at the ?rst node.
In our next example, we generalize the dividend problem to our full 60-step
tree and model a real option for a company to invest in a pro?table project. If the
company invests right away, then it immediately gets some positive cash ?ows and
a positive overall NPV. If it waits, however, then it may be able to avoid investing
for some cases where the project goes bad. There is a cost to waiting because the
company must forego the positive cash ?ows that would have been generated
during this waiting period. These positive cash ?ows are modeled as “dividends”.
One nice feature of real-option problems is that it is reasonable to model these
dividends as a continuous payment of some fraction of the project value. By
modeling dividends as a continuous payment, the construction of the binomial tree
is simpli?ed. We demonstrate this technique in the following example.
EXAMPLE 22.2
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19 and is similar to Example 21.3 from the previous
chapter.) They have already completed several R&D projects with this technology, so they
have eliminated the technical risk for this new project. To begin producing and marketing
to the consumer market would require a new investment of $200M. At the present time,
Fuelco estimates that the completed project would have a present value of $400M (i.e.,
if Fuelco spent $200M to initiate the project, they believe they could spin off the initiated
project for $400M). Fuelco can delay starting the project for up to ?ve years, during which
time they expect this value of the project to ?uctuate, with an annual volatility of 90 percent.
Once initiated, the project is expected to generate annual cash ?ows equal to 10 percent of its
2
We use the operator in Equation (22.18) because of a rounding error.
414 CHAPTER 22 BINOMIAL TREES
value. Thus, if Fuelco delays the project, they will forego these cash ?ows. After ?ve years,
some important Fuelco patents will expire, and they will no longer have the option to
pro?tably enter this new market. If Fuelco does not enter the market, then Project C has no
salvage value.
Problem What is the NPV of Project C?
Solution The problem here is to value Fuelco’s real option to invest. If Fuelco invests
right away, then it would cost $200M and provide a present value of $400M, for a total NPV
of $200M. So why would Fuelco ever decide to wait? Because it is possible that the project
will have terrible performance in the next few years, in which case Fuelco will be happy that
they held on to the $200M. There is a cost to such patience because Fuelco will have to
forego some positive cash ?ows during this waiting period. Because Fuelco can make this
decision at any time, there are an in?nity of possible decision nodes. To get an approximate
answer to the problem, we assume that decisions to invest can only be made once per month,
and we adopt a binomial-tree framework with only two possible branches (up and down)
from each risk node. Even with this assumption, over ?ve years there are still 60 possible
dates in which to invest. Exhibit 22-12 shows the ?rst part of the decision tree.
EXHIBIT 22-12
FUELCO’S PROBLEM, PROJECT C
1
foregone
cash flow
? CF
1
foregone
cash flow
? CF
4
invest –$200M
invest –$200M
3
foregone
cash flow
? CF
5
invest –$200M
5
11
10
13
12
. . .
. . .
6
7
8
9
1–p
1–p
down
1–p
down
p
down
up
$400
wait
up
p
up
p
wait
wait
($400 – CF
1
)*u
($400 – CF
1
)*u
4
2
instant One month One month instant
22.3 DIVIDENDS 415
The ?rst decision occurs at Node 1. As we already discussed, if Fuelco chooses to
invest immediately, then they spend $200M for a project with a value of $400M, as shown at
terminal Node 2. If Fuelco chooses to wait, then some project risk evolves during the ?rst
month (Node 3), during which time Fuelco does not receive any of the project cash ?ows. We
write these cash ?ows as CF
1
, which means “cash ?ows forgone by waiting at Node 1”. At
Node 3, an up move results in a project value of ($400 2 CF
1
) Ã u and a down move leads to
a project value of ($400 2 CF
1
) Ã d. At the end of this ?rst month, Fuelco again makes a
decision about whether to invest (Nodes 4 and 5). This process continues for 59 more
months. To solve the tree, we work backward from Step 60.
Clearly, this decision tree grows very large by Step 60. To make the problem more
manageable, we follow the same procedure as in earlier problems and break the decision tree
into two binomial trees: a base tree and an option tree. Exhibit 22-13 gives the inputs sheet
for these trees. This exhibit includes a row for the dividend yield ( y) and for the dividend
factor, R
yt
5 exp(yt), which is an analogue to the growth factor.
Because the annual dividend yield (10%) is greater than the riskfree interest rate (5%),
Fuelco may indeed want to exercise early at several points in the option tree. As in the previous
example, we will need to alter the option-tree worksheet to allow for early exercise. We refer to
this new worksheet as am-tree. Exhibit 22-14 gives excerpts from the last few steps of
the binomial trees. The ?rst half of the tree gives an excerpt from the base-tree worksheet,
and the second half of the tree gives an excerpt from the am-tree worksheet. All excerpts are
from the middle of the tree at Steps 58, 59, and 60. To build the base tree, we multiply cells by
the up (or down) branch and divide by the dividend factor. (The values of these inputs are
given in Exhibit 22-13.) For example, to compute cell C1 we use the following formula:
C1 5B2 Ã u=R
yt
5$697:40 Ã 1:296681=1:008368 5$896:80: ð22:18Þ
In the base-tree portion of Exhibit 22-14, notice that the rows of the tree do not have a
constant value (e.g., in cell B4 the value of the project is $414.78, whereas in cell D4 the
value is $407.92). This “loss” of value occurs because of the dividends; in binomial trees
without dividends (like Exhibit 22-5), the tree recombines at the same value.
The am-tree tree is solved backward, starting with Step 60. The entries in column G
are the value of the real option in the last period. We calculate these values with the standard
maximum formulas. For example, the value of cell G2 is
G2 5Max ðD2 2$200; $0Þ: ð22:19Þ
EXHIBIT 22-13
INPUTS SHEET FOR FUELCO’S PROBLEM
? 90% t 0.08
r 5% R
ft
1.004175
S 400 u 1.296681
T 5 d 0.7712
X 200 p 0.443357
y 10% R
yt
1.008368
416 CHAPTER 22 BINOMIAL TREES
Next, at Step 59 Fuelco must decide whether to exercise immediately (and receive the value
in the base tree minus $200) or to wait (and receive the expected discounted value of the up
and down branches.) The formula for cell F3 is
F35Max ððp à G21ð12pÞ Ã G4Þ=R
ft
; C32$200Þ 5Max ð$329:78; $333:37Þ 5$333:37:
ð22:20Þ
Thus, Fuelco would choose early exercise in cell F3. This should not be surprising:
because Fuelco knows it will exercise in both successor cells (G2 and G4), it will bene?t by
exercising early and taking the dividend (10 percent annualized), even at the cost of losing
the time value of the strike price (5 percent annualized).
The computer uses the same formulas to solve the tree all the way back to its ?rst cell.
The am-tree worksheet values the real option at $249.66M. Thus, Project C is worth almost
$50M more than the $200M value from immediate investment. ’
SUMMARY
In this chapter we learned about binomial trees, a ?exible and powerful type of decision
tree. In binomial trees, each risk node is followed by two branches: an “up” branch with
probability 5 p, and a down branch with probability 5 1 2 p. In the Cox-Ross-Rubenstein
(CRR) model, the size of the down move is set equal to the reciprocal of the up move: d 5 1/u.
Binomial trees built with the CRR model have several nice features, and modi?ed versions of
the trees can be used to obtain solutions for many complex option features. In this chapter, we
solved examples for options with multiple strike prices on different dates, and for real options
on positive cash-?ow projects.
EXHIBIT 22-14
EXCERPTS FROM TREES FOR FUELCO’S PROBLEM
Base-tree Am-tree
(A) (B) (C) (D) (E) (F) (G)
STEP STEP
ROW 58 59 60 58 59 60
1 $896.80 $696.80
2 $697.40 $685.87 $497.40 $485.87
3 $533.37 $333.37
4 $414.78 $407.92 $214.78 $207.92
5 $317.22 $117.22
6 $246.69 $242.61 $62.18 $42.61
7 $188.67 $18.81
8 $146.72 $144.29 $8.31 $0.00
SUMMARY 417
KEY TERMS
Binomial trees
Recombine
Base tree, option tree
Growth factor
CRR model
Warrants
Dividend factor
REFERENCES
Cox, John C., Steven A. Ross, and Mark Rubinstein, 1979, “Option Pricing: A Simpli?ed Approach”,
Journal of Financial Economics 7, 229À263.
Haug, Espen G., 1997, Option Pricing Formulas, McGraw-Hill, New York.
Hull, John C., 2005, Option, Futures, and Other Derivatives, 6th Edition, Prentice Hall, Upper Saddle
River, NJ.
EXERCISES
22.1 True, False, or Uncertain : Assume that all Black-Scholes assumptions hold. Let C be
the value of a call option with strike price X on underlying stock S and exercise date T in a
world with riskfree interest rate r. This underlying stock has an expected return of µ and an
expected volatility of ?. Now, assume that everyone in the world suddenly becomes more
risk averse, and the new expected return on the underlying stock is u
f
, where µ
f
.µ. There is
no change in ? or r. After this change, the value of C will go down.
22.2 Begin with the same setup as Example 22.1: Bigco’s investment in Drugco for equity
plus warrants. Now, in addition to the strike price of $20 after two years and $50 after ?ve
years, assume that the warrants can also be exercised after three years at a strike of $30 or
after four years at a strike of $40. Assume everything else from the problem is unchanged.
Use bintree to solve for the value of Bigco’s warrants.
22.3 Begin with the same setup as Example 22.2: Fuelco’s investment in Project C. Now, in
addition to the assumptions made in the example, we add an additional possibility: Fuelco
has an option to sell the patents that underlie Project C for $100M in exactly three years.
They can only sell these patents if they have not yet invested the required $200M in the
project. Selling the patents has no effect on any of Fuelco’s other projects. How does this
new option affect the NPV of Project C?
22.4 Begin with the same setup as Example 22.2: Fuelco’s investment in Project C. Now,
suppose we believe that the volatility of the project is really 120 percent. With this high
volatility, a 60-step tree may not be suf?ciently precise. Edit the bintree spreadsheet to build
a 100-step tree, and then compare the option values for N 5 60 and N 5 100. How different
are these values? Do you think it is necessary to build an even larger tree? (This exercise will
be time consuming. It is good practice if you want to learn how to build your own trees.)
418 CHAPTER 22 BINOMIAL TREES
CHAPTER 23
GAME THEORY
R&D DECISIONS are rarely made in isolation from competition. So far, all
our models have ignored the strategic aspects of competition, with potential
competitors modeled as random events that might reduce pro?ts. In a more realistic
model, a company must consider a variety of different strategies in response to
competition, while simultaneously recognizing that competitors will also be mak-
ing similar calculations. The interaction among different decision makers, all of
whom may have different objectives, is the domain of game theory. Despite its fun-
sounding name, game theory has always been concerned with serious matters, with
nuclear deterrence among its earliest topics.
In this chapter, we give an introduction to game theory and discuss several
applications to R&D investing. Although the subject of game theory is vast enough
to justify years of study, the key concepts are accessible to all interested amateurs.
In Section 23.1, we provide a core set of terms and de?nitions and set up a few
canonical games, beginning with the prisoner’s dilemma. In Section 23.2, we
“solve” these canonical games using the powerful concept of the Nash Equilibrium.
In Section 23.3, we introduce a more complex set of games and re?ne the Nash
equilibrium concept to allow for more robust solutions. In Section 23.4, we show
how the game-theory analysis of this chapter can provide fresh insights into real-
option investment problems.
23.1 WHAT IS GAME THEORY?
We begin with the most famous example in all of game theory: the prisoner’s
dilemma. Two people, Al and Bob, have been arrested by the police and are being
held in separate rooms. In each room an interrogator explains to the prisoner that he
should make things easy for himself and “confess” to the crime. (Whether Al and
Bob are actually guilty is immaterial to the problem.) Each prisoner can choose
whether or not to confess. If both prisoners confess, then they will both go to jail for
eight years. If neither prisoner confesses, then the prosecutors will not be able to
419
convict both defendants of the highest crime, but they will still both go to jail
for two years. If, however, only one of the prisoners confesses, then the confessor
will be released without any jail time, while the other prisoner will get 10 years.
Exhibit 23-1 expresses these payoffs in a 2 3 2 matrix. This matrix is called the
normal form of the game.
In this exhibit, the strategies of each player are given in the ?rst column (for
Al) and in the ?rst row (for Bob). The payoffs corresponding to each strategy pair
are given in the corresponding box in the matrix, with Al’s payoff listed ?rst. For
example, if Al chooses don’t confess and Bob chooses confess, then Al gets 10
years and Bob goes free (0 years).
We can also represent the prisoner’s dilemma in a game tree. This game tree,
also known as the extensive form of the game, is shown in Exhibit 23-2.
In Exhibit 23-2, we draw the ?rst decision node for Al, and the second (and
third) decision nodes for Bob. The payoffs are given at the terminal nodes, with
years of jail time expressed as negative numbers: (— Al’s years, — Bob’s years).
Although this representation might imply that Al actually decides before Bob, the
description of the game has the two players making their decisions at the same
time. To illustrate that the decisions are actually simultaneous, the standard
practice is to draw a closed curve around Bob’s two decision nodes; this closed
curve indicates that Bob does not know whether he is at Node 2 or Node 3. He
must make his decision at Nodes 2 and 3 based on his best guess of what Al will
do, just like Al must make his decision at Node 1 based on his best guess of what
Bob will do. This is called a simultaneous game. If Al actually did move ?rst,
then we would erase the closed curve around Nodes 2 and 3, and we would have a
sequential game. In Section 23.2, we learn how to solve for the equilibria of
simultaneous games. In Section 23.3, we learn how to solve for the equilibria in
sequential games. First, we get some practice with drawing the normal and
extensive form for another game.
EXHIBIT 23-1
PRISONER’S DILEMMA, NORMAL FORM
Bob
Confess
Don’t
Confess
A1 Confess 8 years, 0 years,
8 years, 10 years
Don’t 10 years, 2 years,
Confess 0 years 2 years
420 CHAPTER 23 GAME THEORY
EXAMPLE 23.1
Anne and Beth completed a group assignment for their ?nance class. The assignment is due
in ?ve minutes, but neither of them brought it to class. (They each believed that the other
student was going to bring it.) Because this professor never grants any extensions, Anne and
Beth both know that one of them will need to run back to their apartment to print out the
assignment. To decide which one of them must make this long trek in the rain, they resort to
the oldest of games: “odds and evens”. In the odds-and-evens game, one player (here, Anne)
takes “odds”, and one player (here, Beth) takes “evens”. Then, both players simultaneously
show one or two ?ngers. If both players show the same number of ?ngers, then the evens
player (Beth) wins the game. If players show different numbers of ?ngers, then the odds
player (Anne) wins the game.
Problems
(a) Draw the normal form for this game.
(b) Draw the extensive form for this game.
Solutions
(a) The normal form is given in Exhibit 23-3.
EXHIBIT 23-2
PRISONER’S DILEMMA, EXTENSIVE FORM
1
Al
2
3
Bob
Confess
Don't
confess
Don't
confess
Confess
Confess
Don't
confess
(–8, –8)
(0, –10)
(–10, 0)
(–2, –2)
23.1 WHAT IS GAME THEORY? 421
If the players choose a different number of ?ngers, then Anne wins and gets to stay, with
Beth going back to her apartment to get the assignment. If the players choose the same
number of ?ngers, then Beth wins and gets to stay. We give a payoff of one to the player who
wins the game (“stays”), so that the payoffs where Anne wins (odds) are (1, 0), and the
payoffs where Beth wins (evens) are given payoffs of (0, 1).
Games like this are known as zero-sum games or constant-sum games, because there is
a ?xed amount to be won or lost (not necessarily zero), and this ?xed amount must be shared by
the two players. In contrast, in the prisoner’s dilemma, the total amount of jail time was not ?xed.
(b) The extensive form for the odds-and-evens game is given in Exhibit 23-4.
EXHIBIT 23-4
ODDS-AND EVENS-GAME, EXTENSIVE FORM
1
Anne
2
3
Beth
Two
One
Two
One
One
Two
(0, 1)
(0, 1)
(1, 0)
(1, 0)
EXHIBIT 23-3
ODDS-AND-EVENS GAME, NORMAL FORM
Beth
One Two
Anne
One 0, 1
1, 0
1, 0
Two 0, 1
422 CHAPTER 23 GAME THEORY
As in the prisoner’s dilemma game (Exhibit 23-2), we arbitrarily put one of the players
?rst (Anne) and then draw a closed curve around decision nodes 2 and 3 to indicate that Beth
cannot tell which node she is at when she makes her decision.
’
23.2 SIMULTANEOUS GAMES
In the previous section, we drew normal and extensive forms for two games, but we
did not make any statements about optimal strategies or solutions. However,
before proceeding to a solution, we need to de?ne what a “solution” would be. In
game theory, there are many different equilibrium concepts for solving a game.
The unifying theme to all these concepts is that all players must be maximizing their
expected utility subject to some beliefs about other players’ decisions. The concepts
differ only in the precise meaning of “subject to some beliefs”.
The most famous and ?exible of all equilibrium concepts is Nash Equi-
librium (NE). This concept is named for its founder, John Nash, a Nobel Prize
winner in economics and the subject of an Academy Award-winning movie, A
Beautiful Mind. NE requires that each player’s equilibrium strategy must be a best
response to the equilibrium strategies of all other players. Put another way, once
the equilibrium strategies have been written down, no player could improve the
payoff by changing to a different strategy.
For games where the normal form can be easily written down (as in Exhibits
23-1 and 23-3), we can use a simple procedure for ?nding the NE. Exhibit 23-5
illustrates this procedure for the prisoner’s dilemma.
Exhibit 23-5 uses the normal form (Exhibit 23-1) as its starting point and then
circles the best responses for each player. Remember that in each cell of the nor-
mal-form matrix, the ?rst payoff belongs to Al, and the second payoff belongs to
EXHIBIT 23-5
PRISONER’S DILEMMA, NORMAL FORM, WITH BEST RESPONSES
Bob
Confess
Don’t
Confess
A1 Confess 8 years, 0 years,
8 years, 10 years
Don’t 10 years, 2 years,
Confess 0 years 2 years
23.2 SIMULTANEOUS GAMES 423
Bob. Now imagine that Bob believes that Al is going to confess. With this belief,
Bob knows that his payoff will be in the top row of the matrix. Then Bob can either
confess, leading to the upper left cell of (confess, confess) and giving him eight
years, or don’t confess, leading to the upper right cell of (confess, don’t confess)
and giving him 10 years. Because we assume that Bob would prefer to spend fewer
years in prison, we circle his payoff of eight years in the upper left quadrant.
Next, suppose that Bob believes that Al is going to play don’t confess. Now
Bob knows that he is going to be in the bottom row of the matrix. Then, Bob can
either confess, leading to the lower left cell of (don’t confess, confess) and setting
him free with 0 years in prison, or don’t confess, leading to the lower right cell of
(don’t confess, don’t confess) and giving him two years. Again, we assume that Bob
would prefer to spend fewer years in prison, so we circle his payoff of zero years in
the lower left quadrant.
After performing these steps, we have determined Bob’s best responses to
both of Al’s possible strategies. To ?nish the problem, we need to do the same thing
for Al. First, we imagine that Al believes that Bob is going to confess. With this
belief, Al knows that his payoff will be in the left column of the matrix. Then Al
can either confess, leading to the upper left cell of (confess, confess) and giving him
eight years, or don’t confess, leading to the lower left cell of (don’t confess, con-
fess) and giving him 10 years. Because Al would prefer to spend fewer years in
prison, we circle his payoff of eight years in the upper left quadrant.
Finally, suppose that Al believes that Bob is going to play don’t confess. Now
Al knows that he is going to be in the right column of the matrix. Then Bob can
either confess, leading to the upper right cell of (don’t confess, confess) and setting
him free with zero years in prison, or don’t confess, leading to the lower right cell
of (don’t confess, don’t confess) and giving him two years. Again, we assume that
Bob would prefer to spend fewer years in prison, so we circle his payoff of zero
years in the upper right quadrant.
Now, to ?nd the NE, we look for all cells in the matrix where both strategies
have been circled. This requirement yields the upper left quadrant of (confess,
confess), which is the only NE for the game. In this equilibrium, both prisoners will
spend eight years in jail. To both Al and Bob, this is going to seem like a terrible
outcome. If only they could somehow agree to play don’t confess, then they could
each receive two years in prison. It is easy to see, however, that this outcome is not
possible unless the players can make some binding agreement. In the absence of a
binding agreement, both players have an incentive to play confess and to get away
without any jail at all. Indeed, we can see that confess is a dominant strategy for
both players: each player will do better (less jail time) by playing confess than they
will by playing don’t confess, regardless of what the other player does. In the
real world, there are many examples of games like the prisoner’s dilemma: both
players would like to settle on a different outcome (don’t confess, don’t confess),
but both players have an incentive to cheat on this outcome. Some versions of these
games are called arms races, as the next example illustrates.
424 CHAPTER 23 GAME THEORY
EXAMPLE 23.2
Drugco and Pharmco produce the two leading drugs to treat severe ?u symptoms. These are
strong medications available only by prescription, and both ?rms market their medicines
heavily to physicians. Both ?rms are considering large direct-to-consumer advertising plans.
Advertising is very costly, but it would increase awareness of the drugs and help each ?rm in
its competitive position. Each ?rm can independently choose to be aggressive in the direct-
to-consumer market by choosing high advertising or to be less aggressive by choosing low
advertising. If only one of the two ?rms chooses high advertising, then the NPV of that ?rm’s
product (including advertising costs) would be $500M, whereas the NPV of the low
advertising ?rm would be $100M. If both ?rms choose high advertising, then the NPV of
each product would be $200M. If both ?rms choose low advertising, then the NPV of each
product would be $400M.
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-6. We have arbitrarily chosen to put Drugco
?rst and Pharmco second, with a closed curve around Pharmco’s decision nodes (2 and 3) to
denote the simultaneity of the game.
EXHIBIT 23-6
ADVERTISING GAME, EXTENSIVE FORM
1
Drugco
2
3
Pharmco
High
advertising
High
advertising
High
advertising
Low
advertising
Low
advertising
Low
advertising
All payoffs in $millions
(200, 200)
(400, 400)
(500, 100)
(100, 500)
23.2 SIMULTANEOUS GAMES 425
(b) The normal form, with best responses circled, is given in Exhibit 23-7. There is a unique
NE of (High Advertising, High Advertising), where both ?rms have an NPV of $200M.
Notice the similarity of this problem to the prisoner’s dilemma shown in Exhibit 23-5.
As in the prisoner’s dilemma, the players in this game would like to collude on a
different outcome—in this case with both ?rms playing “low advertising”, leading to payoffs
of $400M for both. Unfortunately, this superior outcome (for the ?rms) is not an NE, as both
?rms would have an incentive to deviate and play “high advertising”. For this reason, we
could call this game an “advertising arms race”, with the ?rms engaged in an escalating spiral
of advertising spending. Arms-race games were among the ?rst topics of game theory, as
applied to the ever-increasing military expenditures during the Cold War. ’
Next, we look for the Nash equilibrium for the odds-and-evens game. By
following the same procedures as we did for the prisoner’s dilemma, we can circle
the best responses for each player. This normal form, with best responses circled, is
shown in Exhibit 23-8.
For anyone who has enjoyed the childhood pastime of odds and evens, it will
come as no surprise that there is no clean solution. Anne, who is playing “odds”, always
wants to do the opposite of Beth. Conversely, Beth, who is playing “evens”,
always wants to do the same thing as Anne. When we circle the best responses, there is
no cell in the matrix with two circles. When this happens, we say that there is no pure-
strategyNE. Apure strategyis a strategythat plays one choice all the time: one is a pure
strategy in the odds-and-evens game; confess is a pure strategy in the prisoner’s
dilemma. In contrast, a mixedstrategy combines multiple pure strategies. For example
“play one ?nger 50 percent of the time and play two ?ngers 50 percent of the time” is an
example of a mixed strategy. In his original paper about NE, John Nash proved that
every game has at least one NE. Thus, if there is nopure-strategy NE, then there must be
at least one mixed-strategy NE.
EXHIBIT 23-7
ADVERTISING GAME, NORMAL FORM
Pharmco
High Low
Advertising Advertising
High $200 M, $500 M,
Advertising $200 M $100 M
Drugco
Low $100 M, $400 M,
Advertising $500 M $400 M
426 CHAPTER 23 GAME THEORY
In general, there is no easy way to ?nd all the mixed-strategy NE for a game.
In the special case of games with two players with two strategies each—also called
two-by-two games—we can solve for the mixed-strategy equilibrium by solving
one equation for each player. In the paragraphs below, we solve these equations for
the odds-and-evens game.
Let p be the probability of Anne playing one, so that 1 2 p is the probability
of Anne playing two. With these probabilities, if Beth plays one then she would
receive an expected payoff of
Beth’s expected payoff of playing one ¼ p à 1 þ ð1 2pÞ Ã 0 ¼ p: ð23:1Þ
If Beth plays two, then she would receive an expected payoff of
Beth’s expected payoff of playing two ¼ p à 0 þ ð1 2pÞ Ã 1 ¼ 1 2p: ð23:2Þ
With these expected payoffs, Beth will choose to play one, if and only if
p .1 2 p. Then,
Beth’s expected payoff for the game ¼ Max ðp; 1 2pÞ: ð23:3Þ
Because this is constant-sum game, everything Beth gets is effectively taken
from Anne (e.g., if Beth gets a payoff of p, then Anne gets an expected payoff of
1 2 p). Thus, to maximize her own expected payoff, Anne can just try to minimize
Beth’s maximum payoff. This is called the minimax solution, because a player
tries to “minimize the maximum payoff” of her opponent.
To minimize Beth’s payoff, Anne should set p so that both terms in the
“Max” function are equal to each other:
To minimize Beth’s expected payoff : p ¼ 1 2p-p ¼ 0:5: ð23:4Þ
Next, we repeat these steps, this time with Beth trying to minimize Anne’s
maximum payoff. Let q be the probability of Beth playing one, so that 1 2 q is the
probability of Beth playing two. With these probabilities, if Anne plays one then
she would receive an expected payoff of
EXHIBIT 23-8
ODDS-AND-EVENS GAME, NORMAL FORM, WITH BEST RESPONSES
Beth
One Two
Anne
One 0 ,1 1, 0
Two 1, 0 0 , 1
23.2 SIMULTANEOUS GAMES 427
Anne’s expected payoff of playing one ¼ q à 0 þ ð1 2qÞ Ã 1 ¼ 1 2q: ð23:5Þ
If Anne plays two, then she would receive an expected payoff of
Anne’s expected payoff of playing two ¼ q à 1 þ ð1 2qÞ Ã 0 ¼ q: ð23:6Þ
With these expected payoffs, Anne will choose to play one, if and only if
1 2 q .q. Then,
Anne’s expected payoff for the game ¼ Max ð1 2q; qÞ: ð23:7Þ
To minimize Anne’s payoff, Beth should set q so that both terms in the Max
function are equal to each other:
To minimize Anne’s expected payoff : 1 2q ¼ q-q ¼ 0:5: ð23:8Þ
With these results, we can claimthat ( p 50.5, q 50.5) is a mixed-strategy NEof
the game. To verify this claim, we check that both players are making best responses to
the other player’s choices. This is a trivial proof, for because both players are rando-
mizing 50À50, then it does not matter what the other player does: all possible strategies
lead to a payoff of 0.5. Thus, ( p 5 0.5, q 5 0.5) is a mixed-strategy NE.
Mixed-strategy equilibria are common in competitive zero-sum type games
and sports such as poker, sailing (really!), and penalty shots in soccer. Many sce-
narios from business strategy can mimic these kinds of games. Mixed-strategy
equilibria also show up in technology investing, in the form of a leader-follower
game. Example 23.3 illustrates such a game.
EXAMPLE 23.3
Leadco is the market-leading producer of microprocessors for home and small business
computers. Followco is Leadco’s closest competitor in this market. Both ?rms are currently
working on their next-generation microprocessor. These development projects, carried out in
great secrecy, face typical constraints for microprocessor development: customers demand
many new features, but adding features tends to reduce processor speed. Both Leadco and
Followco believe that the majority of customers want to have more graphics capabilities on
the chip, but the reduction in speed will turn off other customers. Both companies must
decide how much more graphics capability to add, knowing that this addition will reduce the
processor speed.
We summarize the contrasting goals with two possible strategies for each ?rm: more
graphics and faster speed. With a larger installed-base and more brand awareness, Leadco
would like to have the same strategy as Followco because this symmetry will tend to preserve
their current lead. If both companies choose the same strategy, then Leadco would maintain a
75 percent share of the market, and their processor would have an NPV of $6B, with $2B for
Followco. On the other hand, Followco would like to adopt the opposite strategy from
Leadco because they would then have the opportunity to steal some of Leadco’s installed
base. If the two ?rms choose different strategies, then the ?rm with more graphics will have
an NPV of $5B, and the ?rm with faster speed will have an NPV of $4B.
428 CHAPTER 23 GAME THEORY
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-9. From this extensive form, one might think
that more graphics is a “better” strategy because it gives higher payoffs when the players
choose different strategies. This kind of reasoning is dangerous, because, as we will see, a
pure strategy of more graphics is not part of any NE.
(b) The normal form for this game, with best responses circled, is given in Exhibit 23-10.
As in the odds-and-evens game, we ?nd no pure-strategy NE. The reason is that
Leadco always wants to be the same as Followco, whereas Followco wants to be different.
With a simultaneous game, the best strategy is to try to keep the other company guessing.
The game-theoretic way to do this is with a mixed strategy.
To ?nd the mixed-strategy equilibrium, we follow the same steps as we did for the
odds-and-evens game. Let p be the probability of Leadco playing more graphics, so that 1Àp
is the probability of Leadco playing faster speed. With these probabilities, if Followco plays
more graphics then it would receive an expected payoff of
p à $2B þ ð1 2pÞ Ã $5B ¼ $5B2$3B à p: ð23:9Þ
EXHIBIT 23-9
LEADER-FOLLOWER GAME, EXTENSIVE FORM
1
Leadco
2
3
Followco
More
graphics
More
graphics
Faster
speed
Faster
speed
More
graphics
Faster
speed
($6B, $2B)
($5B, $4B)
($4B, $5B)
($6B, $2B)
23.2 SIMULTANEOUS GAMES 429
If Followco plays faster speed, then it would receive an expected payoff of
p à $4B þ ð1 2pÞ Ã $2B ¼ $2B þ $2B à p: ð23:10Þ
Thus, Followco’s expected payoff for the game is
Max ð$5B2$3B Ã p; $2B þ $2B Ã pÞ: ð23:11Þ
To minimize Followco’s payoff, Leadco should set p so that both terms in the Max
function are equal to each other:
$5B2$3B Ã p ¼ $2B þ $2B Ã p - p ¼ 3=5: ð23:12Þ
Next, we repeat these steps, this time with Followco trying to minimize Leadco’s
expected payoff. Let q be the probability of Followco playing more graphics, so that 1 2 q is
the probability of Followco playing faster speed. With these probabilities, if Leadco plays
more graphics then it would receive an expected payoff of
q à $6B þ ð1 2qÞ Ã $5B ¼ $5B þ $1B à q: ð23:13Þ
If Leadco plays faster speed, then it would receive an expected payoff of
q à $4B þ ð1 2qÞ Ã $6B ¼ $6B2$2B à q: ð23:14Þ
Thus, Leadco’s expected payoff for the game is
Max ð$5B þ $1B Ã q; $6B2$2B Ã qÞ: ð23:15Þ
To minimize Leadco’s payoff, Followco should set q so that both terms in the Max
function are equal to each other:
$5B þ $1B Ã q ¼ $6B2$2B Ã q - q ¼ 1=3: ð23:16Þ
Equations (23.12) and (23.16) tell us that the mixed-strategy NE of this game is
( p 5 3/5, q 5 1/3). In words, this means that Leadco plays more graphics 60 percent of the
time, and Followco plays more graphics 33.3 percent of the time. If both ?rms are using
these strategies, then neither ?rm can do better by using any other strategy.
’
EXHIBIT 23-10
LEADER-FOLLOWER GAME, NORMAL FORM
Followco
More Faster
Graphics Speed
More $6B, $5B,
Graphics $2B $4B
Leadco
Faster $4B, $6B,
Speed $5B
$2B
430 CHAPTER 23 GAME THEORY
Thus far in the book, we have performed two kinds of analysis: positive
analysis and normative analysis. Positive analysis aims to describe actual behav-
ior. Our studies of VC returns (chapters 3 and 4), the performance of speci?c VC
investments (Chapter 7), and the frequencies of various contractual terms (chapters
2 and 8) were all examples of positive analysis. Normative analysis aims to describe
optimal behavior. When we presented the modi?ed VC method in Chapter 9, we
did so not because we think VCs actually use this method, but because it is
the “correct” model under certain assumptions. Similarly, all of Part III provides a
normative model for partial valuation. Although the book argues that this framework
is helpful for making investment decisions, it does not claim that current VCs are
actually using this framework. In short, positive analysis attempts to describe the
world “the way it is”, whereas normative analysis attempts to describe the world “the
way it ought to be”. One cannot jump easily from one type of analysis to another.
Game theory is normative analysis. Although game theorists often speak of
“equilibrium predictions”, they do not mean this literally. Instead, game theory
makes the assumption that all players are behaving rationally, and then logically
derives the implications of such behavior for equilibrium outcomes. These equili-
bria are not positive predictions about the way the world is, but instead are nor-
mative predictions about the way the world would be under some strong
assumptions about rationality. Thus, when we say that the equilibrium in Example
23.3 is ( p 53/5, q 51/3), we are not predicting this outcome, but merely estab-
lishing a baseline for rational players. For our purposes, game theory is best used to
force us to think rigorously about all the strategic moves available to all interested
parties. The Nash equilibrium solutions should not be thought of as ?nal answers,
but rather as a structure for understanding these moves.
So far in this chapter, we have analyzed two types of games: arms-race games
(prisoner’s dilemma and Example 23.2), where both players have a dominant
strategy that leads to an unhappy NE, and competitive games like Example 23.3, of
which constant-sum games like odds-and-evens are a special class. A third type
of game commonly appears: the coordination game. In a coordination game, there
are no dominant strategies and more than one possible pure-strategy NE. Example
23.4 gives a typical game of this type.
EXAMPLE 23.4
Gameco and Movieco are the leading developers of DVD technology. In the past, these two
companies were able to agree on identical technical standards, but they are now embroiled in
a ?erce debate about the next generation of technology. Gameco believes that the time is ripe
for a revolutionary change in DVD technology that would provide much larger storage
capacity and allow for highly complex interactive games. Movieco, on the other hand, favors
a more evolutionary change that would maintain a higher degree of backward compatibility.
Because the companies are unable to agree on a standard technology, they have
continued with separate development projects. Other content providers are reluctant to
choose sides, fearing that they may pick the wrong company to back. This delay is damaging
23.2 SIMULTANEOUS GAMES 431
the long-term sales potential of both technologies. If the two companies are unable to settle
on a single technology, then each project would be worth $2B. Both companies would do
better if they could agree on a single standard—but which one? The revolutionary standard
would favor Gameco, with an expected NPV of $10B versus only $4B for Movieco. The
evolutionary standard would favor Movieco, with an expected NPV of $10B versus only $4B
for Gameco. Although this is an ongoing battle with no clear endpoint, we choose to model it
as a single-stage simultaneous game, where each company must decide on a standard.
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all pure-strategy Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-11.
(b) The normal form, with best responses circled, is given in Exhibit 23-12.
This game has two pure-strategy NE: (Revolution, Revolution) and (Evolution, Evo-
lution). From a normative perspective, we cannot say which outcome “should” occur, only
that the companies would rather agree than disagree.
EXHIBIT 23-11
STANDARDS GAME, EXTENSIVE FORM
1
Gameco
2
3
Movieco
Revolution
Revolution
Evolution
Evolution
Revolution
Evolution
($10B, $4B)
($2B, $2B)
($2B, $2B)
($4B, $10B)
432 CHAPTER 23 GAME THEORY
In addition to these two pure-strategy NE, there is also a unique mixed-strategy NE. In
Exercise 23.1, you are asked to solve for this equilibrium.
’
REALITY CHECK: In the real world, these kinds of coordination games are
common. Perhaps the most famous example is the battle between VHS and Beta-
max for the video recording market in the early 1980s. The scenario of Example
23.4, a standards battle for new DVD technology, is still being waged as of this
writing. In practice, these battles tend to get resolved over time as one of the
technologies gains a critical mass of developers and content providers. Once this
happens, the owners of the trailing technology can choose to continue the ?ght (and
get a large share of an ever-shrinking market) or give up and join the leading
technology to get a smaller share of a larger market. The longer the ?ght goes on,
the greater the damage to its potential market. Indeed, some standards battles can
go on for so long that a new technology completely overtakes them. By modeling
these contests as one-step simultaneous games, we lose some important nuances but
still gain insight into the stakes of the battle.
23.3 SEQUENTIAL GAMES
In this section, we analyze sequential games, where players take turns making
moves. These games introduce some new complications, as illustrated by the fol-
lowing entry game. Drugco sells Leau?eau, the market-leading drug for hyper-
tension. This drug is about to lose patent protection for its key ingredient. Generico,
a maker of generic drugs, is considering entry into the hypertension market with the
chemical equivalent of Leau?eau. Under law, if Generico is the ?rst company to
gain approval for a generic version of Leau?eau, then they will be allowed six
months as the only generic competitor. After this six months is over, other
EXHIBIT 23-12
STANDARDS GAME, NORMAL FORM
Movieco
Revolution Evolution
Revolution $10B, $2B,
$4B $2B
Gameco
Evolution $2B, $4B,
$2B $10B
23.3 SEQUENTIAL GAMES 433
companies can enter the market with their own versions. As soon as generic com-
petition intensi?es, the pro?ts for both the incumbent (Drugco) and the ?rst generic
(Generico) would fall signi?cantly. Drugco would like to postpone this date for as
long as possible by “scaring” Generico out of the market. As Generico plans to
introduce their drug, Drugco ?les expensive lawsuits claiming infringement of
patents related to the manufacturing of Leau?eau and prepares to drop the price
of Leau?eau to keep consumers from switching to the generic form during Gen-
erico’s six-month exclusivity period. If Drugco succeeds in scaring Generico away
from entry, then Drugco will increase their NPV by $1B, and Generico will have an
NPV of 0. If Generico enters the market and Drugco chooses to ?ght with these
measures, then both companies will lose $100M. If Generico enters and Drugco
decides not to ?ght, then both companies will make $100M. Exhibit 23-13 gives the
extensive form for this game. Exhibit 23-14 gives the normal form, with best
responses circled.
Exhibit 23-14 shows two NE: (don’t enter, ?ght) and (enter, don’t ?ght). In
the ?rst equilibrium, Generico expects Drugco to ?ght, so it chooses not to enter. If
this were a simultaneous game, then there would be nothing troubling about this
equilibrium. In a sequential game, something might make us uneasy: the Drugco
strategy to ?ght is not a credible threat. It is not a credible threat because if Gen-
erico chooses to enter, then Drugco’s best response would be don’t ?ght. The only
reason that (don’t enter, ?ght) is a NE is that the decision to ?ght is irrelevant if
Generico does not enter. Thus, technically speaking, anything played by Drugco
EXHIBIT 23-13
ENTRY GAME, EXTENSIVE FORM
1
Generico
2
Drugco
Enter
Don't enter
Fight
Don't fight
(–$100M,
–$100M)
($100M,
$100M)
($0, $1000M)
434 CHAPTER 23 GAME THEORY
can be a “best response” to don’t enter. In response to this counterintuitive equi-
librium, game theorists devised a re?nement of NE based on the concept of sub-
games. A subgame is any part of a game that can be cleanly separated from the rest
of the game and analyzed on its own. Graphically, we can identify subgames by
looking at the extensive form. If there are any decision nodes in the tree that do not
have closed curves around them, then we can “snip” the tree at those nodes and
analyze these snipped nodes as part of a subgame. For example, we can snip the
extensive form in Exhibit 23-13 at Node 2, leaving us a subgame with only one
player (Drugco) and that player’s decision to ?ght or don’t ?ght. In simultaneous
games like Examples 21.1 through 21.4, there is no way to snip a decision node off
the tree—after the ?rst node, all other decision nodes had closed curves around them.
Those simultaneous games had no subgames, so no further analysis can be done.
If we do have subgames, then we solve for the NE of each subgame, using
backward induction to solve each subgame in reverse order. The simplest way to do
this for the entry game is by circling best responses in the extensive form. Exhibit
23-15 illustrates this solution method. The subgame following Node 2 has only one
player, so the NE of that subgame is just the optimal move for Drugco, which is
don’t ?ght. If we then back through the tree, Generico should play enter if it expects
that Drugco would play don’t ?ght. We have now solved for the unique subgame-
perfect Nash equilibrium (SPNE) as (enter, don’t ?ght). Thus, for sequential
games, the method of circling best responses in the normal form is no longer
suf?cient. We need to use information about the timing of decisions, and this
information is only available in the extensive form.
Like NE, the SPNE is a normative concept, not a positive prediction. Just
because (enter, don’t ?ght) is the only SPNE does not mean that, in practice,
Drugco won’t be able to scare Generico away from entering. Often, however, we
can model the methods that Drugco can use to succeed in keeping Generico out of
the market. Example 23.5 demonstrates one of these methods, where Drugco uses a
commitment mechanism to make the ?ght threat more credible.
EXHIBIT 23-14
ENTRY GAME, NORMAL FORM
Drugco
Fight Don’t
Fight
Enter $-100M, $100M,
$-100M $100M
Generico
Don’t $0M, $0M,
Enter $1000M $1000M
23.3 SEQUENTIAL GAMES 435
EXAMPLE 23.5
Consider the game shown earlier in Exhibit 23-13. Now, we add an additional move to this
game. Before Generico decides whether to enter (Node 1 in Exhibit 23-13), Drugco can
commit to a ?ght. Drugco makes this commitment by placing $500M in an escrow account
with a specialized “commitment agent”. The terms of this escrow state that if Drugco fails to
?ght, then the $500M will be forfeited to the commitment agent. In all other respects, the
payoffs are the same as in Exhibit 23-13.
Problem Draw the extensive form for this game, identify the subgames, circle the best
responses in each subgame, and solve for the SPNE.
Solution Exhibit 23-16 gives the extensive form for this entry game, with best responses
circled. This game has four subgames. We can snip the tree at Nodes 4 and 5, leaving only
Drugco’s ?ght decision. We can also snip the tree at Nodes 2 and 3, leaving Generico’s
entry decision, to be followed by Drugco’s ?ght decision. (The subgame that follows Node 3
is identical to the full game tree in Exhibit 23-13.) To ?nd the SPNE, we must make sure to
have only NE in each subgame, with the full tree solved by backward induction. We begin
with the bottom half of the tree. At Node 5, Drugco would choose don’t ?ght. If Generico
expects Drugco to play don’t ?ght, then at Node 3, it would choose to enter. Thus, the
SPNE payoffs from the bottom half of the tree are ($100M, $100M), just as we found in
Exhibit 23-13.
EXHIBIT 23-15
ENTRY GAME, EXTENSIVE FORM, WITH SUBGAME PERFECT
STRATEGIES CIRCLED
1
Generico
2
Drugco
Enter
Don't enter
Fight
Don't fight
(–$100M,
–$100M)
($100M,
$100M)
($0, $1,000M)
436 CHAPTER 23 GAME THEORY
In the top half of the tree, we have a different situation. Because Drugco has played
commit, the don’t ?ght strategy at Node 4 would result in a loss of $500M relative to the
don’t ?ght strategy at Node 5. The overall payoff of don’t ?ght then becomes negative
$400M, which is inferior to the ?ght payoff of negative $100M. Thus, at Node 4, Drugco
should ?ght. If Generico expects Drugco to ?ght at Node 4, then it should choose don’t enter
at Node 2. Thus, the SPNE payoffs from the top half of the tree are ($0, $1000M).
To ?nish the solution, we compare Drugco’s payoffs from choosing to commit—the
top half of the tree—which are equal to $1000M, with Drugco’s payoff from playing don’t
commit—the bottom half of the tree—which are equal to $100M. Because the former is
higher than the latter, Drugco’s optimal strategy at Node 1 is to commit. Thus, the unique
SPNE, which must specify at strategy at every node (including nodes that are not reached in
equilibrium!), is (1 5commit, 2 5don’t enter, 3 5enter, 4 5?ght, 5 5don’t ?ght), with
SPNE payoffs of ($0, $1000). ’
The main theme of this example will seem familiar to armchair strategists
everywhere: sometimes you can improve your bargaining position by restricting your
future options. For example, leaders sometimes make public pronouncements—
which are costly to repudiate—committing their organization to some (possibly
unpopular) strategy. Such pronouncements can be effective ways to sti?e internal
dissent because subordinates realize that the leader will “?ght” any attempt to change
the strategy.
EXHIBIT 23-16
ENTRY GAME, WITH COMMITMENT EXTENSIVE FORM
1
2
Generico
Generico
Drugco
4
3
5
Drugco
Drugco
Don't enter
Don't fight
Commit
to fight
Don't
commit
Don't enter
Don't fight
Enter
Fight
Enter
Fight
($0, $1000M)
(–$100M,
–$100M)
($100M,
–$400M)
(–$100M,
–$100M)
($100M,
$100M)
($0,
$1000M)
23.3 SEQUENTIAL GAMES 437
In Example 23-5, Drugco’s commitment device allows it to make a credible
threat of ?ghting the entry of Generico. The game does not have to stop here. Some
clever executive at Generico could approach the “commitment agent” and say,
“Drugco has promised you $500M if we enter and Drugco does not ?ght. As long as
you hold this contract in your hand, we will not enter, and the contract is worthless
to you. Thus, why don’t you just rip up the contract, and we will give you $1?”
If we add this strategy to the game, the new SPNE has the contract ripped up,
and Generico enters. This kind of game can go back and forth, as each player
tries to think of ever more powerful ways to alter the game. Alas, some lawyers
we know insist that most of these fanciful contracts would be unenforceable. Spoil
sports.
Drugco can also rely on “reputation” to make their threat credible. Speaking
loosely, the reputation argument goes like this: “Here at Drugco, we always ?ght
whenever anyone enters our markets. We have done this for decades, and we are
not about to stop know. We realize that it costs us money to ?ght, but in the long
run it saves us even more, because potential competitors are scared away by our
fearsome reputation.” To make this reputation argument more formally, we need to
model an extensive form and see if it works.
As it turns out, reputation stories do not work in ?nite games. If you can
actually write down the terminal nodes of the game, then you will be able to solve
the game backward and SPNE arguments will keep the threats from being
credible. To see this, imagine that the entry game from Exhibit 23-13 is repeated
100 times, always between the same two players. One might think that this would
be a long enough time to gain a reputation, but if we divide the game into sub-
games, we will ?nd that in the 100th playing it is not optimal for Drugco to ?ght,
so thus it is not optimal to ?ght in the 99th playing, the 98th playing, and so on. In
contrast, for an in?nite game, under a wide variety of conditions it will be
possible for Drugco to establish a reputation, and virtually any outcome can
be claimed as part of an equilibrium. Because corporations are, in theory, in?-
nitely lived institutions, reputation effects are supported by game theory and lead
to generally indetermi- nate equilibrium predictions. This paradoxical contrast
between ?nite and in?nite games has been recognized since almost the dawn of
game theory, and the proof that in?nite games can support virtually any equilibria
is so well known that its creator has passed into oblivion, with the proof known
simply as the folk theorem.
23.4 GAME THEORYAND REAL OPTIONS
In Chapter 21, we demonstrated several examples of real options, where ?rms could
pro?tably delay making investment decisions until more information was known.
An important critique of the real-options approach is that it can be misleading when
a ?rm faces competition. The idea of “waiting to invest” can be strategic suicide if a
438 CHAPTER 23 GAME THEORY
competitor can just come along and steal your market. In Example 23-6, we provide
an illustration of this critique.
EXAMPLE 23.6
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19.) They have already completed several R&D
projects with this technology, so they have eliminated the technical risk for this new project.
To begin producing and marketing to the consumer market would require a new investment
of $200M, to be paid in one year. The value of Project C depends on consumer demand and
also depends on whether a competitor, Cellco, also enters this market. To keep things
(relatively) simple, we assume that the beta for the project is zero and that the risk-free rate is
also zero, so all discount rates are zero for the both ?rms.
At time 0, Cellco and Fuelco each decide whether to invest or wait. If one ?rm invests
and the other waits, then the investing ?rm will get the whole market and have an NPV of
$300M, whereas the waiting ?rm will have an NPV of $0. If both ?rms invest, then com-
petition will drive down the pro?ts of both ?rms, which will each have an NPV of $50M. (All
NPVs described in this problem are net of the $200M investment, when the investment is
made. Thus, the gross NPV if both ?rms invest would be $250M.) If both ?rms wait, then
they both get to observe whether demand is “high” or “low”, after which each ?rm decides
whether or not to invest. If demand is “high” (50 percent chance) and only one ?rm chooses
to invest, then that ?rm receives an NPV of $700M, and the other ?rm receives an NPV of
$0. If neither ?rm invests, then both ?rms receive an NPV of $0. If both ?rms invest, then
each ?rm receives an NPV of $200M. If demand is “low” (50 percent chance), and only one
?rm chooses to invest, then that ?rm receives a negative NPV of 2$100M, and the other ?rm
receives an NPV of $0. If neither ?rm invests, then both ?rms receive an NPV of $0. If both
?rms invest, then each ?rm receives a negative NPV of 2$100M.
Problems
(a) Draw the extensive form for this game.
(b) Identify all the subgames.
(c) Solve for the unique SPNE.
Solutions
(a) The extensive form is given in Exhibit 23-17.
(b) To identify the subgames, we look for places where we can “snip” the tree at a decision
node without cutting any closed curves. This procedure yields subgames beginning with
Nodes 8 or 9.
(c) Unlike the entry game in Example 23.5, the subgames for this game include decision
nodes for both players. Thus, to ?nd SPNE for the whole game, we need to consider the NE
of the subgames, not just optimal play for one player in isolation.
We can solve the tree backward by solving for the NE of each subgame. Because each
subgame represents a two-by-two simultaneous game, we can ?nd these NE by circling the
best responses in the normal form. We do this ?rst for the subgame that begins with Node 8.
23.4 GAME THEORY AND REAL OPTIONS 439
The unique NE of this subgame is (Invest, Invest), with payoffs of ($200M, $200M).
We next consider the subgame that begins with Node 9, as shown in Exhibit 23-19. The
unique NE of this subgame is (Don’t Invest, Don’t Invest), with payoffs of (0,0).
EXHIBIT 23-17
FUELCO’S PROJECT C, WITH COMPETITION
1
Fuelco
Cellco
2
3
invest
invest
invest
invest
invest
invest
invest
invest
wait
wait
invest
wait
8
Fuelco
Fuelco
Cellco
Cellco
10
11
9
12
13
4
(50, 50)
5
(300, 0)
6
(0,300)
strong
market
weak
market
7
50%
50%
don't
don't
don't
don't
don't
don't
(200, 200)
(700, 0)
(–100, –100)
(–100, 0)
(0, 700)
(0, 0)
(0, –100)
(0, 0)
EXHIBIT 23-18
PROJECT C, STEP 2, STRONG MARKET, NORMAL FORM
Cellco
Invest Don’t
Invest
Invest $200M, $700 M,
$200M $0M
Fuelco
Don’t $0M, $0M,
Invest $700M $0M
440 CHAPTER 23 GAME THEORY
With NE solutions for the two subgames, we can prune the extensive form, replacing
the decision nodes at 8 and 9 with their respective NE payoffs. With payoffs of ($200M,
$200M) in a strong market and (0,0) in a weak market, Node 7 would have a 50-50 chance of
these two outcomes, for an expected payoff of ($100M, $100M). We then redraw the
extensive form in Exhibit 23-20.
EXHIBIT 23-19
PROJECT C, STEP 2, WEAK MARKET, NORMAL FORM
Cellco
Invest Don’t
Invest
Invest ?$100M, ?$100M,
?$100M $0M
Fuelco
Don’t $0M, $0M,
Invest ?$100M $0M
EXHIBIT 23-20
FUELCO’S PROJECT C, WITH COMPETITION, PRUNED
1
Fuelco
2
3
Cellco
invest
invest
wait
invest
wait
wait
4
(50, 50)
5
(300, 0)
6
(0, 300)
7
(100, 100)
23.4 GAME THEORY AND REAL OPTIONS 441
This pruned version of the extensive form is a one-step simultaneous game with no
subgames. We can solve for the NE of this game by circling the best responses in their
normal form.
The unique NE of this game is (invest, invest), yielding payoffs of ($50M, $50M).
After doing all this work, we can see the prisoner’s dilemma arms race once again rear its
EXHIBIT 23-21
PROJECT C, STEP 1, NORMAL FORM
Cellco
Invest Wait
Invest $50M, $300M,
$50M $0M
Fuelco
Wait $0M, $100M,
$300M $100M
EXHIBIT 23-22
FUELCO’S PROJECT C, WITH COMPETITION, BEST RESPONSES
CIRCLED
1
Fuelco
Cellco
2
3
invest
invest
invest
invest
wait
wait
wait
8
Fuelco
Fuelco
Cellco
Cellco
10
11
9
12
13
4
(50, 50)
5
(300, 0)
6
(0, 300)
strong
market
weak
market
7
50%
50%
don't
don't
don't
(200, 200)
(700, 0)
(–100, –100)
(–100, 0)
(0, 700)
(0, 0)
(0, –100)
(0, 0)
invest
invest
invest
invest
invest
don't
don't
don't
442 CHAPTER 23 GAME THEORY
ugly head: both Fuelco and Cellco would prefer a combined switch to the (wait, wait)
outcome, but this outcome is not a NE because each company would have an incentive to
change its strategy and invest.
Now that we have solved for the NE of all the subgames, we can rewrite the extensive
form for the whole game, with all best responses circled. Exhibit 23-22 shows this solution.
The unique SPNE of the game is (Node 1 5invest, Nodes 2/3 5invest, Node 8 5invest,
Node 9 5don’t invest, Nodes 10/11 5invest, Nodes 12/13 5don’t invest), with an SPNE
payoff of ($50M, $50M). Note that Cellco’s strategies must be the same at nodes 2&3,
10&11, and 12&13 because Cellco is unable to distinguish its exact location at any of these
node pairs.
’
SUMMARY
Game theory is the study of multiplayer decision problems. In this chapter, we learned the
basic tools of game theory, and we applied these tools to the analysis of several prototypical
R&D investment scenarios. We ?rst studied three different types of simultaneous games,
where players make their moves at the same time. The ?rst game we analyzed, an advertising
arms race between two companies, is reminiscent of the classic prisoner’s dilemma: both
companies would like to spend fewer resources on advertising, but competition leads to high
advertising by both. We next analyzed a game between a technology leader and follower. In
this game, the leader would like to maintain the status quo where everyone includes similar
technology features in their products, whereas the follower would like to introduce more
differentiation. In equilibrium, each side tries to keep the other guessing as to its strategy. A
third example was the coordination game, which can occur in battles to set technological
standards. Unlike the arms-race and leader-follower games, standards battles do not have
unique game-theoretic predictions, with many possible standards leading to many possible
equilibrium outcomes.
In the second part of the chapter, we turned our attention to sequential games, in which
players take turns making their moves. We ?rst analyzed a game of market entry, where an
incumbent drug company sought to keep a generic ?rm from marketing a competing product.
These games can allow for rich strategy by all players, with incumbents trying to scare
potential rivals away by making credible threats of litigation and price wars, and potential
entrants working to defuse these threats. Game-theoretic reasoning can also provide fresh
insights into standard real-option investment problems. In our ?nal example of the chapter,
we showed how competition can destroy the option value of waiting and give rise to yet
another prisoner’s dilemma situation.
KEY TERMS
Prisoner’s dilemma
Normal form
Strategies, strategy pair
Payoffs
Game tree
5extensive form
Simultaneous game,
sequential game
Zero-sum games, constant
sum games
Equilibrium concepts
Nash equilibrium (NE)
KEY TERMS 443
Equilibrium strategy
Best response
Dominant strategy
Arms race
Pure strategy, mixed
strategy
Pure-strategy NE, mixed-
strategy NE
Two-by-two games
Minimax solution
Leader-follower games
Positive analysis, normative
analysis
Coordination games
Subgames
Subgame-perfect Nash
equilibrium (SPNE)
Finite games, infinite games
Folk theorem
EXERCISES
23.1 Solve for the mixed-strategy NE in Example 23.4. Does this equilibrium seem like a
realistic outcome for the game? Do you see any conceptual difference between this mixed-
strategy NE and the mixed-strategy NE in the leader-follower game?
23.2 Suppose that the advertising arms race in Example 23.2 is repeated a second time by the
same two ?rms.
(a) Draw an extensive form for the two-period game, showing all strategies for both ?rms
in both periods.
(b) Solve for all the pure-strategy NE of the game.
(c) Solve for the unique SPNE of the game.
23.3 Consider the game modeled in Example 23.6. Now, suppose that the cost of investment
is $280M, instead of the $200M given in the original example. In this case, all the payoffs
after investment should be reduced by $80M as compared to Exhibit 23-17. In this new
game, solve for all the SPNE of the game and compare the payoffs among these SPNE.
23.4 In an enclosed space stand 57 lions and one sheep. The lions, all perfectly rational and
well trained in game theory, would all like to eat the sheep. For simplicity, we imagine that
the lions are numbered from 1 to 57, and sequentially decide whether they would like to eat.
(If the sheep is still alive after lion #57 makes his decision, then lion #1 gets to decide again,
and the process goes around and around forever.) If any lion begins to eat the sheep, then the
other lions will respect his property rights and allow him to ?nish by himself. The sheep is
powerless to stop this. If a lion eats the sheep, then he will fall asleep for one hour, during
which time he becomes defenseless and can be eaten by any other lion. (While awake, a lion
cannot be eaten by another lion.) The best outcome for a lion would be to eat the sheep, fall
asleep, and not be eaten himself. The second best outcome for a lion would be to go hungry.
The worst outcome would be to eat, fall asleep, and be eaten. So, in the unique SPNE of this
game, what happens to the sheep? (Hint: The answer would be different if there were only
56 lions.)
444 CHAPTER 23 GAME THEORY
CHAPTER 24
R&D VALUATION
IN THIS CHAPTER, we pull together everything we have learned in Part IV
and analyze complex examples for Drugco and Fuelco. In the Drugco example in
Section 24.1, we draw on game theory, real options, and Monte Carlo simulation to
evaluate two possible structures for a drug-development strategic alliance. In the
Fuelco example in Section 24.2, we combine the three projects studied in previous
chapters into one metaproject. The resulting analysis combines several linked real
options, including one that requires a binomial tree. Finally, in Section 24.3 we
review some of the key lessons from Part IV and urge readers to see both the forest
and the (decision) trees.
24.1 DRUG DEVELOPMENT
This example uses a similar valuation model as in Examples 20.4 and 21.4, except
that here we allow uncertainty for ef?cacy, alternative ef?cacy, and market size to
be resolved during both Phase II and Phase III.
EXAMPLE 24.1
Drugco is about to begin Phase II trials for Newdrug, at a cost of $50M. If the drug continues
to Phase III trials, then these trials would cost an additional $100M. Drugco is ?nancially
constrained, so it is looking for a partner to help fund the project. Bigco, a potential partner,
has proposed two possible deal structures.
Deal 1 is a standard-looking alliance deal, where Bigco pays an up-front fee of $200M
to acquire all rights to the compound and then pays all the development costs, makes a
milestone payment of $150M on entering Phase III, and makes royalty payments of 5 percent
on sales.
Deal 2 would reduce the up-front payment to $100M, require Drugco to bear 20
percent of the development costs in Phase III, and replace the Phase III milestone with a
larger $300M milestone if Bigco decides to market the product after FDA approval. Deal 2
would have a higher royalty percentage than Deal 1 (10 percent versus 5 percent) and would
give Drugco more control over the project, by allowing it to decide whether the project
advances from Phase II to Phase III. In both deals, if Bigco decides not to market the product,
445
then all rights revert back to Drugco. If Bigco does decide to market the product, then it will
incur marketing costs of $300M in the ?rst year, with these costs increasing annually in
proportion to the 6 percent growth in the size of the market.
Both ?rms expect Phase II trials to take one year, Phase III trials to take two years, and
the FDA approval decision to take one year, so that the FDA decision is expected in four
years total. Based on preclinical testing, both ?rms expect Phase II trial results, E
t
, to be
distributed as N (40, 40). The best alternative drug currently has an ef?cacy of 40, but has
several possible improvements in the works, so its expected ef?cacy after one year (after the
Phase II trials of Newdrug) is A
t
B T (40, 70, 40). Given the side effects of Newdrug and
the risks and bene?ts of alternative treatments, Drugco believes that the FDA will approve
Newdrug if the Phase III trials ?nd an ef?cacy of 30 or greater. Based on the results of the
Phase II trials, Drugco estimates that the ef?cacy results of Phase III will be E BN (E
t
, 20).
During the three years of Phase III trials and FDA decision making, the alternative may
improve again, with a distribution of A BT (A
t
, A
t
+ 50, A
t
). If Newdrug is approved by the
FDA, then its market share will depend on the relative ef?cacy of Newdrug versus the best
available treatment, that is,
Newdrug market share ¼ E
2
=ðE
2
þA
2
Þ: ð24:1Þ
Drugco estimates that the eventual market size of Newdrug in the approval year (in
millions of doses) will be 1,000, but there is considerable uncertainty around this estimate.
Some of this uncertainty will be resolved in the next year (during Phase II trials), with M
t
B
N (1,000, 50), and more uncertainty will be resolved over the following three years, with M
BN (M
t
, 100). Each dose will sell for $1.00, with a production cost of $0.25. On approval,
Newdrug would have 10 years of patent life remaining. After the patent expiration, Drugco
expects generic competition and other improved alternatives to greatly erode the value of
Newdrug, so for simplicity we assume that the continuing value would be zero after the
patent expires. Following earlier examples for Newdrug, we assume a discount rate equal to
the riskfree rate of 5 percent.
Problems
(a) Draw the game tree for this problem, beginning with Drugco’s decision of whether to
take Deal 1 or Deal 2.
(b) Suppose that Drugco decides to take Deal 1. What is the optimal strategy for Bigco
following the Phase III trials? What is the optimal strategy for Bigco following the Phase II
trials? Assuming that Bigco chooses these strategies, what are the expected payoffs to
Drugco and Bigco for Deal 1?
(c) Suppose that Drugco decides to take Deal 2. What is the optimal strategy for Bigco
following the Phase III trials? Given this strategy for Bigco, what is the optimal strategy for
Drugco following the Phase II trials? Assuming that Bigco and Drugco choose these stra-
tegies, what are the expected payoffs to Drugco and Bigco for Deal 2?
(d) What is the unique SPNEof this game? What are the expected payoffs for the equilibrium?
Solutions
(a) We draw the game tree in three pieces. First, Exhibit 24-1 shows the high-level structure
for the tree. The node numbers in this tree correspond to node numbers in the detailed trees
that follow for Deal 1 (Exhibit 24-2) and Deal 2 (Exhibit 24-3).
446 CHAPTER 24 R&D VALUATION
EXHIBIT 24-1
SCHEMATIC FOR THE FULL EXTENSIVE FORM
Take
Deal 1
Take
Deal 2
2
12
1
5
15 19
Drugco
Drugco Bigco
Bigco Bigco
B1(E,M,A),
D1(E,M,A)
0, 0
0, 0
B2(E,M,A),
D2(E,M,A)
(0, –50)
(0, –50)
(100, –100)
(200, –200)
Phase II Phase III
9
. . . . . .
. . . . . .
EXHIBIT 24-2
EXTENSIVE FORM FOR DEAL 1
3 2
A' ~ T(40, 70, 40)
A ~ T(A',A' + 50, A')
M' ~ N(1,000, 50) E' ~ N(40, 40)
E ~ N(E', 20)
same
as 3
same
as 3
same
as 4
same
as 4
Phase II Phase III
same
as 5
5
same
as 5
same
as 9
9
Bigco
4
same
as 8
same
as 8
8
same
as 7
same
as 7
7 6
E ? 30
(0, 0)
(0, 0)
(0, 0)
M ~ N(M', 100)
Bigco
(150, ?250)
abandon
1 year
3 years
don't
market
B1 (E,M,A),
D1 (E,M,A)
24.1 DRUG DEVELOPMENT 447
Before attempting a solution, we note a few important elements of these game trees.
First, in Exhibit 24-1, we see the up-front fees for the two deals yielding payoffs of (200,
2200) in Deal 1 and (100, 2100) in Deal 2. (Drugco’s payoff is always listed ?rst.) Fur-
thermore, because Bigco pays the $50M cost of Phase II in both structures, there is a payoff
of (0, 250) at nodes 2 and 12. In Exhibit 24-2, with the extensive form for Deal 1, the Phase
III continuation decision belongs to Bigco (Node 5). If Bigco decides to continue, then it
pays $100M in costs plus a $150M milestone, yielding aggregate payoffs of (150, 2250). In
the analogue position of Exhibit 24-3, Drugco makes the Phase III continuation decision
(node 15), no milestones are paid, and Drugco incurs $20M of the $100M cost, for aggregate
payoffs of (220, 280). Finally, the marketing decision is always made by Bigco. In Exhibit
24-2, there is no milestone. In Exhibit 24-3, if Bigco decides to market, then it must pay
Drugco a milestone of $300M, leading to aggregate payoffs of (300, 2300).
(b) As is our usual practice, we solve the tree backward. Starting with the terminal nodes
and moving back in time, we arrive at Bigco’s decision about whether or not to market the
product (node 9). In Example 21.4, we solved a very similar problem. All the market
inputs were the same—the only difference is that here, Bigco would have to pay royalties on
5 percent of the gross sales. Exhibit 24-4 gives the full valuation model for Bigco’s decision,
EXHIBIT 24-3
EXTENSIVE FORM FOR DEAL 2
13 12
A' ~ T(40, 70, 40)
A ~ T(A',A' ? 50, A')
M' ~ N(1,000, 50) E' ~ N(40, 40)
E ~ N(E', 20)
same
as 13
same
as 13
same
as 14
same
as 14
Phase II Phase III
same
as 15
15
same
as 15
same
as 19
19
Bigco
14
same
as 18
same
as 18
18
same
as 17
same
as 17
17 16
E ? 30
(0, 0)
(0, 0)
(0, 0)
M ~ N(M', 100)
Drugco
(–20, –80)
abandon
1 year
3 years
don't
(300–300)
market
B2 (E,M,A),
D2 (E,M,A)
448 CHAPTER 24 R&D VALUATION
EXHIBIT 24-4
DCF MODEL, DEAL 1
1 A B C D E F G H I J K L
2 Mean St dev Min Mode Max
3 Efficacy (E
t
) 40 40 40
4 Alternative efficacy (A
t
) 50 40 40 70
5 Starting market size (M
t
) 1,000 1,000 50
6
7 Efficacy (E) 40 40 20
8 Alternative efficacy (A) 67 50 50 100
9 Starting market size (M) 1,000 1,000 100
10 Phase III milestone 150
11 Continuation Threshold 30.1
12 Phase III? 1.0 Bigco NPV (if enter) $388.5
13 Approval threshold 30 Drugco NPV $207.0
14 Price per unit $1.00 Bigco NPV (option) $388.5
15 Royalty rate 5.00%
16 Cost per unit $0.25
17 Market share 26.5% Total Bigco NPV 2$136.1
18 Market growth 6.0% Total Drugco NPV $508.4
19 Discount rate 5.00%
20 Approved? 1
21 Salvage value 42.86
22 $ in millions
23 Year 5 6 7 8 9 10 11 12 13 14
24
25 Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
26 Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
27 Revenue $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
28 Royalty $13.2 $14.0 $14.9 $15.8 $16.7 $17.7 $18.8 $19.9 $21.1 $22.4
29 CGS $66.2 $70.1 $74.4 $78.8 $83.5 $88.6 $93.9 $99.5 $105.5 $111.8
30 Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
31 Bigco profit 2$48.5 2$51.4 2$54.5 2$57.8 2$61.3 2$64.9 2$68.8 2$73.0 2$77.3 2$82.0
32 Drugco profit $13.2 $14.0 $14.9 $15.8 $16.7 $17.7 $18.8 $19.9 $21.1 $22.4
4
4
9
with inputs set to their mean values. The market decision at Node 9 is made with a “Max”
function in cell G14. This function takes the maximum of the NPV of marketing the drug
(cell G12) with the NPV of abandoning the drug (0).
To better understand this worksheet, let’s discuss the special case shown in the
exhibit, with all variables set to their mean values. In Phase II, the mean values are E
t
540, A
t
5(40 170 140)/3 550, and M
t
51,000. In the following solution, we will
demonstrate that the optimal policy for Bigco—with these Phase II outputs for A
t
and
M
t
—is to continue if E
t
.30.1. (Don’t worry about the reason for this number right now.
It is just a coincidence that this cutoff is so close to the FDA threshold of 30.) Because our
example estimate for E
t
is 40, the project continues to Phase III, where the mean outputs
are E540, A5 (50 1100 150)/3 566.7, and M51,000. Because the FDA threshold is
30, Newdrug is approved. Cell G12 tells us that Bigco gets a positive NPV if they decide
to market the drug. Nevertheless, standing at time 0, Bigco would be disappointed with
this outcome because the costs ($200M up-front, $50M for Phase II, $100M for Phase III,
and $150 as a milestone) are higher than the NPV of pro?ts. The “max” function in cell
G14 only tells us that once Bigco had sunk the $500M total into developing the drug, it is
optimal for them to market the drug; overall, they will still wish they had never signed the
contract in the ?rst place. Of course, this is just one special case. To determine if the
overall deal is good for Bigco, we will need to complete our solution and simulate many
different cases.
With an optimal strategy given by the maximum function in Cell G14, we can continue
our backward journey through the tree to arrive at Node 5, the Phase III continuation decision
made by Bigco. In principle, this decision is also made with a “Max” function: Bigco wants
to take the maximum of either (1) NPV of continuing to Phase III, or (2) abandoning the
project. In practice, this maximum computation is much more dif?cult than the analogue at
Node 9. At Node 9, there was no more uncertainty left to be resolved: Bigco already knew
the market size, the ef?cacy for Newdrug, and the ef?cacy of its alternative. Thus, the NPV
of marketing the drug could be computed exactly. At Node 5, there is still uncertainty about
market size, ef?cacy, and alternative ef?cacy. In this case, we cannot simply compute an
NPV, but rather must run simulations to estimate it. Bigco wants to answer the following
question: “Given the Phase II outcomes E
t
, A
t
, M
t
, what is the expected NPV of the project?”
Then, Bigco’s optimal strategy is to continue to Phase III if and only if this expected NPV is
greater than the abandonment value of 0.
There are many ways that a clever analyst could approach this problem. (Indeed, some
software packages will automate the process so that the analyst need not be clever at all.) We
will not attempt to ?nd an ef?cient path to a solution; instead, we break the problem down
into steps to illustrate the general intuition behind the solution. We begin by assuming (for
the moment), that the Phase II outputs for A
t
and M
t
are set to their mean values of 50 and
1,000, respectively. Next, we run simulations for the NPV of the project using various inputs
of E
t
. The results are graphed in Exhibit 24-5. We also graph the NPV50 line. The
intersection of the NPV50 line and the Bigco NPV line occurs when E
t
is equal to 30.14.
This intersection means that, if A
t
550 and M
t
51,000, Bigco will have a positive
expected value only if E
t
.30.14. Thus, if E
t
,30.14, Bigco should abandon the project,
and if E
t
.30.14, they should continue.
Next, we allow the value of A
t
to vary, while still holding M
t
?xed at 1,000. For each
value of A
t
, we run simulations to ?nd the value of E
t
such that the NPV of the project is
equal to zero. Because A
t
is T (40, 70, 40), the range of possible values is limited.
We perform the analysis for every A
t
in the set (40, 45, 50, 55, 60, 65, 70). In each case, we
450 CHAPTER 24 R&D VALUATION
?nd the corresponding E
t
that makes the expected NPV equal to zero. We call this a “zero-
pro?t point”. We ?t a zero-pro?t curve through these points in Exhibit 24-6. (This curve is
nearly a straight line.) Notice that the point (50, 30.14) in the exhibit corresponds to the
intersection shown in Exhibit 24-5.
We are slowly clawing our way toward a solution. At this point, if we knew that M
t
were
equal to 1,000, then we would make the continuation decision by looking at Exhibit 24-6 and
seeing if the pair (A
t
, E
t
) was above or below the zero-pro?t curve. To ?nish the solution, we
need to compute a different curve for each level of M
t
. Although this might sound like a lot of
work, by making a few smart guesses we can use interpolation to build these curves. Exhibit
24-7 shows zero-pro?t curves for a range of values for M
t
.
From these curves, we use interpolation to build curves for intermediate levels of M
t
.
Analysts who want more precise results can estimate more curves and rely less on inter-
polation. In either case, we ?nish the solution by building a lookup table
1
in Excel, where the
entries in the table are taken from the y-axis (E
t
) in Exhibit 24-7, and the rows and columns
of the table are given by the values of A
t
and M
t
. Then, for any given Phase II output (A
t
, M
t
),
we instruct Excel to ?nd the closest match from the table to ?nd the corresponding E
t
to use
as a Phase III continuation threshold. Graphically, the lookup table is equivalent to using
Exhibit 24-7 to identify the correct line (M
t
) and the correct x -coordinate (A
t
), and then
?nding the corresponding y-coordinate (E
t
). Then, if the actual phase II output E
t
is higher
than this point, Bigco continues to Phase III. With this strategy de?ned, we can compute the
expected payoffs for Deal 1 by simulating the whole project from the very beginning
1
Readers unfamiliar with lookup tables should consult a reference on Microsoft Excel. One helpful
reference is Walkenbach (2003), Chapter 12.
EXHIBIT 24-5
BIGCO NPV AS OF PHASE III, AS A FUNCTION OF E
t
ASSUMES
A
t
5 50 AND M
t
5 1,000
1,200
1,000
800
600
400
200
–200
0
B
i
g
c
o
N
P
V
NPV ? 0
20 25 30 35 40
E'
45 50 55 60
24.1 DRUG DEVELOPMENT 451
(node 2). After 1M trials, we get an expected payoff of $400.0M for Bigco and $506.4M for
Drugco. Thus, even though Bigco has a negative NPV using expected values (Exhibit 24-4),
the simulation shows a positive NPV for Deal 1.
EXHIBIT 24-7
BIGCO ZERO-PROFIT CURVES, DEAL 1
M' ? 600
M' ? 700
M' ? 800
M' ? 900
M' ? 1,000
M' ? 1,100
M' ? 1,200
M' ? 1,300
M' ? 1,400
100
90
80
70
60
50
40
30
20
10
0
E'
40 45 50 55
A'
60 65 70
EXHIBIT 24-6
BIGCO ZERO-PROFIT CURVE, ASSUMING THAT M
t
5 1,000
50
40
30
20
10
0
E'
40 45 50 55
A'
60 65 70
452 CHAPTER 24 R&D VALUATION
(c) To evaluate Deal 2, we solve backward the extensive form in Exhibit 24-3. This
solution begins the same way as the solution for Deal 1, with an optimal strategy for Bigco
for the marketing of the project. This decision occurs at Node 19. As in the decision at Node
9 for Deal A, Bigco can make this decision by comparing the NPV of marketing the product
with the NPV of abandoning it. Because uncertainties about ef?cacy, alternative ef?cacy,
and market size have all been resolved, the decision can be made with a simple Max
statement.
Exhibit 24-8 shows the modi?ed spreadsheet model for Deal 2. As in Exhibit 24-4, we
display sample output with all variables set to their mean values. This example is illustrative,
because with these inputs Bigco makes a different decision under Deal 2 than it did under
Deal 1. The Max statement is given in cell G14, as a comparison of cell G12 and $0. Here,
with A567, E540, and M51,000, Bigco chooses to abandon the project. The main driver
of this difference is the need to pay a $300M milestone payment. (In Deal 1, all milestones
had already been paid by this point.) Thus, we can already see that the deal structure can have
an important in?uence on outcomes.
Once we input the max statement for Bigco’s marketing decision, we are ready to
evaluate Drugco’s optimal strategy for the Phase III continuation decision. To do this, we
follow the same steps as we did for Deal 1. Because we have seen these steps already, we will
jump directly to the zero-pro?t curves for Drugco, shown in Exhibit 24-9.
Note that these curves are much lower than the corresponding curves for Bigco in
Exhibit 24-7. The reason for this difference is that Drugco has little to lose by going to Phase
III because it only needs to pay $20M for the trials. Furthermore, FDA approval is pure
upside for Drugco because at the very least they can get salvage value for the drug, and they
may get much more. In contrast, in Deal 1, Bigco has to pay the full $100M for the trials and
also faces the possibility that the drug will be worthless to them even if it is approved. Taken
together, these differences lead Drugco to be far more aggressive in Deal 2 than Bigco is in
Deal 1. It is this power to be aggressive that makes “control” of the decision valuable to
Drugco.
With the Phase III continuation strategy de?ned, we can compute the expected payoffs
for Deal B by simulating the whole project from the very beginning (Node 2). In practice, we
do this using a lookup table in Crystal Ball, just as we did for Deal 1. After 1M trials, we get
an expected payoff of $496.2M for Bigco and $391.5M for Drugco.
(d) Using the results of parts (b) and (c), we are ready to solve for the SPNE of the game.
Because it is Drugco’s choice at Node 1 that determines the deal structure, we need to
compare Drugco’s payoffs under the two deals. Because Deal 1 gives Drugco an expected
payoff of $506.4M and Deal 2 gives Drugco an expected payoff of $391.5M, it should
choose Deal 1. This might be surprising to some readers because Deal 2 provides more
control and a seemingly higher upside from the 10 percent royalty. It is dangerous to rely too
much on your intuition when analyzing complex scenarios. In Deal 2, Drugco controls the
Phase III continuation decision and receives generous milestones and royalties. This back-
loading of bene?ts leads to Bigco being more conservative when deciding whether to market
the product—we can see an example of this conservatism by comparing Bigco’s marketing
decision in Exhibits 24-4 and 24-8. With this conservatism, Newdrug is in fact less likely to
make it to market and earn royalties and milestones for Drugco.
To describe the SPNE of the game, we must write down the strategy at every node,
regardless of whether that node is on the equilibrium path. This is dif?cult to do because the
Phase III continuation decision is quite complex. We will revert to shorthand, relying on Max
24.1 DRUG DEVELOPMENT 453
EXHIBIT 24-8
DCF MODEL—DEAL 2
1 A B C D E F G H I J K L
2 Mean St dev Min Mode Max
3 Efficacy (E
t
) 40 40 40
4 Alternative efficacy (A
t
) 50 40 40 70
5 Starting market size (M
t
) 1,000 1,000 50
6 Efficacy (E) 40 40 20
7 Alternative efficacy (A) 67 50 50 100
8 Starting market size (M) 1,000 1,000 100
9 Cost sharing 0
10 Approval milestone 300
11 Continuation threshold 6.0
12 Phase III? 1 Bigco NPV (if enter) 2 $68.1
13 Approval threshold 30 Drugco NPV $39.7
14 Price per unit $1.00 Bigco NPV (option) $0
15 Royalty rate 10.00%
16 Cost per unit $0.25
17 Market share 26.5% Total Bigco NPV 2$226.2
18 Market growth 6.0% Total Drugco NPV $126.21
19 Discount rate 5.00%
20 Approved? 1
21 Salvage value 32.39
22 $ in millions
23 Year 5 6 7 8 9 10 11 12 13 14
24
25 Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
26 Market share 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5%
27 Revenue $405.0 $429.3 $455.0 $482.3 $511.3 $542.0 $574.5 $608.9 $645.5 $684.2
28 Royalty $40.5 $42.9 $45.5 $48.2 $51.1 $54.2 $57.4 $60.9 $64.5 $68.4
29 CGS $101.2 $107.3 $113.8 $120.6 $127.8 $135.5 $143.6 $152.2 $161.4 $171.1
30 Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
31 Bigco profit $64.5 $68.4 $72.5 $76.8 $81.4 $86.3 $91.5 $97.0 $102.8 $108.9
32 Drugco profit $40.5 $42.9 $45.5 $48.2 $51.1 $54.2 $57.4 $60.9 $64.5 $68.4
4
5
4
functions in Exhibits 24-4 and 24-8 and the zero-pro?t lines in Exhibits 24-7 and 27-9 to
simplify the description of the SPNE strategies:
Unique SPNE:
For Drugco:
At Node 1: choose Deal 1.
At Node 15: use Exhibit 24-9 to make the Phase III continuation decision.
For Bigco
At Node 5: use Exhibit 24-7 to make the Phase III continuation decision.
At Node 9: Use the Max function in cell G14 of Exhibit 24-4.
At Node 19: Use the Max function in Cell G14 of Exhibit 24-8.
Notice that the formal description of the SPNE strategies includes listings for Nodes 15
and 19, even though these nodes are never reached in equilibrium. These SPNE strategies
yield expected payoffs of $506M for Drugco and $400M for Bigco. ’
24.2 ENERGY
In the next example, we combine Fuelco’s Projects A, B, and C as originally modeled
in Examples 21.1, 21.2, and 22.2, respectively. (We make a slight alteration to the
EXHIBIT 24-9
DRUGCO ZERO-PROFIT CURVES, DEAL 2
M' ? 600
M' ? 700
M' ? 800
M' ? 900
M' ? 1,000
M' ? 1,100
M' ? 1,200
M' ? 1,300
M' ? 1,400
40 45 50 55
A'
60 65 70
40
35
25
5
–5
15
30
20
10
–10
0
E'
24.2 ENERGY 455
assumptions for Project C, but otherwise all the numbers are the same here as in the
original examples.) The main twist is that Fuelco must complete both Projects A and
B to have the option to complete Project C. This twist enriches and complicates the
modeling.
EXAMPLE 24.2
Fuelco is considering a development project using its patented fuel-cell technology (“Project
A”). If Fuelco pays $200M to develop the technology, then they can bid for a government
contract. The objective probability of winning the contract is 50 percent, and there is no beta
risk for the government’s decision. If Fuelco’s bid is accepted (one year later), then they can
choose to ?nish the project by accepting the contract (cost 5$300M), when they will earn an
NPV (as of one year from now) of $600M (not including the $300M cost of ?nishing the
project). If they do not receive the contract, then they can still ?nish the development project
(cost 5$300M) but they could only receive $200M for the project by selling it to some
nongovernmental buyer (not including the $300M cost of ?nishing the project). The riskfree
rate is zero. (By itself, this project is identical to the project analyzed in Example 21.1.)
In addition to Project A, Fuelco is also considering a separate investment in fuel-cell
technology designed to replace oil-based energy for some types of engines (“Project B”). By
investing $100M today to start the project, Fuelco would maintain the option to ?nish the
project with a further investment (5 $200M) in one year. If oil prices are at least $60 per
barrel in one year (objective probability 550%), then on completion of the project, Fuelco
would have an NPV (as of one year from now) of $1,000M (not including the $200M cost of
?nishing the project). If oil prices are less than $60 a barrel in one year (objective prob-
ability 550%), then the project would not be economical for most applications and would
have an NPV (one year from now) of $300M (not including the $200M cost of ?nishing the
project). If Fuelco decides not to ?nish the project, then they can sell the technology to a
competitor for $200M, regardless of the price of oil. The beta for the project is unknown, but
we do have some information about oil prices: the market price of a European binary call
option (payoff 5$1) on oil with a strike price of $60 per barrel and an expiration of 1 year is
25 cents. (By itself, this project is identical to the project analyzed in Example 21.2.)
Finally, Fuelco is also considering a consumer application for their patented fuel-cell
technology (“Project C”). Project C would only possible if Projects A and B have already
been completed. To begin producing and marketing to the consumer market would require a
new investment of $200M, made in one year (after A and B have been completed). At the
present time, Fuelco estimates that the completed project would have a present value of
$320M in one year (i.e., if Fuelco spent $200M to initiate the project, they believe they could
spin off the initiated project for $320M). Fuelco can delay starting the project for an addi-
tional ?ve years, during which time they expect this value of the project to ?uctuate, with an
annual volatility of 90 percent. Once initiated, the project is expected to generate annual cash
?ows equal to 10 percent of its value. Thus, if Fuelco delays the project, they will forego
these cash ?ows. After ?ve years, some important Fuelco patents will expire, and they will
not longer have the option to pro?tably enter this new market. If Fuelco does not enter the
market, then Project C has no salvage value. (By itself, this project is similar to the project
analyzed in Example 22.2, except that the initial spin-off value is different ($320M here
versus $400M in Example 22.2, and the riskfree interest rate here is zero.)
456 CHAPTER 24 R&D VALUATION
Problems
(a) Draw the decision tree for Fuelco.
(b) Assuming that Fuelco does complete Project A and B, what would be the value of the
option to do Project C?
(c) What is Fuelco optimal strategy? What is the NPV of this strategy?
Solutions
(a) The decision tree is given in several parts. First, we review the decision trees for each
project separately. The tree for Project A, originally given in Exhibit 21-4, is reproduced in
Exhibit 24-10; the tree for Project B, originally given in Exhibit 21-5, is reproduced in Exhibit
24-9; the tree for Project C, with the same shape but different payoffs as given in Exhibit 22-11,
is reproduced in Exhibit 24-12. Last, after showing the three projects separately, Exhibit 24-13
gives a tree with a schematic version of the full decision problem, showing the decision nodes
and branches for each project, with the event branches omitted.
(b) To ?nd the value of the all the projects combined, we solve backward, beginning with
Project C. The valuation problem here is similar to Example 22.2, except for the difference
in the initial value of the project ($320M here) and in the riskfree rate (0 percent here). To
estimate the value of the option, we use the bintree spreadsheet and build an American
EXHIBIT 24-10
FUELCO’S DECISION TREE (PROJECT A)
2
Don't get contract
Duration ? one year
Cost to start project ? $200M
Get contract
Finish project
Finish project
Abandon
Abandon
3
1
50%
50%
–$300M
–$300M
$600M
$200M
$0
$0
24.2 ENERGY 457
option tree with a possible exercise in every month over a ?ve-year period. This tree is
identical to the tree we built in Example 22.2, except for the small changes in the inputs
worksheet. After making these changes, the spreadsheet gives an option value of $180.77M.
In the interest of simplifying our calculations for the rest of the problem, we round this
value off to $180M.
(c) To value the full set of projects, we need a practical way to combine the trees from
Exhibits 24-10, 24-11 and 24-12. In Exhibit 24-14, we combine Projects A and B into a
single tree, and we combine the risk-neutral probabilities for each type of uncertainty.
For example, because Project A faces only the idiosyncratic risk of the government
contract, the risk-neutral probability of getting the contract is identical to the objective
probability (50 percent). In contrast, the oil prices in Project B do include some market
risk. Luckily for us, the binary call option allows us to solve for the risk-neutral prob-
abilities of 25 percent for high oil prices and 75 percent for low oil prices. (Do you
remember why this is true? If you forgot, see Section 21.4 for an explanation.) Exhibit
24-14 prunes the ?nal decisions for each project, with the extensions for these decisions
shown in Exhibits 24-15, 24-16, 24-17, and 24-18. Following these exhibits, we explain
the trees in more detail.
To see how Exhibit 24-14 has been pruned, we start by looking at Nodes 6 to 9. At
Nodes 6 and 7, Fuelco has elected to start Project B but not Project A. Because A has not
been started, it is not possible to complete both A and B, and thus Project C does not come
EXHIBIT 24-11
FUELCO’S DECISION TREE (PROJECT B)
2
Low oil price
Duration ? one year
Cost to start project ? $100M
High oil price
Finish project
Finish project
Abandon
Abandon
3
1
50%
50%
–$200M
–$200M
$1,000M
$300M
$200M
$200M
458 CHAPTER 24 R&D VALUATION
under consideration at all. Thus, Nodes 6 and 7 reduce to a straightforward analysis of
Project B, which is illustrated in Exhibit 24-11. For Project B, we know it is optimal to
abandon the project when oil prices are low (node 6, $200M) and to ?nish the project when oil
prices are high (node 7, $1,000M2$200M5$800M). With risk-neutral probabilities of 0.75
for low oil prices and 0.25 for high oil prices, the NPV of the “Start A” strategy is 0.75 Ã
200 10.25 Ã 800 2 100 5$250M, which is the same answer we got in Example 21.2.
We turn next to Nodes 8 and 9, where Fuelco has elected to start Project A but not
Project B. Here, as in the previous case, Project C is not possible, because it is not possible to
complete both A and B. Thus, we have a straightforward analysis of Project A, which is
illustrated in Exhibit 24-10. For Project A, we know it is optimal to ?nish the project
if Fuelco gets the contract (node 8, $600M2$300M5$300M) and to abandon the project if
they don’t (node 9, $0). With risk-neutral probabilities of 0.50 for getting the contract and
0.50 for not getting the contract, the NPV of the “Start B” strategy is 0.50 Ã 300 10.50 Ã 0 2
200 52$50M, which is the same answer we got in Example 21.1.
The problem grows more complex when we analyze the “Start both” branch, which
leads to terminal nodes at 10, 11, 12, and 13. To aid in this analysis, Exhibits 24-15 through
EXHIBIT 24-12
FUELCO’S DECISION TREE (PROJECT C)
1
5
3
4
9
$200M invest
$200M invest
1–p
1–p
wait
wait
wait
invest –$200M
down
up
foregone
cash flow
? CF
5
foregone
cash flow
? CF
1
foregone
cash flow
? CF
4
($320 – CF
1
)*d
($320 – CF
1
)*u
6
$320
2
up p
up p
1–p
down
1–p
down
11
13
12
10
Instant Instant One month
One
month
8
7
24.2 ENERGY 459
24-18 show the payoffs in each of these extensions. Consider the payoffs in Exhibit 24-15,
which corresponds to Node 10. At this node, Fuelco has chosen “start both”, and the
uncertainty has resolved to give Fuelco the contract but with low oil prices. The risk-neutral
probability of this branch is equal to the product of the risk-neutral probabilities for “low oil
price” (75 percent) and “get contract” (50 percent). This product is equal to 0.375. Once node
10 is reached, Fuelco has four possible choices, representing the yes/no decision for ?nishing
both projects. The terminal nodes in Exhibit 24-15 show the payoffs from each of these
choices. These payoffs come directly from Exhibits 24-10 and 24-11, with one important
exception: if Fuelco chooses to ?nish both projects, then it receives a “bonus” equal to the
NPV of Project C (5$180 M). Indeed, this bonus—only possible when both A and B have
been completed—makes “?nish both” the optimal decision. This optimal decision is
circled in Exhibit 25-15, with the payoff of $580 M shown for Node 10 in the pruned tree of
Exhibit 24-14.
The payoffs at Nodes 11, 12, and 13 are computed using the same method. For Node
11, Exhibit 24-16 indicates that the optimal strategy is “?nish neither”, with a payoff of
$200M. At nodes 11 and 12, the respective Exhibits 24-17 and 24-18 indicate that “?nish
both” is the optimal strategy. Once we include the payoffs from these strategies into
Exhibit 24-14, we are ready to compute the expected payoff for the “start both” branch as
EXHIBIT 24-13
FUELCO’S DECISION TREE, SCHEMATIC (ALL PROJECTS)
6
2 3
10 8
4 1
9 7
Project A Project B
Project C Project C
Project
B
Project
A
5
start start
get
contract
high oil
wait up wait
invest
invest invest down
don't don't don't low oil
invest
don't
don't
One Year
One Month One Month
(Payoff) (Payoff) (Payoff)
460 CHAPTER 24 R&D VALUATION
Expected payoff of ‘‘start both’’ branch 50:375 Ã 580
10:375 Ã 200 10:125 Ã 1; 280 10:125 Ã 880 2300 ¼ $262:5M:
ð24:2Þ
This payoff is higher than the $250M payoff for “start B”, the 2$50M expected payoff
for “start A”, and the $0 payoff from “start neither”. Thus, Fuelco’s optimal strategy for all
projects is
1. Start Projects A and B.
2. If “low oil” 1“don’t get contract” then abandon both projects, otherwise ?nish both.
3. Follow the optimal strategy of the binomial tree for Project C.
The NPV of this strategy is $262.5M. Note that the optimal strategies for Projects
A and B have been signi?cantly altered by the presence of Project C. Indeed, when we
considered A and B in isolation, we always abandoned these projects in the “low oil” or
“don’t get contract” states. The option to invest in Project C has changed the optimal
investment strategy on other projects and given Fuelco a reason to pursue those projects
EXHIBIT 24-14
FUELCO’S DECISION TREE, PRUNED (ALL PROJECTS), WITH
RISK-NEUTRAL PROBABILITIES
4
2
(0) 1
3 5
Start neither
Start
both
–300
–200
Start A
–100
Start B
(300)
8
(800)
7
(580)
10
(880)
13
(200)
11
(1,280)
12
(200)
6
Get
contract
High
Oil
Low
Oil
0.50 0.25
0.75
0.50
Don't
(0)
9
0.125
0.125 0.375
High/
Don't
High/
Get
Low/
Don't
0.375
Low/
Get
24.2 ENERGY 461
EXHIBIT 24-15
NODE 10, EXPANDED
10
Finish A
Finish B
Finish Both
Finish
Neither
300 ? 200
? 500
300 ? 100 ? 180
? 580
0 ? 200
? 200
0 ? 100
? 100
EXHIBIT 24-16
NODE 11, EXPANDED
11
Finish A
Finish B
Finish Both
Finish
Neither
–100 ? 200
? 100
?100 ? 100 ? 180
? 180
0 ? 200
? 200
0 ? 100
? 100
462 CHAPTER 24 R&D VALUATION
EXHIBIT 24-17
NODE 12, EXPANDED
12
Finish A
Finish B
Finish Both
Finish
Neither
300 ? 200
? 500
300 ? 800 ? 180
? 1280
0 ? 200
? 200
0 ? 800
? 800
EXHIBIT 24-18
NODE 13, EXPANDED
13
Finish A
Finish B
Finish Both
Finish
Neither
?100 ? 200
? 100
?100 ? 800 ? 180
? 880
0 ? 200
? 200
0 ? 800
? 800
24.2 ENERGY 463
mainly for the technological ?exibility for a later project. Although this is an abstract
example, it is illustrative of the kind of strategic thinking that is necessary in R&D
investment. ’
24.3 THE FOREST AND THE TREES
Part IV has been all about trees. We learned about event trees in Chapter 20, decision
trees in Chapter 21, binomial trees in Chapter 22, and game trees in Chapter 23. In
this chapter, we put all these trees together to solve some complex examples. In the
midst of all these trees, it is easy to lose sight of the forest. R&D investing is a highly
uncertain endeavor. In our examples, we pretended to know a lot of things that are
essentially unknowable: starting values for projects, objective probabilities, volati-
lities—all these things are guesses. Given all this uncertainty, why do we bother? We
do it because it is by modeling things carefully that we force rigor into our thought
process. In Example 24.1, this rigor allowed us to see why “control” might not be
worth its costs, because giving to much power to Drugco at one stage can lead Bigco
to grow very conservative at another. These are fundamental insights about the
strategic situation, insights that transcend the speci?c numbers used in the example.
Similarly, the Fuelco problem in Example 24.2—although very unrealistic in the
speci?cs—is illustrative of the interconnections across R&D projects. Many man-
agers have a natural intuition for real options and the value of ?exibility. By running
through a few models, we can begin to quantify and sharpen this intuition.
Although we have applied the models in Part IV to general R&D investment—
rather than to venture capital—the insights of these models can readily be applied to
VC investment. Because VC ?rms are lean organizations staffed mostly by gen-
eralists, most do not have the capabilities (or time) to perform this kind of analysis.
The ?exible spreadsheets included with this book can help to bridge this gap. In all
these cases, it is important to remember the big picture, even when paying close
attention to the details. We must not lose sight of the forest because we are staring at
the trees.
SUMMARY
In this chapter, we pulled together the various methods studied in Part IV. We use these
methods to analyze complex investment problems for Drugco and Fuelco. The framework of
these problems was ?rst introduced in Chapter 19, with the building blocks for the solutions
covered in Chapter 20 (event trees and Monte Carlo analysis), Chapter 21 (decision trees and
real options), Chapter 22 (binomial trees), and Chapter 23 (game trees and game theory).
The main value of working through solutions to these problems is in the process itself;
by providing structure to the decision problem, the analyst can quantify his intuition and gain
a deeper understanding of the strategic nuances of the situation. Although such deep study
464 CHAPTER 24 R&D VALUATION
can reap great rewards, it is dangerous to rely exclusively on the model answers. The most
successful investors are those who ride their visions using a structured investment discipline.
REFERENCES
Walkenbach, John, 2003, Excel 2003 Bible, Wiley, Indianapolis, IN.
EXERCISES
24.1 Use the same setup as in Example 24.1. Suppose that Bigco offers Drugco a third
option, Deal 3. In Deal 3, Bigco retains full control and pays all costs (just like Deal 1), with
one change: instead of paying a $150M milestone for Phase III continuation, Bigco would
pay a $400M milestone if they decide to market Newdrug.
(a) Draw the extensive form for Deal 3.
(b) Suppose that Drugco decides to take Deal 3. What is the optimal strategy for Bigco
following the Phase III trials? What is the optimal strategy for Bigco following the Phase II
trials? Assuming that Bigco chooses these strategies, what are the expected payoffs to
Drugco and Bigco?
(c) Given the choice of Deals 1, 2, and 3, which should Drugco choose?
24.2 Use the same setup as in Example 24.2.
(a) Suppose that the starting value for Project C is $400M. How does that change your
answers to parts (b) and (c)?
(b) Suppose that the starting value for Project C is $200M. How does that change your
answer to parts (b) and (c)?
24.3 Suppose that EBV is considering an equity investment in Drugco to coincide with the
signing of a strategic alliance (Deal 1 from Example 24.1) with Bigco. What suggestions
would you give to EBV of how to think about this investment?
24.4 True, False or Uncertain: A deep understanding of ?nance can help someone make
better venture capital and R&D investment decisions.
EXERCISES 465
APPENDI X A
SAMPLE TERM SHEET
THIS IS a public-domain document from the website of the National
Venture Capital Association. The version in this appendix was last updated in
April 2009.
This sample document is the work product of a coalition of attorneys who
specialize in venture capital ?nancings, working under the auspices of the
NVCA. See the NVCA website for a list of the Working Group members.
This document is intended to serve as a starting point only, and should be
tailored to meet your speci?c requirements. This document should not
be construed as legal advice for any particular facts or circumstances.
Note that this sample presents an array of (often mutually exclusive)
options with respect to particular deal provisions.
PRELIMINARY NOTES
This term sheet maps to the NVCA Model Documents, and for convenience the
provisions are grouped according to the particular Model Document in which
they may be found. Although this term sheet is perhaps somewhat longer than a
“typical” VC Term Sheet, the aim is to provide a level of detail that makes the
term sheet useful as both a road map for the document drafters and as a
reference source for the business people to quickly ?nd deal terms without the
necessity of having to consult the legal documents (assuming of course there have
been no changes to the material deal terms prior to execution of the ?nal
documents).
466
TERM SHEET
FOR SERIES A PREFERRED STOCK FINANCING OF
[INSERT COMPANY NAME], INC.
[___ ___, 200_]
This Term Sheet summarizes the principal terms of the Series A Preferred Stock
Financing of [___________], Inc., a [Delaware] corporation (the “Company”). In
consideration of the time and expense devoted and to be devoted by the Investors
with respect to this investment, the No Shop/Con?dentiality [and Counsel and
Expenses] provisions of this Term Sheet shall be binding obligations of the
Company whether or not the ?nancing is consummated. No other legally binding
obligations will be created until de?nitive agreements are executed and delivered
by all parties. This Term Sheet is not a commitment to invest, and is conditioned
on the completion of due diligence, legal review and documentation that is
satisfactory to the Investors. This Term Sheet shall be governed in all respects by
the laws of the [State of Delaware], and does not constitute an offer to sell or a
solicitation of an offer to buy securities in any state where the offer or sale is not
permitted.
Offering Terms
Closing Date: As soon as practicable following the Company’s
acceptance of this Term Sheet and satisfaction of
the Conditions to Closing (the “Closing”). [provide
for multiple closings if applicable]
Investors: Investor No. 1: [_______] shares ([__]%),
$[_________]
Investor No. 2: [_______] shares ([__]%),
$[_________]
[as well other investors mutually agreed upon by
Investors and the Company]
Amount Raised: $[________], [including $[________] from the con-
version of principal [and interest] on bridge notes].
1
Price Per Share: $[________] per share (based on the capitalization of
the Company set forth below) (the “Original Pur-
chase Price”).
1
Modify this provision to account for staged investments or investments dependent on the achievement
of milestones by the Company.
APPENDIX A SAMPLE TERM SHEET 467
Pre-Money Valuation: The Original Purchase Price is based upon a fully-
diluted pre-money valuation of $[_____] and a
fully-diluted post-money valuation of $[______]
(including an employee pool representing [__]% of
the fully-diluted post-money capitalization).
Capitalization: The Company’s capital structure before and after the
Closing is set forth on Exhibit A.
CHARTER
2
Dividends: [Alternative 1: Dividends will be paid on the Series
A Preferred only on an as-converted basis when, as,
and if paid on the Common Stock.]
[Alternative 2: The Series A Preferred will accrue
dividends at the rate of [__]% per annum[, payable
only when and if declared by the Board] [or upon a
liquidation or redemption.] For any other dividends
or distributions, participation with Common Stock
on an as-converted basis.]
3
EXHIBIT A
PRE- AND POST-FINANCING CAPITALIZATION
Pre-Financing Post-Financing
Security # of Shares % # of Shares %
Common À Founders
Common À Employee Stock Pool
Issued
Unissued
[Common À Warrants]
Series A Preferred
Total
2
The Charter is a public document, ?led with the [Delaware] Secretary of State, which establishes all of
the rights, preferences, privileges and restrictions of the Preferred Stock.
3
In some cases, accrued and unpaid dividends are payable on conversion as well as upon a liquidation
event. Most typically, however, dividends are not paid if the preferred is converted. Another alternative
is to give the Company the option to pay accrued and unpaid dividends in cash or in common shares
valued at fair market value. The latter are referred to as “PIK” (payment-in-kind) dividends.
468 APPENDIX A SAMPLE TERM SHEET
Liquidation Preference: In the event of any liquidation, dissolution or wind-
ing up of the Company, the proceeds shall be paid as
follows:
[Alternative 1 (non-participating Preferred Stock):
First pay the greater of (i) [one] times the Original
Purchase Price [plus accrued dividends] [plus
declared and unpaid dividends] on each share of
Series A Preferred or (ii) such amount as would have
been payable had all shares of Preferred Stock been
converted to Common Stock on each share of Series
A Preferred. The balance of any proceeds shall be
distributed pro rata to holders of Common Stock.]
[Alternative 2 (full participating Preferred Stock):
First pay [one] times the Original Purchase Price
[plus accrued dividends] [plus declared and unpaid
dividends] on each share of Series APreferred. There-
after, the Series A Preferred participates with the
Common Stock pro rata on an as-converted basis.]
[Alternative 3 (cap on Preferred Stock participation
rights): First pay [one] times the Original Purchase
Price [plus accrued dividends] [plus declared and
unpaid dividends] on each share of Series A Preferred.
Thereafter, Series A Preferred participates with Com-
mon Stock pro rata on an as-converted basis until the
holders of Series A Preferred receive an aggregate of
[_____] times the Original Purchase Price per share, at
whichpoint eachholder of Series APreferredis entitled
to receive the greater of (i) that amount per share or (ii)
the amount such holder would receive if all shares of
Series A Preferred Stock had been converted to Com-
mon Stock immediately prior to such liquidation.]
A merger or consolidation (other than one in which
stockholders of the Company own a majority by
voting power of the outstanding shares of the surviv-
ing or acquiring corporation) and a sale, lease,
transfer, exclusive license or other disposition of all
or substantially all of the assets of the Company will
be treated as a liquidation event (a “Deemed Liqui-
dation Event”), thereby triggering payment of the
liquidation preferences described above [unless the
holders of [___]% of the Series A Preferred elect
otherwise].
APPENDIX A SAMPLE TERM SHEET 469
[Investors’ entitlement to their liquidation preference
shall not be abrogated or diminished in event part of
consideration is subject to escrow in connection with a
Deemed Liquidation Event.]
4
Voting Rights: The Series A Preferred Stock shall vote together with
the Common Stock on an as-converted basis, and not
as a separate class, except (i) the Series A Preferred
as a class shall be entitled to elect [_______] [(_)]
members of the Board (the “Series A Directors”),
and (ii) as required by law. The Company’s Certi?-
cate of Incorporation will provide that the number of
authorized shares of Common Stock may be
increased or decreased with the approval of a major-
ity of the Preferred and Common Stock, voting
together as a single class, and without a separate
class vote by the Common Stock, irrespective of the
provisions of Section 242(b)(2) of the Delaware
General Corporation Law.
5
Protective Provisions: [So long as [insert ?xed number, or %, or “any”]
shares of Series A Preferred are outstanding,] in
addition to any other vote or approval required under
the Company’s Charter or By-laws, the Company
will not, without the written consent of the holders of
at least [__]% of the Company’s Series A Preferred,
either directly or indirectly by amendment, merger,
consolidation, or otherwise:
(i) liquidate, dissolve or wind-up the business and
affairs of the Company, or effect any Deemed Liqui-
dation Event or consent to any of the foregoing; (ii)
amend, alter, or repeal any provision of the Certi?cate
4
When a portion of the merger consideration is placed in escrow to secure a company’s indemni?cation
obligations to an acquirer, the company’s stockholders will need to address how the deductions from the
merger consideration used to fund the escrow are to be allocated among themselves. Today most charters
are silent on the subject of escrow allocations, and the parties simply work it out at the time of the M&A
event. However, this provision is intended to cause the parties to at least consider these issues at the time
of the initial investment. Today, the more common approach is simply to allocate the acquisition escrow
pro rata among all stockholders. Section 2.3.4 of the NVCA Model Charter provides for the alternative
approach, namely, allocation of the escrow in a manner that ensures that the Preferred Stock holders
always receive their liquidation preference, even if some or all of the escrow is forfeited. See fn. 25 to the
NVCA Model Charter for examples and a more detailed explanation.
5
For California corporations, one cannot “opt out” of the statutory requirement of a separate class vote by
Common Stockholders to authorize shares of Common Stock.
470 APPENDIX A SAMPLE TERM SHEET
of Incorporation or Bylaws [in a manner adverse to the
Series A Preferred];
6
(iii) create or authorize the
creation of [or issue or obligate itself to issue shares
of,] any other security convertible into or exercisable
for any equity security, having rights, preferences or
privileges senior to or on parity with the Series A
Preferred, or increase the authorized number of shares
of Series A Preferred or of any additional class or
series of capital stock [unless it ranks junior to the
Series APreferred]; (iv) reclassify, alter or amend any
existing security that is junior to or on parity with the
Series A Preferred, if such reclassi?cation, alteration
or amendment would render such other security senior
to or on parity with the Series A Preferred; (v)
purchase or redeemor pay any dividend on any capital
stock prior to the Series A Preferred, [other than stock
repurchased from former employees or consultants in
connection with the cessation of their employment/
services, at the lower of fair market value or cost;]
[other than as approved by the Board, including the
approval of [_____] Series A Director(s)]; (vi) create
or authorize the creation of any debt security [if the
Company’s aggregate indebtedness would exceed
$[____][other than equipment leases or bank lines of
credit]unless such debt security has received the prior
approval of the Board of Directors, including the
approval of [________] Series A Director(s)]; (vii)
create or hold capital stock in any subsidiary that is not
a wholly-owned subsidiary or dispose of any subsidi-
ary stock or all or substantially all of any subsidiary
assets[; or (viii) increase or decrease the size of the
Board of Directors].
Optional Conversion: The Series A Preferred initially converts 1:1 to
Common Stock at any time at option of holder,
subject to adjustments for stock dividends, splits,
combinations and similar events and as described
below under “Anti-dilution Provisions”.
6
Note that as a matter of background law, Section 242(b)(2) of the Delaware General Corporation Law
provides that if any proposed charter amendment would adversely alter the rights, preferences and
powers of one series of Preferred Stock, but not similarly adversely alter the entire class of all Preferred
Stock, then the holders of the impacted series are entitled to a separate series vote on the amendment.
APPENDIX A SAMPLE TERM SHEET 471
Anti-dilution Provisions: In the event that the Company issues additional
securities at a purchase price less than the current
Series A Preferred conversion price, such conversion
price shall be adjusted in accordance with the
following formula:
[Alternative 1: “Typical” weighted average:
CP
2
5CP
1
à ðA1BÞ=ðA1CÞ
CP
2
5Series A Conversion Price in effect immedi-
ately after new issue
CP
1
5Series A Conversion Price in effect immedi-
ately prior to new issue
A5Number of shares of Common Stock deemed to
be outstanding immediately prior to new issue
(includes all shares of outstanding common stock,
all shares of outstanding preferred stock on an as-
converted basis, and all outstanding options on an
as-exercised basis; and does not include any conver-
tible securities converting into this round of ?nancing)
B5Aggregate consideration received by the Cor-
poration with respect to the new issue divided by CP
1
C5Number of shares of stock issued in the subject
transaction]
[Alternative 2: Full-ratchet—the conversion price
will be reduced to the price at which the new shares
are issued.]
[Alternative 3: No price-based anti-dilution protection.]
The following issuances shall not trigger anti-dilu-
tion adjustment:
7
(i) securities issuable upon conversion of any of the
Series A Preferred, or as a dividend or distribution on
the Series A Preferred; (ii) securities issued upon the
conversion of any debenture, warrant, option, or
other convertible security; (iii) Common Stock
issuable upon a stock split, stock dividend, or any
subdivision of shares of Common Stock; and
(iv) shares of Common Stock (or options to purchase
7
Note that additional exclusions are frequently negotiated, such as issuances in connection with
equipment leasing and commercial borrowing. See additional exclusions de?ned as “Exempted Secu-
rities” in Section 4.4.1 of the NVCA Model Charter.
472 APPENDIX A SAMPLE TERM SHEET
such shares of Common Stock) issued or issuable to
employees or directors of, or consultants to, the
Company pursuant to any plan approved by the
Company’s Board of Directors [including at least
[_______] Series A Director(s)] [(v) shares of Com-
mon Stock issued or issuable to banks, equipment
lessors or other ?nancial institutions, or to real
property lessors, pursuant to a debt ?nancing, equip-
ment leasing or real property leasing transaction
approved by the Board of Directors of the Corporation
[, including at least [_______] Series A Director(s)].
Mandatory Conversion: Each share of Series A Preferred will automatically
be converted into Common Stock at the then applic-
able conversion rate in the event of the closing of a
[?rm commitment] underwritten public offering with
a price of [___] times the Original Purchase Price
(subject to adjustments for stock dividends, splits,
combinations and similar events) and [net/gross]
proceeds to the Company of not less than
$[_______] (a “QPO”), or (ii) upon the written
consent of the holders of [__]% of the Series A
Preferred.
8
Pay-to-Play: [Unless the holders of [__]% of the Series A elect
otherwise,] on any subsequent down round all
[Major] Investors are required to participate to the
full extent of their participation rights (as described
below under “Investor Rights Agreement À Right to
Participate Pro Rata in Future Rounds”), unless the
participation requirement is waived for all [Major]
Investors by the Board [(including the vote of [a
majority of] the Series A Director)].
[Alternative 1: [Each share] [applicable portion of
the shares]
9
of Series A Preferred of any [Major]
Investor failing to do so will automatically convert to
8
The per share test ensures that the investor achieves a signi?cant return on investment before the
Company can go public. Also consider allowing a non-QPO to become a QPO if an adjustment is made
to the Conversion Price for the bene?t of the investor, so that the investor does not have the power to
block a public offering.
9
The second formulation serves to have the consequences of the pay-to-play provisions apply on a
proportionate basis (e.g., if Investor plays for
1
/2 of pro rata share, then only
1
/2 of the Investor’s Preferred
converts to common, or does not receive anti dilution adjustment, etc., as applicable).
APPENDIX A SAMPLE TERM SHEET 473
Common Stock and lose the right to a Board seat if
applicable.]
[Alternative 2: [Each share] [applicable portion of
the shares] of any [Major] Investor failing to do so
will automatically [lose anti-dilution rights] [lose
right to participate in future rounds].]
10
Redemption Rights:
11
The Series A Preferred shall be redeemable from
funds legally available for distribution at the option
of holders of at least [__]% of the Series A Preferred
commencing any time after [________] at a price
equal to the Original Purchase Price [plus all accrued
but unpaid dividends]. Redemption shall occur in
three equal annual portions. Upon a redemption
request from the holders of the required percentage
of the Series A Preferred, all Series A Preferred
shares shall be redeemed [(except for any Series A
holders who af?rmatively opt-out)].
12
STOCK PURCHASE AGREEMENT
Representations
and Warranties:
Standard representations and warranties by the Com-
pany. [Representations and warranties by Founders
10
If the punishment for failure to participate is losing some but not all rights of the Preferred (e.g.,
anything other than a forced conversion to common), the Charter will need to have so-called “blank
check preferred” provisions at least to the extent necessary to enable the Board to issue a “shadow” class
of preferred with diminished rights in the event an investor fails to participate. Note that as a drafting
matter it is far easier to simply have (some or all of) the preferred convert to common.
11
Redemption rights allow Investors to force the Company to redeem their shares at cost [plus a small
guaranteed rate of return (e.g., dividends)]. In practice, redemption rights are not often used; however,
they do provide a form of exit and some possible leverage over the Company. While it is possible that the
right to receive dividends on redemption could give rise to a Code Section 305 “deemed dividend”
problem, many tax practitioners take the view that if the liquidation preference provisions in the Charter
are drafted to provide that, on conversion, the holder receives the greater of its liquidation preference or
its as-converted amount (as provided in the NVCA Model Charter), then there is no Section 305 issue.
12
Due to statutory restrictions, it is unlikely that the Company will be legally permitted to redeem in the
very circumstances where investors most want it (the so-called “sideways situation”), investors will
sometimes request that certain penalty provisions take effect where redemption has been requested but
the Company’s available cash ?ow does not permit such redemption—e.g., the redemption amount shall
be paid in the form of a one-year note to each unredeemed holder of Series A Preferred, and the holders
of a majority of the Series A Preferred shall be entitled to elect a majority of the Company’s Board of
Directors until such amounts are paid in full.
474 APPENDIX A SAMPLE TERM SHEET
[regarding technology ownership, con?icting agree-
ments, litigation etc.].]
13
Conditions to Closing: Standard conditions to Closing, which shall include,
among other things, satisfactory completion of ?nan-
cial and legal due diligence, quali?cation of the
shares under applicable Blue Sky laws, the ?ling of
a Certi?cate of Incorporation establishing the rights
and preferences of the Series A Preferred, and an
opinion of counsel to the Company.
Counsel and Expenses: [Investor/Company] counsel to draft closing docu-
ments. Company to pay all legal and administrative
costs of the ?nancing [at Closing], including reason-
able fees and expenses, in an amount not to exceed
[_____], of Investor counsel [, unless the transaction
is not completed because the Investors withdraw
their commitment without cause].
14
Company Counsel: [____________________
____________________
____________________]
Investor Counsel: [____________________
____________________
____________________]
INVESTOR RIGHTS AGREEMENT
Registration Rights:
Registrable Securities: All shares of Common Stock issuable upon conver-
sion of the Series A Preferred and any other
13
Founders’ representations are controversial and may elicit signi?cant resistance. They are more
common in the Northeast and counsel should be warned that they may not be well received elsewhere.
They are more likely to appear if Founders are receiving liquidity from the transaction or if there is
heightened concern over intellectual property (e.g., the Company is a spin-out from an academic
institution or the Founder was formerly with another Company whose business could be deemed
competitive with the Company). Founders’ representations are not common in subsequent rounds, even
in the Northeast, where risk is viewed as signi?cantly diminished and fairly shared by the investors rather
than being disproportionately borne by the Founders.
14
The bracketed text should be deleted if this section is not designated in the introductory paragraph as
one of the sections that is binding upon the Company regardless of whether the ?nancing is
consummated.
APPENDIX A SAMPLE TERM SHEET 475
Common Stock held by the Investors will be deemed
“Registrable Securities”.
15
Demand Registration: Upon earliest of (i) [three-?ve] years after the
Closing; or (ii) [six] months following an initial
public offering (“IPO”), persons holding [__]% of
the Registrable Securities may request [one][two]
(consummated) registrations by the Company of
their shares. The aggregate offering price for such
registration may not be less than $[5-15] million. A
registration will count for this purpose only if (i) all
Registrable Securities requested to be registered are
registered and (ii) it is closed, or withdrawn at the
request of the Investors (other than as a result of a
material adverse change to the Company).
Registration on Form S-3: The holders of [10À30]% of the Registrable Secu-
rities will have the right to require the Company to
register on Form S-3, if available for use by the
Company, Registrable Securities for an aggregate
offering price of at least $[1À5 million]. There will
be no limit on the aggregate number of such Form S-3
registrations, provided that there are no more than
[two] per year.
Piggyback Registration: The holders of Registrable Securities will be entitled
to “piggyback” registration rights on all registration
statements of the Company, subject to the right,
however, of the Company and its underwriters to
reduce the number of shares proposed to be regis-
tered to a minimum of [20À30]% on a pro rata basis
and to complete reduction on an IPO at the under-
writer’s discretion. In all events, the shares to be
registered by holders of Registrable Securities will
be reduced only after all other stockholders’ shares
are reduced.
Expenses: The registration expenses (exclusive of stock transfer
taxes, underwriting discounts and commissions will
be borne by the Company. The Company will also
pay the reasonable fees and expenses [not to exceed
$______,] of one special counsel to represent all the
participating stockholders.
15
Note that Founders/management sometimes also seek limited registration rights.
476 APPENDIX A SAMPLE TERM SHEET
Lock-up: Investors shall agree in connection with the IPO, if
requested by the managing underwriter, not to sell or
transfer any shares of Common Stock of the Com-
pany [(including/excluding shares acquired in or
following the IPO)] for a period of up to [180]
days
16
following the IPO subject to extension to
facilitate compliance with FINRA rules (provided all
directors and of?cers of the Company [and [1À5]%
stockholders] agree to the same lock-up). [Such lock-
up agreement shall provide that any discretionary
waiver or termination of the restrictions of such
agreements by the Company or representatives of
the underwriters shall apply to Investors, pro rata,
based on the number of shares held.]
Management and
Information Rights:
A Management Rights letter from the Company, in a
form reasonably acceptable to the Investors, will be
delivered prior to Closing to each Investor that
requests one.
17
Any [Major] Investor [(who is not a competitor)] will
be granted access to Company facilities and person-
nel during normal business hours and with reason-
able advance noti?cation. The Company will deliver
to such Major Investor (i) annual, quarterly, [and
monthly] ?nancial statements, and other information
as determined by the Board; (ii) thirty days prior to
the end of each ?scal year, a comprehensive operat-
ing budget forecasting the Company’s revenues,
expenses, and cash position on a month-to-month
basis for the upcoming ?scal year[; and (iii) promptly
following the end of each quarter an up-to-date
capitalization table]. A “Major Investor” means
any Investor who purchases at least $[______] of
Series A Preferred.
Right to Maintain
Proportionate
Ownership:
All [Major] Investors shall have a pro rata right, based
on their percentage equity ownership in the Company
[(assuming the conversion of all outstanding Preferred
16
See commentary in fn. 23 and 24 of the NVCA Model Investor Rights Agreement regarding possible
extensions of lock-up period.
17
See commentary in introduction to NVCA Model Managements Rights Letter, explaining purpose of
such letter.
APPENDIX A SAMPLE TERM SHEET 477
Stock into Common Stock and the exercise of all
options outstanding under the Company’s stock
plans)]
18
, to participate in subsequent issuances of
equity securities of the Company (excluding those
issuances listed at the end of the “Anti-dilution
Provisions” section of this Term Sheet. In addition,
should any [Major] Investor choose not to purchase its
full pro rata share, the remaining [Major] Investors
shall have the right to purchase the remaining pro
rata shares.
Matters Requiring
Investor Director
Approval:
19
So long as the holders of Series A Preferred are
entitled to elect a Series A Director, the Company
will not, without Board approval, which approval
must include the af?rmative vote of [one/both] of the
Series A Director(s):
(i) make any loan or advance to, or own any stock
or other securities of, any subsidiary or other
corporation, partnership, or other entity unless it
is wholly owned by the Company; (ii) make any
loan or advance to any person, including, any
employee or director, except advances and similar
expenditures in the ordinary course of business or
under the terms of a employee stock or option plan
approved by the Board of Directors; (iii) guarantee
any indebtedness except for trade accounts of the
Company or any subsidiary arising in the ordinary
course of business; (iv) make any investment
inconsistent with any investment policy approved
by the Board; (v) incur any aggregate indebtedness
in excess of $[_____] that is not already included in
a Board-approved budget, other than trade credit
incurred in the ordinary course of business; (vi) enter
into or be a party to any transaction with any director,
18
See commentary in fn. 40 of the NVCA Model Investor Rights Agreement regarding possible varia-
tions on the calculation of pro-rata rights.
19
Founders will often resist having speci?ed corporate acts subject to approval by the investors’ Board
designee(s). On the other hand, some investors won’t go forward without this provision. An alternative is
to move items from this list to the “protective provisions” of the charter, where they would require a
Preferred stockholder vote. If the investor insists on such provisions, the Company generally would ?nd
the director approval approach preferable, as the director representative on the Board has a ?duciary duty
to the corporation when acting in the capacity of a director. Other formulations could be: requiring the
vote of a supermajority of the Board, or a majority of the non-management directors.
478 APPENDIX A SAMPLE TERM SHEET
of?cer or employee of the Company or any “associ-
ate” (as de?ned in Rule 12b-2 promulgated under
the Exchange Act) of any such person [except
transactions resulting in payments to or by the
Company in an amount less than $[60,000] per
year], [or transactions made in the ordinary course
of business and pursuant to reasonable requirements
of the Company’s business and upon fair and reason-
able terms that are approved by a majority of the
Board of Directors];
20
(vii) hire, ?re, or change the
compensation of the executive of?cers, including
approving any option grants; (viii) change the princi-
pal business of the Company, enter new lines of
business, or exit the current line of business; (ix) sell,
assign, license, pledge or encumber material technol-
ogy or intellectual property, other than licenses
granted in the ordinary course of business; or (x)
enter into any corporate strategic relationship invol-
ving the payment contribution or assignment by the
Company or to the Company of assets greater than
[$100,000.00].]
Non-Competition and
Non-Solicitation
and Agreements:
21
Each Founder and key employee will enter into a
[one] year non-competition and non-solicitation
agreement in a form reasonably acceptable to the
Investors.
Non-Disclosure and
Developments Agreement:
Each current and former Founder, employee and
consultant will enter into a non-disclosure and pro-
prietary rights assignment agreement in a form
reasonably acceptable to the Investors.
Board Matters: [Each non-employee director shall be entitled in such
person’s discretion to be a member of any Board
committee.]
20
Note that Section 402 of the Sarbanes-Oxley Act of 2003 would require repayment of any loans in full
prior to the Company ?ling a registration statement for an IPO.
21
Non-compete restrictions are a matter of state law, and you need to investigate the relevant law in the
state where the employee works (e.g., permissible temporal and geographic scope, what constitutes
adequate consideration). In California, other than in connection with the sale of a business, they are
prohibited.
APPENDIX A SAMPLE TERM SHEET 479
The Board of Directors shall meet at least [monthly]
[quarterly], unless otherwise agreed by a vote of the
majority of Directors.
The Company will bind D&O insurance with a
carrier and in an amount satisfactory to the Board
of Directors. Company shall agree that its indemni-
?cation obligations to Series A Directors are pri-
mary, and obligations of af?liated Investors are
secondary.
22
In the event the Company merges
with another entity and is not the surviving corpora-
tion, or transfers all of its assets, proper provisions
shall be made so that successors of the Company
assume the Company’s obligations with respect to
indemni?cation of Directors.
Employee Stock Options: All employee options to vest as follows: [25% after
one year, with remaining vesting monthly over next
36 months].
[Immediately prior to the Series A Preferred Stock
investment, [______] shares will be added to the
option pool creating an unallocated option pool of
[_______] shares.]
Key Person Insurance: Company to acquire life insurance on Founders
[name each Founder] in an amount satisfactory to
the Board. Proceeds payable to the Company.
RIGHT OF FIRST REFUSAL/CO-SALE AGREEMENT
Right of ?rst Refusal/
Right of Co-Sale
(Take-me-Along):
Company ?rst and Investors second (to the extent
assigned by the Board of Directors,) have a right of
?rst refusal with respect to any shares of capital stock
of the Company proposed to be sold by Founders
[and current and future employees or consultants
22
A 2007 Delaware Chancery Court decision held that an investment fund that itself indemni?ed its
partner who served on a portfolio company board was a co-indemnitor with the portfolio company and,
therefore, the investor director was not entitled to recover from the portfolio company the full amount of
any payments advanced by the portfolio company on behalf of the investor director. Following
that decision, investors will insist on provisions such as the one here, as a provision in the Investor
Rights Agreement and/or as part of a separate Indemni?cation Agreement (see NVCA Model Indem-
ni?cation Agreement).
480 APPENDIX A SAMPLE TERM SHEET
holding greater than [1]% of Company Common
Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of
options)], with a right of oversubscription for Inves-
tors of shares unsubscribed by the other Investors.
Before any such person may sell Common Stock, he
will give the Investors an opportunity to participate
in such sale on a basis proportionate to the amount of
securities held by the seller and those held by the
participating Investors.
23
Lock-Up Founders will not transfer, hedge or otherwise dis-
pose of any capital stock following an IPO for a
period speci?ed by the Company and the managing
underwriter [not to exceed [180] [210] days].
VOTING AGREEMENT
Board
of Directors:
At the initial Closing, the Board shall consist of
[______] members comprised of (i) [Name] as [the
representative designated by [____], as the lead
Investor, (ii) [Name] as the representative designated
by the remaining Investors, (iii) [Name] as the
representative designated by the Founders, (iv) the
person then serving as the Chief Executive Of?cer of
the Company, and (v) [___] person(s) who are not
employed by the Company and who are mutually
acceptable [to the Founders and Investors][to the
other directors].
Drag Along: Holders of Preferred Stock and the Founders [and all
future holders of greater than [1]% of Common
Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of
options)] shall be required to enter into an agreement
with the Investors that provides that such stock-
holders will vote their shares in favor of a Deemed
Liquidation Event or transaction in which 50% or
23
Certain exceptions are typically negotiated, e.g., estate planning or de minimis transfers. Transfers are
sometimes also prohibited to competitors or to other parties to protect con?dential information.
APPENDIX A SAMPLE TERM SHEET 481
more of the voting power of the Company is
transferred and which is approved by [the Board of
Directors] [and the holders of ____% of the out-
standing shares of Preferred Stock, on an as-con-
verted basis].]
24
OTHER MATTERS
Founders’ Stock: All Founders to own stock outright subject to
Company right to buyback at cost. Buyback right
for [__]% for ?rst [12 months] after Closing; there-
after, right lapses in equal [monthly] increments over
following [__] months.
Existing Preferred Stock
25
: The terms set forth above for the Series [_] Preferred
Stock are subject to a review of the rights, prefer-
ences and restrictions for the existing Preferred
Stock. Any changes necessary to conform the exist-
ing Preferred Stock to this term sheet will be made at
the Closing.]
No Shop/Con?dentiality: The Company agrees to work in good faith expedi-
tiously towards a closing. The Company and the
Founders agree that they will not, for a period of
[______] weeks from the date these terms are
accepted, take any action to solicit, initiate, encou-
rage or assist the submission of any proposal,
negotiation or offer from any person or entity other
than the Investors relating to the sale or issuance, of
any of the capital stock of the Company [or the
acquisition, sale, lease, license or other disposition of
the Company or any material part of the stock or
assets of the Company] and shall notify the Investors
promptly of any inquiries by any third parties in
regards to the foregoing. [In the event that the
24
This provision is typically subject to a number of negotiated conditions, including: the representations
and warranties required are limited to authority and title to shares, liability for breaches of representa-
tions by the Company is limited to a pro rata share of any escrow amount withheld, any liability is
several and capped at the stockholder’s purchase price and that the stockholder receive the same form
and amount per share of consideration as other holders of the same class or series of stock.
25
Necessary only if this is a later round of ?nancing, and not the initial Series A round.
482 APPENDIX A SAMPLE TERM SHEET
Company breaches this no-shop obligation and, prior
to [________], closes any of the above-referenced
transactions [without providing the Investors the
opportunity to invest on the same terms as the other
parties to such transaction], then the Company shall
pay to the Investors $[_______] upon the closing of
any such transaction as liquidated damages.]
26
The
Company will not disclose the terms of this Term
Sheet to any person other than of?cers, members of
the Board of Directors and the Company’s accoun-
tants and attorneys and other potential Investors
acceptable to [_________], as lead Investor, without
the written consent of the Investors.
Expiration: This Term Sheet expires on [_______ __, 200_] if
not accepted by the Company by that date.
EXECUTED THIS [__] DAY Of [_______], 20[__].
[SIGNATURE BLOCKS]
26
It is unusual to provide for such “break-up” fees in connection with a venture capital ?nancing, but
might be something to consider where there is a substantial possibility the Company may be sold prior to
consummation of the ?nancing (e.g., a later stage deal).
APPENDIX A SAMPLE TERM SHEET 483
APPENDI X B
THE VCFI SPREADSHEETS
THIS APPENDIX DESCRIBES the spreadsheets and models used in the text.
The spreadsheets are available on the publisher’s websites; the VCV model is
available at VCVtools.com. Section B.1 gives an annotated list of all spreadsheets.
Most of these spreadsheets are self-explanatory and easy to use. For the VCV
model, we present a user’s guide in Section B.2. The VCV model was developed
by Anthony Curnes, Holland Gary, Andrew Metrick, Jonathan Reinstein, David
Smalling, and Rebecca Yang.
B.1 AN ANNOTATED LISTING OF SPREADSHEETS
AND MODELS USED IN THIS BOOK
All spreadsheets were built using Microsoft Excel and carry the .xls extension.
Chapter 6—Betas, with estimates of industry betas for the U.S. market pre-
mium, and country betas for the global market premium.
Chapter 10—VC method, to make investment recommendations using the
standard and modified versions of the VC method.
Chapter 11—DCF, with examples of reality-check models for three compa-
nies, a sample investment function, and industry statistics for DCF inputs.
Chapters 13 through 18—VCV, with templates for the valuation of preferred
stock structures. See Section B.2 for a user’s guide and Section B.3 for
screenshots.
Chapter 22—Bintree, with a 60-step binomial tree and modular worksheets
for underlying asset value and option value.
B.2 THE VCV MODEL
The VCV model is built as a web application. The model consists of four calcu-
lation modules: The European Call Option Calculator, the Random-Expiration (RE)
Call Option Calculator, the FLEX Calculator, and the AUTO Calculator. The
examples using European Call Option and RE Option Calculator are discussed
484
in Chapters 13. We describe below how to enter inputs into FLEX and AUTO
Calculators.
Inputs Common to FLEX and AUTO:
Volatility is in %. For 90%, enter “90”.
Risk Free Rate is in %. For 5%, enter “5”.
Total valuation is in million dollars. For $100M, enter “100”.
Expected Holding Period is in years. For 5 years, enter “5”.
For Inputs Speci?c to FLEX:
Strike Price is in $ millions. For $100M, enter “100”.
Options are calculated as either regular RE options or binary RE options. Select
the correct type by clicking on the tab.
For Inputs Speci?c to AUTO:
Founder’s Shares is in millions. For 10M shares, enter “10”.
Shares are in millions. For example, for 10M shares, enter “10”.
Investment is in $ millions.
RP APP is in $ millions. This input cell is grayed out unless you select RP 1C
or RP 1CP as the security Type.
Security types are abbreviated as follows:
C5Common Stock
CP 5Convertible Preferred
RP 5Redeemable Preferred
RP 1C5Redeemable Preferred and Common
RP 1CP 5Redeemable Preferred and Convertible Preferred
PCP 5Participating Convertible Preferred
PCPC5Participating Convertible Preferred with Cap
Cap is in multiples of the APP. For example, for 3X cap, enter “3”. This input
cell is grayed out unless you select PCPC as the Security Type.
QPO is in multiples of the OPP. For example, for 5X OPP threshold, enter “5”.
This input cell is grayed out unless you select PCP or PCPC as the Security
Type.
Dividends is in monthly rate as percentage of the original APP. For example, for
1% monthly dividends, enter “1”.
Dividends are calculated as either simple dividends or complex dividends. Select
the correct type by clicking on the tab.
B.2 THE VCV MODEL 485
Liquidation Preference is in multiples of APP. For example, for 1X preference,
enter “1”.
GP(%) is in %. For example, for 10%, enter “10”.
Lifetime Fees is in $millions. For example, for $20M, enter “20”.
Committed Capital is in $millions. For example, for $100M, enter “100”.
486 APPENDIX B THE VCFI SPREADSHEETS
APPENDI X C
GUIDE TO CRYSTAL BALL
s
Crystal Ball
s
is a popular simulation program that works as an add-in to Excel. The
software was originally developed by Decisioneering, Inc., a company that provides
risk analysis and decision-making software and solutions.
1
In this appendix, we will
introduce Crystal Ball
s
, provide an overview of functionalities, and solve the all
examples from Chapter 20 and some from Chapter 21 using this software.
2
As we learned in Chapter 20, we can use the randomnumber function of Excel to
runsimulations. However, programmingsimulations inExcel quicklybecome unwieldy
for more complexproblems. Crystal Ball
s
makes it easier toset upsimulationmodels by
providingextra functionalities, whichallowusers tode?ne randomvariable assumptions
for one scenario, to specify run preferences for running the trial multiple times, and to
view graphical and statistical summaries of overall simulation outcomes.
To get started with Crystal Ball
s
, users need to install the program and to
launch the Crystal Ball
s
add-in either by clicking on the Crystal Ball
s
icon or by
going through Start . All Programs . Crystal Ball
s
. Once the program has ?n-
ished loading, a Crystal Ball
s
toolbar should appear at the top of a blank Excel
spreadsheet. Exhibit C-1 describes the buttons of this Crystal Ball
s
toolbar.
Once the program has been successfully launched, the next step is to set up the
simulation model in Crystal Ball
s
. Unlike with Excel, where we need to set up 10,000
rows of the simulation if we want to model 10,000 potential outcomes of project trials,
Crystal Ball
s
allows us to build the model based on only one run of the project
because the program records the individual outcome and runs the model for the
prespeci?ed number of project trials. Crystal Ball
s
then synthesizes the results of all
the runs and presents the summary of outcomes both graphically and statistically.
1. De?ne random number assumptions.
2. De?ne the forecast.
3. Set simulation run preferences.
4. Run the simulation.
5. Analyze the results.
1
Following the acquisition of Decisioneering by Oracle, the software is now sold by Oracle.
2
This appendix was coauthored with Greta Lin. Crystal Ball
s
Edition 7.1.2 was used to solve the
problems in this appendix. For the latest edition of Crystal Ball
s
, see http://www.oracle.com/appserver/
business-intelligence/crystalball/index.html.
487
We will discuss each of these steps in detail as we work through the examples
presented in Chapter 20 of the text using Crystal Ball
s
.
EXAMPLE 20.1
Drugco has just begun Phase I trials for Newdrug. Phase I takes one year and costs
$10 M. Drugco’s scientists estimate that the R&D has a 50 percent chance of
successfully completing Phase I and moving to Phase II. Phase II takes one year and
costs $30 M. If Newdrug enters Phase II, the scientists estimate a 40 percent chance
of successfully completing Phase II and moving to Phase III. Phase III takes three
years (including the time waiting for FDA approval) and costs $60 M. If Newdrug
enters Phase III, the scientists estimate a 50 percent chance of success (5FDA
approval). Drugco management estimates an NPV of $1B at the time of approval. If
the drug fails, then it would be worth nothing. The discount rate is equal to the risk-
free rate of 5 percent per year. All development costs must be paid at the beginning
of the respective phase.
Problem Use Crystal Ball
s
to build a Monte Carlo simulation for Newdrug and con?rm
the same (average) NPV solution as obtained in Chapter 20.
Crystal Ball
s
Solution To solve this problem we need to create a model that replicates
the scenario described earlier. One possible spreadsheet setup is shown in Exhibit C-2. To
then complete the simulation, we need to follow the ?ve main steps of Crystal Ball
s
simulations.
EXHIBIT C-1
CRYSTAL BALL
s
TOOLBAR
488 APPENDIX C GUIDE TO CRYSTAL BALL
s
Step 1: De?ne random number assumptions
In this problem, there are three points of uncertainty.
1. Success of Phase I (Cell C4 of Exhibit C-2)
2. Success of Phase II (Cell C7)
3. Success of Phase III (Cell C10)
These uncertainties are interrelated because Phase II can only be successful if Phase I was
successful, and FDA approval requires Phase I success, Phase II success, and Phase III success.
Therefore, to set up the model we need to de?ne three random numbers. We have
assumed that there is a 50 percent chance of successfully completing Phase I and moving to
Phase II, a 40 percent chance of successfully completing Phase II and moving to Phase III,
and a 50 percent chance of successfully completing Phase III and obtaining FDA approval, so
we should draw our random numbers based on a uniform distribution from 0 to 1. Because
every number between 0 and 1 has an equal probability of being selected, we know that the
number drawn will be less than 0.4 for 40 percent of trials and will be less than 0.5 for 50
percent of trials.
To tell Crystal Ball
s
to generate random numbers based on a uniform distribution, we
need to take the following steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar (located on the far
left—refer back to Exhibit C-1 if necessary).
EXHIBIT C-2
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.1
APPENDIX C GUIDE TO CRYSTAL BALL
s
489
At this point, the Crystal Ball
s
distribution gallery should appear (Exhibit C-3). Select
the uniform distribution and click “OK”.
Next, specify the maximum and minimum values (a and b, respectively) for the range of
the uniform distribution. It is good idea to get in the habit of directly referencing these
cells within the Crystal Ball
s
window to cells from the spreadsheet that contains values
for a and b— this is a good mechanism for tracking and recording the parameters. To do
this, hit the button at the right side of the parameter input space (highlighted by the large
red arrow in Exhibit C-4) within the distribution window and then click on the cell that
contains the correct value on the spreadsheet.
Repeat these steps in order to generate random numbers that simulate the outcomes of
Phase II and Phase III trials.
Once these random number generators have been speci?ed, we need to translate these
random numbers into outcomes. We can do this by writing IF statements, which tell us
whether or not the drug successfully passes a phase based on the random number that is
generated. For Phase I, we stipulate that:
IFðRN,0:5; 1; 0Þ: ½Cell C5 Exhibit CÀ2?
EXHIBIT C-3
CRYSTAL BALL
s
DISTRIBUTION GALLERY
490 APPENDIX C GUIDE TO CRYSTAL BALL
s
Therefore, if the random number is less than 0.5, the drug passes Phase I and a value of 1
is returned in our success indicator cell. On the other hand, if the random number is
greater than 0.5, the drug does not pass Phase I and a value of 0 is given in the success
indicator cell.
These success indicator cells allow us to easily set up the relationships between phases.
Because any number multiplied by 0 is 0, we know that when we multiply success indicator
cells together, the only time we will return a value of 1 is when the drug has successfully
passed all the phases involved in the multiplication.
Step 2: De?ne the forecast
In this example, the outcome we want to forecast is the NPV of the project. To calculate
the NPV of the project, we need to determine the costs and revenues associated with each
EXHIBIT C-4
SPECIFYING THE UNIFORM DISTRIBUTION
APPENDIX C GUIDE TO CRYSTAL BALL
s
491
phase of the project. We know that we incur the $10 M cost of Phase I trials with cer-
tainty. We only incur Phase II costs of $30 M if the project passes Phase I and moves onto
Phase II. Therefore, we multiply the $30 M cost by the Phase I outcome success indicator
value. If Phase I is successful, $30 M is multiplied by 1, if it is unsuccessful $30 M is
multiplied by 0, and no cost is incurred. The same logic holds for the $60 M cost of Phase
III except that we need to multiply by Phase I and Phase II outcome success indicator
values. We only take on Phase III if the project has passed through both phases and
therefore both indicators have a value of 1. Finally, we multiply the potential $1B in
revenues by the Phase I, II, and III outcome success indicators.
Use the 5 percent discount rate and the timing of the trials to discount the potential costs
and revenues appropriately.
Finally de?ne the forecast cell for Crystal Ball
s
by highlighting the cell that contains the
?nal NPV calculation for the scenario (Cell G19 of Exhibit C-2). Then, select “De?ne
Forecast” from the Crystal Ball
s
toolbar (refer back to Exhibit C-1).
When the De?ne Forecast window appears (Exhibit C-5), provide an appropriate name
and specify units of the forecast. Although this example only has one forecast cell,
descriptive names and units become important when there are multiple forecast cells we
wish to analyze.
Step 3: Set simulation run preferences
Select “Run Preferences” from the Crystal Ball
s
toolbar (refer back to Exhibit C-1).
On the trials tab of the Run Preferences window that appears (Exhibit C-6), specify the
number of outcomes you wish Crystal Ball
s
to run. This value should be suf?ciently
large so that Crystal Ball
s
returns approximately the same results each time the simu-
lation is run. However, the larger the number of trials, the more time Crystal Ball
s
will
require to complete the simulation.
EXHIBIT C-5
DEFINE FORECAST WINDOW
492 APPENDIX C GUIDE TO CRYSTAL BALL
s
Step 4: Run the simulation
We are ?nally ready to run the simulation. We can ?rst test to make sure that our
simulation is set up correctly by running the model one trial at a time by hitting the
“Single Step” button of the Crystal Ball
s
toolbar (refer back to Exhibit C-1). One smart
thing to check is to make sure that the NPV of the project is 2$10 M whenever Phase I is
unsuccessful. Similarly, the NPV is $690.5 when all three phases are successful.
Once we are sure the model works, we hit “Reset Simulation” from the toolbar to clear
the history of runs and then we select “Start/Continue Simulation”, which is designated by
the large right arrow in the center of the toolbar (Refer back to Exhibit C-4.)
A control panel should appear to let the user know when the progress of the simulation
including when the trials are complete.
Step 5: Analyze the results
Crystal Ball
s
provides several tools to allow us to analyze results. These analysis tools
are found by clicking on “Forecast Charts” button of the Crystal Ball
s
tool bar (refer
back to Exhibit C-1) and then opening the appropriate forecast window.
We can examine the statistical outputs of the simulation by clicking on View . Statistics
within the Forecast Chart window (Exhibit C-7). As determined in Chapter 20, the
expected NPV of the project, the mean outcome of the simulation, is $43.1 M.
EXHIBIT C-6
RUN PREFERENCES WINDOW
APPENDIX C GUIDE TO CRYSTAL BALL
s
493
’
Example 20.1 used discrete random variables, which we modeled as “1” for
success and “0” for failure. We used IF statements to indicate the success or failure
of the phase based on the random numbers drawn by Crystal Ball
s
. In the next
example, we solve a problem that uses a continuous random variable, which has an
in?nite number of possible outcomes.
EXAMPLE 20.2
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that
we are sure the drug has no side effects, so all that matters for FDA approval is its
ef?cacy. Ef?cacy is distributed E B U[0, 1] and will be revealed after three years
of Phase III trails. The NPV of the drug after three years is $1BÃ E
2
. The discount
rate is equal to the riskfree rate of 5 percent per year. The total cost of R&D is
$100 M and must be paid at the beginning of development.
Problem Use Crystal Ball
s
to run a Monte Carlo simulation to solve for the NPV of the
Newdrug project. The outcome should match our Excel solution from Chapter 20.
EXHIBIT C-7
STATISTICAL OUTPUT OF EXAMPLE 20.1 CRYSTAL BALL
s
SIMULATION
494 APPENDIX C GUIDE TO CRYSTAL BALL
s
Solution Crystal Ball
s
Solution We approach this problem by setting up a spreadsheet
such as in Exhibit C-8 and completing the ?ve step Crystal Ball
s
process.
Step 1: De?ne random number assumptions
As with Example 20.1, our ?rst step is to de?ne our random number assumptions within
Crystal Ball
s
. The one unknown in the problem is the ef?cacy of the drug once it has passed
Phase III. We are given that ef?cacy is uniformly distributed across a range of 0 to 1. Thus,
we need to take the following steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select uniform distribution and click “OK”.
Specify the maximum and minimum values (a and b) for the range of the uniform dis-
tribution in the appropriate cells of the Crystal Ball
s
De?ne Assumption window by
creating links to reference cells on the worksheet.
Step 2: De?ne the forecast
In this problem, we wish to forecast the NPV of the overall project. We were told that we
incur $100 M in R&D costs at the beginning of development with certainty. However,
our value after three years is uncertain. From the discussion in Chapter 20, we know that
F(E) = E, so we can compute our values by taking our random number draw and plugging
directly into the equation that was given:
Value after 3 years ¼ $1B Ã E
2
EXHIBIT C-8
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.2
APPENDIX C GUIDE TO CRYSTAL BALL
s
495
where E is the random value that was drawn within the uniform range. Once we have cal-
culated the value number, we apply the discount rate, and we compute the overall NPV for
the project. We de?ne the cell that contains the overall NPV computation (Cell C11 in
Exhibit C-8) as the forecast cell for Crystal Ball
s
. To do this, highlight this cell and select
“De?ne Forecast” from the Crystal Ball
s
toolbar. When the De?ne Forecast window
appears, name the forecast and de?ne units.
Step 3: Set simulation run preferences
Select “Run Preferences” from the Crystal Ball
s
toolbar. Specify the number of outcomes
you wish Crystal Ball
s
to run on the trials tab of the Run Preferences window that appears.
In the example Crystal Ball
s
output shown in Exhibit C-9, the number of outcomes was set
to 1 M.
Step 4: Run the simulation
Test the spreadsheet if desired by running a “Single Step”. Then “Reset Simulation” and hit
“Start/Continue Simulation”. Crystal Ball
s
will provide updates on the progress of the
simulation.
Step 5: Analyze the results
On examination of the statistical outcomes (Exhibit C-9), we ?nd that as we predicted in the
Excel simulation in Chapter 20, the average NPV of the project is approximately $188 M.
EXHIBIT C-9
STATISTICAL OUTPUT OF EXAMPLE 20.2 CRYSTAL BALL
s
SIMULATION
496 APPENDIX C GUIDE TO CRYSTAL BALL
s
Another tool that Crystal Ball
s
provides for analyzing results is cumulative frequency
charts (Exhibit C-10). We open this chart by clicking on View . Cumulative Frequency
within the Forecast Chart window of Crystal Ball
s
. Within this window we can also examine
the probability that outcomes will fall within a certain range of values.
’
EXAMPLE 20.3
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that
we are sure the drug has no side effects, so all that matters for FDA approval is its
ef?cacy. Ef?cacy is distributed E B LogN[0, 1] and will be revealed after three
years of Phase III trails. The NPV of the drug after three years is $1BÃ E
2
. The
discount rate is equal to the riskfree rate of 5 percent per year. The total cost of
R&D is $100 M and must be paid at the beginning of development.
EXHIBIT C-10
CUMULATIVE FREQUENCY CHART FOR EXAMPLE 20.2
APPENDIX C GUIDE TO CRYSTAL BALL
s
497
Problem Use Crystal Ball
s
to run a Monte Carlo simulation to solve for the NPV of the
Newdrug project. The outcome should match our Excel solution from Chapter 20.
Solution Crystal Ball
s
Solution The only difference between Example 20.2 and 20.3 is
that in 20.2 Phase III ef?cacy is distributed uniformly, whereas in 20.3 Phase III ef?cacy
follows a lognormal distribution. Thus we need to de?ne our random number assumptions
differently, but all the other steps are the same as in Example 20.2.
Step 1: De?ne random number assumptions
The one unknown in the problem is the ef?cacy of the drug once it has passed Phase III. We
are given that ef?cacy is distributed E B LogN[0, 1]. Thus, we need to take the following
steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select lognormal distribution and click “OK”.
As noted in Chapter 20, in the x B LogN[µ, ?] notation, µ and ? are not the mean and
standard deviation (“SD”) of the lognormal distribution, instead they represent the mean and
SD of ln(x). When specifying the parameters of the lognormal distribution within Crystal
Ball
s
, we need to ?nd the actual mean and SD of x. The conversion equations are as follows:
Mean of x when xBLogN½µ; ?? ¼ exp½µ þ?
2
=2? ðC:1Þ
SD of x when xBLogN½µ; ?? ¼ ðexp½2µ þ 2?
2
?ÀÀexp½2µ þ?
2
?Þ
ð1=2Þ
: ðC:2Þ
Solving these equations, we get a mean of 1.65 and an SD of 2.16.
EXHIBIT C-11
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.3
498 APPENDIX C GUIDE TO CRYSTAL BALL
s
Steps 2, 3, and 4
Follow the same steps as in Example 20.2.
Step 5: Analyze the results
As expected based on the Excel simulation from Chapter 20, the average NPV of the project
is approximately $6.3 billion (Exhibit C-12). If we examine the frequency chart of outcomes
(View . Frequency), we see that outcomes are skewed toward lower NPVs because of the
lognormal distribution of Phase III ef?cacy. ’
We are now ready to use Crystal Ball
s
to solve a more complex problem.
Example 20.4 has three sources of uncertainty which each exhibit different dis-
tributions and each uniquely in?uence the outcome.
EXAMPLE 20.4
Drugco has just begun Phase III trials for Newdrug, which has an associated R&D
cost of $100 M. Drugco expects Phase III trials to take two years and the FDA
approval decision to take one year, so that the FDA decision is expected in three
years. Phase II trials were promising, with a score of 40 on the standard medically
EXHIBIT C-12
STATISTICAL OUTCOME AND FREQUENCY CHART FOR
EXAMPLE 20.3
APPENDIX C GUIDE TO CRYSTAL BALL
s
499
recognized scale. (We will refer to this score as the “ef?cacy” of the drug.)
Although the best alternative drug has an ef?cacy of 50, it is not helpful for all
patients. Given the side effects of Newdrug and the risks and bene?ts of alternative
treatments, Drugco believes that the FDA will approve Newdrug if the Phase III
trials ?nd an ef?cacy of 30 or greater. Based on the results of the Phase II trials,
Drugco estimates that the ef?cacy results of Phase III will be E BN(40, 20). (It is
possible for ef?cacy to be negative because some drugs can make symptoms
worse.) During the three years of Phase III trials, it is possible that the alternative
treatments will also improve from their current ef?cacy of 50. Drugco estimates a
?nal distribution for the alternative of A BT(50, 100, 50). If Newdrug is approved
by the FDA, then its market share will depend on the relative ef?cacy of Newdrug
versus the best available treatment, that is,
Newdrug market share ¼ E
2
=ðE
2
þA
2
Þ:
Drugco estimates market size for Newdrug in the approval year (in thousands
of doses) as MBN(1,000, 100), with 6 percent annual growth going forward. Each
dose yields a gross pro?t of $1. To stay in the market, Drugco must spend $300 M
on marketing in the ?rst year, with this sum increasing each year by 6 percent. On
approval, Newdrug would have 10 years of patent life remaining. After the patent
expiration, Drugco expects generic competition and other improved alternatives to
greatly erode the value of Newdrug, so for simplicity we assume that the continuing
value would be zero after the patent expires. Following earlier examples in this
chapter, we assume a discount rate equal to the riskfree rate of 5 percent.
Problem Use Crystal Ball
s
to run a Monte Carlo simulation that estimates the FDA
approval rate and the NPV of Newdrug.
Crystal Ball
s
Solution The three unknowns in this problem are ef?cacy, alternative
ef?cacy, and starting market size. Ef?cacy and starting market size exhibit normal dis-
tributions whereas alternative ef?cacy follows a triangular distribution.
Step 1: De?ne random number assumptions
Enter a default numerical value in the cell that de?nes the random number for ef?cacy
(Cell C5 of Exhibit C-13).
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select “normal distribution” and click “OK”.
Specify the mean and SD of the normal distribution in the appropriate cells of the Crystal
Ball
s
De?ne Assumption window by creating links to reference cells on the worksheet.
In the case of ef?cacy, we are given that the mean value is 40 with a SD of 20.
Repeat the preceding steps to de?ne market starting size as a random number, which is
normally distributed with a mean of 1,000 and a SD of 100 (Cell C7 of Exhibit C-13).
Next we de?ne alternative ef?cacy according to a triangular distribution (Cell C6 of
Exhibit C-13). Again hit “De?ne Assumption”, but this time select “Triangular Dis-
tribution” within the Distribution Gallery.
500 APPENDIX C GUIDE TO CRYSTAL BALL
s
EXHIBIT C-13
SPREADSHEET SETUP FOR EXAMPLE 20.4
5
0
1
Triangular distributions are de?ned by the minimum, likeliest, and maximum values of
the distribution. In the case of alternative ef?cacy, these values are 50, 50, and 100,
respectively
Step 2: De?ne the forecast
In this problem, we wish to forecast two outcomes: the probability of FDA approval and the
NPV of the overall project.
Because we are given that the approval threshold is 30, we know that the drug is approved
whenever the random number draw for Phase III ef?cacy is greater than 30. Thus, we can
forecast the outcome with an IF statement:
IFðPhase III efficacy.30; 1; 0Þ: ½Cell C15 of Exhibit CÀ13?
We de?ne the cell that contains this IF statement as the forecast cell for Crystal Ball
s
.
As before, we do this by highlighting this cell and selecting “De?ne Forecast” from the
Crystal Ball
s
toolbar. When the De?ne Forecast window appears, name the forecast and
de?ne units.
To forecast the NPV of the project we need to construct the DCF model for Newdrug with
the random variables set to their expected values. The key line items of the DCF are
Market share, which is zero if Newdrug is not approved or determined by Newdrug
and Alternative ef?cacies when the drug is approved
Market size, which ?ows from the random draw of the starting market size
Pro?t, which is derived from market size and gross pro?t per unit
Marketing costs, which are only incurred if the drug is approved
An example of the full DCF spreadsheet can be found in Exhibit C-13.
Step 3: Set Simulation run preferences
In the example output shown (Exhibit C-14), 1 M trials were run.
Step 4: Run the simulation
Because the model is complex, it is a good idea to run the model in single steps to check that
only $100 M in costs is incurred when the drug is not approved and to observe pro?tability
when the drug is approved at different Phase III and alternative ef?cacies.
Step 5: Analyze the results
As was discussed in Chapter 20, the simulation reveals that the probability of FDA approval
is 69% and that the maximum NPV of the 1 M draws was more than $6.5B, whereas in the
worst-case scenario the company loses $2.2B. The average NPV for simulation is approxi-
mately $285 M (Exhibit C-14).
On examination of the cumulative frequency chart (Exhibit C-15), we notice an interesting
result of the simulation. We observe that most of the projects have an NPV above 2$100M, the
R&D cost for Phase III. However, some trials resulted in NPV below 2$100 M. These are
502 APPENDIX C GUIDE TO CRYSTAL BALL
s
the runs where the ef?cacy of Newdrug was low and the alternative ef?cacy was high. In these
scenarios, the drug was launched but market share of Newdrug was so low that marketing costs
could not be recouped. In these scenarios, Drugco would have been better off if the company had
abandoned the Newdrug project, even though the drug had been approved. In Example 21.4 of
EXHIBIT C-14
STATISTICAL OUTCOME FOR EXAMPLE 20.4
EXHIBIT C-15
CUMULATIVE FREQUENCY CHART FOR OUTCOMES OF
EXAMPLE 20.4
APPENDIX C GUIDE TO CRYSTAL BALL
s
503
Chapter 21, we revisit Example 20.4 to value this “abandonment” option. We are able to rerun
the Monte Carlo simulation with the additional option by making two simple modi?cations to our
spreadsheet. First, we need to calculate the salvage value according to the information given in
Example 21.4. Then we compare the NPV of abandoning the project to the NPV of launching
Newdrug, and we forecast outcomes based on the higher NPV. We do this with the following
equation:
MAXðNPV if launch drug; Salvage value 2$100MÞ: ðD:3Þ
The results of the Newdrug project with abandonment option are shown in Exhibit C-16.
As discussed in Chapter 21, the average NPV of the simulation with the option is more
than $180 M greater than the average NPV without the option. Also, when we view the
cumulative frequency chart we clearly see that we no longer have runs that result in NPV less
than 2$100 M. ’
We have ?nished solving four examples in which we used Crystal Ball
s
to
simulate project outcomes and forecast NPV in the presence of uncertainty. The
key steps for setting up simulations are de?ning assumptions for random variables
based on different types of distributions, de?ning forecasts, setting run preferences,
and running simulations. We also examined various Crystal Ball
s
tools (e.g.,
statistical outcomes, cumulative frequency charts) that allow us to analyze and
interpret the outcomes of the simulations.
Crystal Ball
s
provides many more features for more advanced users. Two
more functionalities that may be useful when modeling R&D projects are (1) de?ning
dynamic assumptions and (2) de?ning decision variables and tables. To demonstrate
these additional tools, we will work through parts of Exercise 21.4 (Remember that
EXHIBIT C-16
STATISTICAL OUTCOME AND CUMULATIVE FREQUENCY CHART
FOR EXAMPLE 21.4
504 APPENDIX C GUIDE TO CRYSTAL BALL
s
“exercises” are given without solutions at the end of chapters, whereas “examples”
are given in the body of chapters with solutions.)
DEFINING DYNAMIC ASSUMPTIONS
Dynamic assumptions can be used to model situations where uncertainty exists
regarding the parameters of a distribution. In Exercise 21.4, the mean of Phase III
ef?cacy outcomes is dependent on the ef?cacy outcome of Phase II trials, which are,
in turn, determined based on random draws. Speci?cally, we are given the following.
EXERCISE 21.4
“ . . . Phase II trials will take one year and cost $50 M. Following the Phase II trials, Drugco
will learn some information about ef?cacy, denoted as Eu, with Eu B T[0, 80, 40]. If, after
learning this information, Drugco decides to go forward with Phase III trials, then everything
is identical to Example 21.4, except that now the ef?cacy after Phase III trials is distributed
as E B N[Eu, 20]. . .”
To model the dynamic assumption aspect of this scenario, set up the spreadsheet so that
the reference cell for the mean of Phase III trials (Cell F10 of Exhibit C-17) is linked to the
outcome of Phase II (Cell C5). Then, when de?ning assumptions for Phase III trials, reference
this linked cell (Cell F10) to specify the parameters of the distribution within Crystal Ball
s
.
Finally, after all assumptions have been de?ned, reopen the “De?ne Assumption” window for
Cell F10. As compared to the ?rst time you opened this window, you will notice two new
boxes labeled “static” and “dynamic”. Click the “dynamic” box and close the window.
An examination of the summary of outputs (Exhibit C-18) shows that the SD of Phase III
outcomes is much greater than 20 because there is variability in the mean.
EXHIBIT C-17
SPREADSHEET SETUP FOR DEFINING A SIMPLE DYNAMIC
ASSUMPTION
EXERCISE 21.4 505
DEFINING DECISION VARIABLES
AND DECISION TABLES
We can instruct Crystal Ball
s
to test various values for certain inputs by de?ning
that input as a decision variable and then running a decision table. In this example,
we want to determine the minimum value of E’ such that Drugco should continue
on to Phase III trials—that is to establish a “continuation threshold”. The spread-
sheet for this problem is very similar to the earlier solution of Example 21.4, except
that we begin the simulation one year earlier, and Phase III is determined by the
dynamic assumption that we just modeled.
By de?ning the ef?cacy threshold as a decision variable with a minimum of 0
and maximum of 50, we can tell Crystal Ball
s
to run 11 simulations in which only
drugs with Phase II Eu above 0, then 5, then 10, etc. are passed onto Phase III based
on an IF statement that de?nes the “continuation threshold”. The following steps
are necessary to de?ne a decision variable.
Highlight the input cell to be varied (Cell C7 of Exhibit C-19). Then click on the “De?ne
Decision” button of the Crystal Ball
s
toolbar (second button from the left— refer back to
Exhibit C-1 if necessary).
EXHIBIT C-18
STATISTICAL OUTPUT OF PHASE III EFFICACY AS DETERMINED
BY A DYNAMIC ASSUMPTION
506 APPENDIX C GUIDE TO CRYSTAL BALL
s
EXHIBIT C-19
SPREADSHEET SETUP FOR DEFINING DECISION VARIABLE IN EXERCISE 21.4
5
0
7
Once the De?ne Decision Window (Exhibit C-20) appears, name the variable, set the
upper and lower bounds of values to be tested, and decide whether or not input values
should be continuous or discrete.
After the random number assumptions, forecasts, and decision variables are
all de?ned, we are ready to run a decision table.
First we need to set “Run Preferences” so that Crystal Ball
s
selects the same sequence of
random variables to run against the different inputs. This allows us to compare the dif-
ferent mean NPV outcomes for the various continuation thresholds without having to
worry about variability from random number selection. To do this, click on “Run Pre-
ferences” in the Crystal Ball
s
toolbar. When the Crystal Ball
s
window appears, go to the
“Sampling” tab and then enter a seed number 2 for this example, we used an initial seed
value of 999 (Exhibit C-21)
Go to Run . Tools . Decision Table.
Select the target forecast from the menu, click “Next”.
Then select the decision variable from the menu, and click “Next” (Left side of Exhibit C-22).
In this example, we only de?ned one decision variable, but up to two decision variables may
be selected for a decision table.
Specify the other options of the Decision Table such as number of test values, test runs,
and settings while running, and hit “Start” (Right side of Exhibit C-22). For this example,
we could run 51 trials to test every integer continuation threshold between 0 and 50
(inclusive), however, this would be a very time-consuming simulation run, so we will
only run 11 trials to get a sense of outcomes at every multiple of 5.
EXHIBIT C-20
DEFINE DECISION VARIABLE WINDOW
508 APPENDIX C GUIDE TO CRYSTAL BALL
s
The resulting Decision Table will appear in a new spreadsheet (Exhibit C-23). We can
graphically view the data by creating an Excel bar chart from the data.
From the decision table, we see that the average NPV of the project is max-
imized when the continuation threshold is set somewhere between 15 and 20.
Therefore, we should further investigate the ef?cacies in this range. Because decision
EXHIBIT C-21
SPECIFYING THE SEQUENCE OF RANDOM VARIABLES
EXHIBIT C-22
SPECIFYING DECISION VARIABLES AND OPTIONS FOR
THE DECISION TABLE
APPENDIX C GUIDE TO CRYSTAL BALL
s
509
tables are constrained at 10,000 trials for each test value, we can perform a more
re?ned analysis by running each integer value between 15 and 20 through a standard
Crystal Ball
s
run of 500,000 trials by inputting the continuation threshold manually
and then running the simulation six times. We want to continue using the same initial
seed value within “Run Preferences” for these individual runs as with the decision
table so that we continue to eliminate variability from random number selection. As
before, click on “Run Preferences”. When the Crystal Ball
s
window appears, go to
the “Sampling” tab to con?rm the initial seed value.
The outcomes shown in Exhibit C-24 reveal that the Phase II continuation
threshold should be set at around 17 to maximize the average NPV of the project.
This means that Phase II trials with ef?cacies much lower than 17 are not worth
continuing into Phase III because it is unlikely that the Phase III R&D costs can be
recouped. However, trials with ef?cacies above 17 should be continued.
EXHIBIT C-23
RESULTING DECISION TABLE
510 APPENDIX C GUIDE TO CRYSTAL BALL
s
In this Appendix, we solved Chapter 20 and 21 problems using Crystal Ball
s
and discussed some of the more advanced features of the software package. If
possible, you should try solving these examples on your own using Crystal Ball
s
or
another simulation software. Software add-ins like Crystal Ball
s
can be extremely
helpful for setting up and running complex simulations to forecast outcomes in the
presence of uncertainty.
REFERENCES
Gans Noah, Jack Hershey, Anjani Jain, and Ziv Katalan. The Wharton School. OPIM 621: Decision
Models and Uncertainty—Class lecture notes.
Ragsdale, Cliff T., 2004, Spreadsheet Modeling and Decision Analysis, 4th Edition, Thomson/South-
Western, Mason, OH, pp. 595À667.
EXHIBIT C-24
OUTCOMES OF 500,000 TRIAL RUNS WITH DIFFERENT
CONTINUATION THRESHOLDS
REFERENCES 511
GLOSSARY
This glossary includes all key terms given in bold in the text, plus some others that
are helpful for these definitions or for VC practice. When multiple entries have the
same meaning, the definition is given only once, with an “5” for all synonyms. The
definition is typically given for the first alphabetical entry, unless one of the later
entries is much more commonly used. Key terms are given in bold type for their
first appearance in each entry. Many of these terms also have a generic meaning in
English; in most cases, this glossary gives only the meanings relevant to venture
capital and the finance of innovation.
In most cases, we do not give formulas for these terms, relying on verbal
descriptions instead. To see formulas and to read more contextual material for any
of these terms, please consult the index to find places in the text where the terms are
discussed. Some of these key terms are used in multiple ways in the book, which
mirrors the multiple meanings for these terms in VC practice. Rather than pretend
that these confusions do not exist, we have highlighted the distinctions in this
glossary.
Since venture capital is a relatively new academic field, it was helpful in this
book to make up some new terms to aid in the translation between financial eco-
nomics and VC practice. These terms are given in bold italic type. In some cases,
these new terms have a common-sense meaning in English, but are still put in bold
italic type in order to formalize the specific meaning used in this book.
TERMS
Abnormal return: The additional return above the expected return from a factor model.
(5 Alpha)
Absolute return: The amount distributed to the limited partners of a fund, expressed as a
multiple of each dollar contributed by the partners: e.g., over the life of a fund that has
$100M in committed capital, the limited partners receive $200M back. The absolute
return of this fund 5 $200M/$100M 5 2. (5 Investment multiple, 5 Realization
ratio, 5 Value multiple)
Absolute valuation: Any method of valuation that relies on estimates and forecasts made by
the analyst. Discounted cash ?ow analysis is an example of absolute valuation. (See also
Relative valuation.)
Accrued cash dividend: A dividend that adds to the redemption value of preferred stock,
but is not actually paid until a deemed liquidation event.
512
Adjusted conversion price: The conversion price after antidilution protections have taken
effect. (See also Adjusted conversion rate.)
Adjusted conversion rate: The conversion rate after antidilution protections have taken
effect. (See also Adjusted conversion price.)
Aggregate purchase price (APP): The total amount paid for a speci?c class of stock. The
APP is equal to the original purchase price multiplied by the number of shares purchased.
Alpha: English pronunciation of the Greek letter, ?. (5 Abnormal return) (See also Beta.)
American option: An option that can be exercised any time on or before the exercise date.
Angel: A wealthy individual that invests in young, growth companies. An angel differs from
a venture capitalist because the former is using her own money. (5 Angel investors)
Angel investors: (5 Angel)
Annualized return: An asset return expressed on a per-year basis.
APP: acronym for aggregate purchase price.
Applied research: Research intended to translate scienti?c ?ndings into practical uses. (See
also Basic research, Development.)
Arms race: A strategic situation where all parties have an incentive to escalate some activity,
even though all parties would be better off if they could agree not to escalate.
As-if conversion: A feature of PCP and PCPC stock, where the stock receives its
redemption value and also is entitled to participate in the upside “as-if” it had been
converted to common stock.
At the money: An option where the strike price is exactly the same as the current value of
the underlying security.
Barriers to entry: An obstacle, either legal or economic, that prevents or slows down
competition in some market.
Base tree: A binomial tree showing the possible price paths for the underlying security in
an option-pricing problem. (See also Option tree.)
Basic research: Research designed to better understand the universe, without regard for
immediate practical application. (See also Applied research, Development.)
BC(X): Abbreviation for a random-expiration binary call option with a strike price of X.
Best response: In game theory, a move that gives Player A the highest expected payoff
against Strategy Z by Player B is called a best response by A against Z by B. (See also
Nash equilibrium.)
Beta: English pronunciation of the Greek letter, ?. Within the Capital Asset Pricing Model
(CAPM), the beta of an asset is the factor loading of that asset on the market portfolio.
In this model, beta is the regression coef?cient on an asset’s excess returns when it is
regressed on the market premium. Within multifactor models, beta is sometimes used
generically to refer to the loading on any factor. (See also Alpha.)
Binary call option: An option that pays a ?xed amount if the price of an underlying asset is
higher than a preset strike price on an exercise date.
Binomial trees: A decision tree with exactly two branches from each risk node and a ?xed
time period for each branch. Binomial trees are commonly used to value options.
Black-Scholes formula: A valuation formula for European call options.
Boom period: As used in this book, the period between 1995 and 2000, inclusive. (See also
Preboom, Postboom periods.)
GLOSSARY 513
Branch: In a tree, each possible move is represented by a branch.
Breakeven valuation: The total valuation of a company such that LP valuation 5 LP cost.
Broad-base formula: One of the methods used to compute the adjusted conversion price
under weighted average antidilution protections. The broad-base formula gives smaller
adjustments than does the narrow-base formula.
Burn rate: The speed with which a company is using up its cash.
Business plan: A summary document about the business that entrepreneurs show to investors.
Business risks: Risks faced by R&D investors that are correlated with the state of the
economy. These risks are best modeled using real options. (See also Competitive risks,
Technical risks.)
CA: Acronym for Cambridge Associates.
Call option: Gives the holder the right, but not the obligation, to purchase an underlying
security at a strike price.
Cambridge Associates (CA): A gatekeeper and a provider of a net-return index for the VC
industry.
Cap point: The level of proceeds where the liquidation return of PCPC stock is
maximized. (5 W
A
(cap))
Capital call: When the general partner of a fund requests capital from the limited
partners. (5 Drawdown, 5 Takedown)
Capital asset pricing model (CAPM): Model that expresses the expected return of an asset
as a function of the risk-free rate, the market premium, and beta.
Capitalization table: A table prepared as part of the term sheet that lists the stock ownership
of all investors, both before and after the current transaction.
CAPM: acronym for capital asset pricing model
Carried interest: The fund pro?ts paid to the general partner. (5 Carry)
Carried interest basis (5 carry basis): Fund pro?ts are de?ned as total proceeds minus the
carried interest basis. Typically, this basis is set to be either the committed capital or
the investment capital of the fund.
Carry: (5 Carried interest)
Carry basis: (5 Carried interest basis)
Carry%: The percentage level of carried interest. The most common carry% is 20 percent.
Cash distributions: The distribution of cash to limited partners. The alternative to a cash
distribution is an in-kind distribution.
Catch-up provision: When limited partners receive a hurdle return, the general partner
may have a catch-up provision that allows them to receive a share greater than carry%
for some range of pro?ts after the hurdle return is achieved.
CDF: Acronym for cumulative distribution function.
Certi?cate of incorporation: (5 Charter)
Charter: A legal document, setting out the main rules of corporate governance. Key
provisions from the charter are included as part of the term sheet. (5 Certi?cate of
incorporation) (See also Investor Rights Agreement.)
Clawback: If carried interest is received before the entire carried interest basis and hurdle
returns have been paid, and if later proceeds are insuf?cient to reach these thresholds,
514 GLOSSARY
then general partners may be subject to a clawback, where some of the earlier carried
interest must be transferred to the limited partners.
Cliff vesting: When all remaining options (or stock) becomes vested at the same time. (See
also Step vesting.)
Clinical trials: Drug tests in humans for safety and ef?cacy. (5 Human trials)
Closed: In raising a fund, general partners ask limited partners to commit to providing
capital. When the general partners have reached some desirable threshold of committed
capital, they publicly announce that the fund has closed. Despite the ?nality of this term,
some funds close multiple times, each time announcing a new level of committed capital.
(See also Raised.)
Closing: With respect to transactions in portfolio companies, the closing is the formal
signing of all necessary contracts and the transferring of the capital from the fund to the
company.
Commitment period: The time—usually the ?rst ?ve years of life—during which the fund
is permitted to make investments in new portfolio companies. (5 Investment period)
Committed capital: The total amount of capital promised to the fund by the limited
partners.
Common stock: Equity claims that are paid last upon any liquidation of the company. (See
also Preferred stock.)
Comparables analysis: The valuation of an asset by using data on similar assets. (5 Multi-
ples analysis, 5 Method of multiples, 5 Relative valuation)
Competitive advantage: Anything that allows a company to charge prices above marginal
costs.
Competitive risks: Risks faced by R&D investments that are caused by competition from
other entities. Competitive risks are modeled using game theory. (See also Business risks,
Technical risks.)
Compound interest: Interest that is paid on principal and on any interest accrued from
previous periods. (See also Simple interest.)
Compound return: A periodic return calculated by multiplying the subperiod returns.
Constant-sum games: A game where the sum of the payoffs to all players is a constant. (See
also Zero-sum games.)
Continuous random variables: A random variable de?ned on a continuous range, with an
in?nity of possible outcomes. (See also Discrete random variables.)
Continuously compounded returns: Returns with interest compounded at every instant.
(5 Log returns)
Contributed capital: At any given time in the life of the fund, contributed capital is equal to
the sum of invested capital plus all prior management fees.
Conversion condition: An inequality for convertible preferred stock that requires that
conversion value be greater than redemption value. The minimum value of proceeds that
satis?es the conversion condition is called the conversion point.
Conversion-order shortcut: When there are multiple rounds of convertible preferred share-
holders, they would choose to convert in the same order as the redemption value per share.
Conversion point (5 W
A
): The minimum level of proceeds such that the holder of
convertible preferred stock would choose to convert rather than to redeem. The
conversion point is the minimum solution to the conversion condition.
GLOSSARY 515
Convertible preferred (CP): Equity that can either be turned in for its redemption value or
converted to common stock.
Coordination games: Games with multiple pure-strategy Nash equilibria where all players
would prefer any of these equilibria to the nonequilibrium outcomes.
Corporate venture capital: VC investment by corporations. Although traditional VC seeks
to maximize ?nancial returns, corporate venture capital often mixes ?nancial and strategic
goals.
Cost of capital (r): The cost of capital is the risk-adjusted discount rate for an investment
project. In an equilibrium model like the CAPM, the cost of capital is equal to the
expected return.
Country beta: In the global CAPM, the country beta is the factor loading of a country on
the global market premium.
Country risk: The risk that an investment project in a foreign country will fail because of
some political or economic disaster in that country.
Covariance: Covariance measures the extent to which two variables tend to move together.
In ?nancial economics, assets earn excess returns because of the covariance of asset
returns with some price factor. (See also Variance.)
CP: Acronym for convertible preferred
Crossover investing: Investment in public companies by private equity ?rms.
CRR model: Acronym for Cox-Ross-Rubenstein Model, a speci?c method for constructing
binomial trees.
Cumulative distribution function (cdf): The cdf evaluated at point x gives the probability
that the random variable will be less than or equal to x. The cdf evaluated at x is the
integral of the pdf from negative in?nity to x.
Cumulative dividends: Dividends that accrue if not paid. (See also Noncumulative
dividends.)
DCF: Acronym for discounted cash ?ow analysis.
Deal ?ow: The investment opportunities available to a VC. In general, the better a VC ?rm’s
reputation, the better quality is their deal ?ow. (See also Sourcing, Proprietary deal ?ow.)
Decision nodes: The point in a tree where a player must make a decision.
Decision trees: Trees with two types of nodes, risk nodes and decision nodes. (See also
Event trees, Binomial trees, Game trees.)
Deemed liquidation event: (5 Liquidation) An event where certain preferred stock rights
come into force. These events are carefully de?ned in the term sheet. The most common
triggers for a deemed liquidation event are when a portfolio company is purchased or
shut down.
Demand registration rights: Rights that allow preferred stock holders to demand that their
shares be sold in a registered transaction. (See also Registration rights, S-3 registra-
tion rights, Piggyback registration rights.)
Derivative assets: Assets whose value is completely dependent on the value of other assets.
(See also underlying assets.)
Development: When used to describe a type of R&D project, development projects are
those designed to translate scienti?c research into marketable products. (See also Applied
research, Basic research.)
516 GLOSSARY
Discount rate: The rate that equates a $1 today with the expected value of $1 in some future
period.
Discounted cash ?ow (DCF) analysis: A method that values an asset as the sum of the
discounted value of all cash ?ows produced by that asset. DCF analysis is a form of
absolute valuation.
Discrete random variables: A random variable whose possible values are physically sep-
arated when plotted on a real line. (See also Continuous random variables.)
Distress investing: Investing in companies that have a signi?cant risk of going out of
business. (5 Special situations)
Diversi?able risk: Risk that has only a negligible impact on the whole economy (e.g.,
the risk that any speci?c house will burn down is diversi?able risk). (5 Idiosyncratic
risk)
Dividend preference: The restriction that dividends cannot be paid to common stock holders
unless they are ?rst paid to preferred stock holders.
Domestic beta: The regression coef?cient on an asset’s excess returns when it is regressed on
the market premium from its own country. (See also Domestic CAPM.)
Domestic CAPM: A CAPM that uses the market premium from any one country. In
contrast, the global CAPM uses the global market premium. (See also Domestic beta.)
Dominant strategy: In game theory, a strategy that does at least as well as every other
strategy, no matter what strategies are chosen by other players.
Down round: In term sheets, the technical de?nition that round Y is a down round
typically requires that the conversion price for preferred stock in round Y is lower than
the conversion price for preferred stock in Round X, where X ,Y. More generally, we can
also think of a down round occurring if the implied valuation for series X after round Y is
lower than the LP cost of series X.
Dragalong: A right of preferred stock holders to force other investors to sell their stake
in the company, provided that the preferred stock holder has found a buyer for all shares at
the same price. (See also Take-me-along, 5 Tagalong, 5 Right of ?rst offer, 5 Right
of ?rst refusal, 5 Transfer restrictions.)
Drawdown: (5 Capital call, 5 Takedown)
Due diligence: Careful study of all aspects of a potential investment.
Early stage: The de?nitions of early stage, midstage (5 Expansion stage), and later stage
are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that this stage “provides
?nancing to companies completing development where products are mostly in testing or
pilot production”.
Early stage fund: A fund that invests predominantly in early stage companies. (See also
Late-stage fund, Multistage fund.)
Earnings: (5 Net income, 5 Net pro?ts): The difference between revenue and expenses.
Earnings before Interest and Taxes (EBIT): Earnings plus interest expense plus taxes.
EBIT: Acronym for Earnings before Interest and Taxes.
Enterprise value: The market value of all securities issued by a company.
Entrepreneurial ecosystem: A regional community of entrepreneurs, venture capitalists,
technologists, and service providers.
GLOSSARY 517
Equilibrium concept: In game theory, a set of conditions necessary to de?ne an equilibrium.
For example, for the equilibrium concept of Nash equilibrium, the conditions require that
every player give a full menu of strategies at every decision node, with all these strategies
being a best response to the menu provided by all other players.
Equilibrium strategy: In game theory, the strategy for any given player that satis?es a
speci?c equilibrium concept.
Equity market value: (5 market cap, 5 market capitalization)
European call: Gives the holder the right, but not the obligation, to purchase an underlying
security at a strike price on a speci?c expiration date.
European put: Gives the holder the right, but not the obligation, to sell an underlying
security at a strike price on a speci?c expiration date.
Event trees: Trees without any decision nodes. (See also Binomial trees, Decision trees,
Game trees.)
Exercise price: (5 Strike price) (2X, 3X, 4X etc.) excess liquidation preference: The
multiple of aggregate purchase price that holders of preferred stock receive on
redemption. (See also Liquidation preference.)
Excess returns: The difference between the return on a speci?c asset and the risk-free rate
over the same time period.
Exit: This term has two related meanings. First, an exit refers to the sale or initial public
offering (IPO) of a portfolio company. Second, an exit refers to the sale of a VC’s stake
in a portfolio company. These two de?nitions are not always the same (e.g., a VC usually
must hold his stock for at least six months after an IPO). Then, we have the paradox of an
IPO “exit” followed by the VC “exit” six months later.
Exit diagram: On the x-axis, the market value of a company at exit; on the y-axis, the value
of a VC stake in that company at exit. An exit diagram differs from an expiration
diagram in that the former plots values at a VC exit at some unknown exit date, whereas
the latter plots values on a known expiration date.
Exit equation: The value of a VC stake in a company at exit, expressed as a portfolio of
random-expiration options. We obtain exit equations by reading the exit diagram.
Exit valuation: The expected value of a portfolio company, conditional on a successful exit.
Expansion stage: The de?nitions of early stage, midstage (5 Expansion stage), and later
stage are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that “this stage involves
applying working capital to the initial expansion of a company. The company is now
producing, is shipping, and has growing accounts receivables and inventories. It may or
may not be showing a pro?t”.
Expected holding period: The amount of time that a VC expects to hold an investment
before exit.
Expected retention percentage: Suppose a VC fund owns X percent of a company after
making its initial investment. Before an exit occurs, the fund expects that the company
will need to raise more capital by selling additional shares, which will reduce the initial
ownership to Y percent. Then, the expected retention percentage would be Y/X.
Expected return: From a mathematical perspective, the expected return on an investment
is computed by multiplying each possible return by the probability of that return.
In an equilibrium model like the CAPM, the expected return is equal to the cost of capital.
Expiration date: The last possible date that an option can be exercised.
518 GLOSSARY
Expiration diagram: On the x-axis, the market value of the underlying asset on the
expiration date; on the y-axis, the value of an option on that asset. An exit diagram
differs from an expiration diagram in that the former plots values at a VC exit at some
unknown exit date, whereas the latter plots values on a known expiration date.
Expropriation: A fancy way to say “stealing”. Minority investors (like VCs) must always be
on guard for subtle ways that managers and majority investors can expropriate resources
of the company. (5 Investor Expropriation, 5 Self-dealing, 5 Tunneling)
Extensive form: A decision tree with more than one player. In game theory, the normal
form lists all possible strategies for all players; the extensive form provides all the
information available in the normal form, and also shows the timing for all moves.
(5 Game tree)
Factor: A systematic risk in the economy. In the CAPM, the only factor is the market
premium. (5 Risk factor)
Factor model: A model where expected returns are determined by factor loadings on a set
of factors. The CAPM is an example of a factor model, where the market premium is
the factor and beta is the factor loading.
Factor loading: The amount that an asset’s return is related to a speci?c factor. In the
CAPM, the market premium is the factor and beta is the factor loading.
Fama-French Model (FFM): A multifactor model with three factors related to the market
premium, the size of the company, and the growth prospects of the company.
FDA: Acronym for the Food and Drug Administration, a unit of the U.S. government that is
responsible for the regulation of prescription drugs.
FDA approval: The ?nal step before a drug can be legally sold in the United States. (See also
Phase I, Phase II, Phase III, Preclinical.)
FFM: Acronym for the Fama-French Model.
Financial intermediary: Any economic actor that stands between a supplier of capital and
the real investment of that capital.
Financial options: Options on ?nancial assets. In contrast, real options are options on, you
guessed it, real assets.
Financing round: (5 Round) A discrete event where a young company receives capital
from investors. Financing rounds are often referred to sequentially as ?rst round
(5 Series A), second round (5 Series B), etc.
Finite games: A game with a ?nite number of moves for every player. Finite games can be
completely described using the normal form and the extensive form. (See also In?nite
games.)
Firm: In VC, a ?rm is the legal entity that serves as the general partner for a VC fund.
First Round (Series A): The ?rst round of investment by VCs. (See also Financing Round,
Second Round (Series B).)
FOF: Acronym for fund-of-funds.
Folk theorem: Loosely speaking, the folk theorem is that virtually any observed behavior in
an in?nite game can be supported as part of a subgame-perfect Nash equilibrium.
Follow-on investments: Investments made in Round Y by a VC investor in Round X, where
Y . X.
GLOSSARY 519
Full-ratchet antidilution: A strong version of antidilution protection, where the adjusted
conversion price is the lowest price paid by any later-round investor. (See also
Weighted-average antidilution.)
Fully diluted basis: Any computation that assumes the conversion of all preferred stock
and the exercise of all options.
Fully diluted share count: The total number of shares outstanding assuming the conversion
of all preferred stock and the exercise of all options.
Fund: (5 VC fund) A pool of capital used for VC investments. Typically, a VC fund is a
limited partnership with a ?xed lifetime, where the capital is provided by limited
partners and the fund is managed by a VC ?rm acting as the general partner.
Fund-of-funds (FOF): A fund that makes investments in other funds, rather than making
investment directly in portfolio companies.
Game tree: (5 Extensive form) (See alsoEvent trees, Decisiontrees, Binomial trees, Trees.)
Gatekeeper: A consultant who advises limited partners on their fund investments.
General partner (GP): The investment manager of a limited-partnership VC fund.
Geometric mean: For a series of N numbers, the geometric mean is the nth root of the
product of all N numbers.
Global beta: The beta in a global CAPM.
Global CAPM: The CAPM, with the global market premium used as the factor.
Global market premium: The expected excess return of the value-weighted global equity
market.
GP: Acronym for general partner.
GPvaluation: The valuation, using option pricing methods, of the GP’s stake in an investment.
GP%: The expected percentage of partial valuation that belongs to the VC. GP Valuation
5 GP% * partial valuation.
Graduation: In the reality-check DCF model, graduation marks the date where a company
moves from the rapid-growth period to the stable-growth period.
Graduation value: The discounted value of the company at graduation.
Gross investment: The gross amount added to a company’s capital stock in a period.
Gross investment multiple (5 Gross value multiple (GVM)): The total value of all
investments at exit, divided by investment capital.
Gross return: A return calculated before subtracting management fees, carried interest, or
any other investment costs.
Gross value multiple (GVM): (5 Gross investment multiple)
Growth capital: Capital used for VC investing beyond the early stage.
Growth factor: In a binomial tree, the growth factor is the risk-free rate measured over the
step size of the tree.
GVM: Acronym for gross value multiple (5 Gross investment multiple)
Harmonic mean: In a group of numbers, the harmonic mean is the reciprocal of the mean of
the reciprocals (i.e., for N numbers Xi, I 5 1, . . . N, the harmonic mean 5
N=
X
N
i51
1
X
i
Þ
520 GLOSSARY
Hedge funds: Hedge funds comprise a wide class of investment vehicles, with mandates that
include virtually any strategy that can be imagined. Hedge funds differ from mutual funds
in that the former has much lighter regulation. Hedge funds differ from private equity
funds in that the former tends to focus mostly on publicly traded securities, although the
distinctions between these types of funds has blurred somewhat in recent years. With
more liquid investments, hedge funds typically have much shorter lockup periods for
investors than do private equity funds.
Historical return: (5 Realized return) The past return for an asset, fund, or manager.
Hockey stick: (5 J-curve): On the x-axis, the number of years since a fund’s vintage year.
On the y-axis, the IRR of the fund up to that year. For successful funds, this curve takes
the form of a hockey stick, with negative IRRs reported for early years (when manage-
ment fees are paid but before any exits) and higher IRRs in later years (after the best exits
have occurred.)
Human trials: (5 Clinical trials)
Hurdle returns: (5 Preferred returns, 5 Priority returns) A preset level of returns that
the fund must pay to investors before the GP can begin to take any carried interest.
Idiosyncratic risk: (5 Diversi?able risk)
Implied GP valuation: The implied valuation of the GP stake in an investment, based on the
price paid in the most recent round. (See also Implied LP valuation, Implied partial
valuation.)
Implied LP valuation: The implied valuation of the LP stake in an investment, based on the
price paid in the most recent round. (See also Implied GP valuation, Implied partial
valuation.)
Implied partial valuation: The implied valuation of the fund’s stake in an investment, based
on the price paid in the most recent round. Implied partial valuation 5 Implied GP
valuation + Implied LP valuation.
Implied prevaluation (IV
pre
): The implied valuation of a company immediately prior to the
most recent round of investment.
Implied postvaluation (IV
post
): The market value of a company, as implied by the VCV
model, under the assumption that the most recent investors paid fair value, LP valuation
5 LP cost.
Implied valuation: For any piece of a company, the implied valuation of that piece is its
valuation, as implied by the VCV model, under the assumption that the most recent
investors paid fair value, LP valuation 5 LP cost.
In?nite games: Games with an in?nite number of decision nodes for at least one player. (See
also Finite games.)
Initial public offering (IPO): A company’s ?rst sale of securities in public markets.
Historically, IPOs have been the most lucrative exits for VCs.
In-kind distributions: (5 Stock distributions) The distribution of stock to limited
partners. The alternative to an in-kind distribution is a cash distribution.
Integrated markets: When all investors can make investments in any country, we say that
?nancial markets are integrated. (See also Segmented markets.)
Internal rate of return (IRR): Start with a stream of cash ?ows. Compute the NPV of these
cash ?ows as a function of the discount rate. The discount rate that makes this NPV equal
to zero is the IRR.
GLOSSARY 521
In the money: If the price of an underlying asset is above (below) the strike price for a call
(put) option, we say that the option is in the money. (See also Out of the money.)
Invested capital: At any point during the life of a fund, invested capital is equal to the total
amount of capital that has already been invested in portfolio companies. For a fund that
has reached the end of its life, invested capital is equal to investment capital.
Investment capital: The difference between committed capital and lifetime fees.
$investment: The amount of cash invested by the fund in a speci?c round of investment.
Investment multiple: (5 Absolute return, 5 Realization ratio, 5 Value multiple)
Investment period: (5 Commitment period)
Investment rate (IR): (5 Plowback ratio, 5 Reinvestment rate) The percentage of a
company’s earnings that is reinvested into the capital stock of the company.
Investor expropriation: (5 Expropriation, 5 Self-dealing, 5 Tunneling)
Investor Rights Agreement: The portion of the term sheet that lists any special rights of the
investors.
IPO: Acronym for initial public offering.
IR: Acronym for investment rate.
IRR: Acronym for internal rate of return.
IV
pre
: Abbreviation for implied pre-valuation.
IV
post
: Abbreviation for implied post-valuation.
J-curve: (5 Hockey stick).
Later-stage: The de?nitions of early stage, midstage (5 Expansion stage), and later stage
are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that “capital in this stage is
provided for companies that have reached a fairly stable growth rate; that is, companies
that are not growing as fast as the rates attained in the expansion stages”.
Late-stage fund: A fund that invests predominantly in late-stage companies. (See also
Early stage fund, Multistage fund.)
LBO: Acronym for leverage buyout.
Lead investor: In a round of investment, there may be multiple investors that form a
syndicate. In this case, one of the investors will typically take the lead in organizing the
syndicate and negotiating with the portfolio company. If the syndicate receives a single
board seat, then this seat will typically be ?lled by the lead investor.
Leader-follower games: A game where one player (the leader) would like to play the same
strategy as the other player (the follower), whereas the follower would like to play a
different strategy than the leader. Notwithstanding the temporal implications of its name,
leader-follower games are typically simultaneous games.
Least-squares regression: A statistical technique where the analyst attempts to ?nd the best
equation to explain a set of data.
Leveraged buyouts (LBOs): When a company is purchased using a signi?cant amount
of debt.
Levered beta: A beta estimated from a factor model regression using the returns of a
levered asset. If a company has any debt, then the stock of that company is a levered asset.
(See also Unlevered beta.)
License: (5 R&D licensing agreement) A contract between a technology provider
(licensor) and a user of that technology (licensee). The license agreement may be
522 GLOSSARY
exclusive (only the licensee can use the technology) or nonexclusive (the licensor is free
to license the technology to other users).
Licensee: The user of technology in a license.
Licensor: The technology provider in a license.
Lifetime fees: The total amount of management fees that will be paid by limited partners
over the lifetime of a fund.
Limited partner (LP): In a private equity fund, the limited partners provide the capital,
which is then invested by the general partner.
Linear model: A model without any nonlinear interactions between any of the input vari-
ables. For example, if X and Y are input variables that determine Z, then Z 5 2X + 2Y
would be a linear model, whereas Z 5 2X * 2Y would be a nonlinear model.
Liquidation: (5 Deemed liquidation event)
Liquidation preference: In its simplest meaning, a liquidation preference describes the order
in which different security holders are paid in the event of a liquidation. For example, if
we say that the Series B preferred stock has a liquidation preference to the Series A
preferred stock, which in turn has a liquidation preference to the common stock, we are
saying that B gets paid before A, which gets paid before the common stock holders. In a
more complex meaning of the term, some preferred stock holders may have an excess
liquidation preference, which provides a multiple of the aggregate purchase price in a
liquidation. Thus, we could say that Series B has a liquidation preference to Series A,
which has a 2X liquidation preference to the common stock. In this case, we are saying
that Series B gets paid back its aggregate purchase price before Series A, which then
receives two times its aggregate purchase price before the common stock holders get
anything.
Liquidation return: The return on preferred stock in the event of a deemed liquidation
event.
Liquidity risk: The systematic risk for an asset that corresponds with movements in a
liquidity factor. (See also the Pastor-Stambaugh model.)
Lockup: An agreement between the underwriter of an IPO and the prior investors in the
company that prevents these prior investors from selling any of their shares for some
lockup period that follows the IPO.
Log return: (5 Continuously compounded return) The natural logarithm of a periodic
return.
Long position: The ownership of a positive amount of an asset. (See also Short position,
Zero-cost long-short portfolio.)
LP: Acronym for limited partner.
LP cost: The all-inclusive cost to limited partners of a fund investment: LP cost 5
$investment * (committed capital/investment capital).
LP valuation: The valuation, using option pricing methods, of the LP’s stake in an
investment. (See also GP valuation, Partial valuation.)
LP valuation equation: The equation, expressed as a portfolio of options, for the LP
valuation.
Management carve out: At the time of an exit, the portion of proceeds reserved for current
management. Management carve outs are common in cases where managerial stock
options are out of the money at exit.
GLOSSARY 523
Management fees: Regular payments made by limited partners to general partners
intended to cover the ?xed costs of operating the fund.
Management test: “Does the current management have the capabilities to make this business
work?” Along with the market test, the management test is one of the two big-picture
questions about any potential investment.
Market cap: (5 Equity market value 5 Market capitalization) For public companies, the
market capitalization is equal to the total market value (price per share times shares
outstanding) of a company’s common stock.
Market capitalization: (5 Equity market value 5 Market cap).
Market portfolio: In theory, the market portfolio in the CAPM includes all risky assets in
every market around the world. In practice, most analysts include only the common
stocks in a single country (for a domestic CAPM) or in all major world markets (for a
global CAPM).
Market premium: The expected excess return on the market portfolio.
Market risk: (5 Nondiversi?able risk, 5 Systematic risk) Market risk is the component
of asset risk that cannot be diversi?ed away. In the CAPM, market risk is described by the
beta of the security.
Market test: “Does this venture have a large and addressable market?” Along with the
management test, the market test is one of the two big-picture questions about any
potential investment.
Market valuation: Any valuation method that relies on current market prices for a company’s
securities. The market cap is an example of a market valuation for a public company; the
implied valuation is an example of a market valuation for a private company.
Mean: The expected value of a random variable.
Methodof multiples: (5 Comparable analysis, 5 Multiples analysis, 5 Relative valuation)
Mezzanine: This has two meanings within private equity—in both cases the meanings rely
on a generic de?nition of mezzanine as “middle”. In the ?rst meaning, mezzanine refers to
the “middle of capital structure”, as in subordinated debt. This debt is typically
purchased by specialized mezzanine lenders in leveraged buyout transactions. In the
second meaning, mezzanine refers to the “middle of a company’s development”, as in
the last private ?nancing round before an IPO. This second meaning of mezzanine has
gone out of favor in recent years, with most investors substituting terms like growth
capital, expansion stage, or late stage.
Midstage: (5 Expansion stage) (See also Early-stage, Late-stage.)
Midyear correction: In many DCF models, analysts estimate a single cash ?ow at the end of
each year. Because these cash ?ows would in reality be spread across the year, many
analysts shift all cash ?ows back by six months. This can be accomplished by a single
multiplication of the uncorrected NPV by (1 + r)
1/2
, where r is the discount rate.
Milestone payments: Payments made to a licensor based on achievement of speci?c
milestones. In drug development, typical milestones are the achievement of Phase II,
Phase III, and FDA approval. (See also Royalty payments, Up-front payments.)
Minimax solution: In game theory, the solution method where one player seeks to minimize
the maximum payoff of the other player.
Mixed strategy: In game theory, a strategy that includes more than one pure strategy, with
each pure strategy played with positive probability.
524 GLOSSARY
Mixed-strategy NE: A Nash equilibrium where at least one player uses a mixed strategy.
(See also Pure-strategy NE.)
Modi?ed VC method: An adjustment to the standard VC method where the analyst explicitly
take account of management fees and carried interest.
Monitoring: The collection of VC activities to watch over and help portfolio companies.
Monte Carlo analysis: (5 Monte Carlo simulation) The estimation of expected value by
computing the average from a simulated sample of observations.
Monte Carlo simulation: (5 Monte Carlo analysis)
Multifactor models: A model where expected returns are determined by factor loadings
on a set of factors. The Fama-French Model is an example of a multifactor model, with
three factors related to the market premium, the size of the company, and the growth
prospects of the company. (See also Pastor-Stambaugh model (PSM).)
Multiples analysis: (5 Comparable analysis, 5 Method of multiples, 5 Relative
valuation)
Multiple of money: When multiple of money is used in regard to fund returns, it means the
same thing as absolute return, realization ratio, and times money. When a multiple of
money (5 X) is used in regard to the return on a speci?c VC investment, it means “for
every dollar we invested, we got back $X.”
Multistage fund: A VC fund that invests across all stages. (See also Early stage fund,
Late-stage fund.)
Narrow-base formula: One of the methods used to compute the adjusted conversion price
under weighted average antidilution protections. The narrow-base formula provides
larger adjustments than does the broad-base formula.
Nash equilibrium (NE): In game theory, where all players are choosing best responses to
the strategies of the other players. In a NE, no player can bene?t by changing his strategy.
National Venture Capital Association (NVCA): The main organization for venture
capitalists in the United States.
NE: Acronym for Nash equilibrium
Net contributed capital: At any given time in the life of the fund, net contributed capital is
equal to contributed capital, less the cost basis of all exited and written-off investments.
Net income: (5 Earnings, 5 Net pro?ts)
Net invested capital: At any given time in the life of the fund, net invested capital is equal to
invested capital, less the cost basis of all exited and written-off investments.
Net investment (NI): The net amount added to a company’s capital stock in a period: net
investment 5 gross investment À depreciation.
Net pro?ts: (5 Earnings, 5 Net income)
Net return: Return computed after taking account of management fees, carried interest,
and any other investment costs.
NI: Acronym for net investment.
Nodes: In a tree, decision nodes signify where a player must make a move and risk nodes
signify where uncertainty is resolved.
Noncumulative dividends: Dividends that do not accrue across periods. (See also
Cumulative dividends.)
Nondiversi?able risk: (5 Market risk, 5 Systematic risk)
GLOSSARY 525
Nonlinear model: A model with nonlinear interactions between any of the input variables.
For example, if X and Y are input variables that determine Z, then Z 5 2X + 2Y would be a
linear model, whereas Z 5 2X * 2Y would be a nonlinear model.
Normal form: A matrix representation of a game. In a two-player game, one player’s
strategies are represented in the columns and the other player’s strategies are represented
in the rows.
Normative analysis: Research about how things “should” be. In contrast, positive analysis
is research about how things actually are.
NVCA: Acronym for the National Venture Capital Association.
Operating assets: Company assets that are necessary for the production of goods and
services.
OPP: Acronym for original purchase price.
Option to abandon: A real option to abandon a project after it has been started.
Option to delay: A real option to begin a project at a later date.
Option to expand: A real option to expand a project at a later date.
Option to extend: A real option to extend a project at a later date.
Option to shrink: A real option to shrink a project at a later date.
Option to switch: A real option to switch the underlying production process.
Option tree: A type of binomial tree showing the values of an option at each point in time.
(See also Base tree.)
Original purchase price (OPP): The price per share paid in a transaction. (See also
Aggregate purchase price (APP).)
Out of the money: If the price of an underlying security is below (above) the strike price
for a call (put) option, then the option is out-of-the-money. (Also see In the money.)
Partial valuation: The valuation of the fund’s stake, using option-pricing methods. (See also
Total valuation.)
Participating convertible preferred (PCP): Convertible preferred stock that is entitled to
a liquidation return, which includes both its redemption value and as-if conversion into
common stock. PCP is forced to convert to common stock in the event of a quali?ed
public offering.
Participating convertible preferred with cap (PCPC): Identical to PCP, except that the
liquidation return is capped, even if there is no quali?ed public offering.
Pastor-Stambaugh Model (PSM): A multifactor model with four factors related to the
market premium, the size of the company, the growth prospects of the company, and
the liquidity risk of the company. (See also Fama-French Model (FFM).)
Payment-in-kind (PIK) dividends: (5 Stock dividends) Dividends that are paid in stock.
Payoffs: In a tree, we refer to all cash ?ows, positive and negative, as payoffs.
PCP: Acronym for participating convertible preferred.
PCPC: Acronym for participating convertible preferred with cap.
PDF: Acronym for probability density function. This acronym was around for a long time
before Adobe software.
Performance-evaluation regression: The estimation of a factor model on returns gener-
ated by an investment manager. The estimate of alpha—the abnormal return—is then
interpreted as the performance of the manager.
526 GLOSSARY
Periodic return: The return over a set time period from t 2 1 to t: R
t
5 (P
t
+ D
t
)/P
t 2 1
,
where R is the periodic return, P is the price, and D is the dividend (if any).
Perpetuity: A constant payment in every period, forever.
Personal valuation: An analyst’s opinion about the value of an asset. This personal valuation
may rely almost exclusively on the analyst’s forecasts (as in absolute valuation), or
it may use market information from similar assets (as in relative valuation). In contrast, a
market valuation relies exclusively on information embedded in the price of the actual
asset or derivative securities for the asset.
Phase I: The ?rst phase of clinical trials for a drug. Phase I trials test for the safety of the drug
using healthy volunteers. (See also FDA approval.)
Phase II: The second phase of clinical trials for a drug. Phase II trials test for ef?cacy and
safety of the drug using patients who have the relevant disorder. Phase II trials differ from
Phase III trials in that the latter are much larger, take longer, and are more expensive.
(See also FDA approval.)
Phase III: The third and ?nal phase of human trials for a drug. Phase III trials test for ef?cacy
and safety of the drug using patients who have the relevant disorder. Phase II trials differ
from Phase III trials in that the latter are much larger, take longer, and are more expensive.
(See also FDA approval.)
Piggyback registration rights: Rights that allow preferred stock holders to “piggyback”
and sell their shares in an already scheduled registered transaction. Piggyback registra-
tion rights are weaker than demand registration rights, because the former cannot create a
new transaction, but must rely on other investors obtaining a registered transaction. (See
also Registration rights, S-3 registration rights.)
PIK: Acronym for payment-in-kind
Pitch meeting: A meeting where entrepreneurs attempt to sell VCs on making an investment
in their company.
Plowback ratio: (5 Investment rate (IR), 5 Reinvestment rate)
Portfolio company: A company that has received VC investment and has not yet been
exited.
Positive analysis: Research about how things “actually are”. In contrast, normative analysis
is research about how things “should be”.
Postboom period: In this book, the period since 2001. (See also Preboom, boom.)
Postmoney valuation: The $investment divided by the proposed ownership percentage.
(See also Premoney valuation.)
Preboom: In this book, the period before 1995. (See also Boom, Postboom periods.)
Preclinical: The stage of drug testing that precedes clinical trials. (See also Phase I, Phase
II, Phase III, FDA approval.)
Preferred returns: (5 Hurdle returns, 5 Priority returns)
Preferred stock: Equity that is above common stock in the capital structure.
Premoney valuation: The post-money valuation minus the $investment.
Priority returns: (5 Hurdle returns, 5 Preferred returns)
Prisoner’s dilemma: A famous game used to illustrate an arms race.
Private equity: In its broadest meaning, private equity includes all investments that cannot
be resold in public markets. In its more narrow meaning, private equity refers to a class of
GLOSSARY 527
investments, managed by private equity ?rms, which make investments in VC, leveraged
buyouts, mezzanine, or distress.
Probability density function (pdf): For a discrete random variable, the pdf evaluated at
point x is the probability that the random variable is exactly equal to x. For a continuous
random variable, the de?nition is more subtle. In standard continuous distributions, there
are an in?nity of possible outcomes, so the probability of any one outcome is vanishingly
small. To obtain probabilities from continuous functions, we need to integrate that
function over some range. The pdf is the function that we integrate: its inputs are not
exactly probabilities, but are equivalent to probabilities if integrated over a unit interval.
Proceeds: The amount of value (in cash and stock) that is received in an exit.
Proposed%: The shorthand we use in equations to represent the proposed ownership
percentage.
Proposed ownership percentage (5 Proposed%): In any given transaction, the proposed
ownership percentage represents the percentage of fully diluted shares that the VC is
proposing to buy.
Proprietary deal ?ow: When a private equity investor receives investment opportunities
that are not offered to anyone else, we say that he has proprietary deal ?ow. (See also Deal
?ow, Sourcing.)
PSM: Acronym for Pastor-Stambaugh model.
Pure strategy: In game theory, if a player chooses the same move every time, we say that he
is playing a pure strategy. In contrast, a mixed strategy is a combination of several
moves, each with a positive probability of being played.
Pure-strategy NE: A Nash equilibrium where all players choose pure strategies.
QIBs: Acronym for quali?ed institutional buyers.
QPO: Acronym for quali?ed public offering.
QREs: Acronym for quali?ed research expenses.
Quali?ed Institutional Buyers (QIBs): Large institutional investors, who are permitted to
purchases securities under exceptions to the SEC’s registration rules. The main class of
QIBs are institutions that manage more than $100M.
Quali?ed public offering (QPO): An IPO above a minimum size and above a minimum
per-share price. These minimums are speci?ed in the term sheet.
Quali?ed Research Expenses (QREs): R&D expenses that qualify for the R&D tax credit
in the United States.
r: Symbol for the cost of capital.
R: Symbol for the return on capital
R&D: Acronym for research and development.
R&D licensing agreement: (5 License)
R&D tax credit: A program by a government to reduce the tax liability of companies in
some proportion to their R&D expenses. In the United States, the federal government
provides the largest tax credit, and many states and municipalities have smaller programs.
Raised: (5 Closed)
Random-expiration (RE) option: An option with a random and unknown expiration date.
Random-expiration binary call option (BC(X)): A binary call option with a random and
unknown expiration date.
528 GLOSSARY
Rapid-growth period: In the reality-check DCF model, the rapid-growth period is between
exit and graduation.
RE option: Abbreviation for random-expiration option.
Reading the exit diagram: The translation of an exit diagram into a portfolio of random-
expiration options.
Real options: An option on a real asset. In contrast, ?nancial options are options on ?nancial
assets.
Reality-check DCF: A model that uses aggressive data-driven assumptions for growth,
margins, and capital ef?ciency in order to get an absolute valuation for the exit value.
Realization ratio: (5 Investment multiple, 5 Absolute return, 5 Value multiple)
Realized return: This term has two meanings: The ?rst meaning, which is generic for all
?nance, is a synonym for historical returns. The second meaning, specialized for private
equity, refers to a fund’s returns from all exited investments. (See also Unrealized
returns.)
Recombine: If a binomial tree recombines, then each additional step in the tree only
adds one additional branch. In a nonrecombining tree, each additional step doubles the
number of branches. In the CRR model, the up moves and down moves are reciprocals of
each other. Thus, from any starting price, if an underlying asset follows an up move with a
down move, the base tree recombines at the starting price. If the underlying asset pays a
dividend that is proportional to the stock price, then the tree will recombine at a price
slightly below the starting price. If the underlying asset pays a ?xed cash dividend, then
the tree does not recombine.
Redeemable preferred (RP): Preferred stock that pays a redemption value on liquida-
tion, but does not offer the holder the option of conversion to common stock.
Redemption: The act of turning in preferred stock in return for the redemption value.
Redemption rights: The right of preferred stock holders to redeem their stock outside of a
deemed liquidation event. This right is usually less powerful in practice than it is on
paper because preferred stock holders, as equity investors, do not have the power to force
a company into bankruptcy if the company cannot pay the redemption.
Redemption value (RV): The amount paid to the holder of preferred stock on redemption. In
the absence of dividends or excess liquidation preferences, the redemption value is equal
to the aggregate purchase price.
Redemption Value per Share (RVPS): The redemption value of for a speci?c class of
convertible preferred stock divided by the number of shares of common stock on
conversion of that class.
Registration rights: As speci?ed in the term sheet, registration rights give the holders the
power to sell some of their shares in a registered transaction. These rights come in
several different strengths, with demand registration rights being the strongest. (See
also S-3 registration rights, Piggyback registration rights.)
Registered transaction: A transaction on a public exchange that has been approved by the
Securities and Exchange Commission. Restricted stock becomes unrestricted after it is
sold in a registered transaction.
Reinvestment rate: (5 Investment rate (IR), 5 Plowback ratio)
Relative valuation: The valuation of an asset based on the market values of similar assets.
(See also Absolute valuation.)
GLOSSARY 529
Replicating portfolio: A combination of risk-free bonds and risky assets that provides
exactly the same payoffs as a derivative asset.
Required investment: The amount of capital needed for a round of VC investment.
Research and development (R&D): Investment made in basic research, applied research,
or development projects.
Restricted stock: Stock that cannot be sold in a public market, except through a registered
transaction or through a Rule 144 exception to the registration rules. Once a stock has
been sold in a registered or Rule 144 transaction, it becomes unrestricted stock.
Restrictive covenants: Contractual terms in limited partnership agreements that restrict the
activities of the general partner.
Return on capital (R): For a company, the return on capital is an (adjusted) operating pro?t
divided by operating assets. For an investment manager, the return on capital is the
periodic return on the assets under management.
Return on investment (ROI): For a company, ROI is de?ned the same way as R, except that
the pro?ts and assets are measured only for the newly invested capital.
Right of ?rst offer: If Investor X has a right of ?rst offer for investor Y’s shares, then Y must
give X the option to bid on Y’s shares before those shares are offered to anyone else. If Y
turns down X’s offer, then she can sell her shares to other investors, but only if she obtains
a price above X’s initial offer. (See also Take-me-along 5 Tagalong, 5 Right of ?rst
refusal, 5 Dragalong, 5 Transfer restrictions.)
Right of ?rst refusal: The right of ?rst refusal is more powerful than the right of ?rst offer.
If Investor X has a right of ?rst refusal for investor Y’s shares, then Y must give X the
option to buy on Y’s shares at any price that Y has negotiated with an outside bidder. In
this case, few outside bidders are likely to make an offer because they know that X can
just come in and take away the deal. (See also Take-me-along 5 Tagalong, 5 Right of
?rst offer, 5 Dragalong, 5 Transfer restrictions.)
Risk-free rate: The rate of return on securities that have no systematic risk. In the United
States, federal government debt is often considered to be risk free (5 riskless rate).
Riskless rate: (5 risk-free rate).
Risk-neutral: We say that an investor is risk-neutral if her utility function in wealth is a
straight line.
Risk-neutral probabilities: The probabilities that would have to exist if all investors were
risk-neutral and asset prices were the same as in the real world.
Risk factor: (5 Factor)
Risk node: The point in a tree where uncertainty is resolved along multiple branches.
ROI: Acronym for return on investment
Round: (5 Financing round)
Royalty payments: When a product is sold as part of a license agreement, the licensee will
sometimes pay a percentage of sales or gross pro?t to the licensor. (See also Milestone
payments, Up-front payments.)
RP: Acronym for redeemable preferred.
Rule 144: A Securities and Exchange Commission rule that provides exceptions that allow
the public sale of (otherwise) restricted stock.
530 GLOSSARY
Rule 144A: A Securities and Exchange Commission rule that allows the private sale of
restricted stock to quali?ed institutional buyers.
RV: Acronym for redemption value.
RVPS: Acronym for redemption value per share.
S-3 registration rights: A type of demand registration right that only takes effect once the
company is already public. S-3 rights are weaker than regular demand registration rights
because the former cannot be used to force a private company to go public. (See also
Demand registration rights, Piggyback registration rights, Registration rights.)
Sand Hill Econometrics (SHE): A company that produces the Sand Hill Index
s
and its
successor (DowJones Index of Venture Capital), a gross-return index for the VC industry.
Sand Hill Road: The street in Menlo Park, California, that is home to many of the world’s
top VC ?rms.
Screening: The activities of analyzing companies, performing due diligence, and making
investment decisions.
Second Round (Series B): The second occurrence of VC investment. (See also Financing
Round, First Round (Series A).)
Seed stage: An investment in an idea that has not yet become a company. Seed-stage
investments are typically made by angels, not by VCs.
Segmented markets: When investors in countries A and B are unable to make investments in
the other country, we say that these two markets are segmented (See also Integrated
markets.)
Self-dealing: (5 Expropriation, 5 Investor expropriation, 5 Tunneling).
Sequential game: A game where players take turns making moves. (See also Simultaneous
game.)
Series: In VC transactions, preferred stock is referred to by a series letter: Series A, Series
B, etc. The letter usually refers to the round of investment, with Series A referring to ?rst
round and Series B referring to second round, etc. Most of the time that a VC refers to a
“Series A” investment, they mean this as a synonym for “?rst round”. Nevertheless, in
some cases, a VC round will include multiple series, so it is possible for the ?rst round of
investment to include shares labeled as Series A and as Series B.
SHE: Acronym for Sand Hill Econometrics.
Short position: The ownership of a negative amount of an asset. (See also Long position,
Zero-cost long-short portfolio.)
Simple interest: Interest that does not compound (i.e., 5 percent simple interest on $100
would pay $5 every year, even if the previous payments were accrued to the face value).
(See also Compound interest.)
Simultaneous game: A game where players make moves at the same time. (See also
Sequential game.)
Sourcing: The activities performed by VCs to generate deal ?ow.
Special situations: (5 Distress investing)
SPNE: Acronym for subgame-perfect Nash equilibrium.
Stable-growth period: In the reality-check DCF model, the stable-growth period follows
graduation.
GLOSSARY 531
Stale values: When live VC funds report their performance, active investments are usually
reported at the postmoney valuation of their most recent round. Because many of these
companies have had material changes since the last round, we say that these values are
stale. When evaluating the performance of the VC industry using a factor model, we
adjust for stale values by including past observations of the factors in the regression.
Standard VC method: The name for the group of techniques used by VCs to make invest-
ment decisions. The main idea of the standard VC method is to estimate a value for the
company conditional on a successful exit, and then discount that value back to the present
using a high target rate of return. (See also Modi?ed VC method.)
Star fund: A VC fund with committed capital of at least $50M and a value multiple of ?ve
or greater.
Startup stage: A pre-marketing stage of company development that may involve product
development, market research, building a management team, and developing a business
plan.
Step vesting: When some set percentage of options (or stock) becomes vested on a speci?c
date (e.g., if options are 25 percent step vested each year, then the vesting increases from
25 percent to 50 percent to 75 percent to 100 percent over a four-year period). (See also
cliff vesting.)
Stock dividends: (5 Payment-in-kind (PIK) dividends)
Strategic alliance: A long-term contract between two companies that facilitates work toward
a common goal.
Strategic investing: Investing with goals beyond the maximization of ?nancial returns.
Strategy: A complete description of a player’s choices at every decision node.
Strategy pair: The strategies of both players in a two-player game.
Strike price: (5 Exercise price) The price that is paid (received) to purchase (sell) stock
when a call (put) option is exercised.
Style adjustments: Adjustments made to the CAPM to re?ect differential risks for various
classes of stocks. The style adjustments in the Pastor-Stambaugh model are for size,
value, growth, and liquidity.
Subgame-perfect Nash equilibrium (SPNE): A set of strategies that represent Nash equi-
libria on all subgames.
Subgames: A subgame includes any collection of decision nodes that can be “snipped” from
the extensive form without cutting a closed curve around those nodes.
Successful exit: An exit where the company has executed on optimistic (but reasonable)
expectation from the time of the VC investment. Most successful exits end with an IPO or
high-value acquisition.
Superstar fund: A VC fund with committed capital of at least $50M and a value multiple
of ten or greater.
Survivor bias: A statistical bias caused when the data sample includes a disproportionate
number of entries from surviving entities. For example, there would be survivor bias if a
database of VC funds was more likely to include historical data from long-lived VC
?rms.
Syndicate: When multiple VCs invest in the same round, we call this group a syndicate.
Systematic risk: (5 Market risk, 5 Nondiversi?able risk)
532 GLOSSARY
Tagalong: (5 Take-me-along) If shareholder A has a tagalong right relative to shareholder
B, then A can force B to include A in any sale of shares made by B. Typically, this right
gives A a pro rata claim on any stock sales. (See also Right of ?rst offer, Right of ?rst
refusal, Dragalong, Transfer restrictions.)
Takedown: (5 Capital call, 5 Drawdown)
Take-me-along: (5 Tagalong) (See also Right of ?rst offer, Right of ?rst refusal,
Dragalong, Transfer restrictions.)
Target multiple of money: The average multiple of money that a VC expects in a
successful exit. The target multiple of money is a key input in the venture capital
method of valuation.
Target return: Similar to the target multiple of money, but expressed as an annual return.
Technical risks: In R&D investment, the risks that the project will fail for nonmarket
reasons, usually scienti?c or engineering failures. (See also Business risks, Competitive
risks.)
Term Sheet: The summary document describing the key terms of a proposed VC investment.
(See also Charter, Investor Rights Agreement.)
Terminal node: A ?nal point on a game tree. (See also Decision node, Risk node.)
Times money: (5 Absolute return, 5 Value multiple, 5 Multiple of money)
Top-quartile fund: A fund with an IRR among the top 25 percent of all funds in the same
vintage year.
Top-tier ?rm: A generic industry term meant to denote a high reputation ?rm. In this book,
we classify six Tier A ?rms and nine Tier B ?rms in Exhibit 5-2 of Chapter 5.
Total valuation: An analyst’s personal valuation for an entire company. (See also Partial
valuation.)
Tranche: Generically, within ?nance a tranche refers to a slice of the capital structure of a
company or security offering. Within VC, a tranche refers to a slice of a ?nancing round,
with different tranches delivered to the portfolio company at different times.
Transfer restrictions: Any restriction that prevents a shareholder from selling any part of
her shares. (See also Take-me-along 5 Tagalong, 5 Right of ?rst offer, 5 Right of
?rst refusal, 5 Dragalong.)
Trees: Generically, a perennial woody plant with a main trunk. Within economics, a
graphical representation of decisions and risks. (See also Event trees, Decision trees,
Binomial trees, Game trees.)
Tunneling: (5 Investor expropriation, 5 Self-dealing)
Two-by-two games: Games with two players each with two possible strategies.
Underlying asset: An asset on which an option has been written. (See also Derivative
assets.)
Underwriter: Financial intermediary that takes possession of an asset or a risk. In capital
markets, this possession is of a very short duration, with the assets transferred to the
ultimate investors. In these markets, the underwriter’s main job is to identify and sell to
these ultimate investors.
Unlevered beta: A beta estimated from a factor model regression for an unlevered asset.
The equity in an all-equity company is an unlevered asset.
GLOSSARY 533
Unrealized returns: In a VC fund, the unrealized returns are the estimated returns from
investments that have not yet been exited. (See also Realized returns.)
Unrestricted stock: Stock that can be sold to any investor in a public market.
Upfront payments: Payments from a licensee to a licensor made at the beginning of a
license agreement. (See also Milestone payments, Royalty payments.)
Value multiple: (5 Investment multiple, 5 Realization ratio, 5 Absolute return)
Variance: A measure of the dispersion of a random variable. (See also Covariance.)
VC: Acronym for venture capital and for venture capitalist.
VCs: Acronym for venture capitalists.
VC ?rm: (5 Firm)
VC fund: (5 Fund)
VCV model: A Web-based model, developed as a companion to Part III of this book, which
can be used to estimate partial valuation, LP valuation, GP valuation, and implied
valuation.
Venture capital (VC): Capital used by specialized ?nancial intermediaries for investment in
private companies with the intention of helping these companies to grow.
Venture capitalists (VCs): Financial intermediaries who invest in and monitor private
companies with the intention of helping these companies to grow.
Venture capital method of valuation: The name for the group of techniques used by VCs to
make investment decisions. The two versions studied in this book are the standard VC
method and the modi?ed VC method.
Venture period: In the reality-check DCF model, the period that precedes the exit.
Vesting: In VC transactions, managerial stock ownership and option claims are typically
granted over time, in a process called vesting. For speci?c rules of vesting, see the entries
for cliff vesting and step vesting.
Vintage year: Typically de?ned as the calendar year that a VC fund began investing. Fund
performance is often compared with other funds with the same vintage year.
W
A
(cap): Equation shorthand for the cap point.
Weighted-average antidilution: A version of antidilution protection, where the adjusted
conversion price is a weighted average of prices paid by all investors. (See also Broad-
base formula, Narrow-base formula, Full-ratchet antidilution.)
Zero-cost long-short portfolio: A portfolio with an equal amount of investment on both
long and short positions. These zero-cost portfolios are used to construct factors.
Zero-sum games: A game where the sum of the payoffs to all players is zero. (See also
Constant-sum games.)
534 GLOSSARY
INDEX
Abnormal returns, 68, 512
negative, 68
positive, 68
Absolute return, 55, 512
Absolute valuation, 179, 512
Accel Partners, 89
Accrued cash dividends, 153,
282À284, 512
Adjusted conversion price, 173, 513
Adjusted conversion rate, 173, 513
Aggregate purchase price (APP),
149, 252, 513
Alpha, 67, 74, 79, 513
Alternative investments, 5, 7À8
American option pricing, 242À243, 513
American Research and Development
Corporation (ARD), 10
Americanization, 87
Am-tree worksheet, 416
Analysis
normative, 431
positive, 431
Angel investors/angels, 4, 513
Angel shares, exit diagram for, 309,
Annualized returns, 47, 513
Antidilution provisions, 152, 154,
173À176
adjusted conversion price, 173
adjusted conversion rate, 173
full-ratchet, 173
weighted-average, 173
Applied research, 342, 513
Arbitrage, 237
Arms races, 424, 513
As-if conversion, 513
Assets
derivative, 232, 516
underlying, 232, 533
At the money, 242, 513
AUTO Calculator, 255, 484
Banana utility
with bird risk, 70
with weather risk, 72
Barriers to entry, 205, 513
Base trees, 403, 513
base-tree worksheet, 407, 412
Base-case option-pricing assumptions,
253À254
Basic research, 342, 513
Battery Ventures, 91
BC(X) , 513
Benchmark Capital, 89, 126, 138
Best response, 423, 513
Best VCs, 83À98. See also Portfolio ?rms
Group A, 89À91
Accel Partners, 89
Benchmark Capital, 89
Charles River Ventures, 90
Kleiner Perkins Cau?eld & Byers
(KPCB), 90
Matrix Partners, 91
Sequoia Capital, 91
Group B, 91À95
Battery Ventures, 91
Doll Capital Management (DCM), 92
Draper Fisher Jurvetson (DFJ), 92
Institutional Venture Partners, 93
InterWest Partners, 93
Menlo Ventures, 93
New Enterprise Associates (NEA),
93À94
Summit Partners, 94
Technology Crossover Ventures
(TCV), 94
Beta, 66, 74, 79, 513
Binary options, 291À292, 386, 513
Binomial trees, 355, 400À418, 513. See also
Black-Scholes equation; Dividends
base tree, 403
CRR model, 406
535
Binomial trees (continued)
dividends, 411À417
multiple strike prices and early exercise,
409À411
warrants, 409
option tree, 403À404
recombine feature, 403
Bintree.xls spreadsheet, 406À410
Black-Scholes equation/formula, 231,
238À242, 244, 250À251, 368,
400À408, 513
binomial trees and, 400À408
Board of Directors, 160
Board representation, 95À96, 157
Bond values, 235
Boom period, 12À13, 513
Branches, event tree, 358, 514
Breakeven valuation, 252, 514
Broad-base formula, 174, 514
Burn rate, 143, 514
Business plan, 137, 514
Business risks, 347, 514
Busy boards, 96
Buyout, 99
California Public Employee Retirement
System (CALPERS), 61
Californization, 88
Call option, 40, 232, 514
in a decision tree, 401
delay, 381
expand, 381
extend, 381
Cambridge Associates (CA), 50, 59, 112, 118,
124, 514
Cap point, 169, 514
Capital
calls, 21, 514
contributed, 35, 515
cost of, 224À226, 516
net contributed, 35, 525
net invested, 32, 525
Capital asset pricing model (CAPM), 65À69,
514. See also Global CAPM
domestic CAPM, 112
least-squares regression, 67
market risk, 67
nondiversi?able risk, 67
performance evaluation regression, 68
re?ecting covariance of asset’s returns, 67
Capitalization, 150
capitalization table, 148, 514
Carried interest, 11, 32À39, 247À248, 514
carried interest basis, 33, 514
clawbacks, 33, 515
contributed capital, 35, 515
net contributed capital, 35, 525
percentage level of, 33
priority returns, 33, 35, 527
refund of, 37
timing of, 34À35
write downs (partial losses), 36
Carry basis, 514
Cash distributions, 514
Cash ?ow (CF), 200
Catch-up provision, priority returns,
35À36, 514
Certi?cate of Incorporation. See Charter
Channels, 142À143
Charles River Ventures, 90
Charter, 151À155, 514
anti-dilution provisions, 152
deemed liquidation event, 151, 516
dividends, 151, 153
liquidation preference, 151, 153À154, 523
mandatory conversion, 152, 154
optional conversion, 152
protective provisions, 151
redemption rights, 152, 154À155
voting rights, 151, 154
Clawbacks, 33, 514À515
Cli vesting, 159, 515
Clinical trials, 345, 515
Closing, 135, 515
Coase, Ronald, 14
Collateralized debt obligations (CDOs), 352
Collateralized loan obligations (CLOs), 352
Commitment period, 21, 515
Committed capital, 21, 515
by limited partners, 28
Common stock, 150, 167, 515
exit diagram for, 167
Comparables analysis, 214À228, 515
choice of comparable companies, 214
choice of valuation measures, 214
choosing comparable companies, 219À224
cost of capital estimation, 224À226
EV/EBIT, 215
EV/EBITDA, 216
EV/Employees, 217
536 INDEX
EV/Revenue, 216
Price/Book, 217
Price/Earnings, 216
Compensation, venture capital, 32
Competition, 142
Competitive advantage, 205, 515
Competitive risks in drug development,
347, 515
Complex structures, 320À336. See also
Management carve-outs
dealing with partners, 327À329
Series F, exit diagram for, 332
Compound interest, 153, 515
Compound return, 46, 515
Comps. See Comparables analysis
Constant-sum games, 422, 515
Continuous probability distributions
simulation with, 362À373
Continuous random variables, 357, 362, 515
Continuously compounded returns, 238, 515
Contributed capital, 35, 515
Conversion condition, 163À164, 515
Conversion-order shortcut, 278, 515
Conversion point, 163, 515
Convertible preferred (CP) stock, 163, 516
conversion condition, 163À164
exit diagram, 164À165
participating convertible preferred (PCP),
165
participating convertible preferred with cap
(PCPC), 166
Series A CP, 172
Convertible preferred (CP) valuation, 261À263
combining RP and CP, 266À268
comparing RP and CP, 268À269
with excess liquidation preferences or
dividends, 263À266
Coordination games, 431, 516
Corporate Governance, 96
Corporate venture capital, 6, 516
Cost basis, 32
Cost of capital estimation, 224À226, 516
Cost of capital for VC, 65À82. See also Beta
and the banana birds; Capital asset
pricing model (CAPM)
estimating, 74À79
CAPM estimations for VC indices, 74
liquidity risk, 75, 77
SIZE factor, 76
stale values, 75, 78
style adjustments, 75À77
VALUE factor, 76
Country beta, 113, 516
Country risk, 108, 516
global CAPM, 116À117
Covariance, 516
Crossover investing, 94, 516
CRR model (Cox-Ross-Rubenstein),
406, 516
Crystal ball
s
, guide to, 487À511
cumulative frequency chart, 497
decision tables, de?ning, 506À511
decision variables, de?ning, 506À511
dynamic assumptions, de?ning,
505À506
spreadsheet setup for, 489
distribution gallery, 490
forecast, de?ning (Step 2), 491À492, 495,
499, 502
random number assumptions, de?ning
(Step 1), 489À490, 495, 498, 500
results analysis (Step 5), 493, 496,
499, 502
simulation, running (Step 4), 493,
496, 499, 502
simulation run preferences, setting (Step 3),
492À493, 496, 499, 502
toolbar, 488
Cultural dierences, in VC activity 108
Cumulative distribution function (cdf),
362, 516
log-normal CDF, 369
normal CDF, 368
triangular CDF, 372
uniform CDF, 363
Cumulative dividend rights, 153, 516
Currency risk, global CAPM, 115À116
Customers, 141
Dark Side of Valuation, The, 195
Deal ?ow, 137, 516
proprietary deal ?ow, 137
Decision nodes, 379, 516
Decision trees, 355, 379À381, 516
commuting options, 379
with exit, 380
pruned, 380
decision nodes, 379
Deemed liquidation event, 151, 153, 516
Demand registration, 155, 158, 516
INDEX 537
Demand side, 83
Derivative assets, 232, 516
Discounted cash ?ow (DCF) analysis, 180,
195À213, 517. See also Graduation
value; Reality-check model DCF
model
concepts, 196À198
graduation, 196
leverage of VC-backed ?rms, 199
mechanics, 198À203
phases of growth, 196
rapid-growth period, 196
stable-growth period, 196
venture period, 196
Discrete random variables, 357, 362, 517
Distress investing, 8, 517
Diversi?able risk, 66, 517
Dividend preference, 153, 517
Dividends, 151, 153, 259À261, 411À417
am-tree worksheet, 416
base tree, 412
Fuelco’s problem, 416À417
in later rounds, 282À285. See also under
Later-round investments
option tree, 413
Doll Capital Management (DCM), 92
Dollar-denominated bonds, sovereign spread
of, 109
Domestic beta, 113, 517
Domestic CAPM, 112, 517
Dominant strategy, simultaneous game,
424, 517
Doriot, George, 10
Dow Jones Report, 146À148
Down round, 154, 517
Down rounds, question of, 314À317
Series C, exit diagram for, 315À316
Dragalong, 517
Draper Fisher Jurvetson (DFJ), 92
Drawdowns, 21, 517
Drug development, 345À348, 445À455
Investigational New Drug (IND), 346
risks
business, 347À348
competitive, 347À348
technical, 347
stages, 345
FDA approval, 345
Phase I, 345À346
Phase II, 345À346
Phase III, 345
preclinical, 345
Drugco, 395À397
newdrug
DCF model for, 397
decision tree for, 396
Due diligence, 9, 135, 140, 517
Early stage, 517
EarlyBird Ventures (EBV), 22À23, 43À44
Early-stage fund, 21, 517
Earnings before Interest and Taxes (EBIT),
200, 517
Earnings before interest, taxes, depreciation,
and amortization (EBITDA), 215
eBay, 138À139
Economic pro?ts, 84
Economics of VC, 83À86
demand side, 83
supply side, 83À85
Employee stock options, 157À159
Energy innovation, 348À349
fuel cell project, 349
Energy, 455À464
Enterprise value (EV), 199, 215, 517
Entrepreneurial ecosystem, 103À104, 517
Entrepreneurial self-con?dence, 110
Entry game, 433
extensive form, 434
normal form, 435
Equilibrium concepts, 423, 518
Equilibrium strategy, 423, 518
Equity betas, 225
Equity market capitalization, 215
Equity market value, 518
European Call-Option Calculator, 240
European options, 232À234, 518
call option, 232
European put, 233
expiration diagram, 233
put option, 234
European put, 233, 518
Event trees, 355, 357À362, 518
branches, 358
?rst ten draws, 359, 361
risk node, 358
with three risk nodes, 361
terminal node, 358
Excess liquidation preferences, 154, 257À259
Excess returns, 518
538 INDEX
Exercise price, 518
Exit diagram, 164À165, 518
reading, 245À247
Exit diagrams, 518
for angel shares, 309
for carried interest, 247
for common stock, 167
for employees’ shares, 310
for management carve-out, 322, 325
for participating convertible preferred
(PCP), 169
for participating convertible preferred with
cap (PCPC), 170
reading, 245À47
for redeemable preferred (RP), 168
for remaining shares, 323, 326
for Series A, 172, 255, 258, 260, 262,
264À265, 267
for Series B, 274, 275, 313
for Series C, 315
for Series E, 322, 326
for Series F, 302
Exit valuation, 178À180, 518
absolute valuation, 179
relative valuation, 179
Expansion stage, 6, 518
Expected holding period, 518
Expected retention percentage, 178,
182À183, 518
Expected returns, 48, 518
Expected terminal value, 367
Expenses, 155
Expiration date, 232, 518
Expiration diagram, 233, 519
Expiration, 160
Expropriation, 104, 519
Extensive form, game theory,
420À421, 519
Factor loadings, 75, 519
Factor model, 519
Factors, 75, 519
SIZE factor, 76
VALUE factor, 76
Fama-French model (FFM), 75, 519
Fees
lifetime, 30, 523
management, 11, 30À32, 43À45, 524
Financial intermediary, 3, 519
Financial options, 232, 519
Financing round, 15, 519
?rst round (or Series A), 15
second round (or Series B), 15
Finite games, 438, 519
Firms, 21À27, 519
First Round (Series A), 519
FLEX Calculator, 256, 484
Folk theorem, 438, 519
Follow-on investments, 21, 519
Food and Drug Administration (FDA),
345, 519
Founders’ stock, 160À161
Freedom of Information Act (FOIA), 61
Full-ratchet anti-dilution protection,
173, 520
Fully diluted basis, 148, 520
Fully diluted share count, 148, 520
Fund returns, 53À62
de?nitions, 53À59
evidence, 59À62
gross value multiple (GVM), 57À58, 520
internal rate of return (IRR), 54, 521
J-curve, 55À56, 522
top-quartile fund, 60
Venture Economics (VE), 59
VE median and top-quartile returns by
vintage year, 60
Fund-of-funds (FOF), 29, 520
Funds, 21À27, 520
EarlyBird Ventures (EBV), 22À23
early-stage fund, 21
general partner (GP) for, 21
late-stage fund, 21
limited partners (LPs), 21, 27À30. See also
individual entry
multistage fund, 22
Game theory, 419À444
coordination game, 431
description, 419À422
extensive form, 420À421
normal form, 420
normative analysis, 431
odds-and evens-game, extensive
form, 422
odds-and-evens game, normal form, 422
payos, 420
positive analysis, 431
prisoner’s dilemma, 419À421
and real options, 438À443
INDEX 539
Game theory (continued)
sequential games, 420, 433À438. See also
individual entry
simultaneous games, 420, 423À433. See
also individual entry
standards game
extensive form, 432
normal form, 433
strategies, 420
zero-sum games, 422
Game trees, 355, 520
Gatekeeper, 50, 520
General partners (GP), 3, 21À41, 520
income sources, 26À27
carried interest, 26
management fees, 26
restrictions on activities of, 39, 41
Geometric mean, 218, 520
Global beta, 520
Global CAPM, 112À114, 520
extensions to, 114À117
country risk, 116À117
currency risk, 115À116
segmented markets, 117
style adjustments, 114
objective, 114À117
Global distribution of VC investing, 99À111
continental Europe and Asia lagging in,
reasons for, 101À102
country risk, 108
cultural dierences, 108
entrepreneurial ecosystem, 103À104
exits, 101
law and corporate governance, 104À108
dollar-denominated bonds, sovereign spread
of, 109
entrepreneurial self-con?dence, 110
high-tech private-equity investment,
100À101
Asia-Paci?c region, 100
European GDP, 100
Israel, 100
Sweden, 100
United Kingdom, 100
United States, 100
Global Entrepreneurship Monitor, 109À111
Global market premium, 520
Global multifactor model for VC, 118À119
Global Private Equity Report (GPER), 99
Google, 138À139
Graduation, 196, 520
Graduation value, 204À207, 520
barriers to entry, 205
competitive advantage, 205
return on capital as a function of NI, 205
Gross investment, 520
Gross-Return Index, 48À50
Gross returns, 47, 520
Gross value multiple (GVM), 57À58,
125, 520
for ?rst-round investments, 127À128
acquisitions, 127
IPOS, 127
for second-round investments, 130À131
acquisitions, 130
IPOS, 130
for third-round investments, 133À134
acquisitions, 133
IPOS, 133
Growth capital, 7, 520
Growth companies, discounted-cash-?ow
analysis, 195À212
Growth factor, 520
Hamilton Lane Advisors, 59
Harmonic mean, 218, 520
Health care, investment pattern in, 15
Hedge funds, 6, 521
private enquiry and, 7
High-tech private-equity investment, 100
Historical returns, 48, 521
History of venture capital, 10À14
boom period, 12À13
limited partnerships, 11
pension funds, 12
postboom period, 12À13
preboom period, 12
pro?t sharing, 11
Hockey stick pattern of returns, 55, 521
Human Resources, 97
Human trials, 521
Hurdle returns. See Priority returns
Idiosyncratic risk, 66, 521
Implied GP valuation, 311, 521
Implied LP valuation, 311, 521
Implied partial valuation, 311, 521
Implied post-valuation (IV
post
),
305À306, 521
Implied pre-valuation (IV
pre
), 311, 521
540 INDEX
Implied valuation, 305À319, 521. See also
Portfolio value, measurement; Post-
money valuation
confusion, avoiding, 317À318
In the money, 242, 522
Index
gross-return, 48À50
net-return, 50À53
Industry, investments by, 15À18
Industry, venture capital (VC), 3À20
funds ?ow in, 4
Industry returns, 46À53
annualized returns, 47
compound return, 46
de?nitions, 46À48
expected returns, 48
gross returns, 47, 48À50
historical returns, 48
net-return index, 50À53
net returns, 47
periodic return, 46À48
realized returns, 48
Industry Statistics, 198
In?nite games, 438, 521
Information technology (IT), investment
pattern in, 15
Initial public oering (IPO), 3, 101À102, 521
In-kind distributions, 158, 521
Inputs sheet, example of, 408, 416
Inputs tree, example of, 410
Inputs worksheet, 406À408, 410
Institutional Venture Partners, 93
Integrated markets, 111, 521
Interest
carried, 247À248
compound, 153, 515
simple, 153, 531
Internal corporate funds for R&D, 350
Internal growth, 6
Internal rate of return (IRR), 54, 521
International VC, 111À119
baseline model, 112À114
country beta, 113
domestic beta, 113
global CAPM, 112À114. See also
individual entry
cost of capital for, 111À119
global multifactor model, 118À119
InterWest Partners, 93
Invested capital, 32, 522
Investigational New Drug (IND), 346
$Investment, 148, 522
Investment Benchmark Reports (IBR), 59
Investment capital, 30, 522
Investment multiple, 522
Investment period, 21, 522
Investment process, 135À144. See also
Analysis of VC investments
channels, 142À143
closing, 135
competition, 142
customers, 141
due diligence, 135, 140
management test, 137À139, 141
market test, 137À139, 141
money, 143
partners, 143
pitch meeting, 140
post-term-sheet step, 140
preterm-sheet step, 140
product, 142
projections, 142
screening, 135, 137, 140
technology, 142
term sheet, 135
terrible things, 144
themes, 136
transaction terms, 143
Investment rate (IR), 200, 522
Investment recommendation, 183
Investor director approval, matters requiring,
156, 158
Investor expropriation, 104, 522
Investor Rights Agreement, 146,
155À159, 522
board matters, 157
demand registration, 155
employee stock options, 157, 158À159
expenses, 155
key person insurance, 157
lockup, 155
management and information rights, 156
matters requiring investor director
approval, 156, 158
non-competition and non-solicitation and
agreements, 157
non-disclosure and developments
agreement, 157
piggyback registration, 155
registrable securities, 155
INDEX 541
Investor Rights Agreement (continued)
registration on form S-3, 155
registration rights, 155, 158
right to maintain proportionate
ownership, 156
Investors, 148À149
Israel, 100
Japan, 100
J-curve, 55À56, 522
Key person insurance, 157
Kleiner, Perkins Cau?eld & Byers
(KPCB), 61, 90
Later stages, 16
Later-round investments, 272À289
conversion order shortcut, 277À278, 515
dividends in later rounds, 282À285
accrued cash dividends, 282À284
payment-in-kind (PIK) dividends,
284À285, 515
Series B, 272À276
Series C, 278À282
beyond Series C, 285À288
Late-stage fund, 21, 522
Latin America, 104
Law, corporate governance and, 104À108
Lead investor, 91, 522
Leader-follower game, 428, 522
extensive form, 429
normal form, 430
Least-squares regression, 67, 522
Leveraged buyout (LBO) transactions,
7À8, 522
Levered betas, 224, 522
License, R&D, 353, 522
licensee, 523
licensing agreement, 353
licensor, 523
Lifetime fees, 30, 523
Limited partners (LPs), 3, 21, 27À30, 523
committed capital by, 28
corporations, 29
endowments, 28
?nancial institutions, 28
foundations, 28
individuals and families, 29
pension funds, 27
intermediaries in, 29
Linear model, 523
Monte Carlo simulation, 366
Liquidation preference, 151, 153À154, 523
Liquidation return, 523
Liquidity risk, 75, 77, 523
Lockup, 155, 159, 523
Log-normal distribution, 370
Log returns, 238, 523
Long position, 523
Major Investor, 156
Management and information rights, 156
Management carve-outs, 320À327, 523
exit diagram for, 322, 325, 333
remaining shares, exit diagram for,
323, 326
Series E, exit diagram for, 322, 326
Management fees, 11, 30À32, 524
coverage by, 32
investment capital, 30
lifetime fees, 30
realized investments, 32
unrealized investments, 32
Management test, 137À139, 141, 524
Mandatory conversion, 152, 154
Market cap, 215, 524
Market capitalization, 215, 524
Market portfolio, 524
Market premium, 66, 524
Market risk, 67, 524
Market test, 137À139, 524
Market valuation, 317, 524
Matchmaking, 97
Matrix Partners, 91
Mean, 363, 524
geometric, 218
harmonic, 218
Menlo Ventures, 93
Method of multiples, 214, 524
Mezzanine, 7À8, 524
Midstage, 15, 524
Midyear correction, 201, 524
Milestone payments, R&D, 353, 524
Minimax solution, 427, 524
Minority investors, 106
Mixed-strategy NE, 426, 525
Models. See individual entries
Modi?ed VC method, 185À191, 525
11 steps, 187
GP valuation, 186
542 INDEX
LP cost, 186
LP valuation, 186
Monitoring, of venture capital (VC)
board representation, 95
corporate governance, 96
human resources, 97
matchmaking, 97
strategy, 97
Monte Carlo simulation, 357À377, 525.
See also Continuous probability
distributions; Event trees
linear model, 366
nonlinear model, 366
Multifactor models, 525
Multiple of money, 55, 525
Multiple sources of uncertainty,
373À376
simulation with, 373À376
Multiple strike prices and early exercise,
409À411
Multiples analysis, 214À228, 525
Multistage fund, 22, 525
Narrow-base formula, 174, 525
NASDAQ, 5, 92, 222
versus CA Index, 51
versus Sand Hill Index, 49
Nash Equilibrium (NE), 423, 525
National Science Foundation (NSF), 339
research & development de?nitions
from, 343
National Venture Capital Association
(NVCA), 146, 525
Net contributed capital, 35, 525
Net income (= earnings), 525
Net invested capital, 32, 525
Net investment (NI), 200, 525
Net pro?ts, 525
Net-return index, 50À53
Cambridge Associates (CA), 50
CA index
s
versus NASDAQ, 51
Net returns, 47, 525
Netscape, 138
New Enterprise Associates (NEA), 93À94
No shop/con?dentiality, 160
Nodes, 448, 455, 515
decision, 380
Non-competition and non-solicitation and
agreements, 157
Noncumulative dividends, 153, 525
Non-disclosure and developments
agreement, 157
Nondiversi?able risk, 67, 525
Nonlinear model, 526
Monte Carlo simulation, 366
Non-solicitation agreement, 17
Normal form, game theory, 420, 526
Normative analysis, game theory, 431, 526
Odds-and evens-game, extensive form, 422
Odds-and-evens game, normal form, 422
Operating assets, 199, 526
Option pricing, 231À251
American options, 241À243
carried interest as an option, 247À248
European options, 232À234
exit diagrams, reading, 245À247
random-expiration (RE) options,
243À245
using replicating portfolio, 234À237
bond values, 235
option values, 236
replicating portfolio, 234
stock values, 235
Option to abandon, 382, 526
Option to delay, 381, 526
Option to expand, 381, 526
Option to extend, 381, 526
Option to shrink, 382, 526
Option to switch, 382, 526
Option tree, 403À404, 526
Option values, 236
Optional conversion, 152
Option-tree worksheet, 406À408, 410
Organization for Economic Co-operation and
Development (OECD), 340
Original purchase price (OPP), 149, 526.
See also Price per share
Out of the money, 242, 526
Paci?c Corporate Group, 59
Pari passu, 153
Partial implied valuation, 311, 521
Partial valuation, 183, 526
Participating convertible preferred stock
(PCP), 165, 252À271, 290À304, 526
binary options, 291À292
exit diagram for, 291
exit diagram for, 169
Series B and beyond, 296À303
INDEX 543
Participating convertible preferred stock
(PCP) (continued)
exit diagram, 297À298
Series D, 301
Series F, 302
valuation of, 292À294
breakeven valuation, sensitivity
analysis, 293
Series A, exit diagram for, 293
Participating convertible preferred
with cap (PCPC), 166, 252À271,
290, 526
exit diagram for, 170
valuation of, 294À296
Series A, exit diagram for, 295
voluntary conversion for, 170
Partners, dealing with, 143, 327À329
Techco options, exit diagram for, 328
Partnership agreements, 30À41. See also
Restrictive covenants
carried interest, 32À39. See also
individual entry
management fees, 30À32. See also
individual entry
Pastor-Stambaugh model (PSM), 77, 79,
118, 526
Payment-in-kind (PIK) dividends, 153,
284À285, 526
Payments
milestones, 353
royalty, 353
upfront, 353
Payos, game theory, 420, 526
Performance evaluation regression, 68, 526
Periodic return, 46À48, 527
Periods
rapid-growth, 196, 529
stable-growth, 196, 531
venture, 196, 534
Perpetuity, 201, 527
Personal valuation, 317, 527
Piggyback registration, 155, 158, 527
Pitch meeting, 140, 527
post-term-sheet step, 140
pre-term-sheet step, 140
Plowback ratio, 201, 527
Portfolio companies, 3, 527
early-stage, 6
late-stage, 6
mid-stage, 6
Portfolio company status over time,
125À126, 129
assuming no private companies after 10 years
all ?rst-round investments, 126
all second-round investments, 131
all third-round investments, 132
Portfolio ?rms, 95À98
value added and the monitoring of, 95À98
corporate governance, 96
human resources, 97
matchmaking, 97
strategy, 97
Portfolio value, measurement, 310À314
implied GP valuation, 311
implied LP valuation, 311
implied partial valuation, 311
implied prevaluation, 311
Series B, exit diagram for, 313
value division after Series B investment,
311
Positive analysis, game theory, 431, 527
Postboom period, 12À13, 527
Post-money valuation, 149À150, 306À310,
318, 527
angel shares, exit diagram for, 309
employees’ shares, exit diagram, 310
Series A investment
exit diagram for, 308
value division after, 307
Preboom period, 12, 527
Preclinical stage, development, 345, 527
Preferred returns. See Priority returns
Preferred stock valuation, 252À271. See also
Convertible preferred (CP) valuation;
Redeemable preferred (RP) valuation,
254À256
Preferred stock, 150, 163À177, 527
types of, 163À173. See also Antidilution
provisions; Common stock;
Convertible preferred (CP) stock;
Redeemable preferred (RP) stock
Pre-money valuation, 149À150, 527
Price per share, 149
PricewaterhouseCoopers, 99
Pricing options. See Option pricing
Priority returns, 33, 35, 527
catch-up provision, 35À36
Prisoner’s dilemma, 420, 527
Private Equity Analyst, 87
Private Equity International (PEI), 61À62
544 INDEX
Private Equity Performance Monitor, 87
Private equity, 5, 527
and hedge funds, 7
Probabilities, risk-neutral, 461
Probability density function (pdf), 362, 528
log-normal PDF, 369
normal PDF, 367
triangular PDF, 372
uniform PDF, 362
Proceeds, 528
Product, role in investment, 142
Pro?ts, economic, 84
Projections, role in investment, 142
Proposed ownership percentage, 148, 528
Proprietary deal ?ow, 94, 137, 528
Protective provisions, 151
Pure strategy NE, 426, 528
Put option, 234
Quali?ed Institutional Buyers (QIBs),
158, 528
Quali?ed public oering (QPO), 154, 528
Quali?ed Research Expenses (QREs),
350, 528
R&D ?nance, 339À356, 528, 530
applied research, 343À344
basic research, 343À344
development, 343À344
expenditure by source and performer, 343
global stance, 339À345
spending, 340
by industry and industry group, 344
options in, 349À354
banks, 351
government, 349
internal corporate funds, 350
large companies, 353
license, 353
milestone payments, 353
public debt markets, 351
public equity markets, 352
royalty payments, 353
strategic alliance, 353
upfront payment, 353
venture capital, 353
Quali?ed Research Expenses (QREs), 350
R&D share of GDP, 2004À08, 341
R&D tax credit, 350
sources, 354À355
touchstones, 345À349. See also Drug
development; Energy innovation
U.S. R&D funding, 342
R&D licensing agreement, 528
R&D tax credit, 528
R&D valuation, 445À465
drug development, 445À455
energy, 455À464
Fuelco’s decision tree, 457À461
node 10, expanded, 462
node 11, expanded, 462
node 12, expanded, 463
forest and the trees, 464
Random-expiration (RE) options,
243À245, 484, 528
Random-expiration binary call option
(BC(X)), 528
Rapid-growth period, 196, 529
Reading the exit diagram, 529
Real options, 378À399, 529. See also
Decision trees; Risk-neutral
probabilities
Drugco, 395À397
game theory and, 438À443
in R&D, 381À382
call options, 381À382
combinations of options, 382
option to abandon, 382
option to delay, 381
option to expand, 381
option to extend, 381
option to shrink, 382
option to switch, 382
put options, 382
spotting options, 378
valuation of, 382À387
Fuelco Project, 383À387
valuing options, 378
Reality-check model DCF model,
207À212, 529
baseline assumptions for, 207À212
Realization ratio, 55, 529
Realized investments, 32
Realized returns, 48, 529
Realized value multiple, 55
Redeemable preferred (RP) stock/valuation,
165, 254À257, 529
AUTO Calculator, 256
combining RP and CP, 266À268
comparing RP and CP, 268À269
INDEX 545
Redeemable preferred (RP) stock/valuation
(continued)
exit diagram for, 168
FLEX Calculator, 256
Series A RP, 171
Redemption rights, 152, 154À155, 529
Redemption value (RV), 252À271, 529
Redemption value per share (RVPS),
277À289, 529
Regional distribution of VC investment,
18À19
Registered transaction, 529
Registrable securities, 155
Registration on form S-3, 155
Registration rights, 155, 158, 529
demand, 158
in-kind distributions, 158
Piggyback, 158
Rule 144, 158
Rule 144A, 158
S-3, 158
Regression
equation for, 78
least-squares, 67
performance evaluation, 68
Reinvestment rate, 201, 529
Relative valuation, 529
Replicating portfolio, 234À237, 530.
See also under Option pricing
Reputation, of venture capital, 97
Required investment, 179, 530
Research and development (R&D). See R&D
?nance; R&D valuation
Restrictions, 160, 530
transfer restrictions, 160
Restrictive covenants, 39À41, 530
restrictions on fund management, 39À40
restrictions on GP activities, 39, 41
restrictions on investment type,
39, 41
Retention percentage, 182
Return on capital (R), 84, 530
Return on investment (ROI), 84, 530
Returns, VC, 46À64. See also Fund returns;
Industry returns
Right of ?rst oer, 160, 530
Right of ?rst refusal/co-sale agreement and
voting agreement, 159, 530
Board of Directors, 160
Lockup, 159
Right of First Refusal/Co-Sale Agreement,
159À160
Rights, 160
to maintain proportionate ownership, 156
right of ?rst oer, 160
right of ?rst refusal, 160
Risk factor, 530
Risk-free rate, 530
Riskless rate, 530
Risk node, event tree, 358, 530
Risk-neutral probabilities, 388À394, 530
Fuelco Project, 389À391
decision tree, 391
decision tree, pruned, 392
event tree, after node 3, 394
Rounds, 15, 147, 530
Royalty payments, R&D, 353, 530
Rule 144, 158, 530
Rule 144A, 158, 531
S-3 registration rights, 158, 531
Sample term sheet. See Term sheet, sample
Sand Hill Econometrics (SHE), 123, 531
Sand Hill Index
s
, 48À52, 531
San Hill index
s
versus NASDAQ, 49
survivor bias, 52
Screening, 135, 137, 140, 531
Securities and Exchange Commission
(SEC), 5
Seed stage, 15, 531
Segmented markets, 111, 531
global CAPM, 117
Self-dealing, 104, 531
Sensitivity analysis, 190, 191
for breakeven valuation, 256, 258,
261, 263
Sequential games, 420, 433À438, 531
entry game, 433
with commitment extensive form, 437
extensive form, 434, 436
normal form, 435
?nite games, 438
in?nite games, 438
subgames, 435
Sequoia Capital, 91
Series, 16, 531
Series B investment, 272À276
conversion condition, 277
exit diagram for, 274À275
valuation of LP, 274
546 INDEX
Series C investment, 278À282
exit diagram for, 281, 287
Short position, 531
Silicon Valley, location of ?rms in, 87, 103
Simple interest, 153, 531
Simulation, with multiple sources of
uncertainty, 373À376
Simultaneous games, 420, 423À433, 531
advertising game
extensive form, 425
mixed-strategy NE, 426
normal form, 426
pure strategy NE, 426
two-by-two games, 426
arms races, 424
best responses, 423
dominant strategy, 424
equilibrium concepts, 423
equilibrium strategy, 423
leader-follower game, 428
minimax solution, 427
Nash Equilibrium (NE), 423
odds-and-evens game, normal form, with
best responses, 427
SIZE factor, 76
Small Business Act of 1958, 11
Small Business Investment Companies
(SBICs), 11
Sourcing, 137, 531
Special situations, 531
Spotting options, 378
Stable-growth period, 196, 531
Stale values, 75, 78, 532
Standard VC method, 184À185, 532
Standards game, 432, 433
Star fund, 86, 532
Step vesting, 158, 532
Stock
common, 150, 515
preferred, 150, 527
values, 235
Stock dividends, 153, 532
Stock Purchase Agreement, 159
conditions to closing, 159
counsel and expenses, 159
representations and warranties, 159
Stock values, 235
Strategies, 532
game theory, 420, 532
portfolio ?rms, 97
strategic alliance, R&D, 353, 532
strategic investing, 532
Strike price, 232, 532
Style adjustments, 75À77, 532
global CAPM, 114
Subgame perfect Nash equilibrium (SPNE),
435, 532
Subgames, 435, 532
Successful exit, 178, 532
Summit Partners, 94
Superstar fund, 86, 532
Supply side, 83À85
Survivor bias, 52, 532
Syndication, 91, 532
Systematic risk, 67, 532
Tag-along rights, 160, 533
Takedown, 21, 533
Take-me-along rights, 160, 533
Talltree Ventures IV, 44À45
Target multiple of money, 178, 181, 533
Target returns, 178, 180À182, 533
Tax credit, 350
Technical risks in drug development, 347, 533
Technology Crossover Ventures (TCV), 94
Technology, 142
Term sheet, sample, 466À483
existing preferred stock, 482
Founders’ stock, 482
investor rights agreement, 475
Board matters, 479
demand registration, 476
employee stock options, 480
expenses, 476
key person insurance, 480
lock-up, 477
management and information rights, 477
matters requiring investor director
approval, 478
non-competition and non-solicitation and
agreements, 479
non-disclosure and developments
agreement, 479
piggyback registration, 476
registrable securities, 475
registration on Form S-3, 476
registration rights, 475
right to maintain proportionate
ownership, 477
no shop/con?dentiality, 482
INDEX 547
Term sheet, sample (continued)
pre and post-?nancing capitalization, 468
anti-dilution provisions, 472
capitalization, 468
dividends, 468
liquidation preference, 469
mandatory conversion, 473
optional conversion, 471
pay-to-play, 473
pre-money valuation, 468
protective provisions, 470
redemption rights, 474
voting rights, 470
right of ?rst refusal/co-sale agreement, 480
lock-up, 481
right of ?rst refusal/right of co-sale (take-
me-along), 480
stock purchase agreement, 474À475
conditions to closing, 475
counsel and expenses, 475
representations and warranties, 474
voting agreement, 481
Board of Directors, 481
drag along, 481
Term sheets, 9, 135À136, 146À162, 533. See
also Charter; Investor rights agreement
aggregate purchase price (APP), 149
basics, 147À150
capitalization, 150
common stock, 150
expiration, 160
founders’ stock, 160À161
investors, 148À149
no shop/con?dentiality, 160
original purchase price (OPP), 149
post-money valuation, 149À150
preferred stock, 150
pre-money valuation, 149À150
price per share, 149
right of ?rst refusal/co-sale agreement and
voting agreement, 159
rights and restrictions, 160
stock purchase agreement, 159
Terminal node, event tree, 358, 533
Termination, 156
Terrible things, 144
Times money, 533
Top-quartile fund, 60, 533
Top-tier ?rms, 89À95, 533
Total valuation, 179, 317, 533
Tranches, 148, 533
Transaction terms, 143
Transfer restrictions, 160, 533
Trees, 355, 533. See also Event trees
binomial, 355
decision, 355
game, 355
Triangular distribution, 373
Tunneling expropriation, 104, 533
Two-by-two games, 426, 533
Unbiased approximation, 240À241
Underlying asset, 232, 533
Underwriter, 533
Uniform CDF, 363
Uniform PDF, 362
United Kingdom, 99
United States, VC investment patterns in,
14À19
growth stages, 16
early stage ?nancing, 16À17
expansion (mid) stage ?nancing, 16À17
later stage ?nancing, 16À17
seed/startup stage ?nancing, 16À17
investments by industry, 15À18
boom period, 17À18
health care, 15
information technology (IT), 15
postboom period, 17À18
preboom period, 17À18
investments by region, 18À19
Unlevered betas, 224, 533
Unrealized investments, 32
Unrealized returns, 534
Unrealized value multiple, 55
Unrestricted stock, 534
Valuation, 195
VALUE factors, 76
Value multiple, 55, 534
Valuing options, 378
Variables
continuous random, 357, 362
discrete random, 357, 362
Variance, 66, 534
VC method, 178À194, 534
exit valuation, 178À180
expected retention, 178, 182À183
investment recommendation, 183
modi?ed VC method, 185À191
548 INDEX
spreadsheet, 189
standard VC method, 184À185
target returns, 180À182
VCV model, 484À486, 534
AUTO calculator, 484
Euro-option calculator, 484
FLEX calculator, 484
Random-Expiration (RE) option
calculator, 484
Venture capital (VC), 3, 534
characteristics, 3À5
as ?nancial intermediary, 3
helping in companies portfolio, 5
investing in internal growth, 6
investing in private companies, 5
maximizing ?nancial return, 5
Venture capitalists (VCs), 534
exiting, 9À10
investing, 9
monitoring, 9
work of, 9À10
top-tier, 89-95
Venture Economics (VE), 59
Venture period, 196, 534
VentureExpert, 123
VentureSource database, 253
Vesting, 158, 534
cli vesting, 159
step vesting, 158
Vintage year, 22, 534
Volatility ratios, selected countries, 115
Voluntary conversion for the PCPC, 170
Voting agreement, 159À160
Voting rights, 151, 154
Warrants, 409
Weighted-average antidilution protection,
173, 534
Woodward, Susan, 48
Worldwide investments, 99À119. See also
Global distribution of VC investing;
International VC
Write downs, 36
Yahoo!, 138
Zero-cost long-short portfolios, 76, 534
Zero-pro?t curve, 452, 455
Zero-sum games, 422, 534
INDEX 549
doc_394777031.pdf
Venture Capital and Finance of Innovation
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VENTURE CAPITAL &
THE FINANCE OF
INNOVATION
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VENTURE CAPITAL &
THE FINANCE OF
INNOVATION
SECOND EDITION
ANDREW METRICK
Yale School of Management
AYAKO YASUDA
Graduate School of Management, UC Davis
John Wiley & Sons, Inc.
EDITOR Lacey Vitetta
PROJECT EDITOR Jennifer Manias
SENIOR EDITORIAL ASSISTANT Emily McGee
MARKETING MANAGER Diane Mars
DESIGNER RDC Publishing Group Sdn Bhd
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Library of Congress Cataloging-in-Publication Data:
Metrick, Andrew.
Venture capital and the ?nance of innovation / Andrew Metrick, Ayako Yasuda. — 2nd ed.
p. cm.
Includes index.
ISBN 978-0-470-45470-1 (hardback)
1. Venture capital. 2. Technological innovationsÀFinance. I. Yasuda, Ayako. II. Title.
HG4751.M48 2010
332u.04154—dc22
2010020655
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
BRIEF CONTENTS
PREFACE TO 2
ND
EDITION—A READER’S GUIDE vii
ACKNOWLEDGMENTS xiii
CONTENTS xvii
PART I
VC BASICS
CHAPTER 1 THE VC INDUSTRY 3
CHAPTER 2 VC PLAYERS 21
CHAPTER 3 VC RETURNS 46
CHAPTER 4 THE COST OF CAPITAL FOR VC 65
CHAPTER 5 THE BEST VCs 83
CHAPTER 6 VC AROUND THE WORLD 99
PART II
TOTAL VALUATION
CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS 123
CHAPTER 8 TERM SHEETS 146
CHAPTER 9 PREFERRED STOCK 163
CHAPTER 10 THE VC METHOD 178
CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES 195
CHAPTER 12 COMPARABLES ANALYSIS 214
v
PART III
PARTIAL VALUATION
CHAPTER 13 OPTION PRICING 231
CHAPTER 14 THE VALUATION OF PREFERRED STOCK 252
CHAPTER 15 LATER-ROUND INVESTMENTS 272
CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK 290
CHAPTER 17 IMPLIED VALUATION 305
CHAPTER 18 COMPLEX STRUCTURES 320
PART IV
THE FINANCE OF INNOVATION
CHAPTER 19 R&D FINANCE 339
CHAPTER 20 MONTE CARLO SIMULATION 357
CHAPTER 21 REAL OPTIONS 378
CHAPTER 22 BINOMIAL TREES 400
CHAPTER 23 GAME THEORY 419
CHAPTER 24 R&D VALUATION 445
APPENDIX A SAMPLE TERM SHEET 466
APPENDIX B THE VCFI SPREADSHEETS 484
APPENDIX C GUIDE TO CRYSTAL BALL
s
487
GLOSSARY 512
INDEX 535
vi BRIEF CONTENTS
PREFACE TO 2
ND
EDITION—
A READER’S GUIDE
Many interesting developments have occurred in the world of venture capital since
the publication of the first edition of this book in 2006, which prompted us to revise
the book for the second edition. While the organization of the book remains
unchanged, many of the chapters are substantially rewritten. For example, in Chapter
5, we re-ranked top VC firms, incorporating the latest performance statistics, fun-
draising and investment activities, notable exits, and (as always) our subjective
opinions. In Chapter 6, we examine further evidence of the deepening globalization
of the industry. In Chapters 3, 4, and 7, we analyze the impact of the 1999À2000
Internet bubble years on the VC risk and returns, as investments made in those years
are finally mature and thus now a part of the performance evaluation analysis. We
also incorporated expositional improvements throughout the book based on reader
feedback on the first edition.
Another feature of the new edition is that the VCV model, used extensively in
Part III of the book, is now available as a Web-based application available on http://
VCVtools.com. Significant collaborative efforts went into developing this tool,
which we believe will be of interest to a broad audience, including practitioners
interested in valuing VC-backed company stocks and employee stock options.
THE ORGANIZATION OF THIS BOOK
The book is divided into four parts, with six chapters each. Each of these four parts
has a major finance theme: the theme of Part I is the relationship between risk and
return; the theme of Part II is the valuation of high-growth companies; the theme of
Part III is the analysis of capital structure; and the theme of Part IV is the rela-
tionship between strategy and finance. Overall, Parts I and II are heavy on data
and definitions and are intended to provide students with the vocabulary of VC and
knowledge of the key industry facts. Although these two parts contain some new
definitions and approaches, most of the material should seem familiar to a VC
practitioner. In contrast, Parts III and IV are more theory based and provide a new
perspective on the evaluation of VC and other high-technology investments.
Although these latter two parts might seem experimental to a practicing VC,
financial economists will recognize the material as a straightforward translation of
well-known methods.
vii
In Part I, “An Introduction to VC”, we provide an overview of the VC
industry, with discussions of history (Chapter 1), major players (Chapters 2 and 5),
performance measurement (Chapters 3 and 4), and global patterns (Chapter 6). The
discussion of risk and return in Chapters 3 and 4 provide a key translation between
the language of VC and the language of financial economics—a translation that we
rely on heavily throughout the book.
In Part II, “Total Valuation”, we provide data and methods used to value a
high-growth company. We first review the investment process used by VCs and
provide data on their historical performance (Chapter 7). We next describe the
structure of VC transactions (Chapters 8 and 9) and then demonstrate the industry-
standard technique for the valuation of VC investments (Chapter 10). This technique,
known loosely as “the venture capital method”, requires that analysts estimate
company values far into the future. Although such estimates will always contain a
fair amount of guesswork, we show how to use a “reality-check” model to frame
these estimates (Chapter 11) and how to use evidence from comparable companies to
provide an additional input for the investment decision (Chapter 12).
In Part III, “Partial Valuation”, we take the total valuation (Part II) as given
and analyze the special features of VC transactions. In most VC transactions, the
investors receive preferred stock with several special features. When there are
many VC investors, the capital structure of the company grows quite complex, with
each investor holding a unique place in the capital-structure hierarchy of the
company. In Part III, we show how to divide the total valuation of the company into
its component parts (partial valuation) for each investor. The key step in this
analysis is the recognition that all flavors of preferred stock can be represented as a
portfolio of options. In Chapter 13, we show how the classic option-pricing analysis
of Black and Scholes can be extended to VC settings. We then apply this extended
analysis to the valuation of preferred stock (Chapters 14, 15, and 16). The tech-
niques used in these chapters can also be used to refine some industry-standard
measures of company valuation (Chapter 17) and to estimate the partial valuation
of complex nonstandard transaction structures (Chapter 18).
Parts II and III of the book take the perspective of a venture capitalist making
an investment in a high-technology company. In Part IV, we take the perspective of
the company deciding what to do with VC money or other capital. Specifically, we
develop a framework for modeling investment in “research and development”
(R&D). Since VC-backed companies typically spend a significant fraction of their
capital on R&D, an understanding of R&D finance is crucial for both VCs and for
financial decision-makers at technology companies of all sizes. After introducing
typical kinds of R&D investment problems (Chapter 19), we study several of the
most interesting and cutting-edge techniques in finance, including Monte Carlo
analysis (Chapter 20), real options (Chapter 21), binomial trees (Chapter 22),
and game theory (Chapter 23). In Chapter 24, we pull all of these tools together and
solve the investment problems originally posed in Chapter 19.
Several appendices supplement the text. Appendix A provides an example
“term sheet” VC contract developed by the National Venture Capital Association.
viii PREFACE TO 2
ND
EDITION—A READER’S GUIDE
Appendix B provides some basic documentation for the companion spreadsheets
and the web-based valuation model used in the book. Appendix C is a brief primer
on Crystal Ball
s
software, a commercial product from Oracle that is useful for
solving some of the models in Part IV. Finally, a glossary at the end of the book
gives definitions for all key terms used in the book.
WHAT THIS BOOK COVERS . . . AND WHAT
IT DOESN’T
To be successful, VCs must have a broad general knowledge of business and all its
disciplines: marketing, management, finance, operations, accounting, and so on. In
addition, most VCs must acquire specialized knowledge in one or more high-
technology industries. It is not possible to cover all these areas in one textbook, nor
is it advisable to even try. This book focuses almost exclusively on finance, spe-
cifically on the valuation of high-technology investments. The ideal reader is an
MBA student or advanced undergraduate who is both interested in VC and intel-
lectually curious about finance. We wrote the book for this prototypical reader;
your distance from this prototype will likely predict your satisfaction with this
book. In particular, readers looking for a “how to” guide for being a successful VC
are sure to be disappointed. We doubt such a book is even possible, and we are sure
that we could not write it.
For instructors, the 24 chapters of the book can provide for 24 class meetings
with 75 minutes each (530 hours) for a course of the same name as the book. That
is how we taught it at Wharton.
1
Alternatively, a finance course on “Venture
Capital” could omit Part IV of the book and include six additional case-study classes
to fill out a full semester course. For a quarter-length course that meets 20 times for
90 minutes each (530 hours), some chapters can be combined (for example,
chapters 1 and 2, 3 and 4, and 11 and 12) or omitted (e.g., 18, 22À24). For a six-
week course (515 class hours) on “Venture Capital”, the first two parts of the book
can provide a self-contained framework.
For any of these VC courses, many instructors may choose to combine this
book with case studies. At Wharton, we used this book as the main text, with case
studies from the books by Josh Lerner and Felda Hardymon of Harvard Business
School used to illustrate the practical applications of the concepts. Alternatively,
one could use the case studies as the main classroom topics, with this textbook as
background. A companion instructor’s manual suggests some cases that work well
with each of the chapters.
For VC courses taught outside of a finance department, instructors will
rightly want to emphasize different aspects of VC practice. At Yale and UC Davis,
we have a highly successful VC course taught by management faculty—a course
1
Both authors previously taught at Wharton, 1999À2008 for Metrick and 2001À2009 for Yasuda.
PREFACE TO 2
ND
EDITION—A READER’S GUIDE ix
that has virtually no overlap with this book. Furthermore, as one might expect,
courses taught by VC practitioners are often much more “practical”, with many
class sessions dedicated to the nuts and bolts of working with young companies.
While we believe that some chapters of this book could provide useful background
for these practitioner courses, we are certain that most of the book would be useless.
We have found that students can learn a tremendous amount from these practice-
based courses, and have made no attempt to substitute for these valuable lessons.
There are several related topics for which this book has some imperfect
overlap. For example, for courses in “entrepreneurial finance”, students typically
need some exposure to VC. For these students, Part I should be useful, while the
other parts are likely to be overkill. This book takes the perspective of a venture
capitalist—not the perspective of an entrepreneur. The latter perspective requires a
careful study of non-VC sources of capital for young companies, a perspective that
this book does not cover at all. Furthermore, the financial management of young
growth companies is another important topic in entrepreneurial finance. While such
a topic could conceivably have been included in this book, we chose instead to
focus on the valuation aspects of VC finance.
Another topic of some overlap would be a general course on “private equity”.
As will be discussed in Chapter 1, private equity is a broad class of investing that
includes VC as well as investments in leveraged buyouts, mezzanine structures, and
distressed companies. (All these terms will be defined in Chapter 1.) For instructors
of such classes, the usefulness of the book depends on the relative emphasis on VC.
Six weeks (515 hours) of VC can be supported by Parts I and II, supplemented
with (or supplementing) case studies. For private equity courses with less than six
weeks of VC, the reductions can be accomplished in Parts I and II by omitting some
combination of Chapter 5, Chapter 6, and Chapter 9, and combining Chapters 11
and 12 into a single class meeting.
NOTES ON TERMINOLOGY, STYLE,
AND MATHEMATICS
The text assumes that readers have familiarity, but not mastery, of the basic con-
cepts from first-year MBA courses in finance, statistics, and accounting. (For
example, the book assumes that readers know the definitions for “mean” and
“standard deviation”,
2
but does not assume that readers have memorized formulas
for the mean and standard deviation of any specific probability distributions.) Most
of the mathematics in the book goes no further than simple algebra. In Parts III and
IV of the book, we use some basic calculus in a few places, but even there it is more
2
This book follows British style in the “logical” placement of some punctuation marks outside of
quotation marks. This annoys some people. Sorry.
x PREFACE TO 2
ND
EDITION—A READER’S GUIDE
important that readers know what an integral “does” rather than know how to solve
any specific integrals.
The book assumes no prior knowledge of venture capital. All key terms are
given in bold type in their first appearance in the text. Because this book is
attempting to provide a bridge between the language of VC and the language of
finance, it is sometimes helpful to introduce new terminology in order to ease the
translation. Such new terminology is given in bold italic type in its first appearance in
the text. All key terms are listed at the end of the chapter of their first appearance.
At the end of the textbook, a glossary provides definitions for all key terms. The text
uses many acronyms to shorten the exposition. Each acronym is spelled out in its first
appearance, followed by the acronym given in parenthesis: for example, venture
capital (VC). All acronyms are also listed in the glossary.
PREFACE TO 2
ND
EDITION—A READER’S GUIDE xi
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ACKNOWLEDGMENTS
This book would not have been possible without the guidance, encouragement, and
support of many of our academic colleagues; special gratitude goes to Paul
Gompers, Steve Kaplan, Josh Lerner, and David Scharfstein for their continuous
generosity with their knowledge and insights.
We are also indebted to our friends in the VC industry for their willingness to
help us with their time, knowledge and resources. Special thanks to Susan
Woodward, who graciously made available to us the venture capital database at
Sand Hill Econometrics, Mike Holt of Holt Private Equity Consultants for sharing
with us the coveted compensation data from his annual compensation survey, and
John Taylor of National Venture Capital Association for his help with the LP data.
We also thank Louis Radovich for his superb assistance with the analysis of the
Sand Hill Econometrics data.
We continue to rely on the dedication of highly skilled students for development
of the VCVmodel, used inPart III tovalue deal structures withpreferred stockandnow
newly offered as a Web-based application. This valuation model in its current
incarnation would not have been possible without the contribution of Tony Curnes,
Holland Gary, Jonathan Reinstein, David Smalling, and Rebecca Yang. We also thank
Garris Shipon for building the Web application and designing the site (VCVtools.com)
that houses the VCV model, and Greta Lin for co-authoring Appendix C.
The book benefited greatly from the feedback on the first edition from many
individuals, including our former Wharton colleague David Wessels, who taught
courses using the book, and generations of students at Wharton and Yale. Ayako
thanks her colleagues at UC Davis Graduate School of Management for supporting
her in creating a new VC finance course in her first year there, and her MBA
students for being test-marketed for the pre-publication manuscript of the second
edition. Several of our students and colleagues made important contributions to the
first edition of this book, and these contributions are still evident in this new
version: Izhar Armony, Albert Cheng, Christine Chou, Colleen Pontious, and Yin
Yin. We also would like to thank the Mack Center for Technological Innovation at
the Wharton School of the University of Pennsylvania for their generous financial
support for the first edition of the book.
We would also like to thank Lacey Vitetta, Jennifer Manias, Emily McGee, and
Joyce Poh at Wiley for their contributions to the completion of this book. Finally, we
each are most indebted to our families, for making this all possible and worthwhile.
Andrew dedicates the book to: his wife Susie, his son David, and his daughter Amy;
Ayako dedicates the book to: her husband Garris, and her daughter Miumi.
xiii
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For Susie, David, and Amy
AM
For Garris and Miumi
AY
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CONTENTS
PART I
VC BASICS
CHAPTER 1 THE VC INDUSTRY 3
1.1 What Is Venture Capital? 3
1.2 What Do Venture Capitalists Do? 9
1.3 The History of Venture Capital 10
1.4 Patterns of VC Investment in the United States 14
1.4.1 Investments by Stage 14
1.4.2 Investments by Industry 16
1.4.3 Investments by U.S. Region 18
Summary 19
Key Terms 20
References 20
CHAPTER 2 VC PLAYERS 21
2.1 Firms and Funds 21
2.2 The Limited Partners 27
2.3 VC Partnership Agreements 30
2.3.1 Management Fees 30
2.3.2 Carried Interest 32
2.3.3 Restrictive Covenants 39
Summary 41
Key Terms 42
References 42
Exercises 42
Appendices: Key Terms and Conditions for Three VC Funds 43
Appendix 2.A: EarlyBird Ventures I 43
Appendix 2.B: Talltree Ventures IV 44
Appendix 2.C: Owl Ventures IX 45
xvii
CHAPTER 3 VC RETURNS 46
3.1 Industry Returns 46
3.1.1 De?nitions 46
3.1.2 A Gross-Return Index 48
3.1.3 A Net-Return Index 50
3.2 Fund Returns 53
3.2.1 De?nitions 53
3.2.2 Evidence 59
Summary 62
Key Terms 63
References 63
Exercises 63
CHAPTER 4 THE COST OF CAPITAL FOR VC 65
4.1 The Capital Asset Pricing Model 65
4.2 Beta and the Banana Birds 69
4.3 Estimating the Cost of Capital for VC 74
Summary 79
Key Terms 80
References 80
Exercises 80
CHAPTER 5 THE BEST VCs 83
5.1 The Economics of VC 83
5.2 The Best VCs: A Subjective List 86
5.3 VC Value Added and the Monitoring of Portfolio Firms 95
Summary 98
Key Terms 98
References 98
CHAPTER 6 VC AROUND THE WORLD 99
6.1 The Global Distribution of VC Investing 99
6.2 The Cost of Capital for International VC 111
6.2.1 Baseline Model: The Global CAPM 112
6.2.2 Objective and Extensions to the Global CAPM 114
6.2.3 A Global Multifactor Model for Venture Capital 118
Summary 119
Key Terms 119
References 119
Exercises 120
xviii CONTENTS
PART II
TOTAL VALUATION
CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS 123
7.1 VC Investments: The Historical Evidence 123
7.2 The Investment Process 135
Summary 144
Key Terms 145
References 145
CHAPTER 8 TERM SHEETS 146
8.1 The Basics 147
8.1.1 Investors 148
8.1.2 Price Per Share 149
8.1.3 Pre-Money and Post-Money Valuation 149
8.1.4 Capitalization 150
8.2 The Charter 151
8.2.1 Dividends 153
8.2.2 Liquidation Preference 153
8.2.3 Voting Rights and Other Protective Provisions 154
8.2.4 Mandatory Conversion 154
8.2.5 Redemption Rights 154
8.3 Investor Rights Agreement 155
8.3.1 Registration Rights 158
8.3.2 Matters Requiring Investor-Director Approval 158
8.3.3 Employee Stock Options 158
8.4 Other Items 159
8.4.1 Rights and Restrictions 160
8.4.2 Founders’ Stock 161
Summary 161
Key Terms 161
References 162
Exercises 162
CHAPTER 9 PREFERRED STOCK 163
9.1 Types of Preferred Stock 163
9.2 Antidilution Provisions 173
Summary 176
Key Terms 177
CONTENTS xix
Reference 177
Exercises 177
CHAPTER 10 THE VC METHOD 178
10.1 The VC Method: Introduction 178
10.1.1 Exit Valuation 179
10.1.2 Target Returns 180
10.1.3 Expected Retention 182
10.1.4 The Investment Recommendation 183
10.2 The Standard VC Method 184
10.3 The Modi?ed VC Method 185
Summary 192
Key Terms 192
References 192
Exercises 192
CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES 195
11.1 DCF Analysis: Concepts 196
11.2 DCF Analysis: Mechanics 198
11.3 Graduation Value 204
11.4 DCF Analysis: The Reality-Check Model 207
11.4.1 Baseline Assumptions for the
Reality-Check DCF 207
Summary 212
Key Terms 212
References 213
Exercises 213
CHAPTER 12 COMPARABLES ANALYSIS 214
12.1 Introduction to Comparables Analysis 215
12.2 Choosing Comparable Companies 219
12.3 Using Comparable Companies to Estimate the Cost of Capital 224
Summary 226
Key Terms 227
References 227
Exercises 227
Appendix 12.A: Potential Comparables for Semico 228
xx CONTENTS
PART III
PARTIAL VALUATION
CHAPTER 13 OPTION PRICING 231
13.1 European Options 232
13.2 Pricing Options Using a Replicating Portfolio 234
13.3 The Black-Scholes Solution 238
13.4 American Options 242
13.5 Random-Expiration Options 243
13.6 Reading Exit Diagrams 245
13.7 Carried Interest as an Option 247
Summary 248
Key Terms 249
References 249
Exercises 249
Appendix 13.A RE Options: Technical Details 250
CHAPTER 14 THE VALUATION OF PREFERRED STOCK 252
14.1 Base-Case Option-Pricing Assumptions 253
14.2 RP Valuation 254
14.3 Excess Liquidation Preferences 257
14.4 Dividends 259
14.5 CP Valuation 261
14.6 CP with Excess Liquidation Preferences or Dividends 263
14.7 Combining RP and CP 266
14.8 Comparing RP and CP 268
Summary 269
Key Terms 270
References 270
Exercises 270
CHAPTER 15 LATER-ROUND INVESTMENTS 272
15.1 Series B 272
15.2 A Conversion Shortcut 277
15.3 Series C 278
15.4 Dividends in Later Rounds 282
15.4.1 Accrued Cash Dividends 282
15.4.2 PIK Dividends 284
15.5 Beyond Series C 285
CONTENTS xxi
Summary 288
Key Terms 288
Exercises 288
CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK 290
16.1 Binary Options 291
16.2 The Valuation of PCP 292
16.3 The Valuation of PCPC 294
16.4 Series B and Beyond 296
Summary 303
Key Terms 303
References 303
Exercises 303
CHAPTER 17 IMPLIED VALUATION 305
17.1 Post-Money Valuation Revisited 306
17.2 Measurement of Portfolio Value 310
17.3 Down Rounds? 314
17.4 How to Avoid Valuation Confusion 317
Summary 318
Key Terms 318
Exercises 319
CHAPTER 18 COMPLEX STRUCTURES 320
18.1 Management Carve-outs 320
18.2 Dealing with Partners 327
18.3 A Complex Example 329
Summary 334
Key Terms 334
Exercises 334
PART IV
THE FINANCE OF INNOVATION
CHAPTER 19 R&D FINANCE 339
19.1 R&D Around the World 339
xxii CONTENTS
19.2 Two Touchstones 345
19.2.1 Drug Development 345
19.2.2 Energy Innovation 348
19.3 How Is R&D Financed? 349
19.4 Where Do We Go from Here? 354
Summary 355
Key Terms 356
References 356
CHAPTER 20 MONTE CARLO SIMULATION 357
20.1 Event Trees 357
20.2 Simulation with Continuous Probability Distributions 362
20.3 Simulation with Multiple Sources of Uncertainty 373
Summary 376
Key Terms 376
Exercises 376
CHAPTER 21 REAL OPTIONS 378
21.1 Decision Trees 379
21.2 Real Options in R&D 381
21.3 The Valuation of Real Options 382
21.4 Risk-Neutral Probabilities 388
21.5 Drugco, Revisited 395
Summary 398
Key Terms 398
Exercises 398
CHAPTER 22 BINOMIAL TREES 400
22.1 The Black-Scholes Equation, Revisited 400
22.2 Multiple Strike Prices and Early Exercise 409
22.3 Dividends 411
Summary 417
Key Terms 418
References 418
Exercises 418
CHAPTER 23 GAME THEORY 419
23.1 What Is Game Theory? 419
23.2 Simultaneous Games 423
CONTENTS xxiii
23.3 Sequential Games 433
23.4 Game Theory and Real Options 438
Summary 443
Key Terms 443
Exercises 444
CHAPTER 24 R&D VALUATION 445
24.1 Drug Development 445
24.2 Energy 455
24.3 The Forest and the Trees 464
Summary 464
References 465
Exercises 465
APPENDIX A SAMPLE TERM SHEET 466
APPENDIX B THE VCFI SPREADSHEETS 484
APPENDIX C GUIDE TO CRYSTAL BALL
s
487
GLOSSARY 512
INDEX 535
xxiv CONTENTS
PART I
VC BASICS
1
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CHAPTER 1
THE VC INDUSTRY
IN THIS CHAPTER, we provide a de?nition of venture capital (Section 1.1),
take a preliminary look at the activities of venture capitalists (Section 1.2), explore the
history of venture capital (Section 1.3), and review a variety of statistics on the patterns
of venture capital investment (Section 1.4). Throughout this text, we use the abbre-
viation VC to refer to both the venture capital industry and to an individual venture
capitalist.
1.1 WHAT IS VENTURE CAPITAL?
A VC has ?ve main characteristics:
1. A VC is a ?nancial intermediary, meaning that it takes the investors’
capital and invests it directly in portfolio companies.
2. A VC invests only in private companies. This means that once the invest-
ments are made, the companies cannot be immediately traded on a public
exchange.
3. A VC takes an active role in monitoring and helping the companies in its
portfolio.
4. A VC’s primary goal is to maximize its ?nancial return by exiting invest-
ments through a sale or an initial public offering (IPO).
5. A VC invests to fund the internal growth of companies.
Characteristic (1) de?nes VCs as ?nancial intermediaries. This is similar to a
bank, because just as a bank takes money from depositors and then loans it to
businesses and individuals, a VC fund takes money from its investors and makes
equity investments in portfolio companies. Typically, a VC fund is organized as a
limited partnership, with the venture capitalist acting as the general partner
(GP) of the fund and the investors acting as the limited partners (LP).
1
If all goes
1
The organization structure of VC funds will be discussed at length in Chapter 2.
3
well, the VC eventually sells its stake in the portfolio company, returns the money
to its limited partners, and then starts the process all over again with a different
company. Exhibit 1-1 illustrates the key players and the ?ow of funds in the VC
industry.
VCs are often compared to—and confused with—angel investors. Angel
investors, often just called angels, are similar to VCs in some ways but differ
because angels use their own capital and, thus, do not satisfy characteristic (1).
There are many types of angels. At one extreme are the wealthy individuals with no
business background who are investing in the business of a friend or relative. At the
other end are groups of angels with relevant business or technical backgrounds who
have banded together to provide capital and advice to companies in a speci?c
industry. In the latter case, the angel groups look very much like VCs, but the fact
that they use their own capital changes the economics of their decisions: Since they
can keep all the returns to on their labor, they have a correspondingly lower cost of
capital and can invest in deals that would not work for a VC. Although it is dif?cult
to get reliable ?gures on angel investing, the best available survey evidence for
recent years suggests that total angel investments are approximately the same
magnitude as total VC investments.
2
Although the total ?ow of capital is similar,
angels tend to focus on younger companies than do VCs and make a larger number
of smaller investments.
EXHIBIT 1-1
THE FLOW OF FUNDS IN THE VENTURE CAPITAL CYCLE
Portfolio
companies
VC funds
managed by
general partners
(VCs or GPs)
Exits: IPO or
sale of
portfolio
companies
Limited partners
(investors or LPs)
2
The most comprehensive data on the angel market is maintained by the Center for Venture Research at
the University of New Hampshire: http://wsbe.unh.edu/cvr/. Their annual reports on the state of the angel
market provide the evidence cited in this paragraph.
4 CHAPTER 1 THE VC INDUSTRY
Characteristic (2) de?nes VC as a type of private equity. Although the
de?nitions of “private company” and “public company” have some nuances,
the key distinction is that a public company’s securities can be traded in a formal
market, like the NYSE or the NASDAQ, whereas a private company’s securities
cannot. Any company that is publicly traded in the United States must also ?le
regular reports with the Securities and Exchange Commission (SEC) detailing its
?nancial position and material changes to its business. When combined with the
activities of professional traders in public markets, this requirement to ?le creates
signi?cant amounts of information about public companies. In comparison, infor-
mation about private companies is practically nonexistent. Private equity is considered
to be a category of alternative investing, where “alternative” stands in contrast to
“traditional” investing in stocks and bonds.
Characteristic (3) is central on our list—and central to the success of any VC.
Without (3), a VC would only be providing capital, and his success (or failure)
would be entirely due to his ability to choose investments. Although success can, of
course, be entirely built on these choices, the comparative advantage of the VC
would be greatly improved if the investor could also help the company directly.
This help takes many forms. Most notably, VCs typically take at least one
position on the board of directors of their portfolio ?rms. Having board repre-
sentation allows them to provide advice and support at the highest level of the
company. (More than one VC has remarked that his job could be described as being
“a professional board member”.) In addition to board service, VCs often act as
unof?cial recruiters and matchmakers for their portfolio ?rms. Young companies
often have a dif?cult time attracting high-quality talent to a ?edgling operation,
and VCs can signi?cantly mitigate this problem by drawing on their reputation and
industry contacts. A VC who performs these value-added services well has a
sustainable form of competitive advantage over other investors.
Because VCs are ?nancial intermediaries, they need some mechanism to give
money back to their investors. Thus, a savvy VC will only make an investment if he
can foresee a path to exit, with proceeds of this exit returning to the VC and his
investors. Exits can occur through an IPO, with a subsequent sale of the VC stake in
the open market, through a sale of the company to another investor, or through the
sale of the company to a larger company. Because of the need to exit, VCs avoid
investments in “lifestyle” businesses (companies that might provide a good income
to the entrepreneurs, but have little opportunity for a sale or IPO).
Characteristic (4), the requirement to exit and the focus on ?nancial return, is
a key distinction between venture capital and strategic investing done by large
corporations. As a perpetual entity, a corporation can afford to take stakes in other
businesses with the intention of earning income, forming long-term alliances, and
providing access to new capabilities. It is possible for the corporation to maintain
this stake inde?nitely.
A strategic investor may satisfy all the other characteristics, but without the
need to exit, the strategic investor will choose and evaluate investments very dif-
ferently from a VC. In some cases, a corporation may set up an internal venture
1.1 WHAT IS VENTURE CAPITAL? 5
capital division. In the industry, this is referred to as corporate venture capital.
This label can be confusing, as only sometimes do such divisions satisfy
characteristic (4). These corporate VC efforts will often have strategic objectives
other than ?nancial returns and will have neither dedicated supplies of capital nor
an expectation that capital will be returned within a set time period. When (4) is not
satis?ed, the investment activity can take on a very different ?avor than the type
studied in this book.
The requirement to exit provides a clear focus for VC investing activities.
There are over 20 million businesses in the United States; more than 99 percent of
these businesses would meet the government de?nition of a “small business”.
3
In
general, small businesses are dif?cult to exit, and only “large businesses”—those in
the top 1 percent of all businesses—have a realistic chance to go public or be sold
in a liquid acquisition market. It is therefore typical for VCs to invest in small
businesses—but they only do so when these small companies have a realistic
chance to grow enough to become a large company within ?ve to seven years after
the initial investment. Such rapid growth is dif?cult to attain in most industries;
therefore, VCs tend to focus on high-technology industries, where new products can
potentially penetrate (or even create) large markets.
Characteristic (5) refers to “internal growth”, by which we mean that the
investment proceeds are used to build new businesses, not to acquire existing
businesses. Although the legendary VC investments tend to be those adventurous
VCs who backed “three guys in a garage”, the reality of VC investing is much
more varied. As a simple classi?cation, we divide portfolio companies into three
stages: early-stage, mid-stage (also called expansion-stage), and late-stage. At
one extreme, early-stage companies include everything through the initial
commercialization of a product. At the other extreme, late-stage companies are
businesses with a proven product and either pro?ts or a clear path toward pro?t-
ability. A late-stage VC portfolio company should be able to see a plausible exit on
the horizon. This leaves mid-stage (expansion) companies, who represent the vast
landscape between early-stage and late-stage. With all this territory to cover, it is
not surprising that mid-stage investments make up the majority of VC investment.
In Section 1.4.1 of this chapter, we give more precise de?nitions of these stages,
along with evidence about the investment patterns by stage.
Characteristic (5) also allows us to distinguish VC from other types of private
equity. Exhibit 1-2 illustrates the overlapping structure of the four main types of
private equity investing and also shows the intersection of these types with hedge
funds, another category of alternative investments. The relationship between
private equity and hedge funds will be discussed below.
The largest rectangle in the exhibit contains all of alternative investing, of
which private equity and hedge funds are only two of many components. These
components are represented by two smaller rectangles within alternative investing.
3
See http://www.sba.gov/size/
6 CHAPTER 1 THE VC INDUSTRY
The different types of private equity investing are represented by the overlapping
circles within private equity, with some overlap with hedge funds. The sizes of
the circles and rectangles are not matched to the scale of the investing categories,
but rather are intended to illustrate the relative scopes of overlap.
Venture capital sits on the far left of Exhibit 1-2 and intersects with the
mezzanine category. The term mezzanine has developed two distinct meanings
within the private equity industry. The ?rst meaning is a form of late-stage (often
very late-stage) venture capital. Some VC funds do this kind of investing (hence the
intersection); but so do other ?nancial intermediaries, including hedge funds, banks,
insurance companies, specialty ?nance corporations, and non-VC private equity
funds. This ?nancing is typically in the form of subordinated debt (junior to bank
loans), with some additional equity participation in the form of options (warrants)
to buy common stock. Some ?rms refer to this kind of investing as growth capital.
The second meaning of “mezzanine” ?rst arose in the mid-1980s, when investors
began to use the same capital structure—subordinated debt with some equity
participation—to provide another layer of debt ?nancing for highly leveraged
buyout (LBO) transactions. Today, most private equity ?rms with “mezzanine” in
their title are doing this second type of investing.
EXHIBIT 1-2
PRIVATE EQUITY AND HEDGE FUNDS
Venture
Capital Mezzanine
ALTERNATIVE INVESTMENTS
Private Equity
Hedge Funds
Buyout
Distress
1.1 WHAT IS VENTURE CAPITAL? 7
Because the subordinated debt in mezzanine investing will often be attached
to some equity ownership, mezzanine investing can also intersect with the pure
equity investing done in buyouts, the next category in Exhibit 1-2. Buyout investing
is the largest category of private equity, with total funds under management about
three times as great as for venture capital. Buyout investors pursue a variety of
strategies, but a key feature of buyout investors is that they almost always take
majority control of their portfolio companies. (In contrast, VCs usually take
minority stakes in their portfolio companies.) Large buyouts of public companies
typically garner the biggest headlines, and the most famous buyout of all time—the
$25 billion purchase of RJR Nabisco by Kohlberg, Kravis, and Roberts (KKR) in
1989—was the largest transaction of its kind until 2007, when KKR, Texas Paci?c
Group, and Goldman Sachs bought TXU Corp. for $45 billion. In these large
buyouts, the investors put up the equity stake (these days it is usually between 20
and 40 percent of the total purchase price) and then borrow the rest from banks,
public markets (noninvestment grade or “junk bonds”), and mezzanine investors—
hence the term leveraged buyouts (LBOs).
Despite the publicity generated by these large buyouts, most buyout ?rms are
engaged in more everyday deals involving the purchase of “middle-market”
companies. Although some of these so-called middle-market companies may
qualify among the largest 1 percent, many of them still lack the growth potential to
generate much interest from public markets. This is typically because the company
is in an older industry that has more stable cash ?ows and limited potential for
internal growth. In this case, private equity investors can create liquidity for the
current owners through a buyout. Such buyouts do not always include leverage. A
related strategy is “buy-and-build”, where a buyout investor will acquire a series of
?rms in a fragmented industry for the purpose of taking advantage of changes in the
optimal industrial scale. Although buy-and-build is a growth investment strategy,
the growth comes externally from the purchase of existing businesses.
The ?nal category of private equity is distress investing, also called special
situations. As the name suggests, distress investors focus on troubled companies.
Because many distress investments are buyouts, this category intersects with the
previous one. Some private equity investors do both traditional leveraged buyouts
and distress buyouts, but most investors specialize in either one or the other.
A separate category of alternative investing, hedge funds, is also included
in Exhibit 1-2. Hedge funds are ?exible investing vehicles that share many
characteristics of private equity funds, including the limited partnership structure
and the forms of GP compensation. The main difference, however, is that hedge
funds tend to invest in public securities. A good example of this distinction can
be seen in the area of distress investing, the area with the greatest overlap for private
equity and hedge fund investors. The private equity funds that engage in distress
investing usually do so with the intention of gaining control of the distressed
company (or some subset of the company). These investors then operate and
restructure the company before reselling it to another investor or to the public
markets. Hedge funds also engage in distress investing, but their main strategy is to
8 CHAPTER 1 THE VC INDUSTRY
trade in the public securities of distressed companies with the intention of making a
trading pro?t by quickly reselling these securities. In recent years, the distinction
between hedge funds and private equity funds has grown more blurred, with some
hedge funds beginning to invade the traditional private equity territory, particularly
in the buyout and distress space. For now, traditional VC investing, with its long
holding periods and relatively small investments, remains relatively free of hedge
fund involvement.
Although there are exceptions to this pattern, the basic distinction is that
while private equity funds are long-term investors, hedge funds are short-term
traders. Both strategies have the potential for outstanding returns, but the skill sets
and investment approaches are different enough that it is rare that a single indi-
vidual can excel at both. However, because their investments are more liquid than
those for private equity investors, hedge funds can offer their investors faster access
to their money, with withdrawals usually allowed on a quarterly or annual basis.
This is a case of form following function: if you have an investment strategy in
illiquid assets, then you need to lock up your investors for a long period of time
(private equity); if you have an investment strategy in liquid assets, then you can
allow for quicker withdrawals (hedge funds). Although hedge funds have occa-
sionally crossed over to private equity, any large-scale crossover would require a
change of contractual form toward a longer lockup. At that point, they would
become private equity funds.
1.2 WHAT DO VENTURE CAPITALISTS DO?
VC activities can be broken into three main groups: investing, monitoring, and
exiting. In later chapters, we will describe these activities in more detail. For now,
we will give brief summaries of each group and use these summaries to de?ne the
scope of this book.
Investing begins with VCs prospecting for new opportunities and does not end
until a contract has been signed. For every investment made, a VC may screen
hundreds of possibilities. Out of these hundreds, perhaps a few dozen will be worthy
of detailed attention, and fewer still will merit a preliminary offer. Preliminary offers
are made with a term sheet, which outlines the proposed valuation, type of security,
and proposed control rights for the investors. If this term sheet is accepted by the
company, then the VC performs extensive due diligence by analyzing every aspect
of the company. If the VC is satis?ed, then all parties negotiate the ?nal set of terms
to be included in the formal set of contracts to be signed in the ?nal closing. These
investing activities—especially the term sheet valuation and structure—are ideal
topics for ?nancial analysis and are the main subjects of this book.
Once an investment is made, the VC begins working with the company
through board meetings, recruiting, and regular advice. Together, these activities
comprise the monitoring group. Many VCs argue that these activities provide the
best opportunity to add value and are the main source of comparative advantage for
1.2 WHAT DO VENTURE CAPITALISTS DO? 9
a successful VC. This argument may indeed be correct, but monitoring activities do
not lend themselves well to quantitative analysis. Thus, aside from a discussion of
the academic literature in Chapter 5, we will not go into monitoring in this text.
The ?nal group of activities is exiting. As discussed earlier, VCs are ?nancial
intermediaries with a contractual obligation to return capital to their investors. How-
ever, the exit process itself requires knowledge and skills that are somewhat distinct
from the earlier investment and monitoring activities. VCs plan their exit strategies
carefully, usually in consultation with investment bankers. A typical IPO underwritten
by a top investment bank will sell at least $50 million of new stock and have a total
equity value of at least $200 million. Historically, the IPO has been the source of the
most lucrative exits. The mainalternative tothe IPOis a sale toa strategic buyer, usually
a large corporation. Sometimes these sales can be very pro?table for the VC, but only if
there is signi?cant competition for the deal, which often includes the possibility of an
IPO. Financial analysis is crucial for the valuation of IPO ?rms and acquisition can-
didates, and this analysis is discussed at length in the rest of this book.
1.3 THE HISTORY OF VENTURE CAPITAL
Equity investments in risky new ventures are as old as commerce itself. The
modern organizational form of venture capital, however, dates back only to 1946.
Bank lending rules then (and now) looked for evidence that borrowers had
collateral and could make timely payments of interest and principal. Most entre-
preneurial ?rms, however, didn’t meet these standards, so they required risk capital
in the form of equity. There was usually no regular source of such capital, meaning
that entrepreneurs without wealthy friends or family had little opportunity to fund
their ventures. Along came George Doriot to solve this problem. General Doriot, so
called for his rank in the U.S. Army quartermaster’s of?ce during World War II,
recognized the need for risk capital and created a ?rm to supply it. His ?rm,
American Research and Development Corporation (ARD), began operations in
1946 as the ?rst true VC ?rm. Unlike modern funds, it was organized as a cor-
poration and was publicly traded. In its 25-year existence as a public company,
ARD earned annualized returns for its investors of 15.8 percent.
4
ARD also set a
standard for generating these returns that has persisted to the present day. Excluding
the $70,000 investment in their biggest “home run”, the Digital Equipment
Corporation, ARD’s 25-year annualized performance drops to 7.4 percent. Many
modern venture capitalists spend their days searching for their own home runs, now
with more fanciful names like Yahoo!, eBay, and Google—all ?rms that started as
venture capital investments and made legendary reputations for their investors.
Today, venture capital is a well-established business throughout the developed
world, but remains quite geographically concentrated both across and within
4
Fenn, Liang, and Prowse (1998).
10 CHAPTER 1 THE VC INDUSTRY
countries, with the United States still comprising nearly half the VC activity in the
world.
5
Because the United States represents so much of the worldwide VC industry,
the data providers have followed the money, and we now know much more about
American VCs than we do about those of the rest of the world. In this chapter, we
focus on the history and statistics from the well-studied U.S. market, and most of this
book will refer to U.S. data and legal structures. This focus on the United States does
not limit the applicability of the analysis, because most global VCs follow U.S.
practices. Most importantly for our purposes, the ?nancial concepts of VC investing
are universal, and all the quantitative analysis in this book can be applied to VC
investments anywhere in the world. In Chapter 6, we provide statistics on the world
distribution of VC and discuss some reasons for the observed patterns.
General Doriot’s innovationin1946didnot changetheworldovernight, andeven
ten years later the VClandscape remained barren. In recognition of this problem faced
bysmall-growthbusinesses, the U.S. government beganits ownVCefforts as part of the
Small Business Act of 1958, which was legislation that created the Small Business
Administration and allowed the creation of Small Business Investment Companies
(SBICs). Perhaps the greatest success of the SBICprogramwas to provide a vehicle to
train a pool of professional VCs for the later decades. SBICs still exist today and share
many characteristics of modern VC ?rms; however, regulatory restrictions af?liated
with SBICs keep it from becoming the dominant institutional form.
An important milestone for the VC industry came in the 1960s with the
development of the limited partnerships for VC investments. In this arrangement,
limited partners put up the capital, with a few percentage points of this capital paid
every year for the management fees of the fund. The remaining capital is then
invested by the general partner in private companies. Successful investments are
exited, either through a private sale or a public offering, before the ten-year life of
the partnership expires. The most common pro?t-sharing arrangement is an 80À20
split: after returning all the original investment to the limited partners, the general
partner keeps 20 percent of everything else.
This pro?t sharing, known as carried interest, is the incentive that makes
private equity investing so enticing for investment professionals. In recent years,
the most successful general partners have demanded—and received—as much as
30 percent carried interest on new partnerships. Limited partnerships are by far the
most common form of organization in the VC industry, and in Chapter 2 we will
discuss these partnerships in detail.
Despite inroads made by SBICs and the new limited partnerships, total VC
fundraising in the United States was still less than $1 billion a year throughout the
1970s. The next big change for VC came in 1979, when the relaxation of investment
rules for U.S. pension funds led to historically large in?ows from these investors to
the asset class. To this day, pension funds continue to supply nearly half of all the
money for VC in the United States.
5
PricewaterhouseCoopers, Global Private Equity Report 2008, p. 44.
1.3 THE HISTORY OF VENTURE CAPITAL 11
The participation by pension funds hastened the participation by other
institutional investors, and the modern era of venture capital began. Exhibit 1-3
displays the total amount of venture capital invested by year from 1980 to 1994.
Investing activity rose sharply to $3B in 1983 and remained remarkably
stable through the 1980s. After a slight drop in 1990À1991, VC investment began a
steady climb; from $2.2B in 1991, it rose gradually to $4.1B in 1994. We refer to
these ?rst 15 years of the modern VC industry as the preboom period. As shown in
Exhibit 1-4, it was in 1995 that investment really began to grow quickly.
EXHIBIT 1-3
VC INVESTMENT, PREBOOM (IN $B)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994
Source: National Venture Capital Association Yearbooks.
EXHIBIT 1-4
VC INVESTMENT, BOOM AND POSTBOOM (IN $B)
0
20
40
60
80
100
120
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009
Source: 2009 NVCA Yearbook, NVCA website.
12 CHAPTER 1 THE VC INDUSTRY
Exhibit 1-4 shows investment nearly doubling to $7.9B in 1995 (from $4.1B
in 1994) at the beginning of an incredible growth period. This was the dawn of the
Internet era, and some of the VC investments made in 1995 and 1996 had
spectacular returns. This caused institutional investors to rush for a piece of the
asset class, and investments rose to $11.0B in 1996, $14.7B in 1997, and $20.9B
in 1998—before exploding to the previously unimaginable levels of $53.4B in
1999 and $104.0B in 2000. For obvious reasons, we refer to 1995 to 2000 as the
boom period.
As the euphoria faded in the early 21st century, VCs still had large com-
mitments from their investors, and many portfolio companies—funded in the late
1990s and 2000—were hungry for follow-on investments. Still, spending fell to
$40.3B in 2001 before leveling off at between $20B and $30B in the subsequent
years. We refer to the years after 2000 as the postboom period. Indeed, the boom
period ended abruptly at the end of 2000, as investment fell by nearly half from the
fourth quarter of 2000 to the ?rst quarter of 2001.
Although the postboom numbers are well below the peak of 2000, they still
represent a considerable increase on investment prior to 1995. This can be seen by
looking at VC investment as a fraction of GDP, where VC investment hit a new
peak of 0.084 percent in 1983 and fell steadily to its modern all-time low of 0.036
percent in 1991 before rising to 0.058 percent at the end of the preboom period in
1994. The percentage jumped to 0.106 percent to mark the beginning of the boom
period in 1995, then rose steadily to hit 0.571 percent in 1999 and its maximum of
1.045 percent in 2000. In the postboom period, the percentage has leveled off to
about 0.2 percent in 2002À2008, well above the levels of the 1980s and approxi-
mately the same as the percentages in 1997 and 1998.
It is dif?cult to put these investment levels in perspective without some model
of VC’s place in the economy. How can we tell if the new levels of investment
($20À30B, or 0.2 percent of GDP) is too low, too high, or just right? One way to
approach this question is to start with the de?nition of VC at the beginning of this
chapter. There, we discussed how VCs invest in small companies that have the
potential to become large quickly through internal growth. To qualify, a company
usually needs some sort of product innovation, usually a novel item that can
penetrate a large market. Sometimes the proposed innovation is high tech, such as a
new drug or a new type of software. Alternatively, the innovation might be in a
business process, where an early mover could erect barriers to entry by competitors.
Many of the Internet startups took this route, although most of them unfortunately
ignored the requirement that there be a barrier to entry.
With this framework, we can see that it is not just an innovation that is
necessary, but rather an innovation that should be made by a small company. Tre-
mendous innovation goes on all the time in large companies, and large companies are
the optimal place for the majority of high-tech innovations. With large research
staffs, a stockpile of trade secrets, and decades of organizational learning, companies
like IBM, Microsoft, Intel, P?zer, and Merck are factories of innovation. If a small
1.3 THE HISTORY OF VENTURE CAPITAL 13
company proposed to develop, build, and sell a new microprocessor for personal
computers, it would face almost certain failure in the face of the industry giants. If,
however, a small company proposed to develop a small piece of the technology for
such microprocessors—a piece that could be patented and potentially licensed across
a wide range of products—then this might be (and has been) accomplished.
So how much innovation should occur in small companies? In general, this
will depend on the factors that drive the optimal scale of an innovative enterprise.
In the 1990s, communications technology changed radically, with development of
the Internet occurring alongside large price decreases for telecommunications. This
communications revolution was real, even if some potential pro?ts from the
revolution proved to be illusory. Lower costs of communication opened up new
opportunities for market transactions, with lower transaction costs than traditional
methods. According to the theory of the ?rm ?rst introduced by Ronald Coase in
1937, a universal reduction in transaction costs should reduce the optimal scale of
?rms and allow for greater levels of innovation by small companies.
By this reasoning, the higher levels of VC investment that we see today—
as compared to the 1980s—may indeed represent an optimal reaction to structural
changes in the economy. Even the massive investments of 1999 and 2000, although
clearly excessive in some respects, also appear to be at least in part a response to
rapid changes in transaction costs. Prior to the Internet era, national retail brands
required massive infrastructure and logistics support. With the Internet, retailers
could operate from a single location, and consumers could ?nd them from any-
where in the world.
The organizational constraints of large enterprises seemed to prevent the
rapid competitive reactions that could have sti?ed some of these innovations. For
example, large booksellers such as Barnes and Noble already possessed the brand
name, the infrastructure, and the inventory to compete effectively as online
booksellers. Nevertheless, Amazon.com, a venture-backed startup, managed to out-
innovate and out-compete them, to the point that Amazon’s business became far
more valuable than that of its older competitor. Amazon, although among the most
successful, is one of many examples of successful entrants that relied on the new
communications technology.
1.4 PATTERNS OF VC INVESTMENT
IN THE UNITED STATES
In this section, we provide evidence about VC investing by stage, industry, and
region.
1.4.1 Investments by Stage
There are many steps, or stages, to building a new VC-backed business. In Section 1.1,
we introduced the terminology for the three broad stages: early-stage, mid-stage, and
14 CHAPTER 1 THE VC INDUSTRY
late-stage. A more complete description of these stages, along with some sub-
categories, is found in Exhibit 1-5.
EXHIBIT 1-5
STAGES OF GROWTH
6
Seed/Startup Stage Financing
This stage is a relatively small amount of capital provided to an inventor or
entrepreneur to prove a concept. If the initial steps are successful, this may involve
product development, market research, building a management team, and deve-
loping a business plan. This is a pre-marketing stage.
Early Stage Financing
This stage provides ?nancing to companies completing development where pro-
ducts are mostly in testing or pilot production. In some cases, products may have
just been made commercially available. Companies may be in the process of
organizing, or they may already be in business for three years or less. Usually such
?rms will have made market studies, assembled the key management, developed a
business plan, and are ready to or have already started conducting business. This
involves the ?rst round of ?nancing following startup, which includes an institu-
tional venture capital fund. Seed and startup ?nancing tend to involve angel
investors more than institutional investors. The networking capabilities of the
venture capitalists are used more here than in more advanced stages.
Expansion (Mid) Stage Financing
This stage involves applying working capital to the initial expansion of a company.
The company is now producing and shipping and has growing accounts receivable
and inventories. It may or may not be showing a pro?t. Some of the uses of capital
may include further plant expansion, marketing, or development of an improved
product. More institutional investors are likely to be included along with initial
investors from previous rounds. The VC’s role in this stage involves a switch from
a support role to a more strategic role.
Later Stage
Capital in this stage is provided for companies that have reached a fairly stable
growth rate—that is, companies that are not growing as fast as the rates attained in
the expansion stages. Again, these companies may or may not be pro?table, but are
more likely to be pro?table than in previous stages of development. Other ?nancial
characteristics of these companies include positive cash ?ow. This also includes
companies considering IPOs.
6
These descriptions are nearly verbatim from the 2009 National Venture Capital Association Yearbook,
p. 87.
1.4 PATTERNS OF VC INVESTMENT IN THE UNITED STATES 15
The main theme of next exhibit is the steady trend toward later-stage investing.
In the early 1980s, the three categories of “seed/startup”, “early”, and “expansion”
were approximately equal, and “later stage” was the smallest. This pattern re?ects
VC’s focus on true startups in the early years of the industry. Gradually, new VC
?rms were created to focus on later stages, and some of the original ?rms grew so
large from their successes that they needed to ?nd larger investments to put all their
capital to work. By the mid-1990s, expansion stage investments were larger than all
early-stage investments (seed/startup plus other early-stage), and later-stage invest-
ments exceeded those in seed/startup. By the late 1990s, angel investors had largely
replaced VCs at the seed/startup stage, and expansion investments comprised more
than half of all VC investments. More recently, there are modest reversals in this
trend, with the share of startup/seed investments exceeding 5 percent of total for the
?rst time since 1999, while the share of expansion investments declined to less than
40 percent in 2008.
The de?nition of the company stage should not be confused with the de?-
nition of the ?nancing round. The negotiation of a VC investment is a time-
consuming and economically costly process for all parties. Because of these costs,
neither the VCs nor the portfolio ?rms want to repeat the process very often.
Typically, a VC will try to provide suf?cient ?nancing for a company to reach
some natural milestone, such as the development of a prototype product, the
acquisition of a major customer, or a cash-?ow breakeven point. Each ?nancing
event is known as a round, so the ?rst time a company receives ?nancing is
known as the ?rst round (or Series A), the next time is the second round (or
Series B), and so on. With each well-de?ned milestone, the parties can return to
the negotiating table with some new information. These milestones differ across
industries and depend on market conditions; a company might receive several
rounds of investment at any stage, or it might receive suf?cient investment in one
round to bypass multiple stages.
With these de?nitions in hand, we are now ready to examine the investment
patterns by stage. Exhibit 1-6 illustrates these patterns by plotting the percentage of
investment each year by stage.
1.4.2 Investments by Industry
Traditionally, VC investments have been concentrated in two broad sectors: health
care and information technology (IT), where the latter sector is de?ned to include
the communications, semiconductor, software, and hardware industries. This con-
centration is no accident: because VCs invest in small companies with the potential
to quickly grow large, they need to look for businesses with large, addressable
markets. To make headway in such markets, a business usually needs a technological
advantage of some kind—hence the VC focus on the high-tech industries of health
care and IT. Of course, other industries can also provide these opportunities,
16 CHAPTER 1 THE VC INDUSTRY
particularly during times of disruptive economic change. The communications
revolution of the late 1990s provided such an opportunity for Internet-based retail
businesses, and periodic oil shocks have provided the impetus for energy
investments.
Exhibit 1-7 illustrates the industry concentration of VC investment for
three periods: the preboom period of 1980À1994, the boom period of
1995À2000, and the postboom period of 2001À2009. The data show the dom-
inance of IT (including communications, software, hardware, and semi-
conductors/electronics) and health care (including biotech and medical devices)
for VC investment; together, these two sectors comprise about 75 and 80 percent
of all investments in the preboom and postboom period, respectively. During the
boom, media/retail investment had a brief (and expensive) rise, but even then
the main story was the enormous increase in IT relative to health care. Within the
EXHIBIT 1-6
VC INVESTMENT BY STAGE
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
1
9
8
0
1
9
8
2
1
9
8
4
1
9
8
6
1
9
8
8
1
9
9
0
1
9
9
2
1
9
9
4
1
9
9
6
1
9
9
8
2
0
0
0
2
0
0
2
2
0
0
4
2
0
0
6
2
0
0
8
Later Expansion Early Seed/Startup
Source: 2009 NVCA Yearbook, NVCA website.
1.4 PATTERNS OF VC INVESTMENT IN THE UNITED STATES 17
broad IT sector, the two most important industries in the boom and post-
boom periods were communications and software, followed by semiconductors/
electronics and hardware. Within health care, the story has been a gradual
emergence of biotechnology as the dominant industry, receiving almost 60
percent of total health care investment in recent years.
1.4.3 Investments by U.S. Region
With all the evidence of globalization in manufacturing and IT services, the U.S.
regional concentration of VC investment is particularly striking. Since the begin-
nings of the industry, the Silicon Valley area of northern California has remained the
epicenter of VC activity, with a consistent share of about one-third of total U.S. VC
investments per year. The area surrounding Boston has remained a secondary center
for most of this time, with between 10 and 15 percent share of the total. Exhibit 1-8
illustrates the distribution of VC investment for these centers and other U.S. regions
for 2008.
The dominance of Silicon Valley and New England (mainly Boston) hides
some important globalizing forces. Although companies headquartered in these
two regions receive almost half of all VC dollars, much of these funds are then
reinvested in foreign operations, particularly in India, by IT companies. This is a
21st-century phenomenon that has taken the industry by storm. Although it is
EXHIBIT 1-7
VC INVESTMENT BY INDUSTRY
Business/Financial Services
Media/Retail
Industrial/Energy
Medical Devices and Equipment
Biotechnology
Hardware
Semiconductors/Electronics
Software
Communications
0% 5% 10% 15% 20% 25% 30%
Postboom
Boom
Preboom
Source: Various years, NVCA Yearbooks.
18 CHAPTER 1 THE VC INDUSTRY
dif?cult to ?nd hard numbers to document this trend, such outsourcing is a common
topic of conversation among VCs.
SUMMARY
Venture capitalists (VCs) primarily invest in young, high-technology companies that have a
capacity for rapid growth. VCs are a type of ?nancial intermediary that perform three main
functions, which are (1) screening potential investments and deciding on companies to invest in,
(2) monitoring these companies and providing value-added services for them, and (3) exiting
their investments in these companies by selling their stake to public markets or to another buyer.
Venture capital is a form of private equity, which is an investment that cannot be traded in
public markets. Without the information ?ow and liquidity of public markets, VC investing
offers greater opportunities for both huge gains and terrible losses.
The modern VC industry effectively began in 1946 and grew slowly for its ?rst
35 years. Beginning in the early 1980s, new sources of capital from pension funds led to
EXHIBIT 1-8
REGIONAL DISTRIBUTION OF VC INVESTMENT
Silicon valley;
38.8%
Philadelphia; 2.7%
Colorado; 2.9%
DC/Metroplex; 3.5%
Northwest; 4.1%
San Diego;
4.3%
Southeast;
4.4%
Texas; 4.5%
Midwest;
4.8%
NY Metro;
6.6%
LA Orange
County;
7.0%
New England;
11.6%
Other;
4.8%
Source: 2009 NVCA Yearbook.
SUMMARY 19
rapid growth. This period of rapid growth leveled off in the mid-1980s and resumed in the
mid-1990s, culminating in a boom and crash at the turn of the century. The United States is
the world leader in VC, with about 40 percent of the worldwide investment and industry-
leading practices. Within the United States, information technology and health care are the
dominant sectors for VC investment, and Silicon Valley and the area around Boston,
Massachusetts, garner roughly half of all the domestic venture capital.
KEY TERMS
Venture capital (VC) and
venture capitalists (VCs)
Screen
Monitor
Exit
Financial intermediary
Limited partnership, limited
partner, general partner
Portfolio companies
Small Business Investment
Companies (SBICs)
Initial public offering
(IPO)
Angel investors = angels
Alternative investments
Private equity
Strategic investing
Corporate venture capital
Preboom, boom, postboom
periods
Early-stage, mid-stage
(expansion), late-stage
Mezzanine
Growth capital
Leveraged buyouts
(LBOs)
Distress investing5special
situations
Hedge funds
Term sheet
Due diligence
Management fees
Carried interest
Seed stage, Startup stage
Financing Round, First
round (Series A),
Second round (Series B)
REFERENCES
Coase, Ronald, 1937, “The Nature of the Firm”, Economica.
Fenn, George, Nellie Liang, and Stephen Prowse, 1998, “The Private Equity Market: An Overview”,
Financial Markets, Institutions & Instruments 6(4).
National Venture Capital Association, The NVCA Yearbooks, various years.
20 CHAPTER 1 THE VC INDUSTRY
CHAPTER 2
VC PLAYERS
THIS CHAPTER introduces the key players in the VC industry. In Section
2.1, we discuss the relationships among VC ?rms, VC funds, and the VCs who
work at them. In Section 2.2, we provide statistics on the investors in VC funds and
discuss the importance of various investor types. Section 2.3 analyzes the con-
tractual structure and compensation arrangements between VCs and their investors.
2.1 FIRMS AND FUNDS
About 80 percent of the organized VC market is controlled by independent VC ?rms.
VC ?rms are small organizations, averaging about 10 professionals, who serve as the
general partner (GP) for VC funds. A VC fund is a limited partnership with a ?nite
lifetime (usually 10 years plus optional extensions of a few years). The limited
partners (LPs) of VC funds are mostly institutional investors, such as pension funds,
university endowments, and large corporations. When a fund is ?rst raised, the LPs
promise to provide a certain amount of capital, which will be provided either on a set
schedule or at the discretion of the GP. These periodic capital provisions are known
as capital calls, drawdowns, or takedowns. The total amount of capital promised by
the LPs over the lifetime of the fund is called the committed capital of the fund.
1
Once the GP has raised the full amount of committed capital and is ready to start
investing, we say that the fund has been closed. The typical fund will invest in
portfolio companies and draw down capital over its ?rst ?ve years. These years are
known as the investment period or commitment period. After the investment
period is over, the VC can only make follow-on investments in current portfolio
companies. A successful VC ?rm will raise a new fund every few years so that there
is always at least one fund in the investment period at all times.
Most VC ?rms specialize their funds by stage, industry, and/or geography. For
example, an early-stage fund would make initial investments in early-stage compa-
nies, with some capital reserved to make follow-on investments in these companies in
their later stages. A late-stage fund would typically avoid all early-stage companies,
1
Typically, about 1% of the committed capital is provided by the GP itself. Throughout this textbook, we
will ignore this small GP contribution and pretend as if all committed capital is coming from the LPs.
21
focusing on expansion and later-stage investments. Most VC ?rms keep the same stage
focus for all their funds, but some will change focus over time or mix the two strategies
at once in a multistage fund. A few ?rms raise separate early-stage and late-stage
funds for overlapping periods and assign different professionals to each fund.
There is a wide dispersion in the levels of industry focus, with many generalists
(a fund that is willing to invest in both IT and health care is effectively a generalist)
and others with a relatively narrow focus on sectors like energy or ?nancial services.
As for geographic focus, it is important to recognize that much of the activity
experienced by VCs is local, and as a result the location of the VC’s of?ce will
usually be highly correlated with the location of most of their portfolio companies.
Not surprisingly, the geography of VC of?ces is very similar to the geography of VC
investment shown in Exhibit 1-8. Because funds tend to be geographically focused
wherever their of?ces are, the main way to attain reliable geographic diversity is to
have multiple of?ces.
Throughout this book, we will use a few prototype VC funds as example
investors. Because the compensation structures and partnership agreements of VCs
are an important driver of their investment incentives, it is useful to write down
some key terms from these agreements for our prototype funds. We do this in the
appendices to this chapter: Appendix 2.A shows some key terms for EarlyBird
Ventures Fund I, which is a $100M initial fund raised for an early-stage investor;
Appendix 2.B shows some key terms for Talltree Ventures IV, the $250M fourth
fund raised by a multistage ?rm; and Appendix 2.C shows some key terms for Owl
Ventures IX, a $500M ninth fund raised by a late-stage ?rm with a stellar reputation
and excellent track record. We will refer to these appendices several times in this
chapter and later on in the text.
Exhibit 2-1 gives a timeline for several funds for one of our prototype VC
?rms, EarlyBird Ventures (EBV).
2
A ?rm will usually number its successive funds,
so EarlyBird Ventures I is known to be the ?rst fund raised by EBV, EarlyBird
Ventures II was the second fund, and so on. In this example, EBV raises its ?rst
fund, EBV I, in 1994 with $100M in committed capital. (Think of EBV I as
the fund described in Appendix 2.A.) In future years, the performance of EBV I will
be compared to other funds raised in 1994; in industry parlance, all such funds
will have 1994 as their vintage year. This borrowed terminology from the wine
industry is appropriate: just as the weather conditions of certain years are better for
growing grapes, the economic conditions of certain years are better for growing
companies. By comparing the performance of EBV I with other funds of the same
vintage year, future investors can make a fair evaluation of EBV’s performance
as a GP.
3
2
All of our prototype funds are ?ctitious. Any resemblance to real funds, living or dead, are purely
coincidental. In case some readers are wondering, we were not aware at the time of writing this textbook
that there exists an actual early technology investment ?rm called Earlybird in Germany.
3
However, please note that some ?rms keep us on our toes by giving their funds a completely different
name from their ?rm name.
22 CHAPTER 2 VC PLAYERS
By 1998, most of EBV I has been invested. We assume here that EBV I look
good relative to other funds with a 1994 vintage year, so it is able to raise a larger
fund, EBV II, in 1998. It invests this fund rapidly in the boom years of 1999
and 2000 and returns to raise an even larger fund, EBV III, of $1 billion in 2000. By
2000, in addition to EBV III, it has two funds, EBV I and II, which are no longer
making any new investments but still have some investments outstanding. When
the market loses steam, it invests this fund slowly and with much less success than
its earlier funds. Nevertheless, its earlier reputation allows the ?rm to return to the
market, somewhat chastened, and raise a $300M fund, EBV IV, in 2005. By this
point, it has closed out all its investments from EBV I and is still trying to exit a
few investments from EBV II. As for EBV III, most of the portfolio companies
have gone out of business, but it still has modest hopes for some of the survivors.
Four years later, in 2009, EBV raises another $300M fund, EBV V, which is a
respectable size given the generally dif?cult fundraising conditions in the market.
EBV I and II are fully liquidated by then; EBV III is almost mature, but many of its
portfolio companies are still illiquid.
The experience of EBV is typical for top VC ?rms since the mid-1990s. Great
success for investments at the beginningof the boom, combinedwith seemingly endless
opportunities, led many ?rms to raise “megafunds” in 1999 and 2000. Whereas billion
dollar funds were unheardof before, theybecame almost commonplace duringthis time
period. With few exceptions, these funds performed terribly, and the surviving ?rms
have returned to raise much smaller funds in recent years.
We can gain a more detailed picture of these trends by looking at some data
from the National Venture Capital Association. Exhibit 2-2 gives its estimates on
the total number of ?rms, funds, and VC professionals since 1980.
This data echoes the industry cycles discussed in Chapter 1. Between 1997 and
2001, there was a doubling or near doubling of the total number of VC funds, the
total number of VC ?rms, and the size (capital divided by funds or ?rms) of these VC
funds and VC ?rms. The size of the industry hit a plateau in 2001 and stayed steady
between 2002 and 2006. The industry size started to decline in 2007, and between
EXHIBIT 2-1
EARLYBIRD VENTURES TIMELINE
Fund Name Vintage Year Committed Capital
Early Bird Ventures I 1994 $100M
Early Bird Ventures II 1998 $250M
Early Bird Ventures III 2000 $1B
Early Bird Ventures IV 2005 $300M
Early Bird Ventures V 2009 $300M
2.1 FIRMS AND FUNDS 23
2007 and 2008 the capital under management fell 24 percent, while the number of
?rms and the number of principals declined by 13 percent and 16 percent, respec-
tively. The contraction occurred because large funds raised in 2000 were largely
rolled out of the industry’s managed capital and were replaced by much smaller funds
EXHIBIT 2-2
VC INDUSTRY SIZE SINCE 1980
Year
New
Funds
New
Committed
Capital ($B)
Total
Funds
Total
Firms
Total
Committed
Capital ($B)
Total
Principals
(Estimate)
Principals
Per Firm
1980 52 2.0 129 92 4.1 1,435 15.6
1981 75 1.5 188 127 6.1 1,805 14.2
1982 87 1.7 248 162 7.8 2,138 13.2
1983 143 3.9 355 208 11.4 2,600 12.5
1984 116 3.0 459 260 14.6 3,224 12.4
1985 121 4.0 541 297 17.9 3,641 12.3
1986 103 3.8 603 332 21.5 4,038 12.2
1987 116 4.4 681 362 24.2 4,368 12.1
1988 104 4.4 715 377 25.5 4,550 12.1
1989 105 4.9 746 392 28.6 4,770 12.2
1990 87 3.2 734 393 29.2 4,834 12.3
1991 42 2.0 660 373 27.8 4,588 12.3
1992 80 5.2 620 365 28.4 4,563 12.5
1993 88 3.9 625 376 29.8 4,675 12.4
1994 140 8.9 651 389 34.7 4,824 12.4
1995 172 9.9 707 429 40.6 5,320 12.4
1996 162 11.8 773 469 48.9 5,769 12.3
1997 244 19.8 903 548 63.7 6,753 12.3
1998 288 29.7 1,085 624 92 7,550 12.1
1999 451 55.8 1,394 752 145.3 9,123 12.1
2000 653 105.0 1,737 881 225.2 10,684 12.1
2001 321 39.1 1,883 943 253.1 11,340 12.0
2002 206 9.3 1,852 938 253.1 11,186 11.9
2003 163 11.6 1,800 968 254.2 11,112 11.5
2004 219 19.8 1,823 1,003 262.9 10,896 10.9
2005 235 28.7 1,778 1,024 271.4 10,680 10.4
2006 241 31.8 1,722 1,027 278.1 10,260 10.0
2007 247 35.4 1,593 1,019 258.3 8,892 8.7
2008 210 27.9 1,366 882 197.3 7,497 8.5
Source: 2008 and 2009 NVCA Yearbooks.
24 CHAPTER 2 VC PLAYERS
raised in more recent years. Many ?rms that raised funds at the height of the bubble
are winding down their portfolios and exiting the industry, which also contributes to
the decline in the number of ?rms and principals. This trend is likely to continue for
some time to come. Note also that, even with two years of sharp declines, the capital
under management is still higher than the 1999 level.
In most years, the total number of funds is about twice as large as the number of
?rms, indicating that the average ?rm has two funds alive at any given time. Because of
differences in the data collection methods and sample selection, the committed-capital
amounts in Exhibit 2-2 are not directly comparable to the investment totals given in
Exhibits 1-3 and 1-4. Nevertheless, the general trends are very similar.
One striking aspect of these numbers is that there has been a steady rise in the
size of the capital managed per ?rm and per principal up until 2006À2007, while
the number of principals per ?rm itself held steady at around 12 between the mid
1980s and 2002 and even declined to 8.5 by 2008. Thus, the main trend has been a
gradual scaling up of the dollar amount managed per personnel, while the VC ?rms
themselves stayed relatively lean as organizations.
Relative to other investment and professional service ?rms, VC ?rms are quite
top-heavy and rarely showmuch of a pyramid structure. Althoughsome VCs enteredthe
industry directly out of school, most came to VC as a second career and entered
the profession at a fairly senior level, so there are not as many junior people ?oating
around. Although many people would like to know the best way to prepare for a VC
career, there is no “typical” path. Nevertheless, the analysis of hand-collected data on
125 partners from 15 VC ?rms in Wieland (2009) offers some interesting insights.
In this sample, 60 percent of VC partners hold a bachelor’s, master’s, or doc-
torate degree in science or engineering. Particularly common is a bachelor’s degree in
engineering, which 44 percent of the VCs hold. While 25 percent of VCs hold a
master’s degree and 9 percent hold a Ph.D. in engineering or science, the most
common postgraduate degree held by VCs are MBA degrees—62 percent hold them.
A signi?cant minority—16 percent—also hold a bachelor’s degree in business or
economics. As for their professional experience, most of the work experience of
individual VCs comes in the form of having worked in the IT or health care sector
(78%), having startup experience as either entrepreneur (37%) or managing executive
at a startup ?rm (32%), holding experience as line manager at a listed ?rm (38%),
having worked as industrial engineer (31%) or professional scientist (5%), having
worked for another VC ?rm as investment professional (32%), and holding experience
working as strategy consultant (23%) or in ?nance (14%).
4
Although an advanced
degree is not a necessary requirement, the most notable exceptions are second-career
VCs whose ?rst career was as a successful entrepreneur. Indeed, most VCs are in their
second career because few jobs are available to new graduates. These ?rst careers
might be decades long and consist of top management experience, or they might be
4
Zarutskie (2009) studies educational and professional backgrounds of ?rst-time VC funds and report
similar educational backgrounds: 39% of individual VCs hold a degree in either engineering or science
and 58% hold an MBA.
2.1 FIRMS AND FUNDS 25
just a few years long, consisting of a few years of experience at a consulting ?rm or at
an investment bank. Consulting and investment banking are not particularly good
ways to prepare for a VC career; it is just that many top MBA graduates start there, so
that is where the talent is. Many VCs will say that the best preparation for a VC career
is to combine technical expertise with industry experience, particularly if that
experience is at a startup ?rm. Many VC hopefuls are understandably reluctant to
follow this advice, because the VC industry has cyclical and somewhat ?ckle pre-
ferences about exactly what kind of technical experience is useful, and an unlucky
choice of specialization can render a candidate’s expertise to be super?uous.
As for the career progression, it does not have many levels. The top level is
“partner”, with modi?ers in front of that title to indicate experience, past success,
and compensation level (e.g., “Managing General Partner” or “Senior Partner”).
Although some professionals begin their VC careers as partners—either by raising
their own fund or by joining another fund after a very successful ?rst career—most
VCs have to work their way up. There are essentially two tracks to make partner.
One track, typically followed by younger professionals with a few years of pre-VC
experience, is to start as a junior VC with a title like associate, senior associate, or
principal. These professionals are not expected to lead transactions or sit on boards
in their ?rst few years, but rather spend most of their time screening investments,
performing due diligence, and generally helping out the partners. They are expected
to learn the business as apprentices, and if they are successful, their responsibilities
will be gradually increased. Depending on their past experience, the time path to
partnership can vary tremendously. With good timing and good performance, some
junior professionals can make partner in as little as two years. At the other extreme,
some ?rms do not treat these junior positions as being on the partner track, sending
even their most talented associates back out into the world to gain more experience.
Similarly, some ?rms employ recent college graduates as analysts, with tasks
similar to other junior VCs. Although these positions are generally not considered
to be on the partner track, analysts who go on to get advanced degrees have great
positioning to land a partner-track job in the future.
The second track, typically followed by successful entrepreneurs or senior
managers with many years of experience, is to enter with the title of venture
partner. This title does not mean that the new VC is a partner in the sense of sharing
the pro?ts, but rather it is a way to bring in someone trying out VC as a second
career without subjecting them to the same grind or title as a junior professional.
Venture partners would typically be expected to take a lead role on investments and
to use their industry contacts to bring in new business right from the beginning. In
this respect, venture partner is very much a provisional position, with many can-
didates ?nding out that the business is not really for them. With one or two suc-
cessful investments, a venture partner can expect to be admitted into a true partner
role. Indeed, venture partners are often paid only small salaries—the idea being that
if they are successful, they will quickly earn a partnership.
GPs receive their income from two sources—management fees and carried
interest—andthese sources must supply all the compensationfor the VCs. Base salaries
26 CHAPTER 2 VC PLAYERS
can be paid frommanagement fees, and the biggest slice of variable pay comes fromthe
carry. In most funds, the total carry percentage will be divided in advance, with partners
knowing what share of the overall carry they are due to receive. Exhibit 2-3 shows
compensationlevels for salary, bonus, andcarriedinterest for several different jobtitles.
These ?gures are from the annual Private Equity Analyst-Holt Compensation Survey,
which in 2008 received data from46 independent venture capital ?rms for 16 job titles.
Note that salaries are as of April 1st of the survey year, and bonus and carry are earned
the year before. Thus, these compensation levels re?ect fund performance in the year
prior to payment.
The levels are shown for 2008 and for 2009, so one can see the large role
played by market conditions. While the bonus levels are largely unchanged, bonus
and carry declined in 2009 due to dif?cult economic times and tough exit condi-
tions for VC-backed companies.
2.2 THE LIMITED PARTNERS
As mentioned in Chapter 1, the ?rst major burst of VC activity was driven by the
entry of pension funds as limited partners. Since 1980, pension plans—including
those of government entities, private companies, and nonpro?t organizations—have
provided 44 percent of the committed capital in the VC industry. In addition to
pension funds, several other investor groups have played an important role in the
EXHIBIT 2-3
VC COMPENSATION (IN $ THOUSANDS)
2008 2009
Title Salary Bonus Carry Total Salary Bonus Carry Total
Managing GP 688 633 192 1,513 700 350 101 1,151
Senior Partner 595 350 155 1,100 600 200 50 850
Partner 375 150 35 560 350 130 20 500
Principal/VP 240 78 2 320 206 75 6 287
Senior Associate 155 46 0 201 156 44 1 201
Associate 105 33 0 138 105 35 0 140
Analyst 101 15 0 116 100 10 0 110
Venture Partner 250 0 43 293 185 40 12 237
NOTE: 2008 data are April 1, 2008, salaries and bonus and carry earned in 2007. 2009 data are April 1,
2009, salaries and bonus and carry earned in 2008. The ?gures are based on annual compensaton surveys
of VC professionals and samples are not matched across years.
Source: Mike Holt, Founder and Managing Director of Holt Private Equity Consultants and coauthor of
Private Equity Analyst—Holt Compensation Survey.
2.2 THE LIMITED PARTNERS 27
development of VC. Exhibit 2-4 shows the fraction of newly committed capital
from these groups.
5
After pension funds, the next largest investor class is ?nancial institutions,
which includes commercial banks, investment banks, and insurance companies.
Taken together, this group has provided about 18 percent of the committed capital
since 1980. Endowments and foundations are next with 17 percent of the total. This
group is dominated by large private universities and charitable foundations. In
addition to their large supply of capital, these organizations are also the most
successful of the investor classes, with returns that far exceed those of the other
investors.
6
Part of the reason for their success is that they have been active and
consistent investors since the earliest partnerships were formed in the late 1960s
and early 1970s. However, evidence also shows that access to these older funds
EXHIBIT 2-4
COMMITTED CAPITAL BY LIMITED PARTNER TYPE
Pension Funds
Endowments &
Foundations
Individual and Family
Corporations
Financial & Insurance
70%
60%
50%
40%
30%
20%
10%
0%
Year 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
Source: National Venture Capital Association Yearbooks.
5
NVCA stopped reporting this type of data in recent years, but it appears that the fractions among the
groups have not changed signi?cantly. In 2004, the last year the data is publicly available, the breakdown
was pension funds (42%), ?nancial and insurance (25%), Endowments and foundations (21%), Indivi-
dual and family (10%), and Corporations (2%).
6
Lerner, Schoar, and Wongsunwai (2007) document this performance.
28 CHAPTER 2 VC PLAYERS
explains only part of their superior returns, and that the endowments have in fact
also done very well with their recent partnerships.
Since 1980, individuals and families have contributed about 11 percent of total
committed capital, with this fraction falling slightly in recent years. As compared to
other investment classes, this participation by individuals is low. Part of the reason
for this low participation is that the long horizon of VC investment is comparatively
more palatable to institutions than it is to individuals.
Finally, with only 9 percent of the total commitments since 1980, corpora-
tions have played a relatively small role as limited partners as compared to the
important role of their corporate pension plans. Note also that corporate partici-
pation is more variable than it is for other investors, and the importance of cor-
porate LPs has fallen dramatically in recent years. This type of indirect corporate
investment as an LP should not be confused with direct corporate investment in
portfolio companies, a practice that is known as corporate venture capital. Direct
corporate investment is not included in Exhibit 2-4, unless the corporation is
included as an LP in its own ?nite-life corporate VC fund. Because most corporate
VC funds are not organized as ?nite-life limited partnerships, the majority of direct
corporate investment is not included in this exhibit.
Exhibit 2-4 de?nes the fund ?ow by the ultimate source of capital, but in some
cases additional intermediaries stand between the capital provider and the VC. One
group of intermediaries deserves special mention: the fund-of-funds (FOF). An FOF
is typically organized as a limited partnership, with many of the same rules as other
private equity funds, except that, instead of investing directly in companies, the FOF
invests in other private-equity funds. For example, FLAG Venture Management is a
?rmthat invests exclusively in other VC?rms through FOFs. These FOFs can be quite
large: the 2000 Flag Venture Partners Fund IV has committed capital of $650M; other
boom-time FOFs raised multibillion dollar funds. FOFs appeal mostly to wealthy
individuals and small institutions that are not large enough to support a diversi?ed
portfolio of LP commitments. By pooling their resources in a FOF, a group of smaller
investors can gain access to a diversi?ed portfolio of funds and take advantage of the
contacts and skills of the specialized FOF intermediary. During the boom period,
FOFs intermediated about 5 percent of all commitments to VCfunds. FOF ?rms act as
both a GP (to their investors) and an LP (to the funds they invest in). As a GP, they also
charge management fees and (sometimes) carried interest, although these charges are
always considerably lower than those charged by direct investment ?rms.
It is important to note that LPs are not just investors, but also really are
partners in the fund. Although the day-to-day involvement of LPs is limited by law
(otherwise they can lose their limited-liability status), certain LPs are prized as
long-run partners, because they have the industry experience and patience to ride
out industry cycles and stick with their GPs. Such LPs make the fundraising task
much easier for GPs, yielding time savings that can be used to help portfolio
companies and to ?nd new investments.
For this reason, it is no accident that endowments and foundations held their
positions in the top VC funds even as other LPs were beating down the door. It is
2.2 THE LIMITED PARTNERS 29
true that during the boom many top GPs did raise their compensation; but it should
be noted that they did not raise it to market-clearing levels, instead choosing to keep
the same long-term LPs and exclude some newer money. In particular, families and
corporations are seen—perhaps justly—as ?ckle investors and are often shunned by
top GPs. In recent years, there has also been pressure on public pension funds and
public universities to reveal information about the performance of VCs in their
portfolio. A few of these LPs have been forced to reveal performance information,
and this disclosure is the source of some of the data analyzed in later chapters. For a
variety of reasons, most VCs abhor any kind of public disclosure, so a few of the
top GPs have started to bar public LPs from their funds.
2.3 VC PARTNERSHIP AGREEMENTS
Before we are able to understand VC investment decisions, we must ?rst have a
working knowledge of VC partnerships. The VC ?rm serves as the GP of the part-
nership and is compensated by management fees (discussed in Section 2.3.1) and
carried interest (discussed in Section 2.3.2). This compensation structure creates
some differences between the incentives of the GP and the LPs, and many partnership
agreements include several restrictive covenants to mitigate these differences (dis-
cussed in Section 2.3.3). Metrick and Yasuda (2010) analyze terms of fund part-
nership agreements for 94 VC funds and 144 buyout funds, which they obtained from
a large, anonymous LP (the “Investor”); all statistics in Sections 2.3.1 and 2.3.2 are
derived from this paper, and we will refer to this data as the “Investor” data.
2.3.1 Management Fees
VC investing is a long-run business, and investors must often wait many years
before enjoying any return of capital. Nevertheless, the expenses of VC investing
start immediately: salaries must be paid, the lights must stay on, and due diligence
must be performed. Thus, a baseline management fee is necessary. The typical
arrangement is for limited partners to start paying a set percentage of committed
capital every year, most commonly 2.0 percent. Sometimes this fee remains con-
stant for the full 10-year life of the fund, but in most cases the fee drops somewhat
after the ?ve-year investment period is over.
For any given VC fund, we de?ne the lifetime fees as the sum of the annual
management fees for the life of that fund. We de?ne the investment capital of the fund
as being equal to the committed capital of the fund minus the lifetime fees. For example,
Appendix 2.A shows that EBV is a $100M fund with a 10-year life and an annual
management fee of 2 percent for all 10 years. Thus, the fund has lifetime fees of $20M
(5 2% Ã $100M Ã 10 years) and investment capital of $80M (5 $100M2 $20M). As
is typical, in this case the lifetime fees are a nontrivial fraction of committed capital.
EBV will need to earn a 25 percent lifetime return on its investments ($20M on $80M
investment capital) just to earn back the fees and get to breakeven for its investors.
30 CHAPTER 2 VC PLAYERS
Our next example uses a more complex fee schedule.
EXAMPLE 2.1
Owl Ventures has raised their $500 M fund, Owl Ventures IX, with terms as given in
Appendix 2.C. The management fees given in this appendix are as follows.
Management Fees All management fees are computed based on committed capital.
These fees are 2 percent in years 1 and 2, 2.25 percent in years 3 and 4, 2 percent in year 5,
1.75 percent in year 6, 1.50 percent in year 7, 1.25 percent in year 8, 1 percent in year 9, and
0.75 percent in year 10. These fees will be paid quarterly, with equal installments within each
year.
Problem Given this description, what are the lifetime fees and investment capital for this
fund?
Solution This example uses a fee schedule that starts at 2 percent, and then increases to
2.25 percent in years 3 and 4 before falling by 0.25 percent in each subsequent year. Such
“increasing then decreasing” schedules are not unusual, with the logic that fund expenses
often reach their maximum in the middle years of the investment period. To compute the
lifetime fees, we just add up the fees in each year. Thus,
Lifetime fees ¼ committed capital à ð0:02 þ0:02 þ0:0225 þ0:0225 þ0:02 þ0:0175
10:015 þ0:0125 þ0:01 þ0:0075Þ
¼ committed capital à 0:1675 ¼ $500Mà 0:1675 ¼ $83:75M
ð2:1Þ
Then,
Investment capital ¼ committed capital 2lifetime fees ¼ $500M2$83:75M
¼ $416:25M
ð2:2Þ
’
This example follows the industry’s standard practice of computing man-
agement fees on committed capital. At ?rst glance, this method might seem strange,
because other parts of the money management industry have management fees that
are computed based on the market value of the portfolio. Why are VC funds
different?
There are several reasons. First, if management fees were to be based on
portfolio values, then these fees would be low in the ?rst few years (before all the
capital was invested), and the VCs might be unable to cover their ?xed costs.
Second, management fees based on portfolio value would create an incentive for
VCs to invest quickly—and this would result in an inevitable sacri?ce in quality.
Third, because “market” values for the portfolio are hard to calculate for nontraded
companies, the level of fees would be somewhat arbitrary.
Although the computation of management fees on committed capital is the
most standard arrangement, there are other methods. To understand these other
2.3 VC PARTNERSHIP AGREEMENTS 31
methods, we introduce a few new de?nitions. First, realized investments are those
investments that have been exited or those in companies that have been shut down,
and unrealized investments are those investments that have not yet been exited in
companies that still exist. Next, we de?ne the cost basis of an investment as being
equal to the dollar amount of the original investment. Finally, we de?ne invested
capital as the cost basis for the investment capital of the fund that has already been
deployed, and net invested capital is equal to invested capital minus the cost basis
of realized and written-off investments. It is this ?nal de?nition that is most
important for alternative fee structures, for it is common (about 43% of VC funds in
the Investor data employ this rule) to see the management fee base change from
committed to net invested capital after the ?ve-year investment period is over. This
hybrid system minimizes the incentive for ?rms to overinvest in early years,
because the fee is still ?xed for that time period. Also, because it relies on the cost
basis of the investments, it does not require the estimation of market values. In
Exercise 2.2, at the end of this chapter, you are asked to solve for the lifetime fees
for a fund that uses this hybrid system.
There are two other points worth mentioning. First, although management
fees cover most operating expenses, they do not usually cover all of them, and the
LPs will still ?nd that some of their investment capital is going to uses other than
investments. These other operating expenses charged to the fund might include the
organizational costs of setting up the fund, costs of unconsummated transactions,
and certain kinds of professional service expenses. Second, our calculations
assumed that exit proceeds cannot be reinvested into new portfolio companies. In
theory, however, most contracts allow GPs limited reinvestment rights, subject to
certain requirements being met. (The most common requirement would be that the
original investment was exited quickly, such as within one year.) In practice, these
requirements are stringent enough that signi?cant reinvestment is rare. When
reinvestment does occur, the sum of investment capital and lifetime fees would be
greater than committed capital. However, because reinvestment does not incur any
additional management fees, the economics of the reinvestment decision are a bit
different from the economics of the original investment. We will address this
possibility in Exercise 10.1 in Chapter 10.
2.3.2 Carried Interest
The other form of VC compensation is the carried interest, often referred to
simply as the carry. Carried interest enables GPs to participate in the pro?ts of the
fund, and historically it has provided the largest portion of GP compensation.
The basic idea is simple: if the investors commit $100 million to the fund, and total
exit proceeds are $200 million, then the total pro?t is $200M 2 $100M 5 $100M.
If such is the case, then a GP with 20 percent carried interest would receive $20
million of this pro?t. Indeed, this simple example tells a lot of what we need to
know about carried interest. Nevertheless, there are many variations of this basic
story, and these variations are often important and contentious points of
32 CHAPTER 2 VC PLAYERS
negotiation. Variations occur in the percentage level of the carried interest, the
carried interest basis (5 carry basis), the timing of the carried interest, priority
returns, and clawbacks. These terms are de?ned in the following paragraphs.
The most important variation concerns the percentage level of carried
interest. The vast majority of all VC ?rms receive a 20 percent carry. The Investor
data indicates that 95 percent of VC funds had a 20 percent carry, and this per-
centage was equally high if not higher in the past.
7
Indeed, 20 percent is the focal
point for the entire private equity industry and for many other partnership structures
in the investment industry. There is no consensus on the origins of 20 percent as the
focal point for risk-capital pro?t sharing; some industry analysts point to practices
in the oil and gas industry earlier in the 20th century, and others trace the roots back
to Venetian merchants in the late Middle Ages.
8
An 80À20 split even appears in the
book of Genesis.
9
Despite these historical ties, a few successful VCs have managed to buck the
trend, particularly for partnerships raised during the boom period. The Private
Equity Analyst reports that over two dozen GPs of VC funds receive carried interest
of 25 or 30 percent.
10
Some of these high-charging VCs will be discussed in
Chapter 5, along with some of their famous investments and the astronomical
returns they have earned. The remainder of the non-20 percent crowd earns a carry
between 20 and 25 percent, or receives carry on a sliding scale, with 20 percent
earned at ?rst, and some higher number (typically 25%) if certain performance
targets are met.
There is also variation in the carried interest basis, which is the threshold that
must be exceeded before the GPs can claim a pro?t. The majority of ?rms compute
pro?ts as the difference between exit proceeds and committed capital. Committed
capital is used as the basis by 94 percent of VC funds (and 83% of the buyout
funds) in the Investor data, and this has become more of an industry standard over
time. The other 6 percent of funds have the more GP-friendly basis of investment
capital, which enables pro?ts to be de?ned without consideration for fees. For a
pro?table fund with 20 percent carried interest, $100M in committed capital, $20M
in lifetime fees, and $80 million in investment capital, the $20M basis difference
between committed and investment capital would yield a difference in $20M Ã
0.20 5 $4M in carried interest over the life of the fund.
7
See Metrick and Yasuda (2010) and Gompers and Lerner (1999). Most commentators believe that the
percentage will be heading up again as terms become more LP friendly in the postboom period.
8
See Metrick and Yasuda (2010) and also Kaplan (1999).
9
Gen. 47:23-24: “Joseph said to the people, ‘Now that I have bought you and your land today for
Pharaoh, here is seed for you so you can plant the ground. But when the crop comes in, give a ?fth of it to
Pharaoh. The other four-?fths you may keep as seed for the ?elds and as food for yourselves and your
households and your children.’ ” If you read the rest of this Genesis chapter, you will see that Joseph was
acting more as a distress investor than as a VC.
10
Private Equity Analyst, September 1999.
2.3 VC PARTNERSHIP AGREEMENTS 33
EXAMPLE 2.2
A VC ?rm is considering two different structures for its new $100 M fund. Both structures
would have management fees of 2.5 percent per year (on committed capital) for all 10 years.
Under Structure I, the fund would receive a 25 percent carry with a basis of all committed
capital. Under Structure II, the fund would receive a 20 percent carry with a basis of all
investment capital.
Problems
(a) Suppose that total exit proceeds from all investments are $150M over the entire life of
the fund. How much carried interest would be earned under each of these two structures?
(b) For what amount of exit proceeds would these two structures yield the same amount of
carried interest?
Solutions
(a) Under Structure I, the GPs would receive 25 percent of the pro?ts, where pro?ts are de?ned
as the proceeds above committed capital. Therefore, the carried interest under Structure I would
be 0.25 Ã (150 À100) 5 $12.5 M. Under Structure II, the GPs would receive 20 percent of the
pro?ts, where pro?ts are de?ned as the proceeds above investment capital. Given a 2.5 percent
management fee for all 10 years, the lifetime fees are 2.5% Ã 100 M Ã 10 years 5 $25 M, so
investment capital is $100 M2 $25 M5 $75 M. Therefore, the carried interest under Structure
II would be 0.20 Ã (150 2 75) 5 $15 M.
(b) Let Z be de?ned as the total proceeds from all investments. Then, using the solution to
part (a), we can see that the formulas for carried interest under Structures I and II are
Total carried interest under Structure I ¼ 0:25 Ã ðZ2100Þ ð2:3Þ
and
Total carried interest under Structure II ¼ 0:20 Ã ðZ275Þ ð2:4Þ
We next solve for the Z that equates the carried interest under both structures:
0:25 Ã ðZ2100Þ ¼ 0:20 Ã ðZ275Þ -0:05 Ã Z ¼ 10 -Z ¼ 200 ð2:5Þ
When total exit proceeds 5Z 5200, then both structures would provide 0.25 Ã (200 2100) 5
0.20 Ã (200 2 75) 5 $25 M in carried interest.
’
The level and basis of carried interest are the main determinants for the total
dollar amount of GP carried interest. These terms determine how the “pie” of
proceeds is split between the GPs and the LPs. In addition, there are also several
possible methods for the timing of carried interest. Although these methods do not
usually affect the share of the total pie earned by the GP, they do affect how quickly
that pie can be eaten. Because a basic tenet of ?nance is that money now is worth
more than money later, GPs prefer methods that enable them to receive their carried
interest portion as soon as possible.
34 CHAPTER 2 VC PLAYERS
The most LP-friendly method is to require that the whole basis be returned to
LPs before any carried interest is paid. This method is used by about 25 percent of
the funds in the Investor data. To see how timing matters, imagine that this method
was in place for Example 2.2. In that example, we considered two possible
structures for carried interest: Structure I with 25 percent carry and a basis of
committed capital, and Structure II with 20 percent carry and a basis of investment
capital. In part (b) of that example, we found that total exit proceeds of $200M
would lead to $25M of carried interest under both of the proposed structures, with
the remaining $175M going to LPs. Although the $200M pie is shared the same in
both cases, the timing is not. Under structure I, the LPs receive their whole basis of
$100M before all proceeds above $100M are split 75/25. Under structure II, the LPs
also receive their whole basis (only $75M in this case) before all proceeds above
$75M are split 80/20. Thus, GPs get their ?rst dollar more quickly under structure
II, and at any time in the distribution of $200M of total proceeds, structure II will
always have paid at least as much carried interest as structure I.
To understand the alternative methods of carry timing, we make use of the
de?nition of invested capital (introduced in Section 2.3.1) and the related concept of
contributed capital, with the latter being de?ned as the portion of committed capital
that has already been transferred from the LPs to the GPs. Thus, contributed capital is
equal to invested capital plus any management fees paid to date. Analogous to net
invested capital, net contributed capital is equal to contributed capital minus the
cost basis of any realized and written-off investments. According to the Investor data,
another 75 percent of VC funds allow some form of early carry distribution. One such
method only requires the return of either invested capital or contributed capital before
any carried interest can be earned. Clearly, this timing method is more GP-friendly
than requiring the return of the whole basis. Another method, which lies somewhere
between the “return the whole basis” and “return only the invested/contributed
capital” methods, requires the return of invested or contributed capital plus priority
returns. This is fairly common and is found in about 45 percent of VC funds in the
Investor data.
Priority returns—also called preferred returns or hurdle returns—are
another factor affecting the timing of carried interest. With a priority return, the
GP promises some preset rate of return to the LPs before the GPs can collect any
carry. The Investor data indicates that 45 percent of VCs promise some kind of
priority return. Among these funds, 8 percent (per year) return is the most
common, with 71 percent of all funds with priority returns choosing 8 percent;
others range from 5 percent to 10 percent. Priority returns are relatively rare in
funds that focus on early-stage investing, and relatively common in funds that
focus on late-stage investing. It is important to note, however, that the priority
return usually affects the timing and not the total amount of carried interest.
Most priority returns also have a catch-up provision, which provides the GPs
with a greater share of the pro?ts once the priority return has been paid. With a
catch-up, the GP receives this greater share until the preset carry percentage has
been reached.
2.3 VC PARTNERSHIP AGREEMENTS 35
As an illustration of priority returns with a catch-up, consider a $100M fund
with a carry percentage of 20 percent, a carry basis of all committed capital, a
priority return of 8 percent, and a 100 percent catch-up. We’ll keep things simple
and imagine that all committed capital is drawn down on the ?rst day of the
fund, and that there are total exit proceeds of $120M, with $108M of these proceeds
coming exactly one year after the ?rst investment, $2M coming one year later, and
$10M coming the year after that. Under these rules, all $108M of the original
proceeds would go to the LPs. This distribution satis?es the 8 percent hurdle rate
requirement for the $100M in committed capital. One year later, the catch-up
provision implies that the whole $2M would go to the GPs; after that distribution
they would have received 20 percent ($2M) out of the total $10M in pro?ts. For the
?nal distribution, the $10M would be split $8M for the LPs and $2M for the GPs.
Beyond this simple example, the calculations quickly become unwieldy to
handle without a spreadsheet. The key takeaway is that even with a priority return,
the GPs still receive the same fraction of the pro?ts as long as the fund is suf?-
ciently pro?table. In this example, the fund made $20M of pro?ts ($120M of
proceeds on $100M of committed capital), and the GPs received 20 percent ($4M)
of these pro?ts. If, however, the fund had only earned $8M or less of pro?ts over
this time period, then all these pro?ts would have gone to the LPs.
In all but two of all funds with a priority return, there is some catch-up pro-
vision for the GPs. In the two exceptions, there is no catch-up, and thus the GP only
earns carried interest on the portion of pro?ts above the priority return. The absence
of a catch-up affects the share of the pie for the GP, not just the timing of that share.
In the preceding example, having no catch-up would have meant that the GP would
have received only 0.20 Ã ($120M 2 $108M) 5$2.4M of total carried interest.
Finally, some funds require the return of only a portion of contributed (or
invested) capital. For example, one common method is to require the return of the
cost basis of all realized investments, plus all management fees to date and any
write downs (partial losses) known to exist among the unrealized investments. In
most cases, this method is combined with a so-called fair-value test. This test
requires that the estimated values of remaining portfolio investments exceed a
preset percent (e.g., 120%) of the cost basis of these investments. The fair-value test
is found in 14 percent of the Investor data.
The early payment of carried interest can cause complications if the fund starts
off strong but weakens later in life. For example, suppose that a $100M fund has a 20
percent carried interest with a basis of all committed capital, but allows carried
interest to be paid as long as contributed capital has been returned. Then, consider
what happens if the fund is three years into its life, contributed capital is $50M, and it
receives $60M as the proceeds from its ?rst exit. Given the carried interest rules, the
fund would return the ?rst $50M to its LPs, and the remaining $10M would be split
as $8M for the LPs and $2M for the GPs. Now, fast forward ahead to the end of the
fund seven years later, and assume that there were no more exits. Contributed capital
is now the full $100M of committed capital, but the LPs have only received back the
$58M from the ?rst and only exit. According to the rules of carried interest basis,
36 CHAPTER 2 VC PLAYERS
the LPs are entitled to all the exit proceeds up to $100M. This means they need some
way to get the carried interest back from the GPs.
This refund of carried interest is accomplished with a contractual provision
evocatively known as a clawback. There are a variety of ways that clawbacks can
be designed. In practice, however, this implementation can be complicated by many
factors—for example, what if the GPs do not have the money when it comes time to
pay?—so LPs often insist (and receive) contractual guarantees to be paid back from
the individual GPs. The contract also needs to specify whether the clawback will be
net or gross of taxes that the GPs have already paid. Clawbacks become even more
of an issue when there is a priority return—it is easy to imagine how the priority
return might be exceeded in early years but missed in later years. The details here
are too messy for a simple numerical example, so we will use a spreadsheet
example to demonstrate. This exercise also allows us to see how management fees
and carried interest are computed in a more realistic setup.
EXAMPLE 2.3
Owl Ventures has raised their $500 M fund, Owl Ventures III, with terms as given in
Appendix C of this chapter. The terms for carried interest and for the general partner
clawback are
Distributions Distributions in respect of any partnership investment will be made in
the following order of priority:
(i) 100% to the limited partners until they have received an amount equal to their
contributed capital:
(ii) 75% to the limited partners and 25% to the general partners.
General Partner Clawback Obligation Upon the liquidation of the fund, the general
partner will be required to restore funds to the partnership to the extent that it has received
cumulative distributions in excess of amounts otherwise distributable pursuant to the
distribution formula set forth above, applied on an aggregate basis covering all partnership
investments, but in no event more than the cumulative distributions received by the general
partner solely in respect of its carried interest.
Problem Construct an example of fund performance where the clawback provision
would be triggered. In this example, compute the carried interest paid in each year and show
the total amount that must be paid back by the GPs on the liquidation of the ?rm.
Solution Cutting through the legal language, these terms mean that Owl is getting 25
percent carried interest, the carry basis is committed capital, the timing method uses contributed
capital, and there is a clawback at the end of the fund if too much carry has been paid. Exhibit 2-5
shows the spreadsheet output for an example with the clawback provision triggered. ’
In this example, we assume that the investment capital is distributed evenly in
each of the ?rst ?ve years. The returns in year 1 are fantastic, with investments
tripling in value and exited at the end of year 2. These realizations can be seen in the
2.3 VC PARTNERSHIP AGREEMENTS 37
row labeled “distributions” in Exhibit 2-5 and are equal to $250M in year 2. Because
only $186.5M has been contributed by this time (see the “contributed capital” row for
year 2), the GPs are entitled to 25 percent carried interest on the “pro?ts” of $250M
less $186.5M. This carried interest, shown in the “distributions to GPs” row, is equal
to $15.9M.
Following this great year, the investments perform terribly. The spreadsheet
assumes that all investments lose half their value each year, and later distributions are
low to re?ect this poor performance. The formula in the spreadsheet has 10 percent of
portfolio value being distributed in years 3 and 4, with 40 percent (of whatever
remains in each year) being distributed in the remaining years. There are no further
distributions to GPs during the remaining life of the fund.
Upon liquidation of the fund after year 10, we see that contributed capital has
reached the committed capital level of $500M, but that the cumulative distribution to
the LPs is only $344.0M. The clawback provision is thus triggered, and the GPs are
obligated to return all $20.9M of carried interest. In practice, it probably would have
been clear much earlier to all parties that the clawback would be necessary—and to
EXHIBIT 2-5
HYPOTHETICAL CLAWBACK EXAMPLE FOR OWL VENTURES
Year 1 2 3 4 5 6 7 8 9 10 close
Investments 83.3 83.3 83.3 83.3 83.3 0.0 0.0 0.0 0.0 0.0 0.0
Estimated
portfolio value
83.3 333.3 124.9 139.4 146.0 43.8 13.1 3.9 1.2 0.4 0.1
Distributions 0.0 250.0 12.5 13.9 58.4 17.5 5.3 1.6 0.5 0.1 0.1
Cumulative
distributions
0.0 250.0 262.5 276.4 334.8 352.4 357.6 359.2 359.7 359.8 359.9
Distributions to
GPs
0.0 15.9 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Cumulative
distributions to
GPs
0.0 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9 15.9
Distributions
to LPs
0.0 234.1 12.5 13.9 58.4 17.5 5.3 1.6 0.5 0.1 0.1
Cumulative
distributions to
LPs
0.0 234.1 246.6 260.6 319 336.5 341.7 343.3 343.8 343.9 344
Port value after
capital returned
83.3 83.3 112.4 125.5 87.6 26.3 7.9 2.4 0.7 0.2 0.0
Management fee 10.0 10.0 11.3 11.3 10.0 8.8 7.5 6.3 5.0 3.8 0.0
Contributed capital 93.3 186.5 281.0 375.5 468.8 477.5 485.0 491.3 496.3 500.0 500.0
Invested capital 83.3 166.5 249.8 333.0 416.3 416.3 416.3 416.3 416.3 416.3 416.3
Clawback 15.9
38 CHAPTER 2 VC PLAYERS
solve this problem, the GPs could give the money back earlier or just reduce the
management fees to zero for the last few years.
2.3.3 Restrictive Covenants
A VC fund is a long-term commitment. LPs tie up capital with no promise of a
return and little control over the investment activities of the GP. Although the
compensation of the GPs does go some distance toward aligning the incentives of
all parties, several potential problems still exist. Over time, LPs have used a variety
of restrictive covenants in an attempt to mitigate these problems.
Gompers and Lerner (1996) wrote the only academic study of restrictive cove-
nants. Exhibit 2-6 reproduces part of a table from their analysis. They divide covenants
into three broad categories: (1) restrictions on management of the fund, (2) restrictions
on the activities of the GP, and (3) restrictions on the types of investment.
Examples from the ?rst broad category can be seen in each of the sample
agreements in the appendices to this chapter. For example, EBVand Talltree both have
EXHIBIT 2-6
RESTRICTIVE COVENANTS FOR VC FUNDS
Description % of Contracts
Covenants relating to the management of the fund:
Restrictions on size of investment in any one ?rm 77.8
Restrictions on use of debt by partnership 95.6
Restrictions on coinvestment by organization’s earlier or later funds 62.2
Restrictions on reinvestment of partnership’s capital gains 35.6
Covenants relating to the activities of the general partners:
Restrictions on coinvestment by general partners 77.8
Restrictions on sale of partnership interests by general partners 51.1
Restrictions on fund-raising by general partners 84.4
Restrictions on other actions by general partners 13.3
Restrictions on addition of general partners 26.7
Covenants relating to the types of investment:
Restrictions on investments in other venture funds 62.2
Restrictions on investment in public securities 66.7
Restrictions on investments in leveraged buyouts 60.0
Restrictions on investments in foreign securities 44.4
Restrictions on investments in other asset classes 31.1
Total number of partnership agreements in sample 45
Average number of covenant classes 7.9
Average number of covenant classes (weighted by fund size) 8.4
Source: Gompers and Lerner (1996).
2.3 VC PARTNERSHIP AGREEMENTS 39
restrictions for the maximumpercentage of the fundto be invested in any one company.
Exhibit 2-6 shows that similar restrictions were in place in 78 percent of all
sample funds. Why would LPs insist on this restriction? An obvious answer to
this question is “to put a limit on risk”, but this answer is unsatisfying. The
typical investor in VC funds is a large institutional investor who is allocating
only a small portfolio fraction to any particular VC fund; the difference between
25 percent or 50 percent of that allocation going to one speci?c company would
barely affect the risk exposure for their broad portfolio. Instead, the main justi-
?cation for investment limits is related to the incentives of the GPs, speci?cally
the incentives induced by carried interest.
To illustrate the incentive problem, consider the ?ctitious case of Derby
Ventures. The GP of Derby Ventures makes “investments” by placing bets on
horses at a racetrack. This GP has an excellent track record from past bets, and his
LPs expect him to make dozens of small bets so that the law of large numbers
allows his superior skill to show through. The LPs expect this behavior, but it is not
written into the partnership agreement. Now assume that besides being very
knowledgeable about horses, this GP is also a savvy gambler. He realizes that his
superior knowledge would probably be able to produce 20 percent returns on
capital over the next year, giving him a few percentage points in carried interest,
but perhaps not enough to make it worth his while to quit his regular job as a
professor. Alternatively, he can put all his money on one horse, perhaps a ten-to-
one “long shot”. If the horse wins, then the carried interest earned in one day would
be enormous. If the horse loses—well, he can just go back to teaching his classes.
This example captures the main incentive problem for carried interest: it
provides an upside to the GP without the corresponding downside. In option-pricing
language, the GPs effectively hold a call option on the fund portfolio. Readers
familiar with options will know that call options are more valuable when the
underlying security has higher volatility. Thus GPs, as holder of the carried interest
“call option”, have an incentive to increase volatility by betting a lot on one horse,
or investing a lot in one company. (For readers unfamiliar with options, fear not: we
will beat that horse to death starting in Chapter 13.)
The same insight can help us understand the common restriction against funds
taking on debt (96 percent of sample funds). By taking on debt, a fund can amplify the
returns on its portfolio, an ampli?cation that increases risk and, correspondingly,
increases the value of the carried-interest call option. LPs can rein in these adverse
incentives through the use of covenants, but a formal restriction is not always neces-
sary. An alternative approach is to rely on the GPs’ unwillingness to risk their
“reputational capital”. For GPs with a long history and lucrative future—as we assume
exists for Owl Ventures, now on their ninth fund—it may no longer be necessary to
formally restrict their risk-taking behavior. If Derby Ventures fails, its GP can just go
back to teaching. If Owl Ventures fails, then a valuable franchise has been lost.
With 62 percent of sample funds, restrictions on coinvestment with earlier or
later funds by the same partnership are also common. LPs may decide to restrict such
coinvestment to avoid one fund propping up the performance of another. This can be
40 CHAPTER 2 VC PLAYERS
of particular concern around the time that a GP is fundraising for a new fund. For
example, suppose that EBV is trying to raise EBV III, and it is three years into its
investment period on Fund II and seven years into the life of Fund I. Now, when it goes
on the fund-raising trail, potential LPs will scrutinize the performance of Fund I, but
not expect much of the still young Fund II. If Fund II can help Fund I by giving some
newmoney to an otherwise failing company, then the interimreturns of Fund I would
be helped, at the expense of Fund II’s investors.
Our second category of covenants is one that involves restrictions on the
activities of the GP. In general, the covenants in this class are designed to ensure
that the GP’s attention stays focused on the whole portfolio of fund investments.
For example, restrictions on coinvestment by general partners (78 percent of
sample funds) might seem to be counterproductive—shouldn’t LPs be happy to see
GPs with their own money at stake? The problem here is that GPs may focus
excessively on the few investments with a personal stake while ignoring the other
investments. In this case, the GPs may use the fund simply as an opportunity to
cherry-pick a few great investments for themselves. One way to restrict this
practice is for LPs to insist that any personal investments by GPs be proportional
across all fund investments.
Another way to keep the GPs’ attention is to restrict them from raising
another fund before they have invested the present one (84 percent of sample
funds). This is of particular concern for debut funds like EBV, where the GPs may
want to make a quick return to the market to raise larger funds and achieve critical
mass for the management fee.
The third category of covenants includes restrictions designed to keep GPs
focused on the type of investing that they have been hired to do. LPs do not like to
see a GP who was hired to be a VC suddenly turn into an investor in LBOs, public
equities, distressed debt, or other VC funds. This motivation to switch focus can be
surprisingly strong during times of market upheaval. For example, venture perfor-
mance was poor and LBOs were hot in the mid-1980s. Many VCs wanted to try their
hand at this new activity, but the skill set was quite different, and anecdotal evidence
suggests that VCs’ performance in LBOs was terrible. A similar motivation occurred
in the postboom period. As with the other categories of covenants, a strong reputation
and franchise value can reduce the need for formal covenants. However, here even
some of the most famous names in private equity can be tempted to lose their focus,
as was seen many times during the boom and postboom periods.
SUMMARY
The VC fund, organized as a limited partnership, is the main vehicle for VC investing. The
general partner (GP) of a VC fund is a VC ?rm, and the limited partners (LPs) are usually
institutional investors, with pension funds supplying just under half of the total committed
capital in the industry. In the postboom period, there were about 900 active VC ?rms and
1,800 active VC funds.
SUMMARY 41
GPs are compensated with management fees and carried interest. Management fees
are usually about 2.0 percent per year, calculated on the basis of committed capital. Carried
interest—the pro?t participation—is most commonly set at 20 percent of all fund pro?ts.
This compensation structure is designed to help align the incentives of GPs and LPs. To get a
better alignment of incentives, LPs often restrict GP behavior with covenants written into the
partnership agreement.
KEY TERMS
VC firm
General partner (GP)
VC fund
Limited partner (LP)
Capital call
5 Drawdown
5 Takedown
Committed capital
Investment period
5 Commitment period
Follow-on investments
Early-stage fund, late-stage
fund, multistage fund
Raised, closed
Vintage year
Fund-of-funds (FOF)
Management fees
Lifetime fees
Investment capital
Invested capital, net
invested capital
Carried interest
5 Carry
Carried interest basis
5 Carry basis
Contributed capital, net
contributed capital
Priority returns
5 Preferred returns
5 Hurdle returns
Realized returns, unrealized
returns
Catch-up provision
Clawback
Restrictive covenants
Call option
REFERENCES
Gompers, Paul A. and Joshua Lerner, 1996, “The Use of Covenants: An Empirical Analysis of Venture
Partnership Agreements”, Journal of Law and Economics 39(2), 463À498.
Gompers, Paul A. and Joshua Lerner, 1999, “An analysis of compensation in the U.S. venture capital
partnership”, Journal of Financial Economics 51, 3À44.
Kaplan, Steven N., 1999, “Accel VII”, Unpublished case study, available online at http://gsbwww.
uchicago.edu/fac/steven.kaplan/teaching/accel7.pdf.
Lerner, Joshua, Antoinette Schoar, and Wan Wong, 2007, “Smart Institutions, Foolish Choices? The
Limited Partner Performance Puzzle”, Journal of Finance 62(2), 731À764.
Metrick, Andrew and Ayako Yasuda, 2010, “The Economics of Private Equity Funds”, Review of
Financial Studies 23, 2303À2341.
Venture Economics, National Venture Capital Association Yearbook, various years.
EXERCISES
2.1 Suppose that a $200M VC fund has a management fee of 2.5 percent per year for the ?rst
?ve years, with a reduction of 0.25 percent (25 basis points) in each year thereafter. All fees
are paid on committed capital, and the fund has a 10-year life. What are the lifetime fees and
investment capital for this fund?
42 CHAPTER 2 VC PLAYERS
2.2 (This is a little bit tricky.) Suppose that a $1B VC fund has fees of 2.0 percent per year in
all years, with these fees paid on committed capital in the ?rst ?ve years and on net invested
capital for years 6 through 10. You can assume the fund is fully invested by the beginning of
year 6, then realizes 20 percent of its investment capital in each of the following ?ve years.
What are the lifetime fees and investment capital for this fund? (Make assumptions for any
information that you think is still missing from the problem.)
2.3 A VC ?rm is considering two different structures for its new $250M fund. Both struc-
tures would have management fees of 2 percent per year (on committed capital) for all 10
years. Under Structure I, the fund would receive an X percent carry with a basis of all
committed capital. Under Structure II, the fund would receive a Y percent carry with a basis
of all investment capital. For a given amount of (total) exit proceeds 5 $Z, solve for the
amount of carried interest under both structures.
2.4 Talltree Ventures has raised their $250M fund, Talltree Ventures IV, with terms as given in
Appendix 2.B of this chapter. Construct an example of fund performance where the clawback
provision would be triggered. In this example, compute the carried interest paid in each year, and
show the total amount that must be paid back by the GPs upon the liquidation of the fund.
APPENDICES: KEY TERMS AND CONDITIONS
FOR THREE VC FUNDS
These appendices give excerpts from the private placement memoranda for three
(?ctional) VC funds: EarlyBird Ventures I (EBV I) [Appendix 2.A], Talltree
Ventures IV [Appendix 2.B], and Owl Ventures IX [Appendix 2.C]. We will refer
to these appendices throughout the book. All these excerpts are derived from a
more complete memorandum given in Kaplan (1999).
Appendix 2.A: EarlyBird Ventures I
Fund Size $100 million
Term Following the tenth anniversary of the initial closing, the term of the
partnership will expire on December 31st unless extended for up to two consecutive
one-year periods at the discretion of the general partner. This is to permit orderly
dissolution, and no management fees will be charged during any such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st, except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees The annual contributions will equal 2 percent of committed
capital for the ?rst 10 years of the fund. These contributions will be paid quarterly.
APPENDICES: KEY TERMS AND CONDITIONS FOR THREE VC FUNDS 43
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital.
(ii) 80 percent to the limited partners and 20 percent to the general partners.
Diversi?cation and Investment Limits The Fund may not invest more
than 25 percent of aggregate commitments in any single portfolio company.
Appendix 2.B: Talltree Ventures IV
Fund Size $250 million
Term Following the tenth anniversary of the initial closing, the term of the
partnership will expire on December 31st, unless it is extended for up to two
consecutive one-year periods at the discretion of the general partner. This is to
permit orderly dissolution, and no management fees will be charged during any
such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees The annual contributions will equal 2 percent of com-
mitted capital for the ?rst 10 years of the fund. These contributions will be paid
quarterly.
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital, plus a priority return equal to 8 percent (compounded
annually).
(ii) 100 percent to the general partner until the general partner has received catch-
up distributions equal to 20 percent of the sum of such distributions and the
preference distributions in part (i).
(iii) 80 percent to the limited partners and 20 percent to the general partner.
General Partner Clawback Obligation Upon liquidation of the fund, the
general partner will be required to restore funds to the partnership to the extent that it
has received cumulative distributions in excess of amounts otherwise distributable
44 CHAPTER 2 VC PLAYERS
pursuant to the distribution formula set forth above, applied on an aggregate basis
covering all partnership investments, but in no event more than the cumulative dis-
tributions received by the general partner solely in respect of its carried interest.
Diversi?cation and Investment Limits The fund may not invest more
than 20 percent of aggregate commitments in any single portfolio company.
Appendix 2.C: Owl Ventures IX
Fund Size $500 million
Term Following the 10th anniversary of the initial closing, the term of the
partnership will expire on December 31st unless extended for up to two consecutive
one-year periods at the discretion of the general partner. This is to permit orderly
dissolution, and no management fees will be charged during any such extension.
Commitment Period Following the ?fth anniversary of the initial closing,
all partners will be released from any further obligation with respect to their
unfunded commitments on December 31st except to the extent necessary to cover
expenses and obligations of the partnership (including management fees) in an
aggregate amount not to exceed unfunded commitments.
Management Fees All management fees are computed based on committed
capital. These fees are 2 percent in years 1 and 2, 2.25 percent in years 3 and 4, 2
percent in year 5, 1.75 percent in year 6, 1.50 percent in year 7, 1.25 percent in year
8, 1 percent in year 9, and 0.75 percent in year 10. These fees will be paid quarterly,
with equal installments within each year.
Distributions Distributions in respect of any partnership investment will be
made in the following order of priority:
(i) 100 percent to the limited partners until they have received an amount equal to
their contributed capital.
(ii) 75 percent to the limited partners and 25 percent to the general partners.
General Partner Clawback Obligation Upon the liquidation of the fund,
the general partner will be required to restore funds to the partnership to the extent that
it has received cumulative distributions in excess of amounts otherwise distributable
pursuant to the distribution formula set forth above, applied on an aggregate basis
covering all partnership investments, but in no event more than the cumulative dis-
tributions received by the general partner solely in respect of its carried interest.
APPENDICES: KEY TERMS AND CONDITIONS FOR THREE VC FUNDS 45
CHAPTER 3
VC RETURNS
VCS SPEND their time very differently from mutual-fund managers, but
ultimately both groups are measured by their investment returns. If you open the
business section of the newspaper, you can readily see information about mutual-
fund returns, but one must search hard to ?nd any information about VC returns.
Even when such returns are revealed, they are often reported in ways that are not
comparable to standard benchmarks.
In this chapter, we learn how VC returns are measured and take our ?rst glimpse
into the returns data. In Section 3.1, we analyze two main sources of industry level
returns and compare these returns with public market benchmarks. In Section 3.2,
we show how to compute returns at the fund level and discuss several new sources
of fund level data.
3.1 INDUSTRY RETURNS
In this section, we analyze the returns for the entire VC industry. We begin with
some de?nitions.
3.1.1 De?nitions
A periodic return is de?ned as
Periodic return 5R
t
5ðP
t
1D
t
Þ=P
t21
21 ð3:1Þ
where R
t
is the return for period t, P
t
is the value (price) of the portfolio at the end
of period t, D
t
is the dividends (distributions) earned by the portfolio during period
t, and P
t 21
is the value (price) of the portfolio at the end of period t 2 1. The time
period t can be any length, and the return would correspondingly be a “monthly
return”, “quarterly return”, “annual return”, or likewise. For multi-period returns,
we multiply the periodic returns to arrive at the compound return:
Compound return 5ð1 1R
1
Þ Ã ð1 1R
2
Þ Ã . . . Ã ð1 1R
N
Þ 21 ð3:2Þ
46
Because we will often be interested in returns at the annual time horizon, we
can translate T years of multi-period returns into annualized returns as follows:
Annualized return 5ð1 1compound returnÞ
ð1=TÞ
21 ð3:3Þ
For managed portfolios, returns can be expressed either as gross returns
(before subtracting fees and carried interest) or as net returns (after subtracting
fees and carried interest).
EXAMPLE 3.1
The Largeco pension plan has invested in dozens of VC funds. The director of the pension
plan is preparing his annual report to the Largeco board of directors. Summary information
for Largeco’s VC portfolio is given in Exhibit 3-1:
Problem The board has asked for a ?ve-year report of net returns and gross returns by
year, plus the compound returns and annualized returns for all ?ve years. You can assume
that all new investments and management fees are paid at the beginning of the year, and all
distributions were paid at the end of the year.
Solution The gross returns are calculated by comparing the value at the beginning of each
year with the value at the end of each year. (Note that the beginning value in year t is equal to the
ending value in year t 2 1 minus distributions to LPs and GPs. The management fee is paid
separately by the LPs.) Thus, gross returns are 7,200/(4,000 1 2,000) 2 1 5 20 percent for
2004, 8,340/(5,950 1 1,000) 2 1 5 20 percent for 2005, and so on. For net returns, we must
subtract the distributions to GPs (carried interest) fromthe numerator and add the management
fees to the denominator: (7,200 2 250)/(4,000 1 2,000 1 100) 2 1 5 13.9 percent for 2004,
(8,340 2250)/(5,950 11,000 1100) 21 514.8 percent for 2005, and so on. The answers for
all years are given in Exhibit 3-2.
EXHIBIT 3-1
LARGECO PENSION PLAN, VC PORTFOLIO
Year 2004 2005 2006 2007 2008
Beginning Value 4,000 5,950 7,090 9,267 3,884
New Investments 2,000 1,000 1,000 1,000 1,000
Ending Value (before distributions) 7,200 8,340 10,517 5,134 7,814
Distributions to LPs 1,000 1,000 1,000 1,000 1,000
Distributions to GPs 250 250 250 250 250
Management Fees 100 100 100 100 100
3.1 INDUSTRY RETURNS 47
The compound returns are as follows:
Gross compound return51:20
Ã
1:20
Ã
1:30
Ã
0:50
Ã
1:60 21 549:8% ð3:4Þ
and
Net compound return 51:139
Ã
1:148
Ã
1:254
Ã
0:471
Ã
1:518 21 517:2% ð3:5Þ
The gross annualized return is 1.498
(1/5)
2 1 5 8.4 percent, and the net annualized return is
1.172
(1/5)
2 1 5 3.2 percent. ’
It will prove useful to give one ?nal set of return de?nitions. Returns that
have been earned in the past are known as realized returns or historical returns.
Returns that are forecast for the future are known as expected returns. We could
use the modi?er of “realized” or “expected” in front of any of the other return
de?nitions in this chapter. In a well-behaved universe, we would ?nd that average
realized returns would be equal to expected returns for all assets. Our universe is
not so well behaved, which is why so many advertisements tell us that “past per-
formance is no guarantee of future returns”.
3.1.2 A Gross-Return Index
Given current data limitations, a gross-return index is best created from the bottom
up. To construct a bottom-up index, we build a database of all VC investments, do
our best to update the values of these investments over time (including distribu-
tions), and then track the value of the whole set of investments, thus creating a
rolling portfolio for the whole VC industry. This is a herculean task, but luckily all
the work has already been done by Susan Woodward and her company, Sand Hill
Econometrics (SHE).
1
SHE began by combining the databases of the two main industry trackers,
VentureSource (a division of Dow Jones) and Venture Economics (a division of
Thomson Financial). From here, SHE added information from other industry
EXHIBIT 3-2
LARGECO PENSION PLAN, VC PORTFOLIO
Year 2004 2005 2006 2007 2008
Net Return 13.9% 14.8% 25.4% 252.9% 51.8%
Gross Return 20.0% 20.0% 30.0% 250.0% 60.0%
1
Construction of the Sand Hill Index is described in Hall and Woodward (2003).
48 CHAPTER 3 VC RETURNS
sources, from its own base of consulting clients (LPs in VC funds), and from
exhaustive searching of Web resources. The ?nal database includes over 17,000
companies and more than 60,000 ?nancing rounds. It also allows for monthly
updating. The resulting Sand Hill Index
s
is plotted in Exhibit 3-3, using the
available sample period through December 2008.
2
For comparison, we have also
plotted an index for the NASDAQ stock market. The two indices are both nor-
malized to be 100 in December 1988, the month the Sand Hill Econometrics
Venture Index started. The normalized indices are presented in log scale.
Since the inception of the SHE index, the index reached a peak of 2,302 in
August 2000, fell to a postboom low of 915 in February 2003, and recovered to
1,364 by October 2007. Meanwhile, the NASDAQ index peaked at its all-time high
at 1,306 in February 2000, fell to a postboom low of 328 in September 2002, and
reached its post-bubble high at 827 in October 2007. Since October 2007, the SHE
index slid, largely in tandem with the NASDAQ, amid the ?nancial crisis that
EXHIBIT 3-3
SAND HILL INDEX
s
VERSUS NASDAQ
2500
2000
1500
1000
500
400
300
200
100
50
J
a
n
u
a
r
y
-
8
8
J
a
n
u
a
r
y
-
8
9
J
a
n
u
a
r
y
-
9
0
J
a
n
u
a
r
y
-
9
1
J
a
n
u
a
r
y
-
9
2
J
a
n
u
a
r
y
-
9
3
J
a
n
u
a
r
y
-
9
4
J
a
n
u
a
r
y
-
9
5
J
a
n
u
a
r
y
-
9
6
J
a
n
u
a
r
y
-
9
7
J
a
n
u
a
r
y
-
9
8
J
a
n
u
a
r
y
-
9
9
J
a
n
u
a
r
y
-
9
9
J
a
n
u
a
r
y
-
0
0
J
a
n
u
a
r
y
-
0
1
J
a
n
u
a
r
y
-
0
2
J
a
n
u
a
r
y
-
0
3
J
a
n
u
a
r
y
-
0
4
J
a
n
u
a
r
y
-
0
5
J
a
n
u
a
r
y
-
0
6
J
a
n
u
a
r
y
-
0
7
J
a
n
u
a
r
y
-
0
8
Sand Hill Index
NASDAQ
NOTE: The two indices are both normalized to be 100 in December 1988. The normalized indices are
presented in log scale.
Sources: Sand Hill Econometrics (SHE), the Center for Research in Security Prices (CRSP).
2
Sand Hill Econometrics discontinued the index in December 2008 after it reached a licensing agreement
with Dow Jones. A new index called the DowJones Index of Venture Capital (comprising VentureSource
and Sand Hill Econometrics’ proprietary data) will be launched in 2010.
3.1 INDUSTRY RETURNS 49
unfolded in 2008. In December 2008 (the last month the index was calculated), it
stood at 1,110, while the NASDAQ was at 456. The annualized return over the
20-year life of the index is 12.8 percent. In comparison, the NASDAQ index—a
value-weighted index of all NASDAQ stocks, including dividends—had the
annualized return over the same 20-year time period of 7.9 percent. Although
the Sand Hill Index
s
is more than double the NASDAQ index by the end of the
sample period, the former only passes the latter in June 1996, close to the beginning
of the boom period.
3.1.3 A Net-Return Index
The Sand Hill Index
s
is built from a database of portfolio companies. An alter-
native approach is to build a database of funds and combine the returns of these
funds to form an overall industry index. This has been attempted by several groups,
the most comprehensive of which is the Cambridge Associates U.S. Venture
Capital Index
s
, which includes more than 75 percent of the dollars raised by VC
funds since 1981.
3
Cambridge Associates (CA), an investment consultant to
endowments, foundations, and wealthy families, serves as a gatekeeper for
potential LPs. It essentially acts as a paid service that puts CA between the LP and
GP for both the initiation and management of the partnership relationship. This
function gives CA access to information, which it has astutely chosen to aggregate
and analyze.
To construct its index, CA starts with the quarterly reports that GPs provide to
LPs. These reports give “current” valuations for the unrealized portfolio companies
and also summarize the cash ?ows in and out of the fund.
4
CA then aggregates the
total value (realized and unrealized) from each fund in each quarter. By combining
these totals across quarters, it is able to compute an aggregate return and build an
index. Note that CA is using cash ?ows to LPs as the basic unit. Because these cash
?ows include management fees (as negative cash ?ows) and carried interest (as a
reduction of the positive cash ?ows from realized investments), the CA index is
based on net returns and, in principle, should be lower than the corresponding gross
return index constructed by SHE.
The quarterly CA index is available from the ?rst quarter of 1981 through the
last quarter of 2008. To facilitate comparisons with the Sand Hill Index
s
, we set
the CA index value to 100 for the fourth quarter of 1988. Exhibit 3-4 plots the CA
Index versus the NASDAQ index (also normalized to be 100 in the fourth quarter of
1988) in log scale.
3
The Cambridge Associates data can be freely downloaded from https://www.cambridgeassociates.com/
pdf/Venture%20Capital%20Index.pdf.
4
We put “current” between quotes because the valuations are often quite old. In Chapter 4, we discuss
this valuation practice and its implications for performance measurement and for the estimation of the
cost of venture capital.
50 CHAPTER 3 VC RETURNS
The exhibit demonstrates that the CA index has the highest amplitude of all
three series, reaching a maximum of 4,300 in the third quarter of 2000, a postboom
low of 1,386 in the ?rst quarter of 2003, and recovering to its postbubble high of
2,412 in the fourth quarter of 2007. Since then it went down, as expected, and stood
at 2,022 in the fourth quarter of 2008. For the complete, nearly 28-year sample
period of 1981 to 2008, the CA index earned an annualized return of 13.0 percent
versus a 9.0 percent return for the NASDAQ. During the 20-year subperiod from
1988 to 2008—when we also have data for the Sand Hill Index
s
—the CA index
earned annualized returns of 16.2 percent versus 12.8 percent for the Sand Hill
Index
s
and 7.9 percent for the NASDAQ.
The relationship between the Sand Hill Index
s
and the CA Index seems
backward: the net-return index (CA)—which is computed after fees and carried
interest are subtracted out—should be lower than the gross-return index (SHE).
However, here the opposite is true, with the CA index exceeding the Sand Hill
Index
s
by 3.4 percentage points over the common subperiod.
Clearly, something is wrong with at least one of these indices. In fact, both
indices have some weaknesses; but when taken together, they can provide us with
upper and lower bounds for VCperformance. First, consider the CAindex. CAadds to
its database in several ways. One way is by tracking funds for which a CA client is a
current LP. This formof adding data does not induce any bias. However, CAdoes not
have clients in every ?rst-time fund. Suppose that ABC Fund I does not include any
EXHIBIT 3-4
CA INDEX
s
VERSUS NASDAQ
1
9
8
1
Q
1
1
9
8
2
Q
1
1
9
8
3
Q
1
1
9
8
4
Q
1
1
9
8
5
Q
1
1
9
8
6
Q
1
1
9
8
7
Q
1
1
9
8
8
Q
1
1
9
8
9
Q
1
1
9
9
0
Q
1
1
9
9
1
Q
1
1
9
9
2
Q
1
1
9
9
3
Q
1
1
9
9
4
Q
1
1
9
9
5
Q
1
1
9
9
6
Q
1
1
9
9
7
Q
1
1
9
9
8
Q
1
1
9
9
9
Q
1
2
0
0
0
Q
1
2
0
0
1
Q
1
2
0
0
2
Q
1
2
0
0
3
Q
1
2
0
0
4
Q
1
2
0
0
5
Q
1
2
0
0
6
Q
1
2
0
0
7
Q
1
2
0
0
8
Q
1
2
0
0
9
Q
1
100
50
25
500
250
1000
5000
2500
CA index
NASDAQ
NOTE: The two indices are both normalized to be 100 in the fourth quarter of 1988, to make it comparable
to the Sand Hill Econometrics Venture Index, which started in December 1988. The normalized indices
are presented in log scale.
Sources: Cambridge Associates (CA), the Center for Research in Security Prices (CRSP).
3.1 INDUSTRY RETURNS 51
CA clients as LPs. If ABC Fund I performs poorly, it is unlikely there will ever be an
ABCFund II, and CAwill never get to see the returns fromFund I. On the other hand,
if Fund I is successful, then it is more likely that ABC will be able to raise Fund II. If
ABC solicits a CA client for Fund II, then CA will request information on the per-
formance of Fund I, and then add it to its database. This method of data collection
induces a survivor bias—“survivors” have a better chance of showing up in the data,
and this bias causes an overestimate of industry returns. Thus, we think of the CA
index as representing an upper bound on the net returns to VC.
Next, consider the Sand Hill Index
s
. In principle, this index could also suffer
from survivor bias, because we might think that SHE is more likely to learn of the
existence of companies only if they have been successful. Furthermore, additional
biases are possible because valuation information might be missing for nonrandom
reasons (e.g., if the portfolio companies performed poorly). In practice, SHE has
been able to signi?cantly limit these biases through the combination of several
databases and the use of sophisticated statistical techniques designed to handle
missing data. It also has made arduous efforts to track down the exit status of
companies which existing databases list as “private” long after they were ?rst
funded, thus tackling the “zombie company” problem. It is, however, likely that this
index is a bit conservative (bias would be too strong a word here) in the way it
computes VC returns. To understand how conservatism could occur, we must go a
little deeper into the SHE methodology.
Each month, SHE takes a snapshot of all portfolio companies for all VCs. As
discussed earlier, there are several challenges in estimating the value of nontraded
companies, and SHE handles these problems with several careful methods. Because
VCs do not own 100 percent of these companies, the next step is to estimate the
value of the VCs’ portion of each company. This is tricky—indeed, the calculations
to do this estimation will take up the six chapters of Part III in this book—and the
task is made more dif?cult because SHE does not have access to the details of each
transaction. Thus, it is necessary to make an assumption about the form of VC
ownership, and SHE assumes that VCs have proportional (common-stock) own-
ership of these ?rms. This assumption is conservative, because virtually all VCs
own some form of preferred stock, which has valuation advantages over common
stock. A discussion of these advantages will be introduced in Chapter 9 and
extensively analyzed in Part III. For now, it will suf?ce to say that if SHE were to
have assumed some form of preferred stock, then the returns on the Sand Hill
Index
s
would have been a little bit higher. Thus, the Sand Hill Index
s
provides us
with a lower bound on the gross returns to VC.
Taken together, the returns data gives us an upper bound for net returns (the
CA index), and a lower bound for gross returns (the Sand Hill Index
s
). How far
apart are these bounds? The CA Index had an annualized return of 16.2 percent
from the end of 1988 to the end of 2008; the Sand Hill Index
s
had a return of 12.8
percent over the same time period. If we make a back-of-the-envelope estimate of
management fees costs of about 2 percent and carried-interest costs of about
2 percent, then we get a total of 4 percent for fees and carry, yielding an estimated
52 CHAPTER 3 VC RETURNS
net return of 12.8 2 4.0 5 8.8 percent for the Sand Hill Index
s
. This means that
the difference between the upper and lower bounds for VC net returns from 1989 to
2008 is 16.2 2 8.8 5 7.4 percent.
At ?rst glance, these returns demonstrate some advantage for VCover the most
comparable index. Of course, this is not the end of the story, because we have not said
anything about the relative risk of VC versus the NASDAQ; but at this point, a
detailed discussion of risk would take us too far off topic. In Chapter 4, we analyze the
risk of VC in the context of estimating the cost of capital for VC investments. With
that background, we will then be able to analyze the risk-adjusted performance of VC
based on the CAand SHEindices. For now, it will suf?ce to say that this analysis ?nds
that both the net risk-adjusted return (upper bound, from CA) and gross risk-adjusted
return (lower bound, from SHE) are very close to zero.
3.2 FUND RETURNS
In Chapter 4, we will show that the upper bound is zero for the net risk-adjusted
returns to the VC industry. If this is true, then investment in VC only makes sense if
one can identify managers that consistently outperform the rest of the industry.
Luckily for LPs, there is some evidence that such consistent outperformance does
exist. To understand the sources of such performance, we must ?rst learn how fund
level returns are measured.
3.2.1 De?nitions
The industry returns calculated in Section 3.1 started with periodic returns for each
month (Sand Hill) or quarter (CA), and then multiplied these returns to arrive at a
compound return for the whole time period. This is a standard procedure for com-
puting asset returns. It is used for stocks, bonds, and bank deposits, as well as for the
return measurements of mutual funds, hedge funds, and other portfolio managers.
Although this calculation is reasonable for the whole VC industry, it does not seem
reasonable when applied to a single VCfund. The main problemis that VCfunds may
have vastly different amounts of capital invested in different years of the fund, and it
can be misleading to treat all these years equally when computing returns.
To illustrate this problem, imagine that you are an LP in the ABCfund. Suppose
that you have committed $11M to the fund. For simplicity, assume fees and carry are
both zero (so gross returns are equal to net returns). On January 1, 2007, ABC calls
$1M of your investment. On December 31, 2007, it exits this investment and returns
$2M to you. On January 1, 2008, it calls the remaining $10M for another investment.
On December 31, 2008, it exits this second investment for $6M. Given these facts,
what is your annualized return from investing in ABC?
If we follow the same steps as in Section 3.1, then we would calculate the
return for 2007 as (2/1) 2 1 5 100 percent, and for 2008 as (6/10) 2 1 5 240
percent. The compound returns would then be (1 11)Ã (1 20.4) 21 520 percent,
3.2 FUND RETURNS 53
and the annualized returns would be (1.2)
(1/2)
2 1 5 9.5 percent. Although this is
mathematically correct, it is economically misleading. After all, if we ignore the
timing of these cash ?ows, we can see that you gave ABC a total of $11M when it
really only returned $2M1$6M5$8M to you. It just does not seem right to credit
them with a positive return of 9.5 percent.
The problem is that annualized returns weigh each year equally in the calcu-
lation. To get an answer consistent with our intuition, we need to compute an internal
rate of return (IRR), which effectively weighs each dollar equally. To compute the
IRR, we start with the whole streamof cash ?ows. In this case, we have a negative cash
?owof $1Mon January 1, 2007 (the original investment); a positive cash ?owof $2M
on December 31, 2007; a negative cash ?ow of $10M on January 1, 2008; and then a
positive cash ?owof $6M on December 31, 2008 (the ?nal value of the portfolio). To
simplify our calculations, we combine the cash ?ows on December 31, 2007 and
January 1, 2008 to obtain a single negative cash ?ow of $8M for the end of 2007.
We are now ready to move on and answer the following question. Suppose
that the negative cash ?ows were the deposits in a bank, and the positive cash ?ow
was the ?nal bank balance. If such is the case, then what interest rate must this bank
be paying on deposits?
Under this logic, a bank paying an interest rate equal to the IRR would give
us 1M Ã (1 1 IRR)
2
for a two-year deposit of $1M, and 8M Ã (1 1 IRR) for a one-
year deposit of $8M. If we have $6M total from these deposits, then the IRR is the
solution to
6M51M Ã ð11IRRÞ
2
18M Ã ð11IRRÞ ð3:6Þ
We can solve this quadratic equation to obtain a feasible annual IRR 5 231
percent. This negative return seems more consistent with the idea that ABC lost
money overall than the answer given by our previous procedure.
For cash ?ow streams more complex than this example, we would use a com-
puter to calculate the IRR. The IRR plays an important role in VC performance
reporting, but it is not a panacea—and careful observers must be aware of several
weaknesses in the IRR measure. First, one should never forget that the IRRcannot be
directly compared to periodic returns. In the example we just solved, the annualized
returns were about 9.5 percent, whereas the IRR was negative 31 percent. Although
not all differences will be this extreme, such differences are not uncommon. Because
most of the investment world speaks in terms of annualized returns, it is tempting to
compare these returns to IRRs. This temptation should be avoided.
Second, some standard practices of IRR calculation can lead to confusion.
Typically, VC funds will compute a monthly or quarterly IRR from all its cash ?ows,
and then annualize this periodic IRR using Equation (3.3). However, in times of high
returns, an annualized version of a monthly or quarterly IRR will be misleading,
because this exercise implicitly assumes reinvestment even when such reinvestment
has explicitly not occurred. For example, consider a $1M investment that returns
$80,000 every month for one year and then returns $1M at the end of the year. This
cash ?owstreamhas a monthly IRRof 8 percent. So far, so good—the investment has
54 CHAPTER 3 VC RETURNS
clearly returned 8 percent in every month. However, if we annualize this IRR to
(1.08)
12
21, we get an annualized IRR of 151 percent, which is similar to assuming
that all the distributions were reinvested (none were!) and also earned 8 percent per
month. Atrue “annual IRR” of 151 percent should be leaving the investor with $1MÃ
(1 11.51) 5$2.51Mat the end of the year, but the investment strategy followed here
would not do that without some extra help from excellent outside investments.
A third weakness of standard IRR reporting is that it does not usually make a
distinction between realized and unrealized investments. For VC funds that still
have unrealized investments, the IRR takes the value of these unrealized invest-
ments and treats them as a positive cash ?ow in the ?nal period. If a signi?cant
component of the portfolio is unrealized, then the IRR calculation will essentially
just re?ect the subjective valuation of these unrealized investments. In general, the
IRR becomes more informative as the fund realizes more investments.
For this last reason, the IRR is particularly misleading in the ?rst few years of a
fund. Remember that management fees are usually based on committed capital; so
LPs of a $100M fund with 2 percent annual fees would be paying out $2M in fees
each year and would have $80M left for investment capital. Suppose the fund invests
$20M of this investment capital in the ?rst year. Because one year is rarely long
enough to have any exits, it is possible that all this investment capital would still
be kept on the books at cost. The fund would then appear to have earned no gross
returns while still collecting $2Min fees. An IRRcalculation fromthese cash ?ows is
going to give a negative return. If these investments turn out well in the long run, then
the fund will look ?ne by the time of these exits. In the early years, however, it will
appear to charge very high fees compared to invested capital ($2M on $20M of
investments 510 percent in this case) and with little appreciation of the assets. Even
for funds that eventually have high IRRs, a plot of the fund IRR over time will
be negative for the ?rst few years, and then increase rapidly in the later years. The
shape of this plot, shown in Exhibit 3-5, is called a J-curve or a hockey stick.
The IRR is an answer to the question, “How well did you do with my money
while you had it?” Many investors would like to get the answer to a different
question, which asks, “Overall, how much money did you make for me?” The
IRR’s inability to answer this second question is a ?nal weakness. For example,
consider the following two funds. Fund ABC takes a $1M investment at the
beginning of year 1 and then returns $2M at the end of year 1. Fund XYZ takes a
$1M investment at the beginning of year 1 and then returns $32M at the end of year
5. Both funds have an (annual) IRR of 100 percent. Clearly, however, assuming a
normal investment and in?ation environment, fund XYZ will be preferred by all
investors. It would be nice to have a measure of this superior performance. The VC
industry indeed has such a measure, which goes by many names—value multiple,
investment multiple, realization ratio, absolute return, multiple of money,
times money. They all mean the same thing: “For every dollar I gave you, how
much did I get back?” Each of these expressions can be divided into realized and
unrealized investments. For instance, a value multiple is the sum of the realized
value multiple and unrealized value multiple.
3.2 FUND RETURNS 55
EXAMPLE 3.2
The $200M ABC Fund is seven years into its 10-year life. Its annual investments, fees,
distributions, and portfolio value are given in Exhibit 3-6.
EXHIBIT 3-5
THE J-CURVE/HOCKEY STICK PATTERN OF RETURNS
IRR
60%
50%
40%
30%
20%
–20%
10%
–10%
0%
I
R
R
0 1 2
Years since closing
3 4
EXHIBIT 3-6
CASH FLOWS FOR THE ABC FUND
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7
Investments 20.0 30.0 40.0 40.0 30.0 0.0 0.0
Portfolio value 20.0 56.0 112.8 186.6 188.1 195.7 203.5
Total distributions 0.0 0.0 0.0 65.0 37.6 39.1 40.7
Carried interest 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Distributions to LPs 0.0 0.0 0.0 65.0 37.6 39.1 40.7
Cumulative distributions to LPs 0.0 0.0 0.0 65.0 102.6 141.8 182.5
Port value after capital returned 20.0 56.0 112.8 121.6 150.5 156.5 162.8
Management fee 4.0 4.0 4.0 4.0 4.0 4.0 4.0
NOTE: All entries are in $millions.
56 CHAPTER 3 VC RETURNS
Problem Compute the IRR, value multiple, realized value multiple, and unrealized value
multiple for ABC at the end of year 7.
Solution To compute the IRR, we ?rst need to aggregate the investments, fees, and
distributions into a single cash ?ow to LPs as
Cash Flow to LPs 5Distributions to LPs 2new investments
2management fees
ð3:7Þ
These cash ?ows are 2$24M for year 1, 2$34Mfor year 2, 2$44M for year 3, $21Mfor
year 4, $3.6Mfor year 5, $35.1Mfor year 6, and $36.7Mfor year 7. The portfolio value at the end
of year 7 is $162.8M. This value is counted as a positive cash?owfor the IRRcalculation. We can
use a spreadsheet or calculator to compute the IRR of this cash ?ow stream as 23.8 percent.
The value multiple is as follows:
Value Multiple 5ðTotal Distributions to LPs ½all years?
1value of unrealized investmentsÞ=ðInvested Capital
1Management FeesÞ
ð3:8Þ
Total distributions to LPs through year 7 are $182.5M. The value of unrealized invest-
ments 5the portfoliovalue after year 7 5$162.8M. Invested capital is the sumof newinvestments
over all years 5$160M. The total management fees through year 7 5$28M. Thus, the value
multiple 5 ($182.5M 1 $162.8M)/($160M 1 $28M) 5 1.84.
The realized value multiple is as follows:
Realized Value Multiple 5ðTotal Distributions to LPs½all years?Þ
=ðInvested Capital 1Management FeesÞ
5$182:5M=ð$160M1$28MÞ 50:97
ð3:9Þ
The unrealized value multiple is as follows:
Unrealized Value Multiple 5ðValue of unrealized investmentsÞ
=ðInvested Capital 1Management FeesÞ
5$162:8M=ð$160M1$28MÞ 50:87
ð3:10Þ
’
Most LPs compute value multiples on a net basis, with fees and carry already
subtracted; if you read “value multiple” in this book or in the trade press, youcanassume
that it refers to a net value multiple. In some cases, ?rms may report value multiples on a
gross basis, perhaps because the GP team wants to discuss a performance record for a
time periodwhentheywerenot explicitlychargingfees or carry. This canoccur whenthe
GPs’ prior investingexperience tookplace outsidethestandardpartnershipstructure. For
many GPteams raising their ?rst fund, such experience may represent the only evidence
of their past performance. This gross value multiple (GVM) is computed as follows:
GVM5ðTotal distributions to LPs ½all years?
1value of unrealized investments
1carried interestÞ=invested capital
ð3:11Þ
3.2 FUND RETURNS 57
Gross value multiples are also helpful for quickly communicating the raw
investment performance of a GP and for calculating shortcut estimates for carried
interest. Also, we can go back and forth between GVMs and value multiples by
making a few extra calculations. For example, consider a fully invested fund at the
end of its life, so investment capital 5 invested capital, and all investments have
been realized. Then, we can rewrite Equation (3.11) as follows:
GVM5total distributions=investment capital ð3:12Þ
where total distributions include both carried interest plus all LP distributions. We
can then compute its carried interest as
Carried interest 5carry% Ã ðtotal distributions 2carry basisÞ
5carry% Ã ðGVM Ã investment capital 2carry basisÞ
ð3:13Þ
where carry% represents the percentage level of carried interest and the carry basis
is either committed capital or investment capital as speci?ed by the fund partner-
ship agreement. We can now express the (net) value multiple of a completed fund
by rewriting Equation 3.(3.8) in terms of the GVM and other inputs as follows:
Value multiple 5ðtotal distributions to LPsÞ=ðinvestment capital
1management feesÞ
5ðtotal distributions 2carried interestÞ=committed capital
5½GVM Ã investment capital 2carry% Ã ðGVM
à investment capital2carry basisÞ?=committed capital:
ð3:14Þ
Finally, there is one more de?nition that will be useful in later chapters. For
many of our valuation analyses, we will need to estimate the fraction of the
investment that we expect to be paid to the GP as carried interest. For a completed
fund, we de?ne this GP% as
GP%5carried interest=total distributions 5carry%Ã
ðGVM Ã investment capital 2carry basisÞ=
ðGVM Ã investment capitalÞ:
ð3:15Þ
Note that GP% will never be higher than carry%, because carry% is paid on
all pro?ts, whereas GP% is a percentage of total distributions. Since pro?ts will
always be lower than total distributions, GP% will always be lower than carry%.
Also, remember that carry% is a contractual number in the partnership agreement,
whereas GP% is an estimated percentage that depends on the eventual GVM of
the fund.
The following example allows us to practice with these de?nitions.
58 CHAPTER 3 VC RETURNS
EXAMPLE 3.3
XYZ Partners is raising their ?rst fund, XYZ Partners Fund I, with $100M in committed
capital, annual management fees of 2 percent, carried interest of 20 percent, and a carried
interest basis of committed capital. The four individuals on the XYZ team have previously
managed the captive VC portfolio for the Goldenbucks family. During the 10 years of
managing the Goldenbucks’ VC portfolio, the partners did not charge management fees or
carried interest, and they achieved a GVM of 2.5.
Problem
(a) Suppose that XYZ Fund I earns the same GVM as the partners earned for Goldenbucks.
What would be the value multiple be for the fund?
(b) What would be the GP% of the fund?
Solution
(a) To see how this formula would translate into XYZ Fund I, we must make adjustments
for management fees and carried interest. For a $100M fund with 2 percent annual fees,
lifetime fees would be $20M, and investment capital would be $80M. Then, we can sub-
stitute these quantities and GVM 5 2.5 into Equation (3.14) to obtain the following:
Value multiple 5ð2:5 Ã $80MÞ20:20 Ã ðð2:5 Ã $80MÞ2$100MÞ=$100M
5½$200M20:20 Ã ð$100MÞ?=$100M51:8:
ð3:16Þ
(b) From Equation (3.15), we can compute the GP% as
GP%50:20 Ã ð2:5 Ã $80M2$100MÞ=ð2:5 Ã $80MÞ
5$20M=$200M50:10:
ð3:17Þ
’
3.2.2 Evidence
LPs get access to fund level return data through their own databases or through
gatekeepers. Well-known gatekeepers include Cambridge Associates (who release
the aggregate VC index discussed in Section 3.2), Hamilton Lane Advisors, State
Street (who launched its own venture capital and related private equity indices in
2007), and Paci?c Corporate Group. For those of us outside the LP community,
data is harder to ?nd.
The longest-standing source of fund level return data is Venture Economics
(VE). Both GPs and LPs report returns to VE under a strict rule of secrecy, in which
VE promises not to disclose any identifying information about speci?c funds.
Although VE does not provide information about speci?c funds, its summary data
has been an industry standard since the 1980s. The publicly available source for this
data is its annual publication, Investment Benchmarks Report (IBR). In each year of
the IBR, VE gives summary statistics for the vintage year. VE claims to have data
on 25 percent of all funds, and overrepresentation of the largest funds allows this
25 percent to cover over 50 percent of all industry dollars.
3.2 FUND RETURNS 59
Each annual IBR dedicates several pages to each vintage year, with summary
information about IRRs and value multiples during the complete evolution of that
vintage year. Perhaps its most closely watched statistics are the cutoffs for the
median and top-quartile fund for each vintage year. Because VE is the only public
provider of this information, these cutoffs have become the de facto benchmarks.
Because it is very dif?cult to measure risk for individual funds, the dominant
performance measures in the industry are these vintage year comparisons. Exhibit
3-7 displays the median IRR and top-quartile IRRs for all vintages since 1980.
The IBR data shows that median performance peaked for vintage year 1996, and
that the mid-1990s were extremely fortunate years to be raising VCfunds. The median
IRRs of funds raisedin2004and2005are still negative—that is expectedandconsistent
with the J-curve—whereas the poor medianperformance of 1999and 2000funds after a
decade cannot be attributed to the J-curve and seems likely to be with us for good.
Although the detailed VE data is not available to the public, subsets of the data
have been released to academic researchers. These subsets are cleansed of identifying
information, but do include codes that allow researchers to link funds from the same
GP without actually knowing who that GP is. Kaplan and Schoar (2005) use this data
to answer the crucial question posed at the beginning of this section, which asks, “Is
GP performance persistent across funds?” Using several measures of performance,
the authors ?nd that the answer is a clear “yes”. For example, let N 5 the sequence
EXHIBIT 3-7
VE MEDIANS AND TOP-QUARTILE BY VINTAGE YEAR
120.00
100.00
80.00
60.00
40.00
20.00
0.00
?20.00
1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004
Top quartile IRR
Median IRR
I
R
R
(
%
)
Source: Thomson VentureXpert.
60 CHAPTER 3 VC RETURNS
number for funds of a speci?c GP. Kaplan and Schoar found that the IRRof Fund Nis
a signi?cant predictor for the IRR of Fund N 11 and for the IRR of Fund N 12, and
the authors also demonstrate that their results are robust to using other measures of
fund performance and to several differences in fund style.
In recent years, some newdata sources on fund level returns have appeared. This
appearance was driven mostly by media requests to public LPs under the Freedom of
Information Act (FOIA). Public LPs, such as public-pension funds and the endowments
of public universities, fought hard to avoid disclosing the returns on their private equity
portfolios, but ultimately some disclosure was required. FOIA requests uncovered the
returns of several large and experienced LPs, including the University of California,
California Public Employee Retirement System (CALPERS), the University of
Michigan, and the Universityof Texas. These disclosures gave the public its ?rst lookat
the performance of some of the most famous names in VC.
These FOIA disclosures inspired a new entrant into the VC performance
market. Private Equity International (PEI) began by gathering all the information
from FOIA requests and then combining this information with proprietary data
from LPs and GPs. They now offer several products to the general public, including
an annual publication, The Private Equity Performance Monitor (PEPM). This
publication gives performance data for hundreds of funds; we will discuss this
evidence extensively in our listing of the “best VC funds” in Chapter 5.
To give you just a ?avor of the data, Exhibit 3-8 shows the returns and
multiples of Kleiner, Perkins, Cau?eld, & Byers (KPCB), taken from the dis-
closures of the University of California and included in the 2005 PEPM.
Exhibit 3-8 shows why KPCB is so famous. By comparing these results to the
benchmarks in Exhibit 3-7, we can see that every fund from 1980 through 1996 was
above the median IRR. Truly spectacular results were obtained by KPCB VII (1994
vintage) and KPCB VIII (1996 vintage), which achieved value multiples of 32.0 and
17.0, respectively. Furthermore, the 1999 vintage KPCBIXfund, which had a net IRR
of À23.3 percent as of March 2004 and thus looked like the ?rm’s ?rst “loser”, turned
out to be the very best of hundreds of funds raised that year. Why? Because KPCBIX
had about 20M shares of Google, which went public on August 19, 2004, and
regulatory ?lings show that these shares were distributed at about $200 per share.
Assuming that about 14Mof these shares went to LPs (KPCBhas a 30 percent carried
interest), that would mean about $2.8 billion was distributed to LPs. Thus, even if
KPCB gets no other realizations from the entire fund, they would still give their
investors a value multiple of at least 5 (,2800/500) from fund IX.
5
5
While we cannot of?cially verify our assertion that KPCBIXwas a homerun fund, we take comfort fromthe
disclosure that another famous fund that invested in Google, Sequoia Capital III, has a value multiple of 14.84
and a net IRR of 106% as of September 2007 (2008 Private Equity Performance Monitor). This $250M fund
reported a value multiple of 0.44 as of March 2004, prior to the Google IPO; thus an increase of 14.4X(14.84-
0.4) in the value multiple was likely due to the Google exit. The back-of-the-envelope calculation using 30%
carryand20Mshares distributedat $200per shareyields 11.2X(2800/250) incremental contributionof Sequoia’s
Google investment toits fundperformance. The numbers (14.4and11.2) roughlymatch, andif anythingtells us
that our assumptions understate the true exit value of the Google investment for its VC backers.
3.2 FUND RETURNS 61
SUMMARY
VC is a form of private equity, and for many years the returns to VC funds have indeed
been very private. In recent years, however, several new data sources have been made
available so that it is now possible to do some analysis of industry level and fund level
returns. In this chapter, we analyzed two sources of industry level returns: the Cambridge
Associates VC Index
s
(providing an upper bound for the net returns to the industry) and
the Sand Hill Index
s
(providing a lower bound for the gross returns to the industry).
Although both of these indices have superior performance to the NASDAQ, the risk-
adjusted returns (to be studied in detail in Chapter 4) are close to zero. Although the
industry as a whole does not offer superior risk-adjusted performance, the evidence on fund
level returns suggests that top ?rms can consistently outperform their peers. To analyze
fund level performance, it is necessary to use different measures of returns from the
methods used at the industry level. The two main measures of fund level returns are
the IRR and the value multiple, the latter also known by many other names. Fund level data
is available in summary form from Venture Economics and in detailed form from Private
Equity Intelligence.
EXHIBIT 3-8
KLEINER PERKINS CAUFIELD & BYERS FUNDS
Fund Vintage Year
Committed
Capital ($M) Net IRR Value Multiple Date Reported
II 1980 65 50.6% 4.3 Mar-04
III 1982 150 10.2% 1.7 Dec-04
IV 1986 150 11.0% 1.8 Dec-04
V 1989 150 35.7% 4.0 Dec-04
VI 1992 173 39.2% 3.3 Mar-04
VII 1994 225
1
121.7% 32.0 Mar-04
VIII 1996 299 286.6% 17.0 Mar-04
IX 1999 550 223.3% See text Mar-04
X 2000 625 217.5% 0.6 Mar-04
XI 2004 400 NA NA NA
XII 2006 600 NA NA NA
XIII 2008 700 NA NA NA
1
Only $170M of Fund VII was drawn down.
NOTE: There have been no publicly available updates of KPCB funds since December 2004.
Source: Dow Jones LP Galante, 2005 Private Equity Performance Monitor.
62 CHAPTER 3 VC RETURNS
KEY TERMS
Periodic return
Compound return
Annualized return
Gross return
Net return
Realized return
5 historical return
Expected return
Gatekeeper
Survivor bias
Internal rate of return (IRR)
J-curve
5 hockey stick
Value multiple
5 investment multiple
5 realization ratio
5 absolute return
5 multiple of money
5 times money
Realized value multiple,
unrealized value multiple
Gross value multiple
5 gross investment
multiple, etc.
Carry%
GP%
Top-quartile fund
REFERENCES
Hall, Robert E., and Susan Woodward, 2003, “Benchmarking the Returns to Venture”, National Bureau
of Economic Research working paper #10202.
Kaplan, Steven N., and Antoinette Schoar, 2005, “Private Equity Performance: Returns, Persistence, and
Capital Flows”, Journal of Finance 60(4), 1791À1824.
Private Equity Intelligence, The 2005 Private Equity Performance Monitor.
Private Equity Intelligence, The 2008 Private Equity Performance Monitor.
EXERCISES
3.1 The Bigco pension plan has invested in dozens of VC funds. The director of the pension
plan is preparing his annual report to the Bigco board of directors. Summary information for
Bigco’s VC portfolio is given in Exhibit 3-9.
The board has asked for a ?ve-year report of net returns and gross returns by year, plus
the compound returns and annualized returns for all ?ve years. You can assume that all new
investments and management fees were paid for at the beginning of the year, and all dis-
tributions were paid at the end of the year.
3.2 Consider the case of XYZ Partners from Example 3.3. Now, instead of using a GVM of
2.5 (as in the example), assume that this GVM is unknown and equal to K.
(a) For any given K, solve for the carried interest, value multiple, and GP%.
(b) How large must K be for the value multiple to be greater than 3?
(c) How would your answer to parts (a) and (b) change if the carry basis were equal to
investment capital? (In the original example, the carry basis is equal to committed capital.)
3.3 True, False, or Uncertain: If both EBV and Owl have the same GVM, then the value
multiple of Owl will be lower than the value multiple of EBV. (See Appendices 2.A and 2.C
for more information on EBV and Owl.)
EXERCISES 63
3.4 The $600M XYZ Fund has completed its 10-year life. Its annual investments, fees,
distributions, and portfolio value are given in Exhibit 3-10.
(a) Compute the value multiple, realized value multiple, unrealized value multiple, and IRR
for XYZ after every year of its life.
(b) Are these returns an example of the J-curve, or are they an exception?
EXHIBIT 3-10
CASH FLOWS FOR THE XYZ FUND
Year
1
Year
2
Year
3
Year
4
Year
5
Year
6
Year
7
Year
8
Year
9
Year
10
Investments 50.0 100.0 100.0 150.0 100.0 0.0 0.0 0.0 0.0 0.0
Portfolio value 50.0 167.5 326.1 387.8 353.5 381.8 412.3 445.3 480.9 519.4
Carried interest 0.0 0.0 0.0 0.0 0.0 0.0 15.9 17.8 19.2 103.9
Distributions to LPs 0.0 0.0 150.0 200.0 70.7 76.4 66.6 71.2 76.9 415.5
Cumulative
distributions to LPs
0.0 0.0 150.0 350.0 420.7 497.1 563.6 634.9 711.8 1127.3
Port value after
capital returned
50.0 167.5 176.1 187.8 282.8 305.4 329.8 356.2 384.7 0.0
Management fee 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
EXHIBIT 3-9
BIGCO PENSION PLAN, VC PORTFOLIO
Year 2010 2011 2012 2013 2014
Beginning value 10,000 10,300 13,105 5,563 6,332
New investments 2,000 2,000 2,000 2,000 2,000
Ending value (before distributions) 13,800 16,605 9,063 9,832 12,498
Distributions to LPs 3,000 3,000 3,000 3,000 3,000
Distributions to GPs 500 500 500 500 500
Management fees 200 200 200 200 200
64 CHAPTER 3 VC RETURNS
CHAPTER 4
THE COST OF CAPITAL FOR VC
VCS SHOULD make an investment if the expected return on the investment
is higher than the cost of capital. We dedicated part of Chapter 3 to an empirical
analysis of the returns to VC investment. In this chapter, we empirically analyze the
other side of this equation: the cost of capital. The main driver of the cost of capital
is the trade-off between risk and return. This analysis of the risk-return trade-off is
probably the biggest research topic in ?nancial economics. This chapter provides an
introduction to this important topic, with a focus on the implications for the cost of
venture capital.
In Section 4.1 we introduce the capital asset pricing model (CAPM). More than
40 years after its ?rst development, the CAPM remains a workhorse model for
computing the cost of capital. Although the CAPM is widely used, it remains
poorly understood by many practitioners. Indeed, the ideas behind the model are
often counterintuitive, and many people just apply the formulas without knowing
why. In Section 4.2 we tell an economic fairy tale to discuss the CAPM intuition
without all the mathematical details. This same intuition can be applied to more
complicated multifactor models of the cost of capital. In Section 4.3 we introduce
some multifactor models to directly estimate the cost of venture capital.
4.1 THE CAPITAL ASSET PRICING MODEL
Consider two investments: The ?rst investment is a manufacturer of cardboard
boxes (Boxco), an item always in some demand because of its use in transporting
goods around the world. Although the fortunes of this company rise and fall with the
economy, the peaks and valleys are not very extreme. As a ?rst approximation,
the earnings of the company are proportional to world GDP, and world GDP rarely
moves by more than a few percentage points in any given year. Next, consider an
investment in a drug company, currently searching for the cure to some rare disease
(Drugco). The research for this disease has made some progress, but still there is
only a 20 percent chance that the drug will succeed, and we won’t know about this
success for a few years. If it does succeed, then the company will have the exclusive
65
right to market the drug for about 10 years, and it would expect to plow back some
of these earnings into similar R&D efforts in the future. If the drug does not succeed,
then the company will go out of business and be worth nothing. Neither the success of
the project nor the pro?ts from this (or future) projects are at all related to the state
of the world economy. Now, consider two related questions. First, which of these
two companies is “riskier”? Second, which of these companies will have a higher
cost of capital?
If we equate risk with the statistical measure of variance, then Drugco is
riskier.
1
There is an 80 percent chance of complete failure, and even success on the
?rst drug does not guarantee success for the future. Boxco, on the other hand, does not
have a high variance. A wary reader might suspect a trick, and of course there is one.
The performance of Drugco is not related to the global economy. If we split the
ownership of Drugco into thousands of little pieces (shares of stock), and if we ?nd
thousands of companies similar to Drugco, then a portfolio of such investments would
be well diversi?ed and could actually have close to a zero variance. Thus, in this
example, Drugco has only idiosyncratic risk, also called diversi?able risk. On the
other hand, Boxco, despite having a relatively low variance, is perfectly correlated
with the economy. If we break Boxco into thousands of pieces and ?nd thousands of
similar companies, we will still be left with the same variance in our portfolio.
If we accept this discussion of risk, then which of these two companies will
have a higher cost of capital? The classic model used to answer this question is the
Capital Asset Pricing Model (CAPM):
r
i
5R
i
5R
f
1?ðR
m
2R
f
Þ ð4:1Þ
where r
i
is the cost of capital for asset i, R
i
is the expected return for asset i, R
f
represents the risk-free rate for borrowing and lending, R
m
is the return on the
whole market portfolio, and ? (pronounced “beta”) is the level of risk for asset i.
The difference (R
m
2R
f
) is called the market premium. For this model to hold, the
?nancial market needs to be in equilibrium, so that the cost of capital for any
investment is equal to the expected return on that investment. Thus, for the
remainder of this discussion, we refer interchangeably to the “cost of capital” and
“expected return”. Although this might be a boring world to be an investor—
because all assets would trade at “fair” value—it is a very useful world if we are
trying to understand the trade-off between risk and return.
In our well-behaved equilibrium world, the CAPM applies to individual
companies like Drugco or Boxco, but asset i could also represent many other things.
For example:
1. Speci?c capital projects within companies, such as a factory to manufacture
boxes or drugs;
1
If you are unfamiliar with the de?nition of variance, then you are going to be very confused by this
chapter. Sorry.
66 CHAPTER 4 THE COST OF CAPITAL FOR VC
2. An entire industry or asset class, such as “all drug companies”, “small
stocks”, or “venture capital”;
3. The portfolio of a speci?c investment manager, such as a mutual fund or a
venture capital fund.
The key idea of the CAPM is that beta re?ects the covariance of an asset’s
returns with the returns on the overall market. The higher the beta, the higher the
expected return. Beta risk is also called market risk, nondiversi?able risk, or
systematic risk. The mathematics and intuition behind the CAPM implies that beta
risk is the only kind of risk that affects the expected return of an asset. As discussed
earlier for the Drugco example, risks that are uncorrelated with the market are
called diversi?able risk or idiosyncratic risk, and such risks are not compensated by
any extra return.
To make the CAPM operational, we need some way to estimate the variables
of (4.1). For R
i
, we can use the realized returns on asset i. For R
m
, we can use the
realized returns on a portfolio of all publicly traded stocks. For R
f
, we can use
the realized returns on short-term U.S. treasury bills. (Recall from Chapter 3 that
realized returns are the same thing as historical returns.) Then, using these realized
returns, the statistical method of least-squares regression can be used to estimate
beta. The standard approach is to modify Equation (4.1) to
R
it
2R
ft
5?1?ðR
mt
2R
ft
Þ 1e
it
ð4:2Þ
where ?, R
it
, R
mt
, and R
ft
are de?ned similarly to Equation (4.1)—except that in
(4.1) the return variables represented expected returns, whereas in (4.2) they
represent realized returns for period t. The new elements in (4.2) are ? (pronounced
“alpha”), the regression constant; and e
it
, the regression error term.
2
Once we have estimated Equation (4.2), we can use the results to compute a cost
of capital for asset i. The cost of capital is still given by Equation (4.1). To actually
compute this cost, we can substitute the regression estimate of beta into (4.1), but we
still need estimates for the risk-free rate, R
f
, and for the market premium (R
m
2R
f
). For
R
f
, most analysts recommend using the current treasury yield for a horizon that matches
the expected holding period of the investment. Thus, an investment with a ?ve-year
horizon would use the yield on the ?ve-year treasury bond. In this chapter we use a risk-
free rate of 4percent. For (R
m
2R
f
), one possibilityis touse the realizedmarket premium
over some historical period in some country or set of countries. For example, from1926
to 2008, the average market premium in the United States was approximately
7 percent.
3
Also, Welch (2000) ?nds that 7 percent is the average market premium
forecast by a sample of 226 academic ?nancial economists. Based on these two pieces
of evidence, we will use 7 percent as our estimated premiumin this book. Readers with
strong views about the premium should certainly experiment with other numbers.
2
An excellent introduction to regression techniques is Kennedy (2003). This book includes discussions at
several levels of technical detail and succeeds admirably on every level.
3
Ibbotson Associates (2009).
4.1 THE CAPITAL ASSET PRICING MODEL 67
With these estimates for the risk-free rate and the market premium, we can
compute the cost of capital as follows:
r
i
50:04 1
^
? Ã 0:07 ð4:3Þ
where
^
? is the regression estimate for beta. Thus, with a beta of 1, the typical stock
would have an 11 percent cost of capital.
By allowing the possibility of a regression constant (alpha) in Equation (4.2),
we are permitting realized returns on asset i to be higher than its cost of capital,
because the cost of capital is still given by the expected return of Equation (4.1). If
asset i is a managed asset such as a mutual fund or a VC fund, then alpha can be
interpreted as an abnormal return: if alpha is positive, then the manager has
earned a return higher than the cost of capital—a “positive abnormal return”; if
alpha is negative, then the manager has earned a return lower than the cost of
capital—a “negative abnormal return”. This interpretation of alpha as abnormal
returns means that we can use the regression in Equation (4.2) to measure the
investment performance of an asset class or asset manager. For this reason,
Equation (4.2) is sometimes called a performance evaluation regression.
EXAMPLE 4.1
The Largeco pension fund aggregates its entire portfolio every month across all asset classes
and computes its net returns, R
i
. Exhibit 4-1 displays these monthly returns for one year,
along with the market returns and the risk-free treasury bill rates for those months.
EXHIBIT 4-1
LARGEO RETURNS
Month R
i
R
m
R
f
January 1.51% 2.24% 0.07%
February 1.34% 1.49% 0.06%
March 20.39% 21.16% 0.09%
April 22.45% 22.50% 0.08%
May 1.74% 1.35% 0.06%
June 2.33% 2.08% 0.08%
July 23.81% 23.87% 0.10%
August 0.32% 0.16% 0.11%
September 2.25% 1.95% 0.11%
October 2.01% 1.67% 0.11%
November 3.76% 4.68% 0.15%
December 2.43% 3.36% 0.16%
68 CHAPTER 4 THE COST OF CAPITAL FOR VC
Problem Use Equations (4.1) and (4.2) to estimate the beta, alpha, and cost of capital for
the Largeco portfolio. How do you evaluate its investment performance?
Solution Before estimating the regression, we subtract R
f
, the risk-free rate given in the last
column, from both the R
i
and the R
m
columns. We can then estimate Equation (4.2) using a
spreadsheet or other statistical package. The estimates are beta 50.88 and (monthly) alpha 50.07
percent. The alpha estimate is not statistically signi?cant, but it does indicate a positive abnormal
performance of 0.07 percent per month, which we can translate into an annualized alpha of
approximately 0.8 percent. To compute the cost of capital for the Largeco portfolio, we combine
our estimate of beta 50.88 with a market premium of 7 percent and risk-free rate of 4 percent:
r
i
50:04 10:88 Ã 0:07 510:16 percent ð4:4Þ
’
By using Equation (4.2) and allowing for the possibility of abnormal returns, we are
engaging in some seemingly paradoxical mental gymnastics. Equation (4.1)
requires that abnormal returns are zero in the future; that is, the cost of capital must
be exactly equal to the expected return, because there is no alpha in Equation (4.1).
However, once we estimate a nonzero alpha in Equation (4.2), we are willing to
allow some abnormal returns in the past. Presence of a nonzero alpha or abnormal
returns does not contradict Equation (4.1), however, as long as Equation (4.1) holds
on average across all assets. Among ?nancial economists, it is a bit of a cottage
industry to devise statistical tests to measure whether Equation (4.1) does indeed
hold “on average”. Overall, the CAPM held up very well in the 1970s; but
anomalous evidence started to accumulate in the 1980s, and by the 1990s most
researchers came to believe that the model needed some extensions. Nevertheless,
all these extensions are based on the same underlying concepts. In Section 4.2, we
provide some intuition for these concepts; and in Section 4.3, we develop the
extended models and apply them to the estimation of the cost of venture capital.
4.2 BETA AND THE BANANA BIRDS
To gain more intuition about the CAPM, let’s lose all touch with reality and enter
the fantasy world of ?nance professors. Imagine that our entire world is populated
by 100 people, all of whom live on their own island. Travel and trade between
islands is easy and free. Each island has 100 banana trees; these trees will last
forever, and no other trees can ever be planted. Bananas are all that anybody
consumes or ever wants to consume. On average, every year, a tree will produce
200 bananas, so that the whole world produces 200 bananas à 100 trees à 100
islands 52M bananas per year. There is no limit on how many bananas a person
can eat. Although never completely sated, each additional banana provides a little
less happiness than the last one: the 100th banana of the month does not bring as
much pleasure as the 99th. Bananas cannot be stored (they go brown fast, as we
know), so everything produced by the trees must be eaten each year.
4.2 BETA AND THE BANANA BIRDS 69
Of course, the world is not a total paradise—there is some risk. One risk comes
from a ?ock of wild banana birds that settle down onto half the islands every year, and
proceedtoeat all the bananas onthose islands (while theyare still green) sothat the trees
on that island produce no ripe bananas for the entire year. These banana birds seem to
choose their islands randomly, witheachislandhavinga 50percent chance ineachyear.
Thus, the overall number of ripe bananas available to all the islanders is 50%Ã
2M51M, with the other 1M (green) bananas consumed by the birds.
The bird risk is serious, because without any bananas for the year, the islander
will be very hungry. (Being hardy folk, islanders can survive without eating for
many years, but they are not happy about it.) For each individual islander, bird risk
has a high variance: the expected number of bananas is 100 per tree, but this
represents a 50 percent chance of getting 200 bananas per tree and a 50 percent
chance of getting zero bananas per tree. How does this bird risk affect the happiness
of the islanders? We assumed at the beginning of this story that the 100th banana
does not provide as much happiness as the 99th banana, giving us a “banana utility”
function shaped like Exhibit 4-2. An islander with a 50 percent chance at 20,000
bananas and 50 percent chance at 0 bananas would have an expected utility lying at
point B, the midpoint of line AD. She would be better off if she could get to point
C, which is the utility of getting 10,000 bananas for sure. All islanders feel this way,
so they try to construct some diversi?cation strategy to get there.
EXHIBIT 4-2
BANANA UTILITY WITH BIRD RISK
C
B
D
A 10K
Bananas
20K
U
t
i
l
i
t
y
70 CHAPTER 4 THE COST OF CAPITAL FOR VC
One islander hits upon a solution: she takes all her trees and forms a company
and then sells shares in her company to all the other islanders. Each tree on her
island has an expected production of 100 ripe bananas, so the total expected pro-
duction of her island company is 100 Ã 100 510,000 bananas. She divides up 100
shares in her company (1 percent of her company 5one tree for each share), keeps
one share for herself, and offers the other 99 shares to the other islanders. She sets
the price of a share to be one tree; that is, any other islander can buy 1 percent of
her Banana Company by giving up the future rights to one tree from his own island.
How does this deal look for the other islanders? First, note that the expected
return of the deal is zero; each islander expects to get back exactly what she puts in.
By investing one tree from her own island (expected production 5100 ripe
bananas), each islander receives in return 1 percent (5 one tree) of another island
(expected production 5100 ripe bananas). Second, note that the deal will be useful
diversi?cation for the buyer: before the deal, she had a 50 percent chance of getting
20,000 bananas for the year, but also a 50 percent chance of losing everything to the
birds and getting zero. After the deal, the buyer has reduced the chance of getting
zero, with an offsetting reduction in the chance of getting 20,000. A graphical
illustration of this change is shown in Exhibit 4-3. The diversi?cation effectively
moves the extreme outcomes toward the center (from points A and D toward points
A’ and D’). The new expected utility lies at B’, the midpoint of A’D’. Because B’ is
higher than B, the buyer has succeeded in increasing her expected utility.
EXHIBIT 4-3
BANANA UTILITY AFTER DIVERSIFICATION
B'
A'
B
C
D
D'
A 10K
Bananas
20K
U
t
i
l
i
t
y
4.2 BETA AND THE BANANA BIRDS 71
Once one islander gets the idea, all the others can follow. Each islander is
driven by the narrow pursuit of her own diversi?cation. Before long, every islander
has sold shares in her island to every other islander. With each purchase, the buying
islander moves her expected utility line further up, until the extreme points have
converged on point C. When the process is complete, every islander will own one
tree on every island, and they will all be perfectly diversi?ed, with a known con-
sumption of 10,000 bananas, independent of which islands the banana birds land
on. This is the way things work in a well-functioning ?nancial system. The risk of
birds landing on an island is idiosyncratic risk, also called a diversi?able risk: if
everyone tries to run away from this risk, they can successfully do so.
Next, let’s consider a different kind of risk: the weather. Consider again our
banana economy where each banana tree is expected to grow 100 bananas per year,
and nowassume that there are no birds to worry about. In this example, the total of 100
is the average of two possibilities: In a sunny year (50 percent chance), the trees grow
150 bananas each. In a rainy year (50 percent chance), they only grow 50 bananas
each. Thus, each island would grow 100 trees à 150 bananas 515,000 bananas in a
sunny year and 100 Ã 50 55,000 bananas in a rainy year.
How does this weather risk affect the happiness of the islanders? Recall the
banana-utility function (Exhibit 4-4). An islander with a 50 percent chance at
15,000 bananas (sunny year) and a 50 percent chance at 5,000 bananas (rainy year)
EXHIBIT 4-4
BANANA UTILITY WITH WEATHER RISK
C
Y
X
Z
10K 5K
Bananas
15K
U
t
i
l
i
t
y
72 CHAPTER 4 THE COST OF CAPITAL FOR VC
would have an expected utility lying at point Y, the midpoint of line XZ. As in the
case of bird risk, the islanders would like to diversify this risk and get to point C,
which gives them 10,000 bananas for sure.
Diversi?cation worked for bird risk, but it does not work here. The funda-
mental difference is that here, the total production in the world is affected by the
weather. For the population as a whole, there is no way that the islanders can run
away from the weather: if the weather is rainy, then the combined banana con-
sumption in the whole world will still only be 5KÃ 100 5500K, no matter how they
eventually share the bananas. For example, if the islanders try the same trick that
worked for the bird risk—each islander owns one tree on every island—then it will
have no effect on anyone’s banana consumption.
Despite the overall constraint, individual islanders will still have an incentive
to diversify. Imagine that an islander offers a contract to give up 100 bananas when
it is sunny in return for 100 bananas when it is rainy. Would anyone take the other
side of this deal? As in the bird example, the expected return is zero: Because each
outcome has a 50 percent chance, the expected value of the trade is zero bananas.
Here, however, we are asking someone to give up 100 bananas when they feel
relatively hungry (the rainy year) in return for 100 bananas when they feel rela-
tively sated (the sunny year). That is not a fair trade, and nobody is going to take it.
That 5,000th banana is worth more than the 15,000th; thus it will be necessary for
the ?rst islander to offer better terms.
Suppose that some “hardy islanders” are a little less bothered than other
“hungry islanders” when they must go without bananas. Then, while all islanders
are assumed to have a banana utility function shaped something like Exhibit 4-4,
the relative slopes of these utility functions would differ between hardy and hungry
types. In this case, there will be some trades in the banana tree market, with hardy
islanders giving up some bananas in rainy years in return for extra bananas in the
sunny years. Although we would need more information about the precise utility
functions to say exactly what prices will clear this market, we can be con?dent that
an even trade of bananas is not going to do it. Using only the information we have
so far, we know that the hardy islanders would demand a positive expected return to
do any trades from sunny to rainy. This is a feature of market risk, also called
nondiversi?able risk. For example, suppose the hardy and hungry islanders could
agree to a trade of one tree in the sunny season (5 150 bananas) for one tree in the
rainy season (5 50 bananas). In this case, the hardy islanders would be trading an
expected value of 50 Ã 50%525 bananas to get an expected value of 150 Ã 50%5
75 bananas, for an expected return of 75/25 21 5200%.
The reasoning used earlier can be extended to any additional risk in this banana
economy. If this risk is diversi?able, then islanders as a group will be able to run
away from it, and nobody would earn any additional return by agreeing to bear it. On
the other hand, if the risk is nondiversi?able, then the whole economy will not able to
run away from it, and anyone who agrees to bear it will demand an extra return.
These conclusions are not driven by the variance of the underlying risk.
Indeed, the bird risk has a higher variance than the weather risk, as can be seen by
4.2 BETA AND THE BANANA BIRDS 73
comparing Exhibits 4-2 and 4-4. Instead, the main driver of ?nancial risk is co-
variance. With weather risk, the output of each tree perfectly covaries with the
output of the entire economy. Anyone who takes on the risk of another tree is
committing to eat fewer bananas precisely when she (and everyone else) is hungry.
If you don’t pay someone an extra return to accept this risk from you, then she will
not accept it. This is the intuition behind measuring risk with the CAPM beta.
4.3 ESTIMATING THE COST OF CAPITAL FOR VC
Now, we travel back from our fantasy word of banana birds and return to the slightly
more real world of VC. What do you think is the beta of a typical VC investment?
A typical public stock will have a beta of one—do you think the beta on VC will be
higher or lower than one? Usually, most people think of VC as being very “risky”,
but this natural intuition tends to be driven by variance, not by covariance. Because
much of VC risk is diversi?able across many different investments—for example,
the risk that various new technologies will actually “work”—it would be premature
to conclude that the beta risk of VC is higher than it is for public equity.
To evaluate the performance of the whole VC industry, we estimate the
regressioninEquation (4.2) for boththe SandHill Index
s
andthe CAIndex. In the ?rst
case, we use monthly data for all the variables; in the second case, we use quarterly
data. The results are summarized in Exhibit 4-5, with alphas converted to annualized
percentage points in both cases.
The results of the standard CAPM model suggest that VC is less risky than the
market (beta ,1) and that it earns abnormal returns (alpha .0), although this
alpha is only signi?cant in the Sand Hill regression. The alphas are economically
large, giving us an estimated lower bound for abnormal gross returns (Sand Hill)
of 5.7 percent points per year and an estimated upper bound for abnormal net
returns of 6.1 percent per year (CA). If these numbers are correct, then they should
EXHIBIT 4-5
CAPM ESTIMATIONS FOR VC INDICES
Coefficient Sand Hill Index (monthly) CA Index (quarterly)
Alpha (in % per year) 4.92
ÃÃÃ
6.10
Market beta 0.76
ÃÃÃ
0.56
ÃÃÃ
Adjusted R-squared 0.72 0.19
Sample period Jan. 1989 to Dec. 2008
(240 monthly observations)
1981:q2 to 2008:q4
(111 quarterly observations)
NOTE:
ÃÃÃ
,
ÃÃ
, and
Ã
indicate statistical signi?cance at the 1, 5, and 10% level, respectively.
74 CHAPTER 4 THE COST OF CAPITAL FOR VC
have investors ?ocking to the asset class, but unfortunately for VCs, there are
three problems for the interpretation of these results: (1) style adjustments, (2)
liquidity risk, and (3) stale values. These problems are discussed and analyzed
later. The solutions to these problems induce large changes in estimated betas and
alphas.
Problem #1: Style Adjustments
In our regression in Equation (4.2), we estimated the market premium (R
m
2 R
f
)
using historical data on a market portfolio comprised of stocks traded in the
United States. In theory, the market portfolio should include all risky assets, traded
or untraded, everywhere in the world. Thus, this ideal market portfolio would
include the stocks, real estate, private equity, human capital, precious metals,
banana trees, and everything else we could think of—from every country in the
world. Clearly, it is not possible to collect all this data. In Chapter 3, we saw just
how dif?cult it was to collect this data for VC in the United States—and that is one
of the easy categories! The dif?culties of properly measuring the market portfolio
make it very dif?cult to test the CAPM because it is not possible to test the model
with the properly measured market premium. This critique, originally posed by Roll
(1977), was one of several early attacks on the underpinnings of the CAPM.
As part of the ongoing debate on the relevance of the CAPM, ?nancial
economists developed several theoretical models designed to more fully capture all
possible risks. Most of these models used logic similar to our banana economy,
where what people really care about are undiversi?able risks to their consumption.
The market portfolio, however measured, is likely to represent only some of that
risk. At the same time as these theoretical developments, empirical researchers
were demonstrating that the CAPM cannot adequately explain the returns of var-
ious investing styles, such as “small stocks” or “value stocks”. In effect, the
abnormal returns of these styles are too big to be explained by chance, so we can no
longer say that Equation (4.1) holds on average. By the early 1990s, we had
empirical and theoretical objections to the CAPM, but no good model to replace it.
Two researchers, Eugene Fama and Ken French, stepped into this breach with
a new empirical approach, and their Fama-French model (FFM) is now widely
used for estimating the cost of capital.
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1e
it
ð4:5Þ
where ?, ?, R
mt
, R
ft
, and e
it
are de?ned as in Equation (4.2), SIZE
t
and VALUE
t
are
the returns to portfolios of stocks designed to be highly correlated with their
respective investing styles, and ?
size
and ?
value
are the regression coef?cients on
these returns. These portfolios are called factors, so the FFM is a three-factor
model—a market factor, a size factor, and a value factor—and the betas are known
as factor loadings. The market factor, ?rst used in the CAPM model, is computed as
the difference between the return on the market (R
m
) and the return on treasury debt.
In effect, this is a zero-cost portfolio balanced between a 100 percent long position
4.3 ESTIMATING THE COST OF CAPITAL FOR VC 75
in stocks and a 100 percent short position in bonds. The other factors are also com-
puted as the returns to zero-cost long-short portfolios. The SIZE factor has a long
position in small-company stocks and a short position in large-company stocks. The
VALUE factor has a long position in “value” stocks (stocks with a high ratio of book
equity to market value) and a short position in “growth” stocks (stocks with a lowratio
of book equity to market value).
4
To use the results of Equation (4.5) to compute the cost of capital, we need
forecasts for the expected returns to the SIZE and VALUE factors. Over the
1926À2008 period, small stocks outperformed large stocks, and the SIZE factor
had an average return of 3 percent per year. In the last 30 years, however, this size
premium has dropped by about one-third, with an average return of 2 percent per
year in the 1979À2008 period. Based on this evidence, some researchers argue that
the return premium for small stocks has permanently changed. In this book, we will
weigh this recent evidence a bit more heavily than the older evidence and use a
forecast of 2.5 percent for the size factor.
The VALUE factor earned an average return of about 4 percent per year
over the 1926À2009 period, and this return dropped to about 3 percent over the
1979À2009 subperiod. Thus, we will use 3.5 percent as our VALUE forecast in this
book. Interestingly, the VALUE factor has fairly wide swings over some short time
periods. At the height of the boom period, technology growth stocks performed
very well: in the ?ve-year period from January 1995 to December 1999, VALUE
had a negative return of 9 percent per year, including a return of negative 33.4
percent in 1999. Conversely, in the ?ve years from January 2000 through December
2004, VALUE earned a positive return of 13 percent per year. Big difference!
With these forecasts in hand, we can compute a FFM version of the cost of
capital as follows:
r
i
50:04 1
^
? Ã 0:07 1
^
?
size
à 0:025 1
^
?
value
à 0:035 ð4:6Þ
where
^
?,
^
?
size
, and
^
?
value
are the estimated factor loadings on the market, size, and
value factors, respectively. The “typical” stock would have a factor loading of one
on the market factor, and zero on the other two factors, so the typical cost of capital
would be 11 percent, just as in the CAPM. For some stocks, however, the FFM can
give a very different estimate from the CAPM.
If we only need the cost of capital for a public company, then we might stop
right here. The choice of using the CAPM or the FFM often comes down to data
availability and time constraints. CAPM betas are available from many standard
library sources, and in recent years can even be found for free on Yahoo! Finance
4
The original reference for this model, withdetails onthe exact constructionof the factors, is Fama and French
(1993). Anontechnical discussion of the development of the Fama-French model is Fama and French (2004).
The Fama-French size and value factors, called “SMB” and “HML” in the ?nance literature, can be down-
loaded from Ken French’s website at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data library.
html.
76 CHAPTER 4 THE COST OF CAPITAL FOR VC
(http://?nance.yahoo.com). The long tradition of using CAPM betas on Wall Street
means that many ?rms have spreadsheets with built-in beta calculations. One must
work a bit harder to get Fama-French betas, but it is getting easier over time. For
practitioners who want to avoid having to estimate Equation (4.5) themselves, the
betas can now be obtained from several commercial sources.
Problem #2: Liquidity Risk
The Fama-French model is now almost 20 years old, and many challengers have
arrived in that time. For venture capital applications, the most important innovation
is the measurement of liquidity risk developed by Pastor and Stambaugh (2003).
Many practitioners feel that venture capital should earn a higher return because the
investments are illiquid. The Pastor-Stambaugh model (PSM) allows us to esti-
mate this premium using data on VC returns by adding a liquidity factor to the
FFM. Like the value and size factors of the FFM, the liquidity factor is based on
the returns to a zero-cost long-short portfolio—in this case, a portfolio that holds
“low-liquidity” stocks and sells short “high-liquidity” stocks.
5
The idea is that the
returns to this portfolio will re?ect the returns that investors require to hold illiquid
securities. The mathematical representation of the PSM is as follows:
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1?
liq
à LIQ
t
1e
it
ð4:7Þ
where LIQ is the new liquidity factor, ?
liq
is its factor loading, and all other
variables are de?ned as in Equation (4.5). Thus, this version of the PSM is a four-
factor model. The PSM is a young model, and it has not yet penetrated into practice
to the same degree as the FFM. Nevertheless, it is invaluable for our goal of
estimating an illiquidity premium for the cost of venture capital. To obtain a cost
of capital from this model, we need a forecast for the liquidity factor. The available
data to compute this factor only goes back to 1968. In the 1968À2008 period, the
average return to the liquidity factor was 5 percent per year, and we use an expected
return forecast of 5 percent for LIQ.
With the results of estimating Equation (4.7) and forecasts for the expected
returns to the factors, we can use the PSM to estimate a cost of capital as
r
i
50:04 1
^
? Ã 0:07 1
^
?
size
à 0:025 1
^
?
value
à 0:035 1
^
?
liq
à 0:05 ð4:8Þ
where
^
?
liq
is the estimated factor loading on the liquidity factor, and the other
variables are de?ned as in Equation (4.6). As in the case of the FFM, the “typical”
stock would have a factor loading of one on the market factor and zero on the other
factors, so the typical cost of capital would still be 11 percent.
5
The liquidity factor data can be downloaded from Lubos Pastor’s website at http://faculty.chicagobooth
.edu/lubos.pastor/research/liq_data_1962_2008.txt.
4.3 ESTIMATING THE COST OF CAPITAL FOR VC 77
Problem #3: Stale Values
The CA index relies on the quarterly reports made by the GPs. In these reports, GPs
include an estimate of the values for unrealized investments. As mentioned earlier,
these estimates are often based on very old information, leading to the phenomenon
of stale values. Indeed, many GPs simply report all valuations based on the most
recent round of ?nancing, even if a company’s outlook had changed signi?cantly
since that time. During a rising market, this practice is considered to be con-
servative; but in the postboom period, some LPs began to complain that these old
valuations signi?cantly overstated the value of the portfolios and made it dif?cult
for LPs to properly assess their holdings. In either case, it is clear that such
valuations will not re?ect the current market values of the companies.
Stale values cause problems when we estimate the regression models as in
Equations (4.2), (4.5), or (4.7). In particular, our beta estimates will be downward
biased, because the stale prices will not re?ect the full current impact of the market on
the value of VC companies. (For example, if the “true beta” in the CAPM is equal to
one, but only half the companies have updated values, then we will estimate a beta of
only 0.5.) If the beta estimates are downward biased, then all the unexplained returns
are “credited” to alpha, which would then be upward biased in most cases.
These potential biases are particularly severe for the CA index. The Sand Hill
Index
s
uses several statistical adjustments to reduce the stale value problem, but
even these methods cannot completely eliminate it. To adjust our regressions for
stale values, we include past values on the right-hand side of the regressions: two
years of past values for the market factor, and one year of past values for the other
three factors. The PSM regression equation with these past values (shown here for
the monthly return regression using Sand Hill Index
s
returns), called “lags”, is as
follows:
R
vc;t
2R
ft
5
X
23
s 50
?
s
à ðR
m;t 2s
2R
f;t 2s
Þ 1
X
11
s 50
?
size
s
à SIZE
t 2s
1
X
11
s 50
?
value
s
à VALUE
t 2s
1
X
11
s 50
?
liq
s
à LIQ
t 2s
ð4:9Þ
This equation can be estimated using the same techniques as in Exhibit 4-5, where
the effective VC beta on the market is now de?ned as
? 5
X
23
s 50
?
s
ð4:10Þ
with equivalent de?nitions for the other factor loadings, except they are summed
over 12 months instead of 24 (for CA Index returns, we sum over eight quarters for
the market premium factor and over four quarters for the other factors). Thus, the
cost of capital is still given by Equation (4.7).
With these de?nitions in hand, we are prepared to estimate the cost of venture
capital using the PSM (Exhibit 4-6).
78 CHAPTER 4 THE COST OF CAPITAL FOR VC
Our ?rst use of these results is to estimate a cost of venture capital. Substituting
these beta estimates into Equation (4.8) for the SHE index yields the following:
r
i
50:04 11:63 Ã 0:07 20:09 Ã 0:025 20:68 Ã 0:035 10:26 Ã 0:05 514:1% ð4:11Þ
Similarly, substituting the beta estimates for the CA index yields this:
r
i
50:04 1 2:04 Ã 0:07 1 1:04 Ã 0:025 2 1:46 Ã 0:035 1 0:15 Ã 0:05
516:6%
ð4:12Þ
In this book we take the midpoint of the two estimates and round off this cost
of capital for VC to 15 percent. Note that the illiquidity premium is 0.26 Ã 0.05 or
0.15 Ã 0.05, which is approximately equal to 1 percent using either estimate.
Our second use of these results is to evaluate the performance of the VC
industry. With all adjustments taken into account, the alphas for both CA and SHE
are not signi?cantly different from zero. Recall from Chapter 3 that CA represents
an upper bound on the net returns to VC, and SHE represents a lower bound on the
gross returns. Thus, these results suggest a point estimate of 113 basis points
and 26.11 percent (22.11% 24%) for the upper and lower bound of net
abnormal returns.
SUMMARY
Investors cannot do their job without ?rst estimating their cost of capital. In general, the cost
of capital depends on the nondiversi?able risk of an investment. The classic model of
nondiversi?able risk is the capital asset pricing model (CAPM), which relates the cost
of capital to the market (beta) risk of an investment. In recent years ?nancial economists have
EXHIBIT 4-6
PASTOR-STAMBAUGH MODEL ESTIMATION FOR VC INDICES
Coefficient Sand Hill Index (monthly) CA Index (quarterly)
Alpha (in % per year) 22.11 0.13
Market beta 1.63
ÃÃÃ
2.04
ÃÃÃ
Size beta 20.09 1.04
ÃÃÃ
Value beta 20.68
ÃÃÃ
21.46
ÃÃÃ
Liquidity beta 0.26
ÃÃ
0.15
Adjusted R
2
0.83 0.55
Sample period Jan. 1989 to Dec. 2008
(240 monthly observations)
1981:q2 to 2008:q4
(111 quarterly observations)
NOTE:
ÃÃÃ
,
ÃÃ
, and
Ã
indicate statistical signi?cance at the 1, 5, and 10% level, respectively.
SUMMARY 79
extended the CAPM to include other forms of nondiversi?able risk, including factors related
to company size, value/growth status, and liquidity. When estimating the cost of venture
capital, we need to take these additional factors into account, as well as make adjustments for
the slow-moving values in VC portfolios. With these modi?cations, we estimate a cost of
venture capital of 15 percent. We can also use the same models to evaluate the performance
(alpha) of the VC industry. We estimate that the upper bound for the net alpha and the lower
bound for the gross alpha are both very close to zero.
KEY TERMS
Capital asset pricing model
(CAPM)
Multifactor models,
Fama-French Model
(FFM),
Pastor-Stambaugh Model
(PSM)
Variance, covariance
Idiosyncratic risk
5 diversifiable risk
Market portfolio
Beta (?), alpha (?)
Market premium, market
portfolio
Market risk
5 nondiversifiable risk
5 systematic risk
Least-squares regression
Abnormal return
Performance-evaluation
regression
Style adjustments
Liquidity risk
Stale values
Factor loadings
Long position, short
position, zero-cost
long-short portfolio
REFERENCES
Fama, Eugene, and Kenneth French, 1993, “Common Risk Factors in the Returns on Stocks and Bonds”,
Journal of Financial Economics 33(1), 3À56.
Fama, Eugene, and Kenneth French, 2004, “The Capital-Asset-Pricing-Model: Theory and Evidence”,
Journal of Financial Economics 18(3), 25À46.
Ibbotson Associates, 2009, Stocks, Bonds, Bills, and In?ation, Ibbotson Associates, Chicago.
Kennedy, Peter, 2003, A Guide to Econometrics, 5th Edition, MIT Press, Cambridge.
Pastor, Lubos and Robert Stambaugh, 2003, “Liquidity Risk and Expected Stock Returns”, Journal of
Political Economy 111(3), 642À685.
Roll, Richard, 1977, “A Critique of the Asset Pricing Theory’s Tests. Part I: On Past and Potential
Testability of the Theory”, Journal of Financial Economics 4(2), 129À176.
Welch, Ivo, 2000, “Views of Financial Economists on the Equity Premium and on Professional Con-
troversies”, Journal of Business 73(4), 501À538.
EXERCISES
4.1 The Largeco pension fund aggregates its entire portfolio every month across all asset
classes and computes its net returns, R
i
. Exhibit 4-7 displays these monthly returns for one
year, along with the market returns and the risk-free treasury bill rates for those months. Use
Equations (4.1) and (4.2) to estimate the beta, alpha, and cost of capital for the Largeco
portfolio. How do you evaluate its investment performance?
80 CHAPTER 4 THE COST OF CAPITAL FOR VC
4.2 True, False, or Uncertain: Early stage venture capital should earn a higher expected
return than later-stage venture capital, because early stage ventures have a higher failure rate
than later-stage ventures.
4.3 Consider the following three companies:
(i) Gasco owns and operates a chain of gas stations in the northeast United States.
(ii) Fuelco is a prerevenue company that is attempting to develop new fuel cell
technologies to replace the internal combustion engine.
(iii) Combco combines the operations of Gasco and Fuelco.
Use qualitative reasoning to order the cost of capital for these three companies from lowest to
highest. (There is more than one reasonable way to answer this question, but there are also
wrong ways to answer.)
4.4 Largeco pension plan begins investing in VC funds in 2006. They commit to a few new
funds every year. They compute returns to their VC portfolio by adding the cash ?ows they
receive and the reported company values from all their funds. In 2016, the Chief Investment
Of?cer of Largco (you!) asks for a report on Largco’s VC performance over the prior 10
years. The head of the VC team estimates the following CAPM regression:
R
t
2R
ft
5?1?ðR
mt
2R
ft
Þ 1e
it
;
where R
t
is the realized quarterly return on the VC portfolio, R
ft
represents the risk-free rate
for borrowing and lending, R
mt
is the realized return on the market portfolio, ? (beta) is the
EXHIBIT 4-7
LARGECO RETURNS
Month R
i
R
m
R
f
January 1.51% 2.24% 0.07%
February 1.34% 1.49% 0.06%
March 20.39% 21.16% 0.09%
April 22.45% 22.50% 0.08%
May 1.74% 1.35% 0.06%
June 2.33% 2.08% 0.08%
July 23.81% 23.87% 0.10%
August 0.32% 0.16% 0.11%
September 2.25% 1.95% 0.11%
October 2.01% 1.67% 0.11%
November 3.76% 4.68% 0.15%
December 2.43% 3.36% 0.16%
EXERCISES 81
regression slope coef?cient, ? (alpha) is the regression intercept, and e
it
is the regression
error term. All variables are measured quarterly with time periods given by t. The regression
produces statistically signi?cant estimates of ? 50.75 and ?57.50 (annualized), with an R
2
of 0.32. Members of your staff—Albert, Bonnie, Chris, Dave, and Ellen—raise several
concerns with these results. As the Chief Investment Of?cer, you must evaluate these con-
cerns. Which ones (if any) are valid? Which ones (if any) are invalid? For the valid concerns,
is there any possible ?x?
(a) Al thinks that the estimated alpha is too high because of survivor bias.
(b) Bonnie thinks that the estimated beta is too low because of a stale value problem.
(c) Chris thinks that this model does not properly adjust for the high probability of failure
for VC investments.
(d) Dave thinks that this model does not properly adjust for the illiquidity of VC
investments.
(e) Ellen thinks something else is wrong, but she can’t put her ?nger on it.
82 CHAPTER 4 THE COST OF CAPITAL FOR VC
CHAPTER 5
THE BEST VCs
IN THIS CHAPTER we discuss speci?c VC ?rms and their activities in more
detail. The notion that a VC ?rm’s reputation can play a direct role in its future
success is an important theme of this chapter. The empirical support for this notion is
developed in Hsu (2004), who uses a sample of startup companies that received
multiple offers from VCs. Then, using a simple measure of VC reputation, he ?nds
that high-reputation VCs are more likely to have their offers accepted than are low-
reputation VCs. Furthermore, high-reputation VCs pay between 10 and 14 percent
less for shares than do low-reputation VCs. Thus, even if reputation is worth nothing
else, it enables VCs to get cheaper prices and more acceptances for their offers.
Section 5.1 discusses some basic economics of venture capital ?rms, using a simple
model of supply and demand to gain insight into the key drivers of VC performance
and reputation. Section 5.2 provides a subjective listing of 15 “top-tier” VC ?rms.
This list provides an opportunity to discuss the history, performance, and strategies of
some top VC ?rms. In Section 5.3, we discuss how VC skills and reputation can add
value for its portfolio ?rms through monitoring activities: board representation,
corporate governance, human resources, matchmaking, and strategy. These value-
added activities of high-reputation VCs provide one justi?cation for the willingness of
portfolio companies to accept lower prices from these ?rms, as found by Hsu (2004).
5.1 THE ECONOMICS OF VC
In Chapter 3, we discussed evidence of performance persistence among VCs. In
general, performance in one fund helps predict performance in subsequent funds
raised by the same ?rm. Because LPs recognize this relationship, they react to good
performance in Fund X by increasing their demand for Fund X11. An increase in
demand can be met by some combination of an increase in price (carried interest and
management fees) and quantity (size of the fund). It is interesting, however, that VCs
rarely raise prices or quantities to a level that clears the market; there is almost always
excess demand to get into funds raised by successful ?rms. There are two main reasons
for this phenomenon: one from the “supply side” and one from the “demand side”.
83
First, we analyze the supply side. Exhibit 5-1 gives an abstract representation of
the typical dilemma facing a VC. The X-axis represents the total amount of invest-
ment made by a VC for any given time period. To decide on whether to make an
investment, the VC compares the expected return on investment (ROI) with the
appropriate cost of capital for VC(r). As a conceptual device, we imagine that the VC
has ordered his investment ideas frombest to worst, which ensures that the ROI curve
is downward sloping. Furthermore, the VC’s time is limited; so with each additional
investment, he has less time to devote to each of the others, which also counts against
the ROI of each newproject. Fromthe evidence of Chapter 4, we assume that the cost
of capital (r) is constant, equal to 15 percent for all possible projects; therefore, r can
be represented by a straight line. At the optimal investment I
Ã
, the ROI will be exactly
equal to r. Although this marginal investment does not earn any economic pro?ts, the
earlier investments do, with the total economic pro?ts given by the region above r and
below the ROI curve. Another way to compute these pro?ts is by calculating the
return on capital (R), which is de?ned as the average ROI of all investments. At the
optimal investment level, I
Ã
, we have R=R
Ã
. In the language of microeconomics, ROI
is a marginal bene?t, Ris an average bene?t, r is a marginal cost, and economic pro?ts
are given by the product of (R
Ã
2r) and I
Ã
. For any given model used to estimate r, the
difference between R and r will be the alpha for the manager.
Under the representation in Exhibit 5-1, the optimal portfolio size for any VC
is driven by the height and slope of the ROI line with respect to the cost of capital.
VC investing is hard, and we are sure that if we took a random person off the street,
his entire ROI line would lie below the cost of capital, suggesting that this person
has absolutely no ability to make pro?ts on any investments. Some moderately
talented individuals might get one good idea a year, so I
Ã
would be a few million
dollars, with all other investments earning negative economic pro?ts. In all like-
lihood, such individuals would not earn enough money to be professional VCs and
would be better off plying their trade in another profession. The evidence of Chapter 3
suggests that there are a few people with consistent top performance and I
Ã
high
enough to support a lucrative career as a VC. Nevertheless, even these VCs recognize
that most of what they do is not scalable, and there are limits on the total number of
investments that they can make. The numbers from Chapter 2 (Exhibit 2-2) give
estimates of $197B for the total committed capital in the industry, as managed by an
estimated 7,497 VC professionals. This means that the industry is managing about
$26M per investment professional (with just a couple of exceptions). Even the most
famous VCfunds—listed in Exhibit 5-2—usually only manage about $50Mto $100M
per professional. A pyramid-like structure, with junior VCs doing the work with
companies and overseen by a senior VC, has never been a successful VC model.
Thus, to increase the size of a fund, a ?rm would need to hire more senior pro-
fessionals. If these professionals donot have the same quality as the incumbent members
of the ?rm, thenthe overall fundreturns will suffer. Evenif high-qualityprofessionals are
hired, there are still organizational constraints of the VC model: Because most ?rms
allow partners to share in the majority of carried interest from all deals, a large orga-
nization will tend to weaken the incentives for individual partners. Thus, ?rms are
understandably reluctant to increase fund sizes byvery much. One apparent exception to
84 CHAPTER 5 THE BEST VCs
this reluctance occurred during the boomperiod, when capital per partner increased by a
factor of ?ve at many ?rms. The exception can be understood as a natural reaction to
increased investment sizes for each portfolio company combined with shorter holding
periods. In the postboom period, fund sizes have returned closer to historical levels.
This supply-side reasoning can explain why ?rms do not increase fund sizes
to clear the market, but it cannot explain why they do not increase prices (carried
interest) to do so. To explain the failure of prices to clear the market, we need a
demand-side explanation. Of course, some ?rms do raise their carried interest—at
the height of the boom a few dozen VCs had increased carried interest on new funds
to 25 or even 30 percent—but even these ?rms do not raise carried interest as much
as they could have. For example, Accel Partners raised carried interest to 30 percent
in 1999 for its $500M Accel VII fund, but still managed to raise the fund in a few
months and to leave many LPs desiring a higher stake.
1
As a market leader, Kleiner Perkins Cau?eld & Byers was also at a 30 percent
carry and barely had to lift the phone to raise its most recent fund. Surely it could
have raised its carried interest to 35% and still raised the same size fund. The main
EXHIBIT 5-1
RETURNS AND INVESTMENT
120%
70%
–30%
–80%
20%
Return on investment (ROI)
Cost of capital (r)
Return on capital (R)
R*
I*
Investment
R
e
t
u
r
n
r
R
ROI
1
See Kaplan (1999) for a discussion of this Accel fundraising process.
5.1 THE ECONOMICS OF VC 85
reason to avoid doing this is to preserve the long-run value of its franchise. Suppose
it did raise carried interest to 35 percent. At this price, the ?rm would lose some of
its LPs. (If it didn’t lose any, then it should raise the carry even more, right?) These
LPs would be replaced by others who had been clamoring for a place. But now,
fundraising is not so easy anymore. The KPCB partners might have to travel around
a bit and sell themselves. This takes time away from working with their portfolio
companies. Furthermore, the ?rm’s mix of LPs would be different, and some of the
long-serving LPs would be gone. The new LPs, lacking the long-standing rela-
tionship, are less likely to remain loyal if the ?rm has a poor performing fund. If
that occurs, the ?rm would need to take even more time to raise its next fund. The
KPCB partners probably decided that this extra time—and the risk to investor
loyalty—was worth more than the extra return from raising the carried interest on
one fund.
2
5.2 THE BEST VCs: A SUBJECTIVE LIST
In this section, we select the top 15 VC ?rms in the world, using our own arbitrary
and subjective criteria. We do this because it gives us a good chance to discuss the
various strategies employed by the best ?rms in the world and to provide a
springboard for discussing the value of a VC reputation in the rest of the book. Of
course, other market watchers will have different opinions, but this is our book, so
we get our list. The 15 ?rms divide naturally into two groups. The six ?rms in
Group A were the easiest to select, for reasons that will be described later. These
?rms represent our selection as the top six in the world, and we do not think that
this grouping will be very controversial. The nine ?rms in Group B were more
dif?cult to select, and many other ?rms could reasonably have been included.
We begin with a few de?nitions. Although industry participants frequently
refer to top-tier ?rms, it is never clear exactly who belongs in this group. In this
book, when we use the expression top-tier ?rm, we will always be referring to the
15 ?rms on this list. Furthermore, when we refer to a star fund, we mean a speci?c
VC fund with at least $50M in committed capital and a value multiple of ?ve or
greater. A superstar fund must have committed capital of at least $50M and a value
multiple of 10 or greater. It would be ideal if we could also use IRR as part of this
de?nition; but data on IRRs are less complete than are data on value multiples, so
we rely only on the latter for the achievement of star and superstar status.
(Remember that the use of bold italics means that these de?nitions are special to
this book, and are not industry-standard terms.)
2
Yet another bene?t of not clearing the market might be to keep the emergency option of raising annex
funds in times of severe market busts. Both in the aftermath of the dot.com bubble and in 2009, a number
of top-tier VC (and buyout) ?rms (including KPCB) raised annex funds from existing and new investors
to ensure suf?cient capital to feed their existing portfolio companies while the market recovered.
86 CHAPTER 5 THE BEST VCs
A few comments on the criteria used for selection:
1. In the last several years, the industry publication Private Equity Analyst has
reported on ?rms that have been able to raise their carried interest to 30
percent. The publication identi?es eight such VC ?rms, including all six
?rms from Group A. A seventh ?rm, New Enterprise Associates, is included
in Group B. The eighth ?rm, Bain Capital, charged a 30 percent carry on a
VC fund, but had earned its reputation (and an earlier 30 percent carry)
primarily as an LBO ?rm.
2. The Private Equity Performance Monitor, a new industry publication ?rst
discussed in Chapter 3, allows us to observe the performance for 1,193 VC
funds. From this sample of funds, 63 (about 5 percent) have achieved at least
star status. Of these 63 stars, 18 had committed capital of less than $50M, so we
drop them.
3
Of the remaining 45 stars, 14 have achieved superstar status. Only
six?rms have achieveda superstar fundwithat least $100Minsize plus another
star (or better) fund. These are the six ?rms in Group A. (Not coincidentally,
this represents six of the eight ?rms with a con?rmed 30 percent carry.)
3. Items (1) and (2) make it easy to identify the top six ?rms for Group A. To
identify the nine ?rms in Group B, the primary driver was consistency of
top-quartile and top-half performance, presence of star funds (if any),
combined with information on carried interest percentage (when available),
history of innovative VC strategy, and our own subjective view of their
reputation in the industry.
Exhibit 5-2 gives the rankings, along with a few key facts about each ?rm. We
followthe exhibit with a short discussion of each ?rm. We will then use these ?rms as a
reference as we discuss VC activities and competitive advantage in Section 5.3. Note
that four of the top-tier ?rms, including three fromGroup A, are located in Menlo Park,
California, right in the heart of Silicon Valley. Menlo Park is the center of the VC
universe, with about 60 VC?rms, more than 80%of which—including all eight on our
list—have their of?ces on one street: Sand Hill Road. This curious agglomeration of
VCactivity demonstrates a phenomenon that economists call “local network effects”,
where ?rms in the same industry co-locate to take advantage of (and thus add to) the
bene?ts of that local human capital and other shared resources. Although many Silicon
Valley startups are riding the outsourcing wave for some of their corporate functions, it
is telling that the top-management function usually remains in Silicon Valley, and
many of the most successful investors remain onone street in MenloPark. Not onlyhas
this part of VC resisted globalization, but so far it has also resisted Americanization
(most VCremains in small pockets of the United States instead of spreading to cheaper
3
Prevalence of small funds among star funds is expected, and in most cases these are the VC ?rms’ ?rst
funds that had a home run or two. It is much harder for ?rms to repeat the .5X returns with subsequent
larger funds.
5.2 THE BEST VCs: A SUBJECTIVE LIST 87
places in the country), Californization (California VC is overrepresented in Silicon
Valley), and even Menlo Parkization (Sand Hill Road rents must be among the highest
inthe city—whydon’t more VCs move?). This demonstrates that local networkeffects
remain an important brake on the geographic homogenization of economic activity.
In a cross-country echo of the local network effects on Sand Hill Road, we
see that two of the ?rms on the list are located in Waltham, Massachusetts, which
lies within the second-largest VC agglomeration in the world: the Route 128 cor-
ridor around Boston. These two ?rms, Matrix Partners and Charles River Ventures,
are not only in the same town and street (Winter Street—the Sand Hill Road of the
east), but also in the same building (1000 Winter Street). All told, there are 16 VC
?rms in the small town of Waltham, with 13 of them on Winter Street—and six of
them at the same 1000 address. Battery Ventures, another top-tier VC, is only
minutes away in the neighboring town of Wellesley.
There is an important caveat to doing this exercise: as is well known among
industry participants, no one did spectacularly well after 2000, and even the Group A
funds, if they don’t performin the next ?ve years, could be in big trouble. Also, there is
not a lot of data since ?ve years ago to update the list; so the ranking is still largely
EXHIBIT 5-2
TOP-TIER VENTURE CAPITALISTS
Group Name Location Founded
$ under
management
A Accel Partners Palo Alto, CA 1983 $6.0B
Benchmark Capital Menlo Park, CA 1985 $2.9B
Charles River Ventures Waltham, MA 1970 $2.4B
Kleiner Perkins Cau?eld and Byers Menlo Park, CA 1972 $3.3B
Matrix Partners Waltham, MA 1982 $4.1B
Sequoia Capital Menlo Park, CA 1971 $4.0B
B Battery Ventures Wellesley, MA 1983 $3.2B
Doll Capital Management (DCM) Menlo Park, CA 1996 $2.0B
Draper Fisher Jurvetson Menlo Park, CA 1986 $4.4B
Institutional Venture Partners Menlo Park, CA 1974 $2.2B
InterWest Partners Menlo Park, CA 1979 $2.8B
Menlo Ventures Menlo Park, CA 1976 $4.0B
New Enterprise Associates Baltimore, MD 1978 $10.7B
Summit Partners Boston, MA 1984 $11.2B
Technology Crossover Ventures Palo Alto, CA 1995 $7.7B
NOTE: Firms are listed alphabetically within each group.
Source: Dow Jones LP Source Galante, Firm websites.
88 CHAPTER 5 THE BEST VCs
based on the performance from the 1990s and the inferences made from the fact that
these funds are still easily raising funds from LPs (who know the true performance).
Now, let’s go to the list. We begin with the Group A ?rms, in alphabe-
tical order.
Group A
Accel Partners is a ?rmthat rode the boom, had a bumpy ride in the postboomperiod,
and seems to have survived with its stellar reputation bruised but alive. In business
since 1983, it has raised 10 general funds; the most recent, Accel X, closed with
$520M in 2007. In addition to these general funds, Accel was the ?rst major VC to
raise a dedicated “Internet fund”, with the $20M Accel Internet Fund I raised in 1996
and three subsequent Internet funds raised over the next four years. Accel has also
been an innovator in other ways, with geographic expansion (the $500M Accel
Europe fund raised in 2001, second European fund raised with $450Min 2005, and the
$60M Accel India Venture Fund raised in 2008), and a unique partnership with
the most famous name in LBO investing—Kohlberg Kravis Roberts & Co.,
with whom it raised the joint Accel-KKR fund, with $500M in 2000, and two sub-
sequent funds in 2006 and 2008 at $400M and $600M, respectively.
4
Accel’s ?rst star fund was the $135M Accel IV raised in 1993, and it sealed its
reputation with the superstar $150M Accel V fund raised in 1996.
5
By the time of the
$500M Accel VII fund raised in 1999, it had joined the elite with a 30 percent carry.
The ?rmhit rough times with its 2001 Accel VIII fund. Originally, this fund had $1.6B
in committed capital. In the postboom period, it became apparent to Accel and to
many other GPs that the available opportunities were insuf?cient to sustain these
boomtime megafunds, and it subsequently reduced the size of this fund to $680M, but
not before some controversial attempts to extend its investment period on the full
amount. The LP community appears to have forgiven this episode, however, because
it effortlessly raised Accel IX with a 30 percent carry and almost certainly kept its
carry level for Accel X, judging from the LP demand. As of March 2007, Accel VIII
has returned 37 percent of committed capital and has a net IRR of 2.6 percent, which
puts it in the second quartile of its vintage year peers. Its best-known recent invest-
ment is Facebook, which it has yet to exit as of the writing of this book.
Benchmark Capital is the new kid on the block among the Group A ?rms.
Its ?rst fund, the $113M Benchmark Capital Partners Fund raised in 1995, had a
spectacular investment in eBay, which netted the fund (LPs 1GPs) $2.5B on a $5M
investment. eBay was not the only successful exit for this fund, as the fund is
reported to have earned a value multiple of 42X, giving it the highest reported
4
Unless otherwise noted, all citations to fund sizes, vintage years, and carried interest levels, are drawn
from Dow Jones Financial Information Services.
5
Unless otherwise noted, all performance data and citations to star funds or superstar funds are derived
from data from The 2005 and 2008 Private Equity Performance Monitor.
5.2 THE BEST VCs: A SUBJECTIVE LIST 89
multiple of all time. Benchmark II, a $250M fund raised in 1997, reached star status
to give the partners two great successes in a row. With this performance, it was able to
raise its carried interest to a ?at 30 percent by the time of the $1.1B Benchmark IV
fund in 1999. (Its previous funds had used a performance-based sliding scale for the
carry.) Like several other top-tier ?rms, Benchmark has expanded internationally,
with a $500M Europe fund raised in 2000 and a $260M Israel fund raised in 2002.
After successfully raising three Europe funds, Benchmark Europe was spun off in
2007 and changed its name to Balderton Capital; Benchmark Israel raised its second
fund ($250M) in 2005. As of March 2007, the 1999 Benchmark IV has returned 41
percent and has a net IRR of 0.2 percent, putting it in the second quartile among its
vintage year peers. The LPs have stayed loyal in return, and the $400MBenchmark V
fund was raised in 2004, followed by its latest, the $500M Benchmark VI raised in
2008. Its notable recent exits include OpenTable, which went public in May 2009 and
traded up 72% on its ?rst day of trading.
Charles River Ventures is one of the two Group A ?rms from 1000 Winter
Street in Waltham. The ?rm also maintains a smaller of?ce on Sand Hill Road,
giving it a presence in both VC centers. Like many of the other top-tier ?rms, it had
solid performance for many years, performed spectacularly in the boom, faltered in
the postboom period, and has regained its focus and reduced the size of its most
recent fund. Its ?rst star was the $85M 1995 Charles River VII fund. It gained
superstar status with its $100M 1997 VIII fund. Following this fund, it was able to
raise its carried interest to 30 percent, a level it has maintained ever since, most
recently with its $320M Charles River XIV fund raised in 2009. As of December
2006, its 2000 fund (CRV XI) has a net IRR of 0.9 percent, which puts it in the
second quartile of the 2000 vintage funds.
Charles River runs a seed program called QuickStart, which it launched in
2006 after recognizing that advances in technology had enabled Internet startups to
operate with much less cash than traditionally required. In this program, Charles
River invests $250K in the form of a loan to a promising new startup. Startups
accepting loans give Charles River the right to join a ?rst-round syndicate, with the
loan converting to equity at that point.
Our next fund, Kleiner Perkins Cau?eld & Byers (KPCB) was ?rst dis-
cussed in Chapter 3, where we saw evidence of two superstar funds (the $225M
KPCB VII and the $299M VIII), and we deduced that KPCB IX, a $550M fund
raised in 1999, de?ed the gravity of the worst vintage year in VC history and
reached star status with its Google exit. Perhaps even more impressive than these
returns is the list of famous KPCB investments: AOL, Amazon.com, Compaq,
Electronic Arts, Genentech, Google, Idec, Intuit, Juniper Networks, Netscape, Sun,
andSymantec. It is a “who’s who” of successful technologybusinesses, reachingacross
industry lines to leaders in life science, software, hardware, communications, and the
Internet. This performance has been sustained through multiple generations of ?rm
leadershipand seems innodanger of abating. That said, it is a bit troubling that KPCB’s
most recent funds’ (KPCBXÀKPCBXIII) performances are not publicly available as
of the writing of this book.
90 CHAPTER 5 THE BEST VCs
KPCB has recently made big bets in two directions: Asia and green tech-
nology. It closed the $360M China Fund in 2007 and now has two satellite of?ces
in Beijing and Shanghai. It also raised the Green Growth Fund in 2008, which
targets large clean-technology companies.
Matrix Partners shares a building in Waltham with Charles River Ventures
and also maintains a smaller of?ce on Sand Hill Road. Matrix had four straight top-
quartile funds from 1985 to 1997, including one star and two superstar funds: the
$80M 1990 Matrix III fund (star), the $125M 1995 Matrix IV fund (superstar), and
the $200M 1997 Matrix V fund (superstar). Indeed, Matrix came very close to
having two funds with value multiples above 20 (double-superstar?), which has not
even been accomplished by its famous peers from Sand Hill Road. Its investment
record includes several famous names and spans across software, hardware, and
communications, including Apple Computer, Veritas, and Sycamore Networks. Its
2000 Matrix VI has returned only 12 percent of committed capital and has little
chance of ever breaking even, as the remaining portfolio is held at 54 percent of
fund size. In contrast, its 2002 fund (Matrix VII) is doing much better, and has a net
IRR of 12.4 percent, putting it in the top quartile among its peers. In addition to its
latest general fund, the $450M (plus $150M optional fund) Matrix IX, raised in
2009, it also raised a China fund and an India fund in 2008 and 2006, respectively,
thus making inroads to two more fast-growing markets.
Sequoia Capital is certainly KPCB’s strongest competition for the title of
“most famous VC ?rm in the world”. Its investment list is almost as impressive as
KPCB’s—Apple, Cisco, Google, Electronic Arts, Symantec, Yahoo, YouTube—
missing only the life sciences breadth of its neighbor on Sand Hill Road. Note also the
overlap in investments between these two top ?rms. This is the most salient example
of the pervasive syndication of investments among ?rms of similar rank. In a VC
syndicate, a lead investor takes primary responsibility for the investment, usually
making the largest investment and taking the board seat. (In some cases, such as the
Google investment, this role can be shared by co-leads.) The other investors take
smaller stakes and may or may not get a board seat. Syndication helps to spread risk
and gain the bene?ts of larger networks. The prevalence of syndication varies over
time, often depending on the relative supply of capital. In the preboom period, syn-
dication was the norm. During the boom, it was comparatively rare.
Sequoia’s performance has been remarkable. It is the only ?rm in the world
with four con?rmed star funds (three of which were superstars): The $64M 1989
Sequoia V fund (star), the $100M 1993 Sequoia VI fund (superstar), the $150M
1996 Sequoia VII fund (superstar), and the $250M 1998 Sequoia VIII (superstar).
No other ?rm, not even KPCB, can match that record. KPCB’s main claim for the
top spot is that it has earned similar returns with funds about twice the size.
Group B
Battery Ventures is our third ?rm from the Route 128 corridor around Boston.
Relatively young for ?rms on this list (founded in 1983), Battery made up for lost
5.2 THE BEST VCs: A SUBJECTIVE LIST 91
time with six top-quartile funds in its ?rst six attempts, including the star $200M
1997 Battery Ventures IV. It charged a 25 percent carry on its seventh and eighth
funds (raised in 2004 and 2008). Re?ecting the tough economic conditions of
2009À2010, for its latest fundraising efforts for its ninth fund, targeted at $750M,
Battery plans to use a performance-based sliding scale, charging a base carry of 20
percent, which will climb to 30 percent once it returns three times capital to LPs.
Battery has a broad focus—both by stage and industry—and has made headlines by
teaming up with the Blackstone Group, a major LBO ?rm, on several deals.
DCM (Doll Capital Management) is the youngest ?rm in this list of top-tier
VCs—it was founded only in 1996. Though there are many other ?rms with much
longer track records, we pick this ?rm for two reasons. One is its relatively strong
track record in the non-U.S. markets, notably Asia, where we have seen the fastest
growth in recent years. It has had of?ces in Menlo Park, CA, and Beijing, China,
and recently opened a satellite of?ce in Tokyo as well. While many U.S. VC ?rms
have recently started investing in China, few can claim exits yet; in contrast, DCM
invested in the region as early as 2000, and has had a string of successful exits. Its
notable Asia investment exits include 51job (NASDAQ IPO in 2004), VanceInfo
(NYSE IPO in 2007), and Fortinet (NASDAQ IPO in 2009). Its notable domestic
U.S. investment exits include Foundry Networks (1999 IPO), About.com (1999
IPO; then acquired by New York Times; its Japanese af?liate also went public on
JASDAQ), and Neutral Tandem (NASDAQ IPO in 2007). According to the Wall
Street Journal, Fortinet was one of the best-performing VC-backed IPOs in 2009.
Another reason is the premium carry it charges. According to Private Equity
Analyst, its ?fth fund (the 2006 $505M DCM V) and its latest fund (DCM VI,
which is being raised amid the toughest economic conditions in decades) charge a
25 percent carry. We interpret this to be an indication of LPs’ enthusiasm about the
?rm’s international reach and recent successes.
Draper Fisher Jurvetson (DFJ) is an innovative ?rm that has experimented
with several different organizational forms and strategies. Its inclusion on this list
was a dif?cult decision, because not much performance information is available.
The $50M 1995 DFJ III fund reached star status, but we know very little about its
11 subsequent funds, save for the 1999 DFJ ePlanet Ventures (returned 136 percent
and is in the top quartile as of March 2007) and the 2000 DFJ VII (in the second
quartile as of September 2007). We include DFJ as a top-tier ?rm because of its
string of notable successful investments in companies including Skype, Athena-
Health, and Baidu, and because of its reputation as market leaders in extending its
VC brand. The DFJ “af?liate network” includes 17 ?rms across 13 locations on
three continents. Many of these ?rms are cobranded with the DFJ name, such as
Draper Triangle Ventures (Pennsylvania and Ohio), DFJ DragonFund (China), and
DFJ VTB Aurora (Russia).
It charged above-market carried interest of 25 percent from 1999 to 2007. In
its current efforts to raise the $250M DFJ X, it is offering a performance-based
sliding scale, charging a 20 percent base carry until the fund returns 2.5 times the
committed capital, at which point GPs will catch up to 25 percent.
92 CHAPTER 5 THE BEST VCs
Institutional Venture Partners would have made the Group B list in the ?rst
edition of this book, were it not for some uncertainty about its future given sig-
ni?cant personnel turnover at the time. The ?rm has apparently weathered the
transition well, and including it in the Group B list this time was an easy decision
for us, given its remarkable track record. It is a consistent performer with seven out
of its eight funds from 1985 to 2004 in the top half category. Three of them are
in the top quartile, including the 1994 $141M Institutional Venture Partners VI and
the 1996 $187M Fund VII, which were both star funds.
It has two of?ces, one in Menlo Park (on, you guessed it, Sand Hill Road) and
another north of San Francisco in Mill Valley, CA. It invests in late-stage private
technology companies in communications and wireless technology, enterprise IT,
and Internet and digital media. Its famous investments include TiVo, Juniper
Networks, Net?ix, MySQL, and more recently Twitter.
InterWest Partners is an early-stage VC ?rm founded in 1979. It is another
consistent performer, with six out of its seven funds from 1985 to 2005 in the top half
category. Three of them are in the top quartile. Commensurate with its long history
(its ?rst fund was raised in 1980), it boasts a long list of successful exits, with more
than 60 IPOs and nearly 60 upside acquisitions. Its early successes include Silicon
Graphics and Copper Mountain Inc., and its investments are about evenly split
between life sciences and IT areas. Its investments on the IT side are fairly con-
centrated in the San Francisco Bay Area, while its life science investments—which
are often originated in university research centers and in collaborations with bio-
pharmaceutical companies—are geographically more diverse, with locations as
varied as the Rocky Mountain states, San Diego, Northeast, and Florida.
Aside from the public record about its performance, another deciding factor
for including the ?rm on our list was its carried interest level; according to the Wall
Street Journal, it has charged 25 percent carry in the last decade.
Menlo Ventures, together with InterWest Partners, were honorable mentions
in the ?rst edition of this book. Menlo Ventures is an IT shop, meaning it does not
make any investments in life science ?rms, while it is open to investing in early to
late-stage rounds. It has one star fund, which is the 1988 $111M Menlo Ventures
IV; in addition, its 1997 $253M Menlo Ventures VII was almost a star fund, with
4.8X value multiple and a net IRR of 135.6 percent as of September 2007. Its 2001
$1.5B Menlo Ventures IX has a net IRR of 5.4 percent as of September 2007, which
puts it in the second quartile category. It invested in earlier Internet and commu-
nications companies such as Hotmail, Infoseek, and UUNET, and more recently
had successes with Acme Packet (2006 IPO) and Cavium Networks (2007 IPO). Its
slogan, “Big Ideas. Realized”, is quintessential Silicon Valley VC, and the ?rm
states it only targets “large” emerging markets that can support a $100M-per-year
revenue after achieving realistic market shares. Likewise, it has so far stuck to its
U.S.-centric model, with its focus on U.S.-headquartered companies only.
New Enterprise Associates (NEA) holds the distinction of raising the largest
dedicated VC fund in history. Unlike most other megafunds of the boom period, its
$2.3B 2000 NEA X fund was never reduced, and current performance places it
5.2 THE BEST VCs: A SUBJECTIVE LIST 93
among the top-quartile performers for its vintage. It later raised two more $2B1
funds, NEA XII ($2.5B, closed in 2006), and XIII ($2.5B, just closed as of January
2010). NEA’s history includes a remarkable six top-quartile performers, including
star status for the $230M 1993 NEA VI fund. Its famous investments include
Silicon Graphics and Immunex, and it has maintained a strong record across all
parts of the information technology and life sciences sectors, with a recent third
focus on energy investments. Though it still maintains its operations in Baltimore,
most of its investment professionals are located in either Silicon Valley or Chevy
Chase, MD, in the metropolitan DC area.
Like many of its peers, NEA has made efforts to globalize. In 2007, it con-
tributed $30Mfromits twelfth fund to $189MNEA-IndoUS Funds, which will invest
in early-stage IT companies in India. It has also made direct late-stage and growth
equity investments in companies outside of the United States using its core fund. As a
result, its twelfth fund investments consist of about 84 percent North America,
7 percent China, 4 percent India, and 5 percent the rest of the world. NEA is the only
?rm in Group B to have obtained a 30 percent carry, but it has done so while effec-
tively reducing its management fee percentage. Although this demonstrates a com-
mendable willingness to accept nearly exclusively performance-based compensation,
it also suggests slightly less pricing power than is enjoyed by Group A ?rms.
Summit Partners follows a resource-intensive, but very successful, strategy.
To generate investment opportunities, Summit has developed a proprietary database
of small to midsize companies. To maintain this database, Summit employs a
relatively large number of junior professionals to periodically communicate with
representative ?rms. Like many other ?rms, Summit also maintains a signi?cant
presence at technology industry events; but unlike most other ?rms, it takes a
systematic approach to its data gathering at these events, constantly adding to and
re?ning its database. The resulting database is the envy of the industry and often
allows Summit to obtain the holy grail of all private equity investors: proprietary
deal ?ow. Although some of its investments could be classi?ed as mezzanine or
even buyout, the majority remains at the late-stage VC and growth equity level. Its
main competitor in this strategy is TA Associates, but TA’s strategy tilts toward
somewhat larger investments and is typically not classi?ed as a VC. The compe-
tition and ties between these ?rms are quite extensive: Summit was founded when
some TA professionals broke away and formed a new ?rm.
Summit’s performance has been remarkably consistent. All seven core funds
raised since its 1984 founding have IRRs above the median for their vintage years,
and ?ve of these seven are in the top quartile, with the $610 million 1995 Summit
Ventures IV fund achieving star status. Its consistent performance allows it to
charge a 25 percent carried interest. It raised a $1B European growth equity fund in
2008, which is its ?rst non-U.S. fund.
Technology Crossover Ventures (TCV) is true to its name, engaging in
crossover investing that spans late-stage VC and young public companies. This
eclectic strategy has served TCV well, with ?ve straight top-half funds from 1995
to 2004. Its $1.7B 2000 TCV IV returned 79 percent of its capital, has a net IRR of
94 CHAPTER 5 THE BEST VCs
4.4 percent as of September 2007, and is in the second quartile among its vintage
year peers. It wrapped its largest-ever $3B TCV VII in 2007. It previously was
reported to be charging 30 percent for its ?fth fund, raised in 2004, but whether it
continued to charge a premium carry for its latest fund could not be con?rmed as of
the writing of this book.
Unlike many of its peers, TCV has stuck it out with its focus on U.S. domestic
deals—especially those away from the crowded hubs of Menlo Park, CA, and
Waltham, MA. Its portfolio company locations range from Suwanee, GA, to
Melville, NY, as well as Palo Alto and Boston.
This completes our list. Many other highly respected ?rms could reasonably
have displaced some ?rms in Group B. In alphabetical order, these “honorable
mention” ?rms include Columbia Capital (Alexandria, VA), Lightspeed Venture
Partners (Menlo Park, CA), May?eld Fund (Menlo Park, CA), Mohr Davidow
Ventures (Menlo Park), North Bridge Venture Partners (Waltham, MA), Polaris
Venture Partners (Waltham, MA), Sierra Ventures (Menlo Park, CA), TL Ventures
(Wayne, PA), Trinity Ventures (Menlo Park, CA), US Venture Partners (Menlo
Park, CA), and VantagePoint Ventures (San Bruno, CA). Three more ?rms, Bes-
semer Venture Partners (Wellesley Hills, MA), Greylock Partners (Waltham, MA),
and Venrock Associates (NY, NY), have high-pro?le reputations but do not have
suf?cient information in the public domain about past performance or carried
interest, so it is not possible to judge whether they belong in the top tier.
5.3 VC VALUE ADDED AND THE MONITORING
OF PORTFOLIO FIRMS
After studying the list of top-tier VCs, it is natural to wonder how they got there.
What value-added activities do VCs perform, and how does one acquire the skills to
do them well? In Chapter 1, we categorized VC activities into three groups:
investing, monitoring, and exiting. In each of these three groups, there is a potential
for VCs to add value. The investing and exiting groups include many activities that
require ?nancial analysis; Parts II, III, and IV of this book cover these activities in
detail. In contrast, the monitoring of portfolio ?rms, although certainly a crucial
area for VC value added, does not lend itself well to quantitative analysis. Thus, we
restrict our discussion to a brief summary of ?ve main monitoring activities, with
references to the relevant academic literature. In many of these activities, it is the
VC reputation itself that provides a main source of added value.
Board Representation A seat on the board of directors is a key mechanism
for VC monitoring. With a position on the board, a VC has explicit power to
participate in and in?uence corporate activities. The level of board representation
can be a highly contentious negotiation. VCs often want multiple board seats,
whereas entrepreneurs are understandably reluctant to cede much control. In early
round investments, a lead investor will virtually always get at least one board seat
5.3 VC VALUE ADDED AND THE MONITORING OF PORTFOLIO FIRMS 95
and other members of a syndicate will often get seats as well. In later rounds, board
seats are not universal, and some investors will settle for board observer status,
which does not have voting rights.
A VC spends a substantial fraction of his time as a board member. Many of
the other monitoring activities are accomplished in the context of the board role.
Notwithstanding the importance of this role and an enormous academic interest in
studying the workings of corporate boards, we still know very little about how an
individual person can become an effective board member. For obvious reasons,
researchers are rarely invited into boardrooms, so most of what we do know about
boards comes from quantitative studies of the relationship between company per-
formance and various board characteristics.
This academic literature is mostly focused on board structure in public com-
panies, rather than the dynamics within the boardroom. Some of the ?ndings have
some interest for VCs. For example, Yermack (1996) ?nds an inverse relationship
between ?rm market value (per dollar of book assets) and board size. Although the
causality of this ?nding is hotly debated, it is consistent with a tendency for VCs to
favor small boards, sometimes at the cost of offending members of the management
team who expected to be included. In a more cautionary result for VCs, Fich and
Shivdasani (2006) ?nd that public companies with “busy boards”—those where a
majority of outside directors hold three or more directorships—have inferior per-
formance to other companies for a variety of measures. The relevance of this ?nding
for VCs is uncertain, because the outside directors of public companies, unlike VCs,
usually do not consider their directorships to be their full-time job. Nevertheless, the
results suggest that board member effectiveness cannot be scaled inde?nitely.
In a related study, Tian and Wang (2010) develop a measure of VCs’ failure
tolerance and ?nd that IPO ?rms backed by more failure-tolerant VCs are sig-
ni?cantly more innovative, even long after VCs exit the IPO ?rms. Their measure
of failure tolerance is a function of how many rounds (and how long) VCs invested
in a ?rm before its ultimate failure. Since new rounds of ?nancing typically require
board approvals, this measure re?ects existing VCs’ exercise of their voting powers
as board members. The persistence suggests that VCs’ attitudes toward failure have
likely been internalized by the startup ?rms and become part of the ?rm’s culture.
Corporate Governance Corporate governance rules de?ne the power-
sharing relationship between shareholders and managers. In recent years, a large
body of academic research has demonstrated the relationship between corporate
governance rules and corporate performance. The best time to set good rules is
while a company is still small and before it goes public. VCs can and do have
signi?cant input into this process. Hochberg (2005) studies the ?rst proxy state-
ments ?led by public ?rms to determine the in?uence of VC-backing on various
corporate governance rules. She ?nds that VC-backed companies are (1) less likely
to engage in aggressive accounting prior to their IPO, (2) more likely to have
independent boards and board subcommittees, and (3) more likely to separate
the role of chairman and CEO. Although it is always dif?cult to prove causality in
96 CHAPTER 5 THE BEST VCs
these kinds of studies, the analysis does show that these governance differences do
not occur in the presence of large, non-VC shareholders.
Human Resources VCs also spend a large fraction of their time working on
human resource issues at their portfolio companies. This work requires the same set
of skills used to evaluate management during the investment phase, plus the ability
to recruit new managers and replace underperforming ones. In all these activities, a
VC’s reputation can make a huge difference, and the name of a VC investor is often
invoked as a reason to join a company. (We have heard many MBA students, when
describing their prior experience at a startup, say the name of the top-tier VC that
invested in the company even before they said the name and business of the
company!) Hellmann and Puri (2002) studied the human resource practices for a
sample of VC-backed and non-VC-backed companies in Silicon Valley. They
found that VC backing accelerates the hiring of senior executives (such as a VP of
marketing), the adoption of stock option plans, and the turnover of the CEO. As in
the Hochberg study, it is dif?cult to prove causality, but the authors do a good job
of trying. One notable ?nding is that CEO turnover often occurs long after the
original VC ?nancing, suggesting that the ?nancing and the turnover were separate
events. Furthermore, the authors ?nd that the replaced CEOs often stay with
the company in another capacity. This last result suggests that the VCs managed to
keep the skills of a founder-CEO while simultaneously getting a more experienced
CEO to run a larger company.
Matchmaking VCs will often use their contacts and reputation to make
introductions that can lead to new partnerships, customers, and suppliers. As in the
human resource function, the reputation of the VC can often lead to relationships that
would not otherwise be possible. One straightforward method is for VCs to make
connections among their past and current portfolio companies. Academic research on
the ef?cacy of VC matchmaking suggests that VCs do indeed facilitate alliances
among their portfolio ?rms (Lindsey 2008). In this case, a potential portfolio com-
pany should care about the average quality of the other companies in the VC’s
portfolio, because these companies are more likely to be potential partners.
Strategy As advisors to the CEO, VCs have the opportunity to participate in
strategic decisions. This opportunity must be used wisely, as many generalist VCs
are not quali?ed to give strategic advice across all sectors. Indeed, it is in the area of
strategy that it makes the most sense for individual VCs to focus on a speci?c sector
so that they can build the knowledge and experience to add value. For VC ?rms as
whole, the focus on one or two industries can enable the entire organization to
participate as specialists in strategic discussions with the ?rm.
It would be silly to cite any academic literature here. “Strategy” is a large
academic subject unto itself, and to do it justice would require at least a separate
book and certainly a different author. What we can say here is that there is no
existing academic evidence on the strategic contribution of VCs to the success of
their portfolio companies. To the extent that the VCs can make such contributions,
they can certainly be an important source of value added.
5.3 VC VALUE ADDED AND THE MONITORING OF PORTFOLIO FIRMS 97
SUMMARY
A VC’s reputation is a valuable asset. A high-reputation VC is more likely to have its term
sheets accepted and can pay lower prices for shares than do low-reputation VCs. Top-tier
VCs earn their reputations with superior investment performance, and many of these top-tier
?rms raise their carried interest to 25 or even 30 percent. Nevertheless, there is excess
demand by potential LPs to invest in such top-tier VCs, even at these higher prices. VCs
allow this excess demand so that they can maintain long-run relationships with LPs, mini-
mize the time needed for fundraising, and maximize the chance of maintaining their high
reputation. This reputation is valuable not only for striking better deals with portfolio
companies, but also for increasing the value added to these companies. This value is added
through monitoring activities such as board membership, corporate governance, human
resources, matchmaking, and strategy.
KEY TERMS
Return on investment (ROI)
Return on capital (R)
Cost of capital (r)
Top-tier firm
Star fund
Superstar fund
Sand Hill Road
Syndication
Lead investor
Proprietary deal flow
Crossover investing
REFERENCES
Asset Alternatives, 2005, Galante’s Venture Capital & Private Equity Directory. Asset Alternatives,
Private Equity Analyst, various issues.
Fich, Eliezer and Anil Shivdasani, 2006, “Are Busy Boards Effective Monitors?” Journal of Finance
61(2), 689À724.
Hellmann, Thomas, and Manju Puri, 2002, “Venture Capital and Professionalization of Start-up Firms”,
Journal of Finance 57(1), 167À197.
Hochberg, Yael V., 2005, “Venture Capital and Corporate Governance in the Newly Public Firm”,
working paper available at http://www.kellogg.northwestern.edu/faculty/hochberg/htm/.
Hsu, David H., 2004, “What Do Entrepreneurs Pay for Venture Capital Af?liation?” Journal of Finance
59(4), 1805À1844.
Kaplan, Steven N., 1999, “Accel VII”, Unpublished case study, available online at http://faculty
.chicagobooth.edu/steven.kaplan/teaching/accel7.pdf.
Lindsey, Laura, 2008, “Blurring Firm Boundaries: The Role of Venture Capital in Strategic Alliances”,
Journal of Finance 63(3), 1137À1168.
Private Equity Intelligence, 2005, Private Equity Performance Monitor.
Private Equity Intelligence, 2008, Private Equity Performance Monitor.
Tian, Xuan, and Tracy Wang, 2010, “Tolerance for Failure and Corporate Innovation”, available at
http://papers.ssrn.com/sol3/papers.cfm?abstract_id51399707.
Yermack, David, 1996, “Higher Market Valuation of Companies with a Smaller Board of Directors”,
Journal of Financial Economics 40(2), 185À212.
98 CHAPTER 5 THE BEST VCs
CHAPTER 6
VC AROUND THE WORLD
THE MODERN VC industry was born in the United States, but the rest of
the world is catching up. Although the United States still comprises about one-half
of the worldwide VC investment, markets are starting to mature in Europe—
especially the United Kingdom—and in Asia, with exciting developments in the
emerging economies of India and China. Nevertheless, many countries in con-
tinental Europe, Latin America, and Africa continue to lag behind the rest of the
world in VC activity, both in absolute terms and relative to GDP. In Section 6.1, we
document the global distribution of VC activity and discuss several reasons why
this pattern exists. In Section 6.2, we extend our risk-and-return analysis of Chapter
4 to an international setting and suggest several approaches for the estimation of the
cost of capital for international VC.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING
To study the global pattern of VC investing, we face a challenge in de?ning a
consistent set of data across different types of economies. Currently, the best avail-
able data is compiled by the global accounting ?rm PricewaterhouseCoopers in their
Global Private Equity Report (GPER). The GPER combines data from the Money-
Tree survey in the United States (?rst seen in Chapter 1) with similar data from
separate surveys of Europe, Asia, and a few countries in Africa, Latin America, and
Oceania. Because the data is pulled from disparate sources, they have varying levels
of reliability and comparability. All the surveys attempt to measure private equity
investment activity, but the categorization of private equity into “venture capital”,
“buyout”, and other classes are not always consistent. Rather than attempt to stan-
dardize these de?nitions, the GPER uses its consistent industry de?nitions to divide
private equity into “high technology” and “low technology”, with the former group
likely to contain mostly venture capital, and the latter group mostly buyout. Exhibit 6-1
shows the historical pattern of global high-technology private equity investment.
The exhibit shows that worldwide investment displays the same boom and
postboom pattern as found in the United States. (This should not be too surprising,
as the United States represented most of worldwide investment during the boom,
99
and about half during the postboom.) Investment grew in the 1990s and peaked in
2000. It has started to grow again—this time the bulk of the growth coming from
outside the U.S., with $84B of investment in 2008. Exhibit 6-2 shows the national
distribution of high-technology private equity in that year.
With $35.49B, the United States had about 40 percent of the global total of
$84B and about 60 percent more than all Western Europe combined.
1
Furthermore,
the United Kingdom, with less than one-quarter of European GDP, has almost half
the high-tech private equity investment. Still, the gap between the United States and
Europe is at an all-time low, with the difference larger in prior years. The Asia-
Paci?c region (which includes Australia and New Zealand) has grown the fastest in
recent years, and its total investment amount is now for the ?rst time almost equal
to that in Western Europe. A note of caution is warranted in interpreting these
numbers, however: On the one hand, the numbers are likely in?ated by high-tech
buyout transactions in developed countries such as Australia and Japan. On the
other hand, they likely miss low-tech VC activities, notably in China.
2
On a GDP-adjusted basis, Israel, Sweden, and United Kingdom have con-
sistently exhibited high investment intensity over the years, with Israel’s exceeding
EXHIBIT 6-1
GLOBAL HIGH-TECH PRIVATE-EQUITY INVESTMENT (IN $BILLIONS)
140
120
100
80
60
40
20
0
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
(
$
B
)
29
59
119
58
39
42
46
50
82
84
Source: PriceWaterhouseCoopers Global Private Equity Report 2008.
1
The entries in the table do not sum to $84B because some continents are not included in the table.
2
Re?ecting this gap, in 2008 new commitments to Chinese VC funds exceeded $8B (GEM Global Report
2009).
100 CHAPTER 6 VC AROUND THE WORLD
even that of the United States. In Asia, Japan is far behind the United States and the
United Kingdom in investment intensity when adjusted for GDP, whereas Korea
shows a much higher intensity in recent years.
Why is it that VC activity in continental Europe and Asia has historically
lagged behind that of the United States and the United Kingdom? And what has
changed in the recent years? Industry experts have been thinking about this
question for many years and have proposed many possible reasons. Next, we will
discuss ?ve of the main explanations.
Reason #1—Exits Without a doubt, the most important driver of VC
investment is the existence of a lucrative market to exit these investments. Among
VC practitioners, the absence of such a market is often the ?rst explanation as to
why VC activity is lower in some countries than in others. The most pro?table exits
are achieved through initial public offerings (IPOs). If the IPO market is not active,
then VCs are forced to exit through sales to large companies. Although such sales
EXHIBIT 6-2
THE GLOBAL DISTRIBUTION OF HIGH-TECH PRIVATE EQUITY IN
2007, SELECTED COUNTRIES, IN $BILLIONS
North America World Rank Asia
USA 35.49 (1) India 5.17 (3)
Canada 1.18 (15) Korea 3.18 (4)
NA Total 36.67 Singapore 2.89 (6)
New Zealand 2.13 (9)
Western Europe World Rank Japan 1.93 (10)
UK 10.5 (2) China 1.41 (11)
France 3.11 (5) Hong Kong 1.24 (12)
Sweden 2.52 (7) Australia 1.07 (16)
Germany 2.18 (8) Asia-Paci?c
Total (top 20 only)
19.02
Spain 1.20 (14)
Netherlands 1.03 (17)
Switzerland 0.71 (18)
Denmark 0.64 (19) Middle East & Africa
Finland 0.59 (20) Israel 1.20 (13)
W. Europe Total (top 20 only) 22.48
Source: PriceWaterhouseCoopers, Global Private Equity Report 2008.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 101
can sometimes be lucrative, such high-value sales only occur when companies have
the outside opportunity of an IPO.
Exhibit 6-3 shows the ratio of capital raised by IPOs (in $thousands) to GDP
(in $millions) for a select group of countries over the 1996À2000 time period.
EXHIBIT 6-3
RATIO OF CAPITAL RAISED IN IPOS (IN $THOUSANDS) TO GDP (IN
$MILLIONS), 1996 TO 2000
United Kingdom
Hong Kong
Greece
Australia
Canada
Sweden
Italy
Singapore
United States
Korea
Germany
Spain
Japan
France
Egypt
Indonesia
Venezuela
South Africa
India
Argentina
Chile
Israel
Mexico
Brazil
0 2 4 6 8 10 12
Source: Djankov et al. (2008).
102 CHAPTER 6 VC AROUND THE WORLD
There are two main themes in this exhibit. First, the ratio of IPOs to GDP is
relatively low in “low-income” countries. These countries, with low GDP to begin
with, also have low levels of ?nancial development relative to GDP. Note, for
example, the almost nonexistent IPO levels in many Latin American countries. The
second theme is that many of the countries with high VC activity also have high
IPO activity. (The low IPO total for Israel is misleading, as it does not include the
large number of Israeli IPOs sold in the United Kingdom and the United States.)
It is natural to wonder whether the IPO markets induce more VC activity, or
vice versa. There is substantial evidence that the causation indeed runs from vibrant
IPO markets to higher VC activity. In the United States, the historical record
demonstrates a persistent pattern of hot IPO markets leading VCs to raise and invest
more capital. The ?rst such pattern occurred in the late 1960s, when an excellent
IPO market led to successful exits for the ?rst wave of VC limited partnerships,
leading to a record number of VC funds raised in the following years. The next
example came in 1979À1980, driven by regulatory changes that allowed pension
funds to invest in small companies for the ?rst time. This pattern repeated itself in
the mid 1990s, leading up to the massive IPO boom of 1999À2000, which was
followed quickly by record-breaking fundraising by VCs.
This, then, partly explains the rapid growth of high-tech private equity invest-
ment activities in Asia, following strong recent IPO market performances of Chinese
?rms (including those based in Taiwan or Hong Kong) either listing locally or directly
accessing the U.S. stock markets. In fact, after Israel, Chinese companies are the
second group of foreign ?rms who have successfully tapped the U.S. IPO markets in
the recent years. India, in the meantime, has also enjoyed booming domestic equity
markets, which have buoyed the high-tech private equity activities there.
Reason #2—The Entrepreneurial Ecosystem If you are an entrepre-
neur and you could start your company anywhere, where would you go? For the sake of
answeringthis question, assume that youcanspeakall languages andlive anywhere that
you want. Faced with this problem, many entrepreneurs would think about the ease of
setting up their business, ?nding capital and quali?ed employees, and generally
avoiding all hassles so they could focus on their business. Venture capitalists refer
to this set of requirements as an entrepreneurial ecosystem. In a well-functioning
ecosystem, you do not need to train your bankers, lawyers, or accountants to structure a
high-growth business; you do not need to look far to ?nd quali?ed scientists, engineers,
and experienced managers; you do not need to spend hours dealing with (or bribing)
government of?cials. Also, it’s nice if your friends andneighbors don’t thinkthat you’re
crazy just because you’re starting your own business.
Taken together, these requirements seem almost tautological: It is good to
start a business where many other people have started a business. (In other words,
“we do it this way because it has always been done this way”.) We discussed a
similar phenomenon in previous chapters, when we learned of VC clusters within
the United States in Silicon Valley and around Boston.
Although it is dif?cult to identify cause and effect for most aspects of the
entrepreneurial ecosystem, there are some illuminating data points. One interesting
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 103
project (Djankov et al., 2002) analyzed the direct and indirect costs of starting a
company in 85 different countries. For each country, the authors counted the
number of regulatory procedures necessary to start a company. These procedures
include activities necessary in most countries such as checking the uniqueness of
the company’s name, ?ling a certi?cate of incorporation, and opening a bank
account. There are also less common procedures such as proving that the com-
pany’s of?cers do not have a criminal record, designating a bondsman, and pub-
lishing a notice with the business’s location. After counting the procedures in each
country, the authors estimated the number of business days needed to complete all
procedures. Exhibit 6-4 shows their results for a selected group of countries.
As in the IPO/GDP ratio shown in Exhibit 6-3, we see that Canada, Australia,
the United States, and the United Kingdom all perform well by this measure. In each
of those countries, the authors estimate that it takes between two and four business
days to comply with regulations to open a business. In contrast, the corresponding
estimates are 26 days in Japan, 42 days in Germany, 53 days in France, and 62 days
in Italy. Many emerging economies raise even higher hurdles, with estimates of 92
days in China, 104 days in Venezuela, and 149 days in Mozambique.
Although this evidence does not prove a relationship between entry costs and
entrepreneurial activity, it is hard to imagine that high costs of entry are conducive
to start-up activity. If it takes 10 times as long to start a company in continental
Europe than it does in its EU neighbor of the United Kingdom, one can imagine
where entrepreneurs would prefer to locate. With even small differences at one
point in the chain, local network effects can amplify the location incentives, so that
the entrepreneurial ecosystem moves to one place and stays there.
Reason #3—Lawand Corporate Governance Emerging economies in
Asia, Latin America, and Africa have relatively cheap labor supplies and often
underserved local markets. Such conditions would seem ripe for high-growth
business opportunities. We have already spoken about the high costs of entry and
the dif?culty of exiting such investments, but these barriers may have been over-
come were it not for concerns about law, corporate governance, and the enforce-
ment of contracts. Although these issues are of secondary importance in developed
countries, they loom large everywhere else.
The relationship between legal systems and ?nancial development has been a
subject of great academic interest and progress in the last 10 years. Some recent
work on this topic by Simon Djankov, Rafael LaPorta, Florencio Lopez-de-Silanes,
and Andrei Shleifer (DLLS, for short) provides striking evidence about the relation-
ship between law and ?nance. In their paper, the authors worked with lawyers to
quantify the legal protections against self-dealing behavior in 102 different
countries. Self-dealing, also called tunneling or investor expropriation, is a major
concern of VCs in all countries. As de?ned by DLLS, self-dealing occurs when
“those who control a corporation, whether they are managers, controlling share-
holders, or both, can use their power to divert corporate wealth to themselves,
without sharing it with other investors” (Djankov et al., 2008, p. 1).
104 CHAPTER 6 VC AROUND THE WORLD
EXHIBIT 6-4
TIME TO START A BUSINESS, IN DAYS
Canada
Australia
United States
United Kingdom
Sweden
Hong Kong
Singapore
South Africa
Korea
Chile
Israel
Greece
Germany
France
Russia
Poland
Italy
Brazil
Mexico
India
Spain
Bolivia
China
Venezuela
Indonesia
0 20 60 80 100 120 140 40
Egypt
Argentina
Japan
Source: Djankov et al. (2002).
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 105
The authors considered the following prototypical self-dealing transaction:
Mr. James owns 90 percent of Company A (“Seller”) and 60 percent of Company B
(“Buyer”). Buyer proposes to purchase some assets from Seller. Because Mr. James
controls (.50 percent ownership) both companies, he can make this transaction
happen. Because Mr. James owns more of the Seller than he does of the Buyer, he
has an incentive for the Buyer to overpay for the Seller’s assets. What protections
do the minority investors in the Buyer have against this transaction?
The authors considered several different classes of protections. First, what
details of the transaction must be disclosed to minority investors? Second, what rights
do minority (disinterested) investors have to approve the transaction? Third, what
rights do minority investors have to sue Mr. James after the transaction goes through?
For each class of protections, the authors gathered data for a variety of different legal
rights. They combined all these rights into an index of self-dealing. The index goes
from 0 (no protections for minority investors) to 1 (maximum protection). Exhibit 6-5
gives this index for a selection of the 102 countries analyzed in the paper.
It should come as no surprise that law-and-order Singapore tops the list, with
a maximum score of 1.00. Once again, we see above-average scores by the English-
speaking quartet of Canada, Australia, the United States, and the United Kingdom.
With a score of 0.85, France also lies above this average, but many of its con-
tinental European neighbors do not: Germany at 0.28, Spain at 0.37, and Italy at
0.39. Among developing nations in the bottom GDP quartile, the average score is
0.43, with Latin American countries often having the lowest scores.
The table also has some surprises: for example, China’s score of 0.78 and
Indonesia’s score of 0.68 would seem contrary to venture capitalists’ governance
concerns in these two large countries. It is important to remember, however, that
this self-dealing index does not attempt to measure whether the self-dealing laws
are actually enforced. Rather, the index purports to measure whether the self-
dealing laws exist at all. Thus, we can think of the index as measuring Mr. James’s
ability to “steal without breaking the law”.
The main conclusion of the DLLS research is that the index of self-dealing is
correlated with many measures of ?nancial development. For example, the authors
?nd that the ratio of total stock market capitalization to GDP is strongly related to
all the major components of the self-dealing index. Also, comparison of the highest
and lowest countries in Exhibits 6-3, 6-4, and 6-5 will uncover many similarities.
Our focus on the English-speaking countries of Canada, Australia, the United States,
and the United Kingdom was no accident: In addition to the English language, all
four of those countries also share legal origins of English common law.
3
In the DLLS
research, the 21 countries with English common-law systems—including Singapore,
India, Israel, Hong Kong, and South Africa from Exhibit 6-5—have an average self-
dealing index of 0.67. Outside these 21 countries, all other nations in the DLLS study
3
Common-law systems derive a signi?cant amount of their rules from custom and judicial precedent. In
contrast, civil-law systems rely more heavily on legislatures to write laws.
106 CHAPTER 6 VC AROUND THE WORLD
EXHIBIT 6-5
INDEX OF PROTECTIONS AGAINST SELF-DEALING (HIGHER 5
MORE PROTECTIONS)
Singapore
Hong Kong
United Kingdom
France
South Africa
Australia
China
Israel
Indonesia
United States
Canada
Chile
India
Egypt
Japan
Russia
Korea
Argentina
Poland
Italy
Spain
Sweden
Brazil
Germany
Greece
Mexico
Venezuela
Bolivia
0 0.2 0.4 0.6 0.8 1.2 1
Source: Djankov et al. (2008).
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 107
can trace their legal origins to the civil codes of ancient Rome. Such civil codes tend
to provide less protection to minority investors, and the average self-dealing index in
these civil-law countries is 0.37.
Reason #4—Country Risk In emerging markets, many investors are con-
cerned about national-level political and economic risks: corporate assets can be
directly seized, capital controls can keep foreign investors from repatriating pro?ts
or proceeds of a sale, and ?nancial crises can lead to political and social upheaval.
In any of these cases, a VC can lose virtually all his investment, even if the business
was performing well. Collectively, these concerns are called country risk.
Economists have been trying to quantify country risk for many years.
Unfortunately for investors, there is no standard way to do this. Every country—
and every investment within that country—carries a unique set of risks. Companies
with a high level of tangible assets have a greater risk of asset seizures than do
human-capitalÀintensive businesses, and companies related to national interests
can run into dif?culties even in developed countries. The problem is so dif?cult that
many ?rms have carved out a business as “country risk calculators”, performing
estimates for any given project—and charging a tidy sum to do it. The only
component of country risk that lends itself to an easy estimate is the risk of a
government default on its foreign debt. This risk can be measured using the
sovereign spread, usually de?ned as the difference in yield between dollar-
denominated government debt and U.S. government debt of the same duration. For
example, suppose that 10-year Mexican debt, with interest and principal paid in
dollars, has a current yield of 8 percent. If 10-year U.S. government bonds have a
yield of 5 percent, then the sovereign spread for Mexico would be 825 53 percent.
Exhibit 6-6 shows the sovereign spread for 12 developing countries that have
dollar-denominated government debt.
The exhibit shows that most Latin American countries have sovereign
spreads between 1 and 3 percent. Like all reported bond yields, these are not
expected returns, but instead represent the yield-to-maturity on the assumption
that all principal and interest is actually paid back. Thus, the spread represents
the additional amount that must be paid to compensate investors for the risk that
some of these payments will not be made. Indeed, if the beta for a bond is zero, then
the expected return on the bond would be the same as the risk-free rate, with the
entire sovereign spread needed to compensate for expected losses. We discuss these
issues further in Section 6.2. In any case, the sovereign spread can represent only
one component of country risk—the component that is correlated with government
default—and cannot measure risks that exist even when the government itself pays
back its debt. Overall, these different forms of country risk make many VCs wary
of investment in emerging markets.
Reason #5—Cultural Differences When all else fails, we can always
blame “cultural differences” for the global pattern of VC activity. Many observers
have posited that differences in attitudes toward risk, the stigma of failure,
108 CHAPTER 6 VC AROUND THE WORLD
individual expression, and self-con?dence may explain the patterns of entrepre-
neurship across countries. Because VCs cannot invest unless entrepreneurs are
willing to start companies, a dearth of the latter can sti?e a VC industry. For hard
evidence on the relationship between entrepreneurship and cultural attitudes, we
turn to the Global Entrepreneurship Monitor, a project managed at Babson College.
This project documents the entrepreneurship landscape across many countries,
using individual questionnaires as the key survey instrument. Researchers perform
thousands of face-to-face and telephone interviews to measure the extent of
entrepreneurial activity and estimate the determinants of individual participation.
4
Detailed analysis by Arenius and Minniti (2005) and Koellinger et al. (2007) has
demonstrated the important role of cultural factors and personal attitudes on an
individual’s decision to become an entrepreneur, with wide differences across
countries. Exhibit 6-7 illustrates some of these differences. In this exhibit from
Koellinger et al. (2007), we see the percentage of respondents in 18 countries who
answered “yes” to the question: “Do you have the knowledge, skill, and experience
to start a new business?”
The most striking entries in the table are the extraordinary self-con?dence
levels of New Zealanders and the extraordinary lack of self-con?dence among
EXHIBIT 6-6
SOVEREIGN SPREAD OF DOLLAR-DENOMINATED BONDS
R
u
s
s
i
a
S
o
u
t
h
A
f
r
i
c
a
M
e
x
i
c
o
T
u
r
k
e
y
U
k
r
a
i
n
e
B
r
a
z
i
l
V
e
n
e
z
u
e
l
a
C
o
l
o
m
b
i
a
P
h
i
l
i
p
p
i
n
e
s
P
e
r
u
A
r
g
e
n
t
i
n
a
E
c
u
a
d
o
r
6%
5%
4%
3%
2%
1%
0%
Source: Financial Times, April 7, 2006.
4
For a full description of the results and methodology, see The 2009 Global Entrepreneurship Monitor 2009
Global Report, online at http://www3.babson.edu/ESHIP/research-publications/upload/GEM_2009_
Global_Report.pdf.
6.1 THE GLOBAL DISTRIBUTION OF VC INVESTING 109
the Japanese. In general, we see that many English-speaking countries are above
average (38 percent), and most continental European countries are below average.
The authors ?nd a strong correlation between self-con?dence and entrepreneurship
across these 18 countries. Anecdotally, we can see this relationship by comparing
EXHIBIT 6-7
ENTREPRENEURIAL SELF-CONFIDENCE IN 18 COUNTRIES
New Zealand
Hungary
United States
Agentina
Canada
India
Singapore
Poland
Germany
Portugal
Denmark
Italy
Finland
Russia
Israel
Sweden
Korea
Japan
AVERAGE
0% 10% 20% 30% 40% 50% 60% 70%
Source: Koellinger et al. (2007).
110 CHAPTER 6 VC AROUND THE WORLD
the fraction of entrepreneurs in New Zealand—the second-highest in the sample
at 22.5 percent—and Japan—the third-lowest in the sample at 8.3 percent. Note
that these differences in entrepreneurship, although large, are considerably smaller
than the differences in self-con?dence that are reported in Exhibit 6-7. Thus, it is
not just the entrepreneurs who are answering “yes” to the survey question.
Of course, it is possible that residents of all countries have the same under-
lying levels of self-con?dence and differ only in the cultural acceptability of
admitting such self-con?dence to an interviewer. Even in this case, however, such
cultural differences could affect the willingness of individuals to become entre-
preneurs. After all, starting a company is a fairly public way to state one’s self-
con?dence.
The Global Entrepreneurship Monitor has followed up by including a wide
variety of cultural and attitudinal questions in their annual entrepreneurship sur-
veys. We cannot do justice to the richness of the results they report, given the
limited space here, but one interesting indicator that varies quite considerably
across “innovation-driven” (5 developed) countries, according to their report, is
whether the respondents feel that successful entrepreneurs receive a high status in
their society. The percentage of respondents who answer “yes” is 73 percent and 75
percent in the United Kingdom and the United States, respectively, while it is only
49 percent and 50 percent in Belgium and Japan, respectively. Not coincidentally,
these latter countries also scored quite low on the question, “Do you perceive
entrepreneurship as a good career choice?” Forty-six percent in Belgium and 28
percent in Japan said “yes”.
5
6.2 THE COST OF CAPITAL FOR INTERNATIONALVC
In Chapter 4, we estimated the cost of capital for VC in the United States as 15
percent per year. Should this estimate be different for VC investments in other
countries? To gain insight into this question, we need to step into the thorny issues
involved in estimating the cost of capital for international investments. This is a
broad and important topic, and we will not be able to do it full justice here. Instead,
we take a three-step whirlwind tour of the key concepts. In Section 6.2.1 we
introduce a baseline model for the international cost of capital. This model is
similar to the CAPM, but is extended to consider global investments. The key
assumption of this model is that international capital markets are fully integrated,
so that there is a single worldwide price of risk. In Section 6.2.2 we discuss several
objections and extensions to this baseline model to account for currency risk,
country risk, style factors, and the possibility of segmented markets. In Section
6.2.3 we suggest a method to estimate the cost of international VC.
5
GEM (2009).
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 111
6.2.1 Baseline Model: The Global CAPM
In Chapter 4, we introduced the CAPM as our ?rst model of risk and return:
r
i
5R
i
5R
f
1?ðR
m
2R
f
Þ ð6:1Þ
where r
i
is the cost of capital for asset i, R
i
is the expected return for asset i, R
f
represents the risk-free rate for borrowing and lending, R
m
is the return on the
whole market portfolio, and ? (beta) is the level of risk for asset i. In imple-
mentations of this model in the United States, the market premium is typically
estimated on a market portfolio of U.S. stocks. This implementation should pro-
perly be called a domestic CAPM. As ?rst discussed in Chapter 4, the proper
theoretical interpretation of the CAPM requires that this market portfolio must
comprise all assets, traded and untraded, from everywhere in the world. Although
such universal coverage is not possible, it is relatively easy to construct the market
portfolio as a value-weighted portfolio of all traded equities in all world markets.
With a market premium, (R
m
2 R
f
), de?ned as the expected premium on all global
stocks, then we can de?ne Equation (6.1) as the global CAPM.
In the global CAPM, the betas are driven by correlations between asset i and
the global market portfolio. If the ?nancial markets of the world are perfectly
integrated, so that all investors are diversifying among all assets in all countries,
then the global CAPM is a more appropriate model than any domestic CAPM.
Historically, most U.S.-based investors relied on a domestic CAPM because of
limitations on data for global returns. These days, with global returns easily
available, U.S. investors rely on the domestic CAPM either because of inertia or
because of a belief that markets are not perfectly integrated. We discuss the inte-
gration issue further in Section 6.2.2.
For now, we maintain the assumption of perfectly integrated markets, and we
analyze the expected return of investments made outside the United States. To
estimate the model, we need a time series of returns for the global market premium,
for risk-free rates, and for asset i. The historical premium on global stocks is
between 6 and 7 percent. For consistency with our earlier analysis in the United
States, we will use an expected global premium of 7 percent. For now, we will
measure risk-free rates with U.S. government bonds, leaving a discussion of cur-
rency risk for Section 6.2.2. Last, we need a time-series of returns for VC. Now, we
have a major problem because we have no international equivalents for either the
Cambridge Associates or the Sand Hill Econometrics data in the United States.
Furthermore, even if such time series did exist, the small size of the VC markets in
most countries would render these returns to be highly unreliable as predictors of
future performance.
Luckily for us, this problem is quite common in other settings, and analysts
have devised a procedure for making estimates when data is sparse. For example,
consider the investment decision of Telco, a multinational telecommunications
company based in the United States and considering a $100M investment in a
telecom services project in Brazil. To estimate the cost of capital for this
112 CHAPTER 6 VC AROUND THE WORLD
investment, Telco would like to know the average global beta for a telecom
company in Brazil. Although data on global returns is readily available from many
sources, data on individual companies in emerging markets is somewhat harder to
obtain. Furthermore, there may not be very many publicly traded telecom com-
panies in Brazil. In an extreme case, there might be no publicly traded companies in
a country that belong to the same industry.
For this example, Telco can use a three-step procedure to estimate the beta of
their investment. The key assumption behind this procedure is that the domestic beta
of a telecom industry is identical across all countries: that is, the beta of a telecom
company in Brazil relative to the Brazilian stock market is the same as the beta of a
telecom investment in the United States relative to the U.S. market. In the ?rst step of
the procedure, Telco estimates the domestic beta for a similar telecom investment
in the United States; we refer to this estimate as ?
d
. We can obtain this estimate by
regressing the historical returns for the telecom industry in the United States on the
market premium in the United States. Next, Telco estimates the country beta for
the whole Brazilian equity market; we refer to this estimate as ?
c
. We make this
estimate by regressing the historical returns for the Brazilian stock market on the
returns on global market premium. Finally, using the assumption that domestic betas
for telecom are the same across all countries, we have
?
d
5beta of U:S: telecom investment relative to the U:S: stock market
5beta of the Brazilian telecom investment relative to the Brazilian
market; and
?
c
5beta of the Brazilian market relative to the global market
-?
d
à ?
c
5beta of the Brazilian telecom investment relative to the
global market
ð6:2Þ
The Excel ?le betas.xls simpli?es this procedure by providing a wide range of
domestic betas (for industries in the United States) and country betas.
6
In the
industry worksheet of the betas spreadsheet, we can see that the beta for the tele-
com industry in the United States is 1.43. In the countries worksheet, we can see
that the country beta for Brazil is 1.46. Thus, the estimated beta for Telco’s
investment in Brazil is 1.43 Ã 1.46 = 2.08.
EXAMPLE 6.1
Bankco, a multinational ?nancial services company based in the United States, is considering
a consumer-banking investment in Thailand.
6
The industry beta data are from Professor Damodaran’s website; the country beta data are from Reyent
(2009), at http://seekingalpha.com/article/110434-calculating-country-risk-observed-by-betas.
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 113
Problems
(a) Use the betas.xls ?le to estimate the beta for this investment.
(b) With a risk-free rate of 4 percent and a global risk premium of 7 percent, what is the
estimated cost of capital for this investment?
Solution
(a) In the industry worksheet of betas, we can look up the beta for the banking industry
in the United States as 0.71. In the countries worksheet, we can look up the country beta
for Thailand as 0.50. Thus, the estimated beta for Bankco’s investment in Thailand is
0.71 Ã 0.50 = 0.36.
(b) By substituting a global beta of 0.36, a risk-free rate of 4 percent, and a global risk premium
of 7 percent into the global CAPM of Equation (6.1), we obtain a cost of capital of
R
i
50:04 10:36 Ã ð0:07Þ 56:5% ð6:3Þ
’
6.2.2 Objective and Extensions to the Global CAPM
Most objections to the global CAPM are rooted in the belief that the estimated dis-
count rates are “too low”. Example 6-1 provides a typical illustration: the estimated
cost of capital is 6.5 percent, lower than the cost of capital would be for an equivalent
investment in the United States. This lower estimate occurs because the country beta
for Thailand is less than 1. Many analysts are bothered by this, because Thailand
“seems” to be much riskier than the United States. Indeed, the volatility of the Thai
market is almost twice the volatility of the U.S. market. However, it is important to
remember that beta is driven by covariance, not variance. The correlation of the Thai
market with the world market is relatively low: From the perspective of a globally
diversi?ed investor, most of the variance in Thailand is idiosyncratic.
Thailand is not unique. Many developing countries have country betas less
than 1. Exhibit 6-8 shows the volatilities (expressed as a ratio to U.S. market
volatility) and country betas (relative to the global market premium) for select
economies. The exhibit shows that many of these markets have country betas below
1, with both Thailand and India close to 0.5. Do we really think that these countries
should have a lower cost of capital than the United States? For many analysts, this
result is simply too counterintuitive to accept, and several extensions have been
proposed to this baseline model. Next, we will discuss four of these extensions.
Extension #1—Style Adjustments In Chapter 4 we learned that many
economists no longer consider the CAPM to be the best model of expected returns,
with multifactor models such as the Fama-French model (which extends the CAPM
to include size and value/growth factors) and the Pastor-Stambaugh model (which
extends the Fama-French model to include a liquidity factor) doing a better job of
114 CHAPTER 6 VC AROUND THE WORLD
explaining the pattern of realized returns in the United States. The international
evidence for these models is also compelling, and thus it is probably wise to extend
the global CAPM to include these additional factors. In Section 6.2.3, we provide a
suggested method for doing this for the estimation of the cost of capital for
international VC. Nevertheless, the low correlation of the Thai market with the
global premium will still be the main driver of low expected returns for all Thai
investments. Thus, multifactor models, although sensible, do not solve the main
concern that some of these cost-of-capital estimates are “too low”.
Extension #2—Currency Risk The global CAPM ignores differences in
currency across countries. If a U.S.-based investor makes an investment in Thailand,
then revenues from domestic sales will come in Thai currency. If the U.S. company
needs to pay its own investors back in dollars, then they can either hedge the foreign
exchange risk or absorb it—in either case, the potential costs may be large.
To handle currency risk in the context of a factor model, we must ask our-
selves whether such risks are diversi?able. If so, then there is no reason that such
risks should affect expected returns. There is a long history of academic literature
on this question, well beyond the scope of this chapter.
7
The incredibly concise
EXHIBIT 6-8
COUNTRY BETAS AND VOLATILITY RATIOS, SELECTED COUNTRIES
Country Country Beta Volatility Ratio
Brazil 1.46 2.35
Finland 1.29 2.26
Mexico 1.23 1.75
Sweden 1.21 1.17
South Africa 0.91 1.67
Poland 0.84 1.82
Israel 0.78 1.54
China 0.68 1.91
India 0.57 1.80
Thailand 0.50 1.86
Japan 0.46 1.43
Egypt 0.16 1.78
NOTE: Calculated based on daily index stock returns from 1998 to 2008.
Source: http://seekingalpha.com/article/110434-calculating-country-risk-
observed-by-betas.
7
For a longer discussion of this literature, see Solnik and McLeavey (2004), Chapter 4, or Bodnar,
Dumas, and Marston (2004).
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 115
summary of this literature is that, in the long run, currency risks probably have an
expected return of 0, because gains for one currency are exactly offset by losses for
another. In the context of our banana economy of Chapter 4, it should not matter if
some people quote banana prices in euros while others do so in dollars, because
these currency differences have no effect on the overall production of bananas and
thus have no effect on the average level of hunger in the economy. In the short run,
however, it is possible that this long-run relationship breaks down. In our banana
economy, this can occur if, for example, the dollar-currency islanders are more
risk-averse than the euro-currency islanders. In this scenario, the two groups may
bear different amounts of risk in equilibrium, so short-run shocks to the weather
affect the hunger (and currencies) of the two groups disproportionately.
In practice, analysts adjust for short-run differences in currency risk by
adding currency factors to the right-hand side of Equation (6.1). These currency
factors are typically constructed as a historical premium for holding any given
currency, perhaps adjusted for short-run differences in expectations. Solnik and
McLeavey (2004) give an example of such a model. For the applications in this
book, we take the long-run view that the average risk premium is 0, so there is no
adjustment to the cost of capital.
Extension #3—Country Risk In Section 6.2 we discussed “country risk”
as one reason that investors avoid VC in emerging markets. To quantify this
country risk, Exhibit 6-6 displayed the sovereign spread for several developing
countries. It is common practice on Wall Street for analysts to add this sovereign
spread as an additional term on the right-hand side of Equation (6.1). In that case,
an augmented version of the global CAPM is the risk-free rate (from U.S. bonds),
plus beta times the global market premium, plus the sovereign spread. The idea
behind this augmentation is that the sovereign spread, which represents the risk of
government default on its foreign debt, might also be the best available proxy for
the country risk in private investments.
Unfortunately, there are serious problems with this augmented model. The
?rst problem is straightforward: there is no reason to equate the risk of government
default with the risk of private project failure. The second problem is deeper and
concerns the difference between a government bond yield and an expected return.
As we ?rst discussed in Section 6.1, the sovereign spread represents the additional
yield under the assumption that all interest and principal payments are actually
made. This yield is not an expected return, because it assumes no default. It is
entirely possible that expected return on Thai bonds is the same as the expected
return on U.S. bonds. In an equilibrium model like the CAPM, expected returns are
equated with discount rates and the cost of capital. By adding the sovereign spread
to the global CAPM, we can no longer claim to be estimating expected returns,
discount rates, or the cost of capital.
To illustrate this second problem, assume that we knew that the probability of
a government default was exactly 10 percent per year, and all private companies
116 CHAPTER 6 VC AROUND THE WORLD
would go bankrupt in the case of a government default. Furthermore, assume that
this default is independent of the global equity market. Now, in this case, the
sovereign spread would re?ect the yield in the 90 percent of the cases without
default. The spread would be positive to compensate investors for the negative 100
percent return in the case of default. Nevertheless, the expected return on
government debt would be equal to the risk-free rate because, by assumption,
default is uncorrelated with the global market premium.
In this example, the correct way to handle the 10 percent default probability is
not in the discount rate, but in the expected cash ?ows. Indeed, this kind of problem
occurs for every VC investment, foreign or domestic. In Chapter 7, we will show
that a substantial fraction of all VC investments provide no returns to the investors.
In Chapter 10, we will show that this “probability of success” does not affect the
expected return, but rather should be used as a separate input into the valuation
decision.
Extension #4—Segmented Markets So far, we have described three
possible extensions to the global CAPM, but we have argued that none of these
three extensions are likely to explain why estimates seem “too low”. Extension #4
drops the assumption of perfect integration of international ?nancial market.
Without this assumption, we can sometimes estimate a much higher cost of capital.
To see how this works, consider the opposite extreme to perfectly integrated
markets: perfectly segmented markets. Under this extreme assumption, investors
are only permitted to invest in their own countries. Then, there would be no such
thing as the global CAPM. Instead, we would have a different domestic CAPM for
every country. For each country, we would estimate a version of Equation (6.1)
using the market premium from that country. Of course, in this world of perfect
segmentation, it would not make any sense to consider an investment by a U.S.
investor in Thailand—we have assumed that this is impossible. Thus, analysts
sometimes consider a hybrid CAPM, shown in Equation (6.4), which allows for
separate betas and market premia for the global and domestic markets.
r
i
5R
i
5R
f
1?
1
ðR
g
2R
f
Þ 1?
2
ðR
d
2R
f
Þ ð6:4Þ
where r
i
, R
i
, and R
f
are de?ned as in Equation (6.1), R
g
is the return on the global
market portfolio, R
d
is the return on the domestic market portfolio corresponding to
the country of investment i, and ?
1
and ?
2
are the betas on the global premium and
domestic premium, respectively. Equation (6.4) can generate a high cost of capital
because some countries have very high historical premia. Nevertheless, the hybrid
CAPM rests on shaky theoretical foundations. It is very dif?cult to write down a
rigorous model of “partially segmented” markets that would give rise to Equation
(6.4). Furthermore, most limited partners in VC funds are large institutions with the
capability of investing anywhere in the world. Thus, although a hybrid CAPM
might satisfy a craving to obtain a higher estimate for the cost of capital, this
satisfaction would come with some sacri?ce to logical consistency.
6.2 THE COST OF CAPITAL FOR INTERNATIONAL VC 117
6.2.3 A Global Multifactor Model for Venture Capital
So, with all these possible extensions, how should an honest analyst estimate the
cost of capital for international VC? In this book, we suggest an approach that is
internally consistent with the domestic estimate done in Chapter 4. The starting
point is the Pastor-Stambaugh model (PSM) cost-of-capital estimate for the United
States. In Chapter 4, we introduced the PSM model as
R
it
2R
ft
5?1? Ã ðR
mt
2R
ft
Þ 1?
size
à SIZE
t
1?
value
à VALUE
t
1
?
liq
à LIQ
t
1e
it
ð6:5Þ
where ?, ?, R
mt
, R
ft
, and e
it
are de?ned similarly as in Equation (6.1), SIZE
t
,
VALUE
t
, and LIQ
t
are the factor premia for their respective investing styles, and
?
size
, ?
value
, and ?
liq
are the regression coef?cients on these factors. In Chapter 4,
we discussed the historical evidence for each of these factor premia and suggested
estimates of 7 percent (for the market), 2.5 percent (for size), 3.5 percent (for
value), and 5 percent (for liquidity). We then estimated Equation (6.5) for the Sand
Hill Econometrics index and Cambridge Associates index (each with lags) and
obtained estimated coef?cients, as shown in Exhibit 4-6. By substituting these
coef?cients and premia into Equation (6.5), we obtain a cost-of-capital equation of
15 percent.
Now, to estimate the cost of capital for VC in a country other than the United
States, we multiply all the PSMbetas—?, ?
size
, ?
value
, and ?
liq
fromEquation (6.5)—
by the country beta, ?
c
, from the betas.xls ?le. Using the rounded estimate of 15
percent and subtracting the historic average risk-free rate of 4 percent, we obtain
11 percent for the sum of all factor loadings times the historic average factor returns
(? Ã 0.07 1?
size
à 0.025 1?
value
à 0.035 1?
liq
à 0.05). Thus, for an investment in
Thailand, we would multiply all factor loadings by 0.50 (see betas.xls), so we have:
r
i
ðThailandÞ 50:04 10:50 Ã ð0:15 À 0:04Þ 59:5% ð6:7Þ
Some readers might see this estimate, 5.5 percent lower than the corre-
sponding estimate in the United States, and express disbelief. Remember, however,
that we must not confuse a higher probability of failure with a higher cost of capital.
If you believe that investments in Thailand have a higher probably of outright
failure than do similar investments in the United States, then you can take account
of this higher probability in a different part of your valuation calculation. In
Chapter 10, we show exactly how such probabilities can be incorporated into an
investment decision, separate from the cost of capital.
EXAMPLE 6.2
EBV is considering an investment in South Africa.
Problem What is the cost of VC for this investment?
118 CHAPTER 6 VC AROUND THE WORLD
Solution We can see in the betas.xls spreadsheet (and in Exhibit 6-8), that the country
beta for South Africa is 0.91. Thus, the cost of VC for a South African investment can be
estimated by
r
i
ðSouthAfricaÞ 50:04 10:91 Ã ð0:15 À 0:04Þ 514:01% ð6:8Þ
’
SUMMARY
VC is a worldwide industry, but some countries have been more successful than others in
developing a thriving culture of entrepreneurship and VC investment. The United States
continues to lead the world with about half of all high-tech private equity investment—and a
ratio of investment to GDP nearly double that of Western Europe. Within Western Europe,
nearly half of all investment is concentrated in the United Kingdom. We discussed ?ve factors
that help drive VC activity in a country. First, the IPO markets should be active to provide the
possibility of high-value exits. Second, there should be an entrepreneurial ecosystemthat eases
the tasks of setting up new companies and recruiting necessary talent. Third, the legal system
should protect minority investors from self-dealing by owners and managers. Fourth, the level
of political risk should not be so high as to scare VCs away. Fifth, the culture should be sup-
portive of entrepreneurs starting (and sometimes failing) in their ventures.
In Chapter 4, we estimated the cost of capital for VC in the United States to be 15
percent. This estimation is different in every country. In theory, the main driver of these
differences is the country beta, which measures the extent to which a county’s asset markets
are correlated with the global market. Multifactor models like the Pastor-Stambaugh model
can be combined with country betas to provide an estimate of the cost of capital for VC for
any country.
KEY TERMS
Entrepreneurial ecosystem
Self-dealing
5 tunneling
5 investor expropriation
Country risk
Global CAPM, global beta
Domestic CAPM, domestic
beta
Country beta
Integrated markets,
segmented markets
REFERENCES
Arenius, Pia, and Maria Minniti, 2005, “Perceptual Variables and Nascent Entrepreneurship”, Small
Business Economics 24(3), 233À247.
Bodnar, Gordon, Bernard Dumas, and Richard Marston, 2004, “Cross-Border Valuation: The Interna-
tional Cost of Equity Capital”, in The INSEAD-Wharton Alliance on Globalizing: Strategies for
REFERENCES 119
Building Successful Global Businesses, R. Gunther, H. Gatignon, and J. Kimberly, eds., Cambridge
University Press, New York.
Djankov, Simon, Rafael LaPorta, Florencio Lopez-de-Silanes, and Andrei Shleifer, 2002, “The Reg-
ulation of Entry”, Quarterly Journal of Economics 117(1), 1À37.
Djankov, Simon, Rafael LaPorta, Florencio Lopez-de-Silanes, and Andrei Shleifer, 2008, “The Law and
Economics of Self-Dealing”, Journal of Financial Economics 88(3), 430À465.
Global Entrepreneurship Monitor 2009 Global Report, http://www3.babson.edu/ESHIP/research-
publications/upload/GEM_2009_Global_Report.pdf.
Koellinger, Phillip, Maria Minniti, and Christian Schade, 2007, “I Think I Can, I Think I Can: Over-
con?dence and Entrepreneurial Behavior”, Journal of Economic Psychology 28(4), 502À527.
PricewaterhouseCoopers, Global Private Equity Report 2008, http://www.pwc.com/en_GX/gx/investment-
management-real-estate/pdf/2008_global_private_equity_report.pdf.
Reyent, Suna, 2009, “Calculating Country Risk Observed by Betas”, http://seekingalpha.com/article/
110434-calculating-country-risk-observed-by-betas.
Solnik, Bruno and Dennis W. McLeavy, 2004, International Investments, 5th Edition, Addison-Wesley,
Reading, MA.
EXERCISES
6.1 True, False, or Uncertain: Private equity is a substitute for public equity (i.e., if a
country has a relatively active public-equity market, then private-equity activity will be
relatively low).
6.2 True, False, or Uncertain: Countries with common-law based legal systems have
relatively weak protections against investor expropriation.
6.3 Softco, a multinational software company based in the United States, is considering an
investment to produce and sell business software in Mexico. Use the betas.xls ?le to estimate
the beta for this investment.
6.4 Talltree is considering an investment in India. What is the cost of VC for this
investment?
120 CHAPTER 6 VC AROUND THE WORLD
PART II
TOTAL VALUATION
121
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CHAPTER 7
THE ANALYSIS OF VC
INVESTMENTS
IN THIS CHAPTER we introduce the main topic for Parts II and III of this
book: the analysis of VC investments. In the past decade, the data on VC invest-
ments has become much more complete. In Section 7.1 we study this data and
provide key statistics about the distribution of returns to individual VC investments.
In Section 7.2 we turn our attention from data to methodology, and we sketch the
key steps in the investment decision-making process.
7.1 VC INVESTMENTS: THE HISTORICAL
EVIDENCE
For a long time the VC industry existed in a data vacuum. VCs invested billions of
dollars in startup companies with little more than intuition and rules of thumb to
guide them. Ten years ago there was no way to reliably answer basic questions like,
“What fraction of all VC investments goes out of business?” and, “What fraction of
VC investments eventually has IPOs?” To make decisions without this information
is like playing poker without knowing how many aces and kings are in the deck.
Yes, you can do it, but it makes the luck factor loom even larger.
The good news is that this data vacuum has been steadily ?lling over the
past 10 years. The ?rst entrant on the scene was VentureExpert, a product of
Venture Economics (a unit of Thomson Financial), soon to be followed by
VentureSource, a product of Dow Jones. Venture Economics, the producers of
much of the data used in Chapters 1 and 2, began its data collection in the 1970s
but did not track much data on valuations until recent years. VentureSource
(formerly VentureOne) has always been much more comprehensive with valua-
tion data, but its industry coverage was not very broad until the early 1990s. The
next leap forward came from Sand Hill Econometrics (SHE), whom we ?rst met
in Chapter 3 through its VC return index. SHE initially combined data from
Venture Economics and VentureSource, added some information from some
newer providers, and performed some detailed investigations of its own. The SHE
123
database is state of the art and serves as the basis for the statistics presented in this
chapter.
1
To build a VC database requires three main steps. First, one must learn about
investments as they occur. Second, one must track these investments over time. Third,
one must get accurate information about exits. At each of these steps, it is not enough to
knowthat anevent occurred; one must alsoget valuationdata. Without valuationdata, it
is impossible to compute the returns to the VC investors. At each step, there are chal-
lenges. For example, if you miss some companies at their initial investment, but then
pick themup later if they make it to a second or third round, then you run the danger of
introducing survivor bias into the data. (We ?rst saw survivor bias in Chapter 3, when
discussing the Cambridge Associates return index.) Furthermore, even if you gather all
information about the rounds of investment, it is still a big challenge to ?nd out when
companies have gone out of business. Neither VCs nor their companies are eager to
publicize their failures, and SHE expends considerable effort to track these down.
Finally, the valuation data for exits is not always available. IPO exits are always
available, and large-value acquisitions are virtually always disclosed. Nevertheless, in a
signi?cant fraction of small acquisitions, the purchase price is never disclosed.
For any investment, there are four possible outcomes at any point: (1) exited
through an IPO (IPO), (2) exited through an acquisition (ACQ), (3) out of business
before any exit (DEF, for “defunct”), and (4) still a private company in a VC’s
portfolio (PRI). Exhibit 7-1 shows the likelihood for these outcomes as a function
of time since the ?rst round of VC investment, using data from all VC-backed
companies in the SHE database that received their ?rst ?nancing before 2001.
The exhibit shows that by ?ve years after the initial investment, 12.7 percent of
all companies have had an IPO, 24.1 percent have been acquired, 26.1 percent
are defunct (out of business), and 37.1 percent are still private. By 10 years after the
initial investment, the respective percentages are 15.4 percent for IPO, 35.5 percent
for an acquisition, 33.4 percent for defunct, and 15.7 percent for still private.
The largest remaining unresolved issue is the identi?cation of out-of-business
dates. Even with SHE’s efforts, 16 percent of all companies are listed as “still
private” 10 years after their initial investment, and only about one-third are listed as
defunct. Because VC funds ordinarily must exit all their investments within
10 years, the still-private percentage seems too high. It is likely that the vast
majority of these companies has either gone out of business or been “acquired” for
some nominal price.
2
SHE has chosen a reasonable and conservative path of listing
these companies as “still private” when no other information is available. An
alternative assumption would be that these companies have gone out of business,
1
Sand Hill Econometrics entered into a licensing agreement with DowJones (the provider of VentureSource)
in 2009. As a result, it stopped using Venture Economics as a raw data source. The results presented in this
chapter are based on the new version of their database, which excludes data from Venture Economics.
2
VentureSource has two separate categories for asset acquisitions (where a company is liquidated and sells
some of its assets, such as computers, ergonomic chairs, foosball tables, etc.) and other acquisitions. When a
deal is classi?ed as an asset acquisition by VentureSource, Sand Hill classi?es it as “defunct”. That said, it is
possible that some asset acquisitions are classi?ed as “acquired” with an undisclosed price.
124 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
with the exit rate (over the previous 10 years) assumed to be the same as that for the
companies withknownout-of-business dates. Exhibit 7-2is ananalogue toExhibit 7-1,
but now with this more aggressive assumption:
In Exhibit 7-2, the IPO and acquisition percentages are the same as in Exhibit
7-1, but the still-private and out-of-business lines are different. In Exhibit 7-2, by
assumption, no companies are still private after 10 years, with the defunct per-
centage increasing to 49.1 percent.
Both of the prior exhibits show that about 51 percent of all VC investments
end in an IPO or an acquisition, but this does not mean that all these investments
could be labeled as “successes”. For the original (early stage) investors, an IPO is
almost always a pro?table exit, but we cannot say the same thing about all
acquisitions. Exhibit 7-3 shows the likelihood for various ranges of gross value
multiples (GVMs) for both IPOs and acquisitions.
3
The exhibit shows that 53.6 percent of all IPOexits yield value multiples in excess
of ?ve times the original investment (the ?ve highest categories) and 3.3 percent yield
EXHIBIT 7-1
PORTFOLIO COMPANY STATUS OVER TIME: FIRST ROUND
INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since First Venture Round Investment
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
3
Because the SHE data is before fees and carry, the value multiples are “gross” and not “net”.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 125
multiples in excess of 50 times the original investment (the two highest categories). It is
important to note, however, that these multiples represent only the time period fromthe
initial investment by the VC to the IPO date. Because VCs usually do not distribute
stocks to their LPs for at least six months after the IPO, the actual returns to LPs will
differ fromthose inthe SHEdatabase. This six-monthreturnis unlikelytochange the big
picture of Exhibit 7-3, but it can make a huge difference for speci?c investments. For
example, the most successful VC investment of all time is Benchmark Capital $6.7M
investment in eBay. At the time of the eBay IPO in September 1998, eBay’s stock was
pricedat $18per share. The?rst trade onSeptember 24occurredat $54per share, andthe
Benchmark investment was valued at $416M. By the time Benchmark started to dis-
tribute this stock to its LPs six months later, eBay had risen to a (split-adjusted) price
above $600 per share, and the value of the overall stake (GPs 1LPs) was $5.1B.
4
EXHIBIT 7-2
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER 10 YEARS, ALL FIRST-ROUND INVESTMENTS
0 12 24 36 48 60 72 84 96 108
Months Since First Venture Round Investment
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
4
These ?gures are cited in Stross (2000), p. 216, who had the good timing to be writing a book about
Benchmark Capital and following the ?rm from the inside while the eBay investment was happening.
126 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Exhibit 7-3 also shows that the multiples for acquisitions are much lower.
First, note that 37.9 percent of all acquisitions result in a loss (the three lowest
categories). This number is likely to be signi?cantly understated because we are
missing the acquisition price for about one-third of all acquisitions, and these
missing values are almost surely tilted toward lower-return cases. (As mentioned
earlier, missing acquisition values often indicate a going-out-of-business sale. In
contrast, we always know the value of the IPO exit.) Among the cases where we do
know the acquisition value, 20.9 percent yield multiples of ?ve times or greater,
and 0.9 percent yield multiples of 50 times or greater.
We turn next to an analysis of all ?rst-round investments, including defunct
companies. As in Exhibit 7-2, we assume that all private, unexited companies are
defunct after 10 years.
5
For exited companies for which we are missing the exit value,
we impute exit values based on observable investment characteristics such as amount
raised to date, time elapsed since last round, last known value if there is one, whether
acquirer was public or private, and whether the deal was for stock or cash. Exhibit 7-4
shows the wide distribution of multiples for ?rst-round investments. Once we include
EXHIBIT 7-3
GVMs FOR FIRST-ROUND INVESTMENTS: IPOs AND ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.7% 15.1%
0.25 to ,0.50 1.6% 9.3%
0.50 to ,1.00 3.9% 13.6%
1.00 to ,1.50 6.5% 10.7%
1.50 to ,2.00 6.6% 8.2%
2 to ,3 12.1% 10.8%
3 to ,5 15.0% 11.4%
5 to ,10 24.3% 11.4%
10 to ,20 15.6% 5.6%
20 to ,50 10.5% 3.0%
50 to ,100 2.4% 0.6%
.5100 0.8% 0.3%
NOTE: Data includes all ?rst-round investments with
known exit values.
Source: Sand Hill Econometrics.
5
Some of these “still private” companies (as many as one in ?ve) eventually do exit, so to the extent that
we force all of them to have a multiple of 0, our results are conservative.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 127
our conservative assumptions for “still private” companies and for the returns in
acquisitions with unknown prices, we ?nd that 74.22 percent of all ?rst-round
investments lead to a negative return (value multiple below1). On the other end of the
spectrum, 12.0 percent of all ?rst-round investments yield multiples of 5 or greater,
and 0.7 percent yield multiples of 50 or greater.
One caveat to this exercise is that, given the end of the sample period at the end of
2000, the results are disproportionately in?uenced by the record number of investments
made in the tech bubble years of 1999 and 2000. According to the 2009 NVCA
Yearbook, out of 9,052 early stage investments during 1990À2000, 4,553 (about 50%
of all deals) were made in 1999 and 2000. It is all too well-known that many of these
investments, made at the height of the market exuberance about Internet stocks, should
never havebeenmade—andsubsequentlyfailed. Ina sense these wereanomalyyears of
VC investing, probably never to be repeated. If we excluded these two anomaly years
from the analysis, the results would have probably looked a lot different, with a
lower percentage of failures and near failures, and a higher percentage of exits at
multiples of 5 or higher. It will be interesting to update these ?gures in ?ve years, when
we have more information about ?nal outcomes of investments made post-2000.
EXHIBIT 7-4
GVMs FOR ALL FIRST-ROUND INVESTMENTS
Value Multiple Percentage
0 49.10%
.0 to ,0.25 10.68%
0.25 to ,0.50 7.69%
0.50 to ,1.00 6.74%
1.00 to ,1.50 3.53%
1.50 to ,2.00 2.62%
2 to ,3 3.65%
3 to ,5 3.99%
5 to ,10 5.66%
10 to ,20 3.41%
20 to ,50 2.24%
50 to ,100 0.49%
.5100 0.19%
NOTE: These return distributions are estimated using
the information on Exhibits 7-2 and 7-3, with some
additional assumptions (described in the text) to
handle missing exit values. The “still private”
companies after 10 years are assumed to have failed.
Source: Sand Hill Econometrics.
128 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Exhibit 7-5 uses second-round investments and repeats the survival analysis
of Exhibit 7-2. As in Exhibit 7-2, we assume that all companies reported as “still
private” after 10 years by SHE have actually gone out of business at the same rate
as those companies observed to be defunct.
After ?ve years, 27.3 percent of second-round investments have been
acquired, 16.9 percent have had an IPO, 36.3 percent are defunct, and 19.5 percent
are still private. After 10 years, 37.3 percent have been acquired, 19.3 percent have
had an IPO, 43.4 percent are defunct, and, by assumption, none are still private. By
comparing these percentages to their analogues in Exhibit 7-2, we can start to see
some differences between ?rst-round and second-round investments. For the
second-round investments, IPO and ACQ percentages are both higher in all periods,
and the DEF and PRI percentages are lower in all periods (until 10 years, when PRI
is 0 for both.) These differences make sense because later-round investments should
have demonstrated a greater capacity for survival than ?rst-round investments.
Because these higher survival probabilities are well understood by all parties, they
will be factored into the share prices, and hence we cannot infer anything about
EXHIBIT 7-5
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER TEN YEARS, ALL SECOND-ROUND
INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since Second Venture Round
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 129
GVMs or returns from Exhibit 7-5. Instead, we must repeat the analysis of ?rst-
round investments and look directly at the GVMs. Exhibit 7-6 displays ranges of
GVMs for second-round investments with IPO or acquisition exits.
By comparing Exhibits 7-6 and 7-3, we can see that the frequency of very high
returns is signi?cantly reduced in second rounds. For ?rst-round investments, 3.3
percent of all IPOs led to GVMs of 50 or greater. For second rounds, only 0.6 percent
of IPOs led to such extreme outcomes. Similarly, while more than half (53.6%) of all
IPOs had GVMs of 5 or greater for ?rst-round investments, the portion of IPOs with
GVMs of 5 or greater is just over one-third (36.6%) for second-round investments. Of
course, GVMs do not tell the whole story, as they make no allowance for differences
in average holding periods. Exhibits 7-5 and 7-2 demonstrated that average holding
periods are shorter (fewer private ?rms at each point) for second-round investments
than for ?rst-round investments. This shortening of holding periods would tend to
make GVMs look less extreme for second-round investments, even if there were no
difference in annualized returns. Nevertheless, the overall pattern of more extreme
returns for ?rst-round investments still holds, even if we focus on annualized returns.
Exhibit 7-7 gives the GVMs for all second-round investments.
By comparing Exhibits 7-4 and 7-7, we can see that extreme multiples are less
frequent for second-round investments compared to the ?rst-round investments. This
EXHIBIT 7-6
GVMs FOR SECOND-ROUND INVESTMENTS: IPOs AND
ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.8% 20.2%
0.25 to ,0.50 1.1% 11.2%
0.50 to ,1.00 6.4% 14.5%
1.00 to ,1.50 9.9% 9.0%
1.50 to ,2.00 9.9% 8.9%
2 to ,3 15.4% 10.2%
3 to ,5 19.8% 13.1%
5 to ,10 22.0% 8.3%
10 to ,20 10.4% 3.0%
20 to ,50 3.6% 1.1%
50 to ,100 0.5% 0.3%
.5100 0.1% 0.1%
NOTE: Data includes all second-round investments with
known exit values.
Source: Sand Hill Econometrics.
130 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
result is consistent with our ?ndings about IPOs and acquisitions discussed for the
previous exhibit. Among all second-round investments, 0.2 percent had GVMs of 50
or greater, compared to 0.7 percent among all ?rst-round investments. This lower
frequency for great investments is somewhat counterbalanced by a lower frequency
for write-offs, which occur for 46.6 percent of second-round investments compared to
49.1 percent of ?rst-round investments.
Exhibit 7-8 uses third-round investments and repeats the survival analysis of
Exhibits 7-2 and 7-5. As in those previous exhibits, we assume that all companies
reported as “still private” after 10 years have actually gone out of business at the
same rate as those companies observed to be defunct. After ?ve years, 27.10
percent of third-round investments have been acquired, 19.90 percent have had an
IPO, 36.97 percent are defunct, and 16.03 percent are still private. After 10 years,
34.73 percent have been acquired, 21.99 percent have had an IPO, 43.28 percent are
defunct, and, by assumption, none are still private. As compared to second-round
(Exhibit 7-5) investments, we see that failure rates for third round investments are
slightly higher than those for second round investments in the initial months fol-
lowing investments, while after 10 years they are both at about 43%. As for IPO
EXHIBIT 7-7
GVMs FOR ALL SECOND-ROUND INVESTMENTS
Value Multiple Percentage
0 46.56%
.0 to ,0.25 13.34%
0.25 to ,0.50 7.95%
0.50 to ,1.00 6.54%
1.00 to ,1.50 3.69%
1.50 to ,2.00 3.31%
2 to ,3 4.39%
3 to ,5 5.46%
5 to ,10 5.35%
10 to ,20 2.43%
20 to ,50 0.82%
50 to ,100 0.14%
.5100 0.03%
NOTE: These return distributions are estimated using
the information on Exhibits 7-5 and 7-6, with some
additional assumptions to handle missing exit
values. The “still private” companies after 10 years
are assumed to have failed.
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 131
versus ACQ outcomes, third-round investments have slightly higher IPO rates and
lower ACQ rates than second-round investments.
Exhibit 7-9 reports GVMs for IPOs and acquisitions for all investments made
in the third rounds.
6
The evidence of Exhibit 7-9 continues the pattern of later
rounds showing less extreme GVMs than earlier rounds. Only 0.1 percent of IPOs
have GVMs of 50 or greater, and only 20.3 percent have GVMs of 5 or greater. In
comparison, 3.3 percent of ?rst-round investments had GVMs of 50 or greater, and
53.6 percent were 5 or greater. Although some of these differences can be ascribed
to shorter holding periods of third-round investments, the difference still remains if
we examine annualized returns. These patterns are reinforced when we examine the
returns to all third-round investments.
Among third-round investments, only 44.7 percent are writeoffs, as compared to
46.6 percent of second rounds and 49.1 percent of ?rst rounds. On the high end, only 5.6
percent hada valuemultiple of 5or greater, comparedto8.8percent above this threshold
EXHIBIT 7-8
PORTFOLIO COMPANY STATUS OVER TIME, ASSUMING NO PRIVATE
COMPANIES AFTER 10 YEARS, ALL THIRD-ROUND INVESTMENTS
0 12 24 36 48 60 72 84 96 108 120
Months Since Third Round
100
90
80
70
60
50
40
30
20
10
0
P
e
r
c
e
n
t
ACQ
PRI
DEF
IPO
Source: Sand Hill Econometrics.
6
Analysis of fourth-round investments shows that they are similar to third-round investments, with an
even higher concentration of multiples in the range of above 0 and below 5.
132 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
in the second round and 12.0 percent in the ?rst round. The relatively lowfrequency on
the extremes means that 49.7 percent of all third-round investments had multiples in the
range above 0 and below5, compared to 44.7 percent of second rounds and 38.9 percent
of ?rst rounds. It is in this middle range above 0 and below5 that the return advantage of
preferred stock becomes apparent. The GVMs in this chapter are all based on the
baseline SHE assumption that all investments are made in common stock. These
exhibits would look different if we made more realistic assumptions about the security
types in each round. We discuss and value these differences in Part III of the book.
The evidence fromExhibits 7-1 and 7-2 shows that IPO exits occurred for about
15.4 percent of all ?rst-round investments made before 2001, and these investments
were often quite pro?table for the investors. As mentioned before, it is important to note
that these results are disproportionately in?uenced by the unprecedented number of
investments made during the 1999À2000 boomperiod. So in several more years, when
more investments fromthe post-2000 period are included in the completed-investment
sample, wouldthe IPOexit rate start increasingagain?This does not seemlikely, at least
not in the immediate future. The reason is that while the number of VCinvestments has
declined to a more sustainable level in the post-2000 period, the number of VC-backed
IPOs has plummeted even more drastically. Exhibit 7-11 shows this trend.
In particular, the exhibit shows the 10-year, rolling-window averages for the
number of new VC investments and the number of VC-backed IPOs. For 1990, for
example, the average number of new VC investments for the previous 10 years
EXHIBIT 7-9
GVMs FOR THIRD-ROUND INVESTMENTS: IPOs AND ACQUISITIONS
Value Multiple IPO ACQ
,0.25 0.5% 21.6%
0.25 to ,0.50 1.4% 13.2%
0.50 to ,1.00 8.2% 15.2%
1.00 to ,1.50 14.1% 10.2%
1.50 to ,2.00 13.0% 8.7%
2 to ,3 19.2% 11.3%
3 to ,5 23.5% 11.1%
5 to ,10 14.5% 6.6%
10 to ,20 4.6% 1.2%
20 to ,50 1.1% 0.9%
50 to ,100 0.1% 0.1%
.5100 0.0% 0.0%
NOTE: Data includes all third-round investments with
known exit values.
Source: Sand Hill Econometrics.
7.1 VC INVESTMENTS: THE HISTORICAL EVIDENCE 133
(1981À1990) is 508, and the average number of VC-backed IPOs in the previous
10 years is 95. The ratio of the two numbers (shown on the right-hand axis in %) is
a back-of-the-envelope measure of the IPO rate of VC investments. In the ?rst half
of the 1990s, as the number of VC ?nancings stayed low and the IPO market
boomed, this ratio climbed up and peaked at 31 percent in 1994. Near the end of
the decade, however, the number of VC ?nancings ballooned much faster than the
number of VC-backed IPOs, and the ratio rapidly started to decline. By 2000,
the ratio of the two 10-year average numbers is down to 16 percent, which is almost
exactly the same as the IPO rate in Exhibit 7-2 (15%).
Post-2000, the number of investments declined—but never declined to the
level last seen in the early 1990s. Even in 2009, at the depth of the recession, 725
new ?nancings took place, compared to just 417 in 1994. Meanwhile, the number of
VC-backed IPOs continued to stagnate at the level last seen in the late 1980s—less
than 50 a year on average—throughout the ?rst decade of the new century. Thus,
the ratio of the 10-year averages of IPOs and new VC ?nancing keeps going down,
and as of 2009, it is just 5 percent—that is, on average there were only 67 IPOs for
1,260 investments per year.
EXHIBIT 7-10
GVMs FOR ALL THIRD-ROUND INVESTMENTS
Value Multiple Percentage
0 44.71%
.0 to ,0.25 13.54%
0.25 to ,0.50 7.88%
0.50 to ,1.00 6.92%
1.00 to ,1.50 4.94%
1.50 to ,2.00 4.11%
2 to ,3 5.73%
3 to ,5 6.57%
5 to ,10 3.98%
10 to ,20 1.14%
20 to ,50 0.43%
50 to ,100 0.05%
.5100 0.00%
NOTE: These return distributions are estimated using
the information on Exhibits 7-8 and 7-9, with some
additional assumptions to handle missing exit
values. The “still private” companies after 10 years
are assumed to have failed.
Source: Sand Hill Econometrics.
134 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
For this rate to start going back up again, one or both of two things needs to
happen. First, there will have to be more VC-backed IPOs and more IPOs in
general. Second, the number of VC ?nancings will need to go down further. While
some argue precisely both of these things need to take place for the VC model to
start working again, others assert that VC investments need not rely on IPO exits
alone. It will be interesting to revisit this data in several years and ?nd out if
the patterns of VC investment exits evolve further away from IPOs or return to the
long-term historical levels of IPO rates.
7.2 THE INVESTMENT PROCESS
In Chapter 1, we listed several stages a potential VC investment goes though before
any money changes hands. These stages included screening, the term sheet, due
diligence, and closing. Exhibit 7-12 gives an example of the number of investments
that reach each stage of this process for a “typical” VC:
7
EXHIBIT 7-11
10-YEAR AVERAGE VC FINANCINGS AND IPO EXITS, BY ENDING
YEAR
1600
35%
30%
25%
20%
15%
10%
5%
0%
1400
1200
1000
800
600
400
200
0
1
9
8
9
1
9
9
0
1
9
9
1
1
9
9
2
1
9
9
3
1
9
9
4
1
9
9
5
1
9
9
6
1
9
9
7
1
9
9
8
1
9
9
9
2
0
0
0
2
0
0
1
2
0
0
2
2
0
0
3
2
0
0
4
2
0
0
5
2
0
0
6
2
0
0
7
2
0
0
8
2
0
0
9
# of initial VC financings, 10-yr. ave.
# of VC-backed IPOs, 10-yr. ave.
IPO/investments,10-yr. ave.
Source: 2009 NVCA Yearbook, press releases on NVCA website.
7
There is no academic research to back up Exhibit 7-12. These numbers are estimates gleaned from
conversations with VCs and researchers.
7.2 THE INVESTMENT PROCESS 135
The ?rst entry in the exhibit has a wide range, from 100 to 1,000, because the
?rst screening stage is somewhat amorphously de?ned. If we include every busi-
ness idea ever seen by the VC, then the number would be closer to 1,000. If we
include only those ideas that receive any formal attention, then the number would
be closer to 100. In any case, the odds are long to reach the next stage. The exhibit
shows that for every 100 to 1,000 opportunities that cross a VC’s desk, only about
10 will reach the more intensive screening stage that we are calling “preliminary
due diligence”. Of these 10, about 3 will justify a term sheet. Term sheets are
preliminary contracts designed as a starting point for the more detailed negotiations
required for the contract. In Chapter 8 we cover term sheets in detail.
The acceptance of a term sheet by the entrepreneur leads to a more complete
due diligence and contract negotiation. There are many ways that an agreement can
break down between the term sheet and the ?nal investment. Although hard data are
dif?cult to ?nd, some VCs report that only about half of all accepted term sheets
lead to an investment. Thus, the typical VC would need to screen at least 100
companies to make one investment.
As we move down Exhibit 7-12, each successive stage takes progressively more
work. The exact process for each stage varies considerably across ?rms. There is no
consensus on the best practices for each stage, and it is doubtful that such a consensus
will ever occur. Nevertheless, a fewthemes are apparent. First, the existence of a formal
process is highly correlated with the size of the VC?rm. Firms with just a fewpartners
are likely to make decisions as a group, with all partners somewhat informed and
involved in all stages of due diligence and in the investment decision. For midsize ?rms
larger than ?ve or six partners, this group decision making becomes unwieldy, and we
are more likely to see a deal driven by one or two partners, with the full partnership
investing on the basis of a written memo and an oral presentation by the lead partner for
the deal. Such midsize ?rms often attempt to make their investment decisions at reg-
ularly scheduled weekly meetings, where all partners try to participate in person or by
telephone. For the larger ?rms, regular meetings of the entire partnership are not fea-
sible, and commitment decisions are usually made by a committee of senior partners. If
there is an investment committee, then a written memo becomes an important way for
EXHIBIT 7-12
THE INVESTMENT PROCESS
Screening [100À1,000]
Preliminary Due Diligence [10]
Term Sheet [3]
Final Due Diligence [2]
Closing [1]
136 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
other principals to communicate with the committee. Also, large ?rms are the only
place where we ?nd a signi?cant number of junior VCs who do not take the lead on
investments, but whose main role is to screen potential investments, perform due
diligence, and take on various other detail work.
A big component of VC success is the quality of prospects at the screening
stage, also called the deal ?ow. The generation of high-quality deal ?ow, also
called “sourcing”, is a major challenge and takes a big chunk of VC time and
energy. The VCs use a variety of sourcing strategies. In general, the better the
reputation of the VC ?rm, the better the deal ?ow, and the less work the VCs have
to do to get it. In our discussion of Summit Partners in Chapter 5, we mentioned
how its extensive database of private companies often provides it with proprietary
deal ?ow, the holy grail of all private equity investors. Other top-tier VCs will often
garner proprietary deal ?ow through the sheer force of their reputation, as entre-
preneurs will want the famous VC brand attached to their company. These top-tier
VCs receive most of their deal ?ow either from repeat entrepreneurs or as direct
referrals from close contacts. Younger and less-prestigious ?rms also rely on direct
referrals—often from professional service providers such as accountants, lawyers,
and consultants—but also must be more proactive about attending trade shows,
accessing third-party databases, and even cold-calling new ?rms.
Once the deal ?ow is generated, VCs must perform the initial screen. Although
some investments may be screened through informal conversation or fromthird-party
information sources, the majority of investments are screened using a business plan
prepared by the entrepreneur. The business plan gives a summary of all crucial
information about the company; it includes a detailed description of the strategic plan
for the company, the current and potential competitors, and the background of the
management team. Although ?nancial projections are also included, the detail in
these projections varies widely. For early stage companies, the projections usually
focus on the uses of funds; for later-stage companies, the projections should be more
complete ?nancial statements. In general, the VCs (correctly) take all such forecasts
with a grain of salt.
Many academics have studied the screening phase, but lack of access to a broad
database prevents any strong quantitative conclusions. These studies, in addition to
published interviews with famous VCs, do allow for some qualitative conclusions
about the most important elements of the initial screen. These two elements also
remain the key focus of the next phases of diligence. We will call them the market
test and the management test. They can both be phrased as questions:
1. Does this venture have a large and addressable market? (Market test)
2. Does the current management have the capabilities to make this business
work? (Management test)
The market test focuses on whether the company could conceivably lead to a
large exit. For most VCs, a “large” market is one that could sustain a public
company, with a plausible valuation of several hundred million dollars within about
7.2 THE INVESTMENT PROCESS 137
?ve years. A company developing a novel drug to treat breast cancer is going after a
big market; a company developing a novel drug to treat a disease with only 1,000
sufferers worldwide is not. An “addressable” market is one that can conceivably be
entered by a new company. If a company has a new operating system for personal
computers, the potential market is certainly large, but it is quite unlikely that the
product will make any progress against the Microsoft juggernaut.
The market test requires both art and science. The science component is most
important when you are looking at a business with established markets (e.g., breast
cancer), even if the product is novel (e.g., a new drug). The market test is much
more of an art when the VC is evaluating new markets, either because there are
currently no products in that space, or because the products in that space have not
yet found any path to pro?tability. eBay is an example of a company that addressed
a completely new market. Many VCs scoffed at eBay when it ?rst began, and it is
hard to blame them.
8
Even Benchmark Capital, the eventual investor, did not invest
until the company was already pro?table, although one must still admire its ability
to spot the huge market potential that eventually led to a return of nearly 1,000
times the VC investment. Yahoo! and Netscape are other examples of such new
markets from the early Internet era. On the health care side, the investment in
Genentech, the ?rst company based on the new science of DNA replication, also
required high artistry of market vision.
Google is an example of a company that addressed an existing market, but
one without a clear path to pro?tability. In 1999, at the time of Google’s ?rst (and
only) round of institutional VC investment, Internet search was already old news.
All the major Internet portals had search technology, and search was viewed as
something of a commodity tool on these portals, and not one that could garner huge
pro?t by itself. The bet on Google was essentially a bet that its superior search
technology would eventually lead to a shift in consumer practices, allowing a pure
search site to develop its own revenue stream. This kind of investment requires
business vision that is certainly more art than science, and more than one famous
VC has publicly admitted that his vision failed in this case.
9
8
Bessemer Venture Partners, a VC ?rm with many famous successes, humorously admits their oversights
on the website of their “antiportfolio”: http://www.bvp.com/port/anti.asp. In honest moments, many
other VCs would sympathize with Bessemer’s reaction to eBay: “Stamps? Coins? Comic books? You’ve
GOT to be kidding.” Just as good was the reaction of a Bessemer partner upon learning that the student
founders of Google were renting the garage (yes, the garage) of a college friend: “Students? A new
search engine? How can I get out of this house without going anywhere near your garage?”
9
See the previous footnote for Bessemer Venture Partner’s admission. A second admission comes from
Tim Draper of Draper Fisher Jurvetson, one of our top-tier ?rms from Chapter 5. The April 2005 issue of
the Venture Capital Journal summarizes an interview Draper gave to the San Francisco Chronicle, in
which he says he passed on Google because his ?rm had already backed “some 20 other companies
featuring search engine technology.” The same article also states that another top VC admitted—off the
record—to passing on Google.
138 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
Both eBay and Google—the two most successful VC investments of all
time—demonstrate the importance of both sourcing and the initial screen for the
long-term competitive advantage of VCs. In both cases, the opportunities were only
made available to some of the top VCs; “no-name” ?rms never got the chance to
demonstrate their investing vision. Nevertheless, in both cases some of these top
VCs passed on the opportunity, because the large, addressable market was not at all
obvious.
The evaluation of the management team—the management test—is most
qualitative part of screening and due diligence. Many VCs argue that the evaluation
of people is the most important part of their job and believe that success or failure is
driven primarily by the strength of the management team. In evaluating the man-
agement of a start-up company, the VC must form a judgment about both
the individuals and the team. In evaluating individuals, VCs carefully study the
backgrounds and personalities to determine whether the individual has the ability to
carry out her assigned role in the company. The easy cases occur when the indi-
vidual has previous experience in a similar role, which is the main reason that
repeat entrepreneurs are the most prized—particularly the successful ones. Besides
the obvious resume analysis, VCs must use their judgment to decide whether
speci?c individuals have the right temperament to thrive in an entrepreneurial
company. Although many studies have attempted to analyze the characteristics of
successful entrepreneurs, it is fair to say that there is no clear consensus. Instead,
VCs must rely on intuition and experience.
In the evaluation of the entire management team, VCs must make sure that all
the key functions are covered, and that the team dynamics allow all the managers to
play to their strengths. For example, a visionary CEO can act as a great motivator
and salesman for the company, but such CEOs will usually need a strong manager
to handle the details. It is ideal if both roles can coexist, but many times the
visionary will be unwilling to yield operational control, or the detail manager will
be unable to work with a visionary CEO. In many cases VCs may feel that man-
agement teams have most of the necessary skills but lack one crucial component.
This missing piece could be in some speci?c function such as sales or ?nance, or it
could lie in the CEO position. Indeed, many startups are lead by a visionary and
?lled with talent in science and engineering, but lack any managers with entre-
preneurial business experience. In this case, the VC must be able to judge whether
this preexisting team will be able to work with newly recruited players, perhaps
drawn from the VC’s own Rolodex.
The focus on strong management is virtually universal among VCs. An oft-
spoken mantra at VC conferences is, “I would rather invest in strong management
with an average business plan than in average management with a strong business
plan”. This notion is supported by the claims that it is easier for a great management
teamto switch into a newline of business than it is for an average management teamto
execute a good idea. Indeed, claims like this are spoken so often that one might expect
mountains of evidence to support them, but in fact the evidence that does exist points
in the opposite direction. Kaplan, Sensoy, and Stromberg (2005) studied 49 successful
7.2 THE INVESTMENT PROCESS 139
VCinvestments fromtheir early business plans (birth) through their IPOs (exit). They
discovered, to much surprise, that core business lines are remarkably stable frombirth
to exit. On the other hand, management changes are quite common. These results, the
only rigorous evidence that exists on this question, suggest that conventional wisdom
is wrong.
Screening is a crucial step, and poor performance here can ruin the best deal
?ow. There are a variety of approaches to this step. Some ?rms hire junior profes-
sionals to handle much of this task, while the senior VCs focus on later stages of the
investment decision and on the active monitoring of the portfolio companies.
The advantage of this division of labor is that much more time can be dedicated to the
initial screen; the disadvantage is that inexperienced VCs might not do the job as
well. Other ?rms eschewthe use of junior professionals completely, and all screening
is handled by experienced VCs. One can ?nd these ?rms on both ends of the reputation
spectrum, from low-reputation ?rms, who do not have suf?cient deal ?ow and
management fees to justify hiring junior VCs, to high-reputation ?rms, who rely
mostly on referrals froma superior network, thus getting some of the initial screening
for free.
Investments that make it through the screening phase are then subjected to a
preliminary level of due diligence. The screening phase is about identifying
opportunities that meet the market test and the management test; it is a phase
dominated by optimism and happy thoughts. In contrast, due diligence is all about
hard questions and thinking about what can go wrong. The ?rst part of this due
diligence is the meeting of VCs with the company management. This pitch
meeting is a famous touchstone of the VC-entrepreneur relationship. For many
companies, the process ends right there. The pitch meeting is an ideal place to see if
an investment meets the management test, and successful VCs often have a well-
developed sixth sense for sizing up managerial capabilities.
For companies that pass the pitch meeting, the next phase of due diligence
can take many forms. Exhibit 7-12 breaks up the due diligence steps into a pre-
term-sheet step (preliminary diligence) and a post-term-sheet step (?nal diligence).
The fraction of diligence done before the term sheet varies across ?rms, and even
across deals within the same ?rm. In general, the more competitive the deal, the
quicker the ?rm will want to deliver a term sheet, and the more of the diligence that
will be left until afterward. Many term sheets include a period of exclusivity, giving
the VC some time to complete diligence while the company is restricted from
negotiating with other potential investors. In recent years, with less competition and
more wary investors, there has been an increase in the level of diligence done prior
to the term sheet.
Given this variation in the level of diligence in each of these steps, it is not
possible to say what steps belong in the preliminary part and what steps belong in
the ?nal part, so we will just treat both together. Overall, in due diligence the VC
aims to check every part of the company’s story. This is an important part of the
investing process, but one for which we have little hard evidence or academic
research. Thus, given the quantitative focus of this book, it is beyond our scope to
140 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
treat due diligence in detail.
10
Instead we brie?y discuss 12 main topics for a due
diligence investigation: management, market, customers, product, technology,
competition, projections, channels, partners, money, transaction terms, and a ?nal
catchall category of “terrible things”. The ?rst two topics—management and
market—are the two most important, just as they were in the screening phase.
Management
The management test was a key hurdle for the screening stage, and it remains (with the
market test) the most important part of due diligence. At the screening stage,
the management test was about upside, asking whether the present management team
appeared to have the capabilities to execute the company’s business plan. These
questions become much more detailed at the due-diligence stage, with careful eva-
luations of weaknesses on the management team. Often, these evaluations will lead to
VC demands that seasoned executives be hired to ?ll new roles such as CFO or VP of
marketing. This process is only the ?rst step in hands-on recruiting and management
support that VCs provide to their portfolio companies.
In addition to the continued evaluation of managerial capabilities, the due-
diligence stage also includes a detailed level of management vetting. At some ?rms, the
process is just as rigorous as an FBI background check, with job histories, educational
backgrounds, and even personal relationships checked. This vetting function is often
outsourced to specialized agencies.
Market
At the screening stage, the market test required large, addressable markets. In the
due-diligence phase, the ?rst impressions of such markets must be carefully ana-
lyzed. What might have been a quick and dirty estimate now must be backed up by
hard data. Many of the remaining items on this list cover some component of
market due diligence. When all these items are put together, the VC should criti-
cally examine his initial impressions of the overall market and convince himself
(and his partners) that a large, addressable market exists.
Customers
Who are (or will be) the customers for this company? Does the company rely on
just a few key customers? If so, the stability of these relationships must be assessed.
Some VCs will even tag along on a sales call to judge the reaction of potential
customers and to simultaneously evaluate the sales capabilities of the company.
10
Readers interested in a more detailed treatment of due diligence should consult Camp (2002) and
Gladstone and Gladstone (2004).
7.2 THE INVESTMENT PROCESS 141
Product
If the product is already available, how good is it? For certain kinds of products, the
VC can try it out himself. If this is not practical, then at least he can speak with
potential customers to understand the advantages and disadvantages of the product.
In some cases, it is useful to conduct focus groups and surveys. (This last item is
often outsourced.)
Technology
In evaluating technology, it is almost always necessary to consult experts in the
?eld, and access to the right experts is crucial for VCs. One bene?t of high repu-
tation for a VC is the ability to attract a high-quality set of scienti?c advisors for
formal and informal consultations. In addition to the scienti?c evaluation of the
technology, it is also crucial to perform diligence on the legal protection provided
by patents or trade secrets. The best time to ?nd out that a company’s technology
infringes on someone else’s patent is before you make an investment.
Competition
Who is the competition? How will the portfolio company build a sustainable
competitive advantage to compete in this market? Note: If a company claims it has
no competitors or potential competitors, then it is probably wrong. Virtually all
products developed for large, addressable markets will have competition. Under-
estimating the competition is a red ?ag about managerial capabilities.
Projections
All business plans have projections, and of course they are always grossly in?a-
ted.
11
Although such in?ation is expected, it is still important that management
understands how it will grow. If management projects revenue growth of 100
percent over the next year, then at the very least it should have a sales force,
manufacturing plan, and other costs that are consistent with such an increase. Of
course, VCs will make their own projections, but management projections are still a
great window to make sure that the managers really understand their business.
Channels
How does the product actually get sold? A focus on sales channels forces the VC to
understand all the players in the business, both upstream and downstream. In
11
One VC at a top-tier ?rm con?ded a humorous anecdote about one of his ?rm’s portfolio companies.
This particular company received an award from a national magazine as the “fastest growing private
company for the last three years”. Nevertheless, even over this time period the company did not achieve
the management projections from its business plan.
142 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
principle, channel analysis should be an important component of the customer and
projection categories (see earlier discussion). Many potential markets are char-
acterized by standards battles, powerful wholesale players, and relationship-driven
sales at several points in the value chain. Indeed, the analysis of channels is the most
important step in understanding whether a large market is indeed “addressable.”
Partners
Many startup companies are particularly reliant on a few partners. We use the term
“partners” loosely here to mean anything from key suppliers, development partners,
and ?rms with any kind of cooperative agreement. VCs should certainly speak with
any partners and con?rm that the relationships are healthy and stable. A high-
reputation VC can be particularly in?uential in attracting and retaining partners, a
strategy that has particular value in businesses where potential partners and cus-
tomers need to see some evidence of credibility.
Money
How has the company been ?nanced up to this point? How well does it take care of
its cash? What exactly does it intend to do with the investment? VCs should insist
on a high level of ?nancial controls (hence the common requirement to add a CFO)
and should make sure they understand the cash situation of their portfolio com-
panies at all times. Many startups begin on shoestring budget and do not have the
discipline to handle the large new sums from a VC investment. Furthermore, this
analysis must include a reasonable estimate of the total amount of ?nancing that
would be required to reach a successful exit. It is not uncommon for VCs to ?nd
investments that meet the market and management tests but nevertheless are not
viable investments, because their cash needs are so great. The classic example here
is in early stage drug development. To bring a drug through the approval process
has become such an expensive proposition that only a few early stage companies
can qualify for VC ?nancing. Companies with high cash needs are said to have a
high burn rate, meaning that they “burn through cash at a high rate”. The burn rate
can also be used to calculate how long a company can last between rounds of
investment.
Transaction Terms
Although VCs should certainly rely on lawyers for the careful checking of legal
language in the ?nal contracts, there is still work for VCs to do in crafting economic
terms speci?c to each transaction. Many of these terms will be introduced in
Chapter 8 and then discussed in Part III of the book. Transaction terms are a due-
diligence subject, because it is the information uncovered by due diligence that
should lead VCs to ask for (or, in some cases, demand) certain terms in the ?nal
contract. Furthermore, the negotiation of these speci?c terms will often provide
insights into speci?c concerns and private information of management.
7.2 THE INVESTMENT PROCESS 143
Terrible Things
Lots of terrible things can be lurking in the shadows ready to pounce on an
unsuspecting investor. This category encompasses “legal” due diligence (is there
an active or potential lawsuit against the company? Are the ?rms’ incorporation
documents in good order? And so on.). It also includes environmental due diligence
(is the property on a toxic site? Don’t laugh that one off.). Finally, this category is
also a good catchall for anything else that might seem ?shy and require more
digging.
As mentioned earlier, some of this due diligence would be completed before a
term sheet is offered, and some would be completed afterward. Frequently, the ?nal
due diligence will uncover issues that require amending some elements of the term
sheet. Almost always, such amendments improve the terms for the VCs at the
expense of the company. Nevertheless, VCs should resist the temptation to use this
post-due-diligence negotiation as a way to extract extra concessions from their
portfolio companies. Tough negotiation during a period of exclusivity can breed ill
will that lasts for the remainder of the VC’s association with the company. If a poor
relationship begins at this stage, it is often dif?cult for the VC to add value later.
Furthermore, the entrepreneurial community is small enough that bad reputations
can be quickly built, and good reputations can be quickly lost.
Following the acceptance of the term sheet by both parties, the completion of
due diligence, and the negotiation and signing of the ?nal contract, the transaction
closes, often with an anticlimactic wire transfer.
SUMMARY
Before making an investment, a VC must assess the probability of success and potential returns.
The historical evidence can provide a useful benchmark. The extensive database built by Sand
Hill Econometrics tells us that 23.3 percent of all ?rst-round investments eventually had an IPO.
This percentage rises to 28.2 percent for second-round investments and 30.3 percent for third-
round investments. The lower percentage of IPOs in earlier rounds is counterbalanced by higher
returns for these IPOs. Overall, 19.1 percent of all ?rst-round investments earna value multiple of
?ve or more, whereas 43.7 percent return nothing. For second-round investments, we estimate
that 13.7 percent earn a value multiple of ?ve or more, and 38.8 percent return nothing. For later-
round investments, the corresponding percentages are 7.4 percent and 33.7 percent.
Once VCs make an initial screening of an investment, they proceed to a more detailed
level of due diligence. The most important parts of both screening and due diligence are the
assessments of the potential market (“Is it large and addressable?”) and the quality of
management (“Is it good enough to execute the business plan?”). These major questions are
supplemented by analyses in 10 major areas: customers, product, technology, competition,
projections, channels, partners, money, transaction terms, and terrible things.
144 CHAPTER 7 THE ANALYSIS OF VC INVESTMENTS
KEY TERMS
Screening
Term sheet
Due diligence
Closing
Deal flow, sourcing, pro-
prietary deal flow
Business plan
The market test
The management test
Pitch meeting
Burn rate
REFERENCES
Camp, Justin J., 2002, Venture Capital Due Diligence, Wiley, New York.
Gladstone, David, and Laura Gladstone, 2004, Venture Capital Investing, Prentice Hall, Upper Saddle
River, New Jersey.
Kaplan, Steven N., Berk Sensoy, and Per Stromberg, 2009, “Should Investors Bet on the Jockey or
the Horse? Evidence from the Evolution of Firms from Early Business Plans to Public Companies”,
Journal of Finance 64(1), 75À115.
Stross, Randall E., 2000, eBoys, Crown Publishers, New York.
Venture Capital Journal, 2005, April.
REFERENCES 145
CHAPTER 8
TERM SHEETS
IN THIS CHAPTER, we step through a sample term sheet for a $5M invest-
ment. This sample term sheet is a simpli?ed version of the Model Term Sheet
produced by the National Venture Capital Association (NVCA) and is available in
the most up-to-date version on its website.
1
The complete Model Term Sheet, as
last updated April 2009, is given in Appendix A at the back of this book.
A VC typically signals its intention to invest by offering a term sheet to the potential
portfolio company. The company responds by signing the term sheet, rejecting it
completely, or negotiating changes to some of the provisions. If the parties can agree
on a term sheet, then it is signed, and the VC proceeds to a detailed level of due
diligence, usually with a period of exclusivity spelled out in the term sheet. Term
sheets can be thought of as starting points for a good-faith negotiation. Although few
term sheet provisions have binding consequences if they are not followed, the
document still serves as an anchor for all future negotiations between the parties.
Term sheets are broken into sections, with each section providing a summary
for a longer legal document that will be executed at closing. In Section 8.1 we give the
basic opening information of our sample term sheet, including the size of
the investment, the parties involved, and the proposed capitalization for the company.
In Section 8.2 we discuss the Charter section of the termsheet, which includes many
of the most hotly negotiated provisions. In Section 8.3 we cover the Investor Rights
Agreement, a relatively long and technical section of the termsheet. Finally, Section
8.4 covers the remaining portions of the term sheet under the label of “Other Items”.
In most sections of this chapter, we begin with a verbatim reproduction of a
section in the term sheet. This is followed by a discussion of several (but not all) of
the provisions. During this discussion, we often reference the survey ?ndings from the
sixth Edition of the DowJones Venture Capital Deal Terms Report, which is referred to
as the “Dow Jones Report”. This report gives the ?ndings from a recent survey of
completed deals while allowing us to see the relative popularity of different provisions.
1
Check http://www.nvca.org/index.php?option5com_content&view5article&id5108&Itemid5136 for
the most recent version.
146
This chapter contains a good deal of legal jargon and technical terminology.
However, to master the concepts of VC, there is no escaping some of this detail—
but it is helpful to remember the big picture. VCs are usually minority investors in
high-risk businesses, and the investment they provide is at the mercy of a small
number of managers. VC contracts are designed to protect this investment from
expropriation, which can occur either through negligence (low effort by managers)
or malice (stealing or self-dealing). Thus the big picture is that a term sheet
describes the basic structure of a transaction and provides a set of protections
against expropriation.
8.1 THE BASICS
The search for VC funding is time-consuming and economically costly. These costs
make it inef?cient for companies to constantly be looking for new investors.
Instead, as ?rst discussed in Chapter 1, VCs make lumpy investments organized
into sequential rounds. A ?rst-round investment is designated as Series A, a
second-round investment as Series B, and so on. The sample term sheet that fol-
lows describes a Series A investment.
TERM SHEET FOR SERIES A PREFERRED STOCK FINANCING OF
Newco Inc. January 1, 2010
This Term Sheet summarizes the principal terms of the Series A Preferred Stock Financing of
[___________], Inc., a [Delaware] corporation (the “Company”). In consideration of the
time and expense devoted and to be devoted by the Investors with respect to this investment,
the No Shop/Con?dentiality [and Counsel and Expenses] provisions of this Term Sheet shall
be binding obligations of the Company, whether or not the ?nancing is consummated. No
other legally binding obligations will be created until de?nitive agreements are executed and
delivered by all parties. This Term Sheet is not a commitment to invest, and is conditioned on
the completion of due diligence, legal review, and documentation that is satisfactory to the
Investors. This Term Sheet shall be governed in all respects by the laws of the [State of
Delaware], and does not constitute an offer to sell or a solicitation of an offer to buy
securities in any state where the offer or sale is not permitted.
Offering Terms
Closing Date: As soon as practicable following the Company’s acceptance of this Term
Sheet and satisfaction of the Conditions to Closing (the “Closing”).
Investors: Early Bird Ventures I (“EBV”): 5,000,000 shares (33.33%), $5,000,000
Amount Raised: $5,000,000
Price Per Share: $1 per share (based on the capitalization of the Company set forth below)
(the “Original Purchase Price”).
(Continued)
8.1 THE BASICS 147
Pre-Money
Valuation:
The Original Purchase Price is based upon a fully-diluted pre-money
valuation of $10,000,000 and a fully-diluted post-money valuation of
$15,000,000 (including an employee pool representing 15% of the fully-
diluted post-money capitalization).
Capitalization: The Company’s capital structure before and after the Closing is set forth
below:
Pre-Financing Post-Financing
Security # of Shares % # of Shares %
Common—Founders 7,750,000 77.5 7,750,000 51.7
Common—Employee Stock Pool 2,250,000 22.5 2,250,000 15.0
Issued 300,000 3.0 300,000 2.0
Unissued 1,950,000 19.5 1,950,000 13.0
Series A Preferred 0 0.0 5,000,000 33.3
Total 10,000,000 100 15,000,000 100
8.1.1 Investors
This section of the term sheet lists all investors, the dollar amount of their investment
(which we will call the $investment), and the number of shares they receive for this
amount. In this case, the investment implies ownership of 33.33 percent of the
company on a fully diluted basis (which assumes that all preferred stock is converted
and that all options are exercised). The details of the fully diluted share count are
given in the capitalization table immediately preceding this paragraph. We refer to
the 33.33 percent represented by the Series Aas the proposed ownership percentage,
a number that will play an important role in our analysis.
In this term sheet, all of the $investment is paid at one time. In some cases,
the $investment is spread across multiple payments, known as tranches, which
may be contingent on the ?rm reaching some prespeci?ed milestones, such as the
development of a working prototype for a product, the ?rst major customer, or
some speci?c level of sales. The Dow Jones Report tells us that about 19 percent of
all rounds had such tranches in the July 2007ÀJune 2008 period, with this fre-
quency higher in ?rst rounds (Series A) than in later rounds. Anecdotal evidence
suggests that such tranching is more common in weak VC markets (such as the
postboom) than it is in strong markets (such as the boom period).
2
Most analysis in
this book is appropriate only for one-time investments without additional tranches.
The analysis of tranched investments requires speci?c modeling of each milestone.
2
Consistent with this view, the rounds with tranches were 16.5% of total in the July 2006ÀJune 2007
period, according to the Dow Jones Report.
148 CHAPTER 8 TERM SHEETS
The real-options analysis of Chapter 21 can provide some direction for this
modeling, but in general it is not possible to build a general framework that can
handle all possible cases.
8.1.2 Price Per Share
The price per share, also called the original purchase price (OPP), serves as the
basis for many other calculations in VC transactions. In this example, the OPP is
straight forward to compute, because there is only one type of security, and it has a
set number of shares. However, in cases with multiple security types, the OPP
computation can be more arbitrary. We will give an example of such a computation
in Chapter 9.
In this book, we will also use the term aggregate purchase price (APP) to
refer to the price paid for all shares of a security, where APP 5OPP Ã shares
purchased. When there is only one security type, the APP is equal to $investment.
When there are multiple security types, then the exact division of $investment into
the APP for each security is important.
8.1.3 Pre-Money and Post-Money Valuation
Pre-money valuation and post-money valuation are heavily used terms in the VC
industry. In principle, post-money valuation is an analogue to market capitalization
for public companies. To compute (equity) market capitalization for a public
company, we multiply the price per share times the number of shares outstanding.
Post-money valuation is calculated the same way:
Post-money valuation 5price per share à fully diluted share count: ð8:1Þ
For our example, this calculation gives us $1 Ã 15M5$15M. An alternative
way to calculate post-money valuation is as follows:
Post-money valuation 5 $investment=proposed ownership percentage: ð8:2Þ
This method also gives us $15M, this time as $5M/0.3333. Equations (8.1)
and (8.2) are completely equivalent and are used interchangeably in practice.
Pre-money valuation is the market capitalization of the company before the
VC investment. We can compute it by simply subtracting the investment from the
post-money valuation:
Pre-money valuation5post-money valuation2$investment: ð8:3Þ
For our example, we get a pre-money valuation of $15M2$5M5$10M. An
alternative method to compute the pre-money valuation is to multiply the price per
share by the pretransaction shares outstanding:
Pre-money valuation
5price per share à pretransaction ðfully dilutedÞ share count: ð8:4Þ
8.1 THE BASICS 149
The pretransaction share count of 10M includes everything except the VC
shares. We can observe this share count in the ?rst set of columns in the capita-
lization table. Like equation (8.3), this alternative calculation gives us a pre-money
valuation of $1 Ã 10M5$10M.
3
In many VC transactions, the pre-money and post-money valuations are the
key terms discussed by the parties. Although these terms are certainly useful for
quickly communicating some basic aspects of a transaction, it is important to note
that they can be misleading about certain details. Speci?cally, the analogy to
market capitalization breaks down once we acknowledge that preferred stock
(which VCs usually buy) can be quite different from common stock (which
founders usually own). Because the post-money and pre-money calculations do not
distinguish between preferred and common stock, the results of these calculations
do not necessarily re?ect anything about the market value of the company. To
accurately compute the implied market value of a company, we will need the
option-pricing tools developed in Part III of this book. Once these tools have been
developed, we dedicate all of Chapter 17 to this computation.
8.1.4 Capitalization
The ?nal part of this introductory section is the capitalization table. In addition
to the categories used here, a capitalization table might also include shares owned
by previous investors (including angel investors and VCs from earlier rounds) or
additional security types purchased in this round. Some possible security types will
be discussed at length in Chapter 9. For now, we will note without comment that, in
contrast to the common stock held by founders and employees, VCs typically
purchase some form of preferred stock.
The capitalization table will always include a section for the employee stock
pool, which contains shares set aside as incentive compensation for employees. The
employees are usually issued call options on common stock, and the stock pool is used
to provide shares onthe exercise of these options. Because VC-backed companies rely
heavily on options for compensation, VCs typically insist that the expected option
compensation be included in the capitalization table at the time of ?nancing. In our
example, we include a pool that represents 15 percent of the fully diluted share count.
This choice is consistent with historical industry practice according to the DowJones
Report, though there seems to be a downward trend in the most recent two survey
years (2007 and 2008). Also note that this number is lower for later rounds, as they
have more shares issued to investors. Fifteen percent has become a focal point for
stock pools and is both the median and mode in the Dow Jones Report.
3
Equation (8.4) can yield an incorrect answer for pre-money valuation in cases where antidilution
protections have been triggered. Chapter 9 gives an example and a discussion of this point. For safety, an
analyst can always use Equation (8.3) to compute pre-money valuation.
150 CHAPTER 8 TERM SHEETS
8.2 THE CHARTER
The Charter, also known as the Certi?cate of Incorporation, is a public document
?led with the state in which the company is incorporated. In the majority of VC
transactions, this state is Delaware, which has the best-developed and best-understood
corporate law. Among other things, the Charter establishes the rights, preferences,
privileges, and restrictions of each class and series of the company’s stock.
Charter
Dividends: Dividends will be paid on the Series A Preferred on an as-converted basis
when, as, and if paid on the Common Stock.
Liquidation
Preference:
In the event of any liquidation, dissolution, or winding up of the
Company, the proceeds shall be paid as follows:
First pay one times the Original Purchase Price on each share of Series A
Preferred. The balance of any proceeds shall be distributed to holders of
Common Stock.
A merger or consolidation (other than one in which stockholders of the
Company own a majority by voting power of the outstanding shares of
the surviving or acquiring corporation) and a sale, lease, transfer, or other
disposition of all or substantially all of the assets of the Company will be
treated as a liquidation event (a “Deemed Liquidation Event”), thereby
triggering payment of the liquidation preferences described above.
[Investors’ entitlement to their liquidation preference shall not be
abrogated or diminished in the event part of consideration is subject to
escrow in connection with a Deemed Liquidation Event.]
Voting Rights: The Series A Preferred Stock shall vote together with the Common Stock
on an as-converted basis, and not as a separate class, except (i) the Series A
Preferred as a class shall be entitled to elect two members of the Board (the
“Series A Directors”), and (ii) as required by law. The Company’s
Certificate of Incorporation will provide that the number of authorized
shares of Common Stock may be increased or decreased with the approval
of a majority of the Preferred and Common Stock, voting together as a
single class, and without a separate class vote by the Common Stock.
Protective
Provisions:
So long as any shares of Series A Preferred are outstanding, in
addition to any other vote or approval required under the Company’s
Charter or By-laws, the Company will not, without the written consent
of the holders of at least 50% of the Company’s Series A Preferred,
either directly or by amendment, merger, consolidation, or otherwise:
(i) liquidate, dissolve, or wind-up the affairs of the Company, or effect any
Deemed Liquidation Event; (ii) amend, alter, or repeal any provision of the
Certificate of Incorporation or Bylaws; (iii) create or authorize the creation
of or issue any other security convertible into or exercisable for any equity
(Continued)
8.2 THE CHARTER 151
security, having rights, preferences, or privileges senior to or on parity with
the Series A Preferred, or increase the authorized number of shares of
Series APreferred; (iv) reclassify, alter, or amend any existing security that
is junior to or on parity with the Series APreferred, if such reclassification,
alteration, or amendment would render such other security senior to or on
parity with the Series A Preferred; (v) purchase or redeem or pay any
dividend on any capital stock prior to the Series A Preferred; or (vi) create
or authorize the creation of any debt security; (vii) create or hold capital
stock in any subsidiary that is not a wholly owned subsidiary, or dispose of
any subsidiary stock or all or substantially all of any subsidiary assets; or
(viii) increase or decrease the size of the Board of Directors.
Optional
Conversion:
The Series A Preferred initially converts 1:1 to Common Stock at any
time at option of holder, subject to adjustments for stock dividends, splits,
combinations, and similar events and as described below under “Anti-
dilution Provisions”.
Anti-dilution
Provisions:
In the event that the Company issues additional securities at a purchase
price less than the current Series A Preferred conversion price, such
conversion price shall be reduced to the price at which the new shares are
issued.
The following issuances shall not trigger anti-dilution adjustment:
(i) securities issuable upon conversion of any of the Series A Preferred, or
as a dividend or distribution on the Series APreferred; (ii) securities issued
upon the conversion of any debenture, warrant, option, or other convertible
security; (iii) Common Stock issuable upon a stock split, stock dividend, or
any subdivision of shares of Common Stock; and (iv) shares of Common
Stock (or options to purchase such shares of Common Stock) issued or
issuable to employees or directors of, or consultants to, the Company
pursuant to any plan approved by the Company’s Board of Directors.
Mandatory
Conversion:
Each share of Series A Preferred will automatically be converted into
Common Stock at the then-applicable conversion rate (i) in the event of
the closing of an underwritten public offering with a price of 5 times the
Original Purchase Price (subject to adjustments for stock dividends,
splits, combinations and similar events) and net proceeds to the Company
of not less than $15,000,000 (a “Qualified Public Offering” 5“QPO”), or
(ii) upon the written consent of the holders of 75% of the Series A
Preferred.
Redemption
Rights:
The Series A Preferred shall be redeemable from funds legally
available for distribution at the option of holders of at least 50% of
the Series A Preferred commencing any time after the fifth anniversary
of the Closing at a price equal to the Original Purchase Price plus all
accrued but unpaid dividends. Redemption shall occur in three equal
annual portions. Upon a redemption request from the holders of the
required percentage of the Series A Preferred, all Series A Preferred
shares shall be redeemed (except for any Series A holders who
affirmatively optout).
152 CHAPTER 8 TERM SHEETS
8.2.1 Dividends
In public companies, preferred stock is usually issued with the promise of cash
dividends. However, preferred stock in VC transactions rarely promises cash divi-
dends, because portfolio companies are usually cash poor, and these dividends would
accelerate the need for more ?nancing. Instead, some term sheets—like our exam-
ple—will give a dividend preference to preferred stock, meaning that you cannot
pay any dividends to common stock unless you ?rst pay dividends to the preferred.
This is essentially a way to prevent the management of the company from sneaking
cash out to common shareholders. Alternatively, the preferred stock might receive
accrued cash dividends to be paid in cash only upon a deemed liquidation event (see
the Liquidation Preference topic of the Charter for a de?nition).
Finally, the preferred stock might receive stock dividends, which adds the
total holdings of preferred. Such stock is called payment-in-kind (“PIK”) preferred.
Dividend rights may be cumulative or noncumulative—the difference being that
cumulative dividends accrue even if not paid, whereas noncumulative dividends only
accrue during the ?nal period before they are paid. Cumulative dividends can accrue
by simple interest (the same ?at percentage every year on the OPP) or by com-
pound interest (which includes dividends paid on previous dividends.) Overall,
dividends may be either for cash (accrued cash dividends) or stock (PIK dividends),
each type of dividends may be cumulative or noncumulative, and cumulative divi-
dends may be by simple or compound interest. See the NVCA model term sheet in
Appendix A for the example language for several of these cases.
8.2.2 Liquidation Preference
When a company is sold, merged, or shut down—a deemed liquidation event—the
proceeds are distributed to bondholders, preferred stockholders, and common
stockholders, in that order. A liquidation preference tells an investor where she
stands in the capital structure hierarchy. In our example, there is no debt and only
one round of VC investment, so the Series A preferred is getting the ?rst dollar from
any liquidation. When there have been multiple rounds of investment, it is common
for the latest-round investors to get their money back ?rst. Thus, Series D investors
would have liquidation preference to Series C investors, Series C investors would
be preferred relative to Series B, and so on. An alternative to this ordering, known
as “pari passu”, is for all (or some) preferred investors to be paid back at the same
time. The Dow Jones Report ?nds that about two-thirds of deals give the latest-
round investors priority over all other (earlier) classes of preferred stock.
In some cases, investors insist on liquidation preferences in excess of their
original investment. For example, a 2X or 3X liquidation preference requires that the
investor be paid back double or triple, respectively, their original investment before
any of the other (junior) equity claims are paid off. In the term sheet, we would write
a 2X liquidation preference by replacing the second section of the liquidation pre-
ference section with “First pay two times the Original Purchase Price”. The Dow
8.2 THE CHARTER 153
Jones Report ?nds that about one-quarter of all deals contain an excess liquidation
preference, with about 70 percent of these preferences being 2X or less.
8.2.3 Voting Rights and Other Protective Provisions
As discussed earlier, most of what we see in term sheets can be understood as VCs
(the minority shareholders) protecting themselves from expropriation by the majority
shareholders. Several of these methods of protection are contained in the voting
rights and protective provisions part of the term sheet. In our example, the Series A
investors are guaranteed two spots on the board and are also given the power to block
some corporate actions with a separate vote. In the Investor Rights Agreement part
of the term sheet (addressed in Section 8.3), we are told that the board will contain
?ve members in total, with two members selected by Series A, two by the founders,
and one that is acceptable to all parties. Thus in our example, EBV will control
approximately half of the board while only having one-third of the fully diluted
shares. Such shared control is typical following Series A investments, including
more than half of all cases in the Dow Jones Report. In contrast, after receiving
Series B and later rounds of VC ?nancing, boards of ventures are increasingly
controlled collectively by the investors.
The Dow Jones Report ?nds that about three-quarters of all deals contain
some form of antidilution protection. In principle, these provisions protect inves-
tors’ stakes if future investments are done at a lower price per share; such investments
are known in the industry as a down round. The details of antidilution provisions
can quickly get quite messy; we will cover this topic in detail in Chapter 9.
8.2.4 Mandatory Conversion
Convertible preferred stock usually converts to common stock at the discretion of
the investor. Some events, however, may trigger an automatic conversion, such as a
quali?ed public offering (QPO), which is a public offering that meets certain
thresholds (for example, dollars raised or price per share). In our example, the QPO
would require an offering of at least $15M and a price per share of ?ve times the
OPP 5$5 per share.
8.2.5 Redemption Rights
For situations other than liquidation, redemption rights give conditions under which
investors can demand that the company redeem (pay back) their initial investment.
Examples of such conditions include a prespeci?ed length of time or failure to meet
certain milestones. In our example, these rights would commence ?ve years after the
original investment—but in practice, redemption rights are rarely exercised, in part
because the legal status of preferred stock as “equity” restricts the power of preferred
holders to demand repayment of their investment. Although the language of
redemption rights tries to get around these restrictions—for example, “the Series
154 CHAPTER 8 TERM SHEETS
A Preferred shall be redeemable from funds legally available for distribution”—the
reality is that redemption rights don’t provide much leverage unless the company is
cash rich and can easily pay the investors back.
8.3 INVESTOR RIGHTS AGREEMENT
Investor Rights Agreement
Registration Rights:
Registrable Securities: All shares of Common Stock issuable upon conversion of the
Series A Preferred and any other Common Stock held by
the Investors will be deemed “Registrable Securities”.
Demand Registration: Upon earliest of (i) five years after the Closing; or (ii) six months
following an initial public offering (“IPO”), persons holding 25%
of the Registrable Securities may request one (consummated)
registrationbythe Company of their shares. The aggregate offering
price for such registration may not be less than $10 million. A
registration will count for this purpose only if (i) all Registrable
Securities requested to be registered are registered and (ii) it is
closed, or withdrawn at the request of the Investors (other than as a
result of a material adverse change to the Company).
Registration on Form S-3: The holders of 10% of the Registrable Securities will have the
right to require the Company to register on Form S-3, if
available for use by the Company, Registrable Securities for
an aggregate offering price of at least $1 million. There will be
no limit on the aggregate number of such Form S-3 registra-
tions, provided that there are no more than two per year.
Piggyback Registration: The holders of Registrable Securities will be entitled to “piggy-
back” registration rights on all registration statements of the
Company, subject to the right, however, of the Company and its
underwriters to reduce the number of shares proposed to be
registered to a minimumof 30%on a pro rata basis and to complete
reduction on an IPO at the underwriter’s discretion. In all events,
the shares to be registered by holders of Registrable Securities will
be reduced only after all other stockholders’ shares are reduced.
Expenses: The registration expenses (exclusive of stock transfer taxes, under-
writingdiscounts, andcommissions) will be borne bythe Company.
The Company will also pay the reasonable fees and expenses.
Lockup: Investors shall agree in connection with the IPO, if requested by
the managing underwriter, not to sell or transfer any shares of
(Continued)
8.3 INVESTOR RIGHTS AGREEMENT 155
Common Stock of the Company for a period of up to 180 days
following the IPO subject to extension to facilitate compliance
with FINRA rule (provided all directors and officers of the
Company and 5% stockholders agree to the same lockup). Such
lockup agreement shall provide that any discretionary waiver or
termination of the restrictions of such agreements by the
Company or representatives of the underwriters shall apply to
Investors, prorata, based on the number of shares held.
Management and
Information Rights:
A Management Rights letter from the Company, in a form
reasonably acceptable to the Major Investors, will be delivered
prior to Closing to each Investor that requests one.
Any Major Investor will be granted access to Company facilities
and personnel during normal business hours and with reasonable
advance notification. The Company will deliver to the Investor
(i) annual and quarterly financial statements, and other informa-
tion as determined by the Board; (ii) thirty days prior to the end
of each fiscal year, a comprehensive operating budget forecast-
ing the Company’s revenues, expenses, and cash position on a
month-to-month basis for the upcoming fiscal year; and (iii)
promptly following the end of each quarter an up-to-date
capitalization table. A “Major Investor” means any Investor
who purchases at least $1 million of Series A Preferred.
Right to Maintain
Proportionate Ownership:
All Major Investors shall have a pro rata right, based on their
percentage equity ownership in the Company (assuming the
conversion of all outstanding Preferred Stock into Common
Stock and the exercise of all options outstanding under the
Company’s stock plans), to participate in subsequent issuances
of equity securities of the Company (excluding those issuances
listed at the end of the “Anti-dilution Provisions” section of this
Term Sheet). In addition, should any Major Investor choose not
to purchase its full pro rata share, the remaining Major Investors
shall have the right to purchase the remaining pro rata shares.
Matters Requiring
Investor Director
Approval:
So long as the holders of Series A Preferred are entitled to elect
a Series A Director, the Company will not, without Board
approval, which approval must include the affirmative vote of
100% of the Series A Director(s):
(i) make any loan or advance to, or own any stock or other
securities of, any subsidiary or other corporation, partnership, or
other entity, unless it is wholly owned by the Company; (ii) make
any loan or advance to any person, including any employee or
director, except advances and similar expenditures in the ordinary
course of business or under the terms of a employee stock or
option plan approved by the Board of Directors; (iii) guarantee
any indebtedness except for trade accounts of the Company or any
subsidiary arising in the ordinary course of business; (iv) make
any investment inconsistent with any investment policy approved
156 CHAPTER 8 TERM SHEETS
by the Board; (v) incur any aggregate indebtedness in excess of $1
million that is not already included in a Board-approved budget,
other than trade credit incurred in the ordinary course of business;
(vi) enter into orbea party to any transaction with any director,
officer, or employee of the Company or any “associate”
(as defined in Rule 12b-2 promulgated under the Exchange Act)
of any such person except transactions resulting in payments to
or by the Company in an amount less than $60,000 per year [or
transactions made in the ordinary course of business and pursuant
to reasonable requirements of the Company’s business and upon
fair and reasonable terms that are approved by a majority of the
Board of Directors]; (vii) hire, fire, or change the compensation of
the executive officers, including approving any option plans;
(viii) change the principal business of the Company, enter new
lines of business, or exit the current line of business; or (ix) sell,
transfer, license, pledge, or encumber technology or intellectual
property, other than licenses granted in the ordinary course of
business; or (x) enter into any corporate strategic relationship
involving the payment contribution or assignment by the Com-
pany or to the Company of assets greater than $100,000.00.
Non-Competition and
Non-Solicitation
and Agreements:
Each Founder and key employee will enter into a one-year non-
competition and non-solicitation agreement in a form reason-
ably acceptable to the Investors.
Non-Disclosure and
Developments Agreement:
Each current and former Founder, employee, and consultant will
enter into a non-disclosure and proprietary rights assignment
agreement in a form reasonably acceptable to the Investors.
Board Matters: Each non-employee director shall be entitled in such person’s
discretion to be a member of any Board committee.
The Board of Directors shall meet at least quarterly, unless
otherwise agreed by a vote of the majority of Directors.
The Company will bind D&O insurance with a carrier and in an
amount satisfactorytotheBoardof Directors. Companyshall agree
that its indemnification obligations to Series A Directors are
primary, and obligations of affiliated Investors are secondary. In
the event the Company merges with another entity and is not the
surviving corporation, or transfers all of its assets, proper provi-
sions shall be made so that successors of the Company assume
Company’s obligations with respect to indemnification of
Directors.
Employee Stock Options: All employee options to vest as follows: 25%after one year, with
remaining vesting monthly over next 36 months.
Key Person Insurance: Company to acquire life insurance on Founders in an amount
satisfactory to the Board. Proceeds payable to the Company.
8.3 INVESTOR RIGHTS AGREEMENT 157
8.3.1 Registration Rights
Stock purchased in private transactions is restricted. This means that the stock
cannot be sold in a public offering. To lose this restriction, a transaction must be
registered. Registration means ?ling legal documents and disclosing data about
the ?rm to the SEC. This is a costly activity that ?rms like to avoid.
Even if no other shares are being sold, demand registration rights allow
investors to force the company to register a transaction for their shares. Term sheets
spell out exactly how often such rights can be exercised and for how many shares.
S-3 registration rights are weaker than demand rights, because they are only
useful if the company is already reporting to the SEC. Piggyback registration
rights are even weaker than S-3 rights; they allow investors to go along with a
registered transaction already being prepared for other shares. These are much less
costly to a company than demand rights.
Rule 144 is an exception to the registration rules, allowing shares to be sold to
the public after they have been held for a certain period of time (as long as the
company has some other public shares or follows ?ling requirements with the SEC).
As of 2010, the rule allows unlimited sales by non-insiders of otherwise restricted
stock after it has been held for at least one year; such sales can often be made by LPs
after in-kind distributions of stock by the GP. In addition, the rule allows for
unlimited sales by non-insiders after the stock has been held for at least six months
but less than one year, as long as adequate current information about the Company
is publicly available. In contrast, sales by insiders (such as GPs who sit on the board
of the Company) are subject to additional volume and ?ling restrictions. Rule 144A
is another exception that allows resale of stock or debt to Quali?ed Institutional
Buyers (QIBs) outside the registration process; QIBs are institutions with more
than $100 million in investment assets under management. All insider stock tends to
be subject to an additional lockup—often 180 days—after an IPO. This lockup is
contractually imposed by the underwriter and is independent of the SEC restrictions.
8.3.2 Matters Requiring Investor-Director Approval
This category of investor rights attempts to give minority investors protection
against a laundry list of possible expropriation by managers and other investors.
The standardized list in the Newco termsheet contains 10 items. While these lists
can run much longer, the danger of a very long list is that the company will be
hamstrung in its ability to operate the business. Overall, VCs must walk a ?ne line
between protecting their investment and encouraging corporate growth.
8.3.3 Employee Stock Options
When key employees are hired, they are typically given shares or options to buy
shares in the company as part of their compensation. If such shares are promised,
they are usually earned over time, or vested. Step vesting often occurs at annual,
158 CHAPTER 8 TERM SHEETS
quarterly, or monthly increments, usually over periods of three to ?ve years. Cliff
vesting takes place all at one time. Some contracts—like this Newco termsheet—
use step vesting for part of the shares and cliff vesting for the rest. In this case, we
see cliff vesting of 25 percent after one year, with monthly step vesting for the next
36 months. Vesting is sometimes also used for founders’ shares at the time of the
?rst venture capital investment, meaning that a founder who previously “owned”
the whole company must now temporarily hand back his ownership stake and stay
for a few years before he gets it back.
8.4 OTHER ITEMS
Stock Purchase Agreement
Representations and
Warranties:
Standard representations and warranties by the Company.
Conditions to Closing: Standard conditions to Closing, which shall include,among other
things, satisfactory completion of financial and legal due dili-
gence, qualification of the shares under applicable Blue Sky laws,
the filing of a Certificate of Incorporation establishing the rights
and preferences of the Series A Preferred, and an opinion of
counsel to the Company.
Counsel and Expenses: Investor counsel to draft closing documents. Company to pay all
legal and administrative costs of the financing at Closing,
including reasonable fees and expenses of Investor counsel.
Right of First Refusal/Co-Sale Agreement and Voting Agreement
Right of first Refusal/
Right of Co-Sale
(Take-me-Along):
Company first and Investors second (to the extent assigned by the
Board of Directors) have a right of first refusal with respect to any
shares of capital stock of the Company proposed to be sold by
Founders and employees holding greater than 1% of Company
Common Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of options), with a
right of oversubscription for Investors of shares unsubscribed by
the other Investors. Before any such person may sell Common
Stock, he will give the Investors an opportunity to participate in
such sale on a basis proportionate to the amount of securities held
by the seller and those held by the participating Investors.
Lockup: Founders will not transfer, hedge, or otherwise dispose of any
capital stock following an IPO for a period specified by the
Company and the managing underwriter (not to exceed 180 days).
(Continued)
8.4 OTHER ITEMS 159
Board of Directors: At the initial Closing, the Board shall consist of five members
comprised of (i) Joe Veesee, as a representative designated by
EBV, (ii) Jane Vencap as a representative designated by EBV, (iii)
Jim Goodfriend as a representative designated by the Founders, (iv)
Neel Onterpraynoor, the Chief Executive Officer of the Company,
and (v) one person who is not employed by the Company and who
is mutually acceptable to the Founders and Investors.
Other Matters
Founders’ Stock: All Founders to own stock outright, subject to Company’s right to
buyback at cost. Buyback right for 50% for first 12 months after
Closing; thereafter, right lapses in equal monthly increments over
following 36 months.
No Shop/Confidentiality: The Company agrees to work in good faith expeditiously towards a
closing. The Company and the Founders agree that theywill not, for a
period of six weeks from the date these terms are accepted, take any
action to solicit, initiate, encourage, or assist the submission of any
proposal, negotiation, or offer fromany person or entity other than the
Investors relating to the sale or issuance, of any of the capital stock of
the Company or the acquisition, sale, lease, license, or other disposi-
tion of the Company, or any material part of the stock or assets of
the Company, and shall notifythe Investors promptlyof any inquiries
by any thirdparties in regards to the foregoing. The Company will not
disclosethe terms of this TermSheet toanypersonother thanofficers,
members of the Board of Directors, the Company’s accountants and
attorneys, and other potential Investors acceptable to EBV, as lead
Investor, without the written consent of the Investors.
Expiration: This Term Sheet expires on January 8, 2010 if not accepted by the
Company by that date.
8.4.1 Rights and Restrictions
Investors want key personnel in their portfolio ?rms to have ?nancial incentives to
stay and work hard. They also want to prevent founders from exiting in “sweet-
heart” transactions. To achieve these goals, transfer restrictions may be placed on
a founder’s (or an investor’s) shares. Such restrictions may prevent all sales of
founders’ stock without express permission from later investors, or may allow later
investors to participate in such sales (called take-me-along or tag-along rights), or
be offered the shares before anyone else (right of ?rst offer), or have the option to
participate at the price that has been offered by other parties (right of ?rst refusal).
Another type of transfer provision not seen in this term sheet is a drag-along right,
which provides a selling investor with the ability to force other investors to sell
their stakes at the same price. Drag-along rights can be useful for investors who
need to force a sale of the whole ?rm.
160 CHAPTER 8 TERM SHEETS
8.4.2 Founders’ Stock
The buyback right on founders’ stock is usually valid only when founders have been
dismissed from the ?rm “for cause”. The de?nition of “for cause” is often a sticking
point in the ?nal negotiations. Note that this buyback right means that founder
shares are effectively vested at a similar rate to employee options. Although this
might seem unfair—after all, the founders may have been committed to the ?rm for
many years already—the founders are often so crucial to the company that the VC
needs to make sure that they have strong incentives to stick around.
SUMMARY
The term sheet is a preliminary agreement used to anchor the key contractual provisions for a
VC investment. The term sheet begins with the basic information of the investment and
includes a summary for many of the contractual documents needed for the ?nal closing. Most
term sheet provisions can be understood as attempts by minority shareholders (VCs) to
protect themselves from expropriation by managers and majority shareholders. For valuation
purposes, the most important portion of the term sheet is the information about investment
size, price per share, and security type. Most VC securities are preferred stock: the rights of
these preferred shares are described in the company’s Charter. Additional restrictions on
corporate activities and the reporting requirements to the investors are described in the
Investor Rights Agreement.
KEY TERMS
Term Sheet, Charter, Inves-
tor Rights Agreement
Expropriation
Rounds
Series A investment
$investment
Original purchase price
(OPP), Aggregate
purchase price (APP)
Fully diluted basis, fully
diluted share count
Capitalization table
Proposed ownership
percentage
Tranch
Pre-money valuation,
post-money valuation
Deemed liquidation event
Dividend preference
Stock dividends
5 payment-in-kind
(PIK) dividends
Accrued cash dividend
Cumulative dividends,
noncumulative dividends
Simple interest, compound
interest
Liquidation preference, 2X
(3X, 4X, etc.) excess
liquidation preference
Down round
Qualified public offering
(QPO)
Redemption rights
Restricted stock
Registration rights, demand
registration rights, S-3
registration rights,
piggyback registration
rights
Rule 144, Rule 144A
In-kind distributions
Qualified Institutional
Buyers (QIBs)
Lockup
Step vesting, cliff vesting
Transfer restrictions,
take-me-along
5 tag-along, right of first
offer, right of first refu-
sal, drag-along
KEY TERMS 161
REFERENCES
Dow Jones, 2009, Deal Terms Report, 6th Edition, Jersey City, NJ.
National Venture Capital Association, 2009, Model Term Sheet, available at http://www.nvca.org/index.
php?option=com_content&view=article&id=108&Itemid=136.
EXERCISES
8.1 True, False, or Uncertain: After a portfolio company has an IPO, the VCs are free to sell
their stock in this company in the public market.
8.2 EBV is considering a $6M Series A investment for 6M shares of CP at $1 per share. The
proposed capitalization table for Newco is as follows:
(a) What are the OPP and APP for the Series A?
(b) What is the fully diluted share count?
(c) What is the proposed ownership percentage?
(d) What is the post-money valuation?
(e) What is the pre-money valuation?
EXHIBIT 8-1
CAPITALIZATION TABLE FOR NEWCO
Prefinancing Postfinancing
Security # of Shares % # of Shares %
Common—Founders 15,000,000 83.3 15,000,000 62.5
Common—Employee Stock Pool 3,000,000 16.7 3,000,000 12.5
Issued 600,000 3.3 600,000 2.5
Unissued 2,400,000 13.4 2,400,000 10.0
Series A Preferred 0 0.0 6,000,000 25.0
Total 18,000,000 100 24,000,000 100
162 CHAPTER 8 TERM SHEETS
CHAPTER 9
PREFERRED STOCK
IN THE UNITED STATES, VCs almost always use preferred stock in their
transactions. This preferred stock comes in many ?avors. In Section 9.1 of this
chapter, we analyze the main types of preferred stock and learn how to graphically
represent them. Most types of preferred stock are convertible into common stock,
either at the discretion of the investor (voluntary conversion) or when some preset
threshold is reached (automatic conversion). These conversion conditions are
sometimes adjusted due to antidilution protections, as ?rst mentioned in Chapter 8.
In Section 9.2 of this chapter, we provide mathematical formulas and examples to
illustrate the impact of antidilution protections.
9.1 TYPES OF PREFERRED STOCK
In public markets, the vast majority of equity investments are made with common
stock. However, for VC transactions in the United States, nearly all the investments
are made with preferred stock. The key characteristic of preferred stock is that it
has a liquidation preference to common stock. This is seen in the Newco charter of
Chapter 8, where the preferred stock has a liquidation preference (for $5M APP)
and an optional conversion (for 5M shares, representing one-third of the fully
diluted share count). These two features de?ne the Series A Newco stock as con-
vertible preferred (CP). With CP, EBV must decide at the time of exit whether to
redeem (and receive all proceeds up to $5M, but nothing else) or to convert to 5M
shares and receive one-third of all proceeds.
The key step here is the determination of the conversion condition, an
inequality de?ning the level of proceeds where conversion is more valuable than
redemption. We call this level the conversion point. The conversion point for a
Series A investment is written as W
A
. We will need to make this calculation
numerous times in the chapters to follow, thus it will be useful to go through the
procedure carefully this ?rst time.
If EBV chooses to convert, then this conversion would give it 5M shares.
Because the founders have 10M shares, this would give EBV one-third of the ?rm.
For total exit proceeds 5$W, we have
CP ðconversion valueÞ 51=3 Ã $W: ð9:1Þ
163
For proceeds $W, if EBV chooses to redeem the CP, it would receive
CP ðredemption valueÞ 5Minð$5M; $WÞ: ð9:2Þ
To make the conversion decision, EBV compares the value of Equations (9.1) and
(9.2) for any given W. The conversion condition holds when Equation (9.1) is
greater than Equation (9.2). This condition is illustrated in Exhibit 9-1.
The dotted line in Exhibit 9-1 represents conversion (Equation 9.1).The solid
line in Exhibit 9-1 represents redemption (Equation 9.2). EBV’s choice between
conversion and redemption can be made by answering the question, “Do I want to
be on the dotted line or the solid line?” For low values of W, the solid line is above
the dotted line, so the investor is better off redeeming for cash—but for high values
of W, the dotted line is above the solid line, so the investor is better off converting
to common shares. The conversion point occurs when conversion and redemption
are equal, which is found at the intersection of the two lines. The conversion
condition holds for all W above that point.
Conversion Condition: 1=3 Ã W.5-W
A
515 ð9:3Þ
If the proceeds of the liquidation are $15M, then EBV will receive $5 million for
either redeeming or converting. Below $15 million, EBV is better off redeeming.
Above $15 million, it is better off converting. Exhibit 9-2 redraws Exhibit 9-1 to
re?ect this conversion condition and include only the higher of the two lines in
Exhibit 9-1.
We refer to Exhibit 9-2 as an exit diagram because it plots the value of a
security against the value of the whole ?rm at the time of the exit of the investment.
EXHIBIT 9-1
CONVERSION CONDITION FOR CP
5
5
15
W
A
$W
C
P
164 CHAPTER 9 PREFERRED STOCK
We will use exit diagrams extensively when we do valuation of preferred stock in
Part III.
CP is not the only ?avor of preferred stock. Redeemable preferred (RP)
stock has the same liquidation preference as given in the Newco charter, but omits
the conversion features. Thus RP offers no possibility of conversion—and thus no
upside. Although a VC would never accept RP by itself, some transactions will
combine RP with common stock or with CP.
The Model Term Sheet (Appendix A) gives three alternatives for the liqui-
dation preference. The Newco charter from Chapter 8 uses Alternative 1, which is
called CP.
Alternative 1
In the event of any liquidation, dissolution, or winding up of the Company, the
proceeds shall be paid as follows:
First pay one times the Original Purchase Price on each share of Series A
Preferred. The balance of any proceeds shall be distributed to holders of
Common Stock.
A merger or consolidation (other than one in which stockholders of
the Company own a majority by voting power of the outstanding shares of the
surviving or acquiring corporation) and a sale, lease, transfer, or other dis-
position of all or substantially all of the assets of the Company will be treated
as a liquidation event (a “Deemed Liquidation Event”), thereby triggering
payment of the liquidation preferences described above.
The language of Alternative 2 leads to a security called participating con-
vertible preferred (PCP). The text of Alternative 2, which follows, would replace
the second paragraph of Alternative 1 from the preceding.
EXHIBIT 9-2
EXIT DIAGRAM FOR CP
5
5
$W
C
P
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 165
Alternative 2
First pay one times the Original Purchase Price on each share of Series A
Preferred. Thereafter, the Series A Preferred participates with the Common
Stock on an as-converted basis.
By itself, this language implies that the PCP holders would get back the OPP
and then also receive any additional proceeds that would have been garnered if it
had also converted to common stock. In this respect, we could say that PCP is like
having RP plus common stock. It is important to remember, however, that this
liquidation preference only applies in the case of a deemed liquidation event. If the
PCP is converted—perhaps because of a mandatory conversion—then it becomes
just like common stock.
The language of Alternative 3 in the Model Term Sheet is very similar to
Alternative 2, except that there is a cap on the liquidation preference. Thus we refer
to this security as participating convertible preferred with cap (PCPC). The text
of Alternative 3 is given as follows:
Alternative 3
First pay one times the Original Purchase Price on each share of Series
A Preferred. Thereafter, Series A Preferred participates with Common Stock
on an as-converted basis until the holders of Series A Preferred receive an
aggregate of [______] times the Original Purchase Price
The cap is driven by ?lling in the blank space in the last sentence. The language in
these alternatives determines whether the security is common stock, RP, CP, PCP,
or PCPC. In practice, it is much easier to refer to securities with these acronyms
than to write out the liquidation preference; therefore, we will follow that practice
in this book.
To illustrate the differences among these different ?avors of preferred stock,
we draw exit diagrams for each of them in Example 9.1.
EXAMPLE 9.1
EBV is considering a $5M Series A investment in Newco. The founders and employees of
Newco have claims on 10M shares of common (including the stock pool). Thus, we are
adopting the same setup as in the Newco charter in Chapter 8. Now, however, in addition to
the CP structure considered there, EBV is considering six alternative structures for their
investment:
Structure I: 5M shares of common
Structure II: RP ($5M APP)
Structure III: RP 15M shares of common
Structure IV: PCP with participation as if 5M shares of common
Structure V: PCPC with participation as if 5M shares of common, with liquidation return
capped at four times OPP
Structure VI: RP ($4M APP) 15M shares of CP ($1M APP)
166 CHAPTER 9 PREFERRED STOCK
Structures IV and V have mandatory conversion upon a QPO, where a QPO is any
offering of at least $5 per common share and $15M of proceeds. For the purpose of solving
this problem, assume that any exit above $5 per share will qualify as a QPO (i.e., acquisitions
for at least $5 per common share would also be considered to be QPOs).
Problems
(a) Draw an exit diagram for each structure.
(b) Compare the ?ve structures for exit proceeds of $3M, $8M, $32M, $72M, and $96M.
Also include a comparison for the original CP structure from the Newco charter.
Solutions
(a) Structure I is for 5M shares of common, that there would be 15M shares total (10M for
founders and 5M for EBV.) Thus, under this structure EBV would get exactly one-third of all
proceeds for any exit, with an exit diagram as shown in Exhibit 9-3.
As mentioned earlier, it is rare for a VC in the United States to accept common stock
by itself. Outside the United States, this is not unusual.
Structure II would never happen anywhere in the world: no VCs would limit their
upside completely by taking only RP. We include this case only as a building block for the
other structures. With only RP, EBV would receive all proceeds up to $5M, and then nothing
after that. This implies an exit diagram as shown in Exhibit 9-4.
Structure III is the combination of Structures I and II, but we cannot just add the lines
in Exhibits 9-3 and 9-4, because when RP and common coexist, the RP must be paid back
?rst. This raises the question: how much of the $5M investment was used to buy the RP,
and how much was used to buy the common? Although the allocation of value between RP
and common is arbitrary, it does determine the payoff to the Series A as a whole. In different
cases, the allocation of purchase price can determine conversion rates and antidilution
protections. We will return to these issues in Part III. For now, we assume that the whole
EXHIBIT 9-3
EXIT DIAGRAM FOR COMMON STOCK
$W
C
o
m
m
o
n
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 167
$5M purchase price is allocated to the RP (APP 5$5M), with the common “free”.
This assumption eases comparisons of Structure III with the other structures. With this
assumption, under Structure III, EBV would receive all proceeds until $5M, and then one-
third of whatever is left over. This gives us an exit diagram as shown in Exhibit 9-5.
Structure IV is a hybrid of Structures I and III with a cutoff at the QPO threshold. For
exits below the QPO threshold, Structure IV looks like the RP plus common of Structure III,
because EBV would be allowed to both redeem (for $5M) and to participate in the upside as
though it also had 5M of common stock. Above the QPO threshold, there would be automatic
conversion, thus making the PCP look like the common stock of Structure I. The partici-
pation threshold here is ?ve times the original investment, which occurs when the Series A is
worth at least $25M:
1=3 Ã W 5$25M-W5$75M5QPO threshold ð9:4Þ
This implies an exit diagram as shown in Exhibit 9-6. Note that Exhibit 9-6 is just a hybrid of
Exhibit 9-5 (below the W5$75M threshold) and Exhibit 9-3 (above the W5$75M
threshold). At the W5$75 threshold, at the instant before conversion, this structure has a
total value of $5M11/3 Ã ($75M2$5M) 5$28 1/3M. Immediately after conversion, the
value drops to $25M. Hence, the diagram shows a drop of $28 1/3M2$25M5$10/3M.
Structure V may seem similar to Structure IV, but in fact they are quite different. For
Structure IV, automatic conversion occurs at the QPO of $5 per share, which implies that
W
A
5$75M. Although this automatic conversion might still be binding for Structure V, it is
also possible that EBV would choose to convert the PCPC for a lower value of W. To analyze
this voluntary conversion decision, we set up a conversion condition using a redemption
value equal to the PCPC cap at four times the APP (5$20M). We can visualize this con-
version decision as an analogue of Exhibit 9-1.
We can write the corresponding conversion condition as
ðVoluntaryÞ Conversion Condition: 1=3 Ã W.20-W
A
560 ð9:5Þ
EXHIBIT 9-4
EXIT DIAGRAM FOR RP
5
5
$W
R
P
168 CHAPTER 9 PREFERRED STOCK
Because voluntary conversion would occur at W5$60M, the automatic conversion at $75M
is a redundant and nonbinding constraint.
For PCPC, the last step is to determine the level of proceeds W where the redemption
value is capped, which we refer to as the cap point, and write as W
A
(cap). At any exit above
$5M, Structure V would receive back the APP (5$5M) plus one-third of any remaining
proceeds. The cap occurs when this total reaches four times APP 5$20M:
1=3 Ã ðW25MÞ 15M520M-W
A
ðcapÞ 5$50M ð9:6Þ
EXHIBIT 9-5
EXIT DIAGRAM FOR RP + COMMON
$W
S
e
r
i
e
s
A
5
5
S
lo
p
e
=
1
/3
EXHIBIT 9-6
EXIT DIAGRAM FOR PCP
P
C
P
28 1/3
25
5
5 75
$W
Drop
= 10/3
S
lo
p
e
=
1
/
3
9.1 TYPES OF PREFERRED STOCK 169
The careful reader may have noticed this cap point labeled on the YÀaxis of Exhibit 9-7. For
exit proceeds above the cap at W5$50M, the value line is ?at until the conversion point at
W5$60M. Exhibit 9-8 gives the exit diagram.
In this example, the computation of the QPO threshold for PCP and PCPC is relatively
straightforward. The computation becomes more complex when there are multiple rounds of
investment. Readers do not have to worry about this until Chapter 16, but should consider
themselves warned in advance!
EXHIBIT 9-7
VOLUNTARY CONVERSION FOR THE PCPC
$W
20
5
5 50 60
P
C
P
C
Conversion Point
S
lo
p
e
=
1
/
3
P
C
P
C
(
R
e
d
e
m
p
t
io
n
V
a
lu
e
)
P
C
P
C
(
C
o
n
v
e
r
s
io
n
V
a
lu
e
)
EXHIBIT 9-8
EXIT DIAGRAM FOR PCPC
P
C
P
C
S
lo
p
e
=
1
/
3
S
lo
p
e
=
1
/
3
5 50 60
$W
20
5
170 CHAPTER 9 PREFERRED STOCK
Structure VI combines features of Structure II (RP) with the baseline CP from the
Newco term sheet. In this example, there are two types of preferred stock, CP and RP, and
there is no statement about which version would be paid ?rst in a liquidation (term sheets
often omit such information). Because EBV owns all of both the CP and the RP, this liquidity
preference between the two is not relevant for the aggregate value of the Series A; for
simplicity of exposition, we treat the RP as superior to the CP.
To draw the exit diagram, we will ?rst draw the RP and CP separately. Because we
have assumed that the RP has a liquidation preference to the CP, we can draw the exit
diagram for the RP as shown in Exhibit 9-9.
Next, we look at the CP. The CP here is similar to the CP in baseline case, with some
added twists. First, because the RP is paid ?rst, the CP has no value unless the proceeds are
above $4M. Second, because the APP of the 5M shares is only $1M, the conversion con-
dition will come sooner. This conversion condition is as follows:
1=3 Ã ðW 24Þ .1-W
A
57: ð9:7Þ
Next, the exit diagram for the CP is shown in Exhibit 9-10.
The exit diagram for Structure VI is the combination of Exhibits 9-9 and 9-10.
(b) We next solve for the exit value of each structure for all six structures plus the
original CP structure from the Newco charter in Chapter 8. We use the following cases: $3M,
$8M, $32M, $72M, and $96M. Using the diagrams and reasoning from part (a) and Exhibit
9-2, we have the results shown in Exhibit 9-12.
Structure I always receives one-third of all proceeds. Structure II gets all proceeds up
to $5M but nothing more. Structure III does at least as well as other structures in all cases,
receiving all proceeds up to $5M and then one-third of everything that is left over. Structure
IV and Structure V are identical except for the W572 case, where Structure IV (PCP) still
looks like Structure III (RP 1common), but Structure V has converted and looks like
EXHIBIT 9-9
EXIT DIAGRAM FOR THE SERIES A RP
$W
R
P
i
n
S
e
r
i
e
s
A
4
4
9.1 TYPES OF PREFERRED STOCK 171
Structure I. At ?rst glance, one might think that Structure VI would provide a higher payoff
than the RP 1common combination of Structure III, but the exhibit shows this is not the
case. The reason is that once the CP converts, there is only $4M of APP paid for the RP (not
$5M as in Structure III). Finally, the original CP structure from the charter is a hybrid
EXHIBIT 9-11
EXIT DIAGRAM FOR RP + CP
$W
S
e
r
i
e
s
A
5
5
7
S
lo
p
e
=
1
/3
EXHIBIT 9-10
EXIT DIAGRAM FOR THE SERIES A CP
$W
C
P
i
n
S
e
r
i
e
s
A
5 7 4
1
S
l
o
p
e
=
1
/
3
172 CHAPTER 9 PREFERRED STOCK
between structures I and II: it looks like Structure II (RP) for W53 and W58, but looks like
Structure I (common stock) in all other cases. ’
9.2 ANTIDILUTION PROVISIONS
The Newco charter of Chapter 8 gave EBV a form of antidilution protection that
applies in the case of a down round. The two forms of antidilution protection are
full-ratchet and weighted-average. The language in the Newco term sheet of
Chapter 8 is
In the event that the Company issues additional securities at a purchase price
less than the current Series A Preferred conversion price, such conversion
price shall be reduced to the price at which the new shares are issued.
This language corresponds with full-ratchet protection, which the Dow Jones
Report ?nds for 20 percent of all deals that have any antidilution protection. With
full-ratchet adjustment, the Series A adjusted conversion price would be set to the
lowest conversion price of any later stock sale, and the adjusted conversion
rate would then be calculated as OPP divided by adjusted conversion price. To
illustrate how this would work, consider our Series A round of $5 million of
convertible preferred stock at an OPP of $1 per share. Now, assume that one year
later there is a Series B round for $5 million with a price of $0.50 per share, for
10M shares. Given full-ratchet protection, the Series B price of $0.50 would cause
an adjusted conversion price of $0.50 for Series A. The adjusted conversion rate of
the Series A stock would then be $1/$0.50 52. In fact, this same calculation would
occur even if the down round were only for a single share.
Alternatively, in a weighted-average antidilution protection, the Series A
investors would obtain an adjusted conversion price that depends on the size of the
current and past rounds. The exact adjustments depend on whether the formula is
EXHIBIT 9-12
EXIT PROCEEDS UNDER ALL STRUCTURES
Structure (charter)
I II III IV V VI CP
W 5 3 1 3 3 3 3 3 3
W 5 8 2.7 5 6 6 6 5.3 5
Exit W 5 32 10.7 5 14 14 14 13.3 10.7
W 5 72 24 5 27.3 27.3 24 26.7 24
W 5 96 32 5 35.3 32 32 34.7 32
9.2 ANTIDILUTION PROVISIONS 173
broad-base or narrow-base. The NVCA model term sheet in Appendix A gives
the formula for the broad-base weighted average as
CP
2
5adjusted conversion price 5CP
1
à ðA 1BÞ=ðA1CÞ ð9:8Þ
where
CP
2
5 Series A Conversion Price in effect immediately after new issue
CP
1
5 Series A Conversion Price in effect immediately prior to new issue
A 5 Number of shares of Common Stock deemed to be outstanding immediately
prior to new issue (includes all shares of outstanding common stock, all
shares of outstanding preferred stock on an as-converted basis, and all
outstanding options on an as-exercised basis; does not include any con-
vertible securities from this round of financing)
B 5 Aggregate consideration received by the Corporation with respect to the
new issue divided by CP
1
C 5 Number of shares of stock issued in the subject transaction
For our example, we have CP
1
5$1, A515M, B5$5M/$1 55M, and C510M.
Thus, we have
CP
2
ðbroad baseÞ 5$1 Ã ð15M15MÞ=ð15M110MÞ 5$0:80 ð9:9Þ
In a narrow-base weighted-average formula, everything is the same except for the
de?nition of A:
A (narrow-base) 5 Number of shares of Common Stock deemed to be outstanding
immediately prior to new issue (including all shares of out-
standing preferred stock on an as-converted basis, but excluding
all shares of outstanding common stock and all outstanding
options on an as-exercised basis; does not include any con-
vertible securities from this round of ?nancing).
With this change, the narrow-base case for our example gives A55M, so
CP
2
ðnarrow baseÞ 5$1 Ã ð5M15MÞ=ð5M110MÞ 5$0:67 ð9:10Þ
The Dow Jones Report tells us that a weighted-average formula is used in 80
percent of all antidilution provisions; of these weighted-average cases, broad-based
formulas are common, and narrow-based formulas are rarely used.
EXAMPLE 9.2
Suppose EBV makes a $6M Series A investment in Newco for 1M shares at $6 per share.
One year later, Newco has fallen on hard times and receives a $6M Series B ?nancing from
Talltree for 6M shares at $1 per share. The founders and the stock pool have claims on 3M
shares of common stock. Going forward, for brevity we will use the term “employees” to
mean “founders and the stock pool”.
174 CHAPTER 9 PREFERRED STOCK
Problems
Consider the following cases:
Case I: Series A has no antidilution protection.
Case II: Series A has full-ratchet antidilution protection.
Case III: Series A has broad-base weighted-average antidilution protection.
Case IV: Series A has narrow-base weighted-average antidilution protection.
For each of these cases, what percentage of Newco (fully diluted) would be controlled
by EBV following the Series B investment? What would be the post-money and pre-money
valuations?
Solutions Case I: Without any antidilution protection, EBV has 1M shares out of a fully
diluted share count of 1M16M (Series B) 13M employees 510M. Thus, they would
control 10 percent. The Series B investors paid $1 per share, so the post-money valuation
would be 10MÃ $1 5$10M, and the pre-money valuation would be $10M2$6M5$4M.
Case II: With full-ratchet antidilution protection, the Series A adjusted conversion
price would become $1 (the price of the Series B), and EBV would control 6M shares of a
fully diluted share count of 6M16M13M515M for 40 percent. The postmoney valuation
would be 15MÃ $1 5$15M, and the premoney valuation would be $15M2$6M5$9M.
Case III: With broad-base weighted-average antidilution protection, we can use
Equation (9.8) to compute the adjusted conversion price. Using the de?nitions for this equation,
we have A51M13M54M, B5$6M/$6 51M, and C56M. Substituting into (9.8) yields
CP
2
ðbroad baseÞ 5$6 Ã ð4M11MÞ=ð4M16MÞ 5$3: ð9:11Þ
Therefore, EBV would control $6M/ $3 52M shares of a total of 2M16M13M5
11M for 22.2 percent of the company. The postmoney valuation would be 11MÃ $1 5$11M,
and the premoney valuation would be $11M2$6M5$5M.
Case IV: With narrow-base, weighted-average antidilution protection, we must adjust
our de?nition of A in Equation (9.8) to omit the 3M shares held by employees, so A51M.
We then substitute this new A into Equation (9.8) to obtain
CP
2
ðnarrow baseÞ 5$6 Ã ð1M11MÞ=ð1M16MÞ 5$1:71: ð9:12Þ
With this conversion price, EBV obtains approximately 6M/$1.71 53.5M shares,
yielding it 28 percent of the 3.5M16M13M512.5M total shares. The postmoney valuation
would be 12.5M Ã $1 5$12.5M, and the premoney valuation would be $12.5M 2$6M5
$6.5M. ’
In the cases with antidilution protection, if we were to build a cap table, the
number of premoney shares is ambiguous. Some VCs might write the table with
the premoney shares given before the antidilution correction, while others would
write these shares after the correction. Either way is reasonable. However, it would
de?nitely be incorrect in Cases II, III, and IV to compute the premoney valuation as
$1 Ã 6M premoney shares 5$6M. In these cases, the only correct way to compute
premoney valuation is postmoney valuation minus $investment, as shown in the
solution.
9.2 ANTIDILUTION PROVISIONS 175
REALITY CHECK: Antidilution protection provides more protection on
paper than in practice. According to an earlier edition of the Dow Jones Report
(where they ask this question), VCs are forced to waive their antidilution protection
in about 64 percent of the applicable down rounds. Furthermore, it is likely that in
the remaining 36 percent of cases, the protections do not work nearly as strongly
as the contractual language would suggest. What is going on here?
Basically, antidilution protections are useful only when the protected party is
willing to walk away from the deal. If a company is performing poorly and a VC
wants to liquidate but the majority shareholders want to do another round of
?nancing, then the antidilution protection can prove useful. In the majority of cases,
however, the VC wants the new ?nancing and has little leverage to maintain
the protections. If a company needs ?nancing to survive, and the real value of the
company has fallen since the previous round, then most new investors will
insist that the previous investors waive their antidilution rights. Additionally,
triggering the protection would further dilute the incentives of founders and
employees, which the VC also has to take into account.
Consider the full-ratchet case (Case II) from Example 9.2. If this provision is
allowed to stand, then the new investor (Talltree) would receive only 40 percent of
Newco for its $6M. If Talltree expects to get 60 percent of the ?rm for its $6M and
EBV refuses to waive its antidilution rights, then Talltree can simply walk away.
Thus, the antidilution rights do give EBV a seat at the negotiation table, and it may
be able to extract some value—perhaps a small adjustment to its conversion price—
but antidilution rights are simply one of many bargaining chips that EBV can use to
try to get a better deal.
SUMMARY
VCs use preferred stock in most transactions. There are four main types of preferred stock.
Redeemable preferred (RP) stock is a bondlike security that is senior to common stock but
cannot be converted to common stock. No VC would ever accept RP by itself, but would
instead combine it with common stock or another type of preferred stock. Convertible preferred
(CP) stock provides the same downside protection as RP with the additional option of con-
verting to common stock. Participating convertible preferred (PCP) stock provides its holder
with a combination of the downside protection of RP and the upside potential of CP, with the
caveat that the redeemable rights go away upon a quali?ed public offering. Sometimes
the liquidation return to PCP is capped at some preset multiple of the purchase price: We refer
to such securities as participating convertible preferred with cap (PCPC) stock.
VCs often receive antidilution protection on their preferred stock. Such protection
provides the holder with the right to adjust the conversion price of their preferred in the event
of a down round. In theory, such protection gives a VC claims on additional shares in the
event of a down round. In practice, investors in struggling companies are usually forced to
give up these rights to secure a new round of investment. Nevertheless, it is important
to learn how these protections work, if only to know the relative bargaining positions for
various investors.
176 CHAPTER 9 PREFERRED STOCK
KEY TERMS
Conversion condition,
Conversion point 5W
A
Common stock, preferred
stock
Convertible preferred (CP)
Redeemable preferred (RP)
Participating convertible
preferred (PCP)
Participating convertible
preferred with cap
(PCPC)
Cap point 5W
A
(cap)
Exit diagram
Full-ratchet antidilution,
weighted-average
antidilution
Adjusted conversion price,
adjusted conversion rate
Broad-base formula,
narrow-base formula
REFERENCE
Dow Jones, 2009, Venture Capital Deal Terms Report, 6th Edition, Dow Jones, Jersey City, NJ.
EXERCISES
9.1 Suppose that it is one year after EBV’s investment in Newco (using the CP structure
from Exercise 8.2), and Talltree makes a Series B investment for 6M shares of Newco at $0.2
per share. Following the Series B investment, what percentage of Newco (fully diluted)
would be controlled by EBV? Consider the following cases:
Case I: Series A has no antidilution protection.
Case II: Series A has full-ratchet antidilution protection.
Case III: Series A has broad-base weighted-average antidilution protection.
Case IV: Series A has narrow-base weighted-average antidilution protection.
9.2 Suppose that EBV decides to consider six possible structures for the Series A stock in
Exercise 8.2:
Structure I: The original structure considered in Exercise 8.2: 6M shares of CP.
Structure II: 6M shares of common.
Structure III: RP + 6M shares of common.
Structure IV: PCP with participation as-if 6M shares of common.
Structure V: PCPC with participation as-if 6M shares of common, with liquidation return
capped at 5 times OPP.
Structure VI: RP ($4M APP) 15M shares of CP ($2M APP).
Structures IV and V have mandatory conversion upon a QPO, where a QPO is any offering of
at least $5 per common share and $15M of proceeds. For the purpose of solving this problem,
assume that any exit above $5 per share will qualify as a QPO (i.e., acquisitions for at least $5
per common share would also be considered to be QPOs).
Draw an exit diagram for each structure.
EXERCISES 177
CHAPTER 10
THE VC METHOD
THIS CHAPTER INTRODUCES concepts and mechanics for the VC method,
the most common valuation strategy used by venture capitalists. What we call “the
VC method” refers to a wide range of different implementations, all of which share
four common elements. These four elements are discussed in Section 10.1. In
Section 10.2 we discuss and illustrate one speci?c implementation, which we call
the standard VC method. This standard method does not account for management
fees or carried interest, so in Section 10.3 we introduce a modi?ed VC method to
handle these costs.
10.1 THE VC METHOD: INTRODUCTION
There are many different ways to implement the VC method. All these imple-
mentations share four main elements, and the main differences among implemen-
tations are the exact set of steps and ordering of steps. These four main elements are as
follows:
1. An estimate of an exit valuation for the company. The exit valuation is
forward-looking and represents the expected value of the company at the
time of a successful exit, where a successful exit is considered to be an IPO
or equivalent valued sale. This part of the VC method is discussed in Section
10.1.1, with more detail in Chapters 11 and 12.
2. An estimate of the VC’s target multiple of money in a successful exit. Such
multiples may be stated directly (“we look for investments that can earn 5
times our money in ?ve years”) or may be built up from an annual target
return for the IRR of a successful exit. This part of the VC method is dis-
cussed in Section 10.1.2 and is based in part on the analysis from Chapter 4.
3. An estimate of the expected retention percentage between the current
investment and a successful exit. New shares must be issued when the
current investment plus the future cash ?ows of the company are insuf?cient
to fund the growth necessary for a successful exit. Although the current VC
may participate in the future rounds of investment, we still want to know
178
about the reduction to the proposed ownership percentage for the current
investment. For the purposes of the VC method, we view each round as a
stand-alone investment. Retention is discussed in Section 10.1.3.
4. The investment recommendation, where the required investment is com-
pared to the proposed ownership percentage of the total valuation. Total
valuation is de?ned as the exit valuation, multiplied by the expected
retention percentage and divided by the target multiple of money. In most
implementations of the VC method, the investor does not explicitly account
for management fees and carried interest when making the investment
recommendation. An example of this standard approach is given in Section
10.2. In Section 10.3, we show how to modify the standard method to
include management fees and carried interest.
10.1.1 Exit Valuation
A wide range of techniques is employed for the estimation of exit value. In each
case, the focus is on the value of company at the time of a successful exit. The
reason to focus on a successful exit is obvious—that is where the vast majority of
the pro?ts will be made. The de?nition of a successful exit is less obvious. It is
perhaps easiest to talk about what a successful exit does not mean. It does not mean
“everything went perfectly, growth hit the entrepreneur’s most optimistic projec-
tions, and we are all going to be rich beyond our wildest dreams”. It would be
wrong to focus attention on such rare outcomes, because a lot of the expected value
of the company is contained in more modest successes—and because by ignoring
such cases, we would not end up with a good estimate for the total valuation.
Conversely, successful exit does not mean “anything except liquidation”. Many
VC-backed companies end up being acquired with very little money going to the
shareholders. A central idea of the VC method is to ignore these lesser payoffs and
focus attention on the places where the payoffs are signi?cant.
What does “successful exit” mean? The best working de?nition is probably
“an IPO or competitive sale”, where a competitive sale means “we could have done
an IPO, but the sale was better”. For companies where an IPO is unrealistic from
the outset—perhaps because the potential market is more limited—then a compe-
titive sale should mean “acquisition with more than one interested party, in a
situation where we did not have to sell”. In general, we are trying to work through
the case where the business has achieved some major milestones.
Once we have a notion of success in mind, we need to estimate the value of the
company conditional on this success. The two main approaches are relative valua-
tion and absolute valuation. In relative valuation, we ?nd a set of current companies
that are comparable to our company at the time of its (hypothetical) successful exit.
Comparability is usually established based on similarities in industry and growth
potential. We then compute various valuation ratios for these companies, usually
based on multiples of market value to some accounting measure. There is no hard rule
10.1 THE VC METHOD: INTRODUCTION 179
about the best multiple to use—choices are usually governed by industry standards,
where the guiding principle is to use multiples that are the most consistent across
companies. Relative valuation methods are covered in Chapter 12.
Although relative valuation uses the market’s opinion of comparable com-
panies to value the baseline company, absolute valuation re?ects the analyst’s
opinion by using a discounted cash ?ow (DCF) model. This DCF analysis can use a
variety of speci?c techniques, but the underlying idea is to determine the value of
the company by forecasting future cash ?ows and discounting them back at some
appropriate discount rate. Absolute valuation methods are neither better nor worse
than relative valuation methods; both have their strengths and weaknesses, and
careful analysts should do both. Although we will focus (in Chapter 11) on the use
of DCF models for exit valuation, they can also be used as the main method of total
valuation, particularly for later-stage investments.
In addition to the two main methods of relative valuation and absolute
valuation, a third shortcut method may be used to obtain quick inputs for the VC
method. In this shortcut—which we use in the following examples—the analyst
simply uses the average valuation for successful exits in the same industry. For
example, for an investment in the telecommunications industry, suppose that IPOs
in the previous few years have had an average valuation of $300M. Then the
analyst could assume $300M as the exit valuation, and the main valuation task
becomes to estimate the probability of an IPO.
10.1.2 Target Returns
Exit valuations are estimates of company value at some time in the future. To
convert this value to today’s dollars, we need an appropriate discount rate, which
we call the target return. In Chapter 4, we showed how to estimate the cost of VC
by using historical data and a factor model regression. It is important to note,
however, that the target return is not the same thing as the cost of VC. Our estimate
of 15 percent for the cost of VC is appropriate for the typical VC investment. When
VCs discuss target returns, they are referring to successful investments. In a VC
method valuation, only the successful cases are considered, with unsuccessful
failure cases given an effective value of 0. Let p represent the probability of suc-
cess. Then, the expected value at exit is
Expected value at exit 5exit valuation à p: ð10:1Þ
If this exit is expected in T years with no further rounds of investment, then
the present discounted value for this exit is
Present discounted value of exit 5exit valuation à p=ð1 1r
vc
Þ
T
ð10:2Þ
where r
vc
is the cost of venture capital. In Equation 10.2, the expression p/(1 1r
vc
)
T
represents the effective discount factor for the exit valuation; we call the inverse of
this discount factor the target multiple of money and denote it as M. We can also
180 CHAPTER 10 THE VC METHOD
convert the target multiple of money to an annual target return, which is implicitly
computed as:
p=ð1 1r
vc
Þ
T
51=M51=ð1 1Target ReturnÞ
T
ð10:3Þ
Exhibit 10-1 shows output from the worksheet, TARGET, from the VC_
method.xls spreadsheet. The worksheet uses Equations (10.2) and (10.3) to relate
inputs for the cost of venture capital into a matrix of outputs relating the target
return and target multiple of money with the probability of success and the time to
successful exit. For example, if time to exit is ?ve years and the probability of a
successful exit is 20 percent, then we can look in the corresponding cell and ?nd a
target multiple of money of 10.1 (calculated from Equation (10.2), and a target
return of 59 percent per year (calculated from Equation (10.3)).
It might seem as though all these steps require signi?cant guesswork.
Although guesses are certainly required, there are many ways to provide structure
for these guesses using personal experience and historical data. In the exercises at
the end of this chapter, you are asked to use the data from Chapter 7 to evaluate
some speci?c probability assumptions. More generally, however, the estimate of p
is where a VC must use his experience and judgment. What appears to be a wild
guess to the untrained eye can in fact be the exercise of hard-won intuition. For
EXHIBIT 10-1
TARGET RETURNS AND TARGET MULTIPLES OF MONEY
Cost of capital for VC 15.0%
Table of “Target Return” (top cell) and “Target Multiple-of-Money” [M]
(bottom cell)
Probability of successful exit (p)
10.0% 20.0% 25.0% 30.0% 35.0% 40.0% 50.0%
2 264% 157% 130% 110% 94% 82% 63%
13.2 6.6 5.3 4.4 3.8 3.3 2.6
3 148% 97% 83% 72% 63% 56% 45%
15.2 7.6 6.1 5.1 4.3 3.8 3.0
Years To 4 105% 72% 63% 55% 50% 45% 37%
Exit 5 T 17.5 8.7 7.0 5.8 5.0 4.4 3.5
5 82% 59% 52% 46% 42% 38% 32%
20.1 10.1 8.0 6.7 5.7 5.0 4.0
6 69% 50% 45% 41% 37% 34% 29%
23.1 11.6 9.3 7.7 6.6 5.8 4.6
7 60% 45% 40% 37% 34% 31% 27%
26.6 13.3 10.6 8.9 7.6 6.7 5.3
10.1 THE VC METHOD: INTRODUCTION 181
example, many basketball players can correctly assess whether their shots will go in
the basket from the instant the shot leaves their hands. (And for shots that miss, they
have a pretty good idea of where the rebound will go.) Talented scientists are adept
at judging the success probability of an untried experiment. Champion poker
players can estimate not only the mathematical odds of receiving any given card
(that part is easy) but also whether other players are bluf?ng. All these skills
combine some natural intuition with “data”, where the data may be drawn from
daily experience or from past experiments.
10.1.3 Expected Retention
In the valuation of mature companies, a DCF analysis usually includes positive
cash ?ows before the terminal date. In the VC method, the opposite is true: we
must usually account for negative cash ?ows, which then require further rounds of
investment and a reduction in the ownership percentage for previous investors. For
example, if a VC purchases 5M of Newco’s 20M shares in a Series A investment,
then a 5M Series B round will reduce the Series A stake from 25 percent to
20 percent. In that case, we would say that the Series A investors have a retention
percentage of 0.20/0.25 580 percent. Even if the same VC participates by pur-
chasing 1.25M shares of the Series B—thus maintaining a 25 percent stake over
the two rounds—the impact on the 5M share Series A investment remains the
same. If we expect all future rounds to be made at a fair market price, then
the identity of the Series B investor is irrelevant to the Series A investment
decision, and it is necessary to account for future reductions when analyzing the
Series A investment.
The mathematics of retention is straightforward, but the underlying
assumptions—as always—require some educated guesswork. We start with the
number of shares outstanding after the current round of investment. This share total
should include all founders’ shares (including those not yet vested) and all
employee options (including those not yet issued or vested). The reason to include
nonvested and even nonissued options and shares is that we are focused on the
valuation at a successful exit, and all these shares will certainly be issued, vested,
and valuable at such a time. Here we follow the same rule as used for pre-money
valuation (Chapter 8) and include the option pool in the computation of current
shares outstanding.
The next step is to estimate the number of shares necessary to achieve a
successful exit. This estimate should include all new shares issued at an IPO,
assuming that a post-IPO valuation is used as a successful exit. The ratio of current
shares to ?nal (new1current) shares becomes our estimate of the expected
retention. This estimation can be done by appealing to past experience, data on
successful exits, and formal modeling.
We can make a ?rst approximation for retention percentages by examining
data in the Sand Hill Econometrics database. When we analyze the experience for
all IPOs—a simple measure of “success”—we ?nd that the average retention
182 CHAPTER 10 THE VC METHOD
for all ?rst-round investments was about 50 percent, meaning that for every 10
percent of the company owned by a ?rst-round investor, an average of 5 percent
of the company was still owned by that investor after the IPO. Using the same
data, we also ?nd a retention percentage of about 60 percent for second-round
investments, 67 percent for third-round investments, and 70 percent for invest-
ments in the fourth round or later. In this chapter, we will use these estimated
percentages as our retention estimates. In practice, a VC can use specialized
knowledge to adjust these averages for differences in industry, company stage,
and market conditions.
10.1.4 The Investment Recommendation
The ?nal step in any VC method is to make an investment recommendation. The
investment recommendation is always based on a comparison of the investor’s
costs to his bene?ts. In the standard VC method (Section 10.2), the investor’s costs
are just the dollars invested, referred to simply as the required investment. To ?gure
the investor’s bene?ts (the value of his stake in the company), we ?rst need to
calculate the total valuation of the company. This total valuation is effectively the
present discounted value of the exit valuation, with an additional adjustment for the
retention percentage.
The total valuation gives us a valuation for the whole ?rm today, but of
course the investor does not own the whole ?rm. Instead, we need to know the
partial valuation for the fraction of the company claimed by the investor. In Part
III we develop option-pricing tools that allow us to compute this partial valuation
for a range of possible securities and contractual provisions. In this part of the book,
we focus our attention on total valuation and make a simple approximation that
partial valuation is equal to total valuation multiplied by the proposed ownership
percentage. In the standard VC method (Section 10.2), the investment recom-
mendation is based on a comparison of investor costs (the required investment)
with investor bene?ts (partial valuation). In the modi?ed VC method (Section
10.3), we ?rst add management fees to the investor’s costs and then subtract
expected carried interest from the investor’s bene?ts before making the investment
recommendation.
We refer to this ?nal element in the VC method as an “investment recom-
mendation” rather than “investment decision” to emphasize that the calculations are
best used as an input into decision making, and not as a ?nal answer. Valuation is
not an exact science even in the best of conditions; therefore we do not want to rely
too heavily on the conclusions. Nevertheless, the investment recommendation step
is a crucial reality check, and it should not be ignored. Great investments often look
great from all angles, whereas poor investments will give themselves away
somewhere. The prudent investor must be alert to the warning signs. A complete
VC method provides outputs based on a range of possible input values so that the
investor can understand the sensitivity of the recommendations to different
assumptions.
10.1 THE VC METHOD: INTRODUCTION 183
10.2 THE STANDARD VC METHOD
In this section we discuss the most common VC method, which we call the
standard VC method. There are many different ways this standard method can
be implemented—our version is just one example. After we do an example using
this method, we will discuss several possible variations that can be seen in
practice. For all examples in this chapter, we will assume that the VC is pur-
chasing convertible preferred stock, and all statements about ownership per-
centages will be under the assumption that all preferred stock has been converted
to common shares.
Our standard VC method has eight steps:
Step 1: What is the required investment today? (5$I)
Step 2: What is the exit valuation for this company? ($ exit valuation)
Step 3: What is the target multiple of money on our investment? (M)
Step 4: What is the expected retention percentage? (retention)
Step 5: Estimate the total valuation for the company today:
Total valuation 5$ exit valuation à retention=M ð10:4Þ
Step 6: What is the proposed ownership percentage today? ( proposed %)
Step 7: Estimate the partial valuation for this investment:
Partial valuation 5proposed %Ã total valuation: ð10:5Þ
Step 8: Investment Recommendation: Compare partial valuation to required
investment.
EXAMPLE 10.1
EBV is considering a $6M Series A investment in Newco. EBV proposes to structure the
investment as 5M shares of convertible preferred stock. The founders of Newco, who will
continue with the ?rm, currently hold 10M shares of common stock. Thus, following the
Series A investment, Newco will have 10M common shares outstanding and would have
15M shares outstanding upon conversion of the CP. EBV estimates a 30 percent probability
for a successful exit, with an expected exit time in ?ve years.
Problem What is your investment recommendation?
Solution To answer this question, we perform each step of the standard VC method:
Step 1: The required investment 5$I 5$6M.
Step 2: For the exit valuation, we will just do a basic estimate for this example. Let’s suppose
that the 30 percent success probability refers to an IPO exit, and that the average IPO
exit in Newco’s industry is at a valuation of $300M. For now, we will use $300M as
184 CHAPTER 10 THE VC METHOD
our estimate of the exit valuation. (In Chapters 11 and 12, we study exit valuations in
more detail.)
Step 3: With a cost of venture capital of 15 percent (as found in Chapter 4), a successful
exit probability of 30 percent, and a successful exit time of ?ve years, we can
calculate the required multiple of money as
Required multiple of money 5M5ð1 1r
vc
Þ
T
=p 51:15
5
=0:30 56:7: ð10:6Þ
Step 4: For expected retention, we use 50 percent, the average estimate from the SHE
database for successful ?rst rounds.
Step 5: Using the answers to Steps 2 to 4, we can estimate the total valuation as
Total valuation 5exit valuation à retention=M
5$300M Ã 0:50=6:7 5$22:39M:
ð10:7Þ
Step 6: The proposed ownership percentage today is 5M/15M533.3%.
Step 7: The partial valuation is
Partial valuation5proposed %Ã total valuation
50:333 Ã $22:39M5$7:46M
ð10:8Þ
Step 8: Because partial valuation ($7.46M) is greater than the required investment ($6M),
the investment recommendation is positive. ’
This section has discussed one speci?c implementation of the VC method.
There are many other ways that practitioners combine the four main elements of
Section 10.1 into a VC method of valuation. In general, the main differences among
implementations are in the ordering of the steps. For example, one popular
implementation of the VC method is to leave the computation of the proposed
ownership percentage until the last step.
1
This proposed ownership percentage then
becomes a cutoff value for a good investment. Another variation is to leave the exit
valuation until the last step—then the VC method produces a cutoff exit valuation
for a good investment. All these alternative implementations will lead to the same
investment recommendations if the same inputs are used.
10.3 THE MODIFIED VC METHOD
The modi?ed VC method differs from the standard method in the explicit recog-
nition of the costs of VC investing: management fees and carried interest. As
discussed earlier in Section 10.1.2, the standard approach assumes (implicitly) that
such costs are included in the target multiple of money. This assumption is not ideal
1
Lerner (2002) demonstrates an example of this implementation.
10.3 THE MODIFIED VC METHOD 185
for two reasons. First, it mixes costs into the valuation step so that the total
valuation may not be the same across different investors, even if these investors
have the same expectations and value-added for the company. Second, it makes it
dif?cult to be precise about target rates, because many different concepts are being
included in one number. In this section we explain the mechanics for some simple
adjustments for fees and carried interest.
In Chapter 2, we de?ned the lifetime fees as the sum of the annual management
fees for the life of that fund, then the investment capital of the fund as equal to the
committed capital of the fund minus the lifetime fees. For EBV, Appendix 2.A tells
us that the fund has $100M of committed capital, with 2 percent fees charged on this
capital in each year. This implies lifetime fees of $20M and investment capital of
$80M. Next, we add another de?nition: the LP cost of an investment represents the
gross cost (including fees) of an investment to the LPs of the fund. We compute
the LP cost for any investment as
LP cost 5ðcommitted capital=investment capitalÞ Ã $I ð10:9Þ
Thus, for the example of EBV, committed capital is $100M and investment
capital is $80M, so the LP cost is (100/80 Ã $6M) 5$7.5M. The idea behind this
calculation is for the GPs to explicitly consider the true cost of each investment.
Because a $6M investment represents 7.5 percent of the $80M of investment capital,
the GP is effectively “spending” 7.5 percent of the lifetime fees on this investment as
well. After all, if the GP fails to ?nd enough good investments, he can always release
the LPs from their commitments and proportionally reduce the management fees of
the fund. In the postboom period, many VC ?rms did exactly that.
Some VCs object to the modeling of LP cost in this way. Often it seems
that this objection is based on a belief that the management fees should be
considered as “reasonable compensation” for the GP’s time and effort, and the
GP should not make different investments just because of these fees. It is
important to emphasize that our model of LP cost does not mean anything about
the “reasonableness” of management fees. Rather, it just puts GPs on par with
any other honest agent who is providing a service. For example, consumers
frequently must decide whether to repair a broken item or to buy a new one. The
cost of repairing that item is an important input into this decision; to estimate the
cost of repair, one should certainly include the labor costs as one component.
From an economic perspective, these labor costs are no different than the man-
agement fees paid to a GP.
A second modi?cation to the standard VC method is a deduction for carried
interest. The partial valuation of the investment does not belong entirely to the
limited partners. If the overall VC fund is pro?table, some of the proceeds from
the investment will belong to the GPs of the VC fund, and the remainder will go to
the LPs. Thus, in this step, we divide the partial valuation into two components, the
GP valuation (5expected carried interest) and the LP valuation (5partial
valuation2GP valuation). Then the investment recommendation is made by com-
paring LP valuation to LP cost.
186 CHAPTER 10 THE VC METHOD
Conceptually, it is straightforward to think of the GP valuation as repre-
senting the component of partial valuation that belongs to the GP. Mechanically, it
is not so easy to estimate this component. The main problem is that carried interest
in any one investment will depend on the pro?ts (and losses) of all other invest-
ments made by the fund. Because some of these fund investments have not been
made yet, it is not possible to get an exact solution for this problem. Instead, we
attempt only a rough approximation for an entire fund, using the (expected) gross
value multiple (GVM) of the fund as the key input. As ?rst de?ned in Chapter 3
(Equation (3.15)), the GP% for a completed fund is
GP%5carried interest=total distributions
5Carry%Ã ðGVM Ã Investment Capital 2Carry BasisÞ
=ðGVM Ã Investment CapitalÞ
ð10:10Þ
To make Equation (10.10) operational for living funds, we replace the GVM
in the equation with our best guess for the GVM for the fund. We call this guess the
“expected” GVM. If an analyst has special information about any speci?c fund,
then he can use this information in estimating the expected GVM for that fund. For
the general cases studied in this book, we will use an expected GVM of 2.5, which
is the approximate GVM found for the full set of investments in the SHE database.
This GVM tends to differ by round (as shown in the exhibits in Chapter 7), but to
keep things simple we will ignore these differences and just use 2.5 for all examples
in this chapter.
The formula for GP% tells us what part of any investment effectively
“belongs” to the GP. We can then use this GP% to estimate the GP valuation for
any speci?c investment as
GP valuation 5GP%Ã partial valuation ð10:11Þ
and the LP valuation as
LP valuation5Partial valuation 2GP valuation
5ð1 2GP%Þ Ã partial valuation
ð10:12Þ
With these de?nitions, we are ready to list the 11 steps in the modi?ed VC
method. The ?rst 7 steps are the same as in the standard VC method. Steps 8, 9, and
10 are new steps where we calculate LP cost, GP valuation, and LP valuation,
respectively. Step 11 is a revised version of the investment recommendation step.
Modi?ed VC Method: 11 Steps
Step 1: What is the required investment today? (5$I)
Step 2: What is the exit valuation for this company? ($ exit valuation)
Step 3: What is the target multiple of money on our investment? (M)
Step 4: What is the expected retention percentage? (retention)
10.3 THE MODIFIED VC METHOD 187
Step 5: Estimate the total valuation for the company today:
Total valuation 5$ exit valuation à retention=M
Step 6: What is the proposed ownership percentage today? ( proposed %)
Step 7: Estimate the partial valuation for this investment:
Partial valuation 5proposed %Ã total valuation
Step 8: Estimate the LP cost for the investment:
LP cost 5ðcommitted capital=investment capitalÞ Ã $I
Step 9: What is the expected GP% for this investment?
GP%5Carry%Ã ðGVM Ã Investment Capital 2Carry BasisÞ
=ðGVM Ã Investment CapitalÞ
Step 10: Estimate the LP valuation from this investment:
LP valuation 5ð1 2GP%Þ Ã partial valuation
Step 11: Investment Recommendation: Compare LP valuation to LP cost.
EXAMPLE 10.2
Assume the same setup as Example 10.1, except now we will also perform the new Steps 8,
9, and 10 before making an investment recommendation in Step 11.
Problem What is your investment recommendation?
Solution Our starting points are the answers to Steps (1) through (7) in Example 10.1.
Picking up where we left off, we go to Step 8 in the modi?ed VC method:
Step 8: As discussed earlier, annual fees of 2% for 10 years imply lifetime fees of $20M
and investment capital of $80M for this $100M fund. Thus, we can compute the
LP cost as
LP Cost 5ð100=80Þ Ã $6M5$7:5M ð10:13Þ
Step 9: Using a baseline estimate of 2.5 for the GVM, we have
GP%50:20 Ã ð2:5 Ã 80 2100Þ=ð2:5 Ã 80Þ 50:10 ð10:14Þ
188 CHAPTER 10 THE VC METHOD
Step 10: In Example 10.1, we estimated a partial valuation of $7.46M. Thus, the LP
valuation is
LP valuation 5ð1 20:10Þ Ã 7:46M5$6:71M: ð10:15Þ
Step 11: The investment recommendation is based on the comparison between LP
valuation ($6.71M) and LP cost ($7.5M). We can see that the modi?cations
made a big difference: The cost side went up by $1.5M and the bene?ts (to LPs)
fell by $0.75M. Together, these two changes alter our baseline recommendation.
Exhibit 10-2 shows the output for the VC_METHOD worksheet, with results for
both the standard and modi?ed VC method for this example.
We should never rely on a single set of assumptions. In particular, the investment
recommendation will often be sensitive to assumptions about the exit valuation and the success
probability. A sensitivity analysis for these assumptions is given in Exhibit 10-3.
EXHIBIT 10-2
VC METHOD SPREADSHEET
Standard and Modi?ed VC Method
Required Investment $6.00
Exit Valuation $300.00
Target Multiple of Money 6.7
Expected Retention 50.00%
Proposed Ownership Percentage 33.33%
Committed Capital $100
Lifetime Fees $20
Carry% 20.00%
Expected Gross Value Multiple 2.5
GP% 10.00%
Total Valuation $22.39
Partial Valuation $7.46
LP Cost $7.50
GP Valuation $0.75
LP Valuation $6.71
Standard VC Method Recommendation Invest
Modi?ed VC Method Recommendation Do Not Invest
NOTE: All $ in millions.
10.3 THE MODIFIED VC METHOD 189
’
Let’s do one more example of the modi?ed method, this time from the beginning.
EXAMPLE 10.3
Assume that EBV invested in Newco at the terms in Example 10.1, and it is now one year
later. Talltree is considering an $8M Series B investment in Newco. Talltree proposes to
structure the investment as 5M shares of CP. The employees of Newco have claims on 10M
shares of common stock, and the previous venture investors (EBV) hold 5M shares of Series
A CP. Thus, following the Series B investment, Newco will have 10M common shares
outstanding and would have 20M shares outstanding upon conversion of all the CP. Talltree
estimates a 50 percent probability for a successful exit, with an expected exit time in four
years. The $250M Talltree fund has annual fees of 2 percent for each of its 10 years of life
and earns 20 percent carried interest on all pro?ts.
Problem What is your investment recommendation?
Solution To answer this question, we perform each step of the modi?ed VC method:
Step 1: The required investment 5$I 5$8M.
Step 2: We will use the same basic approach as we did in Example 10.1 and use $300M as
our estimate of the exit valuation.
Step 3: With a cost of venture capital of 15%, a successful exit probability of 50%, and a
successful exit time of 4 years, we can calculate the required multiple of money as
Required multiple of money 5M51:154=0:50 53:5 ð10:16Þ
EXHIBIT 10-3
SENSITIVITY ANALYSIS
Sensitivity of LP Valuation
(LP Cost 5 $7.5M for all cases)
Positive investment recommendations given in bold
probability of success (p)
0.2 0.3 0.4
200 2.98 4.47 5.97
Exit valuation 300 4.47 6.71 8.95
400 5.97 8.95 11.93
190 CHAPTER 10 THE VC METHOD
Step 4: For this example, we assume the sample average from the Sand Hill Econometrics
data set for second round investments: retention 560%.
Step 5: Using the answers to Steps 2 to 4, we can estimate the total valuation as
Total valuation 5$300M Ã 0:60=3:5 5$51:43M ð10:17Þ
Step 6: The proposed ownership percentage today is 5M / 20M525%
Step 7: The partial valuation is
Partial valuation 551:43 Ã 0:25 5$12:86M ð10:18Þ
Step 8: Annual fees of 2% for 10 years imply lifetime fees of $50M for this $250M fund.
Thus, the investment capital is $250M2$50M5$200M, and we can compute the
LP cost as
LP Cost 5ð250=200Þ Ã $8M5$10M: ð10:19Þ
Step 9: Using a baseline estimate of 2.5 for the GVM, we have
GP%50:20 Ã ð2:5 Ã 200 2250Þ=ð2:5 Ã 200Þ 50:10 ð10:20Þ
Step 10: The LP valuation is
LP valuation 5ð1 20:10Þ Ã 12:86M5$11:58M: ð10:21Þ
Step 11: The investment recommendation is based on the comparison between LP valuation
($11.58M) and LP cost ($10.00M). Thus, the baseline recommendation is to invest.
A sensitivity analysis for this recommendation is given in Exhibit 10-4.
’
EXHIBIT 10-4
SENSITIVITY ANALYSIS
Sensitivity of LP Valuation
(LP Cost = $10M for all cases)
Positive investment recommendations given in bold
probability of success
0.4 0.5 0.6
200 6.17 7.72 9.26
Exit Valuation 300 9.26 11.58 13.89
400 12.35 15.44 18.52
10.3 THE MODIFIED VC METHOD 191
SUMMARY
The VC method is the most popular valuation technique used by practicing venture capi-
talists. The key elements of this technique are (1) focusing on the value of the company at the
time of a successful exit, (2) using of a high target return re?ecting the signi?cant probability
of failure, (3) accounting for a reduction in the current ownership percentage because of later
rounds of investment, and (4) an investment recommendation. There are many ways that
these elements can be combined—the actual implementation of the VC method is often a
matter of taste. In this chapter, we showed two possibilities. The standard VC method is an
example of the most popular approach; the modi?ed VC method adjusts the standard method
to explicitly account for management fees and carried interest.
KEY TERMS
Exit valuation
Successful exit
Target multiple of money,
Target return
Expected retention
percentage
Required investment
Total valuation
Relative valuation,
Absolute valuation
Standard VC method
Modified VC method
LP cost
Partial valuation
GP valuation
LP valuation
REFERENCES
Lerner, Josh and John Willinge, 2002, A Note on Valuation in Private Equity Settings, HBS Background
Note 297À050.
EXERCISES
10.1 Suppose that the following four funds—all with committed capital of $100M—have
combined to form a syndicate to invest in Newco:
(I) ABC Fund, management fees of 2.5 percent per year of committed capital for all
10 years.
(II) DEF Fund, management fees of 2.5 percent per year for the ?rst 5 years, then decreasing
by 25 basis points per year in each year from 6 to 10. All fees calculated based on committed
capital.
(III) UVW fund, management fees of 2.0 percent per year. During the ?rst 5 years of the
fund, these fees are charged based on committed capital. Beginning in year 6, the fees are
charged based on net invested capital. UVW expects to be fully invested by the beginning of
year 6, and also to have realized 25 percent of all investment capital by this time. In each of
the subsequent 5 years, UVW expects to realize about 15 percent of all investment capital.
(IV) XYZ fund, management fees of 2.0 percent per year of committed capital for all 10
years. The XYZ fund expects to make all exits very quickly and to reinvest capital back into
new investments. The total amount of investments is limited to $100M.
192 CHAPTER 10 THE VC METHOD
(a) Suppose that each fund in the syndicate invests $5M in Newco. What is the LP cost for
each fund?
(b) It is possible that all four funds could agree on all the assumptions to the VC method, but
still disagree about the wisdom of making this investment. Explain the economic logic
behind this possibility.
10.2 EBV is considering a $5M Series A investment in Newco. EBV proposes to structure the
investment as 6M shares of convertible preferred stock. The employees of Newco have claims
on 10M shares of common stock. Thus, following the Series A investment, Newco will have
10M common shares outstanding and would have 16M shares outstanding on conversion of the
CP. EBV estimates a 25 percent probability for a successful exit, with an expected exit time in
5 years and an exit valuation of $500M. The $100M EBV fund has annual fees of 2 percent for
each of its 10 years of life and earns 20 percent carried interest on all pro?ts.
(a) What is your investment recommendation for EBV? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 25 percent is an aggressive
assumption about the probability of success for a ?rst-round investment?
10.3 Assume that EBV invested in Newco at the terms in Exercise 10.2, and it is now one
year later. Talltree is considering a $10M Series B investment in Newco. Talltree proposes to
structure the investment as 8M shares of convertible preferred stock. The employees of
Newco have claims on 10M shares of common stock, and the previous venture investors
(EBV) hold 6M shares of Series A convertible preferred. Thus, following the Series B
investment, Newco will have 10M common shares outstanding, and would have 24M shares
outstanding on conversion of the CP. Talltree estimates a 40 percent probability for a suc-
cessful exit, with an expected exit time in 4 years and an exit valuation of $500M. The
$250M Talltree fund has annual fees of 2 percent for each of its 10 years of life and earns 20
percent carried interest on all pro?ts.
(a) What is your investment recommendation for Talltree? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 40 percent is an aggressive
assumption about the probability of success for a second-round investment?
10.4 Assume that EBV and Talltree invested in Newco at the terms in Exercises 10.2 and
10.3, and it is now one year later. Owl is considering a $20M Series C investment in Newco.
Talltree proposes to structure the investment as 12M shares of convertible preferred stock.
The employees of Newco have claims on 10M shares of common stock, and the previous
venture investors hold 6M shares of Series A convertible preferred (EBV) and 8M shares of
Series B Convertible Preferred (Talltree). Thus, following the Series C investment, Newco
will have 10M common shares outstanding and would have 36M shares outstanding on
conversion of the CP. Owl estimates a 50 percent probability for a successful exit, with an
EXERCISES 193
expected exit time in three years, and an exit valuation of $500M. The $500M Owl fund has
fees as given in Appendix 2.C in Chapter 2.
(a) What is your investment recommendation for Owl? (Show all steps.)
(b) How sensitive is this recommendation to different assumptions about the exit valuation
and the probability of success?
(c) Given the evidence described in Chapter 7, do you think that 50 percent is an aggressive
assumption about the probability of success for a third-round investment?
194 CHAPTER 10 THE VC METHOD
CHAPTER 11
DCF ANALYSIS OF GROWTH
COMPANIES
THE EXIT VALUE is the most important input into the VC method. How
should we estimate this value? There are two types of approaches: discounted cash
?ow (DCF) analysis (absolute valuation) and comparables analysis (relative
valuation). The key idea of absolute valuation is to “make up your own mind” about
the company. You can use all kinds of evidence to inform your decision, but
ultimately you must take a stand on the various inputs necessary to value the
business at a successful exit.
In Section 11.1, we provide a framework for our DCF analysis, breaking down
the valuation problem into three distinct periods in the life cycle of a company: the
venture period (which ends with the exit), a rapid-growth period (which immediately
follows the exit), and a stable-growth period. Cash ?ow analysis is introduced in
Section 11.2 with an explanation of the key formulas and an example DCF calcu-
lation. In Section 11.3, we focus on the transition from rapid to stable growth and the
estimation of the value of the company at the time of this transition. This value,
which we call a “graduation value”, is of particular importance for growth compa-
nies. In Section 11.4, we do a full DCF model for two companies and demonstrate
how to use market data to inform the key drivers of the model. Many of the examples
in this chapter use data from the DCF.xls spreadsheet included with the book.
The topics covered in Chapters 11 and 12 are worthy of an entire book. With
these two chapters, we focus on key valuation concepts and their application to
young growth companies. The general topics of absolute and relative valuation are
covered in more depth in many other books, two of which stand out. The ?rst,
Valuation (Koller et al., 2005), is the most recent valuation book from McKinsey
and Company. This book takes a managerial view toward valuation and value
creation and develops the useful framework for the valuation of growth discussed in
Section 11.3. The second book, The Dark Side of Valuation (Damodaran, 2009), is
a specialized treatment of the valuation of growth companies (and other hard-to-
value assets), written by a ?nance professor who is a proli?c author of valuation
195
books. Professor Damodaran’s website, http://pages.stern.nyu.edu/Badamodar/, is
an excellent source for current data that can be used as inputs and comparisons for
valuation problems.
11.1 DCF ANALYSIS: CONCEPTS
VC-backed companies go through many stages of development. In earlier chapters,
we focused on the stages corresponding to rounds of VC investment; all these
stages effectively occur during the “childhood” of a company. We refer to this
childhood as the venture period. For a successful VC-backed company, an IPO exit
marks the beginning of its adolescence, with a rapid-growth period still to come.
Usually, it is only after many more years that the company will reach maturity and
settle down to a stable-growth period. Exhibit 11-1 gives a schematic example of
these periods, with some appropriate milestones. One of these milestones, which we
call graduation, marks the transition from the rapid-growth period to the stable-
growth period.
At time zero—the initial VC investment—we need to estimate an exit value
for the end of the venture period. The venture period is T years long, where T
typically varies between three and seven years. The exit value will be based on
forecasts for the rapid-growth and stable-growth periods. Thus, in estimating the
exit value, we are imagining the company T years into the future and trying to
EXHIBIT 11-1
PHASES OF GROWTH
S T 0
Rapid-
Growth
Period
Stable-
Growth
Period
graduation exit Venture
Period
Initial VC investment
3 to 7 years long:
ends with IPO or
acquisition
3 to 10 years long:
ends when company
enters period of stable growth
and return on capital and
operating margin approach
industry averages
In perpetuity
return on new
investment close
to the cost
of capital
196 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
?gure out how long rapid growth will be sustained from that point. Although this
may seem to be a daunting exercise, even a cursory treatment can provide useful
insights into the determinants of long-run success for the business and can also help
investors to better understand the dynamics of a company’s industry.
How can we estimate the typical length of a rapid-growth period? We can get
some hints by looking at historical data. Exhibit 11-2 compares the revenue growth
of newly listed public companies to that of their respective industries in the years
following their IPOs.
The key variable in Exhibit 11-2 is the industry-adjusted revenue growth
rate. To obtain this rate, we start by computing the revenue growth rate for each
industry. Then, for each ?rm, we subtract the appropriate industry rate from the ?rm’s
growth rate.
1
We compute the “years since IPO” as the total number of years since the
company ?rst appeared in the S&P database, a comprehensive source of all ?rms
that ?led ?nancial statements with the SEC. The middle line of Exhibit 11-2
shows the median industry-adjusted growth rate, the top line gives the 75th percentile,
and the bottom line gives the 25th percentile. In the ?rst full year after their IPO, ?rms
EXHIBIT 11-2
REVENUE GROWTH COMPARED TO INDUSTRY AVERAGES,
PLOTTED AS A FUNCTION OF “YEARS SINCE IPO”
1 2 3 4
Years since IPO
5 6 7
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
–20.0%
10.0%
–10.0%
0.0%
R
e
v
e
n
u
e
G
r
o
w
t
h
-
I
n
d
u
s
t
r
y
A
v
e
r
a
g
e
75th percentile
25th percentile
median
Source: Wharton Research Data Systems (WRDS), S&P Compustat.
1
Industries are de?ned by the ?rst three digits of the Standard Industrial Classi?cation (SIC) code. These
codes can be viewed at http://www.osha.gov/pls/imis/sic_manual.html.
11.1 DCF ANALYSIS: CONCEPTS 197
grow much faster than their industry: in year 1, the median industry-adjusted growth
rate is 14.7 percent, and the 75th percentile is 57.1 percent. By the ?fth year after the
IPO, however, this median is almost exactly 0; thus, as measured by revenue growth,
we can say that the typical ?rm reaches “maturity” within ?ve years after the IPO.
Also, although some ?rms continue to grow faster than their industry average beyond
year 5, the overall distribution of industry-adjusted growth rates is nearly symmetric
around zero. This symmetry demonstrates that the ?ve-year-old public ?rms are fairly
representative of their industries.
Revenue growth at the industry average is not the only signal that a company
has entered a stable-growth period. A good analyst should also consider the
company’s return on capital (R) and operating margins. During the rapid-growth
phase, we would expect a company to be earning R above the cost of capital (r),
even if these returns are not expected to be realized until several years in the future.
Furthermore, the rapid-growth phase is often characterized by operating margins
lower than industry averages, as companies scale up their production and price
aggressively to gain market share. In the stable-growth phase, both R and operating
margins should settle down to industry averages.
11.2 DCF ANALYSIS: MECHANICS
DCF analysis is the gold standard of valuation. If done properly with accurate
inputs—a big “if ”—a DCF model will produce the “correct” valuation of a ?rm.
For this reason, most investment bankers, ?nancial analysts, and academics make
DCF analysis a centerpiece of their valuation work. Although there are many
different types of DCF models, the simple capital structure of most VC portfolio
companies renders moot many of these differences, so we will be able to con-
centrate on the key concepts common to all types.
All DCF models have two key inputs: Discount rates (the “D” part) and cash
?ows (the “CF” part). Discount rates for venture capital were discussed at length in
Chapter 4. In this chapter, we need discount rates for public companies, so the cost
of venture capital is not directly applicable. There are several options for estimating
discount rates for public companies. The simplest option—used in this chapter—is
to just use the average cost of capital for the company’s industry. The Industry
Statistics worksheet of the DCF.xls spreadsheet provides this data for 100 different
industries. A more complex alternative is to use a smaller group of comparable
companies. This alternative will be discussed in Chapter 12.
We focus most of this section on the computation of cash ?ow. The concept
of cash ?ow is designed to pierce the accounting veil used for ?nancial reporting
and taxes so that we are left with the cash that is actually generated by the business.
Also, we want to compute the cash ?ows generated by all the assets of the ?rm,
irrespective of the types of claims (equity, debt, preferred stock), on those assets.
198 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
To do this, we abstract from the actual capital structure and assume that the ?rm is
all-equity ?nanced. Indeed, the assumption of all-equity ?nancing is very reason-
able for VC-backed companies. Exhibit 11-3 shows the mean and median per-
centage of debt in the capital structure of VC-backed companies in each of the 15
years subsequent to their IPOs. For each ?rm, we compute the enterprise value as
the market value of equity plus the book value of debt and then compute the
percentage of debt in this enterprise value:
We see from these data that even 15 years after their IPOs, VC-backed ?rms
still have only a mean debt percentage of 11.0 and a median percentage of 6.4.
During the rapid-growth phase in the ?rst few years after the IPOs of these ?rms,
their percentages are even lower. Thus, we conclude that the simplifying assumption
of all-equity ?nancing is close to the truth for the vast majority of VC-backed ?rms.
Throughout our analysis, we analyze only operating assets, income, and
expenses. Nonoperating assets would include excess cash, marketable securities, or
EXHIBIT 11-3
LEVERAGE OF VC-BACKED FIRMS
Years Since IPO Mean Median
0 4.7% 1.2%
1 4.0% 1.9%
2 5.7% 2.8%
3 6.8% 3.8%
4 7.2% 3.9%
5 8.1% 4.4%
6 8.2% 5.1%
7 11.1% 6.0%
8 8.7% 5.6%
9 10.6% 6.2%
10 11.0% 6.0%
11 11.8% 6.4%
12 12.4% 8.9%
13 11.0% 7.8%
14 7.7% 4.8%
15 11.0% 6.4%
Source: Michael Roberts, Wharton.
11.2 DCF ANALYSIS: MECHANICS 199
anything else that is unrelated to the revenue-producing business of the company.
Nonoperating assets can comprise a signi?cant fraction of the asset base of mature
companies, and disentangling operating from nonoperating assets can require deep
analysis of accounting statements. In this instance, we are fortunate to be analyzing
companies with short histories, so both the capital structure and asset base are rela-
tively simple, and we can focus our attention on the operating side of the business.
For a company with only operating assets, the standard de?nition of cash
?ow is
CF 5EBITð1 2tÞ 1depreciation 1amortization
2capital expenditures 2NWC
ð11:1Þ
where
CF 5 cash ?ow,
EBIT 5 earnings before interest and taxes,
t 5 the corporate tax rate, and
?NWC 5 ?net working capital 5?net current assets À ? net current liabilities.
Let’s examine each of the terms in Equation (11.1). The ?rst term, EBIT, is the
accounting measure that forms the base for all cash ?ow calculations. For an all-
equity ?rm without nonoperating income or expenses, EBIT is equivalent to pretax
net income. In this case, EBIT (1 2 t) represents the total after-tax income that is
produced by all the assets of the ?rm. This is an accounting measure of income that
includes some noncash expenses and also excludes some cash expenditures. The
included noncash expenses are depreciation and amortization, which reduce EBIT
on the income statement but do not require any direct cash outlays by the ?rm.
Thus, we add both these items back in Equation (11.1). In contrast, capital
expenditures—investments by the company in plant and equipment—are not
treated as an expense on the income statement, but do require a cash outlay. Thus,
we subtract capital expenditures in Equation (11.1). For growing ?rms, it will
usually be the case that capital expenditures exceed depreciation. The remaining
item is ?NWC, the change in net working capital. As a business grows, its working
capital needs will usually grow as well. If working capital goes up, then some extra
cash must be kept in the business, and this will reduce cash ?ow. Thus, we subtract
?NWC in Equation (11.1).
Using Equation (11.1), cash ?ow calculations are straightforward for past
years, when all the inputs are easily available. In DCF valuation, however, we need
inputs for future years; therefore it is necessary to make forecasts, most often for
the next ?ve or ten years. This is not as dif?cult as it sounds because many of the
forecasts will be driven by a few common assumptions. We will demonstrate how
this works in Section 11.3. For now, we focus on the mechanics of Equation (11.1),
with a few additional simpli?cations. First, because we have already assumed an
all-equity ?rm, there will be no interest expense, and EBIT (1 2t) will just be equal
to earnings (E). Second, we assume that amortization—which is most often related to
200 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
the acquisition of assets from other companies—is zero. Finally, we de?ne net
investment (NI) as
NI 5capital expenditures 1?NWC 2depreciation: ð11:2Þ
For some applications, it is helpful to write NI as a fraction of earnings, with
this fraction known as the investment rate (IR):
NI 5IR Ã E: ð11:3Þ
Some authors refer to the investment rate as the plowback ratio (because it
is the fraction of earnings that is “plowed back” into investment) or the rein-
vestment rate.
By substituting Equation (11.2) and Equation (11.3) into Equation (11.1), we
can rewrite cash ?ow as
CF5E2NI 5E2IR Ã E5ð1 2IRÞ Ã E: ð11:4Þ
To complete a DCF calculation, we add the discounted values for each annual
cash ?ow. In principle, one must estimate cash ?ows for every year until the end of
time. At this point, the timing of Exhibit 11-1 comes to rescue us. At graduation,
instead of building a model with forecasts for each year, we exploit the assumptions
of stable growth and compute graduation value as a perpetuity: the NPV of a
perpetual income stream with a constant growth rate and constant discount rate.
The present value of a perpetuity with an initial annual payment (starting in one
year) of X growing at rate g and discounted at rate r is
NPV of perpetuity 5X=ðr 2gÞ: ð11:5Þ
Thus, the graduation value in our DCF can be written as
Graduation Value 5GV5CF
S 11
=ðr 2gÞ 2E
s
à ðg=RðnewÞÞ
2
: ð11:6Þ
With these quantities and de?nitions, we can compute the NPV of the ?rm as
NPV of firm at exit 5
CF
T 11
1 1r
1
CF
T 12
ð1 1rÞ
2
1
. . .
1
CF
T 1n
ð1 1rÞ
n
1
. . .
1
CF
S
1GV
ð1 1rÞ
S 2T
ð11:7Þ
where CF
n
is the cash ?ow in year n. Note that we will use both the growth rate g
and the discount rate r in real terms—that is, they are nominal rates minus the
in?ation rate. The model is thus invariant to in?ation, because it uses real forecasts
and real discount rates. Equation (11.7) implicitly assumes that all cash ?ows occur
2
Note that the second term in Equation (11.6) is a necessary adjustment to make the model invariant to
changes in g when the ?rm’s investment return (in the stable growth period) equals exactly its cost of
capital.
11.2 DCF ANALYSIS: MECHANICS 201
at the end of the year. Because it is more realistic to assume that annual cash ?ows
are spread evenly through the year, many analysts perform a midyear correction
on Equation (11.7) by bringing every cash ?ow forward by six months. Mathe-
matically, this correction is done by multiplying the answer from Equation (11.7)
by the square root of (1 1r). We will use this correction on all the computations in
this chapter.
EXAMPLE 11.1
The projections for Newco’s rapid-growth period are given in Exhibit 11-4. The nominal
discount rate is 11 percent, the stable nominal growth rate is 5 percent, and the in?ation rate
is 3 percent. Thus the real discount rate and stable growth rate are 8 percent and 2 percent,
respectively. We will express everything in real dollars.
Problems
(a) Compute the NI in each period.
(b) Compute CF in each period.
(c) Compute the graduation value.
(d) Compute the NPV of Newco.
(e) Do a sensitivity analysis of this NPV using (real) stable growth rates of 0 percent and 4
percent.
Solutions (a) and (b) The computations for NI and CF are given in Exhibit 11-5 and are
discussed below.
Several assumptions have been made to reach these forecasts. In Section 11.3, we
discuss these assumptions at length; for now, we take these forecasts as given and just work
through the computations of cash ?ow and NPV. The graduation revenue and margin (year 7)
EXHIBIT 11-4
NEWCO CASH FLOW FORECASTS
Year 0 1 2 3 4 5 6 7 8
Revenue 80.0 127.4 175.2 224.7 276.1 332.7 395.6 462.5 471.7
Operating Margin 10.0% 10.7% 11.4% 12.1% 12.9% 13.6% 14.3% 15.0% 15.0%
EBIT 8.0 13.6 20.0 27.3 35.5 45.2 56.5 69.4 70.8
Taxes 3.2 5.5 8.0 10.9 14.2 18.1 22.6 27.7 28.3
E 4.8 8.2 12.0 16.4 21.3 27.1 33.9 41.6 42.5
Depreciation 5.0 7.8 10.6 13.3 16.1 18.9 21.7 24.5 27.3
Gross Investment
(Capex 1 Net
New WC)
32.8 35.6 38.4 41.2 44.0 46.7 49.5 52.3 37.9
202 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
are $462.5M and 15 percent, respectively, and rapid growth rates (matched to historical
average of high growth ?rms) have been assumed between exit and graduation. To achieve
this growth, gross investment increases each year, but as can be seen in Exhibit 11-5, the NI
is constant across years. Then, to compute the cash ?ow, we can use Equation (11.1) for
each year.
(c) The graduation value will be a large part of the value of Newco. Using the assumption of
2 percent annual growth and a stable operating margin of 15 percent, the year 8 forecasts give
an estimated revenue of $471.7M, EBIT of $70.8M, and earnings of $42.5M. The tricky part
here is the forecast of NI. Although we can estimate depreciation using some fraction of the
capital base, the gross investment estimate is not so straightforward. It might seem logical to
forecast NI growth of 2 percent from year 7 to year 8, but this forecast would be a mistake.
NI is needed to fund growth. During the rapid-growth period, the investment rate is almost
always higher than it will be during the stable growth phase. To correctly forecast the
investment rate necessary for stable growth, we need some assumption about the return on
new investment. In these forecasts there is an assumption lurking behind the scenes; this
assumption will be discussed in Section 11.3.
Once we have a forecast for NI in year 8, we can calculate the CF in year 8 as $31.8M.
Then we can use a growth rate of 2 percent in Equation (11.6) to compute GV as
GV531:8=ð0:08 20:02Þ 241:6 Ã ð0:02=0:08Þ 5$520:3M: ð11:8Þ
(d) To compute the NPV, we use Equation (11.7), with a discount rate of 8 percent, GV as
given by Equation (11.8), and annual cash ?ows as given Exhibit 11-5. This yields an NPV of
$279.85M.
(e) To perform a sensitivity analysis using different growth rates, it is tempting to just
substitute these different rates into Equation (11.6). For example, for a growth rate of 3
percent, we would have
GV531:8=ð0:08 20:00Þ 241:6 Ã ð0:00=0:08Þ 5$398M; ð11:9Þ
and for a growth rate of 7 percent we would have
GV531:8=ð0:08 20:04Þ 241:6 Ã ð0:04=0:08Þ 5$775:2M: ð11:10Þ
With these estimates of GV, the NPV would change signi?cantly. Note, however, that
neither of these estimates takes into account any change in investment during the stable
growth period. As discussed earlier in part (c), growth is supported by new investment, and
different levels of growth require different investment rates. Thus, the GVs given in Equa-
tions (11.9) and (11.10) are not correct. To see why this is true, we need to do a little more
work, which we do in Section 11.3. ’
EXHIBIT 11-5
NI AND CF CALCULATIONS
NI 27.8 27.8 27.8 27.8 27.8 27.8 27.8 27.8 10.6
Cash Flow 223.0 219.6 215.8 211.5 26.5 20.7 6.1 13.8 31.8
11.2 DCF ANALYSIS: MECHANICS 203
11.3 GRADUATION VALUE
Equations (11.9) and (11.10) demonstrate that GV can be very sensitive to the
speci?c assumption about growth rates—especially if we are not careful about
adjusting for the correct level of investment. Indeed, this sensitivity is often criti-
cized as the main shortcoming of DCF models, particularly for VC transactions. To
deal with this sensitivity, some analysts use valuation ratios from comparable
companies to estimate graduation values. This book strongly recommends against
using comparable companies to compute graduation values in DCF models. In
Chapter 12, we use comparable companies to estimate exit values as an exercise in
relative valuation. There is nothing wrong with using comparables for relative
valuation. In this chapter, however, we are attempting an absolute valuation using a
DCF. The whole point of a DCF model is to make up your own mind about the
valuation of the company. By using valuation information from comparable com-
panies, you will never form your own opinion, and you will be missing the
opportunity for valuable insight into your investment.
To gain this insight, we begin by analyzing the determinants of growth. Con-
sidering some time period N, where Newco invests NI and earns a return on this new
capital of R. Thus, the new investment provides incremental earnings of NI Ã R. If we
assume that the period N earnings can be sustained inde?nitely without any new
investment (i.e., by simply replacing the old capital as it depreciates), then earnings in
period N11 can be written as
E
N 11
5E
N
1NI Ã R: ð11:11Þ
So the growth rate g is given by
g 5ðE
N 11
2E
N
Þ=E
N
5ðNI Ã RÞ=E
N
5IR Ã R: ð11:12Þ
Thus, growth is the product of the investment rate (IR) with the return on
capital (R). Holding R constant, if a company wants to increase growth, then it must
increase its investment rate. An increase in the investment rate, however, will
decrease cash ?ow (5(1 2 IR) Ã E), so there will always be a tradeoff. If the
investment NI earns a return of R every year in perpetuity, then the NPV of this
investment will be NI Ã R/r. With this equation, it is easy to see that the NPV of
this new investment will be positive if and only if R is greater than r. In other
words, new investment will only increase the value of a company when the return
on capital is greater than the discount rate.
We can gain further insight into the NPV of growth by substituting Equations
(11.4) and (11.12) into Equation (11.6) to obtain the following:
GV 5ð1 2IRÞ Ã E=ðr 2ðIR Ã RÞÞ: ð11:13Þ
Note that if R5r, then Equation (11.13) reduces to GV5E/r, so that gra-
duation value is independent of the investment rate and growth. By using Equation
(11.12), one can also rewrite Equation (11.13) in terms of g instead of IR:
204 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
GV 5ð1 2g=RÞ Ã E=ðr 2gÞ: ð11:14Þ
Koller, Goedhart, and Wessels (2005) refer to Equation (11.14) as “the Zen
of corporate ?nance”, and we agree with them that it is an equation worthy of
some contemplation. In particular, Equations (11.13) and (11.14) remind us that
a company cannot control both g and IR at the same time, and one cannot become
attached to any particular level of growth without recognizing that current cash ?ow
will suffer. Indeed, the relationship between g and IR is even deeper than suggested
by Equations (11.13) and (11.14), because the return on capital should also be a
function of IR.
Exhibit 11-6 is similar to Exhibit 5-1. The optimal NI
Ã
occurs when the (mar-
ginal) return on investment (ROI) is equal to r. By increasing NI further, the com-
pany could increase growth, but only at the cost of reduction in R. Similarly, the
company could increase R by cutting back on NI, but this would reduce growth.
To make Exhibit 11-6 operational, we need some intuition on how to estimate
NI
Ã
and R
Ã
. In general, ROI can only exceed r for investments where the company
has some competitive advantage (e.g., a patent on a key piece of technology, a
period of market exclusivity on a drug, or a powerful brand name). Most forms of
competitive advantage can be sustained only as long as there are barriers to entry.
EXHIBIT 11-6
RETURN ON CAPITAL AS A FUNCTION OF NI
10.0%
9.5%
9.0%
8.5%
8.0%
7.5%
7.0%
6.5%
6.0%
5.5%
5.0%
NI*
ROI
R
r
Return on investment (ROI)
Cost of capital (r)
Return on capital (R)
11.3 GRADUATION VALUE 205
Without barriers to entry, other companies will enter the market and put downward
pressure on ROI. In Section 11.4, we propose a baseline DCF model where R is set
to r for all levels of NI. Then, from this starting point, the analyst can experiment
with various levels of R
Ã
.r.
To illustrate a more complete model, we return to the Newco forecasts from
Example 11.1. The forecasts in this example were generated from a small-scale
model of growth, as shown in Exhibit 11-7. In building this model, we make a
distinction between capital in place at the time of graduation—“old capital”—and
capital created by new investments after graduation—“new capital”. The returns to
old capital are given by R(old), and the returns to new capital are given by R(new).
Unless otherwise noted, all general comments about return on capital refer to
R(new).
The inputs to the model are given in bold type. These inputs then drive the
cash?ow calculations in each year of the model (Exhibit 11-4), with graduation
values implied by the graduation inputs, and intermediate values pinned down by
EXHIBIT 11-7
MODEL ASSUMPTIONS FOR EXAMPLE 11.1
Exit (T) Graduation (S)
Years until Graduation (S-T) 7
Expected In?ation 3.0%
Industry Growth (average, nominal) 5.0%
Extra Growth (above 75th percentile) 0.0%
Revenue 80.0 462.5
Operating Margin 10.0% 15.0%
Tax Rate 40.0% 40.0%
Assets 50.0 244.8
Stable Growth (nominal) 5.0%
Stable Growth (real) 2.0%
Discount Rate (nominal) 11.0% 11.0%
Discount Rate (real) 8.0% 8.0%
R(old) (nominal) 20.0%
R(old) (real) 17.0%
R(new) (real) 8.0%
IR 25.0%
Depreciation % of Assets 10.0%
NPV $279.85
GV $520.27
206 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
matching the ?rm’s revenue growth rates to those of newly-public, rapid-growth
companies in the respective industry. Note that several entries in the table for
the graduation period are not given in bold: revenue, assets, and IR (as well as the
in?ation-adjusted values for r, g, and R(old)). These entries are all determined by
other inputs: the graduation revenue is determined by the exit year revenue and
rapid-growth assumptions; the graduation assets are determined by the graduation
earnings combined with R(old); and the IR is determined by the assumptions about
growth and R(new). This model is given in the Example 11.1 worksheet of the DCF
spreadsheet, and readers are encouraged to experiment with the inputs. This
spreadsheet also contains the investment function worksheet that was used to
generate Exhibit 11-6 (see “exhibit 11.6” tab). By using this function, readers can
input the correct level of R (average return on capital) for any corresponding level
of g or IR.
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL
With this background, we are prepared to sketch a baseline DCF model that can be
used as a starting point for exit valuation. We call this model the reality-check
DCF model.
11.4.1 Baseline Assumptions for the Reality-Check DCF
(I) On the exit date:
(a) Revenue is forecast for the average success case.
(b) Other accounting ratios (not valuation ratios) are estimated using
comparable companies or rule-of-thumb estimates.
(c) The discount rate is estimated from industry averages or comparable
companies (see Chapter 12).
(II) On the graduation date:
(a) The stable nominal growth rate is equal to expected in?ation; thus, the
real growth rate is zero.
(b) The return on new capital—R(new)—is equal to the cost of capital (r).
(c) The return on old capital—R(old)—is equal to the industry-average
return on capital (ROC).
(d) The operating margin is equal to the industry average.
(e) The cost of capital (r) is equal to the industry average cost of capital.
(III) During the rapid-growth period:
(a) The length of the rapid-growth period is between ?ve and seven years.
(b) Average revenue growth is set to the 75th percentile of growth for new
IPO ?rms in the same industry in respective years and is constructed
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 207
from data contained in Growth and Industry Statistics worksheets of
the DCF spreadsheet. Thus, as a baseline assumption, extra growth
(above 75th percentile) in Cell B8 is set to 0%.
(c) Margins, tax rates, and the cost-of-capital all change in equal incre-
ments across years so that exit values reach graduation values in the
graduation year.
These assumptions should be considered as a starting point of analysis; they
are not intended to be de?nitive. For example, Assumption II(b)—that the return
on new capital is equal to the cost of capital—would only be consistent with
optimal investment behavior if the ROI line in Exhibit 11-6 was identical to the
cost of capital line. This is clearly an extreme assumption, which can be relaxed
as the analyst experiments with different inputs necessary to produce any given
valuation. Then, once this experimentation is complete, the analyst can ask
whether these relaxed assumptions are reasonable. For example, we can assume
that R(new) is greater than the cost of capital. This modi?ed assumption could
re?ect an adjustment from the base case based on an investment function like
Exhibit 11-6.
The next two examples illustrate the application of the reality-check model.
EXAMPLE 11.2
EBV is considering an investment in Semico, an early-stage semiconductor company. If
Semico can execute on its business plan, then EBV estimates it would be ?ve years until a
successful exit, when Semico would have about $50M in revenue, a 10 percent operating
margin, a tax rate of 40 percent, and approximately $50M in capital (5assets). Subsequent to
a successful exit, EBV believes that Semico could enjoy seven more years of rapid growth.
Problem To make the transaction work, EBV believes that the exit value must be at least
$300M. How does this compare with the reality-check DCF? How much must the baseline
assumptions change to jeopardize this valuation?
Solutions To get the inputs of the model, we consult the industry statistics worksheet in
DCF.xls. The semiconductor industry is listed in row 86 of this worksheet, which gives us
inputs of R(old) 528.67%, operating margin 527.73%, and r 515.55%. Also, the worksheet
gives the average revenue growth in the industry as 8.70 percent. To ?nd the 75th percentile
for rapid growth, we look in the Growth worksheet of DCF.xls and ?nd the respective annual
growth rate and adjust for the industry and for the in?ation. For example, the 75th percentile
rapid growth phase is 57.20%18.70% 2 3.0%562.9%.
3
Exhibit 11-8 summarizes the results of the reality-check model. The exhibit shows a
baseline reality-check estimate of $206.70M for the NPV. The problem asks us to test
3
Another way to relax the baseline assumptions here is to play with extra growth above the 75th per-
centile. You can experiment with adding an extra 5 percent, say, by entering the value in Cell B8 of the
worksheet. This cell is set to zero as a baseline assumption.
208 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
the sensitivity of this estimate to changes in the inputs and to see what changes would be
necessary to obtain an NPV of $300M. If we experiment with different inputs, we can
quickly see that the model is not sensitive to the stable growth (g) assumptions as long as
R(new) 5r. This is due to the second term in the Graduation Value formula, which
essentially “charges” the ?rm extra NI in year S for additional growth in year S11. So any
increase in g (which increases future CF) is exactly offset by a decline in current CF. If
R(new) .r, then increase g will result in a larger GV and thus also larger NPV. For
example, with g 510% and R(new) 520%, GV increases by $247.79M, and NPV rises to
$321.63. These would be very aggressive assumptions because it would imply a perpetual
return on capital near the same rate as the return earned in the rapid growth phase.
4
EXHIBIT 11-8
REALITY-CHECK DCF MODEL FOR SEMICO
Exit (T) Graduation (S)
Years until Graduation (S2T) 7
Expected In?ation 3.0%
Industry Growth (average, nominal) 8.7%
Extra Growth (above 75th percentile) 0.0%
Revenue 50.0 353.0
Operating Margin 10.0% 27.7%
Tax Rate 40.0% 40.0%
Assets 50.0 228.8
Stable Growth (nominal) 3.0%
Stable Growth (real) 0.0%
Discount Rate (nominal) 15.5% 15.5%
Discount Rate (real) 12.5% 12.5%
R(old) (nominal) 28.7%
R(old) (real) 25.7%
R(new) (real) 12.5%
IR 23.9%
Depreciation % of Assets 10.0%
NPV (with mid-year corrections) $206.70
GV $468.06
4
If R(new) , r, however, increasing g actually has a negative effect on NPV. Why? Because IR 5 g/R
(new), excessive investments when return on investments is low would hurt CF at S 11, and thus GV
shrinks. This is akin to setting NI . NI
Ã
in Exhibit 11-6.
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 209
Similarly, we could get the NPV to almost $300M ($295.87M) by adding extra 10 percent to
the rapid-growth rates from year 1 to year 7 (by entering “10%” to cell B8). Although this
change might seem arbitrary, we can anchor ourselves in the industry data to see just how
extreme this assumption would be. Furthermore, an extra 10 percent growth rate implies that
graduation revenue would be $589.3M, or 70 percent higher than the baseline level. To decide
whether this level is reasonable, we need to rethink our assumptions about market size, pricing,
and market penetration. Of course, we do not have enough data about Semico to make informed
judgments, so all we can do here is experiment with numbers. Next, we consider a more con-
crete example. ’
EXAMPLE 11.3
For the 12 months ended on September 30, 2009, Amgen, a publicly traded biotechnology
company (NASDAQ: AMGN), had $14.6B in revenue, an operating margin of 38.31 percent,
and $29.6B in assets (net of goodwill). Amgen’s enterprise value (on January 30, 2010) was
approximately $55B. It had no signi?cant net debt or interest costs.
Problem Perform a reality-check DCF for Amgen. What assumptions would be neces-
sary to justify Amgen’s current valuation?
Solutions To apply the reality-check DCF, we need to make some forecasts for Amgen’s
stable growth period. In the industry statistics worksheet, Amgen could be included in two
different industries, “biotechnology” and “drugs”, because the company enjoys both the
high growth potential of the biotech industry and the high current pro?tability of drug
companies.
The industry data worksheet shows more favorable averages for the drug industry, so
we give Amgen the bene?t of the doubt and use these estimates: r 511.55 percent,
R(old) 522.57 percent, and margin 530.15 percent.
5
In the past ?ve years, Amgen has
enjoyed growth of about 14 percent per year; for the next ?ve years, the consensus analysts’
forecast is 9 percent per year.
6
For our baseline model, we extend these forecasts for a seven-
year rapid growth period at 9 percent per year. As in all baseline reality-check models, we
assume only in?ationary growth ((real)g 50 percent, in this case) and R(new) 5r. Using
these assumptions, the reality-check DCF is summarized in Exhibit 11-9. The NPV com-
puted there, $56.09B, is almost exactly the actual market value. It turns out that no additional
assumptions are necessary to justify Amgen’s current market valuation. Exhibit 11-10 shows
the sensitivity of this NPV to some changes in the baseline assumptions.
5
Under current accounting rules, R&D is treated as an expense and not as a capital expenditure. Although
this accounting treatment does not affect cash ?ow calculations, it can lead to misleading calculations
about return on capital. For a detailed study of value creation, it makes more sense to treat R&D the same
way as other capital expenditures. This correction is beyond the scope of our treatment of DCF models.
Please see Koller et al. (2005) for a discussion.
6
Source: Yahoo Finance, http://?nance.yahoo.com/q/ae?s=AMGN, January 30, 2010.
210 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
Exhibit 11-10 shows a series of changes that would either positively or negatively
affect NPV. Moving down the rows in Exhibit 11-10 shows the combined impact of all
changes above and including that row. If we assume that Amgen maintains the 14 percent
nominal growth rate for the next seven years, its NPV will go up to $64.97B; further
assuming that R(new) 520 percent (second row) and g 55 percent (third row) raises the
NPV further to $72.59B. Finally, assuming that the operating margin perpetually stays at
38.3 percent pushes up the NPV to $82.93B. These together are very aggressive assumptions
indeed, and do not look very sustainable.
Now what changes to our baseline assumptions could lower the NPV? Recall that we
used industry estimates of the drug industry, since they were more favorable than those of the
biotechnology industry. If the operating margin matches that for the biotechnology industry
(26.9 percent), the NPV declines to $53.61B; increasing the cost of capital (r) to 12.3 percent
lowers NPV to $49.93B; decreasing the return on old capital to 14.8 percent further pushes
NPV down to $40.41B; ?nally, assuming a very conservative growth rate of 5 percent for the
next seven years lowers the NPV to $38.15B.
EXHIBIT 11-9
REALITY-CHECK DCF FOR AMGEN
Exit (T) Graduation (S)
Years until Graduation (S-T) 7
Expected In?ation 3.0%
Analysts’ Estimate (consensus, nominal) 9.0%
Analysts’ Estimate (consensus, real) 6.0%
Revenue 15.6 23.4
Operating Margin 38.3% 30.1%
Tax Rate 40.0% 40.0%
Assets 29.6 21.7
Stable Growth (nominal) 3.0%
Stable Growth (real) 0.0%
Discount Rate (nominal) 11.5% 11.5%
Discount Rate (real) 8.5% 8.5%
R(old) (nominal) 22.6%
R(old) (real) 19.6%
R(new) (real) 8.5%
IR 0.0%
Depreciation % of Assets 10.0%
NPV $56.09
GV $49.58
11.4 DCF ANALYSIS: THE REALITY-CHECK MODEL 211
Of course, an in?nite number of combinations could obtain this result, but Exhibit 11-10
gives the ?avor of what is necessary. Based on these calculations, it appears that Amgen can
justify its January 2010 valuation. ’
SUMMARY
The exit value is the most important input in a VC valuation. To estimate exit values, we
have two main methods: absolute valuation (in this chapter) and relative valuation (in
Chapter 12). All types of absolute valuation can be reduced to some form of discounted cash
?ow (DCF) analysis. To perform a DCF analysis for a venture-backed company, we divide
the company’s life cycle into three parts: the venture period (while the company is still being
funded by VCs), the rapid-growth period (which immediately follows the VC exit), and the
stable-growth period (when growth, margins, and return on capital have settled down to
industry averages). Our reality-check DCF model uses inputs from the beginning of the
rapid-growth and stable-growth periods to determine the key cash ?ows and then computes
the NPV of these cash ?ows using industry average cost of capital.
KEY TERMS
Absolute valuation, relative
valuation
Discounted cash flow
(DCF) analysis
Venture period
Rapid-growth period
Graduation
Stable-growth period
Operating assets
Cash Flow (CF)
Earnings before interest and
taxes (EBIT)
EXHIBIT 11-10
NPV OF AMGEN UNDER DIFFERENT ASSUMPTIONS
Positive Changes to NPV
rapid growth (real) 11.0% $64.97
and R(new) 20.0% $64.97
and g 5.0% $72.59
and operating margin 38% $82.93
Negative Changes to NPV
operating margin 26.9% $53.61
and Cost of capital 12.3% $49.93
and R(old) 14.8% $40.41
and rapid growth (real) 5% $38.15
NOTE: All dollars in billions.
212 CHAPTER 11 DCF ANALYSIS OF GROWTH COMPANIES
Earnings 5Net Income
Net investment (NI)
Investment rate (IR)
5plowback ratio
5reinvestment rate
Perpetuity
Graduation value
Midyear correction
Competitive advantage,
barriers to entry
Reality-check DCF
REFERENCES
Damodaran, Aswath, 2009, The Dark Side of Valuation, Prentice Hall, Upper Saddle River, NJ.
Koller, Tim, Marc Goedhart, and David Wessels, 2005, Valuation: Measuring and Managing the Value
of Companies, Wiley, Hoboken, NJ.
EXERCISES
11.1 EBV is considering an investment in Softco, an early-stage software company. If
Softco can execute on its business plan, then EBV estimates it would be ?ve years until a
successful exit, when Softco would have about $75M in revenue, a 20 percent operating
margin, a tax rate of 40 percent, and approximately $75M in capital. Subsequent to a suc-
cessful exit, EBV believes that Softco could enjoy seven more years of rapid growth. To
make the transaction work, EBV believes that the exit value must be at least $400M. How
does this compare with the reality-check DCF? How much must the baseline assumptions
change to justify this valuation?
11.2 True, False, or Uncertain: Firm value is maximized when the return on capital is
exactly equal to the cost of capital.
11.3 True, False, or Uncertain: If two ?rms have exactly the same balance sheet and income
statement on their respective graduation dates, then the ?rm with the higher growth rate will
also have the higher graduation value.
11.4 Perform a reality-check DCF for a publicly traded company of your choice.
EXERCISES 213
CHAPTER 12
COMPARABLES ANALYSIS
IN THIS CHAPTER we analyze exit values using comparables analysis,
sometimes abbreviated as comps and also known as multiples analysis, method of
multiples, and relative valuation. In the DCF analysis of Chapter 11, we valued
a company based on its cash ?ow and discount rates. DCF analysis is a form
of absolute valuation because it does not use information from relative values of
similar companies. In contrast, in comparables analysis the main idea is to get the
market’s opinion about a company. To do this we ?rst identify a set of similar
companies, and then we analyze a variety of valuation ratios for these companies.
We then use other market information to choose among and combine these various
ratios to arrive at our estimate of the exit valuation.
Suppose we are trying to estimate an exit valuation for Newco. After some
re?ection, we estimate that a success case for Newco would be $50M of revenue in
six years. We also observe that the public companies in Newco’s industry have
enterprise valuations of about 5 times revenue. By applying this same multiple to
Newco, we estimate an exit valuation of $250M. That is a quick-and-dirty example
of comparables analysis. In many cases, VCs will not take this analysis any further.
Sometimes this quick analysis is justi?ed, because a bundle of uncertainties pre-
vents any additional accuracy. In other cases, however, a careful analysis that
combines DCF and comparables can yield insights into valuation anomalies. In this
section we learn the steps necessary to perform a more careful comparables ana-
lysis. These steps expand on the quick-and-dirty analysis in two ways:
1. The choice of valuation measures (Section 12.1)
2. The choice of comparable companies (Section 12.2)
Among VCs, comparables analysis is by far the most popular method of exit
valuation. There is some empirical support for this popularity, as IPO valuation
seems to be driven more by comparables than by DCF analysis. Nevertheless, a
prudent investor should perform both DCF analysis (absolute valuation) and
comparables analysis (relative valuation) before making any investment decision.
In other words, form your own opinion, and then test it against the market.
214
It is important to remember that the valuation methods studied in Chapters 11
and 12 are only providing an analytical framework. By itself, this framework does
not answer the most dif?cult questions of valuation; for example, how do we
forecast “success case” revenue at exit? In the quick-and-dirty example given
above, we used a success-case revenue of $50M for Newco. Where does this
estimate come from? It does not come from ?nancial analysis, but rather from more
general business analysis that must occur during due diligence and investment
screening. There is no magic formula for making these estimates—if there were
such a formula, then venture capital would be an easy profession.
12.1 INTRODUCTION TO COMPARABLES
ANALYSIS
Suppose that we have been asked to estimate an exit valuation for Newco, the
same company analyzed in Example 11.1. In a successful exit, we estimate that the
company will have about 100 employees and generate $80M in revenue, $8M in
EBIT, $13M in EBITDA (5 earnings before interest, taxes, depreciation, and
amortization), $4.8M in earnings, and have $50M in book value of equity. We use
the same ?nancial estimates here as we did for the starting point of our DCF model.
If we attempt to value this company using the tools of DCF analysis, we would
begin at the exit date and forecast the cash ?ows, estimate a cost of capital, and then
compute an NPV for the company. Alternatively, we could ignore our own opinion
and look at how the public market values some similar companies today.
Exhibit 12-1 gives summary ?nancial and market data for four comparable
companies in Newco’s industry. For now, we will ignore the question of how we
identi?ed these speci?c companies, leaving that topic for Section 12.2. To form a
valuation multiple we need both numerators and denominators. The two numerators
most often used in comparables analysis are enterprise value (EV) and equity
market capitalization (5 market cap or equity market value). The former mea-
sures the market value of all the securities of the company, whereas the latter
measures the market value of just the common stock. Next, we need some
denominators. The most intuitive denominators are proxies for cash ?ow. Indeed, all
multiples have some deep connection to a cash ?ow ratio, even if the connection is
not apparent. In the end, however, all that really matters is that investors perceive
some usefulness in a multiple. If a multiple is perceived as useful, then it can be
predictive for the valuation of a comparable company.
For the analysis and exercises in this chapter, we will use six different
multiples:
1. EV/EBIT: EV is the total market value of all securities of the company,
including common stock, long-term debt, preferred stock, and so on.
12.1 INTRODUCTION TO COMPARABLES ANALYSIS 215
In practice, most of EV for public companies is in common stock and long-
term debt. The denominator, EBIT, is often viewed as proportional to a
steady-state cash ?ow measure, in which case the EV/EBIT ratio has an
intuitive interpretation as the ratio of ?rm value to cash ?ow.
2. EV/EBITDA: This is another popular measure, particularly among leveraged-
buyout investors. Like EBIT, some analysts view EBITDA as a cash ?ow
measure. Although this is true in the short run (where capital expenditures to
replace depreciated equipment can be delayed), it is de?nitely not true in the
long run. Nevertheless, even if EV/EBITDA does not have the same cash ?ow
interpretation as EV/EBIT, it can be particularly useful for evaluating
industries that have wide variation in their depreciation practices.
3. EV/Revenue: This is the multiple used in the quick-and-dirty analysis in the
introduction to this chapter. At ?rst glance, this multiple appears completely
divorced from any cash ?ow rationale because no measure of pro?tability is
included in the denominator. Nevertheless, this measure often provides the
most useful valuation ratio, particularly for high-growth industries favored
by VCs. In these industries, many companies have negative EBIT and
EBITDA, thus making it impossible to form reasonable multiples for those
measures. Because revenue is never negative, the EV/Revenue multiple is
always available.
4. Price/Earnings: The ratio of price to earnings, “P/E”, is probably the most
widely known valuation measure. In this context, “price” refers to the price
of a single share of stock, and “earnings” refers to earnings per share. With
company level data, we can compute the P/E ratio by dividing net income
(5 earnings) into market cap. Because earnings accrue only to shareholders
EXHIBIT 12-1
SUMMARY FINANCIAL INFORMATION FOR NEWCO COMPARABLES
ABC DEF GHI JKL
Revenue 80 70 40 55
EBIT 30 5 10 10
EBITDA 50 10 20 20
Net income 17 3 4 6
LTD 10 0 20 10
BV of equity 100 20 50 50
Market cap (Price) 300 280 150 200
EV 310 280 170 210
Employees 300 120 200 50
216 CHAPTER 12 COMPARABLES ANALYSIS
(not bondholders), the P/E numerator uses only the market cap, not the
whole enterprise value.
5. Price/Book: This measure is also popular among Wall Street professionals.
As with the P/E ratio, it is often referred to by the share level term of “price”,
which is then divided by book value per share. With company level data, we
can compute the P/B ratio by dividing book value of common equity into
market cap. As in the case of the P/E ratio, the P/B numerator uses only the
market cap, not the whole enterprise value. An enterprise level equivalent of
P/B would divide the book value of all assets into the EV. This enterprise
measure is popular among academics, but has not caught on much with
practitioners. The P/Bratio is motivated not by cash ?ow, but also by breakup
value. The idea here is that—if we believe the accounting statements—a P/B
ratio below 1 would indicate that the equity holders would be best off by
selling the company, repaying the debt, and pocketing the difference.
6. EV/Employees: Like the EV/Revenue ratio, the EV/Employees ratio would
appear to have no clear connection to either cash ?owor breakup value. As will
be seen below, a connection can indeed be established, but the best reason to
follow this ratio is that it can provide surprising insights in some cases.
Essentially, the logic is that the number of employees is the fastest-moving
measure of potential ?rm size, so even if all other accounting-based ratios are
lagging, the EV/Employee ratio might still provide some insight. Furthermore,
like the EV/Revenue ratio, the EV/Employee ratio will never be negative.
Although we focus attention on these six ratios, there is virtually no limit on
the ratios that are used in practice. In general, when forming a ratio, one starts with
a denominator of interest and then applies either EV or equity market value as the
numerator. One cannot use these numerators interchangeably—for any given
denominator, only one of these numerators would be correct. If the denominator is
an enterprise level quantity (e.g., EBIT, EBITDA, revenue, or employees), then EV
is the correct numerator. If the denominator represents some quantity that only
accrues to equity holders (e.g., earnings or book value of equity), then equity
market value is the correct numerator.
EXAMPLE 12.1
Problem Given the information on comparables in Exhibit 12-1, what is your best
estimate for the relative valuation of Newco?
Solution Exhibit 12-2 gives these valuation multiples for our four comparable compa-
nies, along with the average and median for each multiple:
1
1
In a sample of four companies, the median is the average of the two middle estimates.
12.1 INTRODUCTION TO COMPARABLES ANALYSIS 217
For each multiple and each comparable company, we can compute a comparable
valuation for Newco. For example, our exit revenue estimate (from Chapter 11) is $80M.
Then, using the ABC EV/Revenue multiple of 310/80 5 3.88, we can compute a comparable
valuation of 3.88 Ã $80M 5 $310M for Newco. Using the same procedure, we provide the
complete set of comparable valuations in Exhibit 12-3.
OVERALL AVERAGE5$254:2M
Notice that the medians are never larger than the averages. This is a typical situation for
these multiples, as outliers on the high end can easily skew the averages. For this reason, some
analysts prefer to use the median values when making their ?nal estimates. Other methods to
reduce the in?uence of outliers is to compute the geometric mean (multiply the ratios for all N
?rms and then take the Nth root (e.g., if there are two comparable companies with
EV/EBIT of 12 and 3, then the geometric mean is the square root of 12 Ã 3 and is equal to 6) or
the harmonic mean (take the reciprocal of the mean of the reciprocals, e.g., if there are two
comparable companies with EV/EBIT of 12 and 3, then the harmonic mean is 1 divided by the
arithmetic average of 1/12 and 1/3, and is equal to 4.8).
To decide on our best estimate, we need to go beyond a simple analysis of the averages.
Although the individual implied valuations are all over the map—a high-estimate com-
parable valuation of $700M using the price/book of DEF, down to a low-estimate comparable
EXHIBIT 12-3
IMPLIED VALUATIONS FOR NEWCO USING COMPARABLES
Multiples ABC DEF GHI JKL Average Median
EV/EBIT 83 448 136 168 199.6 152.0
EV/EBITDA 81 364 111 137 172.9 123.5
EV/Revenue 310 320 340 305 318.9 315.0
Price/Book 150 700 150 200 300.0 175.0
Price/Earnings 85 448 180 160 218.2 170.0
EV/Employees 155 350 128 630 315.6 252.5
EXHIBIT 12-2
VALUATION MULTIPLES
Multiples ABC DEF GHI JKL Average Median
EV/EBIT 10.3 56.0 17.0 21.0 26.1 19.0
EV/EBITDA 6.2 28.0 8.5 10.5 13.3 9.5
EV/Revenue 3.9 4.0 4.3 3.8 4.0 3.9
Price/Book 3.0 14.0 3.0 4.0 6.0 3.5
Price/Earnings 17.6 93.3 37.5 33.3 45.5 35.4
EV/Employees 1.0 2.3 0.9 4.2 2.1 1.7
218 CHAPTER 12 COMPARABLES ANALYSIS
valuation of $81M for the EV/EBITDA ratio of ABC—the average comparable valuations are
quite stable across different ratios. Nevertheless, the range of average estimates does vary
from a high of 318.9 for EV/Revenue to a low of 172.9 for EV/EBITDA. Although it would be
prudent to check both the high and low in any sensitivity analysis, one could make a
strong argument that the EV/Revenue estimate is the most realistic. The main support for this
argument is the relative variation of these valuation ratios. We don’t need any fancy math to
see that the EV/Revenue ratio provides by far the most consistent valuations across the dif-
ferent comparable companies. The stability of the EV/Revenue ratio can be seen by inspecting
the columns of Exhibit 12-3, and simple statistics can con?rm this casual inference. The
standard deviations of each row in Exhibit 12-3 are, in order, $163M, $129M, $15M, $268M,
$159M, and $232M. The EV/Revenue comparable has the lowest standard deviation by far.
Even if we were to eliminate all the data from DEF—the company that appears to provide the
most anomalous valuations—it still appears that EV/Revenue provides the most stable
answer.
In summary, if we need to pick one number for an exit valuation, the EV/Revenue
comparable of $318.9M is the most defensible. One can make an argument for adjusting this
number slightly to re?ect the lower comparable valuations from the other ratios, but choosing
the overall average of $254.2M seems too conservative. ’
Exhibits 12-1 and 12-2 use historical data. Many academics and practitioners
argue that valuation ratios are more accurate when using forecast data. For example,
instead of using EBIT or earnings from the most recent ?scal year, the analyst would
substitute forecasts for the next ?scal year or even for the following ?scal year. The
evidence for the superiority of forecasts is compelling, but in this book we still
recommend using the historical estimates as a baseline case. Why? Because the
main purpose of comparables analysis is to get the market’s opinion about valuation.
Once we introduce forecasts into this analysis, we run the risk of con?ating expert
predictions with the market’s opinion. Indeed, many forecasters logically take
market prices into account when making their forecasts, and companies with high
multiples for historical earnings are given higher forecasts for future earnings.
We made a similar argument in Chapter 11 against the use of comparable
company multiples to estimate the graduation value in DCF models. If an analyst
uses forecast multiples in the comparables analysis and then uses similar multiples
as the graduation value in a DCF, then it is possible that lots of work has been done
on two models based on the same set of information. There is nothing wrong with
using forecasts in a comparables analysis as an additional check on your work, but
you should not rely exclusively on these forecasts.
12.2 CHOOSING COMPARABLE COMPANIES
To choose comparable companies, it is important to ?rst understand the connection
between comparables analysis and DCF analysis. Most valuation ratios have some
connection to DCF formulas. Consider a ?rm in a zero-in?ation environment with
12.2 CHOOSING COMPARABLE COMPANIES 219
steady-state growth. Then, the present discounted enterprise value of this ?rm
would be
EV 5CF=r 2g 5CF=ðr 2R Ã IRÞ; ð12:1Þ
where g is the perpetual growth rate of cash ?ows, r is the discount rate, IR is the
investment rate, R is the return on (new) capital, and CF is cash ?ow in the next
period. Equation (12.1) is similar to Equation (11.6), the graduation value for a
DCF model. Next, consider the basic cash ?ow formula from Chapter 11:
CF 5ð1 2IRÞ Ã E5ð1 2IRÞ Ã ð1 2tÞ Ã EBIT; ð12:2Þ
since (1 2 t) Ã EBIT 5 E for all-equity ?rms.
Substituting Equation (12.2) into Equation (12.1) and dividing both sides by
E (or EBIT) yields
EV=E5Market Cap=E5P=E5ð1 2IRÞ=ðr 2R Ã IRÞ; ð12:3Þ
or,
EV=EBIT 5ð1 2tÞ Ã ð1 2IRÞ=ðr 2R Ã IRÞ: ð12:4Þ
We can continue this approach by substituting EBIT 5 Revenue à Margin
into Equation (12.4) and rearranging terms to yield
EV=Revenue 5margin à ð1 2tÞ Ã ð1 2IRÞ=ðr 2R à IRÞ: ð12:5Þ
Then we can disaggregate revenue to be Employees à Revenue per employee,
substitute into Equation (12.5), and rearrange to yield
EV=Employees 5Revenue per employee à Margin
à ð1 2tÞ Ã ð1 2IRÞ=ðr 2R à IRÞ:
ð12:6Þ
Thus, to ?nd comparable companies for P/E or EBIT ratios, we must search
for companies with similar steady-state levels for investment opportunities (for R
and IR), discount rates, and (for EBIT) tax rates. If current operating margins are
not yet at their steady levels, then we might be better off using an EV/Revenue
margin and identifying comparable companies with stable operating margins.
Finally, if revenue is not yet at its steady state (but employees are), then we can use
Equation (12.6). Overall, these equations provide some guidance to analysts as they
search for comparable ?rms. The analysis suggests that we look to ?rms in the same
industry, facing similar investment opportunities, with similar long-run margins
and productivity.
EXAMPLE 12.2
EBV is considering an investment in Semico, an early-stage semiconductor company. (This
is the same company analyzed in Example 11.2.) If Semico can execute on its business plan,
then EBV estimates it would be ?ve years until a successful exit. At that time Semico would
220 CHAPTER 12 COMPARABLES ANALYSIS
have about $50M in revenue, 150 employees, a 10 percent operating margin, a tax rate of 40
percent, and approximately $50M in capital (5 assets). Semico’s business is to design and
manufacture analog and mixed-signal integrated circuits (ICs) for the servers, storage sys-
tems, game consoles, and networking and communication markets. It also plans to expand
into providing customized manufacturing services to customers that outsource manufacturing
but not the design function. It expects to sell its product predominantly to electronic
equipment manufacturers.
Problems
(a) Identify comparable companies for Semico.
(b) Use accounting and market information from these companies to estimate a relative
valuation for Semico.
Solutions
(a) To identify comparable companies, we begin by screening similar-sized companies in
Semico’s industry. Our goal is to ?nd the subset of such companies that are the closest match
for Semico using the variables in Equations (12.3) through (12.6). Many possible databases
can be used for this exercise. A VC with experience in semiconductors might have access to
specialized industry databases. Even without such access, the experienced VC would not
need to start fresh for the analysis, as he would likely be able to make an educated guess
about the identity of the most comparable companies. Because we are starting from relative
ignorance, we will need to cast a wide net in our search.
At the time of this writing, the Yahoo! Finance portal is an excellent (and free) source
of all the necessary data. Using the “Stock Screener” tool,
2
we restrict our search to the
“Semiconductors: Integrated Circuits” industry, which is the closest match to the description
of Semico. The problem states that our success case revenue estimate is $100M. Because we
want companies with similar investment opportunities (which will then imply IR and R), we
don’t want to stray too far from this size, so we look for companies in this industry that have
between $25M and $125M in projected revenue. Using the most recent four quarters of data
(at the time of this analysis, this data usually goes through September 30, 2009), the stock
screener ?nds 13 such companies. Note that we have chosen to screen by revenue rather than
other accounting variables—we do this because revenue will be the best measure of ?rm size,
and ?rm size is probably our best measure of investment opportunities. Enterprise value,
which would also be a measure of ?rm size, would be an incorrect way to screen for
comparable companies. If we were to use EV (or market cap) to choose comparable com-
panies, then we would be implicitly placing restrictions on the valuation ratios.
Once we have identi?ed these 13 candidates, we need to study the descriptions of these
businesses to ?nd those most comparable to Semico. Once again, we are guided by the
variables in Equations (12.3) to (12.6). To ?nd companies with similar investment oppor-
tunities (IR and R), we want companies facing the most similar economic environments—
ideally, companies selling to original equipment manufacturers for ultimate sale into con-
sumer and home of?ce markets. The underlying growth (or decline) of these channels and
markets would then have a similar impact on Semico and its comparable companies. Next,
2
http://screen.yahoo.com/stocks.html.
12.2 CHOOSING COMPARABLE COMPANIES 221
we want as much as possible to match companies based on stable operating margins and
revenue per employee. To do this, we look for companies at a similar point in the supply
chain. In general, companies at similar points in the supply chain (e.g., manufacturer,
wholesaler, or retailer) have similar margins and productivity measures.
After studying the list of 13 companies, we ?nd three that satisfy our criteria for the
closest matches.
3
These companies are: PLX Technology Inc. (NASDAQ GM: PLXT),
Supertex Inc. (NASDAQ GS: SUPX), and Volterra Semiconductor Corporation (NASDAQ
GS: VLTR). Summary ?nancial information for these companies is given in Exhibit 12-4.
(b) This information is much messier than the fantasy case of Example 12.1. One of the
three companies has negative EBIT, EBITDA, and earnings. Furthermore, we note that the
EVs are lower than the market caps for all of the three companies (i.e., these companies have
more cash than debt) so net debt is negative. Based on this data, we construct valuation
multiples and display them in Exhibit 12-5.
The negative multiples in Exhibit 12-5 are problematic. Consider what happens to the
multiple as a company moves from a positive EBIT, to zero, to negative. As EBIT falls close
to zero, the EV/EBIT multiple rises to in?nity, only to change abruptly to a large (absolute)
negative number as EBIT turns negative. As mentioned in Section 12.1, these negative
multiples are a common occurrence for growth companies, hence the reliance on the more
robust multiples of EV/Revenue, Price/Book, and even EV/Employees (though, in this case,
the number of employees is available for only one of the three companies). Exhibit 12-6
gives the implied valuations for these multiples.
Overall Average : $204:6 Overall Median : $193:9
3
For readers who would like to try this analysis on their own, the list of 13 companies is given in
Appendix 12.A.
EXHIBIT 12-4
SUMMARY FINANCIAL INFORMATION FOR SEMICO COMPARABLES
Supertex PLX Volterra Semico Exit Estimates
Revenue 61.17 82.83 104.94 50
EBIT 5.02 280.04 5.61 5
EBITDA 5.55 25.88 18.19 10
Net income 4.91 218.80 10.94 3
LTD 0.00 0.86 0.00 0
BV of equity 179.12 69.32 83.50 50
Market cap (Price) 317.32 180.25 503.03 ??
EV 235.10 128.41 406.92 ??
Employees 352 N/A N/A 150
Source: Yahoo! Finance, January 2010.
222 CHAPTER 12 COMPARABLES ANALYSIS
To put these valuations in perspective, recall from Example 11.2 that the reality-check
DCF provided a baseline estimate of $206.7M. Thus, both the average and median com-
parables are fairly close to the DCF valuation, while the estimates have a wide range.
Overall, the EV/Revenue, Price/Book, and Price/Earnings multiples provide lower estimates
than EV/EBIT and EV/EBITDA multiples. EV/Employees (usually a reliable multiple
because of its relative stability across similar companies) is of little use in this example,
because we do not have the data for two of the three companies.
To go beyond this analysis, we would need to take an even closer look at these com-
parable companies and try to decide whether any of themprovides a particularly close match to
the success case of Semico. This example does not provide enough information about Semico
to allow for this analysis, and it would be rare for this additional precision to be available in a
real-world investment. ’
Example 12.2 is typical for this kind of analysis. With negative EBIT,
EBITDA, and earnings, and non-availability of employee ?gures, we are forced to
rely on revenue and book multiples. Luckily, these multiples provide similar
answers, but we are still left with a signi?cant range of valuation multiples. If, as in
Example 11.2, EBV requires an exit valuation of $300M to justify the investment,
EXHIBIT 12-5
VALUATION MULTIPLES
Multiples Supertex PLX Volterra Average Median
EV/EBIT 46.9 (1.6) 72.6 59.7 NA
EV/EBITDA 42.4 (21.8) 22.4 32.4 NA
EV/Revenue 3.8 1.6 3.9 3.1 3.8
Price/Book 1.8 2.6 6.0 3.5 2.6
Price/Earnings 64.6 (9.6) 46.0 55.3 NA
EV/Employees 0.7 NA NA NA NA
EXHIBIT 12-6
IMPLIED VALUATIONS FOR SEMICO USING COMPARABLES
Multiples Supertex PLX Volterra Average Median
EV/EBIT 234.4 NA 362.9 298.6 NA
EV/EBITDA 423.6 NA 223.7 323.7 NA
EV/Revenue 192.2 77.5 193.9 154.5 192.2
Price/Book 88.6 130.0 301.2 173.3 130.0
Price/Earnings 193.9 NA 137.9 165.9 NA
EV/Employees 100.2 NA NA NA NA
12.2 CHOOSING COMPARABLE COMPANIES 223
then this analysis suggests noninvestment unless EBV believes Semico to have
prospects signi?cantly better than these companies.
We must end this section with one big caveat: comparables analysis is dangerous
for VCinvestors—so be careful! One obvious problemis that an excessive reliance on
comparables analysis can make a VC prone to market fads, with current valuation
ratios taken as long-run predictions. Alas, valuation ratios can change dramatically in
?ve years. Indeed, when the ?rst edition of this book was published four years ago, the
comp valuations tended to be much higher than the reality-check DCF model valua-
tion, re?ecting the market conditions. Today, in 2010, the general pattern is the
opposite. In addition, Equations (12.3) to (12.6) all emphasize the importance of
?nding comparable companies with similar investment opportunities, but the time
difference between the current investment and a successful exit means that we need to
identify public companies today that have investment opportunities similar to those
available for our portfolio company at exit. In the rapidly changing markets frequented
by VCs, this exercise requires a heroic leap of faith. Many VCs rely exclusively on
comparables analysis—this reliance is very dangerous! Although the companies in
Exhibit 12-4 may be in the same business as Semico, the growth prospects for this
business are likely to be very different today from?ve years down the road. Of course,
these challenges are a main reason that VC investing is so dif?cult in the ?rst place.
12.3 USING COMPARABLE COMPANIES TO
ESTIMATE THE COST OF CAPITAL
In Chapter 11, we used the industry-average cost of capital in our DCF calculations.
Although an industry average makes sense for companies in the stable-growth
phase, it may be an underestimate for companies in the rapid-growth phase. In
general, the cost of capital will tend to fall as a company gets older. Thus, for some
applications we might want to estimate the cost of capital at exit by using com-
parable companies. This estimation requires ?ve steps:
1. Identify a set of comparable companies (as in Example 12.2).
2. Estimate a performance evaluation regression (as in Chapter 4) for each of
these companies.
3. Compute the unlevered betas for these companies (described below).
4. Compute the average of these unlevered betas.
5. Use the corresponding cost of capital formula (as in Chapter 4) to estimate
the cost of capital.
Of these ?ve steps, only step (3) is completely new. In our discussion in Chapter 4,
we didnot distinguishbetweenunleveredbetas andleveredbetas, but insteadreferredto
all factor loadings simply as “betas”. In Chapter 11, we also did not consider this dis-
tinction, as we were analyzing all-equity ?rms. Here, however, we must consider the
224 CHAPTER 12 COMPARABLES ANALYSIS
possibility that some of the comparable ?rms will have some debt in their capital
structures, and thus the estimated betas will re?ect both the “unlevered” cost of equity
and the “leverage” costs of debt. In computing the proper cost of capital for exit
valuations, it is necessary to unlever these betas. We illustrate this procedure in Example
12.3. In this example, we use the CAPM (as in Chapter 4) as our model for the cost of
capital. Following the example, we discuss how the computations can be adjusted for
multifactor cases such as the Fama-French model or the Pastor-Stambaugh model.
EXAMPLE 12.2
EBV is considering an investment in Newco—the same company from Examples 11.1 and
12.1. Newco’s comparable companies are given in Exhibit 12.1. In addition to the information
given in that exhibit, EBV estimates that the CAPM betas for these companies are 1.5 for
ABC, 1.0 for DEF, 2.0 for GHI, and 2.0 for JKL.
Problem Use these comparable companies to estimate a discount rate (cost of capital) for
Newco.
Solutions Step 1 is provided for us in Exhibit 12-1, and Step 2 (the CAPM betas) is given
by assumption. If we did not have this assumption, then we could use data on realized returns to
estimate betas as in Chapter 4. Because these regressions use realized stock returns, they
provide estimates of levered betas, also called equity betas. For an all-equity company (or
industry), leverage is zero and the levered beta is the same thing as the unlevered beta. If there
are other assets in the capital structure, then the levered beta will be different from the
unlevered beta. Because our DCF analysis assumes an all-equity company, we may need to
unlever the betas of the comparable companies. This unlevering procedure is the task of Step 3.
In theory, the unlevering process is very complex. The exact formulas for unlevering
depend on the analyst’s assumption about each company’s capital structure policy, and these
formulas can vary across companies and even across time for the same company. Luckily for
us, our focus on high-growth companies means that most of the comparable companies will
have little or no debt. (Indeed, if a comparable company does have a lot of debt, then perhaps
we should rethink whether that company is truly “comparable”.) When debt is small, it does
not matter very much which formula is used, so we choose the simplest one. Also, we assume
that the debt—and any other component of the capital structure—has a beta of zero. In that
case, the relationship between unlevered beta and levered beta can be written as
?
u
5
MC
EV
à ?
l
ð12:7Þ
where ?
u
is the unlevered (CAPM) beta, ?
l
is the levered beta, MC is the market capitali-
zation of equity, and EV is the enterprise value.
4
4
As discussed earlier, this is only one possible variant of the unlevering formula. Speci?cally, this variant
applies when tax shields are discounted at the unlevered cost of equity, and when all other parts of the
capital structure have betas of zero. To read about other variants of this formula, and to learn the
conditions under which they are applicable, see Holthausen and Zmijewski (2010).
12.3 USING COMPARABLE COMPANIES TO ESTIMATE THE COST OF CAPITAL 225
Using Equation (12.7), we can compute the unlevered betas for the comparable
companies. Exhibit 12-1 shows that DEF has no debt, so its ?
u
5 ?
l
5 1.0. For ABC, we
have MC5300 and EV5310, so ?
u
5300/310 Ã 1.5 51.45. For GHI, we have MC5150
and EV5170, so ?
u
5150/170 Ã 2.0 51.76. For JKL we have MC5200 and EV5210, so
?
u
5200/210 Ã 2.0 51.90.
Once we have computed the unlevered betas for all the comparable companies, we
move to Step 4 of the procedure and calculate the average of these betas as (1.0 11.45
11.76 11.90)/4 11.53. Then, for Step 5, we follow the same procedure as in Chapter 4 and
use a risk-free rate of 4 percent and an estimated market premium of 7 percent to estimate the
cost of capital as
r 50:04 11:53 Ã 0:07 514:71 percent: ð12:8Þ
’
In Example 12.3, we used the CAPM to estimate the cost of capital. If we
want to use a multifactor model such as the FFM or PSM, then all we need to do is
compute a separate version of Equation (12.7) for each of the factor loadings, and
then substitute the average of these loadings into the appropriate cost of capital
equation, analogous to Equation (12.8).
Because the unlevering step takes account of the difference between MC and
EV, how should we handle cases like Example 12.2, where companies have excess
cash and negative net debt? In theory, there is no difference in the way we handle
companies with negative debt. Using Equation (12.7), these companies will typi-
cally have unlevered betas higher than their levered betas. In practice, we need to
take special care that the excess cash situation existed during the estimation period
for beta. If the excess cash is a temporary phenomenon, then the estimated betas
may not require any adjustment.
SUMMARY
In this chapter, we showed how to perform a relative valuation analysis using comparable
companies. The ?rst step in this analysis is to choose comparable companies. To ?nd these
companies, we look at all companies in the same industry with revenue close to the forecast
successful-exit case. We then choose the subset of these companies with the closest match for
predicted investment opportunities, operating margins, and discount rates. Once these com-
panies have been chosen, we compute valuation multiples using a variety of measures and
then examine the implied valuations for each company and multiple. Although all multiples
provide some information, we pay particular attention to the multiples that provide the most
stable estimates (lowest standard deviation) across companies. Comparable companies can
also be used to estimate the cost of capital used in DCF analysis. To make these estimates, it is
sometimes necessary to unlever the beta estimates for the comparable companies.
226 CHAPTER 12 COMPARABLES ANALYSIS
KEY TERMS
Comparables analysis
5multiples analysis
5method of multiples
5relative valuation
Market capitalization
5market cap
5equity market value
Enterprise value (EV)
Earnings before interest,
taxes, depreciation, and
amortization (EBITDA)
Geometric mean, harmonic
mean
Unlevered betas, levered
betas
REFERENCES
Holthausen, Robert W., and Mark E., Zmijewski, 2010, Corporate Valuation: Theory, Practice, and
Evidence, forthcoming.
EXERCISES
12.1 Softco, the company valued in Exercise 11.1, is expected to have the following busi-
ness at exit:
Softco provides business process integration software and services for corporations across a
broad range of enterprise markets. Its main product is the Softco business process inte-
gration software platform together with packaged applications and content, where it expects
to derive 75 percent of its revenue. In addition, the company expects to earn the remainder of
its revenue from mainframe outsourcing and midrange systems management.
Use whatever resources you want to identify at least two comparable companies for Softco
and to estimate a relative valuation.
12.2 Consider the following “denominators” suggested as part of a comparables analysis:
(a) Number of unique visitors to a website
(b) Number of patents held by the company
(c) Level of dividends paid to common shareholders
(d) Number of demo software programs downloaded per month
For each of these four denominators, choose the numerator that is most appropriate for doing
comparables analysis.
12.3 True, False, or Uncertain: The harmonic mean will always provide a lower valuation
than the geometric mean, which in turn will always provide a lower valuation than the
median.
12.4 True, False, or Uncertain: The levered beta for a company is always greater than or
equal to the unlevered beta for the same company.
EXERCISES 227
APPENDIX 12.A: POTENTIAL COMPARABLES
FOR SEMICO
(Includes all companies in Yahoo! Finance, in the Semiconductors: Integrated
Circuits industry, with between $25M and $125M in revenue for the 12 months
ending closest to September 30, 2009. All these companies traded on the NASDAQ
as of January 2010, unless otherwise noted below.)
EXHIBIT 12-A
POTENTIAL COMPARABLES FOR SEMICO
API ADVANCED PHOT A (Amex)
WYNX.OB WAYTRONX INC (OTC BB)
AXTI AXT Inc
SATC SatCon Technology Corporation
TXCC TranSwitch Corporation
PXLW Pixelworks, Inc.
SUPX Supertex, Inc.
TUNE Microtune, Inc.
PLXT PLX Technology, Inc.
VLTR Volterra Semiconductor Corporation
EXAR Exar Corporation
OIIM O2Micro International Limited
PSEM Pericom Semiconductor Corporation
228 CHAPTER 12 COMPARABLES ANALYSIS
PART III
PARTIAL VALUATION
229
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CHAPTER 13
OPTION PRICING
PART III PRESENTS an investment framework that demonstrates how
option pricing concepts can be ef?ciently incorporated into VCs’ investment
decisions.
This chapter provides the crucial building blocks for this framework. Option
pricing theory and technology have made considerable progress in the last 35 years,
and we are now at a point where most of the complicated mathematical tasks can be
automated. Indeed, the main purpose of the model accompanying this book is to
provide the automation so that these powerful tools can be used in a fast-moving
VC transaction. Nevertheless, to apply these tools properly it is necessary to have at
least some exposure to the underlying equations. The exposition in this chapter
focuses on the intuition behind these equations with minimum technical detail.
Readers interested in these technical details—or in a more comprehensive survey of
option pricing—are encouraged to look at Hull (2008).
Throughout Part III, we will make many references to the VCV model. Links
to updated versions of this model, with documentation, are available at http://
VCVtools.com. Appendix B of this textbook provides brief descriptions for all the
spreadsheets and models used in this book, with particular attention to VCV.
Nevertheless, readers are encouraged to refer to the most recent version of the
model maintained on the websites, as updates and patches are likely.
In Section 13.1 we discuss European options: options that can only be
exercised on a preset expiration date.
1
In Section 13.2 we demonstrate how to value
a European option using replication techniques. These techniques—with some extra
mathematics—form the basis of the famous Black-Scholes equation. In Section
13.3, we examine this equation—derived under the assumption of liquid markets—
and discuss its applicability to illiquid private companies. In Section 13.4, we
discuss American options, which can be exercised on many possible dates, and in
1
The de?nitions of European options, their exercises, and expiration dates will be provided in Section
13.1. Other option pricing terms used in this introduction are given in the corresponding sections of the
chapter.
231
Section 13.5 we discuss random-expiration options, where the expiration date is
unknown to the option holder. Such random-expiration options are typical for VC,
where exit dates for investments are unknown. In Section 13.6 we show how to
translate exit diagrams (as ?rst introduced in Chapter 9) as a portfolio of options. In
Section 13.7 we reinterpret carried interest as a call option held by GPs on the value
of all fund investments.
13.1 EUROPEAN OPTIONS
Financial options are derivative assets, with their value derived from an
underlying asset. The prototypical ?nancial option is the European call, which
gives the holder the right to buy an underlying asset at a preset strike price on an
expiration date.
For example, consider a European call option to purchase a share of Bigco
stock (the underlying asset) in exactly one year for a strike price of $100 per share.
If Bigco is worth less than $100 per share on the expiration date, then the option
holder will choose not to exercise, and the option will expire worthless. If Bigco is
worth more than $100 per share on the expiration date, then the option holder
would exercise the option, pay $100, and earn a pro?t equal to the difference
between the stock price and $100.
Exhibit 13-1 shows the value of the option as a function of the value of Bigco
on the expiration date. We see from the exhibit that there is a direct relationship
between the value of the call option and the underlying Bigco stock. We refer to
EXHIBIT 13-1
CALL OPTION
C
a
l
l
O
p
t
i
o
n
(
S
t
r
i
k
e
?
1
0
0
)
Bigco's Stock Price
100
232 CHAPTER 13 OPTION PRICING
Exhibit 13-1 as an expiration diagram—a concept related to the exit diagrams
studied in Chapter 9. In an expiration diagram, the date of expiration is known with
certainty. In an exit diagram, the date of exit is unknown and random. In Section 13.6,
we demonstrate the relationship between these two types of diagrams; for now, we
focus on the expiration type.
We can write an equation corresponding to Exhibit 13-1 as
Value of Call with Strike of 100 on its expiration date
5C
1
ð100;1Þ 5MaxðV
1
2100; 0Þ;
ð13:1Þ
where V
1
is the value of Bigco on the expiration date. The value of the call option
will either be zero (if V
1
is less than or equal to 100) or it will be the difference
between V
1
and 100 (if V
1
is greater than 100). We use the operator Max (for
“maximum”) to capture this relationship.
In general, the expiration value of a call option with strike price X and
expiration date T is written as
C
T
ðX;TÞ 5MaxðV
T
2X; 0Þ: ð13:2Þ
Another standard option is the European put, which gives the holder the
right to sell an underlying asset at a preset strike price on an expiration date. For
example, consider a European put option to sell one share of Bigco stock (the
underlying asset) in exactly one year for a strike price of $100 per share. On
the expiration date, if Bigco is worth more than $100 per share, then the option
holder will choose not to exercise, and the option will expire worthless. If Bigco is
worth less than $100 on the expiration date, then the option holder would exercise
the option, receive $100 of proceeds, and earn a pro?t equal to the difference
between the stock price and $100. The expiration diagram for this put option is as
shown in Exhibit 13-2.
The corresponding equation is
Value of Put with Strike of 100 on its expiration date
5P
1
ð100;1Þ 5Maxð100 2V
1
; 0Þ:
ð13:3Þ
The general equation for the expiration value of a European put option with a
strike of X and an expiration of T is
P
T
ðX; TÞ 5MaxðX 2V
T
; 0Þ: ð13:4Þ
Although call options (and their variations) are frequently included in VC
transactions, the explicit use of put options is rare, except for their almost standard
inclusion as part of the VC’s redemption rights. Recall from Chapter 8 that
redemption rights give the investor the option to resell shares back to the ?rm after
some prespeci?ed time period (usually ?ve to seven years) or upon some triggering
event. This type of option is a put option, because the strike price is the resale price.
Notwithstanding this theoretical interpretation, it is very dif?cult to exercise this
redemption right in practical situations, so we will not attempt to value it.
13.1 EUROPEAN OPTIONS 233
13.2 PRICING OPTIONS USING A REPLICATING
PORTFOLIO
The expiration diagrams show the value of an option on the expiration date, T.
Although it is helpful to solve for this date T value (C
T
), we also want to know the
current (date 0) value of the option (C
0
).
EXAMPLE 13.1
Suppose that Bigco is currently trading for $100 per share. We are offered a European call
option to purchase one share with an expiration date in one year. We know that on the
expiration date Bigco stock will sell for either $120 per share (a “good day”) or for $80 per
share (a “bad day”). No other prices are possible. The stock will not pay any dividends during
the year. Risk-free interest rates are zero, so a bond can be purchased (or sold) for a face
value of $100 and have a certain payoff of $100 in one year. Stocks, bonds, and options can
all be bought or sold, long and short, without any transaction costs.
Problem What is the value of the call option today?
Solution This problem may appear to be impossible on ?rst glance: although we know
that there are two possible prices for the stock in one year, we are not told the probabilities of
these two prices. It would seem that the answer must depend on these probabilities, but
surprisingly it does not. This is the strange reality of option pricing. Instead of using
probabilities, we solve for the option price by building a replicating portfolio (a combi-
nation of the stock and the bond that yields the same exact payoffs as the call option).
First, we draw some pictures. For an example with only two possible outcomes, we
can dispense with expiration diagrams and use simple diagrams instead. Because the bond is
riskless, it is worth $100 on both a good day and a bad day.
EXHIBIT 13-2
PUT OPTION
P
u
t
O
p
t
i
o
n
(
S
t
r
i
k
e
?
1
0
0
)
Bigco's Stock Price
100
234 CHAPTER 13 OPTION PRICING
The stock is worth $120 on a good day and $80 on a bad day:
When the stock is worth $120, the call option would be exercised for a pro?t of C
1
(good day) 5$120 2$100 5$20. When the stock is worth $80, the call option would not be
exercised, C
1
(bad day) 5 0.
EXHIBIT 13-4
STOCK VALUES ON GOOD DAY AND BAD DAY
S
0
? 100
S
1
(good day) ? 120
S
1
(bad day) ? 80
EXHIBIT 13-3
BOND VALUES ON GOOD DAY AND BAD DAY
B
0
? 100
B
1
(good day) ? 100
B
1
(bad day) ? 100
13.2 PRICING OPTIONS USING A REPLICATING PORTFOLIO 235
We summarize these outcomes with the equation
C
1
ð100;1Þ 5MaxðS
1
2100; 0Þ: ð13:5Þ
Next, we use some algebra to ?nd the combination of stocks and bonds that provides
exactly the same payoff as the option on both possible days. We write an equation for each
outcome, good or bad, that takes the form
Option Value at Expiration ðgood day or bad dayÞ
5ðShares of StockÞ Ã ðStock ValueÞ 1ðShares of BondÞ Ã ðBond ValueÞ:
ð13:6Þ
Denoting shares of stock as y and shares of the bond as z, we write the equations as
C
1
ðgood dayÞ 520 5120y 1100z; ð13:7Þ
and
C
1
ðbad dayÞ 50 580y 1100z: ð13:8Þ
Equations (13.7) and (13.8) give us two equations and two unknowns (y and z), which
we can then solve to ?nd that y 5 0.5 and z 5 20.4. To check and interpret this solution, we
return to the logic of replication: if we purchase 0.5 shares of the stock and sell (“purchase a
negative amount”) 0.4 shares of the bond, then we exactly replicate the payoffs to the call
option. On a good day, 0.5 shares of stock are worth $120/2 5 $60, and 0.4 shares of the
bond, $40, needs to be paid back. That transaction will net $60 2 $40 5 $20, the same
amount that the call option is worth on the good day. On a bad day, 0.5 shares of stock are
worth $80/2 5 $40, which is exactly the amount needed to pay back 0.4 shares of the bond.
This strategy nets $40 2 $40 5 $0 on the bad day, the same amount as the call option.
These calculations should convince you that the call option provides exactly the
same payoffs as 0.5 shares of stock minus 0.4 shares of the bond. Thus, we should expect
EXHIBIT 13-5
OPTION VALUES ON GOOD DAY AND BAD DAY
C
0
? ??
C
1
(good day) ? 20
C
1
(bad day) ? 0
236 CHAPTER 13 OPTION PRICING
that the value of the call option, at time 0, must be exactly the same as the cost of this
combination:
C
0
50:5 Ã S
0
20:4 Ã B
0
: ð13:9Þ
Equation (13.9) is an option-pricing formula: it expresses the value of the option today
(C
0
) in terms of the observable market prices of the underlying stock (S
0
) and bond (B
0
). We
can substitute these prices to ?nd the dollar value of the option as
C
0
50:5 Ã 100 20:4 Ã 100 5$10: ð13:10Þ
Thus, the value of the call option today is $10. ’
Upon?rst seeingthis answer, manypeople express disbelief. Our solutionmade no
use of any probabilities for the outcomes, nor did we use beta or any other risk measure.
How can it be possible to compute the value of the option without accounting for risk?
It is possible because risk should already be incorporated into the stock price.
The underlying probabilities of good and bad days, and the correlation of the stock
with these good and bad days, should be the main determinant of the stock price.
Because we have already shown that the option is effectively just a combination of
the stock and bond, there is no additional information to be considered.
Option pricing solutions like this rely on arbitrage. Arbitrage is the act of
simultaneously buying and selling the same set of cash ?ows for different prices. In
our example, with no transaction costs, let’s see how arbitrage would work to keep
the price of the option at $10.
First, suppose that someone was willing to buy the option for $11. We could
arbitrage this buyer by selling her an option for $11 and then replicating the option
payoffs by purchasing 0.5 shares of stock and selling 0.4 shares of the bond. As we
showed earlier, this replication strategy costs $10 and gives the same payoffs as the
option on both good and bad days. Thus, today we will pocket the difference
($11 2 $10 5 $1), and tomorrow we will break even for sure. With this strategy,
we could earn $1 on every option without taking on any risk. We will continue to
sell options until the price is driven down to $10.
The same reasoning in reverse demonstrates that the price cannot be less than
$10. For example, suppose that someone is willing to sell the option for $9. We
could then arbitrage this seller by buying the option from him for $9 and then
replicating this (short) option by selling 0.5 shares of stock and buying 0.4 shares of
the bond. This replication strategy will put $10 in our pocket today, enough to pay
$9 for the option and earn a $1 pro?t. As before, the whole transaction will wash
out tomorrow. Again, we would be happy to do this transaction until there is
nobody left willing to sell the option for less than $10.
In this example, the interest rate was set to zero for computational con-
venience. The intuition for the solution is the same for any interest rate. To see this is
true, pick some arbitrary riskless rate, r, replace B
0
5100 in Exhibit 13-3 with B
0
5
100/(1 1r) and then work through the same calculations as we used in the example.
13.2 PRICING OPTIONS USING A REPLICATING PORTFOLIO 237
13.3 THE BLACK-SCHOLES SOLUTION
Example 13.1 assumes only one discrete point where the stock price could change
and only two possible outcomes for this price. This is a great simpli?cation. In
principle, the same replication strategy can be used for any number of price
changes. In Chapter 22, we will show how to build and solve binomial trees for any
?nite number of price changes. Things become particularly interesting when we
take this process to the limit and allow prices to change continuously. In this case, it
is no longer feasible to write a diagram for the in?nity of possible outcomes, but the
insight of Black and Scholes is that a solution can still be obtained by combining a
replication strategy with some clever math. The technical details of their solution
are given in option pricing textbooks such as Hull (2008). For our purposes here, it
suf?ces to sketch the assumptions, give the famous formula, and then discuss the
intuition behind it.
The Black-Scholes solution requires two sets of assumptions. The ?rst set of
assumptions relates to “perfect markets”—markets that are open all the time, allow
assets to be traded in any quantity, have no taxes or transaction costs, and have no
remaining arbitrage possibilities. All these perfect-market assumptions are neces-
sary to obtain a unique price for the option. The second set of assumptions includes
technical restrictions on the statistical properties of stock and bond returns; these
restrictions can be relaxed, if necessary, for more general option pricing solutions.
It is obvious that the assumption of perfect markets does not even hold for
actively traded public stocks. Thus, it is natural to be skeptical of its relevance
for the private markets of VCs. In the “reality check” discussion later, we discuss
the implications of these assumptions for private markets. For now, let us suspend
our skepticism and assume that the assumptions hold.
Under these assumptions, the Black-Scholes formula for the value of a
European call option is
C
0
5Nðd
1
ÞS
0
2Nðd
2
ÞXe
2rT
; ð13:11Þ
where N(.) is the Normal distribution function and
d
1
5½lnðS
0
=XÞ 1ðr 1?
2
=2ÞTÞ?=ð?OTÞ; ð13:12Þ
d
2
5½lnðS
0
=XÞ 1ðr 2?
2
=2ÞT?=ð?OTÞ 5d
1
2?OT; ð13:13Þ
where
T 5years until the expiration date,
? 5the annual volatility of returns, and
r 5the annual riskless rate.
All stock returns and interest rates in the Black-Scholes framework are
expressed as continuously compounded returns, also known as log returns,
because these returns can be calculated as natural log of one plus the periodic
return: log return 5 ln(1 1 periodic return).
238 CHAPTER 13 OPTION PRICING
The Black-Scholes formula may look complex, but is almost an exact ana-
logue of the simple solution for Example 13.1 given in Equation (13.9). The ?rst
terms in these two equations are 0.5 Ã S
0
for Equation (13.9) and N(d
1
)S
0
for
Equation (13.11). In both cases, this is a number between 0 and 1 (N(d
1
) is the
normal distribution function, so it will always give us a probability, which must be
a number between 0 and 1) multiplied by the current stock price.
The interpretation of this multiplier is the answer to the question “How much
stock would I have to purchase today to replicate the option position?” In Example
13.1, the option could either be worth $20 (on a good day) or $0 (on a bad day). The
stock could be worth $120 (on a good day) or $80 (on a bad day). Thus, the option
has a spread of $20 between good and bad days, and the stock has a spread of $40
between good and bad days. This means that after we ?nish the algebra exercise for
replication, we end up with one-half of a share of stock ($40 spread à 1/2) needed to
replicate the $20 spread for the option. In the Black-Scholes case, the math is more
complicated but the idea is the same: after plugging in the inputs to obtain N(d
1
),
we obtain the fraction of stock needed to replicate a single option.
Next, consider the second term in Equations (13.9) and (13.11). These
terms are 0.4B
0
and N(d
2
)Xe
2rT
, respectively. Again, these terms are analogues
of each other. The Xe
2rT
term in Equation (13.10) represents the present dis-
counted value of the strike price. In Example 13.1, we used a riskless bond with a
payoff (or strike price) of B
1
5 $100. Given this, B
0
turns out to be the price of
this bond in period 1, which is also the same thing as the present discounted value
of the strike price.
How about N(d
2
)? This is a number between 0 and 1 that can almost (but not
exactly) be thought of as “the probability that we will exercise the option”. Then,
the whole term N(d
2
) Xe
2rT
can be interpreted as “the probability that we will
exercise the option multiplied by the amount of money that we will need for the
strike price if we do actually exercise”. In Equation (13.11), the 0.4 multiplier in
front of B
0
serves the same purpose. Of course we have not solved for any actual
probabilities, but it is helpful to interpret the multipliers in this way, because it
allows us to see the role that they are playing in the more complex Black-Scholes
formula.
We are nowready to apply the Black-Scholes formula in an example. In this and
all future examples, we will assume that all the Black-Scholes assumptions hold.
EXAMPLE 13.2
Suppose that Bigco is currently trading for $100 per share. We are offered a European call
option to purchase one share with an expiration date in ?ve years. We know that the volatility
of Bigco’s stock is 90 percent per year, and that the stock will not pay any dividends during
the year. The riskless interest rate is 5 percent.
Problem What is the value of the call option today?
13.3 THE BLACK-SCHOLES SOLUTION 239
Solution Because Black and Scholes have done all the hard work for us, the solution here is
just a matter of plugging numbers into the Black-Scholes formula. We have r 55%, ? 590%,
X 5 100, S0 5 100, and T 5 5. We can also use the European Call Option Calculator at
VCVtools.com to calculate the answer as $72.38. Output from this Calculator is shown in
Exhibit 13-6. ’
REALITY CHECK: Is the Black-Scholes solution reasonable for private
companies? The solution requires several assumptions about perfect markets. These
include assumptions that markets are open for trading at all times, that there are no
taxes or transactions costs, and that there are no remaining arbitrage possibilities.
Furthermore, there are additional assumptions about stock and bond returns,
including the assumption that the logarithm of stock returns has a normal dis-
tribution. Many of these assumptions do not even hold for stocks traded on the New
York Stock Exchange, so they will de?nitely not hold for unlisted private com-
panies. Research has shown that when the perfect market assumptions are dropped,
there are many possible option prices that can hold in equilibrium, and without lots
of additional information, it is not possible to predict what the exact solution will
be. Given these concerns, how should we interpret the Black-Scholes solution for
private companies?
Before answering this question, it is important to remember the reason why
we do option valuation for private companies in the ?rst place. For public com-
panies, option pricing is often a serious and exact business, because mistakes can
lead to arbitrage possibilities for other traders—and those on the wrong side of
arbitrage trades can lose money in a hurry. However, the VC problem is different.
Here, our goal is to break a complex transaction down into digestible parts to
provide guidance to an investor about the relative merits of different deal structures.
Having an exact answer would be ideal but it is not crucial. We can live with an
approximate answer, as long as the approximation is unbiased. An unbiased
approximation is sometimes too high and sometimes too low, but the average error
EXHIBIT 13-6
EUROPEAN CALL
European Call
Stock Price 100
Strike Price 100
Volatility (%) 90
Risk Free Rate (%) 5
Time to Expiration 5
Call Option Value 72.38
240 CHAPTER 13 OPTION PRICING
is zero. An unbiased approximation can aid decision making, whereas a biased
approximation would be misleading. Thus, the key question is: “Is the Black-
Scholes solution an unbiased approximation for private companies?” Concerns
about bias fall into two main groups: (1) the need for a “nontradability discount” on
the option and (2) the understatement of volatility when using lognormal returns.
We address these two concerns next.
Some people argue that there should be a nontradability discount subtracted
from the option price. This argument asserts that because standard options can be
traded and hedged, and because no investor would prefer to have a restriction on
trading, the standard options as priced by Black-Scholes should be worth more than
a nontradable option. This argument seems compelling, but we would argue that,
for private companies, it is the nontradable options that can be approximately
priced by Black-Scholes, whereas the tradable options would be biased. Why?
Because the underlying asset here is itself not traded, and any discount for non-
tradability should already be built into the value of this asset. (Recall the discussion
of the liquidity factor in Chapter 4.)
The second main concern about bias comes from the assumption of log-
normal returns. The argument is this: “VC investments do not have returns like
public companies. Instead, a VC investment often returns absolutely nothing, and
occasionally returns a huge amount. This binary type of outcome is not consistent
with a lognormal distribution”. There are two responses to this concern. First, it is
not true that VC returns are binary. We saw in Chapter 7 that many VC outcomes
end up somewhere in the middle. Second, periodic returns that are often very low
(and only sometimes very high) are consistent with lognormality—and in fact, this
is exactly what lognormal returns do look like. Exhibit 13-7 gives an example
EXHIBIT 13-7
FIVE-YEAR COMPOUND RETURNS FOR A LOGNORMAL
DISTRIBUTION
150%
Return
?99% 400%
.198
.009
P
r
o
b
o
f
R
e
t
u
r
n
13.3 THE BLACK-SCHOLES SOLUTION 241
distribution of ?ve-year compound periodic returns using a lognormal distribution
with an annual standard deviation of 90 percent.
This exhibit does not appear to be a bell curve; the low outcomes are much
more prevalent than the high outcomes, and the high outcomes can be very high.
The objection here is usually caused by confusion about the difference between
normal distributions (which look like a bell curve when drawn in periodic returns)
and lognormal distributions (which look like a bell curve if drawn in log returns,
but look like Exhibit 13-7 if drawn in periodic returns.)
This discussion does not attempt to exhaust the possible objections and
responses to the use of the Black-Scholes formula to value options on private
companies, and no doubt this debate will continue. Nevertheless, it does not yet
appear that there is any clear bias in the use of Black-Scholes for these applications,
so we will make use of it in the examples in this book.
13.4 AMERICAN OPTIONS
Thus far, we have worked with European options, where exercise is restricted to the
expiration date. However, most VC options in practice are American options,
which allow for exercise at any time until the expiration date. For example, an
American call option gives the holder the right to buy an underlying asset at a
preset strike price on or before an expiration date, and an American put option
gives the holder the right to sell an underlying asset at a preset strike price on or
before an expiration date.
In discussing these options, it is useful to introduce a few more de?nitions.
First, if the strike price is higher than the current stock price, then a call option is
out of the money. Similarly, if the strike price is lower than the current stock price,
then a call option is in the money. If the strike price is equal to the current
price, then a call option is at the money. For put options, we reverse the out of
the money and in the money de?nitions: puts are out of the money when the strike
price is below the current price and are in the money when the strike price is above
the current price. The at the money de?nition is the same for puts and calls.
For stocks with no dividends, and for diversi?ed investors without immediate
risk management or liquidity concerns, an American call is equivalent to a Eur-
opean call. This is because it is never optimal under these conditions to exercise an
American call early. To see why, consider what might occur before expiration.
First, if the option is out of the money or at the money, then the investor should
certainly not exercise early, because she might as well just buy the (cheaper) stock
instead. Second, if the option is in the money, the investor can continue to earn
interest on the cash needed for the strike price while still effectively enjoying any
price appreciation by waiting to exercise until the expiration date. In this case,
waiting has the extra bene?t that, if the stock price falls below the exercise price
before expiration, the investor will be especially happy that she did not exercise. In
these aspects American calls are equivalent to European calls; thus we can use the
242 CHAPTER 13 OPTION PRICING
same Black-Scholes formula to price both of them. Note that this argument does not
apply if the stock pays dividends, because the investor would forego these divi-
dends in exchange for waiting to exercise.
The same logic does not work for put options, because there are some cases
where exercising early can be optimal. The reason here is that stock prices cannot
fall below zero, so if the price gets very close to zero, it can make sense to exercise
a put early and collect the proceeds. Unfortunately, there is no analytical solution
leading to a single equation to price American puts, and numerical methods must be
used. Lucky for us, put pricing is much less important than call pricing for VC
transactions.
13.5 RANDOM-EXPIRATION OPTIONS
Up to this point, all the options we have discussed have had a ?xed expiration date.
This date might be the only possible time for exercise (European options) or the last
possible time (American options), but in either case there is some end point. In VC
transactions there are often some special conditions that supersede these rules. For
example, as we will show in Chapter 14, convertible preferred stock can be
modeled as a bond plus an embedded call option. However, unlike standard call
options, this embedded option will have a forced exercise in the case of an IPO or
sale of the company, and would expire worthless if the company goes out of
business. In general, many liquidity events for the underlying company will force a
contemporaneous expiration of the embedded option, and in this situation the
investor will face an immediate exercise decision.
The possibility of forced expiration adds another complication to option
pricing, but under some reasonable assumptions, it can be handled without much
dif?culty. For example, take a case where an option has a 50 percent chance of
forced expiration in exactly 5 years, with the remaining 50 percent being the chance
of forced expiration in exactly 10 years. If this is the case, then we can think of this
complex option as the combination of two standard European options: a 50 percent
chance of a European call option with expiration in ?ve years plus a 50 percent chance
of a European call option with expiration in ten years. Because both of these European
call options can be valued using the Black-Scholes formula, then under the
assumptions, the combination option can be priced as the expected value of the two
standard call options.
The same logic can be used when the option has any number of dates for its
possible forced expiration. Suppose that the company’s board of directors sits down
every month and considers whether the time has come to sell the company, have an
IPO, or shut down. If each month is equally probable for exit over a 10-year period,
then any options on this company would have 120 possible expiration dates, each
with a 1/120 chance of happening, and the option could be priced at the expected
value of 120 European call options with expirations of 1 month, 2 months, and so
on, all the way up to 10 years. This calculation is easy for a computer, because all
13.5 RANDOM-EXPIRATION OPTIONS 243
we need is to repeat the same Black-Scholes formula 120 times with a different
input for the expiration date. If we take this process to the limit, then the option
would have a continuous-time probability of forced expiration, an in?nite number
of possible expiration dates, and the expected value of the option would be cal-
culated as an integral of the probability of expiration for any given date multiplied
by the Black-Scholes value of the call option with that expiration.
These options with unknown expiration are important for VC valuation
problems, so we will develop some new terminology for them. We de?ne a random-
expiration (RE) option to have a continuous-time probability, q, of forced
expiration. This forced expiration is random and is uncorrelated with the perfor-
mance of the ?rm or the overall market. RE options do not have ?xed expiration
dates, but for any q we can compute an expected holding period, H. Conveniently,
the math works so that H51/q. Because “expected holding periods” are more
intuitive objects than are “continuous-time probabilities”, we will work through
the book with the former. Appendix 13.A gives more details for the derivation of
the pricing formula for RE options.
The numerical valuation of RE call options is hard for humans, but easy for a
computer; and a template for valuation is available at VCVtools.com (Random
Expiration Call Option Calculator). The only difference in the inputs between a
standard European call and a RE call is that the former gives a time to expiration, T,
whereas the latter gives an expected holding period H. The following example is
identical to Example 13.2 except for the portion in italics.
EXAMPLE 13.3
Suppose that Bigco is currently trading for $100 per share. We are offered a random-
expiration call option to purchase one share with an expected holding period of ?ve years.
We know that the volatility of Bigco’s stock is 90 percent per year, and that the stock will not
pay any dividends during the year. The riskless interest rate is 5 percent.
EXHIBIT 13-8
RANDOM-EXPIRATION CALL
Random Expiration Call
Stock price 100
Strike price 100
Volatility (%) 90
Risk Free Rate (%) 5
Expected Holding period 5
Call Option Value 60.70
244 CHAPTER 13 OPTION PRICING
Problem What is the value of the RE call option today?
Solution As in the previous example, the computer does the hard work. We have r 5
5%, ? 5 90%, X 5 100, S
0
5 100, and H 5 5. The Random Expiration Call Option Cal-
culator at VCVtools.com calculates the answer as $60.70, as shown in Exhibit 13-8. ’
13.6 READING EXIT DIAGRAMS
VCs must often analyze investments with complex payoff structures. In these
structures, VCs do not receive explicit call options, but rather have options
embedded into other securities, such as convertible preferred stock. Because VCs
can make many different rounds of investment, their exit payoffs can look quite
complicated, and it can seem at ?rst glance that no sense can be made of the
investment. However, we will see that it is often possible to translate these complex
investments into a portfolio of options with different strike prices. To do this, we
draw exit diagrams where the x-axis shows the value of the whole company, and the
y-axis gives the fraction of the company represented by a speci?c investment.
These are exit diagrams, not expiration diagrams, because the date of exit (5
expiration of the options) is unknown. Under the assumption that this unknown exit
date follows the statistical distribution discussed in Section 13.5, we can read the
exit diagrams as a portfolio of random-expiration options.
For example, suppose that EBV invests in Newco across several venture
rounds. Exhibit 13-9 represents the value of EBV’s investment as a function of the
proceeds ($W) from selling the whole company.
EXHIBIT 13-9
EXIT DIAGRAM FOR EBV’S STAKE IN NEWCO
S
lo
p
e
?
1
/
4
10 20
$W
V
a
l
u
e
o
f
E
B
V
'
s
S
t
a
k
e
40
13.6 READING EXIT DIAGRAMS 245
In all exit diagrams in this book, we label the x-axis for all in?ection points. We also
label all slopes, except for slopes of zero or one, which will always be left unlabeled.
As the ?gure shows, EBV does not receive anything unless there are proceeds of at
least $10M. Between $10M and $20M, EBV receives all the proceeds, but it receives
none of the proceeds between $20M and $40M, and it receives one-quarter of all
proceeds above $40M. It turns out that it is relatively straightforward to interpret this
exit diagram into a portfolio of options, which we call an exit equation. We call
this process reading the exit diagram. To do so, we start at the origin of the diagram
and read from left to right. At every point that the slope changes, we add (or subtract)
a fraction of a call option, with strike price equal to the corresponding point on the
x-axis, and the fraction equal to the change in slope at that point.
The ?rst slope change occurs at $10M, where the slope goes from 0 to 1. We
write this as the purchase of a full call option with a strike price of 10: C(10). At $20M,
the slope falls by one, represented by the sale of a full call option: 2C(20). Finally, at
$40M, the slope rises to one-quarter: 1/4 C (40). Putting this all together yields
Exit equation5Cð10Þ 2Cð20Þ 11=4 Ã Cð40Þ: ð13:14Þ
Equation (13.14) is the output of reading Exhibit 13-9 as a portfolio of (random-
expiration) call options. Note that we have not put time subscripts on the value of the
call options in Equation (13.14). This is because there is no need for time subscripts on
the call option values, for even though we use exit diagrams for the reading, the
equation holds at all times. In most applications, we will value the options at time zero.
EXAMPLE 13.4
Suppose that Talltree invests in Newco across several venture rounds. After one of these
rounds of investments, Talltree draws an exit diagram as shown in Exhibit 13-10.
EXHIBIT 13-10
EXIT DIAGRAM FOR TALLTREE’S STAKE IN NEWCO
S
l
o
p
e
?
1
/
2
S
lo
p
e
?
1
/4
S
lo
p
e
?
3
/
8
20 30 50
$W
80
V
a
l
u
e
o
f
T
a
l
l
t
r
e
e
'
s
S
t
a
k
e
246 CHAPTER 13 OPTION PRICING
Problem What is the exit equation corresponding to this exhibit?
Solution To answer the question, we read the exit diagram. Talltree will receive one-half
of the ?rst $20M in exit proceeds, all the next $10M (up to $30M total), none of the next
$20M (up to $50M total), one-quarter of the next $30M (up to $80M total), and three-eighths
of everything after that. In this example, we start with a slope of one-half beginning at the
origin. This gives us half of a call option with a strike price of 0: 1/2 C (0). A call option with
strike price of zero is the same thing as owning the asset outright, so we can also write 1/2 C
(0) 5 1/2V, where V is the value of the whole company. At $20M the slope rises to one, an
increase of 1/2 of a unit: 1/2 C (20). At $30M the slope falls to zero, a reduction of one unit:
2C (30). At $50M the slope rises to one-quarter: 1/4 C (50). At $80M the slope rises to 3/8,
an increase of 1/8: 1/8 C (80). Putting this all together yields
Exit equation 51=2 Ã V 11=2 Ã Cð20Þ 2Cð30Þ 11=4 Ã Cð50Þ 11=8 Ã Cð80Þ: ð13:15Þ
’
13.7 CARRIED INTEREST AS AN OPTION
In Chapter 3, we showed how to estimate the carried interest for a fund by using an
estimate for the gross investment multiple combined with knowledge about lifetime
fees and the carry%. This approach gave us a simple formula for GP% (Equation
(3.15)), which we later used in the modi?ed VC method of Chapter 10. With our
new option-pricing tools, we might be tempted to do something fancier. For
example, if a GP has 20 percent carried interest with a committed capital basis, then
we can draw an exit diagram for carried interest as shown in Exhibit 13-11.
EXHIBIT 13-11
EXIT DIAGRAM FOR CARRIED INTEREST
Committed Capital
$W
C
a
r
r
i
e
d
I
n
t
e
r
e
s
t
13.7 CARRIED INTEREST AS AN OPTION 247
We can read this diagram as
Carried Interest 51=5 Ã CðCommitted CapitalÞ: ð13:16Þ
The underlying asset of this call option is the “portfolio of all fund invest-
ments”. For a fund with only one investment, this call option would be easy to
compute, because we could use the volatility of that one investment as an input for
a single random-expiration option. In general, however, the problem is more
complicated because there are multiple investments, each with a different exit date.
Furthermore, if the GP loses money on one investment, it will need to make up
these losses on other investments before any carried interest is earned.
To a ?rst approximation, these complexities can be modeled by changing the
volatility of the underlying option in Equation (13.16). At one extreme, we have
the case mentioned earlier: a VC makes only one investment (or many investments,
all perfectly correlated). In that case, the volatility of the underlying portfolio
would be the same as the volatility of a speci?c investment. At the other extreme,
we can imagine that a single VC fund makes hundreds of investments, with these
investments correlated only through their betas in some factor model. In that case,
the volatility of the whole portfolio would be approximately the same as the
volatility of the underlying factors, as multiplied by their betas. Because a portfolio
with hundreds of investments gains the bene?t of diversi?cation, the volatility
estimate for such a portfolio would be much lower than the corresponding estimate
for a single investment. With a lower volatility estimate, we would obtain a cor-
respondingly lower option value in Equation (13.16).
In reality, the volatility of the VC’s portfolio is likely to be somewhere
between these two extremes. A typical VC fund makes dozens of investments (not
hundreds), and these investments are more correlated than would be implied by
factor models. To ?nd the appropriate volatility for this complex portfolio, we will
need to use mathematical tools beyond the scope of this textbook. Furthermore, to
accurately capture all the variations of carried interest, we need to set up a model
that allows for separate treatment of each investment in the fund’s portfolio. In an
academic paper, Metrick and Yasuda (2010) perform this exercise and estimate GP
% for a wide variety of fee and carry structures. The good news is that these
estimates show that the simple formula of Equation (3.15) does a good job of
approximating the GP% for the most common carry structures. Thus, for this book,
we will use this simple formula in all applications.
SUMMARY
Options often appear in VC transactions, and it is important for investors to learn to spot
these options and to obtain approximate values for them. The fundamental option-pricing
formula is the Black-Scholes equation. The intuition for this equation comes from building a
replicating portfolio from the underlying stock and a riskless bond. By modifying the Black-
Scholes formula to account for random expiration, we can make it more applicable to VC
248 CHAPTER 13 OPTION PRICING
investments. Although the assumptions of the Black-Scholes approach do not hold for private
companies, the Black-Scholes solution still seems to be an unbiased approximation for the
value of options in these companies.
KEY TERMS
Derivative assets, under-
lying assets
Financial options
European call, European put
Strike price
Expiration date
Expiration diagram
European put
Replicating portfolio
Black-Scholes formula
Continuously-compounded
returns
5 log returns
American option
Out of the money
In the money
At the money
Random-expiration (RE)
option
Expected holding period
Reading the exit diagram
Exit equation
REFERENCES
Black, Fischer, and Myron Scholes, 1973, “The Pricing of Options and Corporate Liabilities”, Journal of
Political Economy 81(3), 637À654.
Hull, John, 2008, Options, Futures, and Other Derivatives, 7th Edition, Prentice Hall, Upper Saddle
River, NJ.
Metrick, Andrew, and Ayako Yasuda, 2010, “The Economics of Private Equity Funds”, Review of
Financial Studies 23, 2302-2341.
EXERCISES
13.1 Suppose that Bigco is currently trading for $100 per share. We know that in one year
Bigco stock will sell for either $150 per share (“good day”) or for $75 per share (“bad day”).
No other prices are possible, and the stock does not pay any dividends. The riskless interest
rate is 5 percent, so a bond worth B
1
next year sells for B
0
5B
1
/(1 1r) today. Stocks, bonds,
and options can all be bought or sold, long and short, without any transaction costs.
(a) What is the value of a European call option with a strike price of $100 and expiration in
one year?
(b) What is the value of a European put option with a strike price of $100 and expiration in
one year?
13.2 Suppose that Bigco is currently trading for $100 per share. The stock has an annual
volatility of 90 percent and does not pay any dividends. The riskless interest rate is 5 percent.
(a) What is the value of a European call option with a strike price of $100 and expiration in
10 years?
(b) What is the value of a RE call option with a strike price of $100 and an expected
holding period of 10 years?
EXERCISES 249
13.3 True, False, or Uncertain: Other things equal, an increase in the volatility of the
underlying asset will increase the value of call options on that asset.
13.4 Suppose that Owl invests in Newco across several venture rounds. After one of these
rounds of investments, Owl draws an exit diagram as shown in Exhibit 13-12.
(a) What is the portfolio of options corresponding to this exhibit?
(b) Suppose the founders of Newco own one-half of everything not owned by Owl. What is
the portfolio of options corresponding to the founder’s ownership?
APPENDIX 13.A
RE OPTIONS: TECHNICAL DETAILS
For RE options, the probability q works much like the continuous compounding of
a discount rate. The probability that an option remains alive (does not yet have a
forced expiration) on any given date T can be calculated as e
2qT
, which can be
interpreted as a discount factor at T. A plot of this probability for various levels of q
is shown in Exhibit 13-13.
To determine the probability of a forced expiration at any time T, we multiply
the instantaneous probability of expiration, q, by the probability the option is still
alive at that time, e
2qT
, yielding a probability of qe
2qT
, which is also the probability
distribution function for the exponential distribution. Then, the value of a RE call
option is
Value of RE call option 5
Z
N
0
½SNðd
1
Þ 2Xe
2rT
Nðd
2
Þ?qe
2qT
dT; ð13:17Þ
EXHIBIT 13-12
EXIT DIAGRAM FOR OWL’S STAKE IN NEWCO
20 40 80
S
lo
p
e
?
1
/
2
S
lo
p
e
?
1
/3
S
lope ?
1/6
$W
S
e
r
i
e
s
X
250 CHAPTER 13 OPTION PRICING
where the ?rst part of the integrand is de?ned as in the Black-Scholes formula of
Equation (13.11). This integral is solved numerically in the Random Expiration
Call Option Calculator. Because qe
2qT
is the probability distribution function for
the exponential distribution, we know the mean of this distribution is 1/q (the
expected holding period). We write this mean value throughout the book as H.
EXHIBIT 13-13
SURVIVAL PLOT FOR RE OPTION
P
r
o
b
a
b
i
l
i
t
y
o
p
t
i
o
n
i
s
s
t
i
l
l
a
l
i
v
e
1
.75
.25
1 2 3
q
?
.
1
q
?
.
2
q
?
.
3
T
4
.5
APPENDIX 13.A RE OPTIONS: TECHNICAL DETAILS 251
CHAPTER 14
THE VALUATION OF
PREFERRED STOCK
ALMOST ALL VC investments include some form of preferred stock. In
Chapter 9 we introduced four types of preferred stock: redeemable preferred (RP),
convertible preferred (CP), participating convertible preferred (PCP), and partici-
pating convertible preferred with cap (PCPC). In Chapter 9 we also demonstrated
how to draw exit diagrams for all these types of preferred stock. With the intro-
duction of option-pricing methods in Chapter 13, we are now ready to estimate the
partial valuation of preferred stock structures. In this chapter we learn how to value
Series A investments with RP and CP structures. We will leave the valuation of
later rounds for Chapter 15 and the valuation of PCP and PCPC for Chapter 16. In
all these chapters, we make heavy use of term sheet de?nitions ?rst introduced
in Chapters 8 and 9. If your memory of these earlier chapters is hazy, now would be
a good time to review.
We begin our analysis in Section 14.1 with a discussion of base-case option
pricing assumptions for interest rates, expected holding periods, and volatility. In
Section 14.2 we use these assumptions to analyze a Series A structure of RP and
common stock. This is the most basic of all structures, and it allows us to introduce
some new steps for making investment recommendations. The ?rst step in this
valuation is to determine the redemption value (RV) of the RP. For RP without
dividends or excess liquidation preferences, RV is the same as the aggregate pur-
chase price (APP). Once we have determined the RV, we can draw an exit diagram
for the structure and then read this diagram to obtain an exit equation. Then we
adjust this exit equation for carried interest to obtain an LP valuation equation.
At this point, if we already have an estimate for the total valuation, then we can use
this estimate in the VCV model to compute the LP valuation. Alternatively, if we do
not have an estimate for the total valuation, then we can use the VCV model to
compute the breakeven valuation that equates LP valuation and LP cost. This
breakeven valuation can then be used to inform our investment decision.
252
In Section 14.3, we show how to extend the analysis for excess liquidation
preferences (which make RV greater than APP), and in Section 14.4 we do the
same for dividends (which make RV change over time.) In Section 14.5, we ana-
lyze CP, and in Section 14.6 we extend the CP analysis for excess liquidation
preferences and dividends. Once these building blocks are in place, we can do
partial valuations for structures that combine RP and CP (Section 14.7). We can
also compare investments with different structures (Section 14.8).
14.1 BASE-CASE OPTION-PRICING
ASSUMPTIONS
Before solving any examples, it is helpful to de?ne some base-case option-pricing
assumptions. Unless otherwise noted, for Series A investments we will assume a
riskless interest rate (r) of 5 percent, an expected holding period (H) of 5 years, and
a volatility (?) of 90 percent. For Series B investments we adjust the expected
holding period to be 4 years; for Series C and beyond we adjust it to be 3 years. Of
these assumptions, the riskless interest rate is the easiest to establish. Although we
use 5 percent for the option-pricing examples in Parts III and IV of this book, readers
should adjust this number to re?ect the prevailing riskless (treasury) interest rate at
any time. For the expected holding periods, we rely on (approximate) averages from
the Sand Hill Econometrics database, as seen in Exhibits 7-2, 7-5, and 7-8.
The most dif?cult input is the volatility. For publicly traded stocks, analysts
can estimate volatility by looking at historical returns. Of course, this estimation is
not possible for nontraded private companies. Instead, we rely on a clever technique
developed by Cochrane (2005). In this article, the author begins with a CAPM
model of expected (log) returns, similar to Equation (4.2). He then uses the Ven-
tureSource database to estimate the parameters of Equation (4.2) for the typical
VC-backed company. In Chapter 4, we applied this approach to the analysis of
returns for the entire VC industry. To extend this analysis to speci?c companies, we
have a sample-selection problem: we only observe returns for a company upon
some ?nancing or liquidation event. To solve this problem, Cochrane simulta-
neously estimated thresholds for IPOs and bankruptcy liquidations. With these
thresholds in place, the parameters of the CAPM equation can be estimated, and
these parameters then imply means and standard deviations for returns.
Cochrane’s procedure can be compared to a physics experiment, where a
researcher attempts to infer the motion of particles in a room by using data about
how often these particles strike the walls of the room. Using these methods,
Cochrane estimates an annualized volatility (standard deviation of continuously
compounded returns) of 89 percent. We round this up to 90 percent for the
examples in this book. Although he also attempts to estimate different volatilities
for different industries and for different rounds of investment, these differences are
14.1 BASE-CASE OPTION-PRICING ASSUMPTIONS 253
usually not statistically signi?cant, so we use the same estimate for all examples.
Readers who want to make use of these differences are encouraged to look at
Cochrane’s article.
14.2 RP VALUATION
In the early years of the VC industry, it was popular for investors to receive both RP
and common stock. This combination is useful because the investors are paid back
in the event of a deemed liquidation event, but also have upside potential. Since the
1980s, this structure has been rarely used, but it remains a useful building block for
understanding the valuation of more popular structures.
In a transaction with RP and common stock, the contract must specify what
portion of the investment is being allocated to the RP and what portion is being
allocated to the common stock. This allocation is explicit in the APP used for the
redemption of the RP. Although this allocation might seem arbitrary, it does matter
for valuation, because the RV of the RP is driven by its APP.
EXAMPLE 14.1
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco at $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) From Chapter 10, the formula for LP cost is
LP cost ¼ ðcommitted capital=investment capitalÞ Ã $I: ð14:1Þ
From Appendix 2.A, we can compute that lifetime fees are $20M, so investment
capital is $100M 2 $20M5$80M, and LP cost is 5 (100/80) Ã $6M5$7.5M.
EBV receives the ?rst $5M in proceeds for the RP. Following this redemption, EBV
owns one-third of the common stock (5M out of 15M shares). Thus, the exit diagram for the
Series A is as shown in Exhibit 14-1.
254 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
We can read this exit diagram as
Partial valuation of Series A ¼ V 22=3 Ã Cð5Þ: ð14:2Þ
To solve for LP valuation, we must subtract carried interest from Equation (14.2).
Following the same procedures as in the modi?ed VC method of Chapter 10, we estimate LP
and GP valuation as
LP valuation ¼ partial valuation 2GP valuation; ð14:3Þ
where
GP valuation ¼ GP% Ã partial valuation: ð14:4Þ
As in Chapter 10, we estimate GP% using an expected GVM of 2.5 and the formula
GP% ¼ Carry% Ã ðGVM Ã Investment Capital 2Carry BasisÞ=ðGVM
à Investment CapitalÞ: ð14:5Þ
For EBV, we have a GP% of 0.20 Ã (2.5 Ã 80 2 100)/(2.5 Ã 80) 50.10, which implies
an LP valuation equation of
LP Valuation ¼ 0:9 Ã ½V 22=3 Ã Cð5Þ?: ð14:6Þ
(c) Equation (14.6) expresses the LP valuation of the Series A as a portfolio of options. These
options can be valued using techniques similar to those described in Chapter 13. For example,
the FLEX Calculator at VCVtools.com enables the simultaneous valuation of several options.
The user inputs each component of Equation (14.6), and the calculator values these compo-
nents and adds them together. Using this calculator with base-case option-pricing assumptions
and a total valuation assumption of $18M, we can compute a partial valuation of $7.92M, of
which the LP valuation is $7.13M and the GP valuation is $0.79M.
For most of the examples used in this textbook, the FLEX Calculator will not be
necessary, and we can use built-in valuation functions in the AUTO Calculator at VCVtools.
com. In the AUTOCalculator, users need only to input the properties of the preferred stock and
EXHIBIT 14-1
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
=
1
/3
5
$W
S
e
r
i
e
s
A
14.2 RP VALUATION 255
do not need to solve for the LP valuation equation. The Calculator does this solution auto-
matically and also calculates the speci?c LP valuation for any set of option-pricing assump-
tions. Readers are referred to Appendix B for the documentation of AUTO and FLEX.
(d) The breakeven valuation is the total valuation such that LP valuation 5LP cost. In this
example, we are solving for the total valuation (V) such that
0:9 Ã ½V 22=3 Ã Cð5Þ? ¼ $7:5M: ð14:7Þ
Because V is contained in this equation and also appears indirectly as the underlying asset in
C(5), we must use iterative methods to solve for V. This iterative process is automated in the
AUTO Calculator, where the breakeven valuation is given as standard output. Under base-case
assumptions, the breakeven valuation is $19.19M. Thus, if EBV believes that the total valuation
is $19.19M or greater, then the model would produce a positive investment recommendation.
Although it may be tempting to minimize work and just use the AUTO Calculator to
answer these questions, readers are encouraged to experiment with the FLEX Calculator
to better understand the workings of the model. At some point, every VC will be faced by a
complex problem that does not ?t into the preprogrammed functions in AUTO; when that
happens—as in Chapter 18—he will need to understand how to use FLEX.
(e) As a general rule, the common stock acts like a call option in transactions with RP. The
value of the common stock also increases when volatility or expected holding period
increases. Because the Series A holds all the RP and only a portion of the common stock,
increases in the common stock—at the expense of the RP—will tend to reduce the partial
valuation of the Series A. We can see this effect if we experiment with different option-
pricing assumptions. Other things equal, a volatility of 120 percent implies a breakeven
valuation of $20.39M, which is $1.2M higher than the breakeven valuation under base-case
assumptions (i.e., to obtain a positive investment recommendation, EBV would require a
higher total valuation by $1.2M). Similarly, if we use all base-case assumptions but set the
expected holding period to be seven years, then the breakeven valuation becomes $20.01M,
which is $0.82M higher than the base case.
Although increases in volatility or in the expected holding period will tend to increase
the breakeven valuation, reductions in these inputs will tend to reduce it. For example, if we
start from the base case but change volatility to 60 percent, then the breakeven valuation
becomes $17.90M. Similarly, if we start from the base case but change the expected holding
period to be three years, then the breakeven valuation becomes $17.99M. Exhibit 14-2
displays several combinations of these changes. ’
EXHIBIT 14-2
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 16.93 17.99 19.10
Holding 5 17.90 19.19 20.39
Period 7 18.63 20.01 21.18
256 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
14.3 EXCESS LIQUIDATION PREFERENCES
As ?rst discussed in Chapter 8, a liquidation preference provides superiority in
capital structure in the event that the ?rm is sold or shut down. Preferred stock has a
liquidation preference to common stock, and some classes of preferred stock can
be contractually given a liquidation preference to other classes of preferred
stock. Excess liquidations preferences of 2X or 3X can provide additional value.
For example, suppose a company has 10M shares of common stock and RP with
$10M APP, where the RP has a 2X liquidation preference and thus an RV of $20M.
If the company is then sold, the ?rst $20M of proceeds (two times the original
$10M) will go to the RP holders, and the remainder will be split among the
common shareholders.
EXAMPLE 14.2
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco as $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding. This is the same setup as in Example 14.1, except that now we also add a 2X
excess liquidation preference on the RP.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) With a 2X liquidation preference, the RV is 2 Ã APP 5$10M, so EBV receives the ?rst
$10M in proceeds for the RP. Following this redemption, EBV owns one-third of the
common stock (5M out of 15M shares). Thus, the exit diagram for the Series A is the same as
in Example 14.1, except that the slope does not change until W5$10M.
We can read the exit diagram in Exhibit 14-3 as
Partial Valuation of Series A ¼ V 22=3 Ã Cð10Þ: ð14:8Þ
With GP% 5 0.10 (the same as in Example 14.1), we have
LP Valuation ¼ 0:9 Ã ½V 22=3 Ã Cð10Þ?: ð14:9Þ
14.3 EXCESS LIQUIDATION PREFERENCES 257
(c) Using base-case assumptions with a total valuation of $18M, we can use the AUTO or
FLEX Calculators to compute LP valuation as $8.34M. Thus, in contrast to the base case in
part (c) of Example 14.1, this computation implies a positive investment recommendation
(LP valuation .LP cost).
(d) The VCV model gives a breakeven valuation of $15.64M (i.e., for total valuations above
this cutoff, there is a positive investment recommendation).
(e) The option-pricing assumptions have the same effects as in Example 14.1. Increases in
volatility or expected holding period would decrease the LP valuation and, thus, increase the
breakeven valuation. Exhibit 14-4 demonstrates the sensitivity of the breakeven valuation to
changes in the volatility of the expected holding period. ’
EXHIBIT 14-3
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/3
10
$W
S
e
r
i
e
s
A
EXHIBIT 14-4
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 11.78 13.77 15.59
Holding 5 13.30 15.64 17.58
Period 7 14.47 16.93 18.84
258 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
Reality Check: The preceding analysis assumed that liquidation preferences are
honored in all outcomes, but it can be a lot messier in reality. In many cases,
investors in down rounds of ?nancing will insist that all prior liquidation pre-
ferences be wiped out. Thus, we may be overstating the valuation of the liquidation
preferences as well as the preferred stock itself.
This is a valid objection that can be addressed in several ways. First, analysts
should recognize that the option-pricing valuation of liquidation preferences is
essentially providing an upper bound for their value. It would be nice to compute
exactly how close this bound is to the “true value”, but given current data and
methods, it is not possible to do so. Second, one should not interpret the preceding
objection to mean that liquidation preferences are worth nothing. In most successful
investments, there are no down rounds, so liquidation preferences can be paid
without objection. Even in down rounds, the preferences do provide prior investors
with some protections in the form of additional leverage in the negotiation, thus
functioning as yet another bargaining chip that investors can put on the table.
14.4 DIVIDENDS
As ?rst discussed in Chapter 8, preferred stock can include a cumulative dividend.
This dividend does not pay in cash; instead, it adds to the RV of the preferred and is
paid on exit. These dividends can either be a constant amount paid on the APP
(simple interest) or can compound on past dividends (compound interest). Including
dividends in our analysis is more complex than the inclusion of a liquidation
preference because the RV is changing over time. For RP, it does not matter
whether the dividend is an accrued cash dividend (5liquidation dividend) or a
stock dividend (5PIK dividend). In Example 14.3 we analyze the former case.
EXAMPLE 14.3
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of common stock plus RP with an APP of $5M. (We
will refer to this basket of RP plus common as “the Series A”.) EBV estimates the total
valuation of Newco as $18M, and the employees of Newco have claims on 10M shares of
common stock. Following the Series A investment, Newco will have 15M common shares
outstanding. This is the same setup as in Example 14.1, except now we also add a cumulative
simple dividend of 1 percent per month on the RP, to be paid only if dividends are paid to the
common stock or on the liquidation of the company.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
14.4 DIVIDENDS 259
(c) Suppose that total valuation is $18M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) For computational convenience, it is simplest to express the dividend rate as a con-
tinuous annual rate, which is approximately equal to 12% (51.00% Ã 12) of the APP. Let T
equal the time, in years, between investment and exit for proceeds of $W. Given this case,
the RV of the RP at time T is equal to RV (T) 5$5M (1 10.12T) and the exit diagram for the
Series A is
1
shown in Exhibit 14-5.
The corresponding exit equation for the Series A is
Partial valuation of the Series A ¼ V 22=3 Ã CðRVðTÞÞ: ð14:10Þ
As in the previous examples, GP% is 0.1, so we can write the LP valuation
equation thus:
LP valuation of the Series A ¼ 0:9 Ã ½V 22=3 Ã CðRVðTÞÞ?: ð14:11Þ
1
For compound dividends of 12 percent, the corresponding formula would be RV(T) 5 $5 MÃ e
0.12T
.
EXHIBIT 14-5
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/3
RV(T)
$W
S
e
r
i
e
s
A
260 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
(c) Although these equations are more complex than the analogues from Examples 14.1
and 14.2, it is not a problem for the all-powerful computer. The strike prices for the call
options change over time, but because the RE option already requires us to effectively
compute a separate Black-Scholes formula at every point in time, the computer doesn’t care
if the strike price is different in each of these formulas. Using base-case assumptions with a
total valuation of $18M, we can use the AUTO Calculator to compute the LP valuation as
$7.89M.
(d) The VCV model gives a breakeven valuation of $16.82M.
(e) The option-pricing assumptions have the same effects as in Examples 14.1 and 14.2.
Increases in volatility or expected holding period would decrease the LP valuation and, thus,
increase the breakeven valuation. Exhibit 14-6 demonstrates the sensitivity of the breakeven
valuation to changes in the volatility of the expected holding period.
’
14.5 CP VALUATION
As ?rst discussed in Chapter 9, the key step in the valuation of CP is the deter-
mination of the conversion condition, an inequality de?ning the level of proceeds
where conversion is more valuable than redemption. We call this level of proceeds the
conversion point, and we write the conversion point for a Series Ainvestment as W
A
.
The conversion condition is calculated in the partial valuation step. In other
respects, the valuation of CP is similar to that for RP and common.
EXAMPLE 14.4
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees of
Newco have claims on 10M shares of common stock. Following the Series A investment,
EXHIBIT 14-6
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 14.59 16.14 17.61
Holding 5 14.77 16.82 18.52
Period 7 14.97 17.34 19.16
14.5 CP VALUATION 261
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP.
Problems
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) The LP cost is the same as in Example 14.1 and is equal to $7.5M.
(b) We can calculate the conversion condition as
1=3 Ã W .6-W
A
¼ 18: ð14:12Þ
If the proceeds of the liquidation are exactly $18M, then the investor will receive $6M
for either redeeming or converting. However, if the proceeds are below $18M, he is better off
redeeming. Above $18M the investor is better off converting. Exhibit 14-7 gives the exit
diagram:
We can read this exit diagram as
Partial valuation of Series A ¼ V 2Cð6Þ 11=3 Ã Cð18Þ: ð14:13Þ
Thus, the LP valuation is
LP valuation of Series A ¼ 0:9 Ã ½V 2Cð6Þ 11=3 Ã Cð18Þ?: ð14:14Þ
(c) With base-case assumptions, we can use the VCV model to solve for a breakeven
valuation of $22.38M.
EXHIBIT 14-7
EXIT DIAGRAM FOR THE SERIES A
S
lo
p
e
?
1
/
3
6 18
$W
C
P
262 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
(d)
Note that these option-pricing sensitivities are smaller than those found for RP
structures. The reason for this difference is that CP is harmed less than RP from increases in
volatility and holding period because there is no redemption value at extreme levels. In the
limit, as either of these inputs approaches in?nity, CP looks just like common stock. Indeed,
it is possible for an increase in expected holding period (or volatility) to lead to a decrease in
the breakeven valuation. This can only happen when these inputs start at low levels, as we
see when volatility is at 60 percent, and the expected holding period increases from three to
?ve years. To see how this is possible, consider an extreme case where expected holding
period (or volatility) is zero. Then the CP would convert for sure for any total valuation
above 18M, and thus would be worth exactly the same as the common stock. CP only has
some advantage if there is at least some chance that the redemption feature will be used,
which requires at least some volatility. For “too much” volatility, the redemption feature
becomes relatively worthless (because most redemptions are for close to zero), and the value
of the CP once again is close to common stock.
’
14.6 CP WITH EXCESS LIQUIDATION
PREFERENCES OR DIVIDENDS
Earlier in this chapter we gave extended examples for liquidation preferences and
cumulative dividends for an RP investment. We will not repeat those whole
examples here, but instead will focus only on the parts of the valuation problem that
differ from Example 14.4. As in the earlier example, we analyze accrued cash
dividends, leaving the more complex analysis of stock dividends for Chapter 15.
EXAMPLE 14.5
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees of
EXHIBIT 14-8
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60 90 120
Expected 3 22.50 22.03 22.18
Holding 5 22.47 22.38 22.73
Period 7 22.59 22.68 23.09
14.6 CP WITH EXCESS LIQUIDATION PREFERENCES OR DIVIDENDS 263
Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP. This is the same setup as in Example 14.4, except that we now add a
2X liquidation preference on the CP.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) The crucial difference between this example and the previous one is that the RV of the
CP is now 2 Ã $6M5$12M. Thus, the new conversion condition is
1=3 Ã W.12-W
A
¼ 36: ð14:15Þ
The exit diagram for the CP with a 2X liquidation preference is shown in Exhi-
bit 14-9
We can read Exhibit 14-9 as
Partial valuation of the CP ¼ V 2Cð12Þ 11=3 Ã Cð36Þ: ð14:16Þ
Thus, the LP valuation is
LP valuation of the CP ¼ 0:9 à ½ðV 2Cð12Þ 11=3 à Cð36Þ?: ð14:17Þ
(b) We can use base-case option-pricing assumptions in the VCV model to solve for the
breakeven valuation as $17.67M.
’
EXHIBIT 14-9
EXIT DIAGRAM FOR SERIES A
S
lo
p
e
?
1
/3
12 36
$W
C
P
264 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
EXAMPLE 14.6
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of convertible preferred stock (CP). The employees
of Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP. This is the same setup as in Example 14.4, except that we now add a
cumulative simple dividend of 1 percent per month. This dividend will be paid only if
dividends are paid to the common stock or upon the liquidation of the company.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) We use the same approach to dividends here as we did in Example 14.3, using a con-
tinuous approximation for the dividends and obtaining a redemption value of
RVðTÞ ¼ $6M Ã ð1 10:12TÞ: ð14:18Þ
The conversion condition is
1=3 Ã W .RVðTÞ-W .3 Ã RVðTÞ; ð14:19Þ
which implies an exit diagram as shown in Exhibit 14-10.
This exit diagram looks exactly like Exhibits 14-8 and 14-9, except that the conversion
point is at 3 Ã RV(T) 5$18M Ã (1 10.12T). We can read this diagram as
Partial valuation of the CP ¼ V 2CðRVðTÞÞ 11=3 Ã Cð3 Ã RVðTÞÞ: ð14:20Þ
EXHIBIT 14-10
EXIT DIAGRAM FOR SERIES A
RV(T) 3*RV(T)
$W
C
P
14.6 CP WITH EXCESS LIQUIDATION PREFERENCES OR DIVIDENDS 265
So the LP valuation equation is
LP valuation of the CP ¼ 0:9 Ã ½V 2CðRVðTÞÞ 11=3 Ã Cð3 Ã RVðTÞÞ?: ð14:21Þ
(b) The VCV model gives a breakeven valuation of $19.54M.
’
14.7 COMBINING RP AND CP
In Examples 14.1, 14.2, and 14.3, EBV received a combination of RP and common
stock in the Series A investment. A similar payoff structure can be obtained through
the combination of RP and CP.
EXAMPLE 14.7
Suppose EBV is considering a $10M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of CP ($6M APP) plus RP ($4M APP). The employees
of Newco have claims on 10M shares of common stock. Following the Series A investment,
Newco will have 10M common shares outstanding and would have 15M shares outstanding
on conversion of the CP.
Problems
(a) Find the LP valuation equation for this investment.
(b) Solve for the breakeven valuation of this investment.
Solutions
(a) In this example, there are two types of preferred stock, CP and RP, and there is no
statement about which version would be paid ?rst in a liquidation. This structure is very
similar to the RP 1CP structure that was analyzed as part of Example 9.1. Because EBV
owns all of both the CP and the RP, this liquidity preference between the two is not relevant
for the aggregate value of the Series A; following Example 9.1, we treat the RP as superior
to the CP.
To estimate the partial valuation, we ?rst examine the RP component. Because we
have assumed that the RP has a liquidation preference to the CP, we can draw the exit
diagram for the RP as Exhibit 14-11.
We can read Exhibit 14-11 as
RP in Series A ¼ V 2Cð4Þ: ð14:22Þ
The CP here is similar to the CP in Example 14.4, except that the CP has no value
unless the proceeds are above $4M. The conversion condition for this CP is
1=3 Ã ðW 24Þ . 6-W
A
¼ 22: ð14:23Þ
To draw an exit diagram for the CP, it is as though we take Exhibit 14-7 and shift the
line $4M to the right:
266 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
We can read Exhibit 14-12 as
CP in Series A ¼ Cð4Þ 2Cð10Þ 11=3 Ã Cð22Þ: ð14:24Þ
Then, the partial value of Series A is RP 1CP:
Partial valuation of Series A ¼ V 2Cð10Þ 11=3 Ã Cð22Þ: ð14:25Þ
and the LP valuation is
LP valuation of Series A ¼ 0:9 Ã ½V 2Cð10Þ 11=3 Ã Cð22Þ?: ð14:26Þ
EXHIBIT 14-11
EXIT DIAGRAM FOR SERIES A, RP
4
$W
R
P
i
n
S
e
r
i
e
s
A
EXHIBIT 14-12
EXIT DIAGRAM FOR SERIES A
S
lo
p
e
?
1
/3
4 10 22
$W
C
P
i
n
S
e
r
i
e
s
A
14.7 COMBINING RP AND CP 267
(b) The LP cost is $10M Ã (100/80) 5$12.5M. The AUTO Calculator solves for a breakeven
valuation of $34.90M, where LP valuation 5LP cost.
’
14.8 COMPARING RP AND CP
Now that we have done examples with both RP and CP, we are prepared to analyze
comparisons between these two structures and the implications of these compari-
sons for deal structure negotiation.
EXAMPLE 14.8
Suppose that EBV makes an initial offer to Newco as given in Example 14.1, with the offer
providing $6M for RP (APP5$5M) as well as 5M shares of common stock. The only
difference here is that we assume that the total valuation of the company is $25M. The
entrepreneurs counteroffer with a CP structure. In principle, EBV is not opposed to a CP
structure, but they would like to get the same expected value as they would under the RP
structure. Thus, they are considering two possibilities for their $6M investment:
Structure 1 5RP($5M APP) 15M shares of common stock($1M APP);
Structure 2 5Z shares of CP($6M APP)
Problem For what number of shares Z should EBV be indifferent between Structures 1
and 2?
Solution We will answer this question from the perspective of a limited partner in EBV,
so the key comparison will be between the LP valuations of the two possible structures. Our
goal is to solve for the unknown quantity of shares Z, which would equate the LP valuations
of the two structures. We have already solved for the LP valuation of Structure 1 in Example
14.1. That valuation was given in Equation (14.6). Using the VCV model, we can compute
the LP valuation as $9.32M (when the total valuation is $25M).
In Example 14.4 we did most of the work to solve for the LP valuation in Structure 2.
The only difference here is that instead of receiving 5M shares on conversion (one-third
of the ?rm), EBV would receive Z shares. These Z shares will convert to a fraction of the ?rm
equal to
CP fraction ¼ Z=ð10 1ZÞ: ð14:27Þ
We can then write the general conversion condition as
Z=ð10 1ZÞ Ã W .6-W
A
¼ 6 Ã ð10 1ZÞ=Z: ð14:28Þ
This conversion condition implies an exit diagram for the CP as shown in
Exhibit 14-13.
We can read Exhibit 14-13 as
Partial valuation ðStructure 2Þ ¼ V 2Cð6Þ 1Z=ð10 1ZÞ Ã Cð6 Ã ð10 1ZÞ=ZÞ; ð14:29Þ
268 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
so we have
LP valuation ðStructure 2Þ 50:9 Ã ½V 2Cð6Þ 1Z=ð10 1ZÞ
à Cð6 à ð10 1ZÞ=ZÞ?:
ð14:30Þ
Now we are ready to answer the initial question: What value of Z will equate the LP
valuations for Structure 1 and Structure 2? This can be answered through trial and error by
trying different values for Z, solving for the implied values for the CP fraction and the
conversion point, and then using the VCV model to compute the LP valuation with these
inputs. We can continue this process by trial and error until we obtain an LP valuation answer
of $9.32M, which is the value we found for Structure 1. It is useful to try this brute-force
approach a few times to get a feel for how the valuations change when Z changes. Using this
method, we can obtain a solution of Z56.29M, yielding a CP fraction of 38.6 percent and a
conversion point of $15.39M. ’
SUMMARY
Venture capitalists typically receive preferred stock for their investments. In one structure,
redeemable preferred stock (RP) is combined with common stock to provide both downside
protection and upside potential. This combination of securities can be valued using option-
pricing techniques. Sometimes the RP component includes additional liquidation preferences
that provide the holder with an additional return on a sale or liquidation. Cumulative divi-
dends can also provide the same bene?t, and both of these enhancements can be priced using
small modi?cations to our standard techniques.
EXHIBIT 14-13
EXIT DIAGRAM FOR SERIES A, STRUCTURE 2
S
l
o
p
e
?
1
S
lo
p
e
?
Z
/1
0
?
Z
6 6(10 ? Z)/Z
$W
C
P
SUMMARY 269
Convertible preferred (CP) stock is the most prevalent security in VCtransactions. CP is
a hybrid between RP and common stock, acting like the former when proceeds are lowand like
the latter when proceeds are high. CP can be valued as a bond plus an embedded call option. The
key step in CP valuation is to determine the conversion condition (the level of exit proceeds
necessary to induce the CP holder to convert rather than to redeem the stock). Once we have
mastered the valuation techniques for CP, we can compare transactions with different types of
preferred stock (RP or CP) or with combinations of preferred stock (RP plus CP).
KEY TERMS
Redemption value (RV) LP valuation equation Breakeven valuation
REFERENCES
Cochrane, John, 2005, “The Risk and Return of Venture Capital”, Journal of Financial Economics
75(1), 3À52.
EXERCISES
14.1 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as RP with APP of $4M plus 5M shares of common stock. (We refer
to this basket of RP plus common as “Series A”.) The employees of Newco have claims on
15M shares of common stock. Following the Series A investment, Newco will have 20M
common shares outstanding.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $30M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
14.2 Same setup as Exercise 14.1, except that now EBV is considering two additional
structures:
Alternative I: A 2X liquidation preference on the RP; or
Alternative II: A cumulative compound dividend of 0.75 percent per month, to be paid only if
dividends are paid to the common stock or on the liquidation of the company.
(a) Find the LP valuation equation for both alternatives.
(b) Compute the LP valuation for both alternatives under the assumption that total valua-
tion 5$30M. Which alternative should EBV prefer?
(c) Perform a sensitivity analysis of this preference.
270 CHAPTER 14 THE VALUATION OF PREFERRED STOCK
14.3 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of CP. The employees of Newco have claims on
15M shares of common stock. Following the Series A investment, Newco will have 15M
common shares outstanding, with another 5M shares on conversion of the Series A.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Suppose that total valuation is $30M. What is the LP valuation?
(d) Find the breakeven valuation for the investment under base-case assumptions.
(e) Perform a sensitivity analysis for this breakeven valuation.
14.4 Same setup as Exercise 14.3, except that now EBV is considering two additional
structures:
Alternative I: A 2X liquidation preference on the CP; or
Alternative II: A cumulative compound dividend of 0.75 percent per month, to be paid only if
dividends are paid to the common stock or on the liquidation of the company.
(a) Find the LP valuation equation for both alternatives.
(b) Compute the LP valuation for both alternatives under the assumption that total valua-
tion 5$30M. Which alternative should EBV prefer?
(c) Perform a sensitivity analysis of this preference.
EXERCISES 271
CHAPTER 15
LATER-ROUND INVESTMENTS
THUS FAR WE have analyzed preferred structures only for Series A (?rst-
round) investments. Although Series A is the simplest setting for learning partial
valuation techniques, it is also the least applicable. This is because Series A
investments are made in early stage companies, often without any revenue, where it
is dif?cult to perform total valuations. Thus, the partial valuations—which require
additional assumptions—are even less reliable.
For more mature companies, valuation analysis can be more precise. In later-
round investments, companies often have revenues and sometimes have pro?ts, so
there is a stronger basis for the estimation of total valuations. In addition, the path
to exit can be clearer, so it is easier to estimate exit values and future dilution.
Finally, the required investments often are larger, and the possible investment
structures are more complex, so there is a greater importance of getting the numbers
right. For these reasons, it is important that we extend our methods to later rounds.
In this chapter, we show how to extend our investment framework to Series B and
beyond. We will do three examples: Series B (Section 15.1), Series C (Section
15.2), and then, as an example of a very late round, Series F (Section 15.3).
15.1 SERIES B
EXAMPLE 15.1
Talltree is considering a $12M Series B investment in Newco. Two possible structures are
being considered. Structure 1 is 5M shares of common plus RP with $10M APP and a 2X
liquidation preference. Structure 2 is 10M shares of CP. The other investors are the
employees, who have claims on 10M shares of common, and the Series A investors, EBV,
who have 10M shares of CP with $6M APP. In both of these structures, Series B has a
liquidation preference to Series A. Both Talltree and EBV receive carried interest of 20
percent and charge management fees of 2 percent per year for all 10 years (as shown in the
appendices to Chapter 2).
272
Problems
(a) What is the LP valuation equation and breakeven valuation for Structure 1?
(b) What is the LP valuation equation and breakeven valuation for Structure 2?
(c) Plot the LP valuation for both structures for a range of possible total valuations. For
what total valuation should Talltree be indifferent between the two structures?
Solutions (a) The ?rst step is to compute LP cost. Talltree’s partnership agreement has
the same fee schedule as EBV. On the $250M Talltree fund, this implies lifetime fees of
$50M and investment capital of $200M. Thus, the LP cost for a $12M investment is
LP cost 5ð$250M=$200MÞ Ã 12M5$15M: ð15:1Þ
Next, we estimate partial valuation under Structure 1. With an APP of $10M on the RP
and a 2X liquidation preference, Talltree would receive the ?rst $20M of the proceeds from
any liquidation. After the ?rst $20M, the next $6M would go to EBV to cover the RV5APP
of their Series A CP. Beyond this point ($26M), things get trickier. The next dollar of
proceeds beyond $26M would be shared by the common stockholders, but how many shares
of common stock are outstanding? The founders have 10M, Talltree has 5M, and because
EBV has not yet converted, they have 0. Thus, Talltree has one-third of the outstanding
shares, and the founders have two-thirds. These fractions hold unless the proceeds are high
enough for EBV to convert, at which point there would be 25M shares outstanding and
Talltree would have 5/25. This means that we cannot draw an exit diagram for Talltree until
we solve for EBV’s conversion point.
To determine EBV’s optimal conversion point, we use the same inequality discussed
for the conversion of CP in Chapters 9 and 14. On the left-hand side of the inequality, we put
the amount earned by EBV if they choose to convert. Under conversion, EBV would have
10M shares, for 10/25(52/5) of the total shares outstanding. They would then be entitled to
two-?fths of the proceeds after $20M had been paid back to Talltree: 2/5 Ã (W220). On the
right-hand side of the inequality, we put the amount earned by EBV if they choose to redeem:
$6M. We then solve for the level of proceeds, $W, that leads to conversion.
Series A conversion condition:
2=5 Ã ðW 220Þ .6-W
A
5$35: ð15:2Þ
This inequality completes the picture for all parties. For proceeds of $35M or more,
EBV converts and owns 2/5 of the outstanding shares, Talltree owns 5/25 (51/5), and the
founders own the remaining two-?fths. With this ?nal piece, we are prepared to draw an exit
diagram for the Series B.
Exhibit 15-1 shows Talltree receiving the ?rst $20M of proceeds to pay for their 2X
liquidation preference, nothing of the next $6M, one-third of the next $9M (until W5$35M),
and then one-?fth thereafter. We can read this diagram as
Partial valuation of Series B ðStructure 1Þ 5V 2Cð20Þ 11=3 Ã Cð26Þ
22=15 Ã Cð35Þ:
ð15:3Þ
Because Talltree has carried interest of 20 percent (see Appendix 2.B), the compu-
tation of GP% (when the expected gross value multiple is 2.5) gives the same answer as it did
for EBV (50.10) and we have
15.1 SERIES B 273
LP valuation of Series B ðStructure 1Þ 50:9 Ã ½V 2Cð20Þ
11=3 Ã Cð26Þ 22=15 Ã Cð35Þ?:
ð15:4Þ
Using the VCV model, we can compute the breakeven valuation as $39.32.
(b) We begin again with the LP cost, which is $15M, the same as in part (a). Next, we need to
compute the partial valuation for Structure 2. For low levels of proceeds, the exit diagram is
easy to draw. Talltree receives the ?rst $12M of proceeds to cover redemption of Series B,
and EBV receives the next $6M of proceeds to cover redemption of Series A. Proceeds
above $18M are shared by the common stock holders, but how many of these shares are
outstanding?
Both Series Aand Series Bare CP. The ?rst step in this case—and in all cases with more
than one round of CP—is to determine the order of conversion. This step is tricky, because each
investor’s conversion decision depends on whether the other investor has already converted.
To determine the order of conversion, we ?rst compute the conversion point for each
investor under the assumption that the other investor has not converted. Consider Talltree’s
decision. Assume that proceeds are above $18M, because no investor would convert before
the APPs have been paid back at $18M. After that point, if EBV does not convert the Series
A, then Talltree could either receive $12M for redemption or 1/2Ã(W26M) for conversion.
(After conversion, Talltree would have 10M shares, and the employees would have 10M
shares, while $6M would be paid to redeem the Series A.) Thus, if EBV does not convert,
Talltree’s conversion condition would be
Series B conversion conditionÀSeries A not converted:
1=2 Ã ðW 26MÞ .12M-W
B
5$30M: ð15:5Þ
For EBV, if Talltree does not convert the Series B, then EBV would receive $6M if they
redeem the Series A, and 1/2 Ã (W2 12) if they convert. This implies a conversion condition of
Series A conversion conditionÀSeries B not converted:
1=2 Ã ðW 212MÞ .6M-W
A
5$24M: ð15:6Þ
EXHIBIT 15-1
EXIT DIAGRAM FOR SERIES B, STRUCTURE 1
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1/5
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274 CHAPTER 15 LATER-ROUND INVESTMENTS
A comparison of Equations (15.5) and (15.6) shows that EBV (Series A) would
convert “?rst”, with a conversion point of W
A
5$24M.
Now that we know that Series A converts ?rst, we revisit Talltree’s conversion
decision. Equation (15.5) is no longer relevant, because it was derived under the assumption
that the Series A did not convert. If the Series A does convert, then the Series B is still worth
$12M on redemption. If the Series B converts, however, it would be worth 1/3 Ã W, because
10M shares would now be one-third of the total. This implies a new conversion condition of
Series B conversion condition—Series A converted:
1=3 Ã W .12M-W
B
5$36M: ð15:7Þ
With the conversions solved, we are ready to draw an exit diagram for the Series B
under Structure 2:
This exhibit shows that Talltree receives everything from the ?rst $12M. After that,
they will receive nothing until they convert for one-third of the common stock at $36M. The
corresponding exit equation for Exhibit 15-2 is
Partial valuation of the Series B ðStructure 2Þ 5V 2Cð12Þ 11=3 Ã Cð36Þ: ð15:8Þ
The LP valuation equation is
LP valuation of the Series BðStructure 2Þ 50:9 Ã ½V 2Cð12Þ 11=3 Ã Cð36Þ?: ð15:9Þ
Using the VCV model, we can compute the breakeven valuation as $44.36M.
(c) Now, for each LP valuation Equations [(15.4) and (15.9)], we can use the VCV model and
base-case option pricing assumptions to compute an LP valuation for any given level of total
valuation. Because this is a Series B investment, our base-case assumption is an expected
holding period of four years. Exhibit 15-3 plots LP valuation for each structure. The crossing
point occurs at a total valuation of $61.25M, where both structures yield LP valuations of
EXHIBIT 15-2
EXIT DIAGRAM FOR SERIES B, STRUCTURE 2
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15.1 SERIES B 275
$19.80M. That is, for a total valuation below $61.25M, Talltree should prefer Structure 1; for
a total valuation above $61.25M, Talltree should prefer Structure 2. ’
After analyzing Series B structures, many students wonder why we don’t try
to account for later investments when we ?rst analyze the Series A. Put another
way, why is it all right to just ignore future rounds when we draw exit diagrams?
Because these future rounds will change the exit diagrams of the earlier rounds,
how can these early round diagrams be correct?
To answer these questions, it is helpful to put ourselves in the shoes of a Series
A investor like EBV. At the time of a Series A investment in Newco, EBV fully
expects more investments to be made. Although other investors may lead these later
rounds, EBV may invest in these rounds as well. In either case, as an investor in the
company, EBV has the incentive to drive the best possible bargain for the company
in later rounds. Indeed, the board of directors of Newco has a legal duty to get the
best deal. If the VC market is competitive—and all evidence says that it is—then
these later-round investments should be priced at “fair” levels. In this case, even
through the Series A exit diagrams will change, they should change in a way that
preserves the pre-transaction value of the Series A stake. We can draw an analogy
here to the DCF analysis of Chapter 11. There, if some future investment earns
exactly the cost of capital, this investment has no effect on valuation today. It is the
same thing here: if future rounds are sold at a fair price that re?ects the cost of
venture capital, then these rounds have no effect on the valuation of any stake today.
EXHIBIT 15-3
LP VALUATION OF SERIES B, STRUCTURES 1 AND 2
25 50 75
Total Valuation of Newco
100
35
25
15
5
30
20
10
0
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Structure 1
Structure 2
276 CHAPTER 15 LATER-ROUND INVESTMENTS
15.2 A CONVERSION SHORTCUT
To determine the conversion order in Structure 2 of Example 15.1, we derived a
conversion condition for each investor under the assumption that the other investor
did not convert. When there are only two investors, this does not take much time.
However, this procedure can become unwieldy when there are three or more
investors; because in addition to determining which investor converts ?rst, we must
then repeat the process to determine which investor converts second, third, and so on.
Luckily, a shortcut greatly simpli?es the task of determining conversion
order. Recall the ?rst conversion condition tried for the Series B in Example 15.1:
Series B conversion conditionÀSeries A not converted:
1=2 Ã ðW 26MÞ .12M-W
B
5$30M: ð15:5Þ
This condition means that if EBV does not convert the Series A, then Talltree
would convert the Series B as long as total proceeds are at least $30M. Now, let’s
interpret this equation another way. If, for proceeds of $30M, Talltree decides to
convert and EBV does not, then there would be 20M total shares outstanding, and
the total amount available for the common stock holders would be $30M2$6M
5$24M, because $6M would be needed to pay back EBV when they redeem the
Series A. Thus, the value of each common share would be $24M/20M5$1.20 per
share. This means that, in this case, we can say that Talltree will convert if they
receive at least $1.20 per share.
The $1.20 number is the redemption value per share (RVPS) of the CP: the
RVPS of preferred stock is equal to the total redemption value of the preferred
divided by the number of common shares received on conversion. In this case, the
CP has 12M APP and could convert to 10M shares, $12M/10M5$1.20 per share.
We will get the same RVPS of $1.20 no matter how many other investors have
already converted. To illustrate this point, consider Equation (15.7), the conversion
condition for the Series B when the Series A has already converted:
Series B conversion conditionÀSeries A converted:
1=3 Ã W .12M-W
B
5$36M: ð15:7Þ
With Series A already converted, there will be 30M shares outstanding on
conversion of Series B. Thus, $36M available to the common stock holders is
equivalent to an RVPS of $36M/30M5$1.20 per share.
It is also helpful to review Equation (15.6), EBV’s conversion condition for
the Series A in the case where the Series B has not converted:
Series A conversion condition—Series B not converted:
1=2 Ã ðW 212MÞ .6-W
A
5$24M: ð15:6Þ
For proceeds of $24M, if Series A converts and Series B does not, then there
would be 20M total shares outstanding, and the total amount available for the common
stock holders would be $24M2$12M5$12M, because $12M would be needed to
15.2 A CONVERSION SHORTCUT 277
pay back Talltree when they redeem the Series A. Thus, the value of each common
share would be $12M/20M5$0.60 per share. It is easy to verify that this number is
exactly the same as the RVPS of the Series A ($6M/10M5$0.60).
For Structure 2 in Example 15.1, we found that the Series A converted before
the Series B. We also ?nd that the Series A has a lower redemption value per share
than does the Series B ($0.60 versus $1.20). These two results are logically con-
nected through the conversion-order shortcut: the order of CP investors by their
RVPS, from lowest to highest. The investors will convert in the order of their RVPS
(i.e., the lowest RVPS will convert ?rst, the second-lowest RVPS will convert
second, and so on, and the highest RVPS will convert last). To demonstrate the
application of this shortcut, we do an example of a Series C investment.
15.3 SERIES C
In computing valuations for Series C, we follow the same steps as for Series B. The
analysis is more complicated because of the large range of possible structures
across three rounds. Despite this added complexity, the building blocks of any
partial valuation analysis remain the same no matter how many rounds of invest-
ment have already occurred.
EXAMPLE 15.2
Begin with the same setup as in Example 15.1. Assume that Talltree chose Structure 2 and
invested $12M in a Series B round for CP. It is now one year later, and Owl is considering a
$10M Series C investment in Newco. Structure 1 is 5M shares of common plus RP with $8M
APP and a 3X liquidation preference. Structure 2 is 10M shares of CP. The other investors
are (1) the employees, who have claims on 10M shares of common, (2) the Series A
investors, EBV, who have 10M shares of CP for $6M APP, and (3) the Series B investors,
Talltree, who have 10M shares of CP for $12M APP. In both structures, Series C has a
liquidation preference to Series B, which in turn has a liquidation preference to Series A.
Neither of the previous investors is covered by antidilution protection. As shown in Chapter 2,
the $500M Owl fund has a 25 percent carry and $83.75M in lifetime fees.
Problems
(a) What is the LP valuation equation and breakeven valuation for Structure 1?
(b) What is the LP valuation equation and breakeven valuation for Structure 2?
(c) Plot the LP valuation for both structures for a range of possible total valuations. For
what total valuation should Owl be indifferent between the two structures?
Solutions (a) The ?rst step is to compute LP cost. The $500M Owl fund has lifetime
fees of $83.75M and investment capital of $416.25M. Thus, the LP cost is
LP cost 5ð500=416:25Þ Ã 10M5$12M: ð15:10Þ
278 CHAPTER 15 LATER-ROUND INVESTMENTS
Next, we estimate partial valuation under Structure 1. With an APP of $8M on the RP
and a 3X liquidation preference, Owl would receive the ?rst $24M of the proceeds from any
liquidation. After the ?rst $24M, the next $12M would go to Talltree to cover the RV of their
Series B CP, and the next $6M would go to EBV for RV of the Series A CP. Beyond this
point ($42M), we have to ?gure out the order of conversion for Series A and Series B. In
the previous section, we computed the RVPS for the Series B as $1.20 per share and for the
Series A as $0.60 per share. The Series A is lower, so it converts ?rst.
When EBV converts the Series A, they will own two-?fths (10M/25M) of the
remaining proceeds (W236M). We obtain their conversion condition by comparing this
value to the $6M RV for redemption. Thus, EBV converts the Series A when
Series A conversion conditionÀSeries B not converted:
2=5 Ã ðW 236MÞ .6M-W
A
5$51M: ð15:11Þ
Once EBV converts, then Talltree would own two-sevenths (10M/35M) of the
remaining proceeds (W224M) when they convert, or $12M if they redeem. Thus, Talltree’s
conversion condition is
Series B conversion conditionÀSeries A converted:
2=7 Ã ðW 224MÞ .12M-W
B
566M: ð15:12Þ
With this information, we are prepared to draw an exit diagram for Series C (Structure 1),
as shown in Exhibit 15-4.
For the Series C, Owl gets all of the ?rst $24M in proceeds, nothing for the next $18M
while Series A and B are being paid back, and then one-third of all proceeds (because they
will own 5M out of 15M shares of common) until the Series A is converted at W5$51M.
For proceeds between $51M and $66M, Owl owns one-?fth of the common stock (5M/25M).
After the Series B is converted at W5$66M, Owl owns one-seventh of the common
(5M/35M). We can read Exhibit 15-4 as
EXHIBIT 15-4
EXIT DIAGRAM FOR SERIES C, STRUCTURE 1
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15.3 SERIES C 279
Partial valuation of Series C ðStructure 1Þ 5V 2Cð24Þ 11=3 Ã Cð42Þ
22=15 Ã Cð51Þ 22=35 Ã Cð66Þ:
ð15:13Þ
Owl has carried interest of 25 percent, which is higher than the industry-standard 20
percent carried interest charged by EBV and Talltree. With an expected gross value multiple
of 2.5, Owl has GP% of 0.25 Ã (2.5 Ã 416.25 2 500)/(2.5 Ã 416.25) 50.13. Thus, the GPs
receive an expectation of 13 percent of the partial valuation, and the LPs receive an
expectation of 87 percent.
LP valuation of Series C ðStructure 1Þ 50:87 Ã ½V 2Cð24Þ 11=3 Ã Cð42Þ
22=15 Ã Cð51Þ 22=35 Ã Cð66Þ?:
ð15:14Þ
Using the VCV model, we can compute the breakeven valuation as $25.32.
(b) For Structure 2, we have the same LP cost as in Structure 1: $12M. To complete the next
step, the partial valuation of the Series C, we must ?rst determine the conversion order.
Things look more dif?cult than in earlier examples because we now have three different
rounds of CP, but we can apply the conversion-order shortcut to keep things from getting too
messy. We already know the RVPS for Series A and B to be $0.60 and $1.20, respectively.
For Series C, we can compute the RVPS as $10M/10M5$1.00 per share. Thus, the con-
version order is Series A, then Series C, then Series B. With this ordering determined, we can
compute each conversion point.
EBV (Series A) converts ?rst. Series B and C have not yet converted. When EBV
converts, they receive 10Mshares and get half (10M/20M) of all proceeds after the Series Band
Chave been redeemed (W222M). To obtain their conversion condition we compare this value
to the redemption proceeds of $6M:
Series A conversion conditionÀB and C not converted:
1=2 Ã ðW 222Þ .6-W
A
5$34M: ð15:15Þ
Next to convert is Owl (Series C). Series A has converted and Series B has not. When
Owl converts, they receive 10M shares, the founders will have 10M shares, and EBV will have
10M shares, for a total of 30M shares outstanding. Thus, Owl will receive 10M/30M5one-
third of any proceeds after the Series B has been redeemed (W 2 12M). To obtain their
conversion condition, we compare this value to the redemption proceeds of $10M:
Series C conversion condition—A converted, B not converted:
1=3 Ã ðW 212Þ .10-W
c
5$42M: ð15:16Þ
Series A and C have already converted, so last to convert is Talltree (Series B). Upon
conversion, Talltree receives 10M shares for a total of 40M shares outstanding. Thus,
Talltree would be entitled to one-fourth of the total proceeds, $W, because there are no other
preferred shares outstanding to be redeemed before the common stock. A redemption value
of $12M implies a conversion condition of
Series B conversion condition—Both A and C already converted:
1=4 Ã W .12-W
B
5$48M: ð15:17Þ
We are now ready to draw an exit diagram for the Series C. As holders of the Series C,
Owl would receive the ?rst $10M of proceeds, and then would not receive anything else until
they choose to convert at W5$42M. Upon conversion, Owl would own one-third of the
280 CHAPTER 15 LATER-ROUND INVESTMENTS
common. When Talltree converts the Series B at W5$48M, Owl would then own 10M/
40M51/4 of the common.
We can read Exhibit 15-5 as
Partial valuation of Series C ðStructure 2Þ 5V 2Cð10Þ 11=3 Ã Cð42Þ
21=12 Ã Cð48Þ:
ð15:18Þ
EXHIBIT 15-6
LP VALUATION OF SERIES C, STRUCTURES 1 AND 2
100 125 150 175
Total Valuation of Newco
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40
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EXHIBIT 15-5
EXIT DIAGRAM FOR SERIES C, STRUCTURE 2
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15.3 SERIES C 281
Then, the LP valuation equation is
LP valuation of Series C ðStructure 2Þ 50:87 Ã ½V 2Cð10Þ 11=3 Ã Cð42Þ
21=12 Ã Cð48Þ?:
ð15:19Þ
Using the VCV model, we can compute the breakeven valuation as $47.37.
(c) Now, for each LP valuation Equation (15.14) and (15.19), we can use the VCV model and
base-case option-pricing assumptions to compute an LP valuation for any given level of total
valuation. Because this is a Series C investment, our base-case assumption is an expected
holding period of three years. Exhibit 15-6 plots LP valuation for each structure.
The crossing point occurs at a total valuation of $130.5M, where both structures yield
LP valuations of $29.28M. That is, for a total valuation below $130.5M, Owl should prefer
Structure 1; for a total valuation above $130.5M, Owl should prefer Structure 2. ’
15.4 DIVIDENDS IN LATER ROUNDS
Many VC investors receive dividends on their preferred shares. In Chapter 14 we
showed how to incorporate accrued cash dividends into the valuation of Series A
investments. For later-round investments, we must carefully analyze how dividends
can affect the conversion order and conversion conditions for each round. In
Section 15.4.1., we show how to do this for accrued cash dividends. In Section
15.4.2, we consider the case of stock dividends (5PIK dividends).
15.4.1 Accrued Cash Dividends
EXAMPLE 15.3
We begin with the same setup as in Example 15.2. We assume that Owl chose Structure 2: a
$10M investment for 10M shares of CP (APP 5$10M). The other investors are (1) the
employees, who have claims on 10M shares of common; (2) the Series A investors, EBV,
who have 10M shares of CP for $6M APP; and (3) the Series B investors, Talltree, who have
10M shares of CP for $12M APP. Series C has a liquidation preference to Series B, which in
turn has a liquidation preference to Series A. The new wrinkle we introduce here is that all
preferred investors—Series A, B, and C—have cumulative accrued cash dividends of 1.00%
per month, to be paid only on a deemed liquidation event.
Problem Find the conversion order and conversion conditions for all investors.
Solution We ?rst solve for the conversion order. First, let T be the time elapsed since the
latest round (Series C in this example). We differentiate this from T
X
, the time elapsed since
the time Series X took place. In this case, Series A was two years ago and Series B was one
year ago, so T
A
5T 12, T
B
5T 11, and T
C
5T.
To obtain the RVPS for each series, we can write the RV at time T as
RV
X
ðTÞ 5RV
X
ðat issue of Series XÞ Ã ð1 10:12T
X
Þ ð15:20Þ
282 CHAPTER 15 LATER-ROUND INVESTMENTS
where the subscript “X” represents Series A, B, or C. Then, the RVPS for each Series will
also be a function of T and can be written as
RVPS
A
ðTÞ 5ð1 10:12T
A
Þ Ã $6M=10M5
1 10:12 Ã ðT 12Þ
à $0:6
5 $0:74 10:072 T
ð15:21Þ
RVPS
B
ðTÞ 5ð1 10:12T
B
Þ Ã $12M=10M5
1 10:12 Ã ðT 11Þ
à $1:2
5 $1:34 10:144 T
ð15:22Þ
RVPS
C
ðTÞ 5ð1 10:12TÞ Ã $10M=10M5ð1 10:12TÞ Ã $1:0 5$1 10:12 T ð15:23Þ
The ?rst term (e.g., $0.74 for Series A) for each series represents the amount of
RVPS that it gets if they had a liquidation event today (the day of Series C investment). Note
that this is greater than RVPS at the time of original investments for Series A and B, because
they have accumulated dividends for two years and one year, respectively. The conversion
order when T 50 is therefore A-C-B. The second term represents how RVPS grows for
each series over time as a function of T. Note that A has the lowest slope and B has the
highest slope. Thus, the original conversion order will always be preserved.
The conversion conditions are
Series A conversion condition:
1=2 Ã ½W 2RV
B
ðTÞ 2RV
C
ðTÞ? . RV
A
ðTÞ-W
A
52 Ã RV
A
ðTÞ
1RV
B
ðTÞ 1RV
C
ðTÞ
ð15:24Þ
Series C conversion condition:
1=3 Ã ½W 2RV
B
ðTÞ? . RV
C
ðTÞ-W
C
53 Ã RV
C
ðTÞ 1RV
B
ðTÞ ð15:25Þ
Series B conversion condition:
1=4 Ã W . RV
B
ðTÞ-W
B
54 Ã RV
B
ðTÞ: ð15:26Þ
If we wanted to take next logical step in this solution, we could draw an exit diagram
for the Series C. This diagram would be identical to Exhibit 15-5, except that the relevant
conversion points would be a function of T and use Equations (15.25) and (15.26). These
conversion points would then serve as strike prices for the underlying random-expiration
options. As in the dividend examples of Chapter 14, the VCV model can handle these
changing strike prices without any dif?culty.
The valuation gets trickier if the dividends vary across the different series. For
example, consider the same setup as Example 15.3, except that Series A has cumulative
accrued cash dividends of 2 percent per month, to be paid only on a deemed liquidation
event, Series B has no dividends, and Series C has cumulative accrued cash dividends
of 1.00% per month. How could we ?nd the conversion order now? The RV would a function
of T for Series A and Series C, but not for Series B. Then, the RVPS for each Series would be
RVPS
A
ðTÞ 5ð1 10:24T
A
Þ Ã $0:6 5
1 10:12 Ã ðT 12Þ
à $0:6
5$0:888 10:144T
ð15:27Þ
RVPS
B
ðTÞ 5$1:2 ð15:28Þ
RVPS
C
ðTÞ 5ð1 10:12TÞ Ã $1:0 5$1 10:12T ð15:29Þ
’
15.4 DIVIDENDS IN LATER ROUNDS 283
Now, because these RVPS for each series change with time at differing rates,
the conversion order will not be constant over time. At T 50, RVPS for Series
AÀC are $0.888, $1.20, and $1.00, so we have the same conversion order as in the
Example 15.3: A, C, B. But note that Series A has the highest slope (0.144) and
Series B has the lowest (0). Thus, RVPS for A and C will eventually surpass that for
B as time passes, and moreover RVPS for A will eventually overtake that for C.
Speci?cally, when T.1.67, the Series C RVPS would be above $1.20, so B would
convert before C. When T .2.17, the Series A RVPS would be above $1.20, so B
would convert before A. Finally, when T.4.67, the Series A RVPS would be
above the Series C RVPS, so C would convert before A. From this point forward,
the conversion order would be B, C, A—a complete reversal of the order when
T50. With conversion order changing, we would need different exit diagrams and
exit equations for different ranges of T. At this point, it is no longer very helpful to
draw these diagrams, but the VCV model can still compute the valuations.
15.4.2 PIK Dividends
PIK (payment-in-kind) dividends are paid in stock. Each PIK dividend adds to
the number of shares held by the investor, which will increase both the RV of the
shares (using the same OPP as the investment) and the fraction of the company to
be owned on conversion. These two changes combine to make the conversion
conditions and exit diagrams a bit more complex than they are for accrued cash
dividends.
EXAMPLE 15.4
We begin with the same setup as in Example 15.3. Owl invests $10M in Series C for 10M
shares of CP (APP 5$10M). The other investors are (1) the employees, who have claims on
10M shares of common; (2) the Series A investors, EBV, who have 10M shares of CP for
$6M APP; and (3) the Series B investors, Talltree, who have 10M shares of CP for $12M
APP. The Series C has a liquidation preference to Series B, which in turn has a liquidation
preference to Series A. The difference between this case and Example 15.3 is in the divi-
dends: here, all preferred investors—Series A, B, and C—have cumulative PIK dividends of
1 percent per month.
Problem Find the conversion order and conversion conditions for all investors.
Solution We ?rst solve for the conversion order. As in Example 15.3, we can write the
RVPS for each Series “X” as
RV
X
ðTÞ 5RV
X
ðat issue of Series XÞ Ã ð1 10:12T
X
Þ: ð15:30Þ
Unlike Example 15.3, in this case we must also take account of a change in the number
of shares, which are also growing (through PIK dividends) at a rate of 0.12 per year. The
good news is that the increase in the number of shares will exactly cancel out the increase in
RV, so that the RVPS for each series will not be a function of T:
284 CHAPTER 15 LATER-ROUND INVESTMENTS
Series ARVPSðTÞ 5ð1 10:12T
A
Þ Ã $6M=½ð1 10:12T
A
Þ Ã 10M? 5$0:60 ð15:31Þ
Series B RVPSðTÞ 5ð1 10:12T
B
Þ Ã $12M=½ð1 10:12T
B
Þ Ã 10M? 5$1:20 ð15:32Þ
Series CRVPSðTÞ 5ð1 10:12TÞ Ã $10M=½ð1 10:12TÞ Ã 10M? 5$1:00: ð15:33Þ
Because these are the same RVPS found in Example 15.2, the conversion order will
not be affected and will always be A, C, B. The conversion conditions will change, however,
because ownership fractions (slopes) will change over time, as will the RVs. Denote the
fraction of the ?rm to be held on conversion by Series X as F
X
(T). Then, we can write the
conversion conditions as
Series A conversion condition:
F
A
ðTÞ Ã ½W 2RV
B
ðTÞ 2RV
C
ðTÞ? .RV
A
ðTÞ-
W
A
5RV
A
ðTÞ=F
A
ðTÞ 1RV
B
ðTÞ 1RV
C
ðTÞ;
ð15:34Þ
Series C conversion condition:
F
C
ðTÞ Ã ½W 2RV
B
ðTÞ? .RV
C
ðTÞ-W
C
5RV
C
ðTÞ=F
C
ðTÞ 1RV
B
ðTÞ; ð15:35Þ
Series B conversion condition:
F
B
ðTÞ Ã W .RV
B
ðTÞ-W
B
5RV
B
ðTÞ=F
B
ðTÞ: ð15:36Þ
’
If we were to take this solution to the next logical step, we could draw an exit
diagram for the Series C. This diagram would be identical to Exhibit 15-5, except
now the conversion points and the slopes would be a function of T and use
Equations (15.35), and (15.36). These conversion points then serve as strike prices
for the underlying random-expiration options, with the fractions of these options
determined by the time-varying slopes. Again, although this might look dif?cult to
solve, the VCV model does not mind. As in the earlier example, things get messier
if the investors have different PIK dividends, or if there is a mixture of PIK divi-
dends with accrued cash dividends. Although these complex structures do not yield
helpful exit diagrams, we can still use the VCV model to value them.
15.5 BEYOND SERIES C
From a theoretical perspective, there is nothing new in later round transactions. We
can follow the same steps as used to compute LP valuation in Series A, B, and C. In
this section, we review these steps in the context of a Series F round.
EXAMPLE 15.5
Begin with the same setup as in Example 15.2. Assume that Owl chose Structure 2 and
invested $10M in a Series C round for CP. Following Series C, there were three more rounds
of investment, each for CP, and each made by a separate VC. The details of all rounds are
given below. Liquidation preferences are in reverse order of investment, with F before E
before D, and so on. Assume that Series D, E, and F investors all have committed capital of
$100M investment capital of $80M and carried interest of 20 percent. None of the investors
have any dividends.
15.5 BEYOND SERIES C 285
Series A: $6M for 10M shares (EBV)
Series B: $12M for 10M shares (Talltree)
Series C: $10M for 10M shares (Owl)
Series D: $10M for 10M shares (2X liquidation preference) (Series D investors)
Series E: $10M for 10M shares (3X liquidation preference) (Series E investors)
Series F: $25M for 10M shares (Series F investors)
Problems
(a) What is the conversion order for these investors?
(b) What is formula for the partial valuation of the Series A?
(c) Suppose that the total valuation is $100M. Use the VCV model to compute the LP
valuation for each series.
Solution
(a) For a company with six rounds of investment, we are very happy to have the conversion-
order shortcut. To compute the RVPS for Series D and E, we must not forget the excess
liquidation preferences, which imply redemption values of $20M for Series D and $30M for
Series E. Otherwise, the calculations are similar to those in earlier examples. The RVPS for
each Series is
Series A : $6M=10M5$0:60 ð15:37Þ
Series B : $12M=10M5$1:20 ð15:38Þ
Series C : $10M=10M5$1:00 ð15:39Þ
Series D : $20M=10M5$2:00 ð15:40Þ
Series E : $30M=10M5$3:00 ð15:41Þ
Series F : $25M=10M5$2:50 ð15:42Þ
This implies an order of conversion of A, C, B, D, F, E.
(b) Series A converts ?rst, so as each series converts after it, EBV’s share of the common
stock changes. Because the founders own 10M shares and all series also convert to 10M
shares, EBV’s share will be one-half upon conversion and then will fall to one-third, one-
fourth, one-?fth, one-sixth, and one-seventh with each successive conversion. This will lead
to an exit diagram with many slope changes. To determine the points of these slope changes,
we must compute the conversion conditions for each series. For each series Z, the conversion
condition is computed as
ðFraction of firm owned by Series Z on conversionÞ
à ð$W2total redemption value for all series that convert after Series ZÞ
.total redemption value for Series Z:
ð15:43Þ
These conversion conditions are given following for each series, in the conversion
order as determined by the RVPS:
Series A conversion condition : 1=2 Ã ðW 297Þ .6-W
A
5$109 M ð15:44Þ
286 CHAPTER 15 LATER-ROUND INVESTMENTS
Series C conversion condition : 1=3 Ã ðW 287Þ .10-W
C
5$117 M ð15:45Þ
Series B conversion condition : 1=4 Ã ðW 275Þ .12-W
B
5$123 M ð15:46Þ
Series D conversion condition : 1=5 Ã ðW 255Þ .20-W
D
5$155 M ð15:47Þ
Series F conversion condition : 1=6 Ã ðW 230Þ .25-W
F
5$180 M ð15:48Þ
Series E conversion condition : 1=7 Ã W .30-W
E
5$210M ð15:49Þ
Under these conditions, the exit diagram for Series A is as shown in Exhibit 15-7.
EXHIBIT 15-7
EXIT DIAGRAM FOR SERIES A, AFTER SERIES F
S
l
o
p
e
?
1
/
2
S
l
o
p
e
?
1
/
3
S
lo
p
e
?
1
/4
S
lo
p
e
?
1
/5
Slope ? 1/6
Slope ? 1/7
97 103 109 117 123
$W
155 180 210
S
e
r
i
e
s
A
EXHIBIT 15-8
LP VALUATIONS FROM AUTO CALCULATOR
A B C D E F Founders
Security Type CP CP CP CP CP CP C
Investment ($M) $6.00 $12.00 $10.00 $10.00 $10.00 $25.00
Shares (M) 10 10 10 10 10 10 10
Liquidation Pref (X) 1 1 1 2 3 1
APP ($M) $6.00 $12.00 $10.00 $10.00 $10.00 $25.00
LP Cost ($M) $7.50 $15.00 $12.01 $12.50 $12.50 $31.25
Partial Valuation ($M) $10.07 $10.79 $11.04 $14.07 $20.77 $23.33
GP Valuation ($M) $1.01 $1.08 $1.43 $1.41 $2.08 $2.33
LP Valuation ($M) $9.06 $9.71 $9.60 $12.66 $18.69 $21.00
15.5 BEYOND SERIES C 287
We can read Exhibit 15-7 to obtain the partial valuation of the Series A as follows.
Partial valuation of the Series A
5Cð97Þ 2Cð103Þ 11=2 Ã Cð109Þ 21=6 Ã Cð117Þ 21=12 Ã Cð123Þ
21=20 Ã Cð155Þ 21=30 Ã Cð180Þ 21=42 Ã Cð210Þ:
ð15:50Þ
(c) The LP valuations for all series are given in the (partial) output from the VCV model in
Exhibit 15-8. ’
SUMMARY
Later-round investments provide the most important and interesting environment for our
valuation techniques. To extend our analysis to these later rounds, it is necessary to ?rst
determine the conversion order for the various classes of preferred stock. In this chapter, we
learned how to do this by using the redemption value per share (RVPS) for each class. Once
the conversion order is established, we can compute the conversion conditions for each class
and then use these conditions to draw and read exit diagrams. Dividends can introduce
complications for the drawing of exit diagrams, but these complications are easily handled by
the VCV model.
KEY TERMS
Redemption Value per Share
(RVPS)
Conversion-order
shortcut
EXERCISES
15.1 Consider the following four CP investors:
(1) Series A: $5M APP (and 2X liquidation preference) or converts to 5M shares;
(2) Series B: $10M APP or converts to 8M shares;
(3) Series C: $10M APP or converts to 5M shares;
(4) Series D: $5M APP or converts to 10M shares.
In addition to these investors, the founders hold 10M shares of common.
(a) Find the conversion order for these investors.
(b) Find the conversion conditions for these investors.
(c) Draw and read the exit diagrams following the Series D investment.
(d) Assume that total valuation is $50M. Compute the LP valuation for each series.
15.2 Using the same setup as Example 15.1, compute the LP valuation equation for the
Series A investors (EBV) under Structures 1 and 2 for Series B. For the same range of total
288 CHAPTER 15 LATER-ROUND INVESTMENTS
valuations considered in Exhibit 15-3, which structure would EBV prefer that Talltree
choose?
15.3 Using the same setup as Example 15.2,
(a) Compute the LP valuation for the Series B investors (Talltree) under Structures 1 and 2
for Series C. For the same range of total valuations considered in Exhibit 15-6, which
structure would Talltree prefer that Owl choose?
(b) Compute the LP valuation for the Series A investors (EBV) under Structures 1 and 2 for
Series C. For the same range of total valuations considered in Exhibit 15-6, which
structure would EBV prefer that Owl choose?
15.4 Draw the exit diagrams for Series B-F for Example 15.5.
EXERCISES 289
CHAPTER 16
PARTICIPATING CONVERTIBLE
PREFERRED STOCK
AS FIRST SEEN in Chapter 9, participating convertible preferred stock
(PCP) is a hybrid between an RP plus common structure and a plain common-stock
structure. In a PCP transaction, the investor is allowed to redeem his stock and also
to “participate” in the proceeds paid to the common stock as though he had con-
verted. If the proceeds of any exit reach some preset threshold, then the redemption
component of the PCP goes away, and the investor is forced to convert all the
shares to common. Thus, above this threshold, PCP is just like common stock.
Typically, such thresholds will be stated as a “quali?ed IPO” or as a “quali?ed IPO
or sale”, with a speci?c numerical share price. Sometimes, the threshold may be set
explicitly as a 5X or 10X return, or as a compounded annualized return so that the
threshold changes with the length of the holding period. Furthermore, there may
be an upper limit on the liquidation return, giving rise to the participating con-
vertible preferred with cap (PCPC) structure.
Although simpler CP structures are the norm in rising markets, PCP struc-
tures become more popular in falling markets. For example, during the VC
downturn in the postboom period, PCP structures became very popular, as did
many other investor-favorable terms such as liquidation preferences and antidilu-
tion rights.
1
In general, in falling markets entrepreneurs are often slow to accept the
lower value in their companies, and VCs employ a variety of structures—including
PCP—to maximize as-converted per-share prices while still receiving enough value
to justify the investment.
The de?nition of PCP used here is historically accurate, but some VCs use
“PCP” to mean the same thing as “RP 1 common”. For this usage, we can just
think of the PCP threshold as being set to in?nity, thus making it equivalent to RP
1 common. In this chapter, we use the more ?exible de?nition of PCP that allows
1
See Kaplan and Stromberg (2003) and Asset Alternatives (2005).
290
for a ?nite threshold. To solve for the partial valuation of PCP structures, we
include binary options in the valuation equations. These binary options are intro-
duced in Section 16.1. Section 16.2 demonstrates an investment recommendation
for a Series A PCP investment, Section 16.3 does the same for a PCPC structure,
and Section 16.4 shows how to extend the analysis to later rounds.
16.1 BINARY OPTIONS
To value PCP, we ?rst need to discuss the valuation of binary options. Binary
options pay some ?xed amount (K) if the stock price (S) is above the exercise
price (X) on the expiration date (T). Thus, an exit diagram for a binary option looks
like Exhibit 16-1.
The formula for the pricing of binary options looks similar to the second part
of the Black-Scholes formula 5 KÃ e
2rT
à N(d2), where N(d2) is de?ned the same
way as in Equation (13.13).
In our applications, we will use random-expiration binary calls. Like the
random expiration calls introduced in Chapter 13, we can price an RE binary call by
integrating a regular binary call over time. The formula for an RE binary call,
which we write as K Ã BC(X), is
K Ã BC ðXÞ 5
Z
N
0
Ke
2rT
Nðd
2
Þ Ã qe
2qT
dT ð16:1Þ
where q 5 1/H is the continuous-time probability of expiration, and H is the
expected holding period.
EXHIBIT 16-1
EXIT DIAGRAM FOR A BINARY OPTION
X
K
$W
B
i
n
a
r
y
C
a
l
l
a
t
E
x
p
i
r
a
t
i
o
n
16.1 BINARY OPTIONS 291
EXAMPLE 16.1
Suppose EBV makes a Series A investment in Newco and simultaneously offers the
employees a bonus pool of $5M on any exit where ?rm value exceeds $200M. Currently, the
?rm value of Newco is $40M, and base-case option-pricing assumptions apply.
Problem What is the current value of this bonus incentive?
Solution Under the assumption that the exit date remains independent of the ?rm value,
then we can value this incentive as an RE binary call, with K set to $5M. The FLEX Cal-
culator can be used for this computation. We ?nd a value of $0.12M. ’
16.2 THE VALUATION OF PCP
EXAMPLE 16.2
Suppose that EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCP, with a threshold ?ve times APP (5 $6 per
common share upon conversion). The employees of Newco hold 10M shares of common
stock. Thus, following the Series A investment, Newco will have 10M common shares
outstanding and would have 15M shares outstanding on conversion of the PCP.
Problems
(a) Solve for the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
Solutions
(a) As we have now seen many times in previous chapters, the LP cost for EBV on a $6M
investment is (100/80) Ã $6M 5 $7.5M.
(b) The threshold requires a price of $6 per share (as converted). This implies value of 15M
à $6 5$90M for the whole ?rm. Below the threshold, PCP looks like RP plus common. EBV
receives the ?rst $6M in proceeds for the RP. Following this redemption, EBV owns one-
third of the common stock (5M out of 15M shares).
The only difference between PCP and RP 1 common is that there is a drop in value at
the threshold. Below the threshold, the Series A would receive $6M for redemption plus one-
third of the remaining proceeds: 1/3 Ã (W 2 6). At W 5 90, this total value is
Value of PCP at W 590ðbefore dropÞ 56 11=3 Ã ð90 26Þ 5$34M: ð16:2Þ
Immediately above the threshold, the Series A would no longer receive any redemp-
tion value and would instead be forced to convert and to receive exactly one-third of the
292 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
proceeds. At W 5 90, this share would be worth 1/3 Ã 90 5 $30M. Thus, there is a 34M 2
30M 5 $4M drop at the threshold.
We are now prepared to draw the exit diagram for the Series A, as in Exhibit 16-2.
We can read this diagram as
Partial valuation of Series A5V 22=3 Ã Cð6Þ 24 Ã BCð90Þ: ð16:3Þ
With our now-standard estimate of GP% 5 0.10 for EBV, we have
LP valuation of Series A50:9 Ã ðV 22=3 Ã Cð6Þ 24 Ã BCð90ÞÞ: ð16:4Þ
(c) We can use the VCV model to compute the breakeven valuation as $18.60M.
(d) Exhibit 16-3 shows the sensitivity of the breakeven valuation to various assumptions for
volatility and the expected holding period.
EXHIBIT 16-2
EXIT DIAGRAM FOR THE SERIES A PCP
6 90
30
34
$W
S
e
r
i
e
s
A
P
C
P
S
lo
p
e
=
1
/3
S
lo
p
e
=
1
/3
4
EXHIBIT 16-3
SENSITIVITY ANALYSIS FOR BREAKEVEN VALUATION
Volatility
60% 90% 120%
Expected 3 15.73 17.14 18.49
Holding 5 16.96 18.60 19.98
Period (years) 7 17.90 19.57 20.89
16.2 THE VALUATION OF PCP 293
These sensitivities are similar to those in the RP 1 common structure analyzed in
Example 14.1. The only thing that keeps PCP from being identical to an RP 1 common
structure is the inclusion of the threshold, priced as a binary option in Equation (16.3).
For a total valuation of $20M and base-case option-pricing assumptions, the value of
this binary option, 4 Ã BC(90), is about $0.11M. Whereas standard options increase in value
when volatility increases, binary options do the reverse. For higher levels of volatility, the
value of the binary option decreases, and the PCP structure converges to an RP 1 common
structure. Indeed, as volatility goes to in?nity, all structures will look the same as plain
common stock. Readers are encouraged to experiment with the FLEX Calculator to con?rm
these relationships.
’
16.3 THE VALUATION OF PCPC
PCPC structures include a cap for the liquidation return. In most cases, this cap is
low enough so that conversion occurs by choice at or below the QPO. When
conversion is by choice and occurs at levels below the QPO, the exit diagram will
be smooth, and no binary options need be included in the exit equation. The fol-
lowing example illustrates this case.
EXAMPLE 16.3
Suppose EBV is considering a $6M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCPC, with a threshold at ?ve times APP (5 $6 per
common share on conversion). Furthermore, the liquidation value of the PCPC is capped at
four times the APP (5 $24M). The employees of Newco hold 10M shares of common stock.
Thus, following the Series A investment, Newco will have 10M common shares outstanding
and would have 15M shares outstanding on conversion of the PCP. (Note that this is the same
setup as Example 16.2, with the additional cap at four times APP.)
Problems
(a) Solve for the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
Solutions
(a) As in Example 16.2, the LP cost is $7.5M.
(b) With PCPC, EBV faces a similar decision—redeem or convert—as it would with plain
CP. When we ?rst analyzed PCPCstructures in Chapter 9, we demonstrated that the ?rst step is
to check whether conversion will be mandatory (at the QPO) or voluntary (using a conversion
condition). In this case, mandatory conversion would occur at $6 per share. With 15M shares
outstanding, this QPO would occur when W 5 15M Ã $6 5 $90M.
294 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
The (voluntary) conversion condition for the PCPC is
1=3 Ã W .24-W
A
572: ð16:5Þ
Because Equation (16.5) yields a conversion point ($72M) lower than the mandatory
QPO conversion ($90M), the latter is a redundant and nonbinding constraint: only the
voluntary conversion will matter.
Our next step is to determine the cap point. Because EBV receives the ?rst $6M plus
one-third of the remaining proceeds, the 4X (5 $24M) cap point is
6 11=3ðW 26Þ 524-W
A
ðcapÞ 560M: ð16:6Þ
Using this conversion condition and cap, we can drawthe exit diagramas in Exhibit 16-4.
We can read Exhibit 16-4 as
Partial valuation of Series A5V 22=3 Ã Cð6Þ 21=3 Ã Cð60Þ 11=3 Ã Cð72Þ: ð16:7Þ
Thus, the LP valuation equation for EBV is
LP valuation of Series A50:9 Ã ½V 22=3 Ã Cð6Þ 21=3 Ã Cð60Þ 11=3 Ã Cð72Þ?: ð16:8Þ
(c) We can use the VCV model to compute the breakeven valuation as $18.75M. This is only
$0.15M more than the cutoff without the cap found in Example 16.2.
’
For some applications, it is helpful to express the conversion condition in per-
share terms. Once we do this, we can insert the PCPC into a conversion order.
Although that is not necessary for a Series A investment, it can be useful in later
rounds. In Example 16.3, we could do this by computing
RVPS of Series A PCPC ðat capÞ 5$24M=5M5$4:80 per share: ð16:9Þ
EXHIBIT 16-4
EXIT DIAGRAM FOR SERIES A PCPC
6 60 72
$W
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=
1
/3
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=
1
/3
16.3 THE VALUATION OF PCPC 295
Similarly, we could express the per-share value of the common stock at the cap
by subtracting the APP from the cap and dividing by the number of common shares:
Per-share cap5ð$24M2$6MÞ=5M5$3:60 per share: ð16:10Þ
In words, Equation (16.10) means “the Series A PCPC hits its liquidation cap
when the value of common stock is $3.60 per share”.
Notice that we were able to solve Example 16.3 without using binary options
because voluntary conversion at (W 5 72M) occurred before the QPO (at $90M, as
computed in Example 16.2). If, instead, mandatory conversion at the QPO occurred
at a lower point than voluntary conversion, then binary options will be included. In
those cases, we still must ?nd the cap point because it is possible (but unusual)
for the cap to occur at a point below the QPO. In Example 16.3, this could only
occur if the cap was between 5 and 5.67 times APP. For example, with a cap of 5.5
times APP, the liquidation return would be capped at 5.5 Ã 6M5$33M. The RVPS
for voluntary conversion would be at $33M/5M 5 $6.60 per share, which is higher
than the QPO threshold. Then, the QPO threshold would be the binding constraint.
Nevertheless, we would also have a cap point at
33 56 11=3 Ã ðW 26Þ-W
A
ðcapÞ 587: ð16:11Þ
Thus, at W 5 87, the exit line would go ?at until the QPO at W 5 90, when it
would drop in value from $33M (the cap) to $30M (after conversion).
16.4 SERIES B AND BEYOND
To value PCP in later rounds, we follow the same steps as shown in Chapter 15. If
there are multiple rounds of PCP, then one must be careful to consider the impli-
cations of different QPO thresholds.
EXAMPLE 16.4
Suppose EBV made the transaction as described in Example 16.2. It is now one year later, and
Talltree is considering a $12M Series B investment in Newco. Talltree is considering two
possible structures for the Series B. In Structure 1, Talltree would receive RP ($10M APP) plus
5M shares of common stock. In Structure 2, Talltree would receive 5M shares of PCP with a
threshold of $12 per share. The founders of Newco, who will continue with the ?rm, currently
hold 10Mshares of common stock, and EBVholds 5Mshares of PCP (as-if converted). Talltree
has carried interest of 20 percent, committed capital of $250M, and lifetime fees of $50M.
Problems
(a) Compute the LP cost for the Series B.
(b) What is the LP valuation equation and breakeven valuation for Structure 1?
(c) What is the LP valuation equation and breakeven valuation for Structure 2?
296 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
(d) Plot the LP valuation for both structures for a range of total valuations. For what total
valuation should Talltree be indifferent between the two structures?
Solutions
(a) Because Talltree has committed capital of $250M and lifetime fees of $50M, its
investment capital is $200M and we can compute LP cost as
LP cost 5ð250=200Þ Ã $12M5$15M: ð16:12Þ
(b) To compute LP valuation, we ?rst draw an exit diagram for the Series B. With the RP 1
common structure, Talltree would receive the ?rst $10M of proceeds to redeem the RP, and
EBV (Series A) would receive the next $6M to redeem the PCP. Following these redemp-
tions, there would be 20M shares of common stock, with 5M held by Talltree. Thus, Talltree
would receive one-fourth of the proceeds beyond $16M. The only complication occurs on a
QPO, when EBV must return $6M to the ?rm. This Series A threshold is set at $6 per
common share. With 20M common shares and a $10M redemption for the Series B, total
proceeds at this QPO must be at least 20M Ã $6 1 $10M 5 $130M. Because the $6M
windfall will be shared by all common holders, it provides a jump of $6M Ã 1/4 5 $1.5M for
the Series B.
We can draw the exit diagram for the Series B, Structure 1 as in Exhibit 16-5.
We can read Exhibit 16-5 as
Partial valuation of Series B ðStructure 1Þ
5V 2Cð10Þ 11=4 Ã Cð16Þ 13=2 Ã BCð130Þ:
ð16:13Þ
The LP valuation equation is
LP valuation of Series B ðStructure 1Þ 50:9 Ã ½V 2Cð10Þ 11=4 Ã Cð16Þ
13=2 Ã BCð130Þ?:
ð16:14Þ
We can use the VCV model to compute the breakeven valuation as $49.63M.
EXHIBIT 16-5
EXIT DIAGRAM FOR SERIES B, STRUCTURE 1
10 16 130
$W
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1
3/2
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1
/4
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1
/4
16.4 SERIES B AND BEYOND 297
(c) To compute LP valuation, we ?rst draw an exit diagram for the PCP. For the Series B, a
quali?ed IPO or sale requires a price of $12 per share (as-if converted). This implies a value
of 20M Ã $12 5 $240M for the whole ?rm. We refer to $240M as the “Series B threshold”.
Below the Series B threshold, Structure 2 looks similar to Structure 1, except that that RV of
the Series B is $12M here, as compared to $10M in Structure 1. This yields a $2M difference
in the strike price of all the options (as compared to Structure 1), including a change in the
Series A threshold from $130M in Structure 1 to $132M in Structure 2. The other difference
between Structures 1 and 2 is that there is a drop in value above the Series B threshold.
Below the Series B threshold, the Series B PCP would receive $12M for redemption plus
one-fourth of the remaining proceeds: 1/4 Ã (W 2 12). At W 5 240, this total value is
Value of Structure 2 at W 5240 ðbefore dropÞ 512 11=4 Ã ð240 212Þ
569M:
ð16:15Þ
Immediately above the Series B threshold, the PCP would no longer receive any
redemption value and would instead be forced to convert and to receive exactly one-fourth of
the proceeds.
At W 5 240, this share would be worth 1/4 Ã 240 5 $60M. Thus, there is a 69M 2
60M 5 $9M drop at the threshold.
We are nowprepared to drawthe exit diagramfor the Series B, Structure 2 (Exhibit 16-6).
We can read Exhibit 16-6 as
Partial Valuation of Series B ðStructure 2Þ
5V 2Cð12Þ 11=4 Ã Cð18Þ 13=2 Ã BCð132Þ 29 Ã BCð240Þ:
ð16:16Þ
This implies an LP valuation equation of
LP valuation of Series B ðStructure 2Þ
50:9 Ã ½V 2Cð12Þ 11=4 Ã Cð18Þ 13=2 Ã BCð132Þ 29 Ã BCð240Þ?:
ð16:17Þ
EXHIBIT 16-6
EXIT DIAGRAM FOR SERIES B, STRUCTURE 2
12 18 132 240
9
3/2
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298 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
We can use the VCV model to compute the breakeven valuation as $47.11M.
(d) Exhibit 16-7 shows the sensitivity of LP valuation to different total valuations. Notice
that the values of the two structures are very similar.
We begin the sensitivity diagram for a total valuation close to the cutoff level for both
structures. Above this level, although it is dif?cult to tell the two lines apart, the numbers
indicate the Structure 2 has a slightly higher LP valuation than Structure 1 for virtually all the
range. It is not until the very end—for total valuations close to $148M, that Structure 1 has a
slight advantage. This situation is ideal for the VC because he can con?dently accept
whichever of these structures is more preferred by the entrepreneur.
’
This example illustrates a general rule that can be used in analyzing all PCP
structures. Any Series X PCP that hits its threshold will return the RV of that Series
X (5 RV
X
) to be split among all the common stock holders. If the holder of a
Series Y holds some fraction y of the common stock, then the Series Y will receive
a one-time jump of y à RV
X
at the Series X threshold. For Series X itself, there will
be a drop of RV
X
, but this drop will be reduced by the increase of x à RV
X
, where x
is the fraction of the common stock held by Series X. Thus, the total drop for Series
X at the Series X threshold will be equal to (1 2x) Ã RV
X
.
We next consider a multiround example with both PCP and PCPC along with
several rounds of CP. To solve this example, we must merge the conversion order
EXHIBIT 16-7
LP VALUATION AND COST OF SERIES B, STRUCTURES 1 & 2
Structure 1
Structure 2
LP cost
45
35
25
15
40
30
20
10
5
0
L
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a
t
i
o
n
a
n
d
c
o
s
t
o
f
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s
B
50 75 100
Total valuation of Newco
125 150
16.4 SERIES B AND BEYOND 299
shortcut of Chapter 15 (using RVPS) with the complexities of participation
thresholds and caps.
EXAMPLE 16.5
Talltree is considering a $20M Series F investment in Newco for 10M shares of PCP with a
QPO threshold of $6 per share. The details of the prior rounds are
Series A: 10M shares of CP ($6M APP)
Series B: 10M shares of CP ($10M APP)
Series C: 10M shares of CP ($4M APP and a 3X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 3X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($10M APP).
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. None of these investors are covered by any antidilution
protections. In the event of a liquidation, the preferred stock is redeemed in reverse order of
investment (i.e., the Series F has a preference to the Series E, which has a preference to the
Series D, and so on). In addition to these investors, the employees have claims on 20M shares
of common stock.
Problems
(a) Draw and read the exit diagram for the Series D PCPC.
(b) Compute the breakeven valuation for the Series F under base-case assumptions.
Solutions
(a) First, we ?nd the conversion order for the CP. In order of the RVPS of the CP, we have
Series A: $6M/10M 5 $0.60
Series B: $10M/10M 5 $1.00
Series C: $12M/10M 5 $1.20
Series E: $10M/10M 5 $1.00.
We next add the PCP and PCPC to the ordering. For the Series F PCP, automatic
conversion occurs at a QPO of $6 per share. Because the highest RVPS is $1.20 per share, this
threshold is higher than all conversion points for the CP.
For the Series D PCPC, we ?rst determine if conversion is voluntary or automatic.
Voluntary conversion occurs at the RVPS, with the cap used as the redemption value. Auto-
matic conversion occurs at the QPOof $5. This yields a Series Dconversion at the lesser of the
voluntary conversion at $30M/10M5$3.00 or the automatic conversion at the QPO 5$5.00.
Thus, the QPO threshold is redundant, and conversion will occur voluntarily at $3 per
share, after all the CP has converted (the highest RVPS is $1.20 per share), but before the
Series F PCP at $6 per share.
Finally, we compute the cap point. To make comparisons with the conversion order, it
is helpful to compute this point on a per-share basis. When the PCPC is liquidated, the
holders receive $10M for the liquidation, plus value from the common stock of 10M Ã per-
share value. The cap is reached when
300 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
Series D cap point 5W
D
ðcapÞ 5$10M110M Ã per-share cap 5$30M: ð16:18Þ
Solving for the per-share cap yields
ð$30M2$10MÞ=10M5per-share cap 5$2:00: ð16:19Þ
Thus, the cap will be reached after all the CP has converted, because $2.00 is higher
than the RVPS for each CP series. Taken together, these calculations imply a conversion and
cap order of A ($0.60), B and E together ($1.00), C ($1.20), D (cap) ($2.00), D (conversion)
($3.00), and F ($6.00).
When Series A converts, there will be 50M shares outstanding: 20M from the
employees, 10M each from Series D and Series F (as-if conversion), and the 10M for Series A.
Thus, we can compute the Series A conversion conditions as
Series A conversion condition :1=5 Ã ðW 262Þ .6 -W
A
5$92M: ð16:20Þ
Series B and E convert at the same time, followed by Series C:
Series B conversion condition : 1=7 Ã ðW 242Þ .10-W
B
5$112M; ð16:21Þ
Series E conversion condition : 1=7 Ã ðW 242Þ .10-W
E
5$112M; ð16:22Þ
Series C conversion condition : 1=8 Ã ðW 230Þ .12-W
C
5$126M: ð16:23Þ
Next in order is the Series D cap, followed by the Series D voluntary conversion.
Series D cap : 10 11=8 Ã ðW 230Þ 530 -W
D
ðcapÞ 5$190M; ð16:24Þ
Series D conversion condition : 1=8 Ã ðW 220Þ .30-W
D
5$260M: ð16:25Þ
EXHIBIT 16-8
EXIT DIAGRAM FOR THE SERIES D
30 40 68 92 112 126 190 260 480
$W
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2.5
16.4 SERIES B AND BEYOND 301
For the PCP, the QPO of $6 per share occurs at
Series F conversion condition ðQPOÞ: 80M Ã $6 5W
F
5$480M: ð16:26Þ
At this QPO, Series F will return $20M to the other shareholders and recapture 1/8 Ã
$20M 5 $2.5M for themselves, for a net drop of $20M 2 $2.5M 5 $17.5M. With these
calculations in hand, we are almost ready to draw the exit diagram for the Series D. Because
Series D is paid after Series E and F, they receive no proceeds until W 5 $30M, then they
receive the next $10M, and then nothing until the common stock begins to pay off after all
liquidations are complete at W 5 $68M. From that point, Series D has as-if claims on 10M
shares for one-fourth of the proceeds (employees have 20M shares and Series F has 10M as-if
shares). This fraction then falls off as other series convert. At W 5 $190M, the Series D line
goes ?at, only increase again after voluntary conversion at W 5 $260. Finally, at W 5
$480M, the Series D investors receive $2.5M from the returned redemption value of the
Series F. We can read this diagram as
Partial valuation of the Series D
5Cð30Þ 2Cð40Þ 11=4 Ã Cð68Þ 21=20 Ã Cð92Þ 22=35 Ã Cð112Þ
21=56 Ã Cð126Þ 21=8 Ã Cð190Þ 11=8 Ã Cð260Þ 12:5 Ã BCð480Þ:
ð16:27Þ
(b) Note that over the range of 190 , W , 260, the PCPC is capped so the exit line is ?at.
Over this ?at range for the Series D, all the other common stock holders will receive pro-
ceeds as if the Series D shares did not exist, so their slopes will increase. This can be seen in
the exit diagram for the Series F in Exhibit 16-9.
EXHIBIT 16-9
EXIT DIAGRAM FOR THE SERIES F
20 68 92 112 126 190 260 480
$W
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17.5
302 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
We can read this diagram as
Partial valuation of the Series F
5V 2Cð20Þ 11=4 Ã Cð68Þ 21=20 Ã Cð92Þ 22=35 Ã Cð112Þ 21=56 Ã Cð126Þ
11=56 Ã Cð190Þ 21=56 Ã Cð260Þ 217:5 Ã BCð480Þ:
ð16:28Þ
The LP valuation of the Series F is 90 percent of Equation (16.28). The LP cost is (250/
200) Ã $20M 5 $25M. Finally, we can use the VCV model to compute the breakeven
valuation under base-case assumptions as $132.81M.
’
SUMMARY
Participating convertible preferred stock (PCP) is frequently used in VC transactions. PCP is
similar to structures that combine RP and common stock, with the main difference that the
RP component disappears for exits above some preset threshold. PCPC is a further re?ne-
ment of PCP, where there is a cap on the liquidation return. PCP can be valued by including
binary call options at the threshold points. For transactions where the threshold is far away
from the current valuation, there is little difference between PCP structures and RP plus
common structures. For transactions where the cap is close to the threshold, there is little
difference between PCPC and PCP.
KEY TERMS
Binary call option Random-Expiration
binary call option (BC(X))
REFERENCES
Asset Alternatives, 2005, Deal Terms Report, 2nd Edition, Dow Jones, Jersey City, NJ.
Kaplan, Steven N., and Per Stromberg, 2003, “Financial Contracting Theory Meets the Real World:
Evidence from Venture Capital Contracts”, Review of Economic Studies, April, 281À316.
EXERCISES
16.1 True, False, or Uncertain: Other things equal, the value of a binary call option
decreases as volatility increases.
16.2 Suppose EBV is considering a $5M Series A investment in Newco. EBV proposes to
structure the investment as 5M shares of PCP with a threshold at $3 per share. The employees
of Newco have claims on 15M shares of common stock. Thus, following the Series A
EXERCISES 303
investment, Newco will have 15M common shares outstanding, with another 5M shares on
conversion of the Series A.
(a) Compute the LP cost for this investment.
(b) Solve for the LP valuation equation for this investment.
(c) Find the breakeven valuation for the investment under base-case assumptions.
(d) Perform a sensitivity analysis for this breakeven valuation.
16.3 Consider the same setup as in Example 16.4, except that now there is an additional
possibility, Structure 3, where Talltree would receive 6M shares of CP with $12M APP.
(a) Perform a sensitivity analysis for the LP valuation of Structure 3 versus Structure 2 as a
function of total valuation.
(b) Suppose that total valuation is $100M. For what number of shares, Z, in Structure 3,
should Talltree be indifferent between Structures 2 and 3?
16.4 Consider the following four investors in Newco:
Series A: CP: $5M APP (and 2X liquidation preference) or converts to 5M shares
Series B: RP: $10M APP plus 5M shares of common
Series C: PCP: $10M APP and as-if conversion to 5M shares, with a threshold at
$10 per share
Series D: PCP: $20M APP and converts to 5M shares, with a threshold at $15 per share
In addition to these investors, the employees have claims on 10M shares of common.
All four VC investors have 20 percent carry, committed capital of $250M, and lifetime fees
of $50M. Following the Series D investment, all investors agree that the total valuation of the
?rm is $100M. Base-case option-pricing assumptions apply.
(a) Find the LP valuation equation for each Series.
(b) Compute the LP valuation for each Series.
304 CHAPTER 16 PARTICIPATING CONVERTIBLE PREFERRED STOCK
CHAPTER 17
IMPLIED VALUATION
IN CHAPTER 8, we showed how to calculate post-money valuation, which is
typically interpreted as “the market value of the company implied by the purchase
price in the current round”. For example, if a VC pays $5M to purchase CP
that would convert to one-third of the common stock, then the post-money
valuation would be $15M. From the post-money valuation, we can then compute
the pre-money valuation as the difference between the post-money valuation
and the new investment, which in this case would be $10M.
These simple calculations, although useful for the quick communication of some
critical terms, do not in fact provide an accurate market valuation for the com-
pany. The problem is that these calculations do not account for the special features
of preferred stock, and instead treat all investments as though they were common
stock. Furthermore, standard post-money valuation calculations ignore the extra
costs of management fees and carried interest. In Chapters 13 through 16 we
developed a framework for the valuation of preferred stock. As part of this frame-
work, we computed the breakeven valuation necessary to equate LP valuation and
LP cost. In this chapter, we reinterpret the breakeven valuation as the implied post-
valuation (IV
post
) of the company based on the actual transaction structure. This
implied post-valuation can then be used to estimate the market valuation—which we
call the implied valuation—for any investor’s stake.
Section 17.1 discusses the relationship between IV
post
and post-money
valuation and argues that the former is a more accurate measurement of market
value. This additional accuracy is useful for three reasons. First, strong voices in
the LP community are demanding more accurate interim valuation of companies
from their GPs. Because many of these valuations are inferred from recent
transactions, it is better to use implied post-valuation than post-money valuation.
An application to interim valuation is given in Section 17.2. Second, implied
valuations may also be necessary in contractual disputes, particularly those
focused on the de?nition of a down round. Section 17.3 shows how the concept of
implied valuation can be used to adjudicate such disputes. Third, recent changes in
tax and accounting standards have forced companies to set values for their com-
mon shares for the reporting of executive compensation. The methods introduced in
305
this chapter can be used to provide a rigorous method for estimating the “implied”
market value of this common stock, and can provide an input into the valuation of
executive stock options.
At this point in the book, we have introduced many different terms with
“valuation” as part of their name. In Section 17.4 we review these different terms
and provide some tips on their correct usage.
17.1 POST-MONEY VALUATION REVISITED
The post-money valuation of private companies is often interpreted analogously
to the enterprise value of public companies. For public companies, enterprise value
is computed by adding the market values of all outstanding securities of the com-
pany: common stock, preferred stock, and long-term debt. For many public
companies, it is possible to observe market values for all these securities, so
the computation is easy. For other companies, analysts must use nonmarket infor-
mation to estimate market values for nontraded components of the capital structure.
In any case, no analyst would ever assume that all the securities are equivalent to
common stock, and then just use common stock prices for everything. Nevertheless,
this is exactly what we do for private companies when we calculate post-money
valuation. If a VC pays $5M for CP that would convert to one-third of the common
stock, then we can only interpret post-money valuation as an enterprise value if
we think that each share of CP has the same value as each share of common. As we
know from the previous chapters, this is not correct.
To compute a more accurate version of enterprise value for VC-backed
companies, we use information from the most recent transaction to estimate the
market prices for each security in the capital structure. For example, consider
the value components for Newco after a Series A investment by EBV. Exhibit 17-1
gives a general depiction of the division of value among the LPs of EBV, the GPs
of EBV, and the employees of Newco. The partial valuation of the Series A is
the GP valuation plus the LP valuation. We learned in Chapter 14 how to ?nd the
values of any of these components, assuming that we knew the value of the whole
pie (total valuation). Here we want to answer a different question: Assuming that
EBV paid a fair price for its stake, what is the implied market value for the whole
pie? We write this implied market value as IV
post
Then, using IV
post
as the total
valuation, we can use three steps to solve for the implied valuation of any other
shareholders: (1) draw their exit diagram, (2) read their exit diagram into an exit
equation, and (3) solve their exit equation using IV
post
as the total valuation input
in the VCV model. In many applications, we can use shortcuts to make this pro-
cedure go much faster. Before describing these shortcuts, we do one example the
hard way.
306 CHAPTER 17 IMPLIED VALUATION
EXAMPLE 17.1
Newco has 10 million shares of common stock outstanding. The founder-employees claim
8M of these shares, and angel investors own the other 2M, which they bought for $1 per
share a year ago. Newco management believes that the time is right for a major expansion.
The expansion will require several million dollars over the following two years, but pre-
liminary conversations with VCs have reached an impasse over valuation and dilution of
the current owners. The founders are concerned about control and are thus reluctant to sell
more than 6M shares because doing so would leave them with less than 50 percent of the
business.
Furthermore, the founders also believe that the company has performed well over the
last year and should not have to drop from the $10M post-money valuation after the angel
investment ($1 per share and 10M shares outstanding). Other VCs have disagreed, believing
that the angel investors overpaid, because although the company is pro?table, the upside is
limited. After many failed negotiations with other VCs, Newco ?nally seems close to a deal
with EBV. EBV has offered $6M for RP ($5M APP) plus 6M shares of common stock. Base-
case option-pricing assumptions apply.
Problems Assuming this transaction goes through,
(a) What are the pre- and post-money valuations for Newco?
(b) What is the implied valuation of Newco (5IV
post
)?
(c) What is the implied valuation of the GP stake in Newco?
(d) What is the implied valuation of the angel shares? Has this value fallen since their
purchase one year ago?
(e) What is the implied valuation of the employee shares?
EXHIBIT 17-1
VALUE DIVISION AFTER SERIES A INVESTMENT
Employees
Series A LP
Valuation
Series A GP
Valuation
17.1 POST-MONEY VALUATION REVISITED 307
Solutions
(a) EBV is investing $6M for three-eighths of the common stock of Newco (6M/16M), so
the post-money valuation is $6M/(3/8) 5$16M. The pre-money valuation is $16 2
$6 5$10M.
(b) To ?nd the implied valuation of Newco, we must ?rst compute the formulas for the LP
cost and valuation. Because EBV has $100M of committed capital and $80M of investment
capital, the LP cost is (100/80) Ã $6M5$7.5M. The exit diagram for the Series A is given by
Exhibit 17-2.
We can read this diagram as
Partial valuation of the Series A5V 25=8 Ã Cð5Þ:
ð17:1Þ
Thus, the LP valuation is
LP valuation50:9 Ã ½V 25=8 Ã Cð5Þ?:
ð17:2Þ
Because EBV has “paid” LP cost for this stake, the implied valuation of Newco will be
the V in Equation (17.2) that equates LP valuation and LP cost:
$7:5M50:9 Ã ½IV
post
25=8 Ã Cð5Þ?:
ð17:3Þ
This is exactly the same procedure we use to ?nd the breakeven valuation. Thus, we
can use the VCV model to compute IV
post
5breakeven valuation 5$17.46M.
EXHIBIT 17-2
EXIT DIAGRAM FOR THE SERIES A
5
$W
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308 CHAPTER 17 IMPLIED VALUATION
(c) The GP valuation is
GP valuation 5Partial valuation 2LP valuation 50:1 Ã ½V 25=8 Ã Cð5Þ?:
ð17:4Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of GP stake as $0.83M. Note that we could also just use a shortcut to compute the
GP valuation as (0.1/0.9) Ã LP valuation, where LP valuation 5LP cost 5$7.50M.
(d) To ?nd the implied valuation of the angel shares, we solve for the partial valuation of the
angel shares and then use IV
post
as the total valuation. Because the angels own 2M shares out
of 16M total, the exit diagram for these shares is shown in Exhibit 17-3.
We can read this diagram as
Partial valuation of the angel shares 51=8 Ã Cð5Þ:
ð17:5Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of the angel shares as $1.83M. Because the angels purchased 2M shares for $2M
one year ago, this implied valuation represents a decrease in the value of the shares.
(e) To ?nd the implied valuation of the employee shares, we follow the same procedure as
in part (d). Because the employees have claims on 8M out of 16M shares, their exit diagram
is shown in Exhibit 17-4.
We can read this diagram as
Partial valuation of the employees’ shares 51=2 Ã Cð5Þ:
ð17:6Þ
Using a total valuation 5IV
post
5$17.46M, we can use VCV to compute the implied
valuation of the employee shares as $7.30M.
EXHIBIT 17-3
EXIT DIAGRAM FOR THE ANGEL SHARES
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17.1 POST-MONEY VALUATION REVISITED 309
’
After completing this example, it is easy to verify that the whole pie is the
sum of the slices: IV
post
5$7.50M1$0.83M1$1.83M1$7.30M5$17.46M.
Given that the whole must be the sum of the parts, we could have solved steps (c)
through (e) without using the VCV model—that is, we could solve these parts using
two additional equations: (1) GP valuation 50.1/0.9 Ã LP valuation; and (2) IV of
employee shares 54 Ã IV of angel shares.
17.2 MEASUREMENT OF PORTFOLIO VALUE
In the United States, there is no binding rule for the interim valuation of VC
investments. In practice, many GPs report all investments at cost for the quarterly
reporting to LPs unless there has been a new round of (outside) investment.
However, this practice has come under considerable criticism from the LP com-
munity in the past few years, with most of the criticism focused on the stale values
reported between rounds of ?nancing. The updates based on the actual ?nancing
events have garnered much less attention, as these events would appear to place a
“market” value on the companies. These market values, however, are usually based
on the post-money valuations, which, as we have seen, can be quite misleading as
measures of market value.
Although post-money valuation remains an important concept for quickly
communicating the basics of a transaction, it is simply not an appropriate market
EXHIBIT 17-4
EXIT DIAGRAM FOR THE EMPLOYEES’ SHARES
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310 CHAPTER 17 IMPLIED VALUATION
valuation measure for an honest analyst. Instead, the best estimate is the implied
valuation of the LP stake. Exhibit 17-5 displays the components of total value
following a Series B investment.
If we set the Series B LP valuation 5Series B LP cost, then we can use VCV
to solve for the breakeven valuation 5IV
post
. Then we can follow the same pro-
cedure as in Example 17.1 to compute the implied valuations for any other slice of
the pie. With all these new pieces ?oating around, it is helpful to introduce some
new terminology: after a Series Y investment, the implied LP valuation for
the Series X investment (X # Y) is the LP valuation for the Series X investment,
where the total valuation used for the calculation is set equal to the implied
valuation (IV
post
) after Series Y. Similarly, the implied GP valuation for the Series
X investment (X # Y) is the GP valuation for the Series X investment, where the
total valuation used for the calculation is set equal to the implied valuation (IV
post
)
after Series Y. Finally, the implied partial valuation for the Series X investment (X
# Y) is the partial valuation for the Series X investment, where the total valuation
used for the calculation is set equal to the implied valuation (IV
post
) after Series Y.
We can also write the implied partial valuation for Series X as implied LP
valuation 1implied GP valuation.
With these de?nitions in hand, we can also de?ne IV
pre
, the implied pre-
valuation, as representing the part of IV
post
that is owned by the previous investors.
For a Series Y investment, we can write IV
pre
as
IV
pre
5IV
post
2Series Y implied partial valuation
5IV
post
2Series Y implied LP valuation2Series Y implied GP valuation
EXHIBIT 17-5
VALUE DIVISION AFTER SERIES B INVESTMENT
Employees
Series A LP
Valuation
Series A GP
Valuation
Series B LP
Valuation
Series B GP
Valuation
17.2 MEASUREMENT OF PORTFOLIO VALUE 311
5IV
post
2Series Y LP cost 2Series Y implied GP valuation
5IV
post
2Series Y LP cost 2ðGP%=ð1 2GP%ÞÞ Ã Series Y LP cost
5IV
post
2Series Y LP cost=ð1 2GP%Þ: ð17:7Þ
We could also build IV
pre
from the bottom up. Suppose there has just been a
Series C investment. In this scenario,
IV
pre
5Series A implied partial valuation 1Series B implied partial valuation
1Employee stock implied partial valuation: ð17:8Þ
Let’s do another example.
EXAMPLE 17.2
Same setup as in Example 17.1, but now it is one year later, and Newco needs another
infusion of capital. Talltree is considering a $10M Series B investment for 8M shares of CP.
The option-pricing assumptions remain the same as in Example 17.1, except that now we
assume an expected holding period of four years. Talltree has 20 percent carried interest,
$250M of committed capital, and $50M of lifetime fees.
Problems
(a) After this round with Talltree, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) After this round by Talltree, what is the Series A implied LP valuation?
Solutions
(a) If Talltree pays $10M to purchase 8M shares, they would be purchasing 1/3 of the 24M
common shares outstanding (as-converted), making the post-money valuation $10M/
(1/3) 5$30M. Thus, the pre-money valuation is $30M 2 $10M5$20M.
(b) To compute the implied valuations, we must ?rst compute the formulas for the LP cost
and valuation. LP cost is (250/(250 250)) Ã $10M5$12.5M. Next, we need to ?nd the
conversion condition for Talltree. Because the Series B is the only CP in the capital structure,
we do not need to worry about conversion order. Talltree would receive 1/3 Ã (W25) if it
converts (the $5M is needed to redeem the Series A RP), and $10M if it redeems. Thus,
Talltree’s conversion condition for the Series B is
1=3 Ã ðW 25Þ.10-W
B
5$35M:
ð17:9Þ
The exit diagram for the Series B is given in Exhibit 17-6. We can read this diagram as
Partial valuation of the Series B5V 2Cð10Þ 11=3 Ã Cð35Þ:
ð17:10Þ
Thus, the LP valuation is
LP valuation 50:9 Ã ðV 2Cð10Þ 11=3 Ã Cð35ÞÞ:
ð17:11Þ
312 CHAPTER 17 IMPLIED VALUATION
Now, the ?nal step is to compute the implied post-valuation (5breakeven valuation).
We set LP cost 5LP valuation and solve for IV
post
:
$12:5M5ð0:9Þ Ã ðIV
post
2Cð10Þ 11=3 Ã Cð35ÞÞ:
ð17:12Þ
The VCV model yields a breakeven valuation 5IV
post
5$38.48M. To solve for IV
pre
,
we use Equation (17.7):
IV
pre
5IV
post
2Series B LP Cost=ð1 2GP%Þ
5$38:48M2$12:5M=0:9 5$24:59M:
ð17:13Þ
(c) The easy way to ?nd the implied LP valuation for Series A is to substitute a total
valuation of $38.48M into the AUTO Calculator, and then just look at the answer for the LP
valuation of Series A. Here we will do this calculation the hard way, by ?nding the equation
for this LP valuation and then solving this equation in the FLEX Calculator. We begin by
drawing the exit diagram for the Series A (Exhibit 17-7).
We can read this diagram as
Partial valuation of the Series A ðafter Series BÞ 5Cð10Þ 25=8 Cð15Þ 21=8 Ã Cð35Þ:
ð17:14Þ
This makes the LP valuation
LP valuation ðSeries A after Series BÞ 50:9 Ã ðCð10Þ 25=8 Cð15Þ 21=8 Ã Cð35ÞÞ:
ð17:15Þ
Using a total valuation 5IV
post
, we can use the FLEX Calculator to calculate this
implied LP valuation as $9.70.
EXHIBIT 17-6
EXIT DIAGRAM FOR SERIES B
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17.2 MEASUREMENT OF PORTFOLIO VALUE 313
’
17.3 DOWN ROUNDS?
Another important application of implied valuation occurs in the identi?cation of
down rounds. Although it can sometimes be in the economic or emotional interest
for some parties to pretend that a down round has not occurred, there are other times
when the determination of a down round is crucial for negotiation or contractual
reasons.
EXAMPLE 17.3
Consider the setup given in Example 17.2. It is now one year later, and Newco needs another
infusion of capital. Owl is considering a $12M Series C investment for RP, with APP of
$2M, with a 5X liquidation preference and 8M shares of common. The option-pricing
assumptions remain the same as in Example 17.1, except that now the expected holding
period is three years. Owl has carried interest of 25 percent, committed capital of $500M, and
lifetime fees of $83.75M.
Talltree, the Series B investor, is covered by full-ratchet antidilution protection. The
other investors (particularly the founders and EBV) are denying that this is a down round
and claim that the antidilution protection does not apply. They have two arguments. First,
they claim that the RP should be ignored in these calculations, and thus $12M is being paid
for 8M shares of common, a higher price than paid by Talltree for their CP. Second, they say
that if Talltree insists on counting the RP, it should only count for $2M (its APP), with the
other $10M allocated to the common. Even in this case, they claim that the price is the same
as paid by Talltree. Talltree, in its defense, believes that these arguments greatly understate
EXHIBIT 17-7
EXIT DIAGRAM FOR SERIES A (AFTER SERIES B)
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314 CHAPTER 17 IMPLIED VALUATION
the value of the RP component, and that the implied valuation of the Series B shares will be
lower than its original LP cost. Owl wants the issue resolved before it invests.
Problems
(a) After this round with Owl, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) Is Talltree correct in their assertion that the investment by Owl lowers the implied
valuation of the Series B below its original LP cost?
Solutions
(a) If Owl pays $12M to purchase 8M common shares (ignoring the RP component), it
would be purchasing one-fourth of the of 32M common shares outstanding (as-converted).
This makes the post-money valuation $12M/(1/4) 5$48M, and the pre-money valuation is
$48M 2 $12M5$36M.
(b) To compute the implied valuations, we must ?rst compute the formulas for the LP cost
and valuation. LP cost is 500/(500 283.75) Ã $12M5$14.4M. Next, we need to ?nd the
conversion condition for the Series B, which is still the only CP in the capital structure.
Talltree would receive 1/4 Ã (W215) if it converts ($5M to redeem the Series A RP and
$10M to redeem the Series C RP), and $10M if it redeems. Thus, Talltree’s conversion
condition for the Series B is
1=4 Ã ðW 215Þ .10-W
B
5$55M:
ð17:16Þ
With this information about Series B conversion, we are ready to draw the exit dia-
gram for the Series C as shown in Exhibit 17-8.
EXHIBIT 17-8
EXIT DIAGRAM FOR THE SERIES C
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17.3 DOWN ROUNDS? 315
We can read this diagram as
Partial valuation of the Series C5V 2Cð10Þ 11=3 Ã Cð25Þ 21=12 Ã Cð55Þ:
ð17:17Þ
The terms of the Owl fund differ fromthose of EBVand Talltree. With an expected gross
value multiple of 2.5, Owl has GP% of 0.25 Ã (2.5 Ã 416.25 2 500)/(2.5 Ã 416.25) 50.13.
Thus, the LP valuation is
LP valuation of the Series C50:87 Ã ðV 2Cð10Þ 11=3 Ã Cð25Þ
21=12 Ã Cð55ÞÞ:
ð17:18Þ
Now, the ?nal step is to compute the implied post-valuation, we set LP cost 5LP
valuation and solve for IV
post
.
$14:4M50:87 Ã ðIV
post
2Cð10Þ 11=3 Ã Cð25Þ 21=12 Ã Cð55ÞÞ:
ð17:19Þ
We can use the VCV model to solve for a breakeven valuation 5IV
post
5$49.19M.
Then, we have
IV
pre
549:19 214:40=0:87 5$32:64M:
ð17:20Þ
(c) To determine if there has been a down round, we need to compute the implied LP
valuation for Series B (after Series C) and compare it to the dollars invested by Talltree in
Series B. Again, the easy way is to read the answer out of AUTO Calculator. To do this the
hard way, we ?rst ?nd the formula for the LP valuation. Note that this formula will be
slightly different from what we found in Example 17.2, because now there is a new investor
(Series C) in the capital structure. The LP cost for the Series B is $12.5M (same as in
Example 17.2). The new exit diagram for the Series B is shown in Exhibit 17-9.
EXHIBIT 17-9
EXIT DIAGRAM FOR THE SERIES B (AFTER SERIES C)
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316 CHAPTER 17 IMPLIED VALUATION
We can read this diagram as
Partial valuation of the Series B ðafter Series CÞ
5Cð10Þ 2Cð20Þ 11=4 Ã Cð55Þ:
ð17:21Þ
The LP valuation is
LP valuation ðSeries B after Series CÞ 50:9 Ã ðCð10Þ 2Cð20Þ 11=4 Ã Cð55ÞÞ:
ð17:22Þ
We can solve for the implied LP valuation in the FLEX Calculator by substituting in
total valuation 5IV
post
549.19. This yields an answer of $10.53M.
The ?nal step is to compare this implied LP valuation ($10.53M) to the “price” 5LP
cost originally paid for these Series B shares ($12.50M). As the latter is higher than the
former, we conclude that Talltree is correct in its claim that the Series C is a down round.
’
REALITY CHECK: Although this example gives Talltree some ammuni-
tion in a debate about down rounds, in most real-world transactions the contractual
provisions are worded tightly enough so that the legal de?nition of “down round”
may have nothing to do with the actual economic values computed by implied
valuation. For example, if a down round is explicitly considered as a “lower con-
version price”, then the economic value of all other features may be irrelevant from
a legal perspective. Furthermore, even if all parties were willing to agree that a
down round occurred in Example 17.3, it is not clear how antidilution adjustments
would be computed, because such adjustments usually rely on preset formulas that
can only take account of conversion prices. In practical situations, down-round
computations such as Example 17.3 are more likely to show up in cases where
contracts have not been carefully drafted.
17.4 HOW TO AVOID VALUATION CONFUSION
We have been throwing so many valuation terms around that some readers may be
confused. This short section is intended to review some of the most important
valuation de?nitions. In this section, we use bold type for valuation terms, and bold
italic for valuation terms that are not standard industry usage.
When we “do a valuation” or “value a company”, this is usually referring to
our own opinion about what something is worth. We arrive at this valuation using
DCF, comparables, VC method, or some other valuation technique. You can think
of this as your personal valuation of the company. The total valuation computed in
the VC method is an example of a personal valuation.
Personal valuation has nothing to do with the actual market valuation implied
by a transaction. In fact, the whole challenge of being a successful investor is to ?nd
companies where your personal valuation is higher than the market valuation (and to
be right about it!). Instead, the structure of the actual transaction implies a speci?c
17.4 HOW TO AVOID VALUATION CONFUSION 317
market valuation. The industry-standard approach to the computation of market
valuation is to pretend that the whole purchase price was for common stock, and then
divide this purchase price by the fraction of the company that has been purchased.
This de?nition of the market valuation is called post-money valuation. Post-money
valuation is sometimes a fair approximation for market valuation (such as when
convertible stock is purchased in a high-volatility venture) and sometimes a bad
approximation (such as when common stock is combined with redeemable preferred
stock in a low-volatility venture). In many cases, it is often helpful for a careful
investor or owner to compute a more accurate measure of the market valuation,
which we call the implied post-valuation and write as IV
post
. We compute the
implied post-valuation by ?rst ?nding the LP valuation and then recursively solving
for the total valuation that equates LP valuation and LP cost.
Important points to remember:
1. Do not use your personal valuation when you mean market valuation. If
somebody asks about the post-money valuation of a company, don’t ever
look at your models for the answer. Absolute and relative valuation models
cannot answer this question.
2. Do not use market valuation when you should be using your personal
valuation. If you doing a partial valuation of your stake in a company, the
correct “stock price” to put into option-pricing models is your personal
valuation of the whole company (5total valuation), not the market valuation.
3. It’s ?ne to use post-money valuation if you want to communicate with people,
but don’t forget that, as a proxy for the market valuation of the company, it is
often misleading or just plain wrong. When it is important to knowwhat price
is really being implied by the transaction, you should compute the implied
valuation.
SUMMARY
Pre-money valuation and post-money valuation are used by VCs for many purposes, including
communication, interim valuation for reporting, and as starting points in contractual disputes.
In this chapter, we demonstrated that pre- and post-money valuation are not accurate measures
of value—and in their place we developed alternative measures called implied pre-valuation
and implied post-valuation that are more accurate re?ections of market value.
KEY TERMS
Implied valuation
Market valuation
Implied post-valuation
(IV
post
), implied
pre-valuation (IV
pre
)
Implied LP valuation,
implied GP valuation,
implied partial valuation
Personal valuation
318 CHAPTER 17 IMPLIED VALUATION
EXERCISES
17.1 True, False, or Uncertain: If an investor believes that the total valuation of a company
is higher than the implied post-valuation for the transaction, then he should invest.
17.2 Suppose that EBV is considering a $10M Series A investment in Newco. EBV proposes
to structure the investment as 6M shares of convertible preferred stock (CP) plus RP with
$4M APP. The employees of Newco have claims on 10M shares of common stock. Fol-
lowing the Series A investment, Newco will have 10M common shares outstanding and
would have 16M shares outstanding on conversion of the CP.
(a) After this round, what are the pre- and post-money valuations for Newco?
(b) Find IV
post
and IV
pre
.
17.3 Talltree is considering a $12M Series B investment in Newco for 5M shares of CP with
$12M APP. The other investors are (1) the employees, who have claims on 10M shares of
common; and (2) EBV, the Series A investors, who have 5M shares of CP with $6M APP. In
both of these structures, the Series B has a liquidation preference to Series A. All the parties
agree on an estimate of $30M for the total valuation of Newco.
(a) After this round with Talltree, what are the pre- and post-money valuations for Newco?
(b) What are IV
post
and IV
pre
?
(c) After this round by Talltree, what is the implied LP valuation for the Series A
investment made by EBV?
17.4 Consider the situation given in Example 17.3. After the Series C investment by Owl, is
the Series A implied LP valuation lower than its original LP cost?
EXERCISES 319
CHAPTER 18
COMPLEX STRUCTURES
IN PART III, we have developed a framework for the partial valuation of
many different types of VC structures. Because most VC transactions use standard
security types such as RP, CP, PCP, and PCPC, we are able to automate many of
these techniques in the AUTO calculator of the VCV model. Some transactions,
however, use complex structures that are not easily reduced to a one-size-?ts-all
methodology. In this chapter, we give a few examples of such transactions and
show how to break them down into the same pieces used in the previous chapters.
With practice, analysts can learn to analyze many nonstandard securities using
these techniques. As a general rule, if all securities are paid off only at exit, then
you can write an exit diagram. If you can write an exit diagram, then you can read
the diagram and value the underlying securities. Of course, not all transactions can
be handled within this framework. In particular, if there are intermediate cash
payments (before exit), then the exit diagrams won’t tell the whole story, and the
analytic formulas for RE options do not apply. To value these kinds of transactions,
we need to use techniques developed in Part IV.
18.1 MANAGEMENT CARVE-OUTS
Many times, a complex structure will arise as part of a down round. In these cases,
early expectations for the business have turned out to be too ambitious, but at least
one new investor is convinced that value can still be captured in a new transaction.
In these cases, the new investor often decides that there are insuf?cient incentives
for the management and employees to stay around, and a new employee stock pool
may not solve the problem, because of large preferences that stand before the
common stock. Then, to provide incentives for management to stay around and
work hard, a management carve-out is often made at the time of the new
investment. The simplest type of carve-out is to set aside some fraction of exit
320
proceeds to be given to management.
1
This fraction is often paid from the ?rst
dollar of exit proceeds to incent management for even the smallest exits. We
illustrate this type of carve-out in Example 18.1. More complex incentive schemes
can be provided by lump-sum payments when certain exit thresholds or perfor-
mance targets are met. We illustrate this kind of carve-out in Example 18.2.
EXAMPLE 18.1
Newco has received four rounds of investments (Series A, B, C, and D) for a total of 40M
shares of CP plus 10M shares of common claimed by the employees. After the Series D
investment, Newco falls on hard times. After searching hard for new ?nancing, the investors
?nally agree to $12M Series E investment with Vulture Ventures (VV) for 50M shares of CP
and a 3X liquidation preference. As part of this agreement, all previous investors (Series A
through Series D) give up all their preferred rights and are converted to common stock, so the
capital structure of Newco is now 50M shares of common plus the Series E CP. As part of the
investment, Vulture creates a carve-out: management will receive 10 percent of all exit
proceeds, with a value of this carve-out capped at $5M. Vulture Ventures has $250M of
committed capital, $50M of lifetime fees, and 20 percent carried interest.
Problems
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case assumptions.
Solutions
We begin by drawing the exit diagram for the carve-out in Exhibit 18-1. Management
receives 10 percent of all proceeds up to a total of $5M. This cap is reached when proceeds
are equal to $50M.
We can read this diagram as
Partial valuation of management carve-out 51=10 Ã V 21=10 Ã Cð50Þ: ð18:1Þ
With this equation in hand, we are ready to tackle the Series E stake. The trick here is
to adjust for the change in the redemption value caused by the carve-out. Without the carve-
out, Vulture Ventures would be entitled to the ?rst $36M in proceeds (5$12M APP Ã 3X
liquidation preference.) Although the total RV of Series E is still $36M after the carve-out, it
will now take a little bit longer to get there, because Series E will only receive 90 percent of
the proceeds. Thus, Vulture will receive 90 percent of all proceeds until 36M50.9 Ã W,
which occurs at W5$40M.
1
Management carve-outs in VC transactions should not be confused with the more common meaning of
“carve-out” in mature companies, where a division of a company is separated from the parent and given
an independent existence.
18.1 MANAGEMENT CARVE-OUTS 321
After receiving the RV, Vulture would choose to convert the CP when its conversion
value exceeds the redemption value of $36M. How is this conversion condition affected by
the carve-out? As long as the conversion point occurs above $40M, the only difference would
be the reduction of the maximal $5M carve-out from the exit proceeds:
Series E conversion condition
1=2 Ã ðW 25Þ .36M-W
E
5$77M: ð18:2Þ
We are now ready to draw the exit diagram for the Series E as shown in Exhibit 18-2.
EXHIBIT 18-2
EXIT DIAGRAM FOR THE SERIES E
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EXHIBIT 18-1
EXIT DIAGRAM FOR MANAGEMENT CARVE-OUT
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322 CHAPTER 18 COMPLEX STRUCTURES
We can read this diagram as
Partial valuation of the Series E59=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ: ð18:3Þ
We next analyze the remaining investors—Series A through Series D plus the
employee claims—who collectively own 50 million shares of common stock. This holding
includes complex changes, which are easiest to analyze by reversing our usual order and
doing the exit equation ?rst. Because the 50 million shares held by these remaining investors
include everything not already claimed by Vulture or the carve-out, we can write the exit
equation as the difference between the whole ?rm (V) and the partial valuations given in
Equations (18.1) and (18.3):
Partial valuation of the 50 million remaining shares
5V 2½1=10 Ã V 21=10 Ã Cð50Þ? 2½9=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ?
59=10 Ã Cð40Þ 11=10 Ã Cð50Þ 11=2 Ã Cð77Þ:
ð18:4Þ
We draw this exit diagram in Exhibit 18-3.
(a) To compute the breakeven valuation for the Series E, we use the typical GP% of 0.10
(since VV has carried interest of 20 percent like EBV and Talltree) and subtract the GP
valuation from Equation (18.3) to obtain
LP valuation of Series E50:9 Ã ½9=10 Ã V 29=10 Ã Cð40Þ 11=2 Ã Cð77Þ?: ð18:5Þ
Next, we ?nd the LP cost as ($250M/ $200M) Ã $12M5$15M. The breakeven
valuation (5IV
post
) is found by setting LP valuation 5LP cost. Because this transaction
includes a nonstandard structure (the carve-out), it is necessary to use the FLEX Calculator of
the VCV model for this computation. Under base-case assumptions for a Series E investment,
we ?nd a breakeven valuation 5IV
post
5$24.26M.
EXHIBIT 18-3
EXIT DIAGRAM FOR THE REMAINING SHARES
40 50 77
$W
R
e
m
a
i
n
i
n
g
s
h
a
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s
S
lo
p
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?
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/2
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p
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?
9
/
1
0
18.1 MANAGEMENT CARVE-OUTS 323
(b) Using the IV
post
of $24.26M and the same base-case assumptions as in part (b), we can
use FLEX Calculator to compute the partial valuation of the carve-out (Equation (18.1) as
$1.52M. ’
The previous example used a proportional carve-out. It is also possible to
have discrete payouts at preset trigger points. The next example illustrates this case.
EXAMPLE 18.2
We use the same setup as in Example 18.1, but this time with a different structure for the
management carve-out. Now, following the $12M Series E investment from Vulture Ven-
tures (50M shares of CP with a 3X liquidation preference), management is promised the
following incentives: If Newco has an exit of at least $50M, then the employees will receive
$5M from these proceeds. If Newco has an exit of at least $80M, then the employees will
receive an additional $5M from these proceeds. The earlier investors have 40M shares of
common, and the employees have claims on a further 10M shares.
Problems
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case assumptions.
(c) Compute the implied valuation for the management carve-out under base-case assumptions.
Solutions
We begin by drawing the exit diagram for the carve-out in Exhibit 18-4. Here, we have
discrete jumps in the payouts to management at $50M and $80M.
We can read this diagram as
Partial valuation of management carve-out 55 Ã BCð50Þ 15 Ã BCð80Þ: ð18:6Þ
We next turn to the Series E stake. Now the main complication is to adjust properly for
the discrete payouts. Without doing some calculations, we cannot tell whether the jumps
occur below or above the conversion point. In principle, it is possible that neither payout
occurs before conversion (if W
E
,50), that only the ?rst one does (50 ,W
E
80), or that both
do (W
E
. 80). The only way to know for sure is to compute all the cases and look for logical
contradictions. For example, Series E conversion condition, if occurs below the ?rst payout
(W
E
, 50):
1=2 Ã W .36M-W
E
5$72M: ð18:7Þ
This condition gives us a contradiction, because if W
E
is equal to $72M, we should
have to include a payout (because W
E
.50). Thus, Equation (18.7) is not a proper conversion
condition.
We next consider the possibility that $50M , W
E
, $80M.
324 CHAPTER 18 COMPLEX STRUCTURES
Series E conversion condition, if occurs above the ?rst payout (50M , W
E
, 80M)
1=2 Ã ðW 25Þ .36M-W
E
5$77M: ð18:8Þ
In this case, there is no logical inconsistency, because the condition for being between
the two payouts (50M,W
E
,80M) is consistent with W
E
5$77M. Thus, Equation (18.8) is
a proper conversion condition.
Even though we have found a conversion condition, we still check the last possibility,
W
E
. 80. As we shall see, an interesting surprise awaits us. Series E conversion condition, if
occurs above the second payout (W
E
.$80M):
1=2 Ã ðW 210Þ.36M-W
E
5$82M: ð18:9Þ
Again, there is no logical inconsistency here: W
E
5$82M is higher than the condition
for the second payout, W
E
.80M. It seems as though we have two different conversion
conditions.
How is this possible? It happens because for all exits between $77M and $80M,
Equation (18.8) applies, and it is optimal for Vulture to convert the Series E. However, for an
exit between $80M and $82M, after the second payout is made, Equation (18.9) applies, and
it is no longer optimal to convert. For exits in this range, Vulture would choose to redeem.
They would again convert for any exit above $82M. Their exit diagram is shown in Exhibit
18-5. In complex cases like this, we must take special care to label all the key points to
facilitate our reading of the diagram. For example, at W5$80M, the Series E will suffer
a drop of 3/2 (because instead of 1/2 Ã (W 2 5) 537.5 they drop back to 36) and a slope
change of one-half (because they no longer are converting and getting half of all additional
exit proceeds.)
EXHIBIT 18-4
EXIT DIAGRAM FOR MANAGEMENT CARVE-OUT
50 80
$W
M
a
n
a
g
e
m
e
n
t
c
a
r
v
e
-
o
u
t
5
10
5
5
18.1 MANAGEMENT CARVE-OUTS 325
We can read this diagram as
Partial valuation of the Series E5V 2Cð36Þ 11=2 Ã Cð77Þ 21=2
à Cð80Þ 23=2 à BCð80Þ 11=2 à Cð82Þ:
ð18:10Þ
We next analyze the remaining investors—Series Athrough Series Dplus the employee
claims—who collectively own 50 million shares of common stock. As in Example 18.1, we
write this exit equation as the difference between the whole ?rm (V) and the partial valuations
of the other investors. These partial valuations are given in Equations (18.6) and (18.10):
Partial valuation of the 50 million remaining shares 5V 2½5 Ã BCð50Þ 15 Ã BCð80Þ?
2½V 2Cð36Þ 11=2 Ã Cð77Þ 21=2 Ã Cð80Þ 23=2 Ã BCð80Þ 11=2 Ã Cð82Þ?
5Cð36Þ 25 Ã BCð50Þ 21=2 Ã Cð77Þ 11=2 Ã Cð80Þ 27=2 Ã BCð80Þ 21=2 Ã Cð82Þ
ð18:11Þ
We can draw this exit diagram as shown in Exhibit 18-6.
EXHIBIT 18-5
EXIT DIAGRAM FOR THE SERIES E
36 77 80 82
$W
S
e
r
i
e
s
E
S
lo
p
e
?
1
/
2
S
lo
p
e
?
1
/
2
3/2
EXHIBIT 18-6
EXIT DIAGRAM FOR THE REMAINING SHARES
36 50 77 80 82
$W
R
e
m
a
i
n
i
n
g
s
h
a
r
e
s
S
lo
p
e
?
1
/2
S
lo
p
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?
1
/2
7/2
5
326 CHAPTER 18 COMPLEX STRUCTURES
(b) To compute the breakeven valuation (5IV
post
) for the Series E, we ?rst subtract the GP
valuation from Equation (18.10) to obtain
LP valuation of Series E50:9 Ã ½V 2Cð36Þ 11=2 Ã Cð77Þ 21=2 Ã Cð80Þ
23=2 Ã BCð80Þ 11=2 Ã Cð82Þ?:
ð18:12Þ
As in Example 18.1, it is necessary to use the FLEX Calculator to compute the IV
post
.
Under base-case assumptions for a Series E investment, we ?nd an IV
post
of $22.82M.
(c) Using the IV
post
of $22.82M and the same base-case assumptions as in part (b), we can
use FLEX to compute the partial valuation of the carve-out (Equation (18.6)) as $0.59M.
’
18.2 DEALING WITH PARTNERS
Because VC-backed companies are cash poor, they often must give up equity as
payment in transactions with service providers or other partners. The following
example shows how we could value these transactions.
EXAMPLE 18.3
EBV makes a $10M Series A investment in Newco for 10M shares of CP. The employees
of Newco have claims on 10M shares of common stock. At the same time as this investment,
Newco enters into a transaction with Techco to obtain licenses for some Techco patents. As
consideration for providing these licenses, Techco receives an option to purchase 10M shares
of common stock for $1.50 a share, but this option can only be exercised upon an exit above
$150M. (Assume that this $150M would be adjusted for any future dilution, so that the
threshold is effective for the proceeds owed to the current shareholders.) EBV is aware of
the deal with Techco at the time that they make their Series A investment.
Problems
(a) Draw and read the exit diagrams for Techco and for the Series A.
(b) Compute the breakeven valuation for the Series A investment under base-case
assumptions.
(c) Compute the implied valuation for Techco’s stake under base-case assumptions.
Solutions
(a) We begin with Techco. Their options are valuable only for an exit above $150M. What
happens at this point? Techco exercises their options at a cost of $15M, and receives 10M
shares, which are worth 10M/30M5one-third of the ?rm5$50M. In addition, the $15M total
strike price will be shared equally among the common stock holders, so Techco will effectively
get back one-third of their strike price 5$5M. In the exit diagram, these two pieces will be
represented by a jump up (binary option) representing the pro?t they make on the option
18.2 DEALING WITH PARTNERS 327
transaction ($50M 2 $15M1$5M5$40M), plus a positive slope starting at $150M (regular
call option) representing their new ownership of one-third of the common shares.
We can read this exit diagram as
Partial valuation of Techco options 540 Ã BCð150Þ 11=3 Ã Cð150Þ: ð18:13Þ
To ?nd the value of the Series A, we must ?rst compute the conversion condition. As
in Example 18.2, we don’t know whether this conversion condition occurs before or after the
conversion of Techco’s options, and we don’t have a simple RVPS rule to help us. Thus, we
must check both possibilities.
Series A conversion condition, Techco not yet converted (W
A
, 150):
1=2 Ã W.10-W
A
520: ð18:14Þ
This condition is consistent with W
A
, 150.
Next, we look to check for a conversion condition if Techco has already converted. In
this case, we must add $15M to the proceeds to represent Techco’s exercise payments.
Series A conversion condition, Techco converted (W
A
. 150):
1=3 Ã ðW 115Þ.10-W
A
515: ð18:15Þ
Clearly, Equation (18.15) represents a contradiction with Techco’s threshold of
$150M, so Equation (18.14) is the only valid conversion condition. We can now draw the
exit diagram for the Series A stake as shown in Exhibit 18-8.
We can read this diagram as
Partial Valuation of Series A5V 2Cð10Þ 11=2 Ã Cð20Þ 220 Ã BCð150Þ
21=6 Ã Cð150Þ:
ð18:16Þ
EXHIBIT 18-7
EXIT DIAGRAM FOR THE TECHCO OPTIONS
40
150
$W
T
e
c
h
c
o
o
p
t
i
o
n
s
40
S
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1
/3
328 CHAPTER 18 COMPLEX STRUCTURES
Usually, the part of this diagram that confuses people is the drop of $20M at W5150.
This drop is due to the combination of two effects. First, when Techco exercises their options,
they immediately receive 1/3 of the proceeds, which reduces the value of the EBV stake from
one-half of $150M (5$75M) to one-third of $150M (5$50M). This causes a drop of $25M.
This drop is somewhat cushioned by one-third of the proceeds from the exercise cost (1/3 Ã
$15M5$5M), leaving a total drop of $25M 2 $5M5$20M. Note that this kind of binary
call does not occur when “regular” preferred stock converts, because there is no windfall
pro?t or loss at the time of such conversions. In this example, however, Techco’s options are
well in-the-money before they are allowed to convert them at W5$150M. When they are
?nally able to convert, the resulting pro?ts cause the jumps in the diagrams.
(b) To compute the breakeven valuation (5implied valuation) for the Series A, we ?rst
subtract the GP valuation from Equation (18.16) to obtain
LP valuation of Series E59=10 Ã ½V 2Cð10Þ 11=2 Ã Cð20Þ
220 Ã BCð150Þ 21=6 Ã Cð150Þ?:
ð18:17Þ
The LP cost is ($100M/$80M) Ã $10M5$12.5M. As in the previous examples, it is
necessary to use the FLEX Calculator to compute the IV
post
. Under base-case assumptions for
a Series A investment, we ?nd an IV
post
of $30.52M.
(c) Using the IV
post
of $30.52M and the same base-case assumptions as in part (b), we
can use FLEX to compute the partial valuation of Techco’s options (Equation (18.13))
as $4.58M. ’
18.3 A COMPLEX EXAMPLE
Next, we try to solve a real messy problem. If we can do this, we can do (almost)
anything.
EXHIBIT 18-8
EXIT DIAGRAM FOR THE SERIES A
10 20 150
$W
S
e
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e
s
A
S
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p
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?
1
/
2
S
l
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?
1
/
3
20
18.3 A COMPLEX EXAMPLE 329
EXAMPLE 18.4
We begin with the same setup as in Example 16.5. Talltree has just made a Series F
investment in Newco. The details of the Series F and all prior rounds are given below.
Series A: 10M shares of CP ($6M APP)
Series B: 10M shares of CP ($10M APP)
Series C: 10M shares of CP ($4M APP and a 3X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 3X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($10M APP).
Series F: 10M shares of PCP ($20M APP) with a QPO at $6 per share.
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. In the event of a liquidation, the preferred stock is
redeemed in reverse order of investment (i.e., the Series F has a preference to the Series E,
which has a preference to the Series D, and so on). In addition to these investors, the
employees have claims on 20M shares of common stock.
Now, we add two new features to this capital structure from Example 16.5, with both
of these new features put in place at the same time as the Series F investment. First, the
investors create a management carve-out for 20 percent of the ?rst $50M in exit proceeds.
Second, Newco acquires a smaller competitor, Subco, with the owners of Subco receiving
20M shares of common stock, with a further payment of 10M shares of common stock if the
merged company has an exit exceeding $1000M.
Problems
(a) Compute the breakeven valuation for the Series F under base-case assumptions.
(b) Given this breakeven valuation, compute the implied valuation for the management
carve-out.
(c) Given this breakeven valuation, compute the implied valuation for Subco’s stake.
Solutions
(a) We begin this solution with the same two steps as in Example 16.5. First, we compute
the conversion order for the CP. Second, we insert the PCP and PCPC into this order. In order
of the RVPS of the CP, we have
Series A: $6M/10M5$0.60
Series B: $10M/10M5$1.00
Series C: $12M/10M5$1.20
Series E: $10M/10M5$1.00
We next add the participating preferred to the ordering. For the Series F PCP, auto-
matic conversion occurs at a QPO of $6 per share, which will be after all series of CP have
converted. For the Series D PCPC, we ?rst determine if conversion is voluntary or automatic.
With voluntary conversion at $30M/10M5$3.00 and automatic conversion at the
QPO5$5.00, the QPO threshold is redundant and conversion will occur voluntarily at $3 per
share. Finally, we can compute the Series D per-share cap as
Per-share cap :ð$30M2$10MÞ=10M5$2:00:
330 CHAPTER 18 COMPLEX STRUCTURES
So far, these are exactly the same answers we found in Example 16.5. Our next step is
different, as we must ?nd the trigger point for the Subco incentive. At an exit value of $1B,
even if all shares of CP and PCP have already been converted (yielding a total of 100M
shares outstanding), the proceeds available to the common stock would be $1B 2 $10M (for
the carve-out) 5$990M, for a per-share value of $990/100M5$9.90. Thus, the Subco
trigger will not occur until after all other series have converted.
Taken together, these calculations imply a conversion and cap order of A ($0.60), B
and E together ($1.00), C ($1.20), D (cap) ($2.00), D (convert) ($3.00), F ($6.00), and Subco
incentive ($9.90). Except for the Subco incentive, this is the same answer as we found in
Example 16.5. We diverge more from Example 16.5 when we compute the actual conversion
conditions for all series. Here, we must take account of the management carve-out and of the
additional 20M shares given to Subco. The management carve-out is for the ?rst $50M of
proceeds. As there is a total of $20M1$10M1$10M1$12M1$10M1$6M5$68M
of preferences, we can be con?dent that the carve-out will be complete while preferences are
still being paid, and thus before any of the preferred would choose to convert. Thus, we can
simply add the entire value of the carve-out (50.20 Ã $50M5$10M) as a preference to the
common stock. For the Series A, these preferences total $68M À $6M (the Series A RV)
1$10M (the carve-out) 5$72M. Upon conversion, the 10M shares from Series A would
represent one-seventh of the common stock because 60M shares would already be out-
standing: 20M to the employees, 20M to the previous owners of Subco, 10M (as if) to the
Series D PCPC, and 10M (as if) to the Series F PCP. Thus, we have
Series A conversion condition : 1=7 Ã ðW 272Þ.6-W
A
5$114M: ð18:18Þ
Series B and E convert at the same time, followed by Series C:
Series B conversion condition : 1=9 Ã ðW 252Þ.10-W
B
5$142M: ð18:19Þ
Series E conversion condition : 1=9 Ã ðW 252Þ.10-W
E
5$142M: ð18:20Þ
Series C conversion condition : 1=10 Ã ðW 240Þ.12-W
C
5$160M: ð18:21Þ
Next in order is the Series D cap, followed by the Series D voluntary conversion.
Series D cap : 10 11=10 Ã ðW 240Þ 530-W
D
ðcapÞ 5$240M ð18:22Þ
Series D conversion condition : 1=10 Ã ðW 230Þ.30-W
D
5$330M: ð18:23Þ
At the QPO of $6 per share, the only preference left is the $10M carve-out, so the QPO
occurs at
Series F conversion condition ðQPOÞ: 100M Ã $6 1$10M5W
F
5610: ð18:24Þ
At this QPO, the Series F will return $20M to the other shareholders and thus
recapture 1/10 Ã $20M5$2M for themselves, for a net drop of $20M 2 $2M5$18M.
Finally, we have the contractual condition that the Subco trigger for extra shares is at W
5$1000M. At this trigger, Subco receives 10M additional shares, to raise their stake in the
company from 2/10 to 3/11. At this point, the only liquidation preference still being paid is
the $10M management carve-out, so $1000M 2 $10M5$990M remains for the common.
The additional 10M shares means that the stake of the Series F investor drops by
1=10 Ã 990 21=11 Ã 990 5$9M: ð18:25Þ
18.3 A COMPLEX EXAMPLE 331
With these calculations in hand, we are ready to draw the exit diagram for the Series F,
as shown in Exhibit 18-9.
We can read this diagram as
Partial valuation of the Series F
54=5 Ã V 24=5 Ã Cð25Þ 11=6 Ã Cð78Þ 21=42 Ã Cð114Þ 22=63 Ã Cð142Þ 21=90 Ã Cð160Þ
11=90 Ã Cð240Þ 21=90 Ã Cð330Þ 218 Ã BCð610Þ 29 Ã BCð1; 000Þ 21=110 Ã Cð1; 000Þ
ð18:26Þ
Using our standard GP% of 10 percent, the LP valuation of the Series F is 90 percent
of Equation (18.26). LP cost for Series F is (250/200) Ã $20M5$25M. Finally, we can use
the FLEX Calculator of VCV to compute the breakeven valuation under base-case assump-
tions as $171.10M.
(b) The exit diagram for the management carve-out is shown in Exhibit 18-10.
We can read this diagram as
Partial valuation of the management carve-out 51=5 Ã V 21=5 Ã Cð50Þ: ð18:27Þ
Using base-case assumptions and the breakeven valuation (5IV
post
) from part (a), we
can use FLEX to compute this valuation as $6.96M.
(c) The previous owners of Subco have 20M shares of common stock before their trigger
point at W51,000, when they receive an additional 10M shares. At this trigger point, their
value increases by
3=11 Ã ð1; 000 210Þ 22=10 Ã ð1; 000 210Þ 5$72M: ð18:28Þ
EXHIBIT 18-9
EXIT DIAGRAM FOR THE SERIES F
142 160 240 330 25 78 114 610 1000
$W
S
e
r
i
e
s
F
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/9
S
lo
p
e
=
1
/9
S
lo
p
e
=
1
/7
S
lo
p
e
=
1
/6
S
l
o
p
e
=
4
/
5
S
lo
p
e
=
1
/1
0
S
lo
p
e
=
1
/1
1
18
9
332 CHAPTER 18 COMPLEX STRUCTURES
We can draw the exit diagram for Subco’s stake as shown in Exhibit 18-11. We can
read this diagram as
Partial valuation for Subco’s stake
51=3 Ã Cð78Þ 21=21 Ã Cð114Þ 24=63 Ã Cð142Þ 21=45 Ã Cð160Þ 11=45 Ã Cð240Þ
21=45 Ã Cð330Þ 14 Ã BCð610Þ 172 Ã BCð1; 000Þ 14=55 Ã BCð1; 000Þ:
ð18:29Þ
EXHIBIT 18-11
EXIT DIAGRAM FOR THE SUBCO STAKE
142 160 240 330 78 114 610 1000
$W
S
u
b
c
o
72
4
S
lo
p
e
=
1
/5
S
lo
p
e
=
3
/1
1
S
lo
p
e
=
1
/5
S
lo
p
e
=
1
/5
S
lope = 2/9
S
lo
p
e
=
2
/9
S
lope =
2/7
S
lo
p
e
=
1
/3
EXHIBIT 18-10
EXIT DIAGRAM FOR THE MANAGEMENT CARVE-OUT
50
$W
M
a
n
a
g
e
m
e
n
t
c
a
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v
e
-
o
u
t
S
l
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p
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?
1
/
5
18.3 A COMPLEX EXAMPLE 333
Under base-case assumptions and the IV
post
found in part (a), we can use FLEX to
compute the implied value of this stake as $31.62M.
’
SUMMARY
The option-pricing approach to partial valuation allows us to estimate valuations for virtually
all VC structures. In previous chapters, we derived solutions for structures with the standard
VC securities of RP, CP, PCP, PCPC, and common stock. These structures can be valued
using the prepackaged routines in the AUTO Calculator of VCV. In some cases, however, the
transaction structures can contain unique components that cannot easily be automated. In this
chapter, we demonstrated how to use the techniques of Part III to draw exit diagrams for
these complex structures and then to value these structures using the FLEX Calculator of
VCV. Examples of such complex securities include management carve-outs (where managers
share in exit proceeds with the preferred investors), deals with suppliers or service providers,
or incentives included as part of a merger.
KEY TERMS
Management carve-out
EXERCISES
18.1 Newco has received four rounds of investments (Series A, B, C, and D) for a total of
50M shares of CP plus 10M shares of common claimed by the employees. After the Series D
investment, Newco falls on hard times. After searching hard for new ?nancing, the investors
?nally agree to $10M Series E investment with Vulture Ventures (VV) for 40M shares of CP
and a 2X liquidation preference. As part of this agreement, all previous investors (Series A
through Series D) give up all their preferred rights and are converted to common stock, so the
capital structure of Newco is now 60M shares of common 1the Series E CP. As part of
the investment, Vulture creates a carve-out: management will receive 20 percent of all exit
proceeds, with a value of this carve-out capped at $5M. Vulture Ventures has $250M of
committed capital, $50M of lifetime fees, and 20 percent carried interest.
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case
assumptions.
334 CHAPTER 18 COMPLEX STRUCTURES
18.2 We use the same setup as in Exercise 18.1, but this time with a different structure for
the management carve-out. Now, following the $10M Series E investment from Vulcan
Ventures (40M shares of CP with a 2X liquidation preference), management is promised the
following incentives: If Newco has an exit of at least $40M, then the employees will receive
$5M from these proceeds. If Newco has an exit of at least $60M, then the employees will
receive an additional $5M from these proceeds. The earlier investors have 50M shares of
common, and the employees have claims on a further 10M shares.
(a) Draw and read the exit diagrams for the management carve-out, for the Series E, and for
all other investors combined.
(b) Compute the breakeven valuation for the Series E investment under base-case
assumptions.
(c) Compute the implied valuation for the management carve-out under base-case
assumptions.
18.3 EBV makes a $5M Series A investment in Newco for 5M shares of CP. The employees
of Newco have claims on 10M shares of common stock. At the same time as this transaction,
Newco enters into a transaction with Techco to obtain licenses for some Techco patents. As
consideration for providing these licenses, Techco receives an option to purchase 10M shares
of common stock for $1.00 a share, but this option can only be exercised on an exit above
$100M. (Assume that this $100M would be adjusted for any future dilution, so that the
threshold is effective for the proceeds owed to the current shareholders.) Newco is aware of
the deal with Techco at the time that they make their Series A investment.
(a) Draw and read the exit diagrams for Techco and for the Series A.
(b) Compute the breakeven valuation for the Series A investment under base-case
assumptions.
(c) Compute the implied valuation for Techco’s stake under base-case assumptions.
18.4 Talltree has just made a Series F investment in Newco. The details of the Series F and
all prior rounds are given below.
Series A: 10M shares of CP ($5M APP)
Series B: 10M shares of CP ($8M APP)
Series C: 10M shares of CP ($10M APP and a 2X liquidation preference)
Series D: 10M shares of PCPC ($10M APP), with liquidation return capped at 4X APP
and a QPO at $5 per share.
Series E: 10M shares of CP ($12M APP).
Series F: 10M shares of PCP ($20M APP) with a QPO at $6 per share.
These venture investors all have 20 percent carried interest, $250M in committed
capital, and $50M in lifetime fees. In the event of a liquidation, the preferred stock is
redeemed in reverse order of investment (i.e., the Series F has a preference to the Series E,
which has a preference to the Series D, and so forth). In addition to these investors, the
employees have claims on 10M shares of common stock.
Now, we add two other features to this capital structure. First, the investors create a
management carve-out for 10 percent of the ?rst $50M in exit proceeds. Second, Newco
EXERCISES 335
acquires a smaller competitor, Subco, with the owners of Subco receiving 10M shares of
common stock, with a further payment of 20M shares of common stock if the merged
company has an exit exceeding $805M.
(a) Compute the breakeven valuation for the Series F under base-case assumptions.
(b) Given this breakeven valuation, compute the implied valuation for the management
carve-out.
(c) Given this breakeven valuation, compute the implied valuation for Subco’s stake.
336 CHAPTER 18 COMPLEX STRUCTURES
PART IV
THE FINANCE OF
INNOVATION
337
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CHAPTER 19
R&D FINANCE
RESEARCH AND development (R&D) is critical for economic growth and
improvements in human health and welfare. Indeed, human civilization owes its
existence to prehistoric R&D activity. Some early humans sacri?ced productive
labor time to tinker with toolmaking “technology”, experiment with different forms
of agricultural cultivation, and devise alphabets. All these activities would be
classi?ed today as R&D, which in its of?cial international de?nition “comprises
creative work undertaken on a systematic basis in order to increase the stock of
knowledge, including knowledge of man, culture, and society, and the use of this
stock of knowledge to devise new applications”.
1
In the United States, R&D investment is between $300B and $400B per year
and comprises approximately 2.7 percent of GDP. Because total VC investment has
averaged about $20B per year since 2002, it is clear that the majority of R&D
spending must come from other sources. In Section 19.1, we discuss these sources
and provide data on geographic and sectoral patterns of R&D investment. In this
discussion, we rely on statistics published by the National Science Foundation (NSF)
in their annual reports on worldwide and U.S. R&D. In Section 19.2, we introduce
two R&D examples—a drug development project and fuel cell development pro-
ject—that will serve as touchstones for the remaining chapters of the book. In Section
19.3, we describe the advantages and disadvantages of the various methods to ?nance
such projects. Section 19.4 describes the organization of the remaining chapters and
introduces the tools necessary for the valuation of complex R&D projects.
19.1 R&D AROUND THE WORLD
Worldwide R&D spending is concentrated in developed countries. Exhibit 19-1
shows the distribution of R&D spending for select countries tracked by the
1
This is the of?cial de?nition used by the OECD, as quoted in NSF (2005), p. 7.
339
Organization for Economic Co-operation and Development (OECD) in 2007, the
most recent year with data for all surveyed countries in the most recent NSF
publication. The 30 OECD member countries include all developed economies in
the world and some of the developing economies; Israel, Russia, and China are not
yet member countries of OECD as of the writing of this book.
As shown in the exhibit, the United States has the most R&D among these
developed countries, but the patterns are less skewed than they are for VC spending
(as seen in Chapter 6). Most of these countries spend between 1 and 3 percent of
GDP on R&D, while Japan and Israel spend higher percentages. Most developing
countries spend considerably less, both in absolute terms and as a percentage of
domestic GDP. Exhibit 19-2 tabulates R&D as a percentage of GDP for a broad
range of countries.
Exhibit 19-2 illustrates the strong emphasis on R&D in both Asian and
Nordic countries—it is no accident that these countries have their fair share of high-
technology industries. Low R&D percentages in developed countries (e.g., Spain
and Italy) do not bode well for the long-run competitiveness of these economies.
On the other hand, the low R&D percentages in many developing countries is
probably less of a problem, as these economies can still grow rapidly through
technology transfer from richer nations; inexpensive labor provides incentives for
companies to set up operations in developing countries and to bring advanced
technology with them. For example, while India and Brazil (part of BRIC) are
missing from this OECD survey, UNESCO (2007) reports that their R&D share of
GDP was between 0.5 and 1 percent.
EXHIBIT 19-1
R&D SPENDING IN SELECT COUNTRIES IN 2007
Total OECD 886.3
U.S. 368.8
Japan 147.8
Germany 71.9
France 43.2
UK 38.9
Italy 19.7
Canada
a
23.8
Russia 23.5
China 102.3
Israel 8.8
Figures in PPP $billions.
a
The Canadian statistics is from 2008.
Source: NSF (2010), p. 8.
340 CHAPTER 19 R&D FINANCE
We turn next to the distribution of R&D activity by funding source, type of
R&D organization, and industry. In these exhibits, we focus on data from the United
States, for which we have the longest time series of data. In the United States, the vast
majority of R&Dis funded by either the federal government or by industry. Fifty years
ago the federal government was the main provider of R&D funds; around 1980,
private industry became the main provider. In 2008, the latest year for which the NSF
data is available, industry provided 67 percent of all R&D funding, the federal gov-
ernment provided 26 percent, universities and colleges provided 3 percent, and other
nonpro?t sources provided the remainder. Exhibit 19-3 illustrates these trends, with
spending by source, indexed to in?ation using constant 2000 dollars.
EXHIBIT 19-2
R&D SHARE OF GDP, MOST RECENT YEAR, 2004À2008
Region/country/economy RD/GDP (%) Region/country/economy RD/GDP (%)
North America Central and Eastern Europe
United States (2007) 2.68 Russian Federation (2007) 1.12
Canada (2008) 1.82 Turkey (2007) 0.71
Latin America and Caribbean Czech Republic (2007) 1.54
Mexico (2005) 0.46 Poland (2007) 0.57
Argentina (2007) 0.51 Hungary (2007) 0.97
Western Europe Romania (2007) 0.53
Germany (2007) 2.54 Slovenia (2007) 1.53
France (2007) 2.08 Slovak Republic (2007) 0.46
United Kingdom (2007) 1.79 East, South, West Asia
Italy (2006) 1.13 Japan (2007) 3.44
Spain (2007) 1.27 China (2007) 1.49
Sweden (2007) 3.60 South Korea (2007) 3.47
Netherlands (2007) 1.70 Taiwan (2007) 2.63
Austria (2008) 2.66 Singapore (2007) 2.61
Switzerland (2004) 2.90 Paci?c
Belgium (2007) 1.87 Australia (2006) 2.01
Finland (2008) 3.46 New Zealand (2007) 1.20
Denmark (2007) 2.55 Africa and Middle East
Norway (2007) 1.64 Israel (2007) 4.68
Ireland (2008) 1.45 South Africa (2005) 0.92
Portugal (2007) 1.18 Selected country group
Greece (2007) 0.58 OECD (2007) 2.29
Luxembourg (2007) 1.63 European Union-27 (2007) 1.77
Iceland (2008) 2.76 G-7 countries (2007) 2.53
Source: NSF (2010), p. 8.
19.1 R&D AROUND THE WORLD 341
Since 1953, in?ation-adjusted R&D spending has increased more than eleven-
fold. Federal spending on R&D has been dominated by defense spending since the
beginningof the ColdWar; in 2003, the most recent year inwhichsuchdata is available,
the Department of Defense represents nearly half of the federal R&D budget. The
largest other component of the federal R&D budget is the National Institutes of
Health—a unit of the Department of Health and Human Services—which represents
about one-quarter of the total. The cycles of federal R&D can mostly be attributed to
corresponding cycles in defense spending, most recently for bioterrorism research.
Exhibit 19-3 tells us where the money came from, but not where the money was
spent. For example, in 2008, although the federal government provided 26 percent of
R&D funding, it only performed about 11 percent of this work itself. The other 15
percent was paidout touniversities andtoindustry. Exhibit 19-4illustrates the difference
between the source of funds and the actual performance of R&D. The largest bene?ciary
of federal spending is the academic sector, especially those large universities with
medical centers. Industry also receives a considerable transfer from the federal gov-
ernment, but the vast majority of that spending is for defense-related R&D projects.
Thus far, we have discussed R&D as one broad class of activities. It is also
informative to break R&D into three types: basic research, applied research, and
development. The National Science Foundation’s de?nitions for these three cate-
gories are given in Exhibit 19-5.
Of the $398B of R&D performed in the United States in 2008, approximately
17 percent was basic research, 22 percent was applied research, and 60 percent was
EXHIBIT 19-3
U.S. R&D FUNDING BY SOURCE (IN $B OF 2000 DOLLARS)
350
300
250
200
150
100
50
0
1
9
5
3
1
9
5
5
1
9
5
7
1
9
5
9
1
9
6
1
1
9
6
3
1
9
6
5
1
9
6
7
1
9
6
9
1
9
7
1
1
9
7
3
1
9
7
5
1
9
7
7
1
9
7
9
1
9
8
1
1
9
8
3
1
9
8
5
1
9
8
7
1
9
8
9
1
9
9
1
1
9
9
3
1
9
9
5
1
9
9
7
1
9
9
9
2
0
0
1
2
0
0
3
2
0
0
5
2
0
0
7
$B
Business
Federal government
Other
Total
Source: NSF (2010), p. 5.
342 CHAPTER 19 R&D FINANCE
development. In any R&D project, the basic research must be performed before the
applied research, which must be performed before development. Although some
companies will perform all three steps themselves, it is also common for each step
to take place at a different institution. For example, whereas universities performed
only 13 percent of all R&D in the United States in 2008, they focus almost
EXHIBIT 19-4
R&D EXPENDITURE BY SOURCE AND PERFORMER, 2008
Business Federal
government
Other Academic
80%
70%
60%
50%
40%
30%
20%
10%
0%
Source of funds
Performance of funds
Source: NSF (2010), p. 4.
EXHIBIT 19-5
R&D DEFINITIONS FROM THE NSF
Basic research: The objective of basic research is to gain more comprehensive knowledge or
understanding of the subject under study without speci?c applications in mind. In industry,
basic research is de?ned as research that advances scienti?c knowledge but does not have
speci?c immediate commercial objectives, although it may be performed in ?elds of present
or potential commercial interest.
Applied research: The objective of applied research is to gain the knowledge or under-
standing to meet a speci?c, recognized need. In industry, applied research includes
investigations to discover new scienti?c knowledge that has speci?c commercial objectives
with respect to products, processes, or services.
Development: Development is the systematic use of the knowledge directed toward the
production of useful materials, devices, systems, or methods, including the design and
development of prototypes and processes.
Source: National Science Foundation (2005), p. 7.
19.1 R&D AROUND THE WORLD 343
exclusively on basic research: universities performed about 56 percent of all basic
research in the United States in 2008, with the results broadly disseminated in
academic journals. These results can then provide the background for applied
research and development done by industry.
Exhibit 19-6 provides the breakdown of R&D activity across broad industry
groups.
The exhibit gives the R&D totals for all industry groups and their subgroup
industries that have at least $5B in R&D. The industry group with the highest R&D
by far is “computers and electronic products”. The other manufacturing groups with
EXHIBIT 19-6
R&D BY INDUSTRY AND INDUSTRY GROUP, 2007 IN $BILLIONS
Industry
All
R&D Federal
Company
and other
All industries 269.3 26.6 242.7
Manufacturing industries 187.5 18.2 169.3
Chemicals D D 55.3
Pharmaceuticals and medicines D D 47.6
Machinery 9.9 0.1 9.8
Computer and electronic products 58.6 8.8 49.8
Communications equipment 11.7 0.2 11.4
Semiconductor and other electronic
components
18.7 0.4 18.3
Navigational, measuring, electromedical,
and control instruments
20.4 8.2 12.3
Electrical equipment, appliances, and
components
2.7 0.1 2.6
Transportation equipment D D 31.0
Nonmanufacturing industries 81.8 8.4 73.4
Information D D 28.8
Publishing, including software 20.9 0.0 20.9
Telecommunications D D 3.1
Internet service and data processing
providers
D D 4.2
Professional, scienti?c, and technical
services
40.5 7.6 32.9
Computer systems design and related
services
14.4 0.8 13.6
Scienti?c R&D services 16.8 4.8 12.0
D 5 suppressed to avoid disclosure of con?dential information.
Source: NSF (2009), p. 3.
344 CHAPTER 19 R&D FINANCE
more than $5B in R&D are “transportation equipment”, “machinery”, “electrical
equipment”, and “chemicals”, the latter of which is dominated by the pharma-
ceutical industry.
When the NSF ?rst began gathering R&D statistics, virtually all R&D was
performed by manufacturing ?rms. Over time, with the increased role of service
industries in the U.S. economy, a substantial share of R&D has moved to non-
manufacturing companies. In particular, the high R&D in the “professional, sci-
enti?c, and technical services” group is illustrative of large outsourcing trends in
the U.S. economy—in this case, the outsourcing of R&D to specialized research
organizations. This outsourcing is particularly prominent in the pharmaceutical and
computer industries. Another nonmanufacturing group with more than $5B in R&D
is “Information”, which is dominated by the software industry, but also includes
“Telecommunications” and “Internet service and data processing providers”. These
two categories include both wired and wireless telecommunications carriers,
satellite service providers, and web search portals such as Google and Yahoo!.
19.2 TWO TOUCHSTONES
In this section, we discuss two prototypical projects: drug development (Section
19.2.1) and energy innovation (19.2.2). Because we will return to these projects
frequently in the following chapters, we call them our “touchstones”.
19.2.1 Drug Development
Our ?rst example is drug development by a pharmaceutical company. The phar-
maceutical industry is one of the largest industries in the world in terms of sales,
pro?ts, market capitalization, and R&D. For our purposes, their R&D projects are
particularly interesting, because drug development is carefully regulated by
government agencies. Because of this regulation, drug companies must take their
R&D projects through well-de?ned stages. These stages provide a framework for
modeling the investment decisions. In the United States, the principal regulator is
the Food and Drug Administration (FDA), and the stages are preclinical, Phase I,
Phase II, Phase III, and FDA approval. Here, preclinical refers to all activities
that precede testing in humans. Testing in humans—which includes Phases I, II,
and III—is collectively known as clinical trials or human trials. Once all clinical
trials have been completed, the data is submitted to the FDA, who makes the ?nal
decision allowing (or forbidding) sales to the public.
Typically, scientists work for many years before deciding on a speci?c
compound for testing. During these early years, they use a variety of techniques to
identify candidate compounds; then they screen these compounds in the laboratory,
by using computer models, and in a progression of animals with increasing simi-
larity to humans. All these activities are classi?ed as preclinical. In this preclinical
testing, the researchers are attempting to estimate the potential ef?cacy and side
19.2 TWO TOUCHSTONES 345
effects of the drug. Although all these preclinical activities are costly, the costs
increase substantially once a compound proceeds to clinical trials.
To better understand the stages of a clinical trial, we consider a prototypical
drug development project by Drugco for Newdrug, a chemical compound designed
to treat complications of diabetes. Before any human trials can begin, Drugco must
?le an Investigational New Drug (IND) application with the FDA. If the FDA
accepts the IND, then Phase I trials can begin. In Phase I trials, Newdrug is given to
a small number of healthy volunteers—those without diabetes or any other serious
medical condition. Because Phase I trials take place in healthy subjects, it is not
possible to assess the ef?cacy of the drug. Instead, the purpose of Phase I trials is to
assess the safety of the treatment and to establish some baselines of how the drug is
metabolized in humans. On average, Phase I trials cost about $15M and take one
year to complete.
2
If Phase I trials are “successful”, then Drugco may proceed to Phase II. What
determines success? Obviously, the drug must appear relatively safe. Virtually all
drugs have some side effects, but Drugco must carefully weigh the potential side
effects against its estimated ef?cacy before deciding whether to proceed. While the
FDA will sometimes approve drugs with serious side effects, this is only likely
when the drug ?lls a serious medical need. In addition to safety, Drugco may also
consider any changes in the business conditions related to Newdrug. A lot can
happen in the one year it takes to complete Phase I trials. Drugco would be par-
ticularly aware of any alternative diabetes treatments coming to market and of any
changes in the willingness of insurance companies and government agencies to pay
for diabetes drugs.
Phase II trials are the ?rst opportunity for Drugco to test the ef?cacy of
Newdrug in diabetes patients. On average, these tests use several hundred patients,
take two years, and cost $25M. During these trials, the drug is assessed for both
ef?cacy and side effects. It is important to note that these trials must conform to the
highest standards of medical testing: double-blind randomized trials. In these trials,
some patients receive the actual drug, whereas others receive either an identical-
looking but inactive placebo, or an existing standard treatment. Here, “double-
blind” means that neither the patient nor the treating physician is aware of whether
the patient has received the actual drug or a placebo or standard treatment. This is
important, as some researchers can behave differently toward patients depending on
whether they are given treatments or placebos.
After Phase II, Drugco must decide whether to proceed to Phase III. On
average, Phase III trials take three years and cost $85M. These trials typically
include thousands of patients across several different medical centers. The objec-
tive of this phase is to assess de?nitively the ef?cacy of the new drug compared
with the current “gold standard” treatment for the indication. At the end of Phase III
trials, Drugco will submit all their data to the FDA. In making an approval decision,
2
Cost estimates for clinical trials are from DiMasi et al. (2003).
346 CHAPTER 19 R&D FINANCE
the FDA relies heavily on advisory panels of specialized physicians, who weigh the
potential costs (side effects) and bene?ts (ef?cacy). The FDA would typically take
alternative treatments (or lack thereof) into account when considering the potential
bene?ts of the drug. The FDA approval process takes an average of 18 months
following the completion of Phase III.
Exhibit 19-7 gives a graphical depiction of the Newco project. The exhibit
shows three different types of risks: technical risks, business risks, and compe-
titive risks. Any or all of these risks may play a role at any point in the project.
Technical risks are the most straightforward. For Newdrug, the technical risks are
“Will this drug work?” (ef?cacy) and “Will this drug harm patients?” (side effects).
These technical risks exist at every stage—it is even possible to learn of new side
effects long after a drug has been approved. For valuation purposes, technical risks
are often the easiest to model. There are two reasons for this ease of modeling.
First, as narrowly de?ned scienti?c or engineering projects, it is often possible for
project scientists to accurately estimate the probabilities of success. Scientists, with
long experience and a familiarity with probability and statistics, can provide ana-
lysts with well-informed estimates. Second, as we ?rst studied in Chapter 4,
technical risks often have a zero beta (i.e., no correlation with the market). In this
case, we can use the risk-free rate as the discount rate and do not have to deal with
the complexities of computing a risk-adjusted discount rate. The modeling of
technical risks can often be accomplished using Monte Carlo simulation, a topic to
be covered in Chapter 20.
EXHIBIT 19-7
DRUG DEVELOPMENT
COMPETITIVE RISKS BUSINESS RISKS
Phase I
Safety tests
on healthy
volunteers
Phase II
Medium-scale
efficacy and safety
tests
Phase III
Large-scale
efficacy and safety
tests
FDA Approval?
Based on efficacy
and safety
First to market?
Better
alternative? Pricing Reimbursement
One year avg Two years avg Three years avg 18 months avg
Efficacy and safety
affect market size, share, and growth
TECHNICAL RISKS
19.2 TWO TOUCHSTONES 347
Business risks can take many forms. In general, a business risk relates to changes
in consumer preferences. For example, the demand for Newdrug would be affected by
the performance of the overall economy, because the availability of health insurance
and consumers’ willingness to pay out of pocket would both be affected by the strength
of the labor market. Also, because diabetes strikes disproportionately among older
patients, it is likely that Medicare—government-run health insurance for citizens over
the age of 65—would be a major customer. Thus, Drugco needs to worry about the
pressure of federal budgets. These types of risks would certainly have positive market
betas and would require risk-adjusted discount rates. The computationof these discount
rates requires careful modeling for the timing of various investment decisions. These
models often use decision trees and real-options analysis (to be studied in Chapter 21),
sometimes aided by the use of binomial trees (to be studied in Chapter 22).
Competitive risks relate to the behavior of other companies. For the devel-
opment of Newdrug, Drugco needs to worry about the competitive responses of
other drug companies in the diabetes business. In response to Newdrug, competitors
may accelerate (or decelerate) their own diabetes drug projects. Even if these
competitors do not develop new drugs, they may alter the pricing of existing drugs,
?le lawsuits claiming the infringement of some intellectual property, or increase
their sales efforts on existing drugs. Some of these activities depend on the state of
the economy and hence would carry positive betas and require the calculation
of risk-adjusted discount rates. In any case, competitive risks require careful
modeling using game theory, a topic covered in Chapter 23.
19.2.2 Energy Innovation
Fuelco is considering several development projects using its patented Newcell
technology. Project A is a government contract that requires competitive bidding
against other companies. Project B is a product to be sold to automotive manu-
facturers for eventual resale in consumer projects. Project C is product to be sold
directly to consumers. The technology for Project C requires a successful com-
pletion of Projects A and B as inputs. Exhibit 19-8 sketches the timeline and risks
for these projects.
In the shorthand representation of Exhibit 19-8, we see that each of the three
projects has technical risks, with Project C effectively incorporating technical risks
from Projects A and B in addition to direct risks from Project C. All three projects
may have competitive risks. These risks are clearest for Project A, which must
compete for a government contract against other companies. Business risks may be
largely absent from Project A (if we are willing to believe that the government will
follow through on the contract regardless of economic conditions), but these
business risks are present for Projects B and C. In some cases, long-term contracts
with potential customers can alleviate business risk in the short run (particularly for
Project B), but in the long run it is dif?cult for energy projects to completely
eliminate business risks. For Fuelco, the main business risk is the price of crude oil.
348 CHAPTER 19 R&D FINANCE
If oil is relatively expensive, then there is more scope for alternative energy projects
such as Newcell.
In the Newdrug example of the previous section, the regulatory hurdles
provide us with a clear framework for modeling. Here, we have no such luck. To
model Fuelco’s decisions, we will need to make some informed assumptions about
the length of time for various development steps, the probability of success for
these steps, and the potential market size for each project. Although the Newdrug
problem is relatively tidy, the Newcell problem is much messier and much more
representative of “typical” R&D projects.
19.3 HOW IS R&D FINANCED?
Return now to our ?rst touchstone, Drugco’s R&D project for Newdrug. Suppose
Drugco estimates that the Newdrug project will cost $100M to reach FDA approval.
What options does Drugco have to ?nance this project? In this section, we consider the
following options: (1) government, (2) internal corporate funds, (3) banks, (4) public
debt markets, (5) public equity markets, (6) venture capital, and (7) strategic partners.
1. Government. In the United States, the federal government funds about
25 percent of all R&D. This total funding of $104B in 2008 was performed at
federal, academic, and industrial locations. Although nearly $14B of this
$104B was used for development-stage R&D in industry, the majority of that
$14B was for defense-related projects. Thus, unless Newdrug is believed
to have some biodefense function, it is unlikely that Drugco will be able to
?nance much of their required $100M from direct government sources.
EXHIBIT 19-8
FUEL CELL PROJECT
1 Year Total
Project A
(government contract)
Technical risk A (does tech A work?)
Competitive risk A (do we win the bid?)
Project B
(sold to auto manufacturers)
Technical risk B (does tech B work?)
Business risk B (what happens to oil prices?)
Project C
(sold to consumers)
Technical risk A, B, and C (do tech A,B,C all work?)
Business risk C (what happens to oil prices?)
Competitive risk C (what do other companies do?)
Technical risk is uncorrelated across the three projects
Business risk (oil prices) is correlated across B and C
Competitive risk is uncorrelated across A and C
19.3 HOW IS R&D FINANCED? 349
Nevertheless, although the government is unlikely to be much help in
the direct ?nancing of the Newdrug project, Drugco may receive a sig-
ni?cant bene?t from the tax system. The ?rst bene?t is that, unlike other
investments, R&D spending is treated as an expense for tax purposes, so that
with an effective federal tax rate of 35 percent, (pro?table) companies can
recover more than one-third of their costs when they ?le their taxes. Fur-
thermore, the United States—like most developed countries—has an R&D
tax credit. A $1 credit is more valuable than a $1 deduction, because a $1
deduction only gives a company 35 cents. The federal Research and
Experimentation Tax Credit was ?rst introduced in 1981 and provided
companies with a credit of 25 percent of “incremental” R&D costs, where
these incremental costs are de?ned as Quali?ed Research Expenses
(QREs). Although the de?nition of QREs is complex and often contentious,
on average they comprise about two-thirds of all R&D costs.
From 1981 to 2009, the “temporary” R&D tax credit was extended 14
times, and the credit grew more complex and slightly less generous. In its
most recent form, the typical credit gives companies 20 percent of their
QREs. On December 31, 2009, the latest version of the R&D tax credit
expired. As of this writing (early 2010), a bill extending the credit through
the end of 2010 has passed the House, and is being considered at the Senate
(where, if history is any indication, it will probably pass again). In addition
to the federal tax credit, many states and municipalities have passed their
own R&D tax credits, although total expenditures for these local credits are
far lower than the federal version.
2. Internal corporate funds. A pro?table company can ?nance R&D from its
own positive cash ?ows. Although $100M for Newdrug might seem like a
lot of money, it would only buy a small portion of the R&D at the largest
pharmaceutical companies. We do not have aggregate statistics to tell us the
percentage of R&D ?nanced by internal funds, but we can still draw some
inferences from the data. Exhibit 19-9 gives the size distribution of com-
panies in the United States, along with the R&D spending for each size
group.
We see from this data that more than half of all R&D spending is
made by those companies that have more than 10,000 employees. These
companies collectively employed nearly 10 million people in the United
States alone and had domestic sales of more than 4 trillion dollars in 2007.
Because it is dif?cult to sustain such large enterprises without pro?ts, it is
likely that a large portion of that R&D could be ?nanced by internal funds.
For smaller companies, we cannot be as sure about the availability of
internal funds. For example, the vast majority of publicly traded bio-
technology ?rms has fewer than 500 employees and has a negative cash
?ow. It is safe to assume that—at least for these money-losing companies—
internal funds will not be suf?cient to pay for a $100M project like
Newdrug.
350 CHAPTER 19 R&D FINANCE
3. Banks. In the United States, banks provide the majority of external capital
for small companies. In other developed countries, banks have a near-
monopoly on small-company ?nance. Nevertheless, banks are unlikely to
provide any signi?cant funds for a $100M project like Newdrug. Banks are
?nancial institutions that specialize in making loans backed by collateral
and a demonstrated ability to repay. A typical bank loan would allow a
pro?table manufacturer to invest in plant, property, or equipment. Such
loans rely on the manufacturer’s positive cash ?ow from other operations,
combined with the ability to seize the purchased assets in foreclosure. For
riskier loans, banks often turn to various government guarantees. In the
United States, the largest such programs are run by the Small Business
Administration, which effectively subsidizes loans for “small” companies.
Although such loans are certainly helpful for some development projects,
the maximum loan size is about $1M and would provide little help for
Drugco.
4. Public debt markets. Historically, public markets for corporate debt have
been able to take on projects that are either too large or too risky for an
individual bank. For example, it was European investment in publicly traded
bonds that largely ?nanced the expansion of railroads in the United States.
Although railroads may seem a staid industry today, it was a capital-hungry
and speculative industry in the middle of the nineteenth century. More than
EXHIBIT 19-9
R&D EXPENDITURE AND COMPANY SIZE IN 2007
Size of company
(number of employees) $B
5À24 $10.9
25À49 $7.9
50À99 $10.1
100À249 $13.4
250À499 $8.3
500À999 $14.3
1,000À4,999 $41.1
5,000À9,999 $22.7
10,000À24,999 $45.9
25,000 or more $94.8
Total $269.3
Source: NSF (2009), p. 2.
19.3 HOW IS R&D FINANCED? 351
100 years later, the public bond markets ?lled a ?nancing void for mezza-
nine debt in the large leveraged buyouts of the 1980s. These so-called junk
bonds, junior to bank debt in the capital structure, allowed some LBO
investors to purchase large companies with less than 10 percent of the deal
in equity. Fifteen years later, in the latest credit boom of 2005À2007, the
rapid growth of collateralized debt obligations (CDOs) and collateralized
loan obligations (CLOs) markets helped LBO ?rms to buy even larger
companies, though the debt-to-equity ratio was considerably lower this time
around.
Would public debt markets be willing to ?nance Drugco’s $100M
Newdrug project? It is highly unlikely. Although Newdrug is risky like old-
time railroads and new-age LBOs, it is unlike those projects in its inability
to pay interest in early years. When railroads were successful, they would
have revenues within a few years at most, and most LBOs are even quicker.
Newdrug, on the other hand, is expected to take between ?ve and seven
years before FDA approval is possible. Until that point, the project would
have costs but no revenues. To ?nance such a project would require zero-
coupon bonds, which accrue all interest until their expiration date. However,
a zero-coupon bond on a risky project would require a very high interest
rate. In this case, the bond would pay off zero if the project failed and would
give a large payout, far in the future, if the project succeeded. This sounds a
lot like equity! Indeed, the ?nancial instrument just described is almost the
de?nition of “equity capital”, which we turn to next.
5. Public equity markets. Without question, public equity markets ?nance a
signi?cant fraction of R&D. For evidence, one needs to look no further than
the biotechnology industry. There are currently about 350 publicly traded
biotechnology companies, which collectively have over $40B in sales.
Approximately one-third of these sales are plowed back into R&D. This
industry loses a lot of money: only about one-sixth of all biotech ?rms are
pro?table, and the collective losses for the industry have been between $10B
and $15B per year since 2000. Overall, the industry’s losses are about equal
to its R&D spending, and that money has to come from somewhere. Since
the founding of the industry in the 1970s, biotechnology ?rms have raised
about $150B, about 60 percent of which came from the public markets.
3
From this evidence, we can conclude that public equity markets might
make a dent in the $100M Newdrug project. Indeed, public markets are
capable of funding projects of this size, and many public biotech companies
can largely ?nance their drug development by issuing stock to the public.
For nonpublic companies, however, such issuance would require an IPO.
Historically, biotech companies usually must be in Phase III trials, or at least
3
All statistics on the biotechnology industry are from Burrill (2005).
352 CHAPTER 19 R&D FINANCE
far along in Phase II, before an IPO is possible. Outside the biotech
industry—except during the boom period of the late 1990s—companies
typically need to be pro?table before they can go public. Thus, if Fuelco
(Section 19.2.2) were not already public or pro?table, then it would be
dif?cult for it to use an IPO to raise funds for the fuel cell project.
Overall, public equity markets are an important source of capital for
R&D projects. Nevertheless, even with the other main sources discussed
earlier—governments and internal funds—there are still some ?nancing
gaps that need to be ?lled. In particular, applied research and the earliest
stages of development are ?nancing challenges for negative cash ?ow
companies.
6. Venture capital. Public equity markets have ?nanced approximately 60
percent of the $150B raised by the biotech industry; the other 40 percent
came from VCs. Readers of the previous 18 chapters will already know that
VC is an obvious source to ?ll the ?nancing gap for applied research and
early development-stage projects. Unfortunately for Drugco, many biotech
VCs are wary of investing in projects in Phase I trials. The low probability
of success coupled with large capital needs has pushed most VCs toward
projects at Phase II and beyond. Although some VCs do still invest in at
Phase I, projects like Newdrug face a dif?cult task in attracting VC
investment, and few VCs would be willing (or able) to support Newdrug
through the entire approval process. At some point, Drugco will need to
raise public equity or receive an investment from a larger company.
7. Large companies. If Drugco is a small company without signi?cant internal
funds or access to public markets, then the main alternative to VC is to form
a strategic alliance with a large drug company. Here, we use the term
strategic alliance to mean any long-term agreement between companies.
The most common strategic alliance in high-tech industries is an R&D
licensing agreement, also known simply as a license. In a typical licensing
agreement, the larger company pays the costs for an R&D project performed
by a smaller company in return for receiving some rights to the technology.
In addition to the direct R&D costs, the larger company often provides an
upfront payment at the time the deal is signed and milestone payments as
the project advances. If the larger company has received the rights to sell
products based on the technology, then the agreement would typically
include royalty payments as some fraction of these sales. Finally, in some
cases the larger company will make a direct investment in the smaller
company at the time of the deal.
Suppose that Drugco enters an R&D licensing agreement with Bigco
for the Newdrug project. Drugco expects to need $100M to pay for the
R&D. Bigco agrees to pay these R&D costs, plus a $50M upfront payment
and additional milestone payments of $25M if Newdrug makes it to
Phase II, $50M for Phase III, and $100M for FDA approval. In return,
19.3 HOW IS R&D FINANCED? 353
Bigco receives exclusive worldwide marketing rights for Newdrug, with a
10 percent royalty paid to Drugco on all sales. With this license, Bigco
would expect to pay a total of $100M+ $50M+ $25M+$50M+$100M
5$325M just to get Newdrug approved, plus the royalty on all sales.
Obviously, Bigco only enters this transaction if they believe that the NPV
for their share of the sales is worth this investment. Many deals of this size
or larger are signed every year in the pharmaceutical industry. Overall,
licensing deals are the most important source of ?nance for pharmaceutical
R&D at small companies.
Licensing deals can be both lucrative and complex, with many oppor-
tunities for ?nancial analysis and the use of option-pricing techniques. For
example, consider the following deal in 2005 between Anadys Pharmaceu-
ticals Inc. (the smaller company) and Novartis AG (the larger company):
Novartis gets the exclusive worldwide development, manufacturing, and
marketing rights to Anadys’s ANA975 and other [similar compounds] for
chronic hepatitis B and C viruses and other infectious diseases . . . .
Novartis will pay a $20M up-front license fee, $550M in regulatory and
commercial milestones for the development and marketing of ANA975,
including $10M payment upon a successful IND submission (it antici-
pates a mid-2005 ?ling). Novartis will provide funding for 80.5 percent
of the expenses associated with developing the lead candidate, with
Anadys funding 19.5 percent of the costs. Anadys has a co-promotion
option to keep 35 percent of the U.S. pro?ts if it pays that percentage of
the marketing costs. If Anadys declines the option, it will get royalties on
global sales of the resulting product. No equity was exchanged. (Source:
In Vivo, July/August 2005, p. 92)
This agreement poses several interesting problems for a ?nancial ana-
lyst. In addition to valuing the product conditional on FDA approval (this is
somewhat like a success-case exit valuation), it is necessary to estimate the
probabilities for achieving each milestone and to value the Anadys option to
pay marketing costs. Novartis must make all these estimates before agreeing to
this deal. Unlike leanly staffed VC ?rms, large companies like Novartis often
have specialized groups whose sole purpose is to value these deals. Such
groups are heavy users of the tools studied in the next ?ve chapters.
19.4 WHERE DO WE GO FROM HERE?
In this chapter, we gave brief descriptions of two examples of R&D projects: a
pharmaceutical project (drug development) and an energy project (fuel cell
development). The schematic exhibits that accompanied these descriptions,
354 CHAPTER 19 R&D FINANCE
Exhibits 19-7 and 19-8, summarize the types of risks involved, but do not give us
any speci?c models to analyze. In future chapters, we provide more structure for
these (and other) examples in specialized diagrams known as trees. The following
paragraph describes various types of trees that will be analyzed in the next ?ve
chapters. This description is only intended to provide a road map for Part IV—
readers are not expected to know how to de?ne or use any of these trees until after
they have been covered in the later chapters.
The simplest tree is an event tree, which we will study in Chapter 20. Event
trees are particularly useful for handling technical risks. Once a decision on a
project has been made, event trees help us to value that project. If, instead, we want
a tool to help us decide between different options, we use a decision tree, which
we introduce in Chapter 21. Decision trees are particularly helpful in dealing with
technical risks and business risks that are intertwined with future decisions, with
the trees showing us if any of the key decisions can be delayed until after these
risks have been resolved. Such delay often gives rise to real options, which we also
study in Chapter 21. Binomial trees, studied in Chapter 22, are a special case of
decision trees. In this special case, if we restrict the way that certain risks are
modeled, we can pack a large amount of information into a model. Binomial trees
are particularly useful for the valuation of options that provide some payoffs before
the expiration (or exit) date. In Chapter 23 we introduce game theory and game
trees, which allow us to model the actions of multiple decision makers in one
diagram. Game trees are helpful for modeling competitive risks such as technology
races or competitive bidding. Finally, in Chapter 24 we pull all these tools together
and solve full-blown models for the drug-development and energy-innovation
projects.
SUMMARY
Research and development (R&D) is about 2.7 percent of the U.S. economy and is the
primary driver of long-run economic growth. In the United States, almost two-thirds of R&D
is funded by corporations, with half of that spending occurring in large corporations that have
more than 10,000 employees. R&D investment decisions share many features with VC
investment decisions, with long time horizons, high failure rates, and business risks
embedded in a rapidly changing technological landscape. In this chapter we introduced two
prototypical R&D projects—one in drug development and one in energy innovation. Drug
development takes place in a highly regulated environment, which lends itself to structured
models with well-speci?ed data and milestones. The energy-innovation project is typical of
most other R&D projects, with little regulatory structure and many modeling decisions
necessary for the analyst.
In the previous chapters, we studied the VC industry in great detail. Although VC is an
important contributor to R&D projects at small companies, most R&D is ?nanced from other
sources, including internal cash ?ow, public equity markets, and strategic alliances. R&D
licensing agreements—a type of strategic alliance—play a particularly important role in the
funding of drug development R&D.
SUMMARY 355
KEY TERMS
Research and development
(R&D)
Basic research, applied
research, development
Preclinical, Phase I, Phase
II, Phase III, FDA
approval
Clinical trials
5human trials
Technical risks, business
risks, competitive risks
R&D tax credit
Qualified Research
Expenses (QREs)
Strategic alliance
R&D licensing agreement
5license
Upfront payments, mile-
stone payments, royalty
payments
Trees, event trees, decision
trees, binomial trees,
game trees
REFERENCES
Burrill & Company, 2005, Biotech 2005, Burrill & Company LLC, San Francisco, CA.
DiMasi, Joseph A., Ronald W. Hansen, and Henry G. Grabowski, “The Price of Innovation: New
Estimates of Drug Development Costs”, Journal of Health Economics 22, 151À185.
National Science Foundation, 2005, National Patterns of Research and Development Resources: 2003,
NSF 05À308, Brandon Shackleford, Arlington, VA.
National Science Foundation, 2008, National Patterns of R&D Resources: 2007 Date Update, NSF 08-
318, Mark Boroush, Arlington, VA.
National Science Foundation, 2009, Info Brief, NSF 09À316, Raymond M. Wolfe, Arlington, VA.
National Science Foundation, 2010, Info Brief, NSF 10À312, Mark Boroush, Arlington, VA.
UNESCO Institute for Statistics, 2007, A Global Perspective on Research and Development: Fact Sheet,
UIS/FS/07/05, available at www.uis.unesco.org.
356 CHAPTER 19 R&D FINANCE
CHAPTER 20
MONTE CARLO SIMULATION
IN MANY R&D projects, several random variables can affect the outcome.
To compute the NPVs of these projects, it is necessary to multiply the probability of
each outcome by its corresponding payoff. When many different risks intersect at
one time, this computation can be dif?cult or impossible. To solve this problem,
analysts often use computers to simulate thousands (or millions) of possible out-
comes and then estimate the NPV as the average of these simulated outcomes.
Because these computational methods are reminiscent of games of chance in Monte
Carlo, the most popular method is called Monte Carlo simulation.
In this chapter, we learn the concepts and mechanics behind these simula-
tions. In Section 20.1, we show how to represent uncertainty by using event trees,
and we demonstrate how to solve for the NPV of an event tree by Monte Carlo
simulation. The problems in Section 20.1 use simple discrete random variables
with two possible outcomes: “success” or “failure”. In Section 20.2, we introduce
continuous random variables and demonstrate how to use these variables in
Monte Carlo simulation. The examples in Section 20.1 and 20.2 are relatively
simple and, in fact, could be solved without using simulation. In Section 20.3, we
model a version of the Newdrug project from Chapter 19. In this model, there are
several independent sources of uncertainty, and simulation provides the fastest
route to a solution.
20.1 EVENT TREES
Drugco has just begun Phase III trials for Newdrug. Drugco’s scientists estimate
that the R&D has a 50 percent chance of success (5FDA approval), and Drugco
management estimates an NPV of $1B at the time of approval. If the drug fails,
then it would be worth nothing. The success of the drug will be learned over
the next three years, over which the discount rate is equal to the riskfree rate of
357
5 percent per year.
1
The total cost of R&D is $100M and must be paid at the
beginning of development. Exhibit 20-1 gives a graphical representation of this
information using an event tree.
The event tree uses circles to signify a risk node in the tree. In this case, the
risk node is followed by two possible branches. The success branch has a pro-
bability of 50 percent, leading to a terminal node with a payoff of $1B. The failure
branch has a probability of 50 percent, leading to a terminal node of $0. We can use
all the information in the tree to calculate the expected value of the terminal nodes
as 0.5 Ã $1B5$500M. Using a discount rate of 5 percent for three years, we can
compute the NPV of the new drug as
NPV50:5 Ã $1B=ð1:05Þ
3
2$100M5$331:9M: ð20:1Þ
This is about as easy as a valuation can get: one source of risk, two branches, and
a constant discount rate. For the next ?ve chapters we will take problems like this and
add complications. In many cases, these complications make it dif?cult to calculate
NPVs in simple equations like (20.1). In those cases, Monte Carlo simulation is
often the most ef?cient way to compute the NPV. In Monte Carlo simulation, the
1
Why the riskfree rate? Recall the Boxco versus Drugco example from Chapter 4: if the project only has
technical risk, then this risk can be diversi?ed away and has a zero beta. We discuss discount rates in
more detail in Chapter 21.
EXHIBIT 20-1
EVENT TREE FOR NEWDRUG
Phase III
$–100M
$1B
$0
0.5
0.5
FDA Failure
FDA Approval
3 years
358 CHAPTER 20 MONTE CARLO SIMULATION
analyst generates random numbers and “simulates” thousands of possible outcomes
for the event tree. Then, the average outcome is the expected value of the tree.
In our simple Newdrug tree, the only random variable is FDA approval of the
drug, which has a simple yes/no probability distribution. To simulate this dis-
tribution, we can imagine ?ipping a coin 10,000 times, with each “heads” ?ip
leading to FDA approval, and each “tails” ?ip leading to FDA failure. On average,
this process will give us 5,000 ?ips of heads, so the expected outcome will be the
same as Equation (20.1). To perform this randomization on a computer—a much
more ef?cient way to ?ip a coin—we can either use specialized simulation soft-
ware, or we can program the simulation ourselves using a general package like
Microsoft Excel.
For the next two examples in this chapter, we will show how to do the simu-
lation “the hard way” using Microsoft Excel. By doing some simple examples in
Excel, the reader can learn the intuition and mechanics behind the simulation
methods. For complex examples, programming everything in Excel becomes
unwieldy, and it is much more ef?cient to use a specialized package. In Appendix Cof
this book, we provide a brief users’ guide to Crystal Ball
s
, a popular simulation
program that works as an add-in to Excel. In that appendix, we also provide Crystal
Ball solutions for all the examples in this chapter.
To compute the NPV of Newdrug using Excel, we use the random number
function—the Excel command is “rand()”—to generate a random number between
0 and 1. Then, if this random number is less than or equal to 0.5, we classify
the outcome as FDA approval. If the outcome is greater than 0.5, we classify the
outcome as FDA failure.
Exhibit 20-2 displays the output for 10 draws of the simulation. In the
“Random Number” column, we type the Excel command “rand()”, which yields a
random number between 0 and 1. In the “FDA Approval” column, we use an if
EXHIBIT 20-2
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw Random number 5 rand() FDA approval? NPV
1 0.8172 0 2$100.00
2 0.8729 0 2$100.00
3 0.3396 1 $763.84
4 0.9276 0 2$100.00
5 0.0186 1 $763.84
6 0.6416 0 2$100.00
7 0.4539 1 $763.84
8 0.9188 0 2$100.00
9 0.2199 1 $763.84
10 0.3146 1 $763.84
20.1 EVENT TREES 359
statement: if (Random Number ,0.5, 1, 0), which yields the answer of one if FDA
approval occurs, and zero if it fails.
2
Finally, the NPV column computes the NPV as
FDA Approval à $1B/(105)
3
À $100M. To run multiple draws, we need only type
these formulas into the ?rst row and then copy this row down. (Thus, it is just as
easy to do 10,000 draws as it is to do 10.) The average of the “NPV” column is the
Monte Carlo estimation of the NPV. On average, we should get $331.9M, the same
answer as achieved from Equation (20.1).
Of course, real problems are rarely so simple. A slightly more complex
version of the problem would consider all three phases of the approval process. We
do this in the next example.
EXAMPLE 20.1
Drugco has just begun Phase I trials for Newdrug. Phase I takes one year and costs
$10M. Drugco’s scientists estimate that the R&D has a 50 percent chance of successfully com-
pleting Phase I and moving toPhase II. Phase II takes one year and costs $30M. If Newdrug enters
Phase II, the scientists estimate a 40 percent chance of successfully completing Phase II and
movingtoPhase III. Phase III takes three years (including the time waiting for FDAapproval) and
costs $60M. If Newdrug enters Phase III, the scientists estimate a 50 percent chance of success
(5FDAapproval). Drugco management estimates an NPVof $1B at the time of approval. If the
drug fails, then it would be worth nothing. The discount rate is equal to the risk-free rate of
5 percent per year. All development costs must be paid at the beginning of the respective phase.
Problems
(a) Draw the event tree for the Newdrug project.
(b) Find and solve the formula for the NPV of the Newdrug project.
(c) Build a Monte Carlo simulation for Newdrug and con?rm the same (average) NPV
solution as obtained in part (b).
Solutions
(a) Given the information in the example, we can drawthe event tree as shown in Exhibit 20-3.
(b) In Exhibit 20-3, there is a different probability of success for each stage. Each risk node
in the tree is given a number (1 to 3 in the tree) to help us keep track of things. At any node,
the failure branch ends the project and has a payoff of zero. Only the terminal node with $1B
has a positive payoff. To ?nd the NPV of the project, we must compute the probability of
reaching each node in the tree, and then discount the expected payoffs of those nodes by the
appropriate number of years. Thus, the NPV for Node 1 is À$10M, and
NPV of Node 2 5ð0:5 Ã 2$30MÞ=1:05 5 2$14:3M; ð20:2Þ
NPV of Node 3 5ð0:5 Ã 0:4 Ã 2$60MÞ=ð1:05Þ
2
5 2$10:9M; ð20:3Þ
NPV of terminal node of $1B5ð0:5 Ã 0:4 Ã 0:5 Ã $1BÞ=ð1:05Þ
5
5$78:4M: ð20:4Þ
2
In the actual Excel spreadsheet, we would need to use an exact cell address instead of “random vari-
able”. Similarly, other examples in this chapter will use variable names instead of cell addresses.
360 CHAPTER 20 MONTE CARLO SIMULATION
So the NPV of the whole project is
NPV of project 5$78:4M2$10M2$14:3M2$10:9M5$43:1M: ð20:5Þ
(c) To do a Monte Carlo simulation, we de?ne a random variable in Excel for each risk node
and then combine these random variables with the costs of development and terminal values,
just as in Equation (20.4). Exhibit 20-4 demonstrates an example of this simulation.
In Exhibit 20-4, Phase I success depends only on the outcome of the ?rst random
number [labeled as (1) in the top row of the table], Phase II success depends on the outcome of
EXHIBIT 20-4
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw
(1)
rand()
Phase I
success?
(2)
rand()
Phase II
success?
(3)
rand()
FDA
approval? NPV
1 0.4127 1 0.0373 1 0.7718 0 2$92.99
2 0.8501 0 0.7807 0 0.0544 0 2$10.00
3 0.9134 0 0.8742 0 0.9967 0 2$10.00
4 0.7750 0 0.6548 0 0.2297 0 2$10.00
5 0.9448 0 0.4999 0 0.5549 0 2$10.00
6 0.9625 0 0.5304 0 0.0089 0 2$10.00
7 0.0766 1 0.3117 1 0.5861 0 2$92.99
8 0.1479 1 0.7106 0 0.4112 0 2$38.57
9 0.9461 0 0.3570 0 0.0422 0 2$10.00
10 0.1802 1 0.0104 1 0.0674 1 $690.53
EXHIBIT 20-3
EVENT TREE WITH THREE RISK NODES
Phase I
$–10M
Phase II
–$30M
Phase I
success
Phase I
Failure
Phase II
Failure
FDA
Failure
Phase II
success
Phase III
$–60M
FDA Approval
Year 0 Year 1 Year 2 Year 5
0.5
0.5 0.5 0.6
0.4 0.5
$1B
$0 $0 $0
1 2 3
20.1 EVENT TREES 361
both Phase I and Phase II [labeled as (2) in the top row], and FDA approval requires Phase I
success, Phase II success, plus the outcome of Phase III [labeled as (3) in the top row].
The average estimate from this simulation is $43.1M, the same answer as we obtained
in part (b). ’
20.2 SIMULATION WITH CONTINUOUS
PROBABILITY DISTRIBUTIONS
Example 20.1 used discrete random variables, where the different outcomes can
be separated when plotted on a line, like a “1” for success and a “0” for failure. In
many applications, it is necessary to use continuous random variables, where the
different outcomes have no gaps when plotted on a line. Continuous variables
have an in?nite number of possible outcomes, where the relative likelihoods of
these outcomes is represented as a probability density function (pdf) and drawn as
two-dimensional curve.
The simplest type of continuous distribution is the uniform distribution. If a
variable x is distributed as a uniform distribution with a minimum point of a and
a maximum point of b, then we use the shorthand notation x B U [a, b], where
“B” stands for “is distributed as”. We write the pdf, f(x), as
Uða; bÞ : f ðxÞ 51=ðb 2aÞ: ð20:6Þ
Exhibit 20-5 illustrates this pdf.
For Monte Carlo simulations, we will make heavy use of the cumulative
distribution function (cdf). The cdf, written as F(x), is the area under a pdf up to
EXHIBIT 20-5
UNIFORM PDF
a b
f(x)
1
b-a
362 CHAPTER 20 MONTE CARLO SIMULATION
point x, which can be written as the integral of f(x) from the distribution mini-
mum to x.
The cdf of a uniform distribution is
FðxÞ 5
Z
x
a
1
b 2a
dz 5
x 2a
b 2a
: ð20:7Þ
By construction, all cdfs must be equal to one at the maximum of their range.
The uniform cdf is illustrated in Exhibit 20-6.
In general, the mean (5 expected value) of a continuous random variable, x,
can be written as the integral
Z
N
2N
x à f ðxÞ dx: ð20:8Þ
For a uniform distribution, we have f(x) 5 1/(b 2 a). Also, the upper and
lower bounds are not in?nity, but are given by a and b. Thus, the mean of a uniform
distribution can be solved as
Z
b
a
x Ã
1
b 2a
dx 5
b
a
x
2
2ðb 2aÞ
5
b
2
2a
2
2ðb 2aÞ
5
ðb 1aÞðb 2aÞ
2ðb 2aÞ
5
b 1a
2
: ð20:9Þ
Now, let’s use the uniform distribution in an NPV calculation.
EXHIBIT 20-6
UNIFORM CDF
a b
F(x)
1
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 363
EXAMPLE 20.2
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we are
sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy. Ef?cacy
is distributed E BU [0,1] and will be learned during three years of Phase III trials. The NPV
of the drug after 3 years is $1BÃ E
2
(i.e., even with a low ef?cacy and a high likelihood of
FDA failure, we are still allowing for some salvage value for the project). The discount rate is
equal to the riskfree rate of 5 percent per year. The total cost of R&D is $100 M and must be
paid at the beginning of development.
Problems
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) Why is the answer to part (b) different than the answer to part (c)?
Solutions
(a) We begin with the event tree, given in Exhibit 20-7.
Because the uniform distribution has an in?nity of possible outcomes, we do not bother
drawing lots of branches, but instead draw three branches connected by a curve. The notation
for the distribution— U[0,1]— is then given after an arrow on the middle branch. The top
EXHIBIT 20-7
EVENT TREE FOR NEWDRUG, WITH UNIFORM DISTRIBUTION
Phase III
$–100M
$1B
$1B *E
2
E ~ U[0, 1]
$0
Efficacy?
3 years
364 CHAPTER 20 MONTE CARLO SIMULATION
branch represents the maximum of the distribution (if applicable), and the bottom branch
represents the minimum. The main formula for the terminal nodes is given on the middle
terminal node. In the remaining chapters, we follow this same convention for representing
continuous distributions within trees.
(b) From Equation (20.9), we know that the mean (5 expected value) of a uniform dis-
tribution is equal to (b 1 a)/2. In this case, we have b 5 1 and a 5 0, so the mean is 1/2. If
we substitute E 51/2, then the expected terminal value would be $1BÃ (1/2)
2
5$250 M, and
the NPV would be $250 M/(1.05)
3
2 $100 M 5 $116.0 M.
(c) To simulate from a continuous distribution, we must invert the cdf to ?nd the ef?cacy
(E) that goes with a speci?c random draw. To provide a graphic illustration of this inversion,
consider the following three steps:
Step 1: Draw a random number between 0 and 1.
Step 2: Plot this random number on the Y-axis of the cdf.
Step 3: Find the corresponding point on the X-axis.
The answer to Step 3 is the “draw” from the continuous distribution. These three steps
are illustrated in Exhibit 20-8 for an example draw of rand() 50.748. For this case, the
sampling procedure turns out to be very easy, because the cdf of a U [0,1] distribution is just
F(E) 5E. Nevertheless, for even more complex distributions considered later, we can still
visualize the procedure using the same three steps. Of course, the actual steps are done by a
computer. With our knowledge that F(E) 5E, we build an Excel worksheet to perform the
simulation.
EXHIBIT 20-8
SAMPLE FROM A CDF FOR E B U[0, 1]
STEP 2
STEP 3
1
0, 0
STEP 1
rand()
? 0.748
F(E)
E ? 0.748 1
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 365
Exhibit 20-9 displays sample output from 10 draws.
On average, this simulation yields an estimate of $187.9M for the NPV.
(d) In part (b), we substituted the mean value of E51/2 and solved for an NPV of $116.0M. In
part (c), we used Monte Carlo simulation to estimate an expected NPV of $187.9M. The most
important thing to recognize about this difference is that Monte Carlosimulation is the correct way
to estimate the NPV. The answer in part (b) is wrong. It is wrong because when we have a non-
linear model, it is not correct to simply substitute expected values in for random variables. The
model is nonlinear because it includes a termfor E
2
, the square of ef?cacy. Once we introduce any
nonlinearity, it is nolonger correct tosubstituteexpectedvalues for randomvariables. This is a very
important point that applies to any DCF analysis that has nonlinear interactions between its inputs.
It is ?ne to replace variables by their expected values in a linear model. Suppose, for
example, that the terminal payoffs were written as $1B Ã E. Then, an analyst would get the
same (average) answer from simulation as he would by just substituting E51/2. Exercise
20.1 will ask you to con?rm this result.
’
Mathematical Interlude
Example 20.2 calculated the NPV using a simulation—this is called a “computa-
tional solution”. Alternatively, we could have just derived the formula for the
NPV—this is called an “analytical solution”. To derive an analytical solution with
continuous variables, we take an integral of each possible outcome multiplied by its
probability density. (This is similar to the way we computed the mean of an
expected value in Equations (20.8) and (20.9)). For any outcome, E, the terminal
value is E
2
à $1B. The probability density of that outcome is f(E), so the quotient
EXHIBIT 20-9
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw rand() 5 F(E) 5 E NPV
1 0.2171 2$59.29
2 0.5099 $124.58
3 0.7905 $439.80
4 0.4074 $43.37
5 0.8775 $565.21
6 0.2346 2$52.47
7 0.9779 $726.03
8 0.9250 $639.07
9 0.2250 2$56.26
10 0.5531 $164.31
366 CHAPTER 20 MONTE CARLO SIMULATION
is 5E
2
à $1B à f(E). Then, the expected terminal value is the integral of these quo-
tients for the entire [0,1] range of E. In our example, we have b51 and a 50.
Thus, f(E) 51/(b À a) 51. With this formula, we can compute the expected terminal
value as
Expected terminal value 5
Z
b
a
$1B Ã E
2
dE 5
b
a
$1B Ã
E
3
3
5$333:3M: ð20:10Þ
Then, we can solve for the NPV as
NPV5$333M=ð1:05Þ
3
2$100M5$187:9M: ð20:11Þ
We solved Example 20.2 with a computational solution to illustrate an
important point: Monte Carlo simulation is just a computational method to solve
integrals. For relatively simple problems like Example 20.2, the integral would be
easier to do than the simulation. However, in most real-world problems, it is not
possible to solve the integral. In those cases, Monte Carlo simulation is the best way
to get an answer.
End Mathematical Interlude
Next, we examine two other useful distributions: the normal and the log-normal.
Exhibit 20-10 shows the familiar “bell curve” for the pdf of a normal distribution
with a mean of µ and a standard deviation of ?.
EXHIBIT 20-10
NORMAL PDF
µ–2? µ+2? µ–? µ+? µ
0.45
0.35
0.25
0.15
0.05
0.4
0.3
0.2
0.1
0
f(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 367
The formula, f(x), for this pdf is
Nðµ; ?Þ : f ðxÞ 5
1
?
??????
2?
p exp 2
ðx 2µÞ
2
2?
2
: ð20:12Þ
There is no need to integrate Equation (20.12) to ?nd the mean of the normal
distribution: the mean is already given to us as the parameter µ.
The corresponding cdf is illustrated in Exhibit 20-11.
Log-normal distributions are often used in ?nance for distributions of asset
returns. In a log-normal distribution, the natural log of x(5ln x) is distributed with a
normal distribution (as in 20.12). This has the nice property that x can never be
negative, which is useful for many ?nance applications. We ?rst saw a picture of a
log-normal distribution in Chapter 13, when we studied the Black-Scholes formula.
If x is distributed log-normally, with x B LogN(µ, ?), then the pdf of x is
Log Nðµ; ?Þ : f ðxÞ 5
1
?x
??????
2?
p exp 2
ðln x 2µÞ
2
2?
2
; ð20:13Þ
where the notation “exp[x]” is equivalent to e
x
.
This pdf is illustrated in Exhibit 20-12. In the x BLogN[µ, ?] notation, µ is
not the mean of x, but rather is the mean of ln x. Similarly, ? is not the standard
deviation of x, but is the standard deviation of ln x. To compute the mean of x, we
would integrate x à f(x) from 0 to in?nity, where f(x) is given by Equation (20.13).
The solution to this integral is
mean of x when x BLogN½µ; ?? 5exp½µ1?
2
=2?: ð20:14Þ
EXHIBIT 20-11
NORMAL CDF
µ
F(x)
1
0.8
0.6
0.4
0.2
0
368 CHAPTER 20 MONTE CARLO SIMULATION
This “extra” term of ?
2
/2 might remind some readers of similar terms ?oating
around as part of the Black-Scholes formula (Chapter 13). This similarity is no
coincidence: the Black-Scholes formula uses assumptions about log-normal returns in
continuous time, so the means of these distributions will have the ?
2
/2 term in them.
Exhibit 20-13 illustrates a cdf for a log-normal distribution.
EXAMPLE 20.3
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we are sure
the drug has no side effects, so all that matters for FDA approval is its ef?cacy. Ef?cacy is
distributed EBLogN[0, 1] and will be revealed after three years of Phase III trials. The NPVof
the drug after three years is $1BÃ E
2
. The discount rate is equal to the risk-free rate of 5 percent
per year. The total cost of R&D is $100M and must be paid at the beginning of development.
EXHIBIT 20-12
LOG-NORMAL PDF
0.5
0.4
0.3
0.2
0.1
0
f(x)
EXHIBIT 20-13
LOG-NORMAL CDF
1
0.8
0.6
0.4
0.2
0
F(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 369
Problems
(a) Draw the event tree for this project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to estimate the NPV of the project.
Solutions
(a) The event tree is identical to Exhibit 20-7, except that we replace the uniform dis-
tribution with a log-normal distribution.
(b) From Equation (20.14), we know that the mean of Log N[0,1] is equal to exp[0 11/2 Ã
(1)
2
] 5exp[1/2] 51.65. Substituting this mean for E yields an expected terminal value of
$2.72B and
NPV5$2:72B=ð1:05Þ
3
2$100M5$2:25B: ð20:15Þ
Because this is a nonlinear model, we know that $2.25B is not the correct NPV for the
project.
(c) To solve for the correct NPV, we set up a Monte Carlo simulation as in Exhibit 20-9. To
perform this simulation, we make use of the Microsoft Excel built-in function to give the
inverse of the cdf for a log-normal distribution. The syntax for this function is loginv[(F(x),
µ, ?], so we can do simulations by substituting the random number function, rand(), for F(x).
After 1,000,000 draws, this simulation gave an average NPV of $6.24B. This is
much higher than the answer in part (b), which demonstrates the importance of using
simulation in this example. Why is this answer much higher? Because the log-normal
distribution is not symmetric—extreme outcomes are possible only in the long “right-tail”
of Exhibit 20-12. When extreme outcomes are possible, the square term exacerbates these
EXHIBIT 20-14
EVENT TREE FOR NEWDRUG, WITH LOG-NORMAL DISTRIBUTION
Phase III
$–100M
$1B
$1B *E
2
E ~ LogN[0, 1]
$0
Efficacy?
3 years
370 CHAPTER 20 MONTE CARLO SIMULATION
outcomes into extreme values for the NPV. We can see an example of such an extreme
outcome in draw #1 of Exhibit 20-15. ’
Although many other distributions are useful for analysts, in this book we will
use only the uniform, normal, log-normal, and one other—the triangular distribution.
Unlike the other distributions used in this book, triangular distributions are rarely
found “in nature”. Instead, these distributions are an invention of analysts looking for
a shorthand way to express their intuition about relative likelihoods on a ?xed range.
A triangular distribution is described by three parameters—minimum (a), maximum
(b), and mode (c)—with notation T (a, b, c), with a pdf that looks like Exhibit 20-16.
EXHIBIT 20-15
MONTE CARLO SIMULATION: FIRST TEN DRAWS
Draw rand() 5 F(E) E NPV
1 0.9931 11.7513 $119,190.77
2 0.4724 0.9332 $652.31
3 0.0474 0.1882 2$69.41
4 0.8850 3.3221 $9,433.84
5 0.7578 2.0123 $3,397.88
6 0.8735 3.1363 $8,397.22
7 0.9013 3.6301 $11,283.62
8 0.9246 4.2056 $15,178.48
9 0.4581 0.9001 $599.87
10 0.3610 0.7007 $324.11
EXHIBIT 20-16
TRIANGULAR PDF
a c b
2/(b–a)
f(x)
20.2 SIMULATION WITH CONTINUOUS PROBABILITY DISTRIBUTIONS 371
Because the triangular distribution is not found in most standard textbooks,
it will be useful for us to take some time to discuss a few of the key properties for
this distribution. To be a proper pdf, the total area under the f(x) curve must be
equal to a total probability of 100 percent. Because the triangular distribution is
indeed a triangle, its area is equal to 1/2 à base à height. Writing the base as 5
maximum 2 minimum 5 b 2 a, and the height at the mode (point c) as h,
we have
Area 51=2 Ã ðb 2aÞ Ã h 51-h 52=ðb 2aÞ; ð20:16Þ
which is given as the maximum height in Exhibit 20-16. Because the density begins
at zero at point a, rises linearly to its maximum height at point c, and then falls
linearly back to zero at point b, we can write the equation for the pdf as
for x ,c :
2
b 2a
Ã
x 2a
c 2a
5
2 Ã ðx 2aÞ
ðb 2aÞ Ã ðc 2aÞ
:
Tða; b; cÞ : f ðxÞ 5
For x $c :
2
b 2a
Ã
b 2x
b 2c
5
2 Ã ðb 2xÞ
ðb 2aÞ Ã ðb 2cÞ
:
ð20:17Þ
The mean of a triangular distribution is 5(a 1b 1c)/3. We will use this
mean in our solution to Example 20.4.
The cdf for this triangular distribution is illustrated in Exhibit 20-17.
EXHIBIT 20-17
TRIANGULAR CDF
a c b
1
F(x)
372 CHAPTER 20 MONTE CARLO SIMULATION
20.3 SIMULATION WITH MULTIPLE SOURCES
OF UNCERTAINTY
With the tools of the earlier sections, we are ready to tackle a more complex
problem.
EXAMPLE 20.4
Drugco has just begun Phase III trials for Newdrug at a cost of $100M. Drugco expects Phase III
trials to take two years and the FDAapproval decision to take one year, so that the FDAdecision
is expected in three years. Phase II trials were promising, with a score of 40 on the standard
medically recognized scale. (We will refer to this score as the “ef?cacy” of the drug.) Although
the best alternative drug has an ef?cacy of 50, it is not helpful for all patients. Given the side
effects of Newdrug and the risks and bene?ts of alternative treatments, Drugco believes that the
FDA will approve Newdrug if the Phase III trials ?nd an ef?cacy of 30 or greater. Based on the
results of the Phase II trials, Drugco estimates that the ef?cacy results of Phase III will be EBN
(40, 20). (It is possible for ef?cacy to be negative because some drugs can make symptoms
worse.) During the three years of Phase III trials, it is possible that the alternative treatments will
also improve from their current ef?cacy of 50. Drugco estimates a ?nal distribution for the
alternative of ABT(50, 100, 50). If Newdrug is approved by the FDA, then its market share will
depend on the relative ef?cacy of Newdrug versus the best available treatment, that is,
Newdrug market share 5E
2
=ðE
2
1A
2
Þ: ð20:18Þ
Drugco estimates market size for Newdrug in the approval year (in millions of doses) as
M B N(1000, 100), with 6 percent annual growth going forward. Each dose yields a gross
pro?t of $1. To stay in the market, Drugco must spend $300M on marketing in the ?rst year,
with this sum increasing each year by 6 percent. Upon approval, Newdrug would have 10 years
of patent life remaining. After the patent expiration, Drugco expects generic competition and
other improved alternatives to greatly erode the value of Newdrug, so for simplicity we assume
that the continuing value would be zero after the patent expires. Following earlier examples
in this chapter, we assume a discount rate equal to the riskfree rate of 5 percent.
Problems
(a) Draw the event tree for the valuation of Newdrug.
(b) What is the probability of FDA approval for Newdrug?
(c) What is the expected value in three years for A, the ef?cacy of the best alternative
treatment?
(d) Suppose that all random variables are exactly equal to their expected values. What
would be the NPV of Newdrug?
(e) Use Monte Carlo simulation to estimate the NPV of Newdrug.
Solutions
(a) The event tree is given in Exhibit 20-18.
20.3 SIMULATION WITH MULTIPLE SOURCES OF UNCERTAINTY 373
The ?rst year of pro?ts following the terminal nodes with E.30(FDA approval) 5
M Ã E
2
/(E
2
1A
2
) À $300M. For years 2 through 10, multiply pro?ts in the previous year by
1.06, then sum all years and discount by 1.05 per year to get the NPV.
(b) Ef?cacy is distributed as N[40, 20], so we can estimate the probability that E . 30 by
using the cdf for this distribution, F(E):
Probability of approval 5Prob ðE .30Þ 51 2Fð30Þ 50:69: ð20:19Þ
Thus, there is a 69 percent chance that a draw from the N[40, 20] distribution will be
greater than 30. (The normal cdf can be accessed as a built-in function of Microsoft Excel
called “normdist”.)
(c) As mentioned earlier in our discussion of triangular distributions, the mean of a triangular
distribution is equal to (a 1b 1c)/3. In this case, we have a 5 50, b 5 100, and c 5 50, so
Expected value of the alternative treatment 5ð50 1100 150Þ=3 566:7: ð20:20Þ
(d) Exhibit 20-19 provides a DCFmodel for calculating the NPVof Newdrug. The bolded cells
in the model are the randomvariables: ef?cacy, alternative ef?cacy, and starting market size. In
this model, each of the randomvariables is set at its expected value. Ef?cacy is distributed as N
[40, 20] and so is set to 40. Alternative ef?cacy is distributed T[50, 100, 50] and so is set to 66.7
(as discussed in part (c)). Starting market size is distributed as N[1000, 100] and so is set to1000.
At these expected values, Newdrug is approved by the FDA, the market share is equal to 26.5
percent (540
2
/(40
2
166.7
2
), and pro?ts in the ?rst year postapproval (5year 4 of the model)
are equal to gross pro?ts of 0.265 Ã 1000, minus marketing costs of $300M5À$35.3M. The
overall NPV (as of year 0) is then equal to 2$410.6M.
(e) To perform a Monte Carlo simulation on this model, we need to make separate draws for
each of the random variables. Because three random variables feed into a multiyear model, it
would be unwieldy (but not impossible) to build this simulation directly in Excel. Instead, we
EXHIBIT 20-18
EVENT TREE FOR NEWDRUG
Alternative:
A ~ T[50,100,50]
Market size:
M ~ N[1000,100]
Efficacy:
E ~ N[40,20]
Same
as 2
Same
as 3
Same
as 2
Same
as 3
Phase III
–$100M
1 2 3
If E ? 30
3 years
$0
See below
for payoffs
at terminal
nodes
374 CHAPTER 20 MONTE CARLO SIMULATION
EXHIBIT 20-19
DCF MODEL FOR NEWDRUG, ALL VARIABLES SET TO THEIR EXPECTED VALUES
Mean Stdev Min Mode Max
Efficacy 40 40 20
Alternative efficacy 67 50 50 100
Starting market size 1,000 1,000 100
Approval threshold 30
Gross profit per unit 1
Market share 26.5%
Market growth 6.0%
Discount rate 5.00%
approved? 1
$ in millions
Year 3 4 5 6 7 8 9 10 11 12
Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
Gross profit $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
Profit 2$35.3 2$37.4 2$39.7 2$42.0 2$44.6 2$47.2 2$50.1 2$53.1 2$56.3 2$59.6
NPV as of year 0 2$410.6
3
7
5
suggest using a specialized program like Crystal Ball. In Appendix C, we show how to use
Crystal Ball, and we discuss the implementation of Crystal Ball for the model in Exhibit 20-19.
After 1M draws, the simulation gives an average NPV of $285.9M, which is signi?cantly higher
than the NPV found in part (d). Sixty-nine percent of the draws resulted in FDA approval (as
solved in part (b)). The outcomes below À$100M occur when gross pro?ts are less than the
$300M marketing costs. An example of such an outcome is given in Exhibit 20-19. One might
think that Drugco should simply abandon the project if projected pro?ts are negative. This
reasoning is absolutely correct, but it is not yet built into this model. To allow Drugco this kind
of ?exibility, we will need to use decision trees and real options. We will learn these tools in
Chapter 21, and we will extend Example 20.4 to allow for such ?exibility in Example 21.4.
’
SUMMARY
R&D investment decisions often require the analysis of several risks at the same time. These
risks can often be modeled as random variables and represented in an event tree. If the analyst
needs to estimate the NPV of an R&D project, then she will need to posit the probability dis-
tributions of these random variables. In this chapter, we learned some basic properties of four
different continuous probability distributions: uniform, normal, log-normal, and triangular. In
some cases, a model may be simple enough to allow an analytical solution for the NPV of an
R&Dproject. In many cases, however, the analyst must ?nd a computational solution by using
Monte Carlo simulation. In Monte Carlo simulation, the computer makes draws from each
probability distribution for each draw of the simulation. The estimated answer is the average
answer over many draws. Simple simulations can be performed using Microsoft Excel. For
more complex simulations, it is helpful to use a specialized package such as Crystal Ball.
Appendix C shows how to solve all the examples from this chapter using Crystal Ball.
KEY TERMS
Monte Carlo simulation
5 Monte Carlo analysis
Discrete random variables,
continuous random
variables
Event tree
Risk node, terminal node
Branch
Probability density
function (pdf)
Cumulative distribution
function (cdf)
Mean
Nonlinear model, linear
model
EXERCISES
20.1 Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we
are sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy.
Ef?cacy is distributed E BU[0, 1] and will be learned during three years of Phase III trials.
The NPV of the drug after three years is $1B Ã E. The discount rate is equal to the riskfree
rate of 5 percent per year. The total cost of R&D is $100M and must be paid at the beginning
376 CHAPTER 20 MONTE CARLO SIMULATION
of development. (Note that this problem is identical to Example 20.2 except for the formula
for the NPV after three years.)
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) On average, will the answer to part (b) be different than the answer to part (c)?
20.2 Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that we
are sure the drug has no side effects, so all that matters for FDA approval is its ef?cacy.
Ef?cacy is distributed E B T[0, 1, 0.4] and will be learned during three years of Phase III
trials. The NPV of the drug after three years is $1BÃ E
2
. The discount rate is equal to the
risk-free rate of 5 percent per year. The total cost of R&D is $100 M and must be paid at
the beginning of development. (This is tricky, because Microsoft Excel does not have a built-
in function for the Triangular distribution. To solve this, you will either need to be creative or
use Crystal Ball.)
(a) Draw an event tree for the Newdrug project.
(b) What is the NPV of Newdrug if ef?cacy is set equal to its expected value?
(c) Use Monte Carlo simulation to solve for the NPV of the Newdrug project.
(d) On average, will the answer to part (b) be different than the answer to part (c)?
20.3 True, False, or Uncertain: Done properly, analytical solutions and computational
solutions will give the same result every time.
20.4 Consider the same problem as in Example 20.4, except that now we add two additional
types of uncertainty. In Example 20.4, we assumed that the gross pro?t per unit was ?xed at
$1. Now, we assume that this gross pro?t is distributed as T[$0.50, $1.50, $1], with this level
learned on FDA approval and then ?xed for the life of the product. Next, if Newdrug is
approved, then there is a 10 percent chance every year that a superior product will be
introduced by a competitor. If this superior product is introduced, then Newdrug’s sales are
cut in half for all future years (relative to what they would have been without this superior
product.) Only one superior product can be introduced in each year, but it is possible for
such products to be introduced in multiple years. For example, if a superior product occurs in
year 6 and in year 8, then Newdrug would have one-half of its original (Example 20.4) sales
in years 6 and 7, and then one-quarter of its original sales in year 8 and beyond.
(a) Use Monte Carlo simulation to solve for the NPV of Newdrug.
EXERCISES 377
CHAPTER 21
REAL OPTIONS
YOU ARE stranded alone on a desert island. For the sake of argument, we
assume that you would like to get off this island. You have a ?are gun with one
charge. You see a plane ?ying overhead. The plane is not directly over the island,
so you are uncertain if your ?are will be visible. Do you ?re? If you do ?re, it will
be your only shot. If you don’t ?re, what are the chances that a plane will ever ?y
any closer?
In making this decision, you are considering a real option. Real options are
created whenever you face a decision that is costly to reverse. In the desert island
example, the ?ring of the gun is irreversible. You can delay ?ring the gun (thus
preserving the “option” to ?re), but you are uncertain about the outcome. If you do
?re, the real option is exercised, as your only ?are has been spent. It is not easy to
solve this problem. To do it right, you would need to estimate various probabilities
and make complex calculations—all in the short time before the plane goes by.
The solving of real options problems has two parts. The ?rst part is “spotting
options” and the second part is “valuing options”. To spot options, we need to have
a deep understanding of the whole decision landscape. In our desert island case, this
would only require that you realize that the gun has only one ?are. In other
situations, an analyst must be clever enough to recognize (or create) real options
where none are obvious.
In Section 21.1, we show how real options can be represented in a decision
tree. In Section 21.2, we classify different types of real options that are relevant for
R&D decisions. In Section 21.3, we show how to value these options using
replication—the same technique ?rst studied in Chapter 13. In Section 21.4, we
demonstrate another solution technique: risk-neutral valuation. Finally, in Section
21.5, we apply real-options methodology to extend our Drugco example from the
previous chapter.
378
21.1 DECISION TREES
When a decision maker is considering all possibilities, it is helpful to sketch all
possible events and decisions in a decision tree. A decision tree adds decision
nodes to an event tree (Chapter 20). Exhibit 21-1 gives a decision tree for Joe
Veesee’s drive home from work.
Upon leaving his garage, Joe has two choices: he can take the highway or he
can take “back roads”. This choice is represented with a box at the decision node.
If he takes back roads, then he will get home in 20 minutes for sure. If he takes
the highway, there is some traf?c risk. This risk is represented by a risk node
(circle) in the tree. When there is no traf?c on the highway, it is Joe’s fastest route
(15 minutes). If there is traf?c on the highway, then the same commute would
take 30 minutes. Based on past experience, Joe knows that there is a 40 percent
chance of traf?c (and a 60 percent chance of “no traf?c”), so his expected commute
time if he takes the highway is 0.6 Ã 15 1 0.4 Ã 30 5 21 minutes. If Joe cares only
about the average time of his commute, then he would compare the expected
commute times for each of his choices and then pick the faster (back roads) route.
So far, this is a straightforward problem. Joe has to make an irreversible
decision right at the beginning, and then nature takes its course. The problem gets
more interesting if we give Joe the “option” of getting off the highway. For
example, suppose that traf?c conditions can be observed once he enters the high-
way (but not before) and that after only a few minutes of such traf?c he can exit the
highway and take an alternate route. This alternate route is not as fast as the original
“back roads” option, but it is not as slow as staying on the highway with traf?c.
Exhibit 21-2 gives a decision tree for Joe’s commuting problem with this new exit
option.
EXHIBIT 21-1
COMMUTING OPTIONS
highway
back
roads
20 15
30
traffic
40%
no
traffic
60%
1
2
21.1 DECISION TREES 379
Decision trees are solved backward. Consider Joe’s decision at Node 3. If he
chooses toexit the highway, his commute will be 25minutes. If hechooses tostayonthe
highway, his commute will be 30 minutes. Thus, he should choose to exit the highway.
Conversely, at Node 4 his fastest option is to stay on the highway, for a commute time
of 15minutes. With this information, we can prune the decisiontree byreplacing Nodes
3 and 4 with their optimal decisions. This pruning yields Exhibit 21-3. Next, we
EXHIBIT 21-3
COMMUTING OPTIONS, PRUNED
highway
back
roads
20
15
4
25
3
traffic
40%
no
traffic
60%
Stay on
highway
Exit highway
1
2
EXHIBIT 21-2
COMMUTING OPTIONS, WITH EXIT
highway
back
roads
20
15
30
25
22
traffic
40%
no
traffic
60%
Stay on
highway
Stay on
highway
Exit
highway
Exit
highway 1
2 3
4
380 CHAPTER 21 REAL OPTIONS
compute the expectedvalue at Node 2 as 0.4 Ã 2510.6 Ã 15519minutes. Because this
is less than the 20 minutes for “back roads”, the optimal decision at Node 1 is to take the
highway.
21.2 REAL OPTIONS IN R&D
As mentioned in the introduction, real options occur whenever you face a decision
that is costly to reverse. Anybody who shies away from commitment with the
excuse that “I am just trying to keep my options open” is indeed doing exactly that:
commitment implies some cost for reversing the decision. Real option analysis is an
attempt to quantify the value of “?exibility”. In R&D settings, there are many
possible applications. Most of these applications can be classi?ed more naturally as
either call options or put options—but keep in mind that for a decision maker
considering whether to take “Action A” or “Action B”, it is often possible to
rede?ne a call option on Action A as a put option on Action B.
The following discussion describes six different types of real options. This is
by no means a comprehensive list.
Call Options
The Option to Delay: Drugco has possible development projects based on
the same science behind Newdrug. Drugco scientists are not sure if these new
projects will work, but they expect to learn more about the probabilities of success
after learning whether the original Newdrug project is successful. Examples 21.1
and 21.2 analyze options to delay.
The Option to Expand: Semico is considering whether to add capacity to
their microchip fabrication plant. The value of an added-capacity plant depends on
the demand for Semico’s chips. If Semico can wait and learn more about demand
before deciding whether to add capacity, then this is a type of call option.
1
The Option to Extend: Autoco currently builds its Oldcar at an aging plant
in Michigan. The assembly lines in this plant are so outdated that Autoco loses
money manufacturing Oldcar, and it looks like the brand is slowly dying. If we
know with certainty that the demand for the brand will never pick up, then it is best
to shut down the plant today. But Autoco management believes that there is
some chance that the demand will be high again in the near future, so keeping the
1
In recessions, new investments decline because many companies decide to keep their expansion options
alive and not exercise them. In recoveries, the opposite happens À ?nally companies see enough positive
signs in the economy and decide to exercise their options, so investments surge. See, for example,
“Radical Shifts Take Hold in U.S. Manufacturing”, Wall Street Journal, February 3, 2010.
21.2 REAL OPTIONS IN R&D 381
plant open gives them an option to extend the brand for a few more years at a
moderate cost.
2
Put Options
The Option to Abandon: Drugco is currently developing Newdrug to treat
diabetes. Drugco scientists believe it is likely that Newdrug will be approved by the
FDA, but this approval is still three years away. In the meantime, alternative
treatments might be improved, the expected market for Newdrug might shrink, and
pricing pressures might harm margins for the drug. Although it is possible that
Newdrug will be a blockbuster, it is also possible that it will be a money loser (after
marketing costs). Drugco would like to continue trials for the drug while preserving
the option to abandon the project later on if it proves to be unpro?table. We analyze
this case in Example 21.4.
The Option to Shrink: This is the ?ip side of the option to expand, con-
sidered earlier. If Semico needed to wait a year before deciding whether to reduce
some capacity, then it would be a type of put option.
Combinations of Options
Option to Switch: Joe Veesee’s commuting problem in Section 21.1 is an
example of a switching option. Switching options can be calls, puts, or a combi-
nation of the two. It is more natural to think of the option on the asset that has some
uncertainty. Hence, for Joe Veesee, it was a put option because he would have to
“sell” the road that he was already on. Alternatively, if Joe could start on the back
roads, listen to the traf?c report on the radio, and then switch to the highway if there
was no traf?c, then he would be “buying” a new road, and it would be a call option.
Finally, if both the back roads and the highway had uncertainty, and Joe could learn
about the traf?c on both roads and switch back and forth, then he would hold a
combination of puts and calls.
21.3 THE VALUATION OF REAL OPTIONS
The valuation of real options is essentially about solving for the correct discount
rate. The easiest problems to solve are those with no beta risk, so that all discount
rates are equal to the riskfree rate.
2
As of 2010, it looks like the Big 3 let this option expire for Saturn, Pontiac, and a few other brands.
382 CHAPTER 21 REAL OPTIONS
EXAMPLE 21.1 (Fuelco)
Fuelco is considering a development project using its patented fuel-cell technology. (This
corresponds to “Project A” as originally discussed in Chapter 19.) If Fuelco pays $200M to
start the project, then they are permitted to bid for a government contract. The objective
probability of winning the contract is 50 percent, and there is no beta risk for the govern-
ment’s decision. If Fuelco’s bid is accepted (one year later), then they can choose to ?nish the
project by accepting the contract (cost 5 $300M), when they will earn an NPV (as of one
year from now) of $600M (not including the $300M cost of ?nishing the project). If they do
not receive the contract, then they can still ?nish the development project (cost 5 $300M),
but they could only receive $200M for the project by selling it to some nongovernmental
buyer (not including the $300M cost of ?nishing the project). The riskfree rate is zero.
Problems
(a) Draw the tree for Fuelco’s problem under the assumption that it starts the project.
(b) Compute the NPV for the project. Should Fuelco start the project?
Solutions
(a) Based on the information given in the example, we draw Fuelco’s decision tree as shown
in Exhibit 21-4.
(b) To compute the NPV, we prune the tree at Nodes 2 and 3 by ?nding Fuelco’s optimal
decision at each node. At Node 2, Fuelco would receive 600M2300M5300M for ?nishing
the project, and 0 for abandoning it. Thus, the project should be ?nished if Node 2 is reached.
At Node 3, Fuelco would receive 200M 2 300M 5 2100M for ?nishing the project and 0
EXHIBIT 21-4
FUELCO’S DECISION TREE (PROJECT A)
Get contract
Don't get contract
$600M
$200M
$0
$0
2
3
1
50%
50%
?$300M
?$300M
Abandon
Abandon
Finish project
Finish project
Duration ? one year
Cost to start project ? $200M
21.3 THE VALUATION OF REAL OPTIONS 383
for abandoning it. Thus, the project should be abandoned if Node 3 is reached. To complete
the solution, we compute the expected value of receiving the contract, discount this expected
value by the riskfree rate (conveniently equal to 0), and subtract the cost to start the project
(5 $200M):
NPV of project 5ð0:5 Ã 300 10:5 Ã 0Þ 2200 5 250M ð21:1Þ
Because the NPV is negative, Fuelco should not start the project.
’
In Example 21.2, we computed the NPV for Fuelco’s project by using
backward induction, the objective probabilities of success, and a riskfree discount
rate. This riskfree discount rate was appropriate because we assumed a zero beta for
the government’s decision to award the contract. The decision problem is more
complex when there is beta risk in the underlying project.
EXAMPLE 21.2
In addition to the government contract considered in Example 21.1, Fuelco is also con-
sidering a separate investment in fuel-cell technology designed to replace oil-based energy
for some types of engines.(This corresponds to “Project B” as ?rst discussed in Chapter 19.)
By investing $100M today to start the project, Fuelco would maintain the option to ?nish the
project with a further investment (5 $200M) in one year. If oil prices are at least $60 per
barrel in one year (objective probability 5 50%), then on completion of the project, Fuelco
would have an NPV (as of one year from now) of $1,000M (not including the $200M cost of
?nishing the project). If oil prices are less than $60 a barrel in one year (objective probability 5
50%), then the project would not be economical for most applications and would have an NPV
(one year fromnow) of $300M(not including the $200Mcost of ?nishing the project). If Fuelco
decides not to ?nish the project, then they can sell the technology to a competitor for $200M,
regardless of the price of oil. The beta for the project is unknown, but we do have some
information about oil prices: the market price of a European binary call option (payoff 5$1) on
oil with a strike price of $60 per barrel and an expiration of 1 year is 25 cents.
Problems
(a) Draw the tree for Fuelco’s problem under the assumption that it starts the project.
(b) Compute the NPV for the project. Should Fuelco start the project?
Solutions
(a) We draw Fuelco’s decision tree in Exhibit 21-5.
(b) We solve backward by ?nding the optimal decisions at Nodes 2 and 3. In both
cases, abandonment would result in a payoff of $200M. At Node 2, Fuelco would receive
1,000M 2 200M 5 800M by ?nishing the project, so it should ?nish. At Node 3, Fuelco
would receive 300M 2 200M 5 100M by ?nishing the project, so they should abandon and
receive $200M. Pruning the tree to re?ect these decisions leaves us with Exhibit 21-6.
384 CHAPTER 21 REAL OPTIONS
At this point, it is easy to compute the expected future value of the project (in one
year) as 0.5 Ã 800M 1 0.5 Ã 200M 5 $500M, but what discount rate should we use to bring
this value back to today? Before proceeding to the correct answer, let’s consider two
incorrect alternatives: (1) the riskfree rate and (2) the cost of capital for the binary option
given in the problem.
EXHIBIT 21-5
FUELCO’S DECISION TREE (PROJECT B)
High oil price
Low oil price
$1,000M
$300M
$200M
$200M
2
3
1
50%
50%
?$200M
?$200M
Abandon
Abandon
Finish project
Finish project
Duration ? one year
Cost to start project ? $100M
EXHIBIT 21-6
FUELCO’S DECISION TREE (PROJECT B, PRUNED)
High oil price
Low oil price
1
50%
50%
$800M
Finish project
Duration ? one year
Cost to start project ? $100M
2
$200M
Abandon
3
21.3 THE VALUATION OF REAL OPTIONS 385
If we use a riskfree rate of zero, then the NPV of the project would be $500M 2
$100M 5 $400M. This would be correct if and only if there is no beta risk associated with
the project. In Example 21.1, we were able to use the riskfree rate for exactly this reason:
under the assumption that the government’s decision had no beta risk, the appropriate dis-
count rate was the riskfree rate. In Example 21.2, the value of the project is based on the price
of oil. Do oil prices have beta risk? Lucky for us, we do not have to answer this question in a
vacuum, as the example provides us with pricing information for a binary option on oil
prices. This option pays $1 if oil prices are high (50 percent chance), so it has an expected
future value of 50 cents. With a price today of 25 cents, the option has an expected return of
100 percent. Clearly, this return is signi?cantly higher than the riskfree rate of zero, so
there must be some beta risk in oil prices. Thus, it would not be appropriate to use the
riskfree rate to discount the returns to Project B. As our next alternative, we consider using
the same discount rate of 100 percent that applies for the binary option. In this case, the NPV
of the project would be 500M/(1 1 1) 2 100M5 $150M. Why is this wrong? Because there
is absolutely no reason to believe that Project B has the same beta risk as the binary option.
Although it is tempting to think that exposure to oil risk makes these two assets equivalent,
this equivalence is incorrect. To see why this is true, imagine a leveraged version of the binary
option where an investor combines 25 cents of capital with 75 cents of borrowed money to buy
4 options (5 25 cents à 4 5 $1 cost). In this case, the payoffs in the next period when oil
prices are high would be $4 (option payoff) 2 $0.75 (loan payback) 5 $3.25. When oil prices
are low, the payoffs would be $0 (option payoff) 2 $0.75 (loan payback) 5 2$0.75. Thus, the
expected value of this leveraged option would be 0.50 Ã 3.25 1 0.50 Ã 20.75 5 $1.25, for a
whopping expected return of 400 percent on the 25-cent investment. As in the original binary
option, these payoffs depend only on the oil price. Note, however, that the expected returns are
very different: 400 percent here versus 100 percent for the original option.
Because we cannot blindly apply the discount rate from the binary option, it is
necessary to ?nd another solution. Instead of computing a discount rate directly, we can
adopt the replicating-portfolio approach ?rst discussed in Chapter 13. Although the appli-
cations in Chapter 13 were for ?nancial options, the same approach can also be applied for
real options like Project B.
To build a replicating portfolio, we begin with two “known” assets: the binary call and
a riskfree bond. The binary call is worth 25 cents today. In one year, if oil prices are high,
the binary call is worth $1, and if oil prices are low, the binary call is worth $0. Because the
riskfree rate is zero, the price of the bond today is the same as its value in both the high-
price and low-price cases next year. For convenience, we set this value to be $1 in all cases,
but we could equally well choose any other value. (After the solution, we will demonstrate
why this is so.) The asset to be priced is the value of Project B in one year, after the oil price
is known. The value of the project is $800M in the high-price state and $200M in the low-
price state.
Next, we build a portfolio of binary options and riskfree bonds that provides exactly
the same payoff as Project B in both states. As in Chapter 13, we write an equation for each
outcome, high or low, that takes the form
Project Value at Expiration ðhigh price or low priceÞ
5ðShares of binary optionÞÃðbinary option value 5$1 if high price; $0 if low priceÞ
1ðShares of BondÞ Ã ðBond Value 5$1 in both casesÞ: ð21:2Þ
386 CHAPTER 21 REAL OPTIONS
Denoting shares of the binary option as y and shares of the bond as z, we write the
equations as
Project B ðhigh oil priceÞ 5800M5y 1z; ð21:3Þ
and
Project B ðlow oil priceÞ 5200M5z: ð21:4Þ
Equations (21.3) and (21.4) give us two equations and two unknowns (y and z), which
we can solve to ?nd that y 5 600M and z 5 200M. To check this solution, we return to the
logic of replication: if we purchase 600M binary options and 200M bonds, then we exactly
replicate the payoffs to the call option. If oil prices are high, 600M binary options would be
worth $600, and 200M bonds would be worth $200, for a total of $800M, the same value as
Project B. If oil prices are low, then the binary options are worthless, whereas the bonds are
still worth $200M, also the same value as Project B.
Now, to ?nd the present value of owning Project B (not including the $100M cost of
investment today), we compute the cost of the replicating portfolio
Value of Project B ðnot including today’s 100M investmentÞ
5600M Ã BC
0
1200M Ã B
0
5600M Ã 0:25 1200M5$350M
ð21:5Þ
This solution of $350M represents the value of Project B once the initial
$100M investment has been made. The total NPV of the project should include this $100M
investment and is equal to 350M 2 100M 5 $250M. Nevertheless, the $350M ?gure is still
an important input into our analysis, as it represents the total valuation for the project after
the investment. That is, after making the initial $100M investment, if Fuelco wanted to sell
all the rights to Project B (including the right to ?nish the project), they would use $350M as
their total valuation. One application of the total valuation is to compute the appropriate
discount rate for Project B. Earlier we computed the expected value of Project B to be
$500M. Thus, if the total valuation (after the initial investment) is $350M, then the expected
return on Project B would be 500M/350M 2 1 5 43 percent. Recall that the expected return
on the binary option was much higher (100 percent). Why the difference? Equation (21.5)
gives us the answer. Project B is just like a $350M portfolio with $200M invested in the
riskfree bond and $150M invested in the binary option. This portfolio is less risky than a 100
percent allocation in the binary option, so the expected return is lower.
When setting up this problem, we used a bond price of $1 and claimed that the exact price
does not matter. With the solution in hand, we can check that claim. If, for example, we had
chosen a bond price of $2, then Equations (21.2) and (21.3) would have included a “2 Ã z ”
term, the solution for z would have been 100M (instead of 200M), and the contribution of
the bonds to the Project B value (the 200M Ã B
0
term in Equation (21.5)) would have been
100M Ã $2 5 $200M, the same amount as we found when using $1 for the bond price. In
general, for any bond price B
0
, we would obtain a solution of z 5200/B
0
, with a contribution to
the Project B value of B
0
à 200/B
0
5 $200M. ’
21.3 THE VALUATION OF REAL OPTIONS 387
21.4 RISK-NEUTRAL PROBABILITIES
In this section, we introduce an alternate solution method based on risk-neutral
probabilities. Risk-neutral probabilities are from the world of make-believe. We
“make believe” that all investors are completely risk-neutral, and then we ask, “In
this make-believe world, what probabilities would lead to the same asset prices as
we observe in the real world?” Once we obtain these probabilities, we then use
them to price any asset in the economy. The key feature of a risk-neutral world is
that beta does not matter: in a risk-neutral world, nobody cares about any kind of
risk, and all assets have an expected return equal to the riskfree rate. An extra $1
of consumption means the same thing to a poor person as it does to a rich person. In
the banana-bird language of Chapter 4, we could say that each extra banana is
worth the same no matter how many bananas have already been eaten. The banana-
utility functions would be straight lines, with no curvature.
To make this concept more concrete, we return to Fuelco’s problem in
Example 21.2. In that example, the objective probability of a high oil price was
given as 50 percent. In the solution, we found that the expected return on a binary
option—with a price of 25 cents and paying $1 in the state with a high oil price—
was 100 percent. In a risk-neutral world, the same 25-cent binary option still exists,
but now the return on this option must be equal to the riskfree rate of zero. We can
use this information to solve for the risk-neutral probabilities. Let p
t
represent the
risk-neutral probability of a high oil price. Then, the expected value of the option in
one year in a risk-neutral world would be given by
Expected value of the option at expiration 5p
t
à $1 1ð1 2p
t
Þ Ã $0: ð21:6Þ
Because the price of the option is $0.25, the expected return on the option would be
Expected return on the option 5½p
t
à $1 1ð1 2p
t
Þ Ã $0?=0:25 21: ð21:7Þ
If we set this expected return to be equal to the riskfree rate (5 0), then we
can solve for p
t
5 0.25. Thus, in a risk-neutral world, the probability of a high oil
price must be 25 percent. Now, the nice thing about this make-believe number is
that we can use it to solve for option prices. For example, we can now write
Fuelco’s tree as shown in Exhibit 21-7.
The only difference between Exhibits 21-6 and 21-7 is that the probabilities
have shifted from 50/50 (in Exhibit 21-6) to 25/75 (in Exhibit 21-7). The key
conceptual distinction is that in the “real world” of Exhibit 21-6, we did not know
the proper discount rate, and we had to build a replicating portfolio to solve for the
NPV of the project. In the “make-believe” risk-neutral world of Exhibit 21-7,
we know that all assets must earn the riskfree rate of zero percent, so we can
compute the NPV of Project B (not including the initial $100M investment as)
Value of Project Bðnot including today’s 100M investmentÞ
5800M Ã 0:25 1200M Ã 0:75 5$350M;
ð21:8Þ
which is exactly the same solution as found by replication.
388 CHAPTER 21 REAL OPTIONS
This solution method is very powerful and is used in many ?nance applica-
tions. Nevertheless, many students ?nd the whole topic to be somewhat magical
and confusing. If you are confused, then you are not alone, as many of the smartest
?nancial economists were also puzzled by these concepts at ?rst. We can gain some
conceptual understanding by reexamining the replicating-method solution of
Example 21.2. In that example, we knew that the objective probability of a high oil
price was 50 percent, but the solution never used this information. Indeed, the
probabilities were completely extraneous. We have seen this phenomenon before:
in Chapter 13, in our very ?rst option pricing problem (Example 13.1), we solved
for an option price without ever knowing the probabilities. Instead, we used only
the market prices of the underlying assets—a stock in Example 13.1, and a binary
option in Example 21.2. Probabilities are unnecessary because the options are
derivative assets, and all the probability information is already embodied in the
underlying assets.
Once we notice that the probabilities are not used, it gives us license to make
up whatever probabilities that we want. We then use this freedom to create our
make-believe risk-neutral world. We imagine that everyone is risk neutral; this
implies that all assets earn the riskfree rate, and the riskfree return then implies
some speci?c probabilities. Then, we have bootstrapped our way to alternative
solution method, because if everyone is risk-neutral, then it is easy to price all
assets as equal to their expected values, discounted by the riskfree rate.
In the Fuelco example, we were very lucky to have information about a
binary call option. This information allowed us to easily compute the risk-neutral
EXHIBIT 21-7
FUELCO’S DECISION TREE (PROJECT B, PRUNED) RISK-NEUTRAL
WORLD
High oil price
Low oil price
1
25%
75%
$800M
Finished project
$200M
Abandon
Duration ? one year
Cost to start project ? $100M
2
3
21.4 RISK-NEUTRAL PROBABILITIES 389
probabilities. We are rarely so lucky. In the next example, we must ?gure out the
risk-neutral probabilities using a more roundabout method.
EXAMPLE 21.3
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19) They have already completed several R&D
projects with this technology, so they have eliminated the technical risk for this new project.
To begin producing and marketing to the consumer market would require a new investment
of $150M, to be paid in one year. The value of Project C depends on consumer demand. If
demand is “high” (50 percent chance), then the value of the project would be $600M (one
year from now). If demand is “low” (50 percent chance), then the value of the project would
be $200M. If Fuelco chooses not to undertake the project, then they can still sell some of the
related patents to another ?rm. If demand is “high” (50 percent chance), then the salvage
value of these patents would be $300M (one year from now). If demand is “low” (50 percent
chance), then the salvage value of these patents would be $100M. Selling the patents has no
effect on any of Fuelco’s other projects. We will use the CAPM to estimate expected returns
in this problem, where the expected market premium is 7 percent, and the riskfree rate is
5 percent.
Problems
(a) Draw Fuelco’s decision tree, where its ?rst decision (Node 1) is whether to invest in the
project immediately (at a cost of $150M), or to wait one year before making an investment
decision.
(b) Suppose that Fuelco chooses to invest at Node 1. Under this assumptions, solve for the
NPV of the project as a function of its beta. Compute this value in the special cases of ? 5 1
and ? 5 0.
(c) Suppose that Fuelco chooses to wait at Node 1. Use replication methods to solve for the
NPV of this decision.
(d) What is the value of the real option to wait at Node 1?
(e) Compute the risk-neutral probabilities of high demand and low demand under the same
cases as in part (b). Use these risk-neutral probabilities to calculate the NPV of waiting.
Verify that these NPVs are the same as found in part (c).
Solutions
(a) Fuelco’s decision tree is given in Exhibit 21-8.
(b) If Fuelco chooses to invest at Node 1, then there are no further decisions to make. If
demand is high, then the value of the project would be $600M. If demand is low, then the
value of the project would be $150M. To compute the present value of choosing invest at
node 1, we discount the expected value (5 0.5 Ã 600M 1 0.5 Ã 200M 5 400M) by the
appropriate discount rate. For now, we ignore the $150M cost to add the capacity. We can
compute the appropriate discount rate using the CAPM as
r 5R
f
1?ðR
m
2R
f
Þ 50:05 1? Ã 0:07: ð21:9Þ
390 CHAPTER 21 REAL OPTIONS
Thus, the present value of the project with commitment can be written as a function of ?, V
(?), as
Vð?Þ 5400=ð1:05 1? Ã 0:07Þ: ð21:10Þ
Then, V(0) 5 400/1.05 5 381.0, and V(1) 5 400/1.12 5 357.1.
Note that these calculations represent a “present value” for the project, but not a “net
present value”. If we want an NPV, we need to subtract the $150M cost of adding capacity.
Because this cost is committed to be paid in one year, we should discount it by the riskfree
rate, so that the NPV of the project with commitment would be
NPVð?Þ 5Vð?Þ 2150=1:05: ð21:11Þ
(c) If Fuelco chooses to wait at Node 1, we must still take account of the option to invest in
one year. If demand is strong, it would be optimal to invest (600M 2 150M . 300M). If
demand is weak, it would not be optimal to invest (200M 2 150M , 100M). Thus, the
pruned version of the tree is shown in Exhibit 21-9.
EXHIBIT 21-8
FUELCO’S DECISION TREE
Invest
Invest
Don't
Invest
Don't
Strong market
Weak market
Weak market
Strong market
Wait
?$150M
(to be paid at terminal nodes)
?$150M
$600M
$600M
$200M
$200M
$100M
$300M
?$150M
1 year
50%
50%
50%
50%
1
2
3
4
5
NOTE: The branches
after nodes 2 and 3
are perfectly correlated.
21.4 RISK-NEUTRAL PROBABILITIES 391
In part (b), we were able to solve for the present value of invest as a function of beta.
To solve for the present value of wait is a harder problem, because we do not know the beta
for the bottom half of the tree. We can solve for this NPV by building a replicating portfolio
that combines the top half of the tree (with the present value solved in part (b)) and a riskfree
bond. As we learned in Example 21.2, the exact expiration value of the bond is not important,
so we arbitrarily set it to be equal to the cost of adding capacity 5$150M. Denoting “shares”
of the added-capacity factory as y and shares of the bond as z, we write the replicating
equations as
Value of waiting ðstrong demandÞ 5450M5600y 1150z; ð21:12Þ
and
Value of waiting ðweak demandÞ 5100M5200y 1150z: ð21:13Þ
Equations (21.12) and (21.13) give us two equations and two unknowns, which we can
solve for y 5 0.875 and z 5 20.5. The cost of this replicating portfolio will be the same as
the NPV of the project with ?exibility.
NPV of project with flexibility50:875 Ã Vð?Þ 20:5 Ã B
0
50:875 Ã Vð?Þ 20:5 Ã 150=1:05;
ð21:14Þ
EXHIBIT 21-9
FUELCO’S DECISION TREE, PRUNED
Invest
Strong market
Weak market
Weak market
Strong market
Wait
?$150M
$600M
$200M
50%
50%
50%
50%
1
2
3
NOTE: The branches
after nodes 2 and 3
are perfectly correlated.
$450M
Invest
$100M
Don't
4
5
392 CHAPTER 21 REAL OPTIONS
where V(?) is given by Equation (21.10). For ? 5 0 we have V(0) 5 381.0, and thus
NPV of project with flexibility ð? 50Þ
0:875 Ã 381:0 20:5 Ã 150=1:05 5261:9:
ð21:15Þ
For ? 5 1 we have
NPV of project with flexibility ð? 51Þ
0:875 Ã 357:1 20:5 Ã 150=1:05 5241:1:
ð21:16Þ
(d) To compute the option value of waiting, we compare the NPV of project with com-
mitment to the NPV of project with ?exibility. The difference between these NPVs is the
value of the waiting “option”:
Option value of waiting 5NPV of project with flexibility
2NPV of project with commitment
ð21:17Þ
The NPV of project with commitment is given by Equation (21.11). The NPV of
project with ?exibility is given by Equation (21.14). By substituting these equations in
Equation (21.17), we obtain
Option Value of Waiting ð? 50Þ 5$261:9M2$238:1M5$23:8M ð21:18Þ
and
Option Value of Waitingð? 51Þ 5$241:1M2$214:3M5$26:8M: ð21:19Þ
(e) Let p
t
be the probability of strong demand in a risk-neutral world. Then, the present
value of investing at node 1 (5 V
t
) in the risk-neutral world would be
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05: ð21:20Þ
Now, to ?gure out the appropriate risk-neutral probabilities, we set V
t
equal to V (?).
For example, when ? 5 1, we have V (1) 5 357.1. In a risk-neutral world, p
t
is set so that the
value of the asset V
t
would also be equal to 357.1:
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05 5Vð1Þ 5357:1-p
t
50:4375: ð21:21Þ
This answer can be interpreted the following way: “If everyone was risk-neutral and
the probability of strong demand was 43.75 percent, then the Project C would be worth
$357.1M today and would have an expected return of 5 percent.” Using this risk-neutral
probability, we can rewrite Exhibit 21-9 as shown in Exhibit 21-10.
Now, we can solve for the expected terminal value of waiting as
Expected terminal value 50:4375 Ã 450 10:5625 Ã 100 5253:125: ð21:22Þ
In the risk-neutral world, all assets must earn the riskfree rate, so the NPV is
NPV5253:125=1:05 5$241:1M: ð21:23Þ
This is the same answer we found in part (c).
If we do the same steps for the case of ? 5 0, things turn out to be simpler. When ? 5
0, we have V (1) 5 381.0. In a risk-neutral world, p
t
is set so that the value of the asset V
t
would also be equal to 380.1:
V
t
5½p
t
à 600 1ð1 2p
t
Þ Ã 200?=1:05 5Vð0Þ 5380:1-p
t
50:5: ð21:24Þ
21.4 RISK-NEUTRAL PROBABILITIES 393
Thus, when ? 5 0, the risk-neutral probability is exactly the same as the objective
probability. You should think about this result and convince yourself of its generality.
When ? 5 0, the investment already earns the riskfree rate, so risk-neutral people would
feel right at home. Because p
t
5 0.5, we can compute the NPV by using the event tree in
Exhibit 21-10. The expected terminal value of waiting is
Expected terminal value 50:5 Ã 450 10:5 Ã 100 5275: ð21:25Þ
In the risk-neutral world, all assets must earn the riskfree rate, so the NPV is
NPV5275=1:05 5$261:9M: ð21:26Þ
This is the same answer we found in part (c) for the ? 5 0 case.
’
Please note that the betas and risk do matter here: our answers in the ? 5 0
and ? 5 1 cases are different. “Risk-neutral option pricing” just means that all the
relevant information about betas is already built into the underlying asset prices,
represented here by V (?). Once we know the underlying asset prices, we can
compute option values based on these assets without ever again using betas or
expected returns.
As a special case, any time we have ? 5 0, we can just use objective
probabilities and the riskfree rate. This shortcut comes in very handy when the only
risks we face are (diversi?able) technical risks. We see an example of this shortcut
in the next section.
EXHIBIT 21-10
FUELCO’S EVENT TREE, AFTER NODE 3
4
$450M
Invest
5
$100M
Don't
p' ? 43.75%
(1–p') ? 56.25%
Weak demand
Strong demand
3
394 CHAPTER 21 REAL OPTIONS
21.5 DRUGCO, REVISITED
In this section, we take another look at the long Drugco example from the last chapter.
Our new version is identical to Example 20.4 from the previous chapter, except that
now we allow Drugco to abandon the Newdrug project even after it has been approved.
The new text in this example (as compared to Example 20.4) is given in italics.
EXAMPLE 21.4
Drugco has just begun Phase III trials for Newdrug. Drugco expects Phase III trials to take
two years and the FDA approval decision to take one year, so that the FDA decision is
expected in three years. Phase II trials were promising, with a score of 40 on the standard
medically recognized scale. (We will refer to this score as the “ef?cacy” of the drug.)
Although the best alternative drug has an ef?cacy of 50, it is not helpful for all patients.
Given the side effects of Newdrug and the risks and bene?ts of alternative treatments,
Drugco believes that the FDA will approve Newdrug if the Phase III trials ?nd an ef?cacy of
30 or greater. Based on the results of the Phase II trials, Drugco estimates that the ef?cacy
results of Phase III will be E BN (40, 20). (It is possible for ef?cacy to be negative because
some drugs can make symptoms worse.) During the three years of Phase III trials, it is
possible that the alternative treatments will also improve from their current ef?cacy of 50.
Drugco estimates a ?nal distribution for the alternative of A BT (50, 100, 50). If Newdrug is
approved by the FDA, then its market share will depend on the relative ef?cacy of Newdrug
versus the best available treatment, that is,
Newdrug market share 5E
2
=ðE
2
1A
2
Þ: ð21:27Þ
Drugco estimates market size for Newdrug in the approval year (in thousands of doses)
as M BN (1,000, 100), with 6 percent annual growth going forward. Each dose yields a gross
pro?t of $1. Following FDA approval, with all uncertainty about market size and ef?cacy
known, Drugco can decide either to enter or not to enter the market. If they do not enter, then
they can still sell the approved drug to a European company for $100M Ã E/(E 1A). If they do
enter, then to stay in the market, Drugco must spend $300M on marketing in the ?rst year, with
this sum increasing each year by 6 percent. Upon approval, Newdrug would have 10 years of
patent life remaining. After the patent expiration, Drugco expects generic competition and
other improved alternatives to greatly erode the value of Newdrug, so for simplicity we will
assume that the continuing value would be zero after the patent expires. We assume that
Newdrug faces only technical risk and that the riskless rate is 5 percent.
Problems
(a) Draw the decision tree for the valuation of Newdrug.
(b) Use Monte Carlo simulation to estimate the NPV of Newdrug.
Solutions
(a) The decision tree is given in Exhibit 21-11. This tree is identical to the event tree in
Exhibit 20-18 (from Example 20.4), except for the additional decision nodes at the end of the
21.5 DRUGCO, REVISITED 395
tree. At these decision nodes, Drugco must decide whether or not to enter the market. If
Drugco enters the market, then they earn pro?ts of M Ã E
2
/(E
2
1 A
2
) Ã $300M in the ?rst
year, with increases of 6 percent in each subsequent year up to year 10. If they choose not to
enter the market, then Drugco can sell Newdrug for $100 Ã E/(E 1 A).
(b) Exhibit 21-12 provides a DCF model for calculating the NPV of Newdrug. This model
is identical to Exhibit 20-19 (from Example 20.4) except for two additional cells used for the
decision calculation. These additional cells are given in bold type. The ?rst bolded cell is
the discounted salvage value 5$100 Ã E/ [(E1A) Ã (1.05)
3
]. This cell is set to its expected
value in the exhibit. The middle bolded cell represents the NPV with commitment. This cell
is set to its average over 1M draws, $285.9M, the same average as computed in Chapter 20,
$285.9M. The bottom bolded cell is the NPV with the option to abandon, computed in each
draw by comparing the NPVs in the previous two shaded cells. After 1M draws, the average
NPV was $473.8M, a signi?cant increase over the NPV with commitment. (This example is
also discussed in Appendix C.)
At “enter” terminal nodes, the ?rst year of pro?ts 5 M Ã E
2
/(E
2
1 A
2
) 2 $300M. For
years 2 through 10, multiply pro?ts in the previous year by 1.06, then sum all years and
discount by 1.05 per year to get the NPV.
EXHIBIT 21-11
DECISION TREE FOR NEWDRUG
Alternative:
A ~ T[50,100,50]
Market size:
M ~ N[1000,100]
Efficacy:
E ~ N[40,20]
Same
as 3
Same
as 2
Same
as 3
Same
as 2
Phase III
?$100M
Same
as 4
1 2 3 4
don't
enter
(sell Newdrug)
$100 * E/
(E ? A)
enter
See below
for payoff
E ? 30
$0
3 years
396 CHAPTER 21 REAL OPTIONS
EXHIBIT 21-12
DCF MODEL FOR NEWDRUG
Mean Stdev Min Mode Max
Ef?cacy 40 40 20
Alternative ef?cacy 67 50 50 100
Starting market size 1,000 1,000 100
Approval threshold 30
Gross pro?t per unit 1
Market share 26.5%
Market growth 6.0%
Discount rate 5.00%
approved? 1
Discounted salvage value 32.39
$ in millions
Year 4 5 6 7 8 9 10 11 12 13
Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
Gross pro?t $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
Pro?t 2$35.3 2$37.4 2$39.7 2$42.0 2$44.6 2$47.2 2$50.1 2$53.1 2$56.3 2$59.6
NPV (if enter) 285.9
NPV (with option) 473.8
’
3
9
7
SUMMARY
Real options are ?nance-speak for “?exibility”; real options are created when costly deci-
sions can be delayed. A commuter has a real option to switch from a congested highway to
back roads; a fuel company has a real option to abandon its fuel-cell project if oil prices are
low; a semiconductor company has a real option to expand its factory if demand is strong. A
good analyst must learn to spot real options by keeping an open mind and developing a deep
understanding of his business. Once spotted, real options can be represented in decision trees
and valued using two main techniques. The ?rst technique, replication, is useful for simple
problems but unwieldy for complex problems. The second technique, risk-neutral valuation,
relies on a key insight learned from replication: option-pricing formulas do not rely on risk
aversion—if everyone is highly risk-averse we still get the same answer as the one we get if
everyone is risk-neutral. With this insight, we pretend that we live in a make-believe world
where everyone is risk-neutral, and then use the probabilities from this make-believe world to
price options. This powerful method can be extended to complex examples by using binomial
trees, a topic studied in the next chapter.
KEY TERMS
Real options
Decision trees
Decision nodes
The option to delay
The option to expand
The option to extend
The option to abandon
The option to shrink
The option to switch
Risk-neutral probabilities
EXERCISES
21.1 True, False, or Uncertain : In a risk-neutral world, all assets earn a zero rate of return.
21.2 True, False, or Uncertain : To use risk-neutral valuation, we assume that the under-
lying asset only faces technical risks.
21.3 Semico is considering whether to add capacity to their microchip fabrication plant.
Adding capacity would cost $600M, to be paid in one year. The value of an added-capacity
plant depends on the demand for Semico’s chips. If demand is “high” (25 percent chance),
then the value of the added-capacity plant would be $1,600M (one year from now). If
demand is “low” (75 percent chance), then the value of the added-capacity plant would be
$400M. If Semico chooses to keep the current capacity, then there is no incremental cost. If
demand is “high” (25 percent chance), then the value of the current-capacity plant would be
$600M (one year from now). If demand is “low” (75 percent chance), then the value of the
current-capacity plant would be $400M. We will use the CAPM to estimate expected returns
in this problem, where the expected market premium is 7 percent, and the riskfree rate is
5 percent.
398 CHAPTER 21 REAL OPTIONS
(a) Draw the decision tree for Semico’s problem, where its ?rst decision (node 1) is
whether to commit today to add capacity at a cost of $600M (to be paid in one year), or to
wait one year until information about demand is revealed.
(b) Suppose that Semico chooses to commit at node 1. Solve for the NPV of the project as a
function of its beta. Compute this value in the special cases of ? 5 1 and ? 5 0.
(c) Suppose that Semico chooses to wait at node 1. Use replication methods to solve for the
NPV under the same cases as in part (b).
(d) What is the value of the real option to wait?
(e) Compute the risk-neutral probabilities of high demand and low demand under the same
cases as in part (b). Use these risk-neutral probabilities to calculate the NPV of the project
with ?exibility. Verify that these NPVs are the same as found in part (c).
21.4 (This problem takes some work. For some guidance, see the last example in Appendix
C, which solves a slightly easier version of the problem.) Begin with the same setup as in
Example 21.4, except that now it is one year earlier, and Drugco is deciding whether to
proceed with Phase II trials. Phase II trials will take one year and cost $50M. Following the
Phase II trials, Drugco will learn some information about ef?cacy, denoted as E
t
, with E
t
BT
[0, 80, 40], and about alternative ef?cacy denoted as A
t
BT[50, 80, 50]. If, after learning this
information, Drugco decides to go forward with Phase III trials, then everything is identical to
Example 21.4, except that now the ef?cacy after Phase III trials is distributed as E BN[E
t
, 20],
and alternative ef?cacy is distributed as ABT[A
t
, A
t
1 50, A
t
]. All risks are technical risks, so
all betas are zero and the appropriate discount rate is the riskfree rate of 5 percent.
(a) For what values of E
t
should Drugco continue on to Phase III trials?
(b) What is the NPV of Newdrug at the beginning of Phase II trials?
EXERCISES 399
CHAPTER 22
BINOMIAL TREES
INCHAPTER 21, we learned about risk-neutral probabilities and showed how
to use these probabilities to solve one-step option-pricing problems. In this chapter,
we extend the risk-neutral approach to multistep problems using binomial trees. In
a binomial tree, we restrict all risk nodes to have only two branches, and we set the
moves in those branches by a speci?c formula. In Section 22.1, we show how
binomial trees can be used to approximate the Black-Scholes formula for European
options. The advantage of binomial trees over analytical formulas is that the former
can be used even when underlying assets have dividends or changes in volatility, and
when the options allow for early exercise, have multiple strike prices on different
dates, and have other special features. In Section 22.2, we value an option on Drugco
with early exercise and multiple strike prices; in Section 22.3, we value a real option
for Fuelco with early exercise and dividend payments. Indeed, the main concepts
behind binomial trees allow analysts to handle virtually any complication that nature
can throw at them. For this reason, binomial trees are the main tools used to analyze
complex derivatives on Wall Street and complex real options on Main Street.
22.1 THE BLACK-SCHOLES EQUATION, REVISITED
Bigco stock currently trades for $S per share. Joe Trader holds a (European) call
option with a strike price of $X and an expiration date of one year. The riskfree rate
is r, and Bigco stock has an annualized volatility of ?. As is usual in option-pricing
problems, we assume that these are continuously compounded returns. In Chapter
13, we learned how to value this call option using the Black-Scholes formula. In
this chapter, we learn a new valuation technique based on binomial trees. The
advantage of binomial trees is that they are ?exible enough to handle many
deviations from the Black-Scholes assumptions. However, before we introduce
these deviations, we demonstrate how to build and solve binomial trees for standard
European call options.
We begin by expressing Joe’s call option as a decision tree (Exhibit 22-1).
400
Node 1 is a risk node, and Node 2 is a decision node. At node 1, we draw a
one-year stock return, R, from a log-normal distribution. This is a continuously
compounded return, so the new stock price is then equal to S Ã exp(R). Working
backward, we can see that Joe’s optimal decision at Node 2 would be to exercise if
S Ã exp(R) is greater than X, the exercise price. This gives us a terminal value of
Max[S Ã exp(R), 0] at each possible terminal node.
The hard part about this problem is ?guring out the correct discount rate to
use for the terminal values. This problem is so hard that we didn’t have a solution
until Black and Scholes. When we ?rst saw this solution in Chapter 13, we did
not have all the tools and language to properly discuss all its implications. Now, we
do have this language, so let’s take another look. The Black-Scholes equation for a
European call option is
C
0
5Nðd
1
ÞS
0
2Nðd
2
ÞXe
2rT
; ð22:1Þ
where N (.) is the Normal distribution function and
d
1
5½lnðS
0
=XÞ 1ðr 1?
2
=2ÞTÞ?=ð?OTÞ; ð22:2Þ
d
2
5½lnðS
0
=XÞ 1ðr 2?
2
=2ÞT?=ð?OTÞ 5d
1
2?OT; ð22:3Þ
where T 5 years until the expiration date, ? 5 the annual volatility of returns, and r 5
the annual riskfree rate.
When this solution was ?rst unveiled by its authors, the most surprising part
was that the expected return of the stock does not appear anywhere in the formula.
EXHIBIT 22-1
CALL OPTION IN A DECISION TREE
1 2
Same
as 2
Same
as 2
R ~ LogN[µ–?
2
/2, ?]
S* exp(R) – X
Exercise
Don't
Exercise
0
1 Year
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 401
Take a look again—there is no µ to be found. The only return that appears is the
riskfree rate, r. What is happening here? It all comes back to the logic of repli-
cation. The Black-Scholes logic is the same as the replication logic that we used to
value options in chapters 13 and 21. In replication, we match the option payoffs by
constructing portfolios of riskfree bonds plus underlying risky assets. When we do
this, all information about probabilities, risk aversion, and expected returns is
already embodied in the price of the underlying risky asset. If expected returns
change, then the stock price S
0
would change. Thus, option prices do depend on
expected returns, but only indirectly through the price of the underlying asset.
The insight about expected returns led directly to the development of risk-
neutral probabilities. The idea is that because expected returns and objective
probabilities do not appear anywhere in the formula, then any set of probabilities
that gives the same stock price should also imply the correct option price. We
demonstrated applications of risk-neutral probabilities in Chapter 21. In those
applications, the use of risk-neutral probabilities was limited to one-step trees. The
real power of the risk-neutral insight is that it can be applied to multistep trees. In
the most widely used applications, these trees have exactly two branches after every
risk node: hence, they are called binomial trees. Exhibit 22-2 gives an example of a
three-step binomial tree applied to Joe Trader’s example. In this exhibit, we break
the one-year time period into three subperiods of four months each. Then, in each
EXHIBIT 22-2
A BINOMIAL TREE
9
10
8
7
Su Su
S
S
p p
p
p
p
p
1-p
1-p
1-p
1-p
1-p
1-p
Sd
Sd
Su
3
Su
2
Sd
2
Sd
3
1
3
2
4
5
6
exercise
exercise
exercise
exercise
don't
don't
don't
don't
0
0
0
0
Su
3
– X
Sd
3
– X
Su – X
Sd – X
4 months
Step 2
4 months
Step 3
4 months
Step 1
Set u ? 1/d
402 CHAPTER 22 BINOMIAL TREES
subperiod, we allow only two possible movements for the stock price, an “up”
movement or a “down” movement.
In this tree, there are three different steps, each lasting four months. In each step,
the stock price can either go up (with a return 5 u), or down (with a return 5 d 5 1/u).
Thus, after the ?rst step (Node 1), we have two possible outcomes: a stock price of Su
(Node 2) or a stock price of Sd (Node 3). From Node 2, once again the stock can go up
or down. If the stock goes up, then the value is Su
2
(Node 4), and if it goes down, then
the value is Sdu 5 S (Node 5). The nice feature of binomial trees is that they
recombine, so that the down movement from Node 2 leads to the same stock price as
an up movement from Node 3. With our assumption that u 5 1/d, this recombination
occurs at the same price across each two time periods.
After all three risk steps, we reach the decision nodes of the tree. At each
decision node, Joe should exercise if the stock is valued higher than the exercise
price. In solving binomial trees, it is often helpful to construct two separate
binomial trees: a base tree and an option tree. The base tree gives only the values
of the underlying asset. We build a base tree forward at each node by multiplying
the previous price by either u or d. Exhibit 22-3 gives the base tree for Joe’s option.
Once the base tree is constructed, we solve the option tree backward, starting
with the decision nodes 7 through 10 at time 5 T. At each decision node, we set the
value of the call option equal to the Max (S
T
2 X, 0). Then, we compute
the expected discounted value of the call option at each prior node as
C
T 21
5 p à C
T
ðfrom up nodeÞ 1ð1 2pÞC
T
ðfrom down nodeÞ ½ ?=R
ft
; ð22:4Þ
EXHIBIT 22-3
BASE TREE
Su
S
S
u
u
u
u
d
u
d
u
d
d
d
d
Sd
Su
2
Sd
2
1
3
2
4
5
6
4 months
Step 2
4 months
Step 3
4 months
Step 1
Set u ? 1/d
7
Su
3
10
Sd
3
8
Su
9
Sd
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 403
where R
ft
is the appropriate riskfree discount rate for a time step length of t.
Exhibit 22-4 illustrates this option tree.
To understand the option tree, we must begin at the decision nodes: 7 to 10.
Each of the decision nodes, 7 to 10, contains an equation C
M
5 Max (S
M
2 X, 0),
where M is the node number and S
M
is the terminal value from that node, as taken
from the base tree. Next, we solve backward from these terminal nodes, taking the
expected discounted value at each previous node. For example, consider Node 4.
From Node 4, there will be a probability p of an up move to Node 7 and a pro-
bability (1 2 p) of a down move to Node 8. The expected value of these moves is p
à C
7
1 (1 2 p) Ã C
8
. Because this move take t units of time, we must discount this
expected value by R
ft
, which yields a discounted value of C
4
5 (p à C
7
1 (1 2 p) Ã
C
8
)/R
ft
. (R
ft
is known as the periodic growth factor of the tree.) We solve every risk
node in the tree using exactly the same formula. When we ?nally reach C
1
, we get a
solution for the starting value of the call option.
To transform the general solution of Exhibit 22-4 into a numerical solution,
we apply the same risk-neutral approach as in Chapter 21. First, we need to derive
the appropriate risk-neutral probabilities (p and 1 2 p) and the appropriate size
EXHIBIT 22-4
OPTION TREE
9
10
8
7
p p
p
p
p
p
1-p
1-p
1-p
1-p
1-p
1-p
1
3
2
4
5
6
exercise
exercise
exercise
exercise
don't
don't
don't
don't
0
0
0
0
Su
3
– X
Sd
3
– X
Su – X
Sd – X
4 months
Step 2
4 months
Step 3
4 months
Step 1
C
1
? (pC
2
+ (1 – p)C
3
)/R
ft
C
2
? (pC
4
+ (1 – p)C
5
)/R
ft
C
3
? (pC
5
+ (1 – p)C
6
)/R
ft
C
6
? (pC
9
+ (1 – p)C
10
)/R
ft
C
10
? Max (Sd
3
– X,0)
C
7
? Max (Su
3
– X,0)
C
9
? Max (Sd – X,0)
C
8
? Max (Su – X,0)
C
5
? (pC
8
+ (1 – p)C
9
)/R
ft
C
4
? (pC
7
+ (1 – p)C
8
)/R
ft
404 CHAPTER 22 BINOMIAL TREES
of the up and down movements (u and d). Thus, we have three unknown parameters,
p, u, and d. To solve for these parameters, we need three equations. Just our luck, we
have exactly three equations: one for the expected return (which must be equal to the
riskfree rate, r, in our risk-neutral world), one for the volatility (which must be equal
to ?, the “known” volatility of the stock), and a ?nal equation with our assumption
that d 5 1/u.
We begin with the expected return equation. In Exhibit 22-2, the length of the
whole tree is one year, and the length of each step on the tree is four months. For
generality, we write the length of the whole tree as T and the length of each step as
t 5T/N, where N is the number of steps in the tree. Then, the risk-free return (5
growth factor) over each step size t is R
ft
5 exp(r à t). Then, using the up and down
movements in the tree, we can write this growth factor as
R
ft
5expðr à tÞ 5p à u 1ð1 2pÞ Ã d: ð22:5Þ
We next write an equation for the variance of returns. The variance of returns
in each full year in the tree is ?
2
. Because variance is additive over time, the
variance of returns for the whole tree must be ?
2
à T, and the variance of returns in
each step in the tree must be ?
2
à t. In general, the formula for the variance of
returns, R, can be written as
Variance of returns; R5Expected value ½R
2
? 2ðExpected Value ½R?Þ
2
: ð22:6Þ
We now replace each term of Equation (22.6). As stated earlier, the left-hand
side of the equation is equal to ?
2
à t. Next, the ?rst term on the right-hand side can
be written by multiplying the probability of each branch by the square of the return
on each branch:
Expected value ½R
2
? 5p à u
2
1ð1 2pÞ Ã d
2
: ð22:7Þ
Finally, we can write the second term on the right-hand side of Equation
(22.6) by squaring the expected return from Equation (22.5)
ðExpected Value ½R?Þ
2
5ðp à u 1ð1 2pÞ Ã dÞ
2
: ð22:8Þ
Next, we substitute Equations (22.7) and (22.8) into (22.6) to obtain
Variance of returns; R5?
2
à t 5p à u
2
1ð1 2pÞ Ã d
2
2ðp à u 1ð1 2pÞ Ã dÞ
2
:
ð22:9Þ
Now Equations (22.5) and (22.9) can be combined with our assumption that
d 51/u to give us three equations and three unknowns. The hard part is over, and
the rest is algebra. We can use these equations to solve for the unknown variables as
p 5
R
ft
2d
u 2d
ð22:10Þ
22.1 THE BLACK-SCHOLES EQUATION, REVISITED 405
where
R
ft
5expðr à tÞ;
u 5expð?
??
t
p
Þ; and
d 5expð2?
??
t
p
Þ:
ð22:11Þ
The solution in Equations (22.10) and (22.11) was ?rst proposed by Cox, Ross,
and Rubinstein (1979) and is known as the CRR model. The key assumption of the
CRR model is that d 5 1/u, which leads to a tree like Exhibit 22-2, with nodes that
recombine at the same value as previous nodes on the same row of the tree. There are
many other methods to build binomial trees, but we will exclusively use the CRR
model in this chapter. Please see Hull (2005) for a discussion of other methods.
For concreteness, let’s assume that for Joe Trader’s Bigco option, we have a
starting stock price of $100, a strike price of $50, a volatility ? 5 60 percent, and
a riskfree interest rate of r 5 5 percent. With a three-step tree (N 5 3) and a
one-year option (T 5 1), we have t 5 1/3 (four months), so that
R
ft
5expðr à tÞ 5expð0:05 à 1=3Þ 51:017 ð22:12Þ
Now, we are ready to solve for u, d, and p as
u 5expð?
??
t
p
Þ 5expð0:6 Ã
???????
1=3
p
Þ 51:414; ð22:13Þ
d 51=u 50:0707; and ð22:14Þ
p 5
R
ft
2d
u 2d
5
1:017 20:707
1:414 20:707
50:438: ð22:15Þ
To solve for the option value, we use these numbers to build the base tree, and
then we substitute the terminal values into the option tree and solve backward.
Exhibits 22-5 and 22-6 give these two trees. Readers can compare the analytical
formulas in Exhibits 22-3 and 22-4 with their numerical solutions in Exhibits 22-5
and 22-6 and see that the solutions are consistent. To make it easier to read these
trees, we put the numerical values inside in the nodes, with the node label (#1, #2,
etc.) given above the nodes.
Exhibit 22-6 gives a solution of $54.91 for C
1
(the ?rst entry in the tree). To
check this solution, we can use the European Call Option Calculator of the VCV
model, where these same inputs yield a solution of $54.52. Because we know that
the Black-Scholes solution in European Call Calculator is correct, the three-step
tree is off by $0.39, which is less than 1 percent of the true value. To achieve more
precise estimates, we need to use a larger tree with shorter time steps. There are
many commercial sources for binomial trees.
1
For this book, we use a relatively
small tree, ?xed at 60 steps, included in a spreadsheet named as bintree.xls. This
spreadsheet contains three linked worksheets: inputs, base-tree, and option-tree.
1
For inexpensive versions, see the software included with Hull (2005) and Haug (1998).
406 CHAPTER 22 BINOMIAL TREES
EXHIBIT 22-5
JOE’S PROBLEM, BASE TREE
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
u ? 1.41
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
d ? 0.71
1
3
5
6
4
2
4 months
Step 2
4 months
Step 3
4 months
Step 1
7
$282.70
10
$35.37
8
$141.40
9
$70.72
$100.00
$141.40
$199.93
$100.00
$50.02
$70.72
EXHIBIT 22-6
JOE’S PROBLEM, OPTION TREE
exercise
don't
exercise
don't
exercise
don't
exercise
don't
1
4
5
6
2
3
$93.04
$54.91 $100.00
$8.93
$232.70
$0
$91.40
$0
$20.72
$0
–$14.63
$0
$0
10
9
$20.72
8
$91.40
0.438
0.438
0.438
0.562
0.562
0.562
0.438
0.562
0.438
0.562
0.438
0.562
7
$232.70
$50.83
$150.96
$26.83
407
The inputs worksheet converts assumptions for interest rates, volatility, and time-
to-expiration into outputs for t, u, d, and p, and then the base-tree worksheet builds
a base tree from these outputs. The worksheet then solves a European call-option tree.
To solve more complex options, we usually need to copy and alter the option-tree
worksheet. We will describe how to do this in Examples 22.1 and 22.2.
Exhibit 22-7 shows a portion of the inputs sheet for Joe’s problem.
In Exhibit 22-7, the inputs are given on the left, and the outputs are given
on the right. With N 5 60, the time steps are 1/60 of a year, and the growth factor
(5 exp(r à t)) is 1.000834 for each step. From this inputs sheet, we build a base
tree with 60 steps in the base-tree worksheet. Of course, this whole worksheet is
much too large to display on the printed page. At step 1 there is one risk node, at
step 2 there are two risk nodes, . . ., all the way up to 60 risk nodes at step 60.
Overall, there are 1 1 2 1 3 1 ?1 60 5 1,830 risk nodes in the tree, followed
by 61 terminal nodes after Step 60. The option-tree worksheet then takes the 61
terminal nodes from the base-tree worksheet, “decides” whether to exercise based on
Max(S
60
2$50, 0), and then solves backward exactly as in Exhibits 22-4 and 22-6.
The answer of $54.53 is displayed at the base of the option-tree worksheet. This
answer is only $0.01 away from the Black-Scholes solution found in European Call
Calculator.
Note that the actual option-tree worksheet does not include branches after
the decision nodes. Instead, the decision-node cells use the “max” function in
Microsoft Excel. This is a space-saving device that is particularly useful when
we alter the sheet to value American options, where every time period includes
both a risk node and a decision node. American options will be discussed in
Section 22.3.
EXHIBIT 22-7
THE INPUTS SHEET FOR JOE’S PROBLEM
? 60% t 0.02
R 5% R
ft
1.000834
S 100 u 1.080539
T 1 d 0.925464
X 50 p 0.486021
408 CHAPTER 22 BINOMIAL TREES
22.2 MULTIPLE STRIKE PRICES AND
EARLY EXERCISE
In the previous section, we showed that binomial trees can approximate the Black-
Scholes solution. By itself, this approximation does not buy us anything because we
already had an analytical solution for European options. The real payoff of bino-
mial trees comes when we introduce complications that cannot be handled by
Black-Scholes, or by any other analytical formula. In this section, we use binomial
trees to value an option with two different strike prices on two different dates. The
options analyzed in Example 22.1 are warrants. Warrants are call options that are
issued by companies on their own stock; in contrast, regular call options are issued
by some third party. Although there are some valuation differences between call
options and warrants, we will sidestep these differences by making some subtle
assumptions in the example, so that we can just treat these warrants as regular
call options. Readers interested in exploring the differences between warrants and
options are encouraged to look at Chapter 11 of Hull (2005).
EXAMPLE 22.1
Drugco is a publicly traded biotechnology company with several drugs in development, but no
products on the market. To raise capital for the development of Newdrug, Drugco enters a
strategic alliance with Bigco. In return for marketing rights for Newdrug, Bigco will pay for
clinical trials and will give drugco up-front and milestone payments. Bigco also agrees to make
an equity investment in Drugco, purchasing 10 million shares at the market price of $10 per
share and also receiving warrants to purchase an additional 10 million shares. (The market price
of $10 includes the market reaction to the Bigco alliance.) These warrants can either be
exercised in exactly two years at a strike price of $20 per share or in exactly ?ve years, with a
strike price of $50 per share. Drugco does not pay dividends and has no plans (or cash) to do so
for at least the next ?ve years. The expected volatility of Drugco stock is 60 percent per year.
Problem What is the value of Bigco’s warrants?
Solution If not for the step up in the exercise price, this would be a straightforward
option pricing problem and could be solved by the Black-Scholes equation. With the step
up, we need to use a binomial tree to solve the problem. We start by building the base
tree, which is invariant to strike-price complications. If we use bintree.xls, then we have a
60-step tree. With T 5 5 years, then t 5 5/60 5 1/12 5 0.833 5 one month. Exhibit 22-8
shows the other inputs for the tree.
From these inputs, the base-tree worksheet builds values for the stock. Now, the tricky
part—how do we build and solve the option tree? Option trees are always solved backward.
We start at the exercise date, after all 60 steps of the tree. At that point, the exercise decision
is the “normal” one: exercise if and only if the stock price is greater than the exercise price
(5$50). Because this is the standard approach in the option tree, we do not need to make any
22.2 MULTIPLE STRIKE PRICES AND EARLY EXERCISE 409
changes. Similarly, to compute the discounted value at steps 59, 58, . . ., 25, we can just
follow the same procedure as in earlier examples. The only complication occurs at Step 24,
which is after two years of the tree. At this step, Bigco has another choice to make: it can
either exercise the option, and receive an immediate payoff of S
24
2 $20, or let the ?rst
exercise date expire and receive the present discount value of the option that would ordi-
narily be calculated for that node of the tree.
Exhibit 22-9 gives portions of Steps 24 and 25 for various trees associated with
Bigco’s two-strike problem. Column (A) gives the row number, so that we can refer to cells
in the tree as we would in a spreadsheet. Column (B) shows all possible payoffs in the upper
half of the base tree at Step 24: these payoffs are copied from the base-tree worksheet. The
next four columns, (C) through (F), show Steps 24 and 25 from two different versions of
the option-tree worksheet. The ?rst version is the standard option-tree worksheet included
in the bintree ?le. This sheet is shown in columns (C) and (D), and it is a standard European
call without allowing for the possibility of an early exercise at Step 24. The second version,
named as early-tree and shown in columns (E) and (F), modi?es the ?rst version to allow for
early exercise.
To build the early-tree worksheet, we start with a copy of option-tree. In early-tree, all
columns from Step 25 to Step 60 are identical to the corresponding columns in option-tree.
This is illustrated in part by column (F) in the exhibit, which is identical to column (D). Next,
we edit the cells in Step 24 of column (E) to re?ect the possibility of early exercise at a strike
of $20. For example, to compute the entry for cell E2, we write
E2 5Max ðB2 2$20; C2Þ: ð22:16Þ
Equation (22.16) states that, at Step 24, Bigco can either choose to exercise and
receive the stock value (cell B2) minus the strike price ($20), or it can choose to hold onto the
option and receive the expected discounted value of a one-strike option (cell C2). We then
repeat this same formula for all cells in column (E). These are the only changes that are
needed to solve the two-strike tree. By examining the exhibit, we can see that Bigco would
choose to exercise early in all cases at row 20 and above. If we then look at the solution in
Step 1 of the tree (not shown in the exhibit), we get an option value of $2.15. In contrast,
the one-strike tree yields an option value of $1.87. Thus, the possibility of early exercise
EXHIBIT 22-8
INPUTS TREE FOR BIGCO’S PROBLEM
? 60% T 0.08
r 5% R
ft
1.004175
S 10 U 1.18911
T 5 D 0.840965
X 50 P 0.4688
410 CHAPTER 22 BINOMIAL TREES
at $20 gives an incremental value of $2.15 2$1.87 5$0.28 per option, making Bigco’s 10M
options worth $2.8M. ’
22.3 DIVIDENDS
Many public companies pay periodic dividends on common stock, and these
dividends can complicate the valuation of call options. For non-dividend-paying
EXHIBIT 22-9
EXCERPTS FROM TREES FOR EARLY-STRIKE DECISION
(A) (B) (C) (D) (E) (F)
Base-tree Option-tree Early-tree
Step 24 Step 24 Step 25 Step 24 Step 25
1 716.44 716.44
2 638.75 595.92 618.75
3 494.25 494.25
4 451.74 409.21 431.74
5 337.38 337.38
6 319.48 277.55 299.48
7 226.93 226.93
8 225.94 185.09 205.94
9 149.61 149.61
10 159.79 120.66 139.79
11 96.06 96.06
12 113.01 76.38 93.01
13 59.62 59.62
14 79.92 46.60 59.92
15 35.48 35.48
16 56.52 27.19 36.52
17 20.08 20.08
18 39.97 15.04 19.97
19 10.71 10.71
20 28.27 7.83 8.27
21 5.35 5.35
22 19.99 3.81 3.81
23 2.47 2.47
24 14.14 1.71 1.71
25 1.05 1.05
26 10.00 0.71 0.71
27 0.41 0.41
22.3 DIVIDENDS 411
stocks, a diversi?ed investor that holds American call options should never exercise
early. The logic for waiting until the very end—?rst discussed in Chapter 13—is
that the option holder can earn the interest on the strike price without giving up
anything. If the stock pays dividends, then waiting to exercise until the end may no
longer be optimal. Unfortunately, analytical solutions are usually not possible for
these problems. Thus, most analysts build binomial trees to compute numerical
solutions for American options on dividend-paying stocks.
Consider Joe’s three-step problem, as ?rst illustrated in Exhibit 22-2. Now,
let’s add a dividend in the second-to-last period (eight months into the year) that is
equal to 10 percent of the stock value. Now, if Joe decides to exercise after eight
months, he would receive the whole value of the stock (including the 10 percent
dividend). If, instead, he decides to wait until the full year is over, then the 10
percent dividend gets paid out after eight months, and the stock price falls by
10 percent before making an up or down move in the last period. Exhibit 22-10
illustrates the new base tree under this assumption.
EXHIBIT 22-10
JOE’S PROBLEM, BASE TREE, WITH DIVIDENDS
$100.00
$141.40
$70.72
3
2
1
$100.00
5
$90.00
$199.93
4
$179.94
$50.02
6
$45.02
0.438
0.438
0.438
0.562
0.438
0.438
0.562
0.562
0.438
0.562
0.562
0.562
Dividend
? $19.99
Dividend
? $10.00
Dividend
? $5.00
7
$254.43
8
$127.26
9
$63.65
10
$31.84
412 CHAPTER 22 BINOMIAL TREES
In Exhibit 22-11, we show the option tree, an analogue to Exhibit 22-6 from
the no-dividend case. In this tree, we divided nodes 4, 5, and 6 into two nodes each.
For example, Node 4 is now a decision node for early exercise, and Node 4A is a
risk node that is only relevant if Joe decides to wait at Node 4. Although these
nodes would not be divided in the bintree spreadsheet, it is useful to divide them in
the exhibit to make comparisons to decision trees.
As always, we solve the option tree backward. In nodes 7 through 10, Joe
needs only to compare payoffs at the terminal nodes. If he chooses to exercise, then
the option would be worth S
T
2 $50, where S
T
is taken from the corresponding
terminal node of the base tree; if he chooses not to exercise, then the option is
worth $0. We then assign each terminal node (7 though 10) with the maximum of
S
T
2 $50 and $0.
Continuing our backward march through the tree, we next come to risk nodes
4A, 5A, and 6A. Joe will only reach these nodes if he chooses to wait at decision
EXHIBIT 22-11
JOE’S PROBLEM, OPTION TREE, WITH DIVIDENDS
1
2
$204.43
$77.26
$13.65
–$18.16
exercise
exercise
exercise
exercise
exercise
exercise
wait
wait
wait
exercise
$0
$0
$0
$0
don't
don't
don't
don't
$0
10
9
$13.65
6
5
3
$24.79
$92.22
4
8
$77.26
7
$204.43
0.438
0.438
0.438
0.438
0.438
0.438
0.562
0.562
0.562
0.562
0.562
0.562
$40.83
5A
$130.97
$149.93
$50.00
$0.02
4A
$5.88
6A
$53.43
4 months 4 months 4 months
$5.88
$50.00
$149.93
22.3 DIVIDENDS 413
Nodes 4, 5, and 6, respectively. To compute the expected value at these risk nodes,
we take 0.438 Ã the up branch 1 0.562 Ã the down branch, discounted by R
ft
5
1.017 (from Equation (22.12)). For example, at Node 4A we have
2
Value at Node 4A5ð0:438 Ã $204:43 10:562 Ã $77:26Þ=1:017 $130:97 ð22:17Þ
Now, at Node 4, Joe can either choose to wait (and receive a discounted
expected value of $130.97) or exercise immediately. If he exercises immediately,
then he will get the stock before it pays the dividend. This is the key factor
driving the possibility of early exercise. Thus, with early exercise he would get
the full value of the stock before the dividend, minus the strike price of $50:
$199.93 2 $50 5$149.93. The decision at Node 4 is to take the maximum of the
waiting value ($130.97) and the early exercise value ($149.93). We then type this
maximum into Node 4 in the tree.
With similar comparisons, we can see that early exercise is optimal at Nodes
4 and 5, but not at Node 6. We then back the expected values up through risk nodes
2 and 3, and ?nally back to the base of the tree at Node 1. This procedure yields an
option value of $53.43 at the ?rst node.
In our next example, we generalize the dividend problem to our full 60-step
tree and model a real option for a company to invest in a pro?table project. If the
company invests right away, then it immediately gets some positive cash ?ows and
a positive overall NPV. If it waits, however, then it may be able to avoid investing
for some cases where the project goes bad. There is a cost to waiting because the
company must forego the positive cash ?ows that would have been generated
during this waiting period. These positive cash ?ows are modeled as “dividends”.
One nice feature of real-option problems is that it is reasonable to model these
dividends as a continuous payment of some fraction of the project value. By
modeling dividends as a continuous payment, the construction of the binomial tree
is simpli?ed. We demonstrate this technique in the following example.
EXAMPLE 22.2
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19 and is similar to Example 21.3 from the previous
chapter.) They have already completed several R&D projects with this technology, so they
have eliminated the technical risk for this new project. To begin producing and marketing
to the consumer market would require a new investment of $200M. At the present time,
Fuelco estimates that the completed project would have a present value of $400M (i.e.,
if Fuelco spent $200M to initiate the project, they believe they could spin off the initiated
project for $400M). Fuelco can delay starting the project for up to ?ve years, during which
time they expect this value of the project to ?uctuate, with an annual volatility of 90 percent.
Once initiated, the project is expected to generate annual cash ?ows equal to 10 percent of its
2
We use the operator in Equation (22.18) because of a rounding error.
414 CHAPTER 22 BINOMIAL TREES
value. Thus, if Fuelco delays the project, they will forego these cash ?ows. After ?ve years,
some important Fuelco patents will expire, and they will no longer have the option to
pro?tably enter this new market. If Fuelco does not enter the market, then Project C has no
salvage value.
Problem What is the NPV of Project C?
Solution The problem here is to value Fuelco’s real option to invest. If Fuelco invests
right away, then it would cost $200M and provide a present value of $400M, for a total NPV
of $200M. So why would Fuelco ever decide to wait? Because it is possible that the project
will have terrible performance in the next few years, in which case Fuelco will be happy that
they held on to the $200M. There is a cost to such patience because Fuelco will have to
forego some positive cash ?ows during this waiting period. Because Fuelco can make this
decision at any time, there are an in?nity of possible decision nodes. To get an approximate
answer to the problem, we assume that decisions to invest can only be made once per month,
and we adopt a binomial-tree framework with only two possible branches (up and down)
from each risk node. Even with this assumption, over ?ve years there are still 60 possible
dates in which to invest. Exhibit 22-12 shows the ?rst part of the decision tree.
EXHIBIT 22-12
FUELCO’S PROBLEM, PROJECT C
1
foregone
cash flow
? CF
1
foregone
cash flow
? CF
4
invest –$200M
invest –$200M
3
foregone
cash flow
? CF
5
invest –$200M
5
11
10
13
12
. . .
. . .
6
7
8
9
1–p
1–p
down
1–p
down
p
down
up
$400
wait
up
p
up
p
wait
wait
($400 – CF
1
)*u
($400 – CF
1
)*u
4
2
instant One month One month instant
22.3 DIVIDENDS 415
The ?rst decision occurs at Node 1. As we already discussed, if Fuelco chooses to
invest immediately, then they spend $200M for a project with a value of $400M, as shown at
terminal Node 2. If Fuelco chooses to wait, then some project risk evolves during the ?rst
month (Node 3), during which time Fuelco does not receive any of the project cash ?ows. We
write these cash ?ows as CF
1
, which means “cash ?ows forgone by waiting at Node 1”. At
Node 3, an up move results in a project value of ($400 2 CF
1
) Ã u and a down move leads to
a project value of ($400 2 CF
1
) Ã d. At the end of this ?rst month, Fuelco again makes a
decision about whether to invest (Nodes 4 and 5). This process continues for 59 more
months. To solve the tree, we work backward from Step 60.
Clearly, this decision tree grows very large by Step 60. To make the problem more
manageable, we follow the same procedure as in earlier problems and break the decision tree
into two binomial trees: a base tree and an option tree. Exhibit 22-13 gives the inputs sheet
for these trees. This exhibit includes a row for the dividend yield ( y) and for the dividend
factor, R
yt
5 exp(yt), which is an analogue to the growth factor.
Because the annual dividend yield (10%) is greater than the riskfree interest rate (5%),
Fuelco may indeed want to exercise early at several points in the option tree. As in the previous
example, we will need to alter the option-tree worksheet to allow for early exercise. We refer to
this new worksheet as am-tree. Exhibit 22-14 gives excerpts from the last few steps of
the binomial trees. The ?rst half of the tree gives an excerpt from the base-tree worksheet,
and the second half of the tree gives an excerpt from the am-tree worksheet. All excerpts are
from the middle of the tree at Steps 58, 59, and 60. To build the base tree, we multiply cells by
the up (or down) branch and divide by the dividend factor. (The values of these inputs are
given in Exhibit 22-13.) For example, to compute cell C1 we use the following formula:
C1 5B2 Ã u=R
yt
5$697:40 Ã 1:296681=1:008368 5$896:80: ð22:18Þ
In the base-tree portion of Exhibit 22-14, notice that the rows of the tree do not have a
constant value (e.g., in cell B4 the value of the project is $414.78, whereas in cell D4 the
value is $407.92). This “loss” of value occurs because of the dividends; in binomial trees
without dividends (like Exhibit 22-5), the tree recombines at the same value.
The am-tree tree is solved backward, starting with Step 60. The entries in column G
are the value of the real option in the last period. We calculate these values with the standard
maximum formulas. For example, the value of cell G2 is
G2 5Max ðD2 2$200; $0Þ: ð22:19Þ
EXHIBIT 22-13
INPUTS SHEET FOR FUELCO’S PROBLEM
? 90% t 0.08
r 5% R
ft
1.004175
S 400 u 1.296681
T 5 d 0.7712
X 200 p 0.443357
y 10% R
yt
1.008368
416 CHAPTER 22 BINOMIAL TREES
Next, at Step 59 Fuelco must decide whether to exercise immediately (and receive the value
in the base tree minus $200) or to wait (and receive the expected discounted value of the up
and down branches.) The formula for cell F3 is
F35Max ððp à G21ð12pÞ Ã G4Þ=R
ft
; C32$200Þ 5Max ð$329:78; $333:37Þ 5$333:37:
ð22:20Þ
Thus, Fuelco would choose early exercise in cell F3. This should not be surprising:
because Fuelco knows it will exercise in both successor cells (G2 and G4), it will bene?t by
exercising early and taking the dividend (10 percent annualized), even at the cost of losing
the time value of the strike price (5 percent annualized).
The computer uses the same formulas to solve the tree all the way back to its ?rst cell.
The am-tree worksheet values the real option at $249.66M. Thus, Project C is worth almost
$50M more than the $200M value from immediate investment. ’
SUMMARY
In this chapter we learned about binomial trees, a ?exible and powerful type of decision
tree. In binomial trees, each risk node is followed by two branches: an “up” branch with
probability 5 p, and a down branch with probability 5 1 2 p. In the Cox-Ross-Rubenstein
(CRR) model, the size of the down move is set equal to the reciprocal of the up move: d 5 1/u.
Binomial trees built with the CRR model have several nice features, and modi?ed versions of
the trees can be used to obtain solutions for many complex option features. In this chapter, we
solved examples for options with multiple strike prices on different dates, and for real options
on positive cash-?ow projects.
EXHIBIT 22-14
EXCERPTS FROM TREES FOR FUELCO’S PROBLEM
Base-tree Am-tree
(A) (B) (C) (D) (E) (F) (G)
STEP STEP
ROW 58 59 60 58 59 60
1 $896.80 $696.80
2 $697.40 $685.87 $497.40 $485.87
3 $533.37 $333.37
4 $414.78 $407.92 $214.78 $207.92
5 $317.22 $117.22
6 $246.69 $242.61 $62.18 $42.61
7 $188.67 $18.81
8 $146.72 $144.29 $8.31 $0.00
SUMMARY 417
KEY TERMS
Binomial trees
Recombine
Base tree, option tree
Growth factor
CRR model
Warrants
Dividend factor
REFERENCES
Cox, John C., Steven A. Ross, and Mark Rubinstein, 1979, “Option Pricing: A Simpli?ed Approach”,
Journal of Financial Economics 7, 229À263.
Haug, Espen G., 1997, Option Pricing Formulas, McGraw-Hill, New York.
Hull, John C., 2005, Option, Futures, and Other Derivatives, 6th Edition, Prentice Hall, Upper Saddle
River, NJ.
EXERCISES
22.1 True, False, or Uncertain : Assume that all Black-Scholes assumptions hold. Let C be
the value of a call option with strike price X on underlying stock S and exercise date T in a
world with riskfree interest rate r. This underlying stock has an expected return of µ and an
expected volatility of ?. Now, assume that everyone in the world suddenly becomes more
risk averse, and the new expected return on the underlying stock is u
f
, where µ
f
.µ. There is
no change in ? or r. After this change, the value of C will go down.
22.2 Begin with the same setup as Example 22.1: Bigco’s investment in Drugco for equity
plus warrants. Now, in addition to the strike price of $20 after two years and $50 after ?ve
years, assume that the warrants can also be exercised after three years at a strike of $30 or
after four years at a strike of $40. Assume everything else from the problem is unchanged.
Use bintree to solve for the value of Bigco’s warrants.
22.3 Begin with the same setup as Example 22.2: Fuelco’s investment in Project C. Now, in
addition to the assumptions made in the example, we add an additional possibility: Fuelco
has an option to sell the patents that underlie Project C for $100M in exactly three years.
They can only sell these patents if they have not yet invested the required $200M in the
project. Selling the patents has no effect on any of Fuelco’s other projects. How does this
new option affect the NPV of Project C?
22.4 Begin with the same setup as Example 22.2: Fuelco’s investment in Project C. Now,
suppose we believe that the volatility of the project is really 120 percent. With this high
volatility, a 60-step tree may not be suf?ciently precise. Edit the bintree spreadsheet to build
a 100-step tree, and then compare the option values for N 5 60 and N 5 100. How different
are these values? Do you think it is necessary to build an even larger tree? (This exercise will
be time consuming. It is good practice if you want to learn how to build your own trees.)
418 CHAPTER 22 BINOMIAL TREES
CHAPTER 23
GAME THEORY
R&D DECISIONS are rarely made in isolation from competition. So far, all
our models have ignored the strategic aspects of competition, with potential
competitors modeled as random events that might reduce pro?ts. In a more realistic
model, a company must consider a variety of different strategies in response to
competition, while simultaneously recognizing that competitors will also be mak-
ing similar calculations. The interaction among different decision makers, all of
whom may have different objectives, is the domain of game theory. Despite its fun-
sounding name, game theory has always been concerned with serious matters, with
nuclear deterrence among its earliest topics.
In this chapter, we give an introduction to game theory and discuss several
applications to R&D investing. Although the subject of game theory is vast enough
to justify years of study, the key concepts are accessible to all interested amateurs.
In Section 23.1, we provide a core set of terms and de?nitions and set up a few
canonical games, beginning with the prisoner’s dilemma. In Section 23.2, we
“solve” these canonical games using the powerful concept of the Nash Equilibrium.
In Section 23.3, we introduce a more complex set of games and re?ne the Nash
equilibrium concept to allow for more robust solutions. In Section 23.4, we show
how the game-theory analysis of this chapter can provide fresh insights into real-
option investment problems.
23.1 WHAT IS GAME THEORY?
We begin with the most famous example in all of game theory: the prisoner’s
dilemma. Two people, Al and Bob, have been arrested by the police and are being
held in separate rooms. In each room an interrogator explains to the prisoner that he
should make things easy for himself and “confess” to the crime. (Whether Al and
Bob are actually guilty is immaterial to the problem.) Each prisoner can choose
whether or not to confess. If both prisoners confess, then they will both go to jail for
eight years. If neither prisoner confesses, then the prosecutors will not be able to
419
convict both defendants of the highest crime, but they will still both go to jail
for two years. If, however, only one of the prisoners confesses, then the confessor
will be released without any jail time, while the other prisoner will get 10 years.
Exhibit 23-1 expresses these payoffs in a 2 3 2 matrix. This matrix is called the
normal form of the game.
In this exhibit, the strategies of each player are given in the ?rst column (for
Al) and in the ?rst row (for Bob). The payoffs corresponding to each strategy pair
are given in the corresponding box in the matrix, with Al’s payoff listed ?rst. For
example, if Al chooses don’t confess and Bob chooses confess, then Al gets 10
years and Bob goes free (0 years).
We can also represent the prisoner’s dilemma in a game tree. This game tree,
also known as the extensive form of the game, is shown in Exhibit 23-2.
In Exhibit 23-2, we draw the ?rst decision node for Al, and the second (and
third) decision nodes for Bob. The payoffs are given at the terminal nodes, with
years of jail time expressed as negative numbers: (— Al’s years, — Bob’s years).
Although this representation might imply that Al actually decides before Bob, the
description of the game has the two players making their decisions at the same
time. To illustrate that the decisions are actually simultaneous, the standard
practice is to draw a closed curve around Bob’s two decision nodes; this closed
curve indicates that Bob does not know whether he is at Node 2 or Node 3. He
must make his decision at Nodes 2 and 3 based on his best guess of what Al will
do, just like Al must make his decision at Node 1 based on his best guess of what
Bob will do. This is called a simultaneous game. If Al actually did move ?rst,
then we would erase the closed curve around Nodes 2 and 3, and we would have a
sequential game. In Section 23.2, we learn how to solve for the equilibria of
simultaneous games. In Section 23.3, we learn how to solve for the equilibria in
sequential games. First, we get some practice with drawing the normal and
extensive form for another game.
EXHIBIT 23-1
PRISONER’S DILEMMA, NORMAL FORM
Bob
Confess
Don’t
Confess
A1 Confess 8 years, 0 years,
8 years, 10 years
Don’t 10 years, 2 years,
Confess 0 years 2 years
420 CHAPTER 23 GAME THEORY
EXAMPLE 23.1
Anne and Beth completed a group assignment for their ?nance class. The assignment is due
in ?ve minutes, but neither of them brought it to class. (They each believed that the other
student was going to bring it.) Because this professor never grants any extensions, Anne and
Beth both know that one of them will need to run back to their apartment to print out the
assignment. To decide which one of them must make this long trek in the rain, they resort to
the oldest of games: “odds and evens”. In the odds-and-evens game, one player (here, Anne)
takes “odds”, and one player (here, Beth) takes “evens”. Then, both players simultaneously
show one or two ?ngers. If both players show the same number of ?ngers, then the evens
player (Beth) wins the game. If players show different numbers of ?ngers, then the odds
player (Anne) wins the game.
Problems
(a) Draw the normal form for this game.
(b) Draw the extensive form for this game.
Solutions
(a) The normal form is given in Exhibit 23-3.
EXHIBIT 23-2
PRISONER’S DILEMMA, EXTENSIVE FORM
1
Al
2
3
Bob
Confess
Don't
confess
Don't
confess
Confess
Confess
Don't
confess
(–8, –8)
(0, –10)
(–10, 0)
(–2, –2)
23.1 WHAT IS GAME THEORY? 421
If the players choose a different number of ?ngers, then Anne wins and gets to stay, with
Beth going back to her apartment to get the assignment. If the players choose the same
number of ?ngers, then Beth wins and gets to stay. We give a payoff of one to the player who
wins the game (“stays”), so that the payoffs where Anne wins (odds) are (1, 0), and the
payoffs where Beth wins (evens) are given payoffs of (0, 1).
Games like this are known as zero-sum games or constant-sum games, because there is
a ?xed amount to be won or lost (not necessarily zero), and this ?xed amount must be shared by
the two players. In contrast, in the prisoner’s dilemma, the total amount of jail time was not ?xed.
(b) The extensive form for the odds-and-evens game is given in Exhibit 23-4.
EXHIBIT 23-4
ODDS-AND EVENS-GAME, EXTENSIVE FORM
1
Anne
2
3
Beth
Two
One
Two
One
One
Two
(0, 1)
(0, 1)
(1, 0)
(1, 0)
EXHIBIT 23-3
ODDS-AND-EVENS GAME, NORMAL FORM
Beth
One Two
Anne
One 0, 1
1, 0
1, 0
Two 0, 1
422 CHAPTER 23 GAME THEORY
As in the prisoner’s dilemma game (Exhibit 23-2), we arbitrarily put one of the players
?rst (Anne) and then draw a closed curve around decision nodes 2 and 3 to indicate that Beth
cannot tell which node she is at when she makes her decision.
’
23.2 SIMULTANEOUS GAMES
In the previous section, we drew normal and extensive forms for two games, but we
did not make any statements about optimal strategies or solutions. However,
before proceeding to a solution, we need to de?ne what a “solution” would be. In
game theory, there are many different equilibrium concepts for solving a game.
The unifying theme to all these concepts is that all players must be maximizing their
expected utility subject to some beliefs about other players’ decisions. The concepts
differ only in the precise meaning of “subject to some beliefs”.
The most famous and ?exible of all equilibrium concepts is Nash Equi-
librium (NE). This concept is named for its founder, John Nash, a Nobel Prize
winner in economics and the subject of an Academy Award-winning movie, A
Beautiful Mind. NE requires that each player’s equilibrium strategy must be a best
response to the equilibrium strategies of all other players. Put another way, once
the equilibrium strategies have been written down, no player could improve the
payoff by changing to a different strategy.
For games where the normal form can be easily written down (as in Exhibits
23-1 and 23-3), we can use a simple procedure for ?nding the NE. Exhibit 23-5
illustrates this procedure for the prisoner’s dilemma.
Exhibit 23-5 uses the normal form (Exhibit 23-1) as its starting point and then
circles the best responses for each player. Remember that in each cell of the nor-
mal-form matrix, the ?rst payoff belongs to Al, and the second payoff belongs to
EXHIBIT 23-5
PRISONER’S DILEMMA, NORMAL FORM, WITH BEST RESPONSES
Bob
Confess
Don’t
Confess
A1 Confess 8 years, 0 years,
8 years, 10 years
Don’t 10 years, 2 years,
Confess 0 years 2 years
23.2 SIMULTANEOUS GAMES 423
Bob. Now imagine that Bob believes that Al is going to confess. With this belief,
Bob knows that his payoff will be in the top row of the matrix. Then Bob can either
confess, leading to the upper left cell of (confess, confess) and giving him eight
years, or don’t confess, leading to the upper right cell of (confess, don’t confess)
and giving him 10 years. Because we assume that Bob would prefer to spend fewer
years in prison, we circle his payoff of eight years in the upper left quadrant.
Next, suppose that Bob believes that Al is going to play don’t confess. Now
Bob knows that he is going to be in the bottom row of the matrix. Then, Bob can
either confess, leading to the lower left cell of (don’t confess, confess) and setting
him free with 0 years in prison, or don’t confess, leading to the lower right cell of
(don’t confess, don’t confess) and giving him two years. Again, we assume that Bob
would prefer to spend fewer years in prison, so we circle his payoff of zero years in
the lower left quadrant.
After performing these steps, we have determined Bob’s best responses to
both of Al’s possible strategies. To ?nish the problem, we need to do the same thing
for Al. First, we imagine that Al believes that Bob is going to confess. With this
belief, Al knows that his payoff will be in the left column of the matrix. Then Al
can either confess, leading to the upper left cell of (confess, confess) and giving him
eight years, or don’t confess, leading to the lower left cell of (don’t confess, con-
fess) and giving him 10 years. Because Al would prefer to spend fewer years in
prison, we circle his payoff of eight years in the upper left quadrant.
Finally, suppose that Al believes that Bob is going to play don’t confess. Now
Al knows that he is going to be in the right column of the matrix. Then Bob can
either confess, leading to the upper right cell of (don’t confess, confess) and setting
him free with zero years in prison, or don’t confess, leading to the lower right cell
of (don’t confess, don’t confess) and giving him two years. Again, we assume that
Bob would prefer to spend fewer years in prison, so we circle his payoff of zero
years in the upper right quadrant.
Now, to ?nd the NE, we look for all cells in the matrix where both strategies
have been circled. This requirement yields the upper left quadrant of (confess,
confess), which is the only NE for the game. In this equilibrium, both prisoners will
spend eight years in jail. To both Al and Bob, this is going to seem like a terrible
outcome. If only they could somehow agree to play don’t confess, then they could
each receive two years in prison. It is easy to see, however, that this outcome is not
possible unless the players can make some binding agreement. In the absence of a
binding agreement, both players have an incentive to play confess and to get away
without any jail at all. Indeed, we can see that confess is a dominant strategy for
both players: each player will do better (less jail time) by playing confess than they
will by playing don’t confess, regardless of what the other player does. In the
real world, there are many examples of games like the prisoner’s dilemma: both
players would like to settle on a different outcome (don’t confess, don’t confess),
but both players have an incentive to cheat on this outcome. Some versions of these
games are called arms races, as the next example illustrates.
424 CHAPTER 23 GAME THEORY
EXAMPLE 23.2
Drugco and Pharmco produce the two leading drugs to treat severe ?u symptoms. These are
strong medications available only by prescription, and both ?rms market their medicines
heavily to physicians. Both ?rms are considering large direct-to-consumer advertising plans.
Advertising is very costly, but it would increase awareness of the drugs and help each ?rm in
its competitive position. Each ?rm can independently choose to be aggressive in the direct-
to-consumer market by choosing high advertising or to be less aggressive by choosing low
advertising. If only one of the two ?rms chooses high advertising, then the NPV of that ?rm’s
product (including advertising costs) would be $500M, whereas the NPV of the low
advertising ?rm would be $100M. If both ?rms choose high advertising, then the NPV of
each product would be $200M. If both ?rms choose low advertising, then the NPV of each
product would be $400M.
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-6. We have arbitrarily chosen to put Drugco
?rst and Pharmco second, with a closed curve around Pharmco’s decision nodes (2 and 3) to
denote the simultaneity of the game.
EXHIBIT 23-6
ADVERTISING GAME, EXTENSIVE FORM
1
Drugco
2
3
Pharmco
High
advertising
High
advertising
High
advertising
Low
advertising
Low
advertising
Low
advertising
All payoffs in $millions
(200, 200)
(400, 400)
(500, 100)
(100, 500)
23.2 SIMULTANEOUS GAMES 425
(b) The normal form, with best responses circled, is given in Exhibit 23-7. There is a unique
NE of (High Advertising, High Advertising), where both ?rms have an NPV of $200M.
Notice the similarity of this problem to the prisoner’s dilemma shown in Exhibit 23-5.
As in the prisoner’s dilemma, the players in this game would like to collude on a
different outcome—in this case with both ?rms playing “low advertising”, leading to payoffs
of $400M for both. Unfortunately, this superior outcome (for the ?rms) is not an NE, as both
?rms would have an incentive to deviate and play “high advertising”. For this reason, we
could call this game an “advertising arms race”, with the ?rms engaged in an escalating spiral
of advertising spending. Arms-race games were among the ?rst topics of game theory, as
applied to the ever-increasing military expenditures during the Cold War. ’
Next, we look for the Nash equilibrium for the odds-and-evens game. By
following the same procedures as we did for the prisoner’s dilemma, we can circle
the best responses for each player. This normal form, with best responses circled, is
shown in Exhibit 23-8.
For anyone who has enjoyed the childhood pastime of odds and evens, it will
come as no surprise that there is no clean solution. Anne, who is playing “odds”, always
wants to do the opposite of Beth. Conversely, Beth, who is playing “evens”,
always wants to do the same thing as Anne. When we circle the best responses, there is
no cell in the matrix with two circles. When this happens, we say that there is no pure-
strategyNE. Apure strategyis a strategythat plays one choice all the time: one is a pure
strategy in the odds-and-evens game; confess is a pure strategy in the prisoner’s
dilemma. In contrast, a mixedstrategy combines multiple pure strategies. For example
“play one ?nger 50 percent of the time and play two ?ngers 50 percent of the time” is an
example of a mixed strategy. In his original paper about NE, John Nash proved that
every game has at least one NE. Thus, if there is nopure-strategy NE, then there must be
at least one mixed-strategy NE.
EXHIBIT 23-7
ADVERTISING GAME, NORMAL FORM
Pharmco
High Low
Advertising Advertising
High $200 M, $500 M,
Advertising $200 M $100 M
Drugco
Low $100 M, $400 M,
Advertising $500 M $400 M
426 CHAPTER 23 GAME THEORY
In general, there is no easy way to ?nd all the mixed-strategy NE for a game.
In the special case of games with two players with two strategies each—also called
two-by-two games—we can solve for the mixed-strategy equilibrium by solving
one equation for each player. In the paragraphs below, we solve these equations for
the odds-and-evens game.
Let p be the probability of Anne playing one, so that 1 2 p is the probability
of Anne playing two. With these probabilities, if Beth plays one then she would
receive an expected payoff of
Beth’s expected payoff of playing one ¼ p à 1 þ ð1 2pÞ Ã 0 ¼ p: ð23:1Þ
If Beth plays two, then she would receive an expected payoff of
Beth’s expected payoff of playing two ¼ p à 0 þ ð1 2pÞ Ã 1 ¼ 1 2p: ð23:2Þ
With these expected payoffs, Beth will choose to play one, if and only if
p .1 2 p. Then,
Beth’s expected payoff for the game ¼ Max ðp; 1 2pÞ: ð23:3Þ
Because this is constant-sum game, everything Beth gets is effectively taken
from Anne (e.g., if Beth gets a payoff of p, then Anne gets an expected payoff of
1 2 p). Thus, to maximize her own expected payoff, Anne can just try to minimize
Beth’s maximum payoff. This is called the minimax solution, because a player
tries to “minimize the maximum payoff” of her opponent.
To minimize Beth’s payoff, Anne should set p so that both terms in the
“Max” function are equal to each other:
To minimize Beth’s expected payoff : p ¼ 1 2p-p ¼ 0:5: ð23:4Þ
Next, we repeat these steps, this time with Beth trying to minimize Anne’s
maximum payoff. Let q be the probability of Beth playing one, so that 1 2 q is the
probability of Beth playing two. With these probabilities, if Anne plays one then
she would receive an expected payoff of
EXHIBIT 23-8
ODDS-AND-EVENS GAME, NORMAL FORM, WITH BEST RESPONSES
Beth
One Two
Anne
One 0 ,1 1, 0
Two 1, 0 0 , 1
23.2 SIMULTANEOUS GAMES 427
Anne’s expected payoff of playing one ¼ q à 0 þ ð1 2qÞ Ã 1 ¼ 1 2q: ð23:5Þ
If Anne plays two, then she would receive an expected payoff of
Anne’s expected payoff of playing two ¼ q à 1 þ ð1 2qÞ Ã 0 ¼ q: ð23:6Þ
With these expected payoffs, Anne will choose to play one, if and only if
1 2 q .q. Then,
Anne’s expected payoff for the game ¼ Max ð1 2q; qÞ: ð23:7Þ
To minimize Anne’s payoff, Beth should set q so that both terms in the Max
function are equal to each other:
To minimize Anne’s expected payoff : 1 2q ¼ q-q ¼ 0:5: ð23:8Þ
With these results, we can claimthat ( p 50.5, q 50.5) is a mixed-strategy NEof
the game. To verify this claim, we check that both players are making best responses to
the other player’s choices. This is a trivial proof, for because both players are rando-
mizing 50À50, then it does not matter what the other player does: all possible strategies
lead to a payoff of 0.5. Thus, ( p 5 0.5, q 5 0.5) is a mixed-strategy NE.
Mixed-strategy equilibria are common in competitive zero-sum type games
and sports such as poker, sailing (really!), and penalty shots in soccer. Many sce-
narios from business strategy can mimic these kinds of games. Mixed-strategy
equilibria also show up in technology investing, in the form of a leader-follower
game. Example 23.3 illustrates such a game.
EXAMPLE 23.3
Leadco is the market-leading producer of microprocessors for home and small business
computers. Followco is Leadco’s closest competitor in this market. Both ?rms are currently
working on their next-generation microprocessor. These development projects, carried out in
great secrecy, face typical constraints for microprocessor development: customers demand
many new features, but adding features tends to reduce processor speed. Both Leadco and
Followco believe that the majority of customers want to have more graphics capabilities on
the chip, but the reduction in speed will turn off other customers. Both companies must
decide how much more graphics capability to add, knowing that this addition will reduce the
processor speed.
We summarize the contrasting goals with two possible strategies for each ?rm: more
graphics and faster speed. With a larger installed-base and more brand awareness, Leadco
would like to have the same strategy as Followco because this symmetry will tend to preserve
their current lead. If both companies choose the same strategy, then Leadco would maintain a
75 percent share of the market, and their processor would have an NPV of $6B, with $2B for
Followco. On the other hand, Followco would like to adopt the opposite strategy from
Leadco because they would then have the opportunity to steal some of Leadco’s installed
base. If the two ?rms choose different strategies, then the ?rm with more graphics will have
an NPV of $5B, and the ?rm with faster speed will have an NPV of $4B.
428 CHAPTER 23 GAME THEORY
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-9. From this extensive form, one might think
that more graphics is a “better” strategy because it gives higher payoffs when the players
choose different strategies. This kind of reasoning is dangerous, because, as we will see, a
pure strategy of more graphics is not part of any NE.
(b) The normal form for this game, with best responses circled, is given in Exhibit 23-10.
As in the odds-and-evens game, we ?nd no pure-strategy NE. The reason is that
Leadco always wants to be the same as Followco, whereas Followco wants to be different.
With a simultaneous game, the best strategy is to try to keep the other company guessing.
The game-theoretic way to do this is with a mixed strategy.
To ?nd the mixed-strategy equilibrium, we follow the same steps as we did for the
odds-and-evens game. Let p be the probability of Leadco playing more graphics, so that 1Àp
is the probability of Leadco playing faster speed. With these probabilities, if Followco plays
more graphics then it would receive an expected payoff of
p à $2B þ ð1 2pÞ Ã $5B ¼ $5B2$3B à p: ð23:9Þ
EXHIBIT 23-9
LEADER-FOLLOWER GAME, EXTENSIVE FORM
1
Leadco
2
3
Followco
More
graphics
More
graphics
Faster
speed
Faster
speed
More
graphics
Faster
speed
($6B, $2B)
($5B, $4B)
($4B, $5B)
($6B, $2B)
23.2 SIMULTANEOUS GAMES 429
If Followco plays faster speed, then it would receive an expected payoff of
p à $4B þ ð1 2pÞ Ã $2B ¼ $2B þ $2B à p: ð23:10Þ
Thus, Followco’s expected payoff for the game is
Max ð$5B2$3B Ã p; $2B þ $2B Ã pÞ: ð23:11Þ
To minimize Followco’s payoff, Leadco should set p so that both terms in the Max
function are equal to each other:
$5B2$3B Ã p ¼ $2B þ $2B Ã p - p ¼ 3=5: ð23:12Þ
Next, we repeat these steps, this time with Followco trying to minimize Leadco’s
expected payoff. Let q be the probability of Followco playing more graphics, so that 1 2 q is
the probability of Followco playing faster speed. With these probabilities, if Leadco plays
more graphics then it would receive an expected payoff of
q à $6B þ ð1 2qÞ Ã $5B ¼ $5B þ $1B à q: ð23:13Þ
If Leadco plays faster speed, then it would receive an expected payoff of
q à $4B þ ð1 2qÞ Ã $6B ¼ $6B2$2B à q: ð23:14Þ
Thus, Leadco’s expected payoff for the game is
Max ð$5B þ $1B Ã q; $6B2$2B Ã qÞ: ð23:15Þ
To minimize Leadco’s payoff, Followco should set q so that both terms in the Max
function are equal to each other:
$5B þ $1B Ã q ¼ $6B2$2B Ã q - q ¼ 1=3: ð23:16Þ
Equations (23.12) and (23.16) tell us that the mixed-strategy NE of this game is
( p 5 3/5, q 5 1/3). In words, this means that Leadco plays more graphics 60 percent of the
time, and Followco plays more graphics 33.3 percent of the time. If both ?rms are using
these strategies, then neither ?rm can do better by using any other strategy.
’
EXHIBIT 23-10
LEADER-FOLLOWER GAME, NORMAL FORM
Followco
More Faster
Graphics Speed
More $6B, $5B,
Graphics $2B $4B
Leadco
Faster $4B, $6B,
Speed $5B
$2B
430 CHAPTER 23 GAME THEORY
Thus far in the book, we have performed two kinds of analysis: positive
analysis and normative analysis. Positive analysis aims to describe actual behav-
ior. Our studies of VC returns (chapters 3 and 4), the performance of speci?c VC
investments (Chapter 7), and the frequencies of various contractual terms (chapters
2 and 8) were all examples of positive analysis. Normative analysis aims to describe
optimal behavior. When we presented the modi?ed VC method in Chapter 9, we
did so not because we think VCs actually use this method, but because it is
the “correct” model under certain assumptions. Similarly, all of Part III provides a
normative model for partial valuation. Although the book argues that this framework
is helpful for making investment decisions, it does not claim that current VCs are
actually using this framework. In short, positive analysis attempts to describe the
world “the way it is”, whereas normative analysis attempts to describe the world “the
way it ought to be”. One cannot jump easily from one type of analysis to another.
Game theory is normative analysis. Although game theorists often speak of
“equilibrium predictions”, they do not mean this literally. Instead, game theory
makes the assumption that all players are behaving rationally, and then logically
derives the implications of such behavior for equilibrium outcomes. These equili-
bria are not positive predictions about the way the world is, but instead are nor-
mative predictions about the way the world would be under some strong
assumptions about rationality. Thus, when we say that the equilibrium in Example
23.3 is ( p 53/5, q 51/3), we are not predicting this outcome, but merely estab-
lishing a baseline for rational players. For our purposes, game theory is best used to
force us to think rigorously about all the strategic moves available to all interested
parties. The Nash equilibrium solutions should not be thought of as ?nal answers,
but rather as a structure for understanding these moves.
So far in this chapter, we have analyzed two types of games: arms-race games
(prisoner’s dilemma and Example 23.2), where both players have a dominant
strategy that leads to an unhappy NE, and competitive games like Example 23.3, of
which constant-sum games like odds-and-evens are a special class. A third type
of game commonly appears: the coordination game. In a coordination game, there
are no dominant strategies and more than one possible pure-strategy NE. Example
23.4 gives a typical game of this type.
EXAMPLE 23.4
Gameco and Movieco are the leading developers of DVD technology. In the past, these two
companies were able to agree on identical technical standards, but they are now embroiled in
a ?erce debate about the next generation of technology. Gameco believes that the time is ripe
for a revolutionary change in DVD technology that would provide much larger storage
capacity and allow for highly complex interactive games. Movieco, on the other hand, favors
a more evolutionary change that would maintain a higher degree of backward compatibility.
Because the companies are unable to agree on a standard technology, they have
continued with separate development projects. Other content providers are reluctant to
choose sides, fearing that they may pick the wrong company to back. This delay is damaging
23.2 SIMULTANEOUS GAMES 431
the long-term sales potential of both technologies. If the two companies are unable to settle
on a single technology, then each project would be worth $2B. Both companies would do
better if they could agree on a single standard—but which one? The revolutionary standard
would favor Gameco, with an expected NPV of $10B versus only $4B for Movieco. The
evolutionary standard would favor Movieco, with an expected NPV of $10B versus only $4B
for Gameco. Although this is an ongoing battle with no clear endpoint, we choose to model it
as a single-stage simultaneous game, where each company must decide on a standard.
Problems
(a) Draw the extensive form for this game.
(b) Draw the normal form for this game and solve for all pure-strategy Nash equilibria.
Solutions
(a) The extensive form is given in Exhibit 23-11.
(b) The normal form, with best responses circled, is given in Exhibit 23-12.
This game has two pure-strategy NE: (Revolution, Revolution) and (Evolution, Evo-
lution). From a normative perspective, we cannot say which outcome “should” occur, only
that the companies would rather agree than disagree.
EXHIBIT 23-11
STANDARDS GAME, EXTENSIVE FORM
1
Gameco
2
3
Movieco
Revolution
Revolution
Evolution
Evolution
Revolution
Evolution
($10B, $4B)
($2B, $2B)
($2B, $2B)
($4B, $10B)
432 CHAPTER 23 GAME THEORY
In addition to these two pure-strategy NE, there is also a unique mixed-strategy NE. In
Exercise 23.1, you are asked to solve for this equilibrium.
’
REALITY CHECK: In the real world, these kinds of coordination games are
common. Perhaps the most famous example is the battle between VHS and Beta-
max for the video recording market in the early 1980s. The scenario of Example
23.4, a standards battle for new DVD technology, is still being waged as of this
writing. In practice, these battles tend to get resolved over time as one of the
technologies gains a critical mass of developers and content providers. Once this
happens, the owners of the trailing technology can choose to continue the ?ght (and
get a large share of an ever-shrinking market) or give up and join the leading
technology to get a smaller share of a larger market. The longer the ?ght goes on,
the greater the damage to its potential market. Indeed, some standards battles can
go on for so long that a new technology completely overtakes them. By modeling
these contests as one-step simultaneous games, we lose some important nuances but
still gain insight into the stakes of the battle.
23.3 SEQUENTIAL GAMES
In this section, we analyze sequential games, where players take turns making
moves. These games introduce some new complications, as illustrated by the fol-
lowing entry game. Drugco sells Leau?eau, the market-leading drug for hyper-
tension. This drug is about to lose patent protection for its key ingredient. Generico,
a maker of generic drugs, is considering entry into the hypertension market with the
chemical equivalent of Leau?eau. Under law, if Generico is the ?rst company to
gain approval for a generic version of Leau?eau, then they will be allowed six
months as the only generic competitor. After this six months is over, other
EXHIBIT 23-12
STANDARDS GAME, NORMAL FORM
Movieco
Revolution Evolution
Revolution $10B, $2B,
$4B $2B
Gameco
Evolution $2B, $4B,
$2B $10B
23.3 SEQUENTIAL GAMES 433
companies can enter the market with their own versions. As soon as generic com-
petition intensi?es, the pro?ts for both the incumbent (Drugco) and the ?rst generic
(Generico) would fall signi?cantly. Drugco would like to postpone this date for as
long as possible by “scaring” Generico out of the market. As Generico plans to
introduce their drug, Drugco ?les expensive lawsuits claiming infringement of
patents related to the manufacturing of Leau?eau and prepares to drop the price
of Leau?eau to keep consumers from switching to the generic form during Gen-
erico’s six-month exclusivity period. If Drugco succeeds in scaring Generico away
from entry, then Drugco will increase their NPV by $1B, and Generico will have an
NPV of 0. If Generico enters the market and Drugco chooses to ?ght with these
measures, then both companies will lose $100M. If Generico enters and Drugco
decides not to ?ght, then both companies will make $100M. Exhibit 23-13 gives the
extensive form for this game. Exhibit 23-14 gives the normal form, with best
responses circled.
Exhibit 23-14 shows two NE: (don’t enter, ?ght) and (enter, don’t ?ght). In
the ?rst equilibrium, Generico expects Drugco to ?ght, so it chooses not to enter. If
this were a simultaneous game, then there would be nothing troubling about this
equilibrium. In a sequential game, something might make us uneasy: the Drugco
strategy to ?ght is not a credible threat. It is not a credible threat because if Gen-
erico chooses to enter, then Drugco’s best response would be don’t ?ght. The only
reason that (don’t enter, ?ght) is a NE is that the decision to ?ght is irrelevant if
Generico does not enter. Thus, technically speaking, anything played by Drugco
EXHIBIT 23-13
ENTRY GAME, EXTENSIVE FORM
1
Generico
2
Drugco
Enter
Don't enter
Fight
Don't fight
(–$100M,
–$100M)
($100M,
$100M)
($0, $1000M)
434 CHAPTER 23 GAME THEORY
can be a “best response” to don’t enter. In response to this counterintuitive equi-
librium, game theorists devised a re?nement of NE based on the concept of sub-
games. A subgame is any part of a game that can be cleanly separated from the rest
of the game and analyzed on its own. Graphically, we can identify subgames by
looking at the extensive form. If there are any decision nodes in the tree that do not
have closed curves around them, then we can “snip” the tree at those nodes and
analyze these snipped nodes as part of a subgame. For example, we can snip the
extensive form in Exhibit 23-13 at Node 2, leaving us a subgame with only one
player (Drugco) and that player’s decision to ?ght or don’t ?ght. In simultaneous
games like Examples 21.1 through 21.4, there is no way to snip a decision node off
the tree—after the ?rst node, all other decision nodes had closed curves around them.
Those simultaneous games had no subgames, so no further analysis can be done.
If we do have subgames, then we solve for the NE of each subgame, using
backward induction to solve each subgame in reverse order. The simplest way to do
this for the entry game is by circling best responses in the extensive form. Exhibit
23-15 illustrates this solution method. The subgame following Node 2 has only one
player, so the NE of that subgame is just the optimal move for Drugco, which is
don’t ?ght. If we then back through the tree, Generico should play enter if it expects
that Drugco would play don’t ?ght. We have now solved for the unique subgame-
perfect Nash equilibrium (SPNE) as (enter, don’t ?ght). Thus, for sequential
games, the method of circling best responses in the normal form is no longer
suf?cient. We need to use information about the timing of decisions, and this
information is only available in the extensive form.
Like NE, the SPNE is a normative concept, not a positive prediction. Just
because (enter, don’t ?ght) is the only SPNE does not mean that, in practice,
Drugco won’t be able to scare Generico away from entering. Often, however, we
can model the methods that Drugco can use to succeed in keeping Generico out of
the market. Example 23.5 demonstrates one of these methods, where Drugco uses a
commitment mechanism to make the ?ght threat more credible.
EXHIBIT 23-14
ENTRY GAME, NORMAL FORM
Drugco
Fight Don’t
Fight
Enter $-100M, $100M,
$-100M $100M
Generico
Don’t $0M, $0M,
Enter $1000M $1000M
23.3 SEQUENTIAL GAMES 435
EXAMPLE 23.5
Consider the game shown earlier in Exhibit 23-13. Now, we add an additional move to this
game. Before Generico decides whether to enter (Node 1 in Exhibit 23-13), Drugco can
commit to a ?ght. Drugco makes this commitment by placing $500M in an escrow account
with a specialized “commitment agent”. The terms of this escrow state that if Drugco fails to
?ght, then the $500M will be forfeited to the commitment agent. In all other respects, the
payoffs are the same as in Exhibit 23-13.
Problem Draw the extensive form for this game, identify the subgames, circle the best
responses in each subgame, and solve for the SPNE.
Solution Exhibit 23-16 gives the extensive form for this entry game, with best responses
circled. This game has four subgames. We can snip the tree at Nodes 4 and 5, leaving only
Drugco’s ?ght decision. We can also snip the tree at Nodes 2 and 3, leaving Generico’s
entry decision, to be followed by Drugco’s ?ght decision. (The subgame that follows Node 3
is identical to the full game tree in Exhibit 23-13.) To ?nd the SPNE, we must make sure to
have only NE in each subgame, with the full tree solved by backward induction. We begin
with the bottom half of the tree. At Node 5, Drugco would choose don’t ?ght. If Generico
expects Drugco to play don’t ?ght, then at Node 3, it would choose to enter. Thus, the
SPNE payoffs from the bottom half of the tree are ($100M, $100M), just as we found in
Exhibit 23-13.
EXHIBIT 23-15
ENTRY GAME, EXTENSIVE FORM, WITH SUBGAME PERFECT
STRATEGIES CIRCLED
1
Generico
2
Drugco
Enter
Don't enter
Fight
Don't fight
(–$100M,
–$100M)
($100M,
$100M)
($0, $1,000M)
436 CHAPTER 23 GAME THEORY
In the top half of the tree, we have a different situation. Because Drugco has played
commit, the don’t ?ght strategy at Node 4 would result in a loss of $500M relative to the
don’t ?ght strategy at Node 5. The overall payoff of don’t ?ght then becomes negative
$400M, which is inferior to the ?ght payoff of negative $100M. Thus, at Node 4, Drugco
should ?ght. If Generico expects Drugco to ?ght at Node 4, then it should choose don’t enter
at Node 2. Thus, the SPNE payoffs from the top half of the tree are ($0, $1000M).
To ?nish the solution, we compare Drugco’s payoffs from choosing to commit—the
top half of the tree—which are equal to $1000M, with Drugco’s payoff from playing don’t
commit—the bottom half of the tree—which are equal to $100M. Because the former is
higher than the latter, Drugco’s optimal strategy at Node 1 is to commit. Thus, the unique
SPNE, which must specify at strategy at every node (including nodes that are not reached in
equilibrium!), is (1 5commit, 2 5don’t enter, 3 5enter, 4 5?ght, 5 5don’t ?ght), with
SPNE payoffs of ($0, $1000). ’
The main theme of this example will seem familiar to armchair strategists
everywhere: sometimes you can improve your bargaining position by restricting your
future options. For example, leaders sometimes make public pronouncements—
which are costly to repudiate—committing their organization to some (possibly
unpopular) strategy. Such pronouncements can be effective ways to sti?e internal
dissent because subordinates realize that the leader will “?ght” any attempt to change
the strategy.
EXHIBIT 23-16
ENTRY GAME, WITH COMMITMENT EXTENSIVE FORM
1
2
Generico
Generico
Drugco
4
3
5
Drugco
Drugco
Don't enter
Don't fight
Commit
to fight
Don't
commit
Don't enter
Don't fight
Enter
Fight
Enter
Fight
($0, $1000M)
(–$100M,
–$100M)
($100M,
–$400M)
(–$100M,
–$100M)
($100M,
$100M)
($0,
$1000M)
23.3 SEQUENTIAL GAMES 437
In Example 23-5, Drugco’s commitment device allows it to make a credible
threat of ?ghting the entry of Generico. The game does not have to stop here. Some
clever executive at Generico could approach the “commitment agent” and say,
“Drugco has promised you $500M if we enter and Drugco does not ?ght. As long as
you hold this contract in your hand, we will not enter, and the contract is worthless
to you. Thus, why don’t you just rip up the contract, and we will give you $1?”
If we add this strategy to the game, the new SPNE has the contract ripped up,
and Generico enters. This kind of game can go back and forth, as each player
tries to think of ever more powerful ways to alter the game. Alas, some lawyers
we know insist that most of these fanciful contracts would be unenforceable. Spoil
sports.
Drugco can also rely on “reputation” to make their threat credible. Speaking
loosely, the reputation argument goes like this: “Here at Drugco, we always ?ght
whenever anyone enters our markets. We have done this for decades, and we are
not about to stop know. We realize that it costs us money to ?ght, but in the long
run it saves us even more, because potential competitors are scared away by our
fearsome reputation.” To make this reputation argument more formally, we need to
model an extensive form and see if it works.
As it turns out, reputation stories do not work in ?nite games. If you can
actually write down the terminal nodes of the game, then you will be able to solve
the game backward and SPNE arguments will keep the threats from being
credible. To see this, imagine that the entry game from Exhibit 23-13 is repeated
100 times, always between the same two players. One might think that this would
be a long enough time to gain a reputation, but if we divide the game into sub-
games, we will ?nd that in the 100th playing it is not optimal for Drugco to ?ght,
so thus it is not optimal to ?ght in the 99th playing, the 98th playing, and so on. In
contrast, for an in?nite game, under a wide variety of conditions it will be
possible for Drugco to establish a reputation, and virtually any outcome can
be claimed as part of an equilibrium. Because corporations are, in theory, in?-
nitely lived institutions, reputation effects are supported by game theory and lead
to generally indetermi- nate equilibrium predictions. This paradoxical contrast
between ?nite and in?nite games has been recognized since almost the dawn of
game theory, and the proof that in?nite games can support virtually any equilibria
is so well known that its creator has passed into oblivion, with the proof known
simply as the folk theorem.
23.4 GAME THEORYAND REAL OPTIONS
In Chapter 21, we demonstrated several examples of real options, where ?rms could
pro?tably delay making investment decisions until more information was known.
An important critique of the real-options approach is that it can be misleading when
a ?rm faces competition. The idea of “waiting to invest” can be strategic suicide if a
438 CHAPTER 23 GAME THEORY
competitor can just come along and steal your market. In Example 23-6, we provide
an illustration of this critique.
EXAMPLE 23.6
Fuelco is considering a consumer application for their patented fuel-cell technology. (This
corresponds to Project C from Chapter 19.) They have already completed several R&D
projects with this technology, so they have eliminated the technical risk for this new project.
To begin producing and marketing to the consumer market would require a new investment
of $200M, to be paid in one year. The value of Project C depends on consumer demand and
also depends on whether a competitor, Cellco, also enters this market. To keep things
(relatively) simple, we assume that the beta for the project is zero and that the risk-free rate is
also zero, so all discount rates are zero for the both ?rms.
At time 0, Cellco and Fuelco each decide whether to invest or wait. If one ?rm invests
and the other waits, then the investing ?rm will get the whole market and have an NPV of
$300M, whereas the waiting ?rm will have an NPV of $0. If both ?rms invest, then com-
petition will drive down the pro?ts of both ?rms, which will each have an NPV of $50M. (All
NPVs described in this problem are net of the $200M investment, when the investment is
made. Thus, the gross NPV if both ?rms invest would be $250M.) If both ?rms wait, then
they both get to observe whether demand is “high” or “low”, after which each ?rm decides
whether or not to invest. If demand is “high” (50 percent chance) and only one ?rm chooses
to invest, then that ?rm receives an NPV of $700M, and the other ?rm receives an NPV of
$0. If neither ?rm invests, then both ?rms receive an NPV of $0. If both ?rms invest, then
each ?rm receives an NPV of $200M. If demand is “low” (50 percent chance), and only one
?rm chooses to invest, then that ?rm receives a negative NPV of 2$100M, and the other ?rm
receives an NPV of $0. If neither ?rm invests, then both ?rms receive an NPV of $0. If both
?rms invest, then each ?rm receives a negative NPV of 2$100M.
Problems
(a) Draw the extensive form for this game.
(b) Identify all the subgames.
(c) Solve for the unique SPNE.
Solutions
(a) The extensive form is given in Exhibit 23-17.
(b) To identify the subgames, we look for places where we can “snip” the tree at a decision
node without cutting any closed curves. This procedure yields subgames beginning with
Nodes 8 or 9.
(c) Unlike the entry game in Example 23.5, the subgames for this game include decision
nodes for both players. Thus, to ?nd SPNE for the whole game, we need to consider the NE
of the subgames, not just optimal play for one player in isolation.
We can solve the tree backward by solving for the NE of each subgame. Because each
subgame represents a two-by-two simultaneous game, we can ?nd these NE by circling the
best responses in the normal form. We do this ?rst for the subgame that begins with Node 8.
23.4 GAME THEORY AND REAL OPTIONS 439
The unique NE of this subgame is (Invest, Invest), with payoffs of ($200M, $200M).
We next consider the subgame that begins with Node 9, as shown in Exhibit 23-19. The
unique NE of this subgame is (Don’t Invest, Don’t Invest), with payoffs of (0,0).
EXHIBIT 23-17
FUELCO’S PROJECT C, WITH COMPETITION
1
Fuelco
Cellco
2
3
invest
invest
invest
invest
invest
invest
invest
invest
wait
wait
invest
wait
8
Fuelco
Fuelco
Cellco
Cellco
10
11
9
12
13
4
(50, 50)
5
(300, 0)
6
(0,300)
strong
market
weak
market
7
50%
50%
don't
don't
don't
don't
don't
don't
(200, 200)
(700, 0)
(–100, –100)
(–100, 0)
(0, 700)
(0, 0)
(0, –100)
(0, 0)
EXHIBIT 23-18
PROJECT C, STEP 2, STRONG MARKET, NORMAL FORM
Cellco
Invest Don’t
Invest
Invest $200M, $700 M,
$200M $0M
Fuelco
Don’t $0M, $0M,
Invest $700M $0M
440 CHAPTER 23 GAME THEORY
With NE solutions for the two subgames, we can prune the extensive form, replacing
the decision nodes at 8 and 9 with their respective NE payoffs. With payoffs of ($200M,
$200M) in a strong market and (0,0) in a weak market, Node 7 would have a 50-50 chance of
these two outcomes, for an expected payoff of ($100M, $100M). We then redraw the
extensive form in Exhibit 23-20.
EXHIBIT 23-19
PROJECT C, STEP 2, WEAK MARKET, NORMAL FORM
Cellco
Invest Don’t
Invest
Invest ?$100M, ?$100M,
?$100M $0M
Fuelco
Don’t $0M, $0M,
Invest ?$100M $0M
EXHIBIT 23-20
FUELCO’S PROJECT C, WITH COMPETITION, PRUNED
1
Fuelco
2
3
Cellco
invest
invest
wait
invest
wait
wait
4
(50, 50)
5
(300, 0)
6
(0, 300)
7
(100, 100)
23.4 GAME THEORY AND REAL OPTIONS 441
This pruned version of the extensive form is a one-step simultaneous game with no
subgames. We can solve for the NE of this game by circling the best responses in their
normal form.
The unique NE of this game is (invest, invest), yielding payoffs of ($50M, $50M).
After doing all this work, we can see the prisoner’s dilemma arms race once again rear its
EXHIBIT 23-21
PROJECT C, STEP 1, NORMAL FORM
Cellco
Invest Wait
Invest $50M, $300M,
$50M $0M
Fuelco
Wait $0M, $100M,
$300M $100M
EXHIBIT 23-22
FUELCO’S PROJECT C, WITH COMPETITION, BEST RESPONSES
CIRCLED
1
Fuelco
Cellco
2
3
invest
invest
invest
invest
wait
wait
wait
8
Fuelco
Fuelco
Cellco
Cellco
10
11
9
12
13
4
(50, 50)
5
(300, 0)
6
(0, 300)
strong
market
weak
market
7
50%
50%
don't
don't
don't
(200, 200)
(700, 0)
(–100, –100)
(–100, 0)
(0, 700)
(0, 0)
(0, –100)
(0, 0)
invest
invest
invest
invest
invest
don't
don't
don't
442 CHAPTER 23 GAME THEORY
ugly head: both Fuelco and Cellco would prefer a combined switch to the (wait, wait)
outcome, but this outcome is not a NE because each company would have an incentive to
change its strategy and invest.
Now that we have solved for the NE of all the subgames, we can rewrite the extensive
form for the whole game, with all best responses circled. Exhibit 23-22 shows this solution.
The unique SPNE of the game is (Node 1 5invest, Nodes 2/3 5invest, Node 8 5invest,
Node 9 5don’t invest, Nodes 10/11 5invest, Nodes 12/13 5don’t invest), with an SPNE
payoff of ($50M, $50M). Note that Cellco’s strategies must be the same at nodes 2&3,
10&11, and 12&13 because Cellco is unable to distinguish its exact location at any of these
node pairs.
’
SUMMARY
Game theory is the study of multiplayer decision problems. In this chapter, we learned the
basic tools of game theory, and we applied these tools to the analysis of several prototypical
R&D investment scenarios. We ?rst studied three different types of simultaneous games,
where players make their moves at the same time. The ?rst game we analyzed, an advertising
arms race between two companies, is reminiscent of the classic prisoner’s dilemma: both
companies would like to spend fewer resources on advertising, but competition leads to high
advertising by both. We next analyzed a game between a technology leader and follower. In
this game, the leader would like to maintain the status quo where everyone includes similar
technology features in their products, whereas the follower would like to introduce more
differentiation. In equilibrium, each side tries to keep the other guessing as to its strategy. A
third example was the coordination game, which can occur in battles to set technological
standards. Unlike the arms-race and leader-follower games, standards battles do not have
unique game-theoretic predictions, with many possible standards leading to many possible
equilibrium outcomes.
In the second part of the chapter, we turned our attention to sequential games, in which
players take turns making their moves. We ?rst analyzed a game of market entry, where an
incumbent drug company sought to keep a generic ?rm from marketing a competing product.
These games can allow for rich strategy by all players, with incumbents trying to scare
potential rivals away by making credible threats of litigation and price wars, and potential
entrants working to defuse these threats. Game-theoretic reasoning can also provide fresh
insights into standard real-option investment problems. In our ?nal example of the chapter,
we showed how competition can destroy the option value of waiting and give rise to yet
another prisoner’s dilemma situation.
KEY TERMS
Prisoner’s dilemma
Normal form
Strategies, strategy pair
Payoffs
Game tree
5extensive form
Simultaneous game,
sequential game
Zero-sum games, constant
sum games
Equilibrium concepts
Nash equilibrium (NE)
KEY TERMS 443
Equilibrium strategy
Best response
Dominant strategy
Arms race
Pure strategy, mixed
strategy
Pure-strategy NE, mixed-
strategy NE
Two-by-two games
Minimax solution
Leader-follower games
Positive analysis, normative
analysis
Coordination games
Subgames
Subgame-perfect Nash
equilibrium (SPNE)
Finite games, infinite games
Folk theorem
EXERCISES
23.1 Solve for the mixed-strategy NE in Example 23.4. Does this equilibrium seem like a
realistic outcome for the game? Do you see any conceptual difference between this mixed-
strategy NE and the mixed-strategy NE in the leader-follower game?
23.2 Suppose that the advertising arms race in Example 23.2 is repeated a second time by the
same two ?rms.
(a) Draw an extensive form for the two-period game, showing all strategies for both ?rms
in both periods.
(b) Solve for all the pure-strategy NE of the game.
(c) Solve for the unique SPNE of the game.
23.3 Consider the game modeled in Example 23.6. Now, suppose that the cost of investment
is $280M, instead of the $200M given in the original example. In this case, all the payoffs
after investment should be reduced by $80M as compared to Exhibit 23-17. In this new
game, solve for all the SPNE of the game and compare the payoffs among these SPNE.
23.4 In an enclosed space stand 57 lions and one sheep. The lions, all perfectly rational and
well trained in game theory, would all like to eat the sheep. For simplicity, we imagine that
the lions are numbered from 1 to 57, and sequentially decide whether they would like to eat.
(If the sheep is still alive after lion #57 makes his decision, then lion #1 gets to decide again,
and the process goes around and around forever.) If any lion begins to eat the sheep, then the
other lions will respect his property rights and allow him to ?nish by himself. The sheep is
powerless to stop this. If a lion eats the sheep, then he will fall asleep for one hour, during
which time he becomes defenseless and can be eaten by any other lion. (While awake, a lion
cannot be eaten by another lion.) The best outcome for a lion would be to eat the sheep, fall
asleep, and not be eaten himself. The second best outcome for a lion would be to go hungry.
The worst outcome would be to eat, fall asleep, and be eaten. So, in the unique SPNE of this
game, what happens to the sheep? (Hint: The answer would be different if there were only
56 lions.)
444 CHAPTER 23 GAME THEORY
CHAPTER 24
R&D VALUATION
IN THIS CHAPTER, we pull together everything we have learned in Part IV
and analyze complex examples for Drugco and Fuelco. In the Drugco example in
Section 24.1, we draw on game theory, real options, and Monte Carlo simulation to
evaluate two possible structures for a drug-development strategic alliance. In the
Fuelco example in Section 24.2, we combine the three projects studied in previous
chapters into one metaproject. The resulting analysis combines several linked real
options, including one that requires a binomial tree. Finally, in Section 24.3 we
review some of the key lessons from Part IV and urge readers to see both the forest
and the (decision) trees.
24.1 DRUG DEVELOPMENT
This example uses a similar valuation model as in Examples 20.4 and 21.4, except
that here we allow uncertainty for ef?cacy, alternative ef?cacy, and market size to
be resolved during both Phase II and Phase III.
EXAMPLE 24.1
Drugco is about to begin Phase II trials for Newdrug, at a cost of $50M. If the drug continues
to Phase III trials, then these trials would cost an additional $100M. Drugco is ?nancially
constrained, so it is looking for a partner to help fund the project. Bigco, a potential partner,
has proposed two possible deal structures.
Deal 1 is a standard-looking alliance deal, where Bigco pays an up-front fee of $200M
to acquire all rights to the compound and then pays all the development costs, makes a
milestone payment of $150M on entering Phase III, and makes royalty payments of 5 percent
on sales.
Deal 2 would reduce the up-front payment to $100M, require Drugco to bear 20
percent of the development costs in Phase III, and replace the Phase III milestone with a
larger $300M milestone if Bigco decides to market the product after FDA approval. Deal 2
would have a higher royalty percentage than Deal 1 (10 percent versus 5 percent) and would
give Drugco more control over the project, by allowing it to decide whether the project
advances from Phase II to Phase III. In both deals, if Bigco decides not to market the product,
445
then all rights revert back to Drugco. If Bigco does decide to market the product, then it will
incur marketing costs of $300M in the ?rst year, with these costs increasing annually in
proportion to the 6 percent growth in the size of the market.
Both ?rms expect Phase II trials to take one year, Phase III trials to take two years, and
the FDA approval decision to take one year, so that the FDA decision is expected in four
years total. Based on preclinical testing, both ?rms expect Phase II trial results, E
t
, to be
distributed as N (40, 40). The best alternative drug currently has an ef?cacy of 40, but has
several possible improvements in the works, so its expected ef?cacy after one year (after the
Phase II trials of Newdrug) is A
t
B T (40, 70, 40). Given the side effects of Newdrug and
the risks and bene?ts of alternative treatments, Drugco believes that the FDA will approve
Newdrug if the Phase III trials ?nd an ef?cacy of 30 or greater. Based on the results of the
Phase II trials, Drugco estimates that the ef?cacy results of Phase III will be E BN (E
t
, 20).
During the three years of Phase III trials and FDA decision making, the alternative may
improve again, with a distribution of A BT (A
t
, A
t
+ 50, A
t
). If Newdrug is approved by the
FDA, then its market share will depend on the relative ef?cacy of Newdrug versus the best
available treatment, that is,
Newdrug market share ¼ E
2
=ðE
2
þA
2
Þ: ð24:1Þ
Drugco estimates that the eventual market size of Newdrug in the approval year (in
millions of doses) will be 1,000, but there is considerable uncertainty around this estimate.
Some of this uncertainty will be resolved in the next year (during Phase II trials), with M
t
B
N (1,000, 50), and more uncertainty will be resolved over the following three years, with M
BN (M
t
, 100). Each dose will sell for $1.00, with a production cost of $0.25. On approval,
Newdrug would have 10 years of patent life remaining. After the patent expiration, Drugco
expects generic competition and other improved alternatives to greatly erode the value of
Newdrug, so for simplicity we assume that the continuing value would be zero after the
patent expires. Following earlier examples for Newdrug, we assume a discount rate equal to
the riskfree rate of 5 percent.
Problems
(a) Draw the game tree for this problem, beginning with Drugco’s decision of whether to
take Deal 1 or Deal 2.
(b) Suppose that Drugco decides to take Deal 1. What is the optimal strategy for Bigco
following the Phase III trials? What is the optimal strategy for Bigco following the Phase II
trials? Assuming that Bigco chooses these strategies, what are the expected payoffs to
Drugco and Bigco for Deal 1?
(c) Suppose that Drugco decides to take Deal 2. What is the optimal strategy for Bigco
following the Phase III trials? Given this strategy for Bigco, what is the optimal strategy for
Drugco following the Phase II trials? Assuming that Bigco and Drugco choose these stra-
tegies, what are the expected payoffs to Drugco and Bigco for Deal 2?
(d) What is the unique SPNEof this game? What are the expected payoffs for the equilibrium?
Solutions
(a) We draw the game tree in three pieces. First, Exhibit 24-1 shows the high-level structure
for the tree. The node numbers in this tree correspond to node numbers in the detailed trees
that follow for Deal 1 (Exhibit 24-2) and Deal 2 (Exhibit 24-3).
446 CHAPTER 24 R&D VALUATION
EXHIBIT 24-1
SCHEMATIC FOR THE FULL EXTENSIVE FORM
Take
Deal 1
Take
Deal 2
2
12
1
5
15 19
Drugco
Drugco Bigco
Bigco Bigco
B1(E,M,A),
D1(E,M,A)
0, 0
0, 0
B2(E,M,A),
D2(E,M,A)
(0, –50)
(0, –50)
(100, –100)
(200, –200)
Phase II Phase III
9
. . . . . .
. . . . . .
EXHIBIT 24-2
EXTENSIVE FORM FOR DEAL 1
3 2
A' ~ T(40, 70, 40)
A ~ T(A',A' + 50, A')
M' ~ N(1,000, 50) E' ~ N(40, 40)
E ~ N(E', 20)
same
as 3
same
as 3
same
as 4
same
as 4
Phase II Phase III
same
as 5
5
same
as 5
same
as 9
9
Bigco
4
same
as 8
same
as 8
8
same
as 7
same
as 7
7 6
E ? 30
(0, 0)
(0, 0)
(0, 0)
M ~ N(M', 100)
Bigco
(150, ?250)
abandon
1 year
3 years
don't
market
B1 (E,M,A),
D1 (E,M,A)
24.1 DRUG DEVELOPMENT 447
Before attempting a solution, we note a few important elements of these game trees.
First, in Exhibit 24-1, we see the up-front fees for the two deals yielding payoffs of (200,
2200) in Deal 1 and (100, 2100) in Deal 2. (Drugco’s payoff is always listed ?rst.) Fur-
thermore, because Bigco pays the $50M cost of Phase II in both structures, there is a payoff
of (0, 250) at nodes 2 and 12. In Exhibit 24-2, with the extensive form for Deal 1, the Phase
III continuation decision belongs to Bigco (Node 5). If Bigco decides to continue, then it
pays $100M in costs plus a $150M milestone, yielding aggregate payoffs of (150, 2250). In
the analogue position of Exhibit 24-3, Drugco makes the Phase III continuation decision
(node 15), no milestones are paid, and Drugco incurs $20M of the $100M cost, for aggregate
payoffs of (220, 280). Finally, the marketing decision is always made by Bigco. In Exhibit
24-2, there is no milestone. In Exhibit 24-3, if Bigco decides to market, then it must pay
Drugco a milestone of $300M, leading to aggregate payoffs of (300, 2300).
(b) As is our usual practice, we solve the tree backward. Starting with the terminal nodes
and moving back in time, we arrive at Bigco’s decision about whether or not to market the
product (node 9). In Example 21.4, we solved a very similar problem. All the market
inputs were the same—the only difference is that here, Bigco would have to pay royalties on
5 percent of the gross sales. Exhibit 24-4 gives the full valuation model for Bigco’s decision,
EXHIBIT 24-3
EXTENSIVE FORM FOR DEAL 2
13 12
A' ~ T(40, 70, 40)
A ~ T(A',A' ? 50, A')
M' ~ N(1,000, 50) E' ~ N(40, 40)
E ~ N(E', 20)
same
as 13
same
as 13
same
as 14
same
as 14
Phase II Phase III
same
as 15
15
same
as 15
same
as 19
19
Bigco
14
same
as 18
same
as 18
18
same
as 17
same
as 17
17 16
E ? 30
(0, 0)
(0, 0)
(0, 0)
M ~ N(M', 100)
Drugco
(–20, –80)
abandon
1 year
3 years
don't
(300–300)
market
B2 (E,M,A),
D2 (E,M,A)
448 CHAPTER 24 R&D VALUATION
EXHIBIT 24-4
DCF MODEL, DEAL 1
1 A B C D E F G H I J K L
2 Mean St dev Min Mode Max
3 Efficacy (E
t
) 40 40 40
4 Alternative efficacy (A
t
) 50 40 40 70
5 Starting market size (M
t
) 1,000 1,000 50
6
7 Efficacy (E) 40 40 20
8 Alternative efficacy (A) 67 50 50 100
9 Starting market size (M) 1,000 1,000 100
10 Phase III milestone 150
11 Continuation Threshold 30.1
12 Phase III? 1.0 Bigco NPV (if enter) $388.5
13 Approval threshold 30 Drugco NPV $207.0
14 Price per unit $1.00 Bigco NPV (option) $388.5
15 Royalty rate 5.00%
16 Cost per unit $0.25
17 Market share 26.5% Total Bigco NPV 2$136.1
18 Market growth 6.0% Total Drugco NPV $508.4
19 Discount rate 5.00%
20 Approved? 1
21 Salvage value 42.86
22 $ in millions
23 Year 5 6 7 8 9 10 11 12 13 14
24
25 Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
26 Market share 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5% 26.5%
27 Revenue $264.7 $280.6 $297.4 $315.3 $334.2 $354.2 $375.5 $398.0 $421.9 $447.2
28 Royalty $13.2 $14.0 $14.9 $15.8 $16.7 $17.7 $18.8 $19.9 $21.1 $22.4
29 CGS $66.2 $70.1 $74.4 $78.8 $83.5 $88.6 $93.9 $99.5 $105.5 $111.8
30 Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
31 Bigco profit 2$48.5 2$51.4 2$54.5 2$57.8 2$61.3 2$64.9 2$68.8 2$73.0 2$77.3 2$82.0
32 Drugco profit $13.2 $14.0 $14.9 $15.8 $16.7 $17.7 $18.8 $19.9 $21.1 $22.4
4
4
9
with inputs set to their mean values. The market decision at Node 9 is made with a “Max”
function in cell G14. This function takes the maximum of the NPV of marketing the drug
(cell G12) with the NPV of abandoning the drug (0).
To better understand this worksheet, let’s discuss the special case shown in the
exhibit, with all variables set to their mean values. In Phase II, the mean values are E
t
540, A
t
5(40 170 140)/3 550, and M
t
51,000. In the following solution, we will
demonstrate that the optimal policy for Bigco—with these Phase II outputs for A
t
and
M
t
—is to continue if E
t
.30.1. (Don’t worry about the reason for this number right now.
It is just a coincidence that this cutoff is so close to the FDA threshold of 30.) Because our
example estimate for E
t
is 40, the project continues to Phase III, where the mean outputs
are E540, A5 (50 1100 150)/3 566.7, and M51,000. Because the FDA threshold is
30, Newdrug is approved. Cell G12 tells us that Bigco gets a positive NPV if they decide
to market the drug. Nevertheless, standing at time 0, Bigco would be disappointed with
this outcome because the costs ($200M up-front, $50M for Phase II, $100M for Phase III,
and $150 as a milestone) are higher than the NPV of pro?ts. The “max” function in cell
G14 only tells us that once Bigco had sunk the $500M total into developing the drug, it is
optimal for them to market the drug; overall, they will still wish they had never signed the
contract in the ?rst place. Of course, this is just one special case. To determine if the
overall deal is good for Bigco, we will need to complete our solution and simulate many
different cases.
With an optimal strategy given by the maximum function in Cell G14, we can continue
our backward journey through the tree to arrive at Node 5, the Phase III continuation decision
made by Bigco. In principle, this decision is also made with a “Max” function: Bigco wants
to take the maximum of either (1) NPV of continuing to Phase III, or (2) abandoning the
project. In practice, this maximum computation is much more dif?cult than the analogue at
Node 9. At Node 9, there was no more uncertainty left to be resolved: Bigco already knew
the market size, the ef?cacy for Newdrug, and the ef?cacy of its alternative. Thus, the NPV
of marketing the drug could be computed exactly. At Node 5, there is still uncertainty about
market size, ef?cacy, and alternative ef?cacy. In this case, we cannot simply compute an
NPV, but rather must run simulations to estimate it. Bigco wants to answer the following
question: “Given the Phase II outcomes E
t
, A
t
, M
t
, what is the expected NPV of the project?”
Then, Bigco’s optimal strategy is to continue to Phase III if and only if this expected NPV is
greater than the abandonment value of 0.
There are many ways that a clever analyst could approach this problem. (Indeed, some
software packages will automate the process so that the analyst need not be clever at all.) We
will not attempt to ?nd an ef?cient path to a solution; instead, we break the problem down
into steps to illustrate the general intuition behind the solution. We begin by assuming (for
the moment), that the Phase II outputs for A
t
and M
t
are set to their mean values of 50 and
1,000, respectively. Next, we run simulations for the NPV of the project using various inputs
of E
t
. The results are graphed in Exhibit 24-5. We also graph the NPV50 line. The
intersection of the NPV50 line and the Bigco NPV line occurs when E
t
is equal to 30.14.
This intersection means that, if A
t
550 and M
t
51,000, Bigco will have a positive
expected value only if E
t
.30.14. Thus, if E
t
,30.14, Bigco should abandon the project,
and if E
t
.30.14, they should continue.
Next, we allow the value of A
t
to vary, while still holding M
t
?xed at 1,000. For each
value of A
t
, we run simulations to ?nd the value of E
t
such that the NPV of the project is
equal to zero. Because A
t
is T (40, 70, 40), the range of possible values is limited.
We perform the analysis for every A
t
in the set (40, 45, 50, 55, 60, 65, 70). In each case, we
450 CHAPTER 24 R&D VALUATION
?nd the corresponding E
t
that makes the expected NPV equal to zero. We call this a “zero-
pro?t point”. We ?t a zero-pro?t curve through these points in Exhibit 24-6. (This curve is
nearly a straight line.) Notice that the point (50, 30.14) in the exhibit corresponds to the
intersection shown in Exhibit 24-5.
We are slowly clawing our way toward a solution. At this point, if we knew that M
t
were
equal to 1,000, then we would make the continuation decision by looking at Exhibit 24-6 and
seeing if the pair (A
t
, E
t
) was above or below the zero-pro?t curve. To ?nish the solution, we
need to compute a different curve for each level of M
t
. Although this might sound like a lot of
work, by making a few smart guesses we can use interpolation to build these curves. Exhibit
24-7 shows zero-pro?t curves for a range of values for M
t
.
From these curves, we use interpolation to build curves for intermediate levels of M
t
.
Analysts who want more precise results can estimate more curves and rely less on inter-
polation. In either case, we ?nish the solution by building a lookup table
1
in Excel, where the
entries in the table are taken from the y-axis (E
t
) in Exhibit 24-7, and the rows and columns
of the table are given by the values of A
t
and M
t
. Then, for any given Phase II output (A
t
, M
t
),
we instruct Excel to ?nd the closest match from the table to ?nd the corresponding E
t
to use
as a Phase III continuation threshold. Graphically, the lookup table is equivalent to using
Exhibit 24-7 to identify the correct line (M
t
) and the correct x -coordinate (A
t
), and then
?nding the corresponding y-coordinate (E
t
). Then, if the actual phase II output E
t
is higher
than this point, Bigco continues to Phase III. With this strategy de?ned, we can compute the
expected payoffs for Deal 1 by simulating the whole project from the very beginning
1
Readers unfamiliar with lookup tables should consult a reference on Microsoft Excel. One helpful
reference is Walkenbach (2003), Chapter 12.
EXHIBIT 24-5
BIGCO NPV AS OF PHASE III, AS A FUNCTION OF E
t
ASSUMES
A
t
5 50 AND M
t
5 1,000
1,200
1,000
800
600
400
200
–200
0
B
i
g
c
o
N
P
V
NPV ? 0
20 25 30 35 40
E'
45 50 55 60
24.1 DRUG DEVELOPMENT 451
(node 2). After 1M trials, we get an expected payoff of $400.0M for Bigco and $506.4M for
Drugco. Thus, even though Bigco has a negative NPV using expected values (Exhibit 24-4),
the simulation shows a positive NPV for Deal 1.
EXHIBIT 24-7
BIGCO ZERO-PROFIT CURVES, DEAL 1
M' ? 600
M' ? 700
M' ? 800
M' ? 900
M' ? 1,000
M' ? 1,100
M' ? 1,200
M' ? 1,300
M' ? 1,400
100
90
80
70
60
50
40
30
20
10
0
E'
40 45 50 55
A'
60 65 70
EXHIBIT 24-6
BIGCO ZERO-PROFIT CURVE, ASSUMING THAT M
t
5 1,000
50
40
30
20
10
0
E'
40 45 50 55
A'
60 65 70
452 CHAPTER 24 R&D VALUATION
(c) To evaluate Deal 2, we solve backward the extensive form in Exhibit 24-3. This
solution begins the same way as the solution for Deal 1, with an optimal strategy for Bigco
for the marketing of the project. This decision occurs at Node 19. As in the decision at Node
9 for Deal A, Bigco can make this decision by comparing the NPV of marketing the product
with the NPV of abandoning it. Because uncertainties about ef?cacy, alternative ef?cacy,
and market size have all been resolved, the decision can be made with a simple Max
statement.
Exhibit 24-8 shows the modi?ed spreadsheet model for Deal 2. As in Exhibit 24-4, we
display sample output with all variables set to their mean values. This example is illustrative,
because with these inputs Bigco makes a different decision under Deal 2 than it did under
Deal 1. The Max statement is given in cell G14, as a comparison of cell G12 and $0. Here,
with A567, E540, and M51,000, Bigco chooses to abandon the project. The main driver
of this difference is the need to pay a $300M milestone payment. (In Deal 1, all milestones
had already been paid by this point.) Thus, we can already see that the deal structure can have
an important in?uence on outcomes.
Once we input the max statement for Bigco’s marketing decision, we are ready to
evaluate Drugco’s optimal strategy for the Phase III continuation decision. To do this, we
follow the same steps as we did for Deal 1. Because we have seen these steps already, we will
jump directly to the zero-pro?t curves for Drugco, shown in Exhibit 24-9.
Note that these curves are much lower than the corresponding curves for Bigco in
Exhibit 24-7. The reason for this difference is that Drugco has little to lose by going to Phase
III because it only needs to pay $20M for the trials. Furthermore, FDA approval is pure
upside for Drugco because at the very least they can get salvage value for the drug, and they
may get much more. In contrast, in Deal 1, Bigco has to pay the full $100M for the trials and
also faces the possibility that the drug will be worthless to them even if it is approved. Taken
together, these differences lead Drugco to be far more aggressive in Deal 2 than Bigco is in
Deal 1. It is this power to be aggressive that makes “control” of the decision valuable to
Drugco.
With the Phase III continuation strategy de?ned, we can compute the expected payoffs
for Deal B by simulating the whole project from the very beginning (Node 2). In practice, we
do this using a lookup table in Crystal Ball, just as we did for Deal 1. After 1M trials, we get
an expected payoff of $496.2M for Bigco and $391.5M for Drugco.
(d) Using the results of parts (b) and (c), we are ready to solve for the SPNE of the game.
Because it is Drugco’s choice at Node 1 that determines the deal structure, we need to
compare Drugco’s payoffs under the two deals. Because Deal 1 gives Drugco an expected
payoff of $506.4M and Deal 2 gives Drugco an expected payoff of $391.5M, it should
choose Deal 1. This might be surprising to some readers because Deal 2 provides more
control and a seemingly higher upside from the 10 percent royalty. It is dangerous to rely too
much on your intuition when analyzing complex scenarios. In Deal 2, Drugco controls the
Phase III continuation decision and receives generous milestones and royalties. This back-
loading of bene?ts leads to Bigco being more conservative when deciding whether to market
the product—we can see an example of this conservatism by comparing Bigco’s marketing
decision in Exhibits 24-4 and 24-8. With this conservatism, Newdrug is in fact less likely to
make it to market and earn royalties and milestones for Drugco.
To describe the SPNE of the game, we must write down the strategy at every node,
regardless of whether that node is on the equilibrium path. This is dif?cult to do because the
Phase III continuation decision is quite complex. We will revert to shorthand, relying on Max
24.1 DRUG DEVELOPMENT 453
EXHIBIT 24-8
DCF MODEL—DEAL 2
1 A B C D E F G H I J K L
2 Mean St dev Min Mode Max
3 Efficacy (E
t
) 40 40 40
4 Alternative efficacy (A
t
) 50 40 40 70
5 Starting market size (M
t
) 1,000 1,000 50
6 Efficacy (E) 40 40 20
7 Alternative efficacy (A) 67 50 50 100
8 Starting market size (M) 1,000 1,000 100
9 Cost sharing 0
10 Approval milestone 300
11 Continuation threshold 6.0
12 Phase III? 1 Bigco NPV (if enter) 2 $68.1
13 Approval threshold 30 Drugco NPV $39.7
14 Price per unit $1.00 Bigco NPV (option) $0
15 Royalty rate 10.00%
16 Cost per unit $0.25
17 Market share 26.5% Total Bigco NPV 2$226.2
18 Market growth 6.0% Total Drugco NPV $126.21
19 Discount rate 5.00%
20 Approved? 1
21 Salvage value 32.39
22 $ in millions
23 Year 5 6 7 8 9 10 11 12 13 14
24
25 Market size 1,000 1,060 1,124 1,191 1,262 1,338 1,419 1,504 1,594 1,689
26 Market share 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5% 40.5%
27 Revenue $405.0 $429.3 $455.0 $482.3 $511.3 $542.0 $574.5 $608.9 $645.5 $684.2
28 Royalty $40.5 $42.9 $45.5 $48.2 $51.1 $54.2 $57.4 $60.9 $64.5 $68.4
29 CGS $101.2 $107.3 $113.8 $120.6 $127.8 $135.5 $143.6 $152.2 $161.4 $171.1
30 Marketing costs $300.0 $318.0 $337.1 $357.3 $378.7 $401.5 $425.6 $451.1 $478.2 $506.8
31 Bigco profit $64.5 $68.4 $72.5 $76.8 $81.4 $86.3 $91.5 $97.0 $102.8 $108.9
32 Drugco profit $40.5 $42.9 $45.5 $48.2 $51.1 $54.2 $57.4 $60.9 $64.5 $68.4
4
5
4
functions in Exhibits 24-4 and 24-8 and the zero-pro?t lines in Exhibits 24-7 and 27-9 to
simplify the description of the SPNE strategies:
Unique SPNE:
For Drugco:
At Node 1: choose Deal 1.
At Node 15: use Exhibit 24-9 to make the Phase III continuation decision.
For Bigco
At Node 5: use Exhibit 24-7 to make the Phase III continuation decision.
At Node 9: Use the Max function in cell G14 of Exhibit 24-4.
At Node 19: Use the Max function in Cell G14 of Exhibit 24-8.
Notice that the formal description of the SPNE strategies includes listings for Nodes 15
and 19, even though these nodes are never reached in equilibrium. These SPNE strategies
yield expected payoffs of $506M for Drugco and $400M for Bigco. ’
24.2 ENERGY
In the next example, we combine Fuelco’s Projects A, B, and C as originally modeled
in Examples 21.1, 21.2, and 22.2, respectively. (We make a slight alteration to the
EXHIBIT 24-9
DRUGCO ZERO-PROFIT CURVES, DEAL 2
M' ? 600
M' ? 700
M' ? 800
M' ? 900
M' ? 1,000
M' ? 1,100
M' ? 1,200
M' ? 1,300
M' ? 1,400
40 45 50 55
A'
60 65 70
40
35
25
5
–5
15
30
20
10
–10
0
E'
24.2 ENERGY 455
assumptions for Project C, but otherwise all the numbers are the same here as in the
original examples.) The main twist is that Fuelco must complete both Projects A and
B to have the option to complete Project C. This twist enriches and complicates the
modeling.
EXAMPLE 24.2
Fuelco is considering a development project using its patented fuel-cell technology (“Project
A”). If Fuelco pays $200M to develop the technology, then they can bid for a government
contract. The objective probability of winning the contract is 50 percent, and there is no beta
risk for the government’s decision. If Fuelco’s bid is accepted (one year later), then they can
choose to ?nish the project by accepting the contract (cost 5$300M), when they will earn an
NPV (as of one year from now) of $600M (not including the $300M cost of ?nishing the
project). If they do not receive the contract, then they can still ?nish the development project
(cost 5$300M) but they could only receive $200M for the project by selling it to some
nongovernmental buyer (not including the $300M cost of ?nishing the project). The riskfree
rate is zero. (By itself, this project is identical to the project analyzed in Example 21.1.)
In addition to Project A, Fuelco is also considering a separate investment in fuel-cell
technology designed to replace oil-based energy for some types of engines (“Project B”). By
investing $100M today to start the project, Fuelco would maintain the option to ?nish the
project with a further investment (5 $200M) in one year. If oil prices are at least $60 per
barrel in one year (objective probability 550%), then on completion of the project, Fuelco
would have an NPV (as of one year from now) of $1,000M (not including the $200M cost of
?nishing the project). If oil prices are less than $60 a barrel in one year (objective prob-
ability 550%), then the project would not be economical for most applications and would
have an NPV (one year from now) of $300M (not including the $200M cost of ?nishing the
project). If Fuelco decides not to ?nish the project, then they can sell the technology to a
competitor for $200M, regardless of the price of oil. The beta for the project is unknown, but
we do have some information about oil prices: the market price of a European binary call
option (payoff 5$1) on oil with a strike price of $60 per barrel and an expiration of 1 year is
25 cents. (By itself, this project is identical to the project analyzed in Example 21.2.)
Finally, Fuelco is also considering a consumer application for their patented fuel-cell
technology (“Project C”). Project C would only possible if Projects A and B have already
been completed. To begin producing and marketing to the consumer market would require a
new investment of $200M, made in one year (after A and B have been completed). At the
present time, Fuelco estimates that the completed project would have a present value of
$320M in one year (i.e., if Fuelco spent $200M to initiate the project, they believe they could
spin off the initiated project for $320M). Fuelco can delay starting the project for an addi-
tional ?ve years, during which time they expect this value of the project to ?uctuate, with an
annual volatility of 90 percent. Once initiated, the project is expected to generate annual cash
?ows equal to 10 percent of its value. Thus, if Fuelco delays the project, they will forego
these cash ?ows. After ?ve years, some important Fuelco patents will expire, and they will
not longer have the option to pro?tably enter this new market. If Fuelco does not enter the
market, then Project C has no salvage value. (By itself, this project is similar to the project
analyzed in Example 22.2, except that the initial spin-off value is different ($320M here
versus $400M in Example 22.2, and the riskfree interest rate here is zero.)
456 CHAPTER 24 R&D VALUATION
Problems
(a) Draw the decision tree for Fuelco.
(b) Assuming that Fuelco does complete Project A and B, what would be the value of the
option to do Project C?
(c) What is Fuelco optimal strategy? What is the NPV of this strategy?
Solutions
(a) The decision tree is given in several parts. First, we review the decision trees for each
project separately. The tree for Project A, originally given in Exhibit 21-4, is reproduced in
Exhibit 24-10; the tree for Project B, originally given in Exhibit 21-5, is reproduced in Exhibit
24-9; the tree for Project C, with the same shape but different payoffs as given in Exhibit 22-11,
is reproduced in Exhibit 24-12. Last, after showing the three projects separately, Exhibit 24-13
gives a tree with a schematic version of the full decision problem, showing the decision nodes
and branches for each project, with the event branches omitted.
(b) To ?nd the value of the all the projects combined, we solve backward, beginning with
Project C. The valuation problem here is similar to Example 22.2, except for the difference
in the initial value of the project ($320M here) and in the riskfree rate (0 percent here). To
estimate the value of the option, we use the bintree spreadsheet and build an American
EXHIBIT 24-10
FUELCO’S DECISION TREE (PROJECT A)
2
Don't get contract
Duration ? one year
Cost to start project ? $200M
Get contract
Finish project
Finish project
Abandon
Abandon
3
1
50%
50%
–$300M
–$300M
$600M
$200M
$0
$0
24.2 ENERGY 457
option tree with a possible exercise in every month over a ?ve-year period. This tree is
identical to the tree we built in Example 22.2, except for the small changes in the inputs
worksheet. After making these changes, the spreadsheet gives an option value of $180.77M.
In the interest of simplifying our calculations for the rest of the problem, we round this
value off to $180M.
(c) To value the full set of projects, we need a practical way to combine the trees from
Exhibits 24-10, 24-11 and 24-12. In Exhibit 24-14, we combine Projects A and B into a
single tree, and we combine the risk-neutral probabilities for each type of uncertainty.
For example, because Project A faces only the idiosyncratic risk of the government
contract, the risk-neutral probability of getting the contract is identical to the objective
probability (50 percent). In contrast, the oil prices in Project B do include some market
risk. Luckily for us, the binary call option allows us to solve for the risk-neutral prob-
abilities of 25 percent for high oil prices and 75 percent for low oil prices. (Do you
remember why this is true? If you forgot, see Section 21.4 for an explanation.) Exhibit
24-14 prunes the ?nal decisions for each project, with the extensions for these decisions
shown in Exhibits 24-15, 24-16, 24-17, and 24-18. Following these exhibits, we explain
the trees in more detail.
To see how Exhibit 24-14 has been pruned, we start by looking at Nodes 6 to 9. At
Nodes 6 and 7, Fuelco has elected to start Project B but not Project A. Because A has not
been started, it is not possible to complete both A and B, and thus Project C does not come
EXHIBIT 24-11
FUELCO’S DECISION TREE (PROJECT B)
2
Low oil price
Duration ? one year
Cost to start project ? $100M
High oil price
Finish project
Finish project
Abandon
Abandon
3
1
50%
50%
–$200M
–$200M
$1,000M
$300M
$200M
$200M
458 CHAPTER 24 R&D VALUATION
under consideration at all. Thus, Nodes 6 and 7 reduce to a straightforward analysis of
Project B, which is illustrated in Exhibit 24-11. For Project B, we know it is optimal to
abandon the project when oil prices are low (node 6, $200M) and to ?nish the project when oil
prices are high (node 7, $1,000M2$200M5$800M). With risk-neutral probabilities of 0.75
for low oil prices and 0.25 for high oil prices, the NPV of the “Start A” strategy is 0.75 Ã
200 10.25 Ã 800 2 100 5$250M, which is the same answer we got in Example 21.2.
We turn next to Nodes 8 and 9, where Fuelco has elected to start Project A but not
Project B. Here, as in the previous case, Project C is not possible, because it is not possible to
complete both A and B. Thus, we have a straightforward analysis of Project A, which is
illustrated in Exhibit 24-10. For Project A, we know it is optimal to ?nish the project
if Fuelco gets the contract (node 8, $600M2$300M5$300M) and to abandon the project if
they don’t (node 9, $0). With risk-neutral probabilities of 0.50 for getting the contract and
0.50 for not getting the contract, the NPV of the “Start B” strategy is 0.50 Ã 300 10.50 Ã 0 2
200 52$50M, which is the same answer we got in Example 21.1.
The problem grows more complex when we analyze the “Start both” branch, which
leads to terminal nodes at 10, 11, 12, and 13. To aid in this analysis, Exhibits 24-15 through
EXHIBIT 24-12
FUELCO’S DECISION TREE (PROJECT C)
1
5
3
4
9
$200M invest
$200M invest
1–p
1–p
wait
wait
wait
invest –$200M
down
up
foregone
cash flow
? CF
5
foregone
cash flow
? CF
1
foregone
cash flow
? CF
4
($320 – CF
1
)*d
($320 – CF
1
)*u
6
$320
2
up p
up p
1–p
down
1–p
down
11
13
12
10
Instant Instant One month
One
month
8
7
24.2 ENERGY 459
24-18 show the payoffs in each of these extensions. Consider the payoffs in Exhibit 24-15,
which corresponds to Node 10. At this node, Fuelco has chosen “start both”, and the
uncertainty has resolved to give Fuelco the contract but with low oil prices. The risk-neutral
probability of this branch is equal to the product of the risk-neutral probabilities for “low oil
price” (75 percent) and “get contract” (50 percent). This product is equal to 0.375. Once node
10 is reached, Fuelco has four possible choices, representing the yes/no decision for ?nishing
both projects. The terminal nodes in Exhibit 24-15 show the payoffs from each of these
choices. These payoffs come directly from Exhibits 24-10 and 24-11, with one important
exception: if Fuelco chooses to ?nish both projects, then it receives a “bonus” equal to the
NPV of Project C (5$180 M). Indeed, this bonus—only possible when both A and B have
been completed—makes “?nish both” the optimal decision. This optimal decision is
circled in Exhibit 25-15, with the payoff of $580 M shown for Node 10 in the pruned tree of
Exhibit 24-14.
The payoffs at Nodes 11, 12, and 13 are computed using the same method. For Node
11, Exhibit 24-16 indicates that the optimal strategy is “?nish neither”, with a payoff of
$200M. At nodes 11 and 12, the respective Exhibits 24-17 and 24-18 indicate that “?nish
both” is the optimal strategy. Once we include the payoffs from these strategies into
Exhibit 24-14, we are ready to compute the expected payoff for the “start both” branch as
EXHIBIT 24-13
FUELCO’S DECISION TREE, SCHEMATIC (ALL PROJECTS)
6
2 3
10 8
4 1
9 7
Project A Project B
Project C Project C
Project
B
Project
A
5
start start
get
contract
high oil
wait up wait
invest
invest invest down
don't don't don't low oil
invest
don't
don't
One Year
One Month One Month
(Payoff) (Payoff) (Payoff)
460 CHAPTER 24 R&D VALUATION
Expected payoff of ‘‘start both’’ branch 50:375 Ã 580
10:375 Ã 200 10:125 Ã 1; 280 10:125 Ã 880 2300 ¼ $262:5M:
ð24:2Þ
This payoff is higher than the $250M payoff for “start B”, the 2$50M expected payoff
for “start A”, and the $0 payoff from “start neither”. Thus, Fuelco’s optimal strategy for all
projects is
1. Start Projects A and B.
2. If “low oil” 1“don’t get contract” then abandon both projects, otherwise ?nish both.
3. Follow the optimal strategy of the binomial tree for Project C.
The NPV of this strategy is $262.5M. Note that the optimal strategies for Projects
A and B have been signi?cantly altered by the presence of Project C. Indeed, when we
considered A and B in isolation, we always abandoned these projects in the “low oil” or
“don’t get contract” states. The option to invest in Project C has changed the optimal
investment strategy on other projects and given Fuelco a reason to pursue those projects
EXHIBIT 24-14
FUELCO’S DECISION TREE, PRUNED (ALL PROJECTS), WITH
RISK-NEUTRAL PROBABILITIES
4
2
(0) 1
3 5
Start neither
Start
both
–300
–200
Start A
–100
Start B
(300)
8
(800)
7
(580)
10
(880)
13
(200)
11
(1,280)
12
(200)
6
Get
contract
High
Oil
Low
Oil
0.50 0.25
0.75
0.50
Don't
(0)
9
0.125
0.125 0.375
High/
Don't
High/
Get
Low/
Don't
0.375
Low/
Get
24.2 ENERGY 461
EXHIBIT 24-15
NODE 10, EXPANDED
10
Finish A
Finish B
Finish Both
Finish
Neither
300 ? 200
? 500
300 ? 100 ? 180
? 580
0 ? 200
? 200
0 ? 100
? 100
EXHIBIT 24-16
NODE 11, EXPANDED
11
Finish A
Finish B
Finish Both
Finish
Neither
–100 ? 200
? 100
?100 ? 100 ? 180
? 180
0 ? 200
? 200
0 ? 100
? 100
462 CHAPTER 24 R&D VALUATION
EXHIBIT 24-17
NODE 12, EXPANDED
12
Finish A
Finish B
Finish Both
Finish
Neither
300 ? 200
? 500
300 ? 800 ? 180
? 1280
0 ? 200
? 200
0 ? 800
? 800
EXHIBIT 24-18
NODE 13, EXPANDED
13
Finish A
Finish B
Finish Both
Finish
Neither
?100 ? 200
? 100
?100 ? 800 ? 180
? 880
0 ? 200
? 200
0 ? 800
? 800
24.2 ENERGY 463
mainly for the technological ?exibility for a later project. Although this is an abstract
example, it is illustrative of the kind of strategic thinking that is necessary in R&D
investment. ’
24.3 THE FOREST AND THE TREES
Part IV has been all about trees. We learned about event trees in Chapter 20, decision
trees in Chapter 21, binomial trees in Chapter 22, and game trees in Chapter 23. In
this chapter, we put all these trees together to solve some complex examples. In the
midst of all these trees, it is easy to lose sight of the forest. R&D investing is a highly
uncertain endeavor. In our examples, we pretended to know a lot of things that are
essentially unknowable: starting values for projects, objective probabilities, volati-
lities—all these things are guesses. Given all this uncertainty, why do we bother? We
do it because it is by modeling things carefully that we force rigor into our thought
process. In Example 24.1, this rigor allowed us to see why “control” might not be
worth its costs, because giving to much power to Drugco at one stage can lead Bigco
to grow very conservative at another. These are fundamental insights about the
strategic situation, insights that transcend the speci?c numbers used in the example.
Similarly, the Fuelco problem in Example 24.2—although very unrealistic in the
speci?cs—is illustrative of the interconnections across R&D projects. Many man-
agers have a natural intuition for real options and the value of ?exibility. By running
through a few models, we can begin to quantify and sharpen this intuition.
Although we have applied the models in Part IV to general R&D investment—
rather than to venture capital—the insights of these models can readily be applied to
VC investment. Because VC ?rms are lean organizations staffed mostly by gen-
eralists, most do not have the capabilities (or time) to perform this kind of analysis.
The ?exible spreadsheets included with this book can help to bridge this gap. In all
these cases, it is important to remember the big picture, even when paying close
attention to the details. We must not lose sight of the forest because we are staring at
the trees.
SUMMARY
In this chapter, we pulled together the various methods studied in Part IV. We use these
methods to analyze complex investment problems for Drugco and Fuelco. The framework of
these problems was ?rst introduced in Chapter 19, with the building blocks for the solutions
covered in Chapter 20 (event trees and Monte Carlo analysis), Chapter 21 (decision trees and
real options), Chapter 22 (binomial trees), and Chapter 23 (game trees and game theory).
The main value of working through solutions to these problems is in the process itself;
by providing structure to the decision problem, the analyst can quantify his intuition and gain
a deeper understanding of the strategic nuances of the situation. Although such deep study
464 CHAPTER 24 R&D VALUATION
can reap great rewards, it is dangerous to rely exclusively on the model answers. The most
successful investors are those who ride their visions using a structured investment discipline.
REFERENCES
Walkenbach, John, 2003, Excel 2003 Bible, Wiley, Indianapolis, IN.
EXERCISES
24.1 Use the same setup as in Example 24.1. Suppose that Bigco offers Drugco a third
option, Deal 3. In Deal 3, Bigco retains full control and pays all costs (just like Deal 1), with
one change: instead of paying a $150M milestone for Phase III continuation, Bigco would
pay a $400M milestone if they decide to market Newdrug.
(a) Draw the extensive form for Deal 3.
(b) Suppose that Drugco decides to take Deal 3. What is the optimal strategy for Bigco
following the Phase III trials? What is the optimal strategy for Bigco following the Phase II
trials? Assuming that Bigco chooses these strategies, what are the expected payoffs to
Drugco and Bigco?
(c) Given the choice of Deals 1, 2, and 3, which should Drugco choose?
24.2 Use the same setup as in Example 24.2.
(a) Suppose that the starting value for Project C is $400M. How does that change your
answers to parts (b) and (c)?
(b) Suppose that the starting value for Project C is $200M. How does that change your
answer to parts (b) and (c)?
24.3 Suppose that EBV is considering an equity investment in Drugco to coincide with the
signing of a strategic alliance (Deal 1 from Example 24.1) with Bigco. What suggestions
would you give to EBV of how to think about this investment?
24.4 True, False or Uncertain: A deep understanding of ?nance can help someone make
better venture capital and R&D investment decisions.
EXERCISES 465
APPENDI X A
SAMPLE TERM SHEET
THIS IS a public-domain document from the website of the National
Venture Capital Association. The version in this appendix was last updated in
April 2009.
This sample document is the work product of a coalition of attorneys who
specialize in venture capital ?nancings, working under the auspices of the
NVCA. See the NVCA website for a list of the Working Group members.
This document is intended to serve as a starting point only, and should be
tailored to meet your speci?c requirements. This document should not
be construed as legal advice for any particular facts or circumstances.
Note that this sample presents an array of (often mutually exclusive)
options with respect to particular deal provisions.
PRELIMINARY NOTES
This term sheet maps to the NVCA Model Documents, and for convenience the
provisions are grouped according to the particular Model Document in which
they may be found. Although this term sheet is perhaps somewhat longer than a
“typical” VC Term Sheet, the aim is to provide a level of detail that makes the
term sheet useful as both a road map for the document drafters and as a
reference source for the business people to quickly ?nd deal terms without the
necessity of having to consult the legal documents (assuming of course there have
been no changes to the material deal terms prior to execution of the ?nal
documents).
466
TERM SHEET
FOR SERIES A PREFERRED STOCK FINANCING OF
[INSERT COMPANY NAME], INC.
[___ ___, 200_]
This Term Sheet summarizes the principal terms of the Series A Preferred Stock
Financing of [___________], Inc., a [Delaware] corporation (the “Company”). In
consideration of the time and expense devoted and to be devoted by the Investors
with respect to this investment, the No Shop/Con?dentiality [and Counsel and
Expenses] provisions of this Term Sheet shall be binding obligations of the
Company whether or not the ?nancing is consummated. No other legally binding
obligations will be created until de?nitive agreements are executed and delivered
by all parties. This Term Sheet is not a commitment to invest, and is conditioned
on the completion of due diligence, legal review and documentation that is
satisfactory to the Investors. This Term Sheet shall be governed in all respects by
the laws of the [State of Delaware], and does not constitute an offer to sell or a
solicitation of an offer to buy securities in any state where the offer or sale is not
permitted.
Offering Terms
Closing Date: As soon as practicable following the Company’s
acceptance of this Term Sheet and satisfaction of
the Conditions to Closing (the “Closing”). [provide
for multiple closings if applicable]
Investors: Investor No. 1: [_______] shares ([__]%),
$[_________]
Investor No. 2: [_______] shares ([__]%),
$[_________]
[as well other investors mutually agreed upon by
Investors and the Company]
Amount Raised: $[________], [including $[________] from the con-
version of principal [and interest] on bridge notes].
1
Price Per Share: $[________] per share (based on the capitalization of
the Company set forth below) (the “Original Pur-
chase Price”).
1
Modify this provision to account for staged investments or investments dependent on the achievement
of milestones by the Company.
APPENDIX A SAMPLE TERM SHEET 467
Pre-Money Valuation: The Original Purchase Price is based upon a fully-
diluted pre-money valuation of $[_____] and a
fully-diluted post-money valuation of $[______]
(including an employee pool representing [__]% of
the fully-diluted post-money capitalization).
Capitalization: The Company’s capital structure before and after the
Closing is set forth on Exhibit A.
CHARTER
2
Dividends: [Alternative 1: Dividends will be paid on the Series
A Preferred only on an as-converted basis when, as,
and if paid on the Common Stock.]
[Alternative 2: The Series A Preferred will accrue
dividends at the rate of [__]% per annum[, payable
only when and if declared by the Board] [or upon a
liquidation or redemption.] For any other dividends
or distributions, participation with Common Stock
on an as-converted basis.]
3
EXHIBIT A
PRE- AND POST-FINANCING CAPITALIZATION
Pre-Financing Post-Financing
Security # of Shares % # of Shares %
Common À Founders
Common À Employee Stock Pool
Issued
Unissued
[Common À Warrants]
Series A Preferred
Total
2
The Charter is a public document, ?led with the [Delaware] Secretary of State, which establishes all of
the rights, preferences, privileges and restrictions of the Preferred Stock.
3
In some cases, accrued and unpaid dividends are payable on conversion as well as upon a liquidation
event. Most typically, however, dividends are not paid if the preferred is converted. Another alternative
is to give the Company the option to pay accrued and unpaid dividends in cash or in common shares
valued at fair market value. The latter are referred to as “PIK” (payment-in-kind) dividends.
468 APPENDIX A SAMPLE TERM SHEET
Liquidation Preference: In the event of any liquidation, dissolution or wind-
ing up of the Company, the proceeds shall be paid as
follows:
[Alternative 1 (non-participating Preferred Stock):
First pay the greater of (i) [one] times the Original
Purchase Price [plus accrued dividends] [plus
declared and unpaid dividends] on each share of
Series A Preferred or (ii) such amount as would have
been payable had all shares of Preferred Stock been
converted to Common Stock on each share of Series
A Preferred. The balance of any proceeds shall be
distributed pro rata to holders of Common Stock.]
[Alternative 2 (full participating Preferred Stock):
First pay [one] times the Original Purchase Price
[plus accrued dividends] [plus declared and unpaid
dividends] on each share of Series APreferred. There-
after, the Series A Preferred participates with the
Common Stock pro rata on an as-converted basis.]
[Alternative 3 (cap on Preferred Stock participation
rights): First pay [one] times the Original Purchase
Price [plus accrued dividends] [plus declared and
unpaid dividends] on each share of Series A Preferred.
Thereafter, Series A Preferred participates with Com-
mon Stock pro rata on an as-converted basis until the
holders of Series A Preferred receive an aggregate of
[_____] times the Original Purchase Price per share, at
whichpoint eachholder of Series APreferredis entitled
to receive the greater of (i) that amount per share or (ii)
the amount such holder would receive if all shares of
Series A Preferred Stock had been converted to Com-
mon Stock immediately prior to such liquidation.]
A merger or consolidation (other than one in which
stockholders of the Company own a majority by
voting power of the outstanding shares of the surviv-
ing or acquiring corporation) and a sale, lease,
transfer, exclusive license or other disposition of all
or substantially all of the assets of the Company will
be treated as a liquidation event (a “Deemed Liqui-
dation Event”), thereby triggering payment of the
liquidation preferences described above [unless the
holders of [___]% of the Series A Preferred elect
otherwise].
APPENDIX A SAMPLE TERM SHEET 469
[Investors’ entitlement to their liquidation preference
shall not be abrogated or diminished in event part of
consideration is subject to escrow in connection with a
Deemed Liquidation Event.]
4
Voting Rights: The Series A Preferred Stock shall vote together with
the Common Stock on an as-converted basis, and not
as a separate class, except (i) the Series A Preferred
as a class shall be entitled to elect [_______] [(_)]
members of the Board (the “Series A Directors”),
and (ii) as required by law. The Company’s Certi?-
cate of Incorporation will provide that the number of
authorized shares of Common Stock may be
increased or decreased with the approval of a major-
ity of the Preferred and Common Stock, voting
together as a single class, and without a separate
class vote by the Common Stock, irrespective of the
provisions of Section 242(b)(2) of the Delaware
General Corporation Law.
5
Protective Provisions: [So long as [insert ?xed number, or %, or “any”]
shares of Series A Preferred are outstanding,] in
addition to any other vote or approval required under
the Company’s Charter or By-laws, the Company
will not, without the written consent of the holders of
at least [__]% of the Company’s Series A Preferred,
either directly or indirectly by amendment, merger,
consolidation, or otherwise:
(i) liquidate, dissolve or wind-up the business and
affairs of the Company, or effect any Deemed Liqui-
dation Event or consent to any of the foregoing; (ii)
amend, alter, or repeal any provision of the Certi?cate
4
When a portion of the merger consideration is placed in escrow to secure a company’s indemni?cation
obligations to an acquirer, the company’s stockholders will need to address how the deductions from the
merger consideration used to fund the escrow are to be allocated among themselves. Today most charters
are silent on the subject of escrow allocations, and the parties simply work it out at the time of the M&A
event. However, this provision is intended to cause the parties to at least consider these issues at the time
of the initial investment. Today, the more common approach is simply to allocate the acquisition escrow
pro rata among all stockholders. Section 2.3.4 of the NVCA Model Charter provides for the alternative
approach, namely, allocation of the escrow in a manner that ensures that the Preferred Stock holders
always receive their liquidation preference, even if some or all of the escrow is forfeited. See fn. 25 to the
NVCA Model Charter for examples and a more detailed explanation.
5
For California corporations, one cannot “opt out” of the statutory requirement of a separate class vote by
Common Stockholders to authorize shares of Common Stock.
470 APPENDIX A SAMPLE TERM SHEET
of Incorporation or Bylaws [in a manner adverse to the
Series A Preferred];
6
(iii) create or authorize the
creation of [or issue or obligate itself to issue shares
of,] any other security convertible into or exercisable
for any equity security, having rights, preferences or
privileges senior to or on parity with the Series A
Preferred, or increase the authorized number of shares
of Series A Preferred or of any additional class or
series of capital stock [unless it ranks junior to the
Series APreferred]; (iv) reclassify, alter or amend any
existing security that is junior to or on parity with the
Series A Preferred, if such reclassi?cation, alteration
or amendment would render such other security senior
to or on parity with the Series A Preferred; (v)
purchase or redeemor pay any dividend on any capital
stock prior to the Series A Preferred, [other than stock
repurchased from former employees or consultants in
connection with the cessation of their employment/
services, at the lower of fair market value or cost;]
[other than as approved by the Board, including the
approval of [_____] Series A Director(s)]; (vi) create
or authorize the creation of any debt security [if the
Company’s aggregate indebtedness would exceed
$[____][other than equipment leases or bank lines of
credit]unless such debt security has received the prior
approval of the Board of Directors, including the
approval of [________] Series A Director(s)]; (vii)
create or hold capital stock in any subsidiary that is not
a wholly-owned subsidiary or dispose of any subsidi-
ary stock or all or substantially all of any subsidiary
assets[; or (viii) increase or decrease the size of the
Board of Directors].
Optional Conversion: The Series A Preferred initially converts 1:1 to
Common Stock at any time at option of holder,
subject to adjustments for stock dividends, splits,
combinations and similar events and as described
below under “Anti-dilution Provisions”.
6
Note that as a matter of background law, Section 242(b)(2) of the Delaware General Corporation Law
provides that if any proposed charter amendment would adversely alter the rights, preferences and
powers of one series of Preferred Stock, but not similarly adversely alter the entire class of all Preferred
Stock, then the holders of the impacted series are entitled to a separate series vote on the amendment.
APPENDIX A SAMPLE TERM SHEET 471
Anti-dilution Provisions: In the event that the Company issues additional
securities at a purchase price less than the current
Series A Preferred conversion price, such conversion
price shall be adjusted in accordance with the
following formula:
[Alternative 1: “Typical” weighted average:
CP
2
5CP
1
à ðA1BÞ=ðA1CÞ
CP
2
5Series A Conversion Price in effect immedi-
ately after new issue
CP
1
5Series A Conversion Price in effect immedi-
ately prior to new issue
A5Number of shares of Common Stock deemed to
be outstanding immediately prior to new issue
(includes all shares of outstanding common stock,
all shares of outstanding preferred stock on an as-
converted basis, and all outstanding options on an
as-exercised basis; and does not include any conver-
tible securities converting into this round of ?nancing)
B5Aggregate consideration received by the Cor-
poration with respect to the new issue divided by CP
1
C5Number of shares of stock issued in the subject
transaction]
[Alternative 2: Full-ratchet—the conversion price
will be reduced to the price at which the new shares
are issued.]
[Alternative 3: No price-based anti-dilution protection.]
The following issuances shall not trigger anti-dilu-
tion adjustment:
7
(i) securities issuable upon conversion of any of the
Series A Preferred, or as a dividend or distribution on
the Series A Preferred; (ii) securities issued upon the
conversion of any debenture, warrant, option, or
other convertible security; (iii) Common Stock
issuable upon a stock split, stock dividend, or any
subdivision of shares of Common Stock; and
(iv) shares of Common Stock (or options to purchase
7
Note that additional exclusions are frequently negotiated, such as issuances in connection with
equipment leasing and commercial borrowing. See additional exclusions de?ned as “Exempted Secu-
rities” in Section 4.4.1 of the NVCA Model Charter.
472 APPENDIX A SAMPLE TERM SHEET
such shares of Common Stock) issued or issuable to
employees or directors of, or consultants to, the
Company pursuant to any plan approved by the
Company’s Board of Directors [including at least
[_______] Series A Director(s)] [(v) shares of Com-
mon Stock issued or issuable to banks, equipment
lessors or other ?nancial institutions, or to real
property lessors, pursuant to a debt ?nancing, equip-
ment leasing or real property leasing transaction
approved by the Board of Directors of the Corporation
[, including at least [_______] Series A Director(s)].
Mandatory Conversion: Each share of Series A Preferred will automatically
be converted into Common Stock at the then applic-
able conversion rate in the event of the closing of a
[?rm commitment] underwritten public offering with
a price of [___] times the Original Purchase Price
(subject to adjustments for stock dividends, splits,
combinations and similar events) and [net/gross]
proceeds to the Company of not less than
$[_______] (a “QPO”), or (ii) upon the written
consent of the holders of [__]% of the Series A
Preferred.
8
Pay-to-Play: [Unless the holders of [__]% of the Series A elect
otherwise,] on any subsequent down round all
[Major] Investors are required to participate to the
full extent of their participation rights (as described
below under “Investor Rights Agreement À Right to
Participate Pro Rata in Future Rounds”), unless the
participation requirement is waived for all [Major]
Investors by the Board [(including the vote of [a
majority of] the Series A Director
[Alternative 1: [Each share] [applicable portion of
the shares]
9
of Series A Preferred of any [Major]
Investor failing to do so will automatically convert to
8
The per share test ensures that the investor achieves a signi?cant return on investment before the
Company can go public. Also consider allowing a non-QPO to become a QPO if an adjustment is made
to the Conversion Price for the bene?t of the investor, so that the investor does not have the power to
block a public offering.
9
The second formulation serves to have the consequences of the pay-to-play provisions apply on a
proportionate basis (e.g., if Investor plays for
1
/2 of pro rata share, then only
1
/2 of the Investor’s Preferred
converts to common, or does not receive anti dilution adjustment, etc., as applicable).
APPENDIX A SAMPLE TERM SHEET 473
Common Stock and lose the right to a Board seat if
applicable.]
[Alternative 2: [Each share] [applicable portion of
the shares] of any [Major] Investor failing to do so
will automatically [lose anti-dilution rights] [lose
right to participate in future rounds].]
10
Redemption Rights:
11
The Series A Preferred shall be redeemable from
funds legally available for distribution at the option
of holders of at least [__]% of the Series A Preferred
commencing any time after [________] at a price
equal to the Original Purchase Price [plus all accrued
but unpaid dividends]. Redemption shall occur in
three equal annual portions. Upon a redemption
request from the holders of the required percentage
of the Series A Preferred, all Series A Preferred
shares shall be redeemed [(except for any Series A
holders who af?rmatively opt-out)].
12
STOCK PURCHASE AGREEMENT
Representations
and Warranties:
Standard representations and warranties by the Com-
pany. [Representations and warranties by Founders
10
If the punishment for failure to participate is losing some but not all rights of the Preferred (e.g.,
anything other than a forced conversion to common), the Charter will need to have so-called “blank
check preferred” provisions at least to the extent necessary to enable the Board to issue a “shadow” class
of preferred with diminished rights in the event an investor fails to participate. Note that as a drafting
matter it is far easier to simply have (some or all of) the preferred convert to common.
11
Redemption rights allow Investors to force the Company to redeem their shares at cost [plus a small
guaranteed rate of return (e.g., dividends)]. In practice, redemption rights are not often used; however,
they do provide a form of exit and some possible leverage over the Company. While it is possible that the
right to receive dividends on redemption could give rise to a Code Section 305 “deemed dividend”
problem, many tax practitioners take the view that if the liquidation preference provisions in the Charter
are drafted to provide that, on conversion, the holder receives the greater of its liquidation preference or
its as-converted amount (as provided in the NVCA Model Charter), then there is no Section 305 issue.
12
Due to statutory restrictions, it is unlikely that the Company will be legally permitted to redeem in the
very circumstances where investors most want it (the so-called “sideways situation”), investors will
sometimes request that certain penalty provisions take effect where redemption has been requested but
the Company’s available cash ?ow does not permit such redemption—e.g., the redemption amount shall
be paid in the form of a one-year note to each unredeemed holder of Series A Preferred, and the holders
of a majority of the Series A Preferred shall be entitled to elect a majority of the Company’s Board of
Directors until such amounts are paid in full.
474 APPENDIX A SAMPLE TERM SHEET
[regarding technology ownership, con?icting agree-
ments, litigation etc.].]
13
Conditions to Closing: Standard conditions to Closing, which shall include,
among other things, satisfactory completion of ?nan-
cial and legal due diligence, quali?cation of the
shares under applicable Blue Sky laws, the ?ling of
a Certi?cate of Incorporation establishing the rights
and preferences of the Series A Preferred, and an
opinion of counsel to the Company.
Counsel and Expenses: [Investor/Company] counsel to draft closing docu-
ments. Company to pay all legal and administrative
costs of the ?nancing [at Closing], including reason-
able fees and expenses, in an amount not to exceed
[_____], of Investor counsel [, unless the transaction
is not completed because the Investors withdraw
their commitment without cause].
14
Company Counsel: [____________________
____________________
____________________]
Investor Counsel: [____________________
____________________
____________________]
INVESTOR RIGHTS AGREEMENT
Registration Rights:
Registrable Securities: All shares of Common Stock issuable upon conver-
sion of the Series A Preferred and any other
13
Founders’ representations are controversial and may elicit signi?cant resistance. They are more
common in the Northeast and counsel should be warned that they may not be well received elsewhere.
They are more likely to appear if Founders are receiving liquidity from the transaction or if there is
heightened concern over intellectual property (e.g., the Company is a spin-out from an academic
institution or the Founder was formerly with another Company whose business could be deemed
competitive with the Company). Founders’ representations are not common in subsequent rounds, even
in the Northeast, where risk is viewed as signi?cantly diminished and fairly shared by the investors rather
than being disproportionately borne by the Founders.
14
The bracketed text should be deleted if this section is not designated in the introductory paragraph as
one of the sections that is binding upon the Company regardless of whether the ?nancing is
consummated.
APPENDIX A SAMPLE TERM SHEET 475
Common Stock held by the Investors will be deemed
“Registrable Securities”.
15
Demand Registration: Upon earliest of (i) [three-?ve] years after the
Closing; or (ii) [six] months following an initial
public offering (“IPO”), persons holding [__]% of
the Registrable Securities may request [one][two]
(consummated) registrations by the Company of
their shares. The aggregate offering price for such
registration may not be less than $[5-15] million. A
registration will count for this purpose only if (i) all
Registrable Securities requested to be registered are
registered and (ii) it is closed, or withdrawn at the
request of the Investors (other than as a result of a
material adverse change to the Company).
Registration on Form S-3: The holders of [10À30]% of the Registrable Secu-
rities will have the right to require the Company to
register on Form S-3, if available for use by the
Company, Registrable Securities for an aggregate
offering price of at least $[1À5 million]. There will
be no limit on the aggregate number of such Form S-3
registrations, provided that there are no more than
[two] per year.
Piggyback Registration: The holders of Registrable Securities will be entitled
to “piggyback” registration rights on all registration
statements of the Company, subject to the right,
however, of the Company and its underwriters to
reduce the number of shares proposed to be regis-
tered to a minimum of [20À30]% on a pro rata basis
and to complete reduction on an IPO at the under-
writer’s discretion. In all events, the shares to be
registered by holders of Registrable Securities will
be reduced only after all other stockholders’ shares
are reduced.
Expenses: The registration expenses (exclusive of stock transfer
taxes, underwriting discounts and commissions will
be borne by the Company. The Company will also
pay the reasonable fees and expenses [not to exceed
$______,] of one special counsel to represent all the
participating stockholders.
15
Note that Founders/management sometimes also seek limited registration rights.
476 APPENDIX A SAMPLE TERM SHEET
Lock-up: Investors shall agree in connection with the IPO, if
requested by the managing underwriter, not to sell or
transfer any shares of Common Stock of the Com-
pany [(including/excluding shares acquired in or
following the IPO)] for a period of up to [180]
days
16
following the IPO subject to extension to
facilitate compliance with FINRA rules (provided all
directors and of?cers of the Company [and [1À5]%
stockholders] agree to the same lock-up). [Such lock-
up agreement shall provide that any discretionary
waiver or termination of the restrictions of such
agreements by the Company or representatives of
the underwriters shall apply to Investors, pro rata,
based on the number of shares held.]
Management and
Information Rights:
A Management Rights letter from the Company, in a
form reasonably acceptable to the Investors, will be
delivered prior to Closing to each Investor that
requests one.
17
Any [Major] Investor [(who is not a competitor)] will
be granted access to Company facilities and person-
nel during normal business hours and with reason-
able advance noti?cation. The Company will deliver
to such Major Investor (i) annual, quarterly, [and
monthly] ?nancial statements, and other information
as determined by the Board; (ii) thirty days prior to
the end of each ?scal year, a comprehensive operat-
ing budget forecasting the Company’s revenues,
expenses, and cash position on a month-to-month
basis for the upcoming ?scal year[; and (iii) promptly
following the end of each quarter an up-to-date
capitalization table]. A “Major Investor” means
any Investor who purchases at least $[______] of
Series A Preferred.
Right to Maintain
Proportionate
Ownership:
All [Major] Investors shall have a pro rata right, based
on their percentage equity ownership in the Company
[(assuming the conversion of all outstanding Preferred
16
See commentary in fn. 23 and 24 of the NVCA Model Investor Rights Agreement regarding possible
extensions of lock-up period.
17
See commentary in introduction to NVCA Model Managements Rights Letter, explaining purpose of
such letter.
APPENDIX A SAMPLE TERM SHEET 477
Stock into Common Stock and the exercise of all
options outstanding under the Company’s stock
plans)]
18
, to participate in subsequent issuances of
equity securities of the Company (excluding those
issuances listed at the end of the “Anti-dilution
Provisions” section of this Term Sheet. In addition,
should any [Major] Investor choose not to purchase its
full pro rata share, the remaining [Major] Investors
shall have the right to purchase the remaining pro
rata shares.
Matters Requiring
Investor Director
Approval:
19
So long as the holders of Series A Preferred are
entitled to elect a Series A Director, the Company
will not, without Board approval, which approval
must include the af?rmative vote of [one/both] of the
Series A Director(s):
(i) make any loan or advance to, or own any stock
or other securities of, any subsidiary or other
corporation, partnership, or other entity unless it
is wholly owned by the Company; (ii) make any
loan or advance to any person, including, any
employee or director, except advances and similar
expenditures in the ordinary course of business or
under the terms of a employee stock or option plan
approved by the Board of Directors; (iii) guarantee
any indebtedness except for trade accounts of the
Company or any subsidiary arising in the ordinary
course of business; (iv) make any investment
inconsistent with any investment policy approved
by the Board; (v) incur any aggregate indebtedness
in excess of $[_____] that is not already included in
a Board-approved budget, other than trade credit
incurred in the ordinary course of business; (vi) enter
into or be a party to any transaction with any director,
18
See commentary in fn. 40 of the NVCA Model Investor Rights Agreement regarding possible varia-
tions on the calculation of pro-rata rights.
19
Founders will often resist having speci?ed corporate acts subject to approval by the investors’ Board
designee(s). On the other hand, some investors won’t go forward without this provision. An alternative is
to move items from this list to the “protective provisions” of the charter, where they would require a
Preferred stockholder vote. If the investor insists on such provisions, the Company generally would ?nd
the director approval approach preferable, as the director representative on the Board has a ?duciary duty
to the corporation when acting in the capacity of a director. Other formulations could be: requiring the
vote of a supermajority of the Board, or a majority of the non-management directors.
478 APPENDIX A SAMPLE TERM SHEET
of?cer or employee of the Company or any “associ-
ate” (as de?ned in Rule 12b-2 promulgated under
the Exchange Act) of any such person [except
transactions resulting in payments to or by the
Company in an amount less than $[60,000] per
year], [or transactions made in the ordinary course
of business and pursuant to reasonable requirements
of the Company’s business and upon fair and reason-
able terms that are approved by a majority of the
Board of Directors];
20
(vii) hire, ?re, or change the
compensation of the executive of?cers, including
approving any option grants; (viii) change the princi-
pal business of the Company, enter new lines of
business, or exit the current line of business; (ix) sell,
assign, license, pledge or encumber material technol-
ogy or intellectual property, other than licenses
granted in the ordinary course of business; or (x)
enter into any corporate strategic relationship invol-
ving the payment contribution or assignment by the
Company or to the Company of assets greater than
[$100,000.00].]
Non-Competition and
Non-Solicitation
and Agreements:
21
Each Founder and key employee will enter into a
[one] year non-competition and non-solicitation
agreement in a form reasonably acceptable to the
Investors.
Non-Disclosure and
Developments Agreement:
Each current and former Founder, employee and
consultant will enter into a non-disclosure and pro-
prietary rights assignment agreement in a form
reasonably acceptable to the Investors.
Board Matters: [Each non-employee director shall be entitled in such
person’s discretion to be a member of any Board
committee.]
20
Note that Section 402 of the Sarbanes-Oxley Act of 2003 would require repayment of any loans in full
prior to the Company ?ling a registration statement for an IPO.
21
Non-compete restrictions are a matter of state law, and you need to investigate the relevant law in the
state where the employee works (e.g., permissible temporal and geographic scope, what constitutes
adequate consideration). In California, other than in connection with the sale of a business, they are
prohibited.
APPENDIX A SAMPLE TERM SHEET 479
The Board of Directors shall meet at least [monthly]
[quarterly], unless otherwise agreed by a vote of the
majority of Directors.
The Company will bind D&O insurance with a
carrier and in an amount satisfactory to the Board
of Directors. Company shall agree that its indemni-
?cation obligations to Series A Directors are pri-
mary, and obligations of af?liated Investors are
secondary.
22
In the event the Company merges
with another entity and is not the surviving corpora-
tion, or transfers all of its assets, proper provisions
shall be made so that successors of the Company
assume the Company’s obligations with respect to
indemni?cation of Directors.
Employee Stock Options: All employee options to vest as follows: [25% after
one year, with remaining vesting monthly over next
36 months].
[Immediately prior to the Series A Preferred Stock
investment, [______] shares will be added to the
option pool creating an unallocated option pool of
[_______] shares.]
Key Person Insurance: Company to acquire life insurance on Founders
[name each Founder] in an amount satisfactory to
the Board. Proceeds payable to the Company.
RIGHT OF FIRST REFUSAL/CO-SALE AGREEMENT
Right of ?rst Refusal/
Right of Co-Sale
(Take-me-Along):
Company ?rst and Investors second (to the extent
assigned by the Board of Directors,) have a right of
?rst refusal with respect to any shares of capital stock
of the Company proposed to be sold by Founders
[and current and future employees or consultants
22
A 2007 Delaware Chancery Court decision held that an investment fund that itself indemni?ed its
partner who served on a portfolio company board was a co-indemnitor with the portfolio company and,
therefore, the investor director was not entitled to recover from the portfolio company the full amount of
any payments advanced by the portfolio company on behalf of the investor director. Following
that decision, investors will insist on provisions such as the one here, as a provision in the Investor
Rights Agreement and/or as part of a separate Indemni?cation Agreement (see NVCA Model Indem-
ni?cation Agreement).
480 APPENDIX A SAMPLE TERM SHEET
holding greater than [1]% of Company Common
Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of
options)], with a right of oversubscription for Inves-
tors of shares unsubscribed by the other Investors.
Before any such person may sell Common Stock, he
will give the Investors an opportunity to participate
in such sale on a basis proportionate to the amount of
securities held by the seller and those held by the
participating Investors.
23
Lock-Up Founders will not transfer, hedge or otherwise dis-
pose of any capital stock following an IPO for a
period speci?ed by the Company and the managing
underwriter [not to exceed [180] [210] days].
VOTING AGREEMENT
Board
of Directors:
At the initial Closing, the Board shall consist of
[______] members comprised of (i) [Name] as [the
representative designated by [____], as the lead
Investor, (ii) [Name] as the representative designated
by the remaining Investors, (iii) [Name] as the
representative designated by the Founders, (iv) the
person then serving as the Chief Executive Of?cer of
the Company, and (v) [___] person(s) who are not
employed by the Company and who are mutually
acceptable [to the Founders and Investors][to the
other directors].
Drag Along: Holders of Preferred Stock and the Founders [and all
future holders of greater than [1]% of Common
Stock (assuming conversion of Preferred Stock and
whether then held or subject to the exercise of
options)] shall be required to enter into an agreement
with the Investors that provides that such stock-
holders will vote their shares in favor of a Deemed
Liquidation Event or transaction in which 50% or
23
Certain exceptions are typically negotiated, e.g., estate planning or de minimis transfers. Transfers are
sometimes also prohibited to competitors or to other parties to protect con?dential information.
APPENDIX A SAMPLE TERM SHEET 481
more of the voting power of the Company is
transferred and which is approved by [the Board of
Directors] [and the holders of ____% of the out-
standing shares of Preferred Stock, on an as-con-
verted basis].]
24
OTHER MATTERS
Founders’ Stock: All Founders to own stock outright subject to
Company right to buyback at cost. Buyback right
for [__]% for ?rst [12 months] after Closing; there-
after, right lapses in equal [monthly] increments over
following [__] months.
Existing Preferred Stock
25
: The terms set forth above for the Series [_] Preferred
Stock are subject to a review of the rights, prefer-
ences and restrictions for the existing Preferred
Stock. Any changes necessary to conform the exist-
ing Preferred Stock to this term sheet will be made at
the Closing.]
No Shop/Con?dentiality: The Company agrees to work in good faith expedi-
tiously towards a closing. The Company and the
Founders agree that they will not, for a period of
[______] weeks from the date these terms are
accepted, take any action to solicit, initiate, encou-
rage or assist the submission of any proposal,
negotiation or offer from any person or entity other
than the Investors relating to the sale or issuance, of
any of the capital stock of the Company [or the
acquisition, sale, lease, license or other disposition of
the Company or any material part of the stock or
assets of the Company] and shall notify the Investors
promptly of any inquiries by any third parties in
regards to the foregoing. [In the event that the
24
This provision is typically subject to a number of negotiated conditions, including: the representations
and warranties required are limited to authority and title to shares, liability for breaches of representa-
tions by the Company is limited to a pro rata share of any escrow amount withheld, any liability is
several and capped at the stockholder’s purchase price and that the stockholder receive the same form
and amount per share of consideration as other holders of the same class or series of stock.
25
Necessary only if this is a later round of ?nancing, and not the initial Series A round.
482 APPENDIX A SAMPLE TERM SHEET
Company breaches this no-shop obligation and, prior
to [________], closes any of the above-referenced
transactions [without providing the Investors the
opportunity to invest on the same terms as the other
parties to such transaction], then the Company shall
pay to the Investors $[_______] upon the closing of
any such transaction as liquidated damages.]
26
The
Company will not disclose the terms of this Term
Sheet to any person other than of?cers, members of
the Board of Directors and the Company’s accoun-
tants and attorneys and other potential Investors
acceptable to [_________], as lead Investor, without
the written consent of the Investors.
Expiration: This Term Sheet expires on [_______ __, 200_] if
not accepted by the Company by that date.
EXECUTED THIS [__] DAY Of [_______], 20[__].
[SIGNATURE BLOCKS]
26
It is unusual to provide for such “break-up” fees in connection with a venture capital ?nancing, but
might be something to consider where there is a substantial possibility the Company may be sold prior to
consummation of the ?nancing (e.g., a later stage deal).
APPENDIX A SAMPLE TERM SHEET 483
APPENDI X B
THE VCFI SPREADSHEETS
THIS APPENDIX DESCRIBES the spreadsheets and models used in the text.
The spreadsheets are available on the publisher’s websites; the VCV model is
available at VCVtools.com. Section B.1 gives an annotated list of all spreadsheets.
Most of these spreadsheets are self-explanatory and easy to use. For the VCV
model, we present a user’s guide in Section B.2. The VCV model was developed
by Anthony Curnes, Holland Gary, Andrew Metrick, Jonathan Reinstein, David
Smalling, and Rebecca Yang.
B.1 AN ANNOTATED LISTING OF SPREADSHEETS
AND MODELS USED IN THIS BOOK
All spreadsheets were built using Microsoft Excel and carry the .xls extension.
Chapter 6—Betas, with estimates of industry betas for the U.S. market pre-
mium, and country betas for the global market premium.
Chapter 10—VC method, to make investment recommendations using the
standard and modified versions of the VC method.
Chapter 11—DCF, with examples of reality-check models for three compa-
nies, a sample investment function, and industry statistics for DCF inputs.
Chapters 13 through 18—VCV, with templates for the valuation of preferred
stock structures. See Section B.2 for a user’s guide and Section B.3 for
screenshots.
Chapter 22—Bintree, with a 60-step binomial tree and modular worksheets
for underlying asset value and option value.
B.2 THE VCV MODEL
The VCV model is built as a web application. The model consists of four calcu-
lation modules: The European Call Option Calculator, the Random-Expiration (RE)
Call Option Calculator, the FLEX Calculator, and the AUTO Calculator. The
examples using European Call Option and RE Option Calculator are discussed
484
in Chapters 13. We describe below how to enter inputs into FLEX and AUTO
Calculators.
Inputs Common to FLEX and AUTO:
Volatility is in %. For 90%, enter “90”.
Risk Free Rate is in %. For 5%, enter “5”.
Total valuation is in million dollars. For $100M, enter “100”.
Expected Holding Period is in years. For 5 years, enter “5”.
For Inputs Speci?c to FLEX:
Strike Price is in $ millions. For $100M, enter “100”.
Options are calculated as either regular RE options or binary RE options. Select
the correct type by clicking on the tab.
For Inputs Speci?c to AUTO:
Founder’s Shares is in millions. For 10M shares, enter “10”.
Shares are in millions. For example, for 10M shares, enter “10”.
Investment is in $ millions.
RP APP is in $ millions. This input cell is grayed out unless you select RP 1C
or RP 1CP as the security Type.
Security types are abbreviated as follows:
C5Common Stock
CP 5Convertible Preferred
RP 5Redeemable Preferred
RP 1C5Redeemable Preferred and Common
RP 1CP 5Redeemable Preferred and Convertible Preferred
PCP 5Participating Convertible Preferred
PCPC5Participating Convertible Preferred with Cap
Cap is in multiples of the APP. For example, for 3X cap, enter “3”. This input
cell is grayed out unless you select PCPC as the Security Type.
QPO is in multiples of the OPP. For example, for 5X OPP threshold, enter “5”.
This input cell is grayed out unless you select PCP or PCPC as the Security
Type.
Dividends is in monthly rate as percentage of the original APP. For example, for
1% monthly dividends, enter “1”.
Dividends are calculated as either simple dividends or complex dividends. Select
the correct type by clicking on the tab.
B.2 THE VCV MODEL 485
Liquidation Preference is in multiples of APP. For example, for 1X preference,
enter “1”.
GP(%) is in %. For example, for 10%, enter “10”.
Lifetime Fees is in $millions. For example, for $20M, enter “20”.
Committed Capital is in $millions. For example, for $100M, enter “100”.
486 APPENDIX B THE VCFI SPREADSHEETS
APPENDI X C
GUIDE TO CRYSTAL BALL
s
Crystal Ball
s
is a popular simulation program that works as an add-in to Excel. The
software was originally developed by Decisioneering, Inc., a company that provides
risk analysis and decision-making software and solutions.
1
In this appendix, we will
introduce Crystal Ball
s
, provide an overview of functionalities, and solve the all
examples from Chapter 20 and some from Chapter 21 using this software.
2
As we learned in Chapter 20, we can use the randomnumber function of Excel to
runsimulations. However, programmingsimulations inExcel quicklybecome unwieldy
for more complexproblems. Crystal Ball
s
makes it easier toset upsimulationmodels by
providingextra functionalities, whichallowusers tode?ne randomvariable assumptions
for one scenario, to specify run preferences for running the trial multiple times, and to
view graphical and statistical summaries of overall simulation outcomes.
To get started with Crystal Ball
s
, users need to install the program and to
launch the Crystal Ball
s
add-in either by clicking on the Crystal Ball
s
icon or by
going through Start . All Programs . Crystal Ball
s
. Once the program has ?n-
ished loading, a Crystal Ball
s
toolbar should appear at the top of a blank Excel
spreadsheet. Exhibit C-1 describes the buttons of this Crystal Ball
s
toolbar.
Once the program has been successfully launched, the next step is to set up the
simulation model in Crystal Ball
s
. Unlike with Excel, where we need to set up 10,000
rows of the simulation if we want to model 10,000 potential outcomes of project trials,
Crystal Ball
s
allows us to build the model based on only one run of the project
because the program records the individual outcome and runs the model for the
prespeci?ed number of project trials. Crystal Ball
s
then synthesizes the results of all
the runs and presents the summary of outcomes both graphically and statistically.
1. De?ne random number assumptions.
2. De?ne the forecast.
3. Set simulation run preferences.
4. Run the simulation.
5. Analyze the results.
1
Following the acquisition of Decisioneering by Oracle, the software is now sold by Oracle.
2
This appendix was coauthored with Greta Lin. Crystal Ball
s
Edition 7.1.2 was used to solve the
problems in this appendix. For the latest edition of Crystal Ball
s
, see http://www.oracle.com/appserver/
business-intelligence/crystalball/index.html.
487
We will discuss each of these steps in detail as we work through the examples
presented in Chapter 20 of the text using Crystal Ball
s
.
EXAMPLE 20.1
Drugco has just begun Phase I trials for Newdrug. Phase I takes one year and costs
$10 M. Drugco’s scientists estimate that the R&D has a 50 percent chance of
successfully completing Phase I and moving to Phase II. Phase II takes one year and
costs $30 M. If Newdrug enters Phase II, the scientists estimate a 40 percent chance
of successfully completing Phase II and moving to Phase III. Phase III takes three
years (including the time waiting for FDA approval) and costs $60 M. If Newdrug
enters Phase III, the scientists estimate a 50 percent chance of success (5FDA
approval). Drugco management estimates an NPV of $1B at the time of approval. If
the drug fails, then it would be worth nothing. The discount rate is equal to the risk-
free rate of 5 percent per year. All development costs must be paid at the beginning
of the respective phase.
Problem Use Crystal Ball
s
to build a Monte Carlo simulation for Newdrug and con?rm
the same (average) NPV solution as obtained in Chapter 20.
Crystal Ball
s
Solution To solve this problem we need to create a model that replicates
the scenario described earlier. One possible spreadsheet setup is shown in Exhibit C-2. To
then complete the simulation, we need to follow the ?ve main steps of Crystal Ball
s
simulations.
EXHIBIT C-1
CRYSTAL BALL
s
TOOLBAR
488 APPENDIX C GUIDE TO CRYSTAL BALL
s
Step 1: De?ne random number assumptions
In this problem, there are three points of uncertainty.
1. Success of Phase I (Cell C4 of Exhibit C-2)
2. Success of Phase II (Cell C7)
3. Success of Phase III (Cell C10)
These uncertainties are interrelated because Phase II can only be successful if Phase I was
successful, and FDA approval requires Phase I success, Phase II success, and Phase III success.
Therefore, to set up the model we need to de?ne three random numbers. We have
assumed that there is a 50 percent chance of successfully completing Phase I and moving to
Phase II, a 40 percent chance of successfully completing Phase II and moving to Phase III,
and a 50 percent chance of successfully completing Phase III and obtaining FDA approval, so
we should draw our random numbers based on a uniform distribution from 0 to 1. Because
every number between 0 and 1 has an equal probability of being selected, we know that the
number drawn will be less than 0.4 for 40 percent of trials and will be less than 0.5 for 50
percent of trials.
To tell Crystal Ball
s
to generate random numbers based on a uniform distribution, we
need to take the following steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar (located on the far
left—refer back to Exhibit C-1 if necessary).
EXHIBIT C-2
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.1
APPENDIX C GUIDE TO CRYSTAL BALL
s
489
At this point, the Crystal Ball
s
distribution gallery should appear (Exhibit C-3). Select
the uniform distribution and click “OK”.
Next, specify the maximum and minimum values (a and b, respectively) for the range of
the uniform distribution. It is good idea to get in the habit of directly referencing these
cells within the Crystal Ball
s
window to cells from the spreadsheet that contains values
for a and b— this is a good mechanism for tracking and recording the parameters. To do
this, hit the button at the right side of the parameter input space (highlighted by the large
red arrow in Exhibit C-4) within the distribution window and then click on the cell that
contains the correct value on the spreadsheet.
Repeat these steps in order to generate random numbers that simulate the outcomes of
Phase II and Phase III trials.
Once these random number generators have been speci?ed, we need to translate these
random numbers into outcomes. We can do this by writing IF statements, which tell us
whether or not the drug successfully passes a phase based on the random number that is
generated. For Phase I, we stipulate that:
IFðRN,0:5; 1; 0Þ: ½Cell C5 Exhibit CÀ2?
EXHIBIT C-3
CRYSTAL BALL
s
DISTRIBUTION GALLERY
490 APPENDIX C GUIDE TO CRYSTAL BALL
s
Therefore, if the random number is less than 0.5, the drug passes Phase I and a value of 1
is returned in our success indicator cell. On the other hand, if the random number is
greater than 0.5, the drug does not pass Phase I and a value of 0 is given in the success
indicator cell.
These success indicator cells allow us to easily set up the relationships between phases.
Because any number multiplied by 0 is 0, we know that when we multiply success indicator
cells together, the only time we will return a value of 1 is when the drug has successfully
passed all the phases involved in the multiplication.
Step 2: De?ne the forecast
In this example, the outcome we want to forecast is the NPV of the project. To calculate
the NPV of the project, we need to determine the costs and revenues associated with each
EXHIBIT C-4
SPECIFYING THE UNIFORM DISTRIBUTION
APPENDIX C GUIDE TO CRYSTAL BALL
s
491
phase of the project. We know that we incur the $10 M cost of Phase I trials with cer-
tainty. We only incur Phase II costs of $30 M if the project passes Phase I and moves onto
Phase II. Therefore, we multiply the $30 M cost by the Phase I outcome success indicator
value. If Phase I is successful, $30 M is multiplied by 1, if it is unsuccessful $30 M is
multiplied by 0, and no cost is incurred. The same logic holds for the $60 M cost of Phase
III except that we need to multiply by Phase I and Phase II outcome success indicator
values. We only take on Phase III if the project has passed through both phases and
therefore both indicators have a value of 1. Finally, we multiply the potential $1B in
revenues by the Phase I, II, and III outcome success indicators.
Use the 5 percent discount rate and the timing of the trials to discount the potential costs
and revenues appropriately.
Finally de?ne the forecast cell for Crystal Ball
s
by highlighting the cell that contains the
?nal NPV calculation for the scenario (Cell G19 of Exhibit C-2). Then, select “De?ne
Forecast” from the Crystal Ball
s
toolbar (refer back to Exhibit C-1).
When the De?ne Forecast window appears (Exhibit C-5), provide an appropriate name
and specify units of the forecast. Although this example only has one forecast cell,
descriptive names and units become important when there are multiple forecast cells we
wish to analyze.
Step 3: Set simulation run preferences
Select “Run Preferences” from the Crystal Ball
s
toolbar (refer back to Exhibit C-1).
On the trials tab of the Run Preferences window that appears (Exhibit C-6), specify the
number of outcomes you wish Crystal Ball
s
to run. This value should be suf?ciently
large so that Crystal Ball
s
returns approximately the same results each time the simu-
lation is run. However, the larger the number of trials, the more time Crystal Ball
s
will
require to complete the simulation.
EXHIBIT C-5
DEFINE FORECAST WINDOW
492 APPENDIX C GUIDE TO CRYSTAL BALL
s
Step 4: Run the simulation
We are ?nally ready to run the simulation. We can ?rst test to make sure that our
simulation is set up correctly by running the model one trial at a time by hitting the
“Single Step” button of the Crystal Ball
s
toolbar (refer back to Exhibit C-1). One smart
thing to check is to make sure that the NPV of the project is 2$10 M whenever Phase I is
unsuccessful. Similarly, the NPV is $690.5 when all three phases are successful.
Once we are sure the model works, we hit “Reset Simulation” from the toolbar to clear
the history of runs and then we select “Start/Continue Simulation”, which is designated by
the large right arrow in the center of the toolbar (Refer back to Exhibit C-4.)
A control panel should appear to let the user know when the progress of the simulation
including when the trials are complete.
Step 5: Analyze the results
Crystal Ball
s
provides several tools to allow us to analyze results. These analysis tools
are found by clicking on “Forecast Charts” button of the Crystal Ball
s
tool bar (refer
back to Exhibit C-1) and then opening the appropriate forecast window.
We can examine the statistical outputs of the simulation by clicking on View . Statistics
within the Forecast Chart window (Exhibit C-7). As determined in Chapter 20, the
expected NPV of the project, the mean outcome of the simulation, is $43.1 M.
EXHIBIT C-6
RUN PREFERENCES WINDOW
APPENDIX C GUIDE TO CRYSTAL BALL
s
493
’
Example 20.1 used discrete random variables, which we modeled as “1” for
success and “0” for failure. We used IF statements to indicate the success or failure
of the phase based on the random numbers drawn by Crystal Ball
s
. In the next
example, we solve a problem that uses a continuous random variable, which has an
in?nite number of possible outcomes.
EXAMPLE 20.2
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that
we are sure the drug has no side effects, so all that matters for FDA approval is its
ef?cacy. Ef?cacy is distributed E B U[0, 1] and will be revealed after three years
of Phase III trails. The NPV of the drug after three years is $1BÃ E
2
. The discount
rate is equal to the riskfree rate of 5 percent per year. The total cost of R&D is
$100 M and must be paid at the beginning of development.
Problem Use Crystal Ball
s
to run a Monte Carlo simulation to solve for the NPV of the
Newdrug project. The outcome should match our Excel solution from Chapter 20.
EXHIBIT C-7
STATISTICAL OUTPUT OF EXAMPLE 20.1 CRYSTAL BALL
s
SIMULATION
494 APPENDIX C GUIDE TO CRYSTAL BALL
s
Solution Crystal Ball
s
Solution We approach this problem by setting up a spreadsheet
such as in Exhibit C-8 and completing the ?ve step Crystal Ball
s
process.
Step 1: De?ne random number assumptions
As with Example 20.1, our ?rst step is to de?ne our random number assumptions within
Crystal Ball
s
. The one unknown in the problem is the ef?cacy of the drug once it has passed
Phase III. We are given that ef?cacy is uniformly distributed across a range of 0 to 1. Thus,
we need to take the following steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select uniform distribution and click “OK”.
Specify the maximum and minimum values (a and b) for the range of the uniform dis-
tribution in the appropriate cells of the Crystal Ball
s
De?ne Assumption window by
creating links to reference cells on the worksheet.
Step 2: De?ne the forecast
In this problem, we wish to forecast the NPV of the overall project. We were told that we
incur $100 M in R&D costs at the beginning of development with certainty. However,
our value after three years is uncertain. From the discussion in Chapter 20, we know that
F(E) = E, so we can compute our values by taking our random number draw and plugging
directly into the equation that was given:
Value after 3 years ¼ $1B Ã E
2
EXHIBIT C-8
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.2
APPENDIX C GUIDE TO CRYSTAL BALL
s
495
where E is the random value that was drawn within the uniform range. Once we have cal-
culated the value number, we apply the discount rate, and we compute the overall NPV for
the project. We de?ne the cell that contains the overall NPV computation (Cell C11 in
Exhibit C-8) as the forecast cell for Crystal Ball
s
. To do this, highlight this cell and select
“De?ne Forecast” from the Crystal Ball
s
toolbar. When the De?ne Forecast window
appears, name the forecast and de?ne units.
Step 3: Set simulation run preferences
Select “Run Preferences” from the Crystal Ball
s
toolbar. Specify the number of outcomes
you wish Crystal Ball
s
to run on the trials tab of the Run Preferences window that appears.
In the example Crystal Ball
s
output shown in Exhibit C-9, the number of outcomes was set
to 1 M.
Step 4: Run the simulation
Test the spreadsheet if desired by running a “Single Step”. Then “Reset Simulation” and hit
“Start/Continue Simulation”. Crystal Ball
s
will provide updates on the progress of the
simulation.
Step 5: Analyze the results
On examination of the statistical outcomes (Exhibit C-9), we ?nd that as we predicted in the
Excel simulation in Chapter 20, the average NPV of the project is approximately $188 M.
EXHIBIT C-9
STATISTICAL OUTPUT OF EXAMPLE 20.2 CRYSTAL BALL
s
SIMULATION
496 APPENDIX C GUIDE TO CRYSTAL BALL
s
Another tool that Crystal Ball
s
provides for analyzing results is cumulative frequency
charts (Exhibit C-10). We open this chart by clicking on View . Cumulative Frequency
within the Forecast Chart window of Crystal Ball
s
. Within this window we can also examine
the probability that outcomes will fall within a certain range of values.
’
EXAMPLE 20.3
Drugco has just begun Phase III trials for Newdrug. For simplicity, we assume that
we are sure the drug has no side effects, so all that matters for FDA approval is its
ef?cacy. Ef?cacy is distributed E B LogN[0, 1] and will be revealed after three
years of Phase III trails. The NPV of the drug after three years is $1BÃ E
2
. The
discount rate is equal to the riskfree rate of 5 percent per year. The total cost of
R&D is $100 M and must be paid at the beginning of development.
EXHIBIT C-10
CUMULATIVE FREQUENCY CHART FOR EXAMPLE 20.2
APPENDIX C GUIDE TO CRYSTAL BALL
s
497
Problem Use Crystal Ball
s
to run a Monte Carlo simulation to solve for the NPV of the
Newdrug project. The outcome should match our Excel solution from Chapter 20.
Solution Crystal Ball
s
Solution The only difference between Example 20.2 and 20.3 is
that in 20.2 Phase III ef?cacy is distributed uniformly, whereas in 20.3 Phase III ef?cacy
follows a lognormal distribution. Thus we need to de?ne our random number assumptions
differently, but all the other steps are the same as in Example 20.2.
Step 1: De?ne random number assumptions
The one unknown in the problem is the ef?cacy of the drug once it has passed Phase III. We
are given that ef?cacy is distributed E B LogN[0, 1]. Thus, we need to take the following
steps:
Enter a default numerical value in the cell that de?nes the random number.
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select lognormal distribution and click “OK”.
As noted in Chapter 20, in the x B LogN[µ, ?] notation, µ and ? are not the mean and
standard deviation (“SD”) of the lognormal distribution, instead they represent the mean and
SD of ln(x). When specifying the parameters of the lognormal distribution within Crystal
Ball
s
, we need to ?nd the actual mean and SD of x. The conversion equations are as follows:
Mean of x when xBLogN½µ; ?? ¼ exp½µ þ?
2
=2? ðC:1Þ
SD of x when xBLogN½µ; ?? ¼ ðexp½2µ þ 2?
2
?ÀÀexp½2µ þ?
2
?Þ
ð1=2Þ
: ðC:2Þ
Solving these equations, we get a mean of 1.65 and an SD of 2.16.
EXHIBIT C-11
SPREADSHEET SETUP FOR CRYSTAL BALL
s
SIMULATION OF
EXAMPLE 20.3
498 APPENDIX C GUIDE TO CRYSTAL BALL
s
Steps 2, 3, and 4
Follow the same steps as in Example 20.2.
Step 5: Analyze the results
As expected based on the Excel simulation from Chapter 20, the average NPV of the project
is approximately $6.3 billion (Exhibit C-12). If we examine the frequency chart of outcomes
(View . Frequency), we see that outcomes are skewed toward lower NPVs because of the
lognormal distribution of Phase III ef?cacy. ’
We are now ready to use Crystal Ball
s
to solve a more complex problem.
Example 20.4 has three sources of uncertainty which each exhibit different dis-
tributions and each uniquely in?uence the outcome.
EXAMPLE 20.4
Drugco has just begun Phase III trials for Newdrug, which has an associated R&D
cost of $100 M. Drugco expects Phase III trials to take two years and the FDA
approval decision to take one year, so that the FDA decision is expected in three
years. Phase II trials were promising, with a score of 40 on the standard medically
EXHIBIT C-12
STATISTICAL OUTCOME AND FREQUENCY CHART FOR
EXAMPLE 20.3
APPENDIX C GUIDE TO CRYSTAL BALL
s
499
recognized scale. (We will refer to this score as the “ef?cacy” of the drug.)
Although the best alternative drug has an ef?cacy of 50, it is not helpful for all
patients. Given the side effects of Newdrug and the risks and bene?ts of alternative
treatments, Drugco believes that the FDA will approve Newdrug if the Phase III
trials ?nd an ef?cacy of 30 or greater. Based on the results of the Phase II trials,
Drugco estimates that the ef?cacy results of Phase III will be E BN(40, 20). (It is
possible for ef?cacy to be negative because some drugs can make symptoms
worse.) During the three years of Phase III trials, it is possible that the alternative
treatments will also improve from their current ef?cacy of 50. Drugco estimates a
?nal distribution for the alternative of A BT(50, 100, 50). If Newdrug is approved
by the FDA, then its market share will depend on the relative ef?cacy of Newdrug
versus the best available treatment, that is,
Newdrug market share ¼ E
2
=ðE
2
þA
2
Þ:
Drugco estimates market size for Newdrug in the approval year (in thousands
of doses) as MBN(1,000, 100), with 6 percent annual growth going forward. Each
dose yields a gross pro?t of $1. To stay in the market, Drugco must spend $300 M
on marketing in the ?rst year, with this sum increasing each year by 6 percent. On
approval, Newdrug would have 10 years of patent life remaining. After the patent
expiration, Drugco expects generic competition and other improved alternatives to
greatly erode the value of Newdrug, so for simplicity we assume that the continuing
value would be zero after the patent expires. Following earlier examples in this
chapter, we assume a discount rate equal to the riskfree rate of 5 percent.
Problem Use Crystal Ball
s
to run a Monte Carlo simulation that estimates the FDA
approval rate and the NPV of Newdrug.
Crystal Ball
s
Solution The three unknowns in this problem are ef?cacy, alternative
ef?cacy, and starting market size. Ef?cacy and starting market size exhibit normal dis-
tributions whereas alternative ef?cacy follows a triangular distribution.
Step 1: De?ne random number assumptions
Enter a default numerical value in the cell that de?nes the random number for ef?cacy
(Cell C5 of Exhibit C-13).
Hit the “De?ne Assumption” button on the Crystal Ball
s
toolbar.
From the Distribution Gallery that appears, select “normal distribution” and click “OK”.
Specify the mean and SD of the normal distribution in the appropriate cells of the Crystal
Ball
s
De?ne Assumption window by creating links to reference cells on the worksheet.
In the case of ef?cacy, we are given that the mean value is 40 with a SD of 20.
Repeat the preceding steps to de?ne market starting size as a random number, which is
normally distributed with a mean of 1,000 and a SD of 100 (Cell C7 of Exhibit C-13).
Next we de?ne alternative ef?cacy according to a triangular distribution (Cell C6 of
Exhibit C-13). Again hit “De?ne Assumption”, but this time select “Triangular Dis-
tribution” within the Distribution Gallery.
500 APPENDIX C GUIDE TO CRYSTAL BALL
s
EXHIBIT C-13
SPREADSHEET SETUP FOR EXAMPLE 20.4
5
0
1
Triangular distributions are de?ned by the minimum, likeliest, and maximum values of
the distribution. In the case of alternative ef?cacy, these values are 50, 50, and 100,
respectively
Step 2: De?ne the forecast
In this problem, we wish to forecast two outcomes: the probability of FDA approval and the
NPV of the overall project.
Because we are given that the approval threshold is 30, we know that the drug is approved
whenever the random number draw for Phase III ef?cacy is greater than 30. Thus, we can
forecast the outcome with an IF statement:
IFðPhase III efficacy.30; 1; 0Þ: ½Cell C15 of Exhibit CÀ13?
We de?ne the cell that contains this IF statement as the forecast cell for Crystal Ball
s
.
As before, we do this by highlighting this cell and selecting “De?ne Forecast” from the
Crystal Ball
s
toolbar. When the De?ne Forecast window appears, name the forecast and
de?ne units.
To forecast the NPV of the project we need to construct the DCF model for Newdrug with
the random variables set to their expected values. The key line items of the DCF are
Market share, which is zero if Newdrug is not approved or determined by Newdrug
and Alternative ef?cacies when the drug is approved
Market size, which ?ows from the random draw of the starting market size
Pro?t, which is derived from market size and gross pro?t per unit
Marketing costs, which are only incurred if the drug is approved
An example of the full DCF spreadsheet can be found in Exhibit C-13.
Step 3: Set Simulation run preferences
In the example output shown (Exhibit C-14), 1 M trials were run.
Step 4: Run the simulation
Because the model is complex, it is a good idea to run the model in single steps to check that
only $100 M in costs is incurred when the drug is not approved and to observe pro?tability
when the drug is approved at different Phase III and alternative ef?cacies.
Step 5: Analyze the results
As was discussed in Chapter 20, the simulation reveals that the probability of FDA approval
is 69% and that the maximum NPV of the 1 M draws was more than $6.5B, whereas in the
worst-case scenario the company loses $2.2B. The average NPV for simulation is approxi-
mately $285 M (Exhibit C-14).
On examination of the cumulative frequency chart (Exhibit C-15), we notice an interesting
result of the simulation. We observe that most of the projects have an NPV above 2$100M, the
R&D cost for Phase III. However, some trials resulted in NPV below 2$100 M. These are
502 APPENDIX C GUIDE TO CRYSTAL BALL
s
the runs where the ef?cacy of Newdrug was low and the alternative ef?cacy was high. In these
scenarios, the drug was launched but market share of Newdrug was so low that marketing costs
could not be recouped. In these scenarios, Drugco would have been better off if the company had
abandoned the Newdrug project, even though the drug had been approved. In Example 21.4 of
EXHIBIT C-14
STATISTICAL OUTCOME FOR EXAMPLE 20.4
EXHIBIT C-15
CUMULATIVE FREQUENCY CHART FOR OUTCOMES OF
EXAMPLE 20.4
APPENDIX C GUIDE TO CRYSTAL BALL
s
503
Chapter 21, we revisit Example 20.4 to value this “abandonment” option. We are able to rerun
the Monte Carlo simulation with the additional option by making two simple modi?cations to our
spreadsheet. First, we need to calculate the salvage value according to the information given in
Example 21.4. Then we compare the NPV of abandoning the project to the NPV of launching
Newdrug, and we forecast outcomes based on the higher NPV. We do this with the following
equation:
MAXðNPV if launch drug; Salvage value 2$100MÞ: ðD:3Þ
The results of the Newdrug project with abandonment option are shown in Exhibit C-16.
As discussed in Chapter 21, the average NPV of the simulation with the option is more
than $180 M greater than the average NPV without the option. Also, when we view the
cumulative frequency chart we clearly see that we no longer have runs that result in NPV less
than 2$100 M. ’
We have ?nished solving four examples in which we used Crystal Ball
s
to
simulate project outcomes and forecast NPV in the presence of uncertainty. The
key steps for setting up simulations are de?ning assumptions for random variables
based on different types of distributions, de?ning forecasts, setting run preferences,
and running simulations. We also examined various Crystal Ball
s
tools (e.g.,
statistical outcomes, cumulative frequency charts) that allow us to analyze and
interpret the outcomes of the simulations.
Crystal Ball
s
provides many more features for more advanced users. Two
more functionalities that may be useful when modeling R&D projects are (1) de?ning
dynamic assumptions and (2) de?ning decision variables and tables. To demonstrate
these additional tools, we will work through parts of Exercise 21.4 (Remember that
EXHIBIT C-16
STATISTICAL OUTCOME AND CUMULATIVE FREQUENCY CHART
FOR EXAMPLE 21.4
504 APPENDIX C GUIDE TO CRYSTAL BALL
s
“exercises” are given without solutions at the end of chapters, whereas “examples”
are given in the body of chapters with solutions.)
DEFINING DYNAMIC ASSUMPTIONS
Dynamic assumptions can be used to model situations where uncertainty exists
regarding the parameters of a distribution. In Exercise 21.4, the mean of Phase III
ef?cacy outcomes is dependent on the ef?cacy outcome of Phase II trials, which are,
in turn, determined based on random draws. Speci?cally, we are given the following.
EXERCISE 21.4
“ . . . Phase II trials will take one year and cost $50 M. Following the Phase II trials, Drugco
will learn some information about ef?cacy, denoted as Eu, with Eu B T[0, 80, 40]. If, after
learning this information, Drugco decides to go forward with Phase III trials, then everything
is identical to Example 21.4, except that now the ef?cacy after Phase III trials is distributed
as E B N[Eu, 20]. . .”
To model the dynamic assumption aspect of this scenario, set up the spreadsheet so that
the reference cell for the mean of Phase III trials (Cell F10 of Exhibit C-17) is linked to the
outcome of Phase II (Cell C5). Then, when de?ning assumptions for Phase III trials, reference
this linked cell (Cell F10) to specify the parameters of the distribution within Crystal Ball
s
.
Finally, after all assumptions have been de?ned, reopen the “De?ne Assumption” window for
Cell F10. As compared to the ?rst time you opened this window, you will notice two new
boxes labeled “static” and “dynamic”. Click the “dynamic” box and close the window.
An examination of the summary of outputs (Exhibit C-18) shows that the SD of Phase III
outcomes is much greater than 20 because there is variability in the mean.
EXHIBIT C-17
SPREADSHEET SETUP FOR DEFINING A SIMPLE DYNAMIC
ASSUMPTION
EXERCISE 21.4 505
DEFINING DECISION VARIABLES
AND DECISION TABLES
We can instruct Crystal Ball
s
to test various values for certain inputs by de?ning
that input as a decision variable and then running a decision table. In this example,
we want to determine the minimum value of E’ such that Drugco should continue
on to Phase III trials—that is to establish a “continuation threshold”. The spread-
sheet for this problem is very similar to the earlier solution of Example 21.4, except
that we begin the simulation one year earlier, and Phase III is determined by the
dynamic assumption that we just modeled.
By de?ning the ef?cacy threshold as a decision variable with a minimum of 0
and maximum of 50, we can tell Crystal Ball
s
to run 11 simulations in which only
drugs with Phase II Eu above 0, then 5, then 10, etc. are passed onto Phase III based
on an IF statement that de?nes the “continuation threshold”. The following steps
are necessary to de?ne a decision variable.
Highlight the input cell to be varied (Cell C7 of Exhibit C-19). Then click on the “De?ne
Decision” button of the Crystal Ball
s
toolbar (second button from the left— refer back to
Exhibit C-1 if necessary).
EXHIBIT C-18
STATISTICAL OUTPUT OF PHASE III EFFICACY AS DETERMINED
BY A DYNAMIC ASSUMPTION
506 APPENDIX C GUIDE TO CRYSTAL BALL
s
EXHIBIT C-19
SPREADSHEET SETUP FOR DEFINING DECISION VARIABLE IN EXERCISE 21.4
5
0
7
Once the De?ne Decision Window (Exhibit C-20) appears, name the variable, set the
upper and lower bounds of values to be tested, and decide whether or not input values
should be continuous or discrete.
After the random number assumptions, forecasts, and decision variables are
all de?ned, we are ready to run a decision table.
First we need to set “Run Preferences” so that Crystal Ball
s
selects the same sequence of
random variables to run against the different inputs. This allows us to compare the dif-
ferent mean NPV outcomes for the various continuation thresholds without having to
worry about variability from random number selection. To do this, click on “Run Pre-
ferences” in the Crystal Ball
s
toolbar. When the Crystal Ball
s
window appears, go to the
“Sampling” tab and then enter a seed number 2 for this example, we used an initial seed
value of 999 (Exhibit C-21)
Go to Run . Tools . Decision Table.
Select the target forecast from the menu, click “Next”.
Then select the decision variable from the menu, and click “Next” (Left side of Exhibit C-22).
In this example, we only de?ned one decision variable, but up to two decision variables may
be selected for a decision table.
Specify the other options of the Decision Table such as number of test values, test runs,
and settings while running, and hit “Start” (Right side of Exhibit C-22). For this example,
we could run 51 trials to test every integer continuation threshold between 0 and 50
(inclusive), however, this would be a very time-consuming simulation run, so we will
only run 11 trials to get a sense of outcomes at every multiple of 5.
EXHIBIT C-20
DEFINE DECISION VARIABLE WINDOW
508 APPENDIX C GUIDE TO CRYSTAL BALL
s
The resulting Decision Table will appear in a new spreadsheet (Exhibit C-23). We can
graphically view the data by creating an Excel bar chart from the data.
From the decision table, we see that the average NPV of the project is max-
imized when the continuation threshold is set somewhere between 15 and 20.
Therefore, we should further investigate the ef?cacies in this range. Because decision
EXHIBIT C-21
SPECIFYING THE SEQUENCE OF RANDOM VARIABLES
EXHIBIT C-22
SPECIFYING DECISION VARIABLES AND OPTIONS FOR
THE DECISION TABLE
APPENDIX C GUIDE TO CRYSTAL BALL
s
509
tables are constrained at 10,000 trials for each test value, we can perform a more
re?ned analysis by running each integer value between 15 and 20 through a standard
Crystal Ball
s
run of 500,000 trials by inputting the continuation threshold manually
and then running the simulation six times. We want to continue using the same initial
seed value within “Run Preferences” for these individual runs as with the decision
table so that we continue to eliminate variability from random number selection. As
before, click on “Run Preferences”. When the Crystal Ball
s
window appears, go to
the “Sampling” tab to con?rm the initial seed value.
The outcomes shown in Exhibit C-24 reveal that the Phase II continuation
threshold should be set at around 17 to maximize the average NPV of the project.
This means that Phase II trials with ef?cacies much lower than 17 are not worth
continuing into Phase III because it is unlikely that the Phase III R&D costs can be
recouped. However, trials with ef?cacies above 17 should be continued.
EXHIBIT C-23
RESULTING DECISION TABLE
510 APPENDIX C GUIDE TO CRYSTAL BALL
s
In this Appendix, we solved Chapter 20 and 21 problems using Crystal Ball
s
and discussed some of the more advanced features of the software package. If
possible, you should try solving these examples on your own using Crystal Ball
s
or
another simulation software. Software add-ins like Crystal Ball
s
can be extremely
helpful for setting up and running complex simulations to forecast outcomes in the
presence of uncertainty.
REFERENCES
Gans Noah, Jack Hershey, Anjani Jain, and Ziv Katalan. The Wharton School. OPIM 621: Decision
Models and Uncertainty—Class lecture notes.
Ragsdale, Cliff T., 2004, Spreadsheet Modeling and Decision Analysis, 4th Edition, Thomson/South-
Western, Mason, OH, pp. 595À667.
EXHIBIT C-24
OUTCOMES OF 500,000 TRIAL RUNS WITH DIFFERENT
CONTINUATION THRESHOLDS
REFERENCES 511
GLOSSARY
This glossary includes all key terms given in bold in the text, plus some others that
are helpful for these definitions or for VC practice. When multiple entries have the
same meaning, the definition is given only once, with an “5” for all synonyms. The
definition is typically given for the first alphabetical entry, unless one of the later
entries is much more commonly used. Key terms are given in bold type for their
first appearance in each entry. Many of these terms also have a generic meaning in
English; in most cases, this glossary gives only the meanings relevant to venture
capital and the finance of innovation.
In most cases, we do not give formulas for these terms, relying on verbal
descriptions instead. To see formulas and to read more contextual material for any
of these terms, please consult the index to find places in the text where the terms are
discussed. Some of these key terms are used in multiple ways in the book, which
mirrors the multiple meanings for these terms in VC practice. Rather than pretend
that these confusions do not exist, we have highlighted the distinctions in this
glossary.
Since venture capital is a relatively new academic field, it was helpful in this
book to make up some new terms to aid in the translation between financial eco-
nomics and VC practice. These terms are given in bold italic type. In some cases,
these new terms have a common-sense meaning in English, but are still put in bold
italic type in order to formalize the specific meaning used in this book.
TERMS
Abnormal return: The additional return above the expected return from a factor model.
(5 Alpha)
Absolute return: The amount distributed to the limited partners of a fund, expressed as a
multiple of each dollar contributed by the partners: e.g., over the life of a fund that has
$100M in committed capital, the limited partners receive $200M back. The absolute
return of this fund 5 $200M/$100M 5 2. (5 Investment multiple, 5 Realization
ratio, 5 Value multiple)
Absolute valuation: Any method of valuation that relies on estimates and forecasts made by
the analyst. Discounted cash ?ow analysis is an example of absolute valuation. (See also
Relative valuation.)
Accrued cash dividend: A dividend that adds to the redemption value of preferred stock,
but is not actually paid until a deemed liquidation event.
512
Adjusted conversion price: The conversion price after antidilution protections have taken
effect. (See also Adjusted conversion rate.)
Adjusted conversion rate: The conversion rate after antidilution protections have taken
effect. (See also Adjusted conversion price.)
Aggregate purchase price (APP): The total amount paid for a speci?c class of stock. The
APP is equal to the original purchase price multiplied by the number of shares purchased.
Alpha: English pronunciation of the Greek letter, ?. (5 Abnormal return) (See also Beta.)
American option: An option that can be exercised any time on or before the exercise date.
Angel: A wealthy individual that invests in young, growth companies. An angel differs from
a venture capitalist because the former is using her own money. (5 Angel investors)
Angel investors: (5 Angel)
Annualized return: An asset return expressed on a per-year basis.
APP: acronym for aggregate purchase price.
Applied research: Research intended to translate scienti?c ?ndings into practical uses. (See
also Basic research, Development.)
Arms race: A strategic situation where all parties have an incentive to escalate some activity,
even though all parties would be better off if they could agree not to escalate.
As-if conversion: A feature of PCP and PCPC stock, where the stock receives its
redemption value and also is entitled to participate in the upside “as-if” it had been
converted to common stock.
At the money: An option where the strike price is exactly the same as the current value of
the underlying security.
Barriers to entry: An obstacle, either legal or economic, that prevents or slows down
competition in some market.
Base tree: A binomial tree showing the possible price paths for the underlying security in
an option-pricing problem. (See also Option tree.)
Basic research: Research designed to better understand the universe, without regard for
immediate practical application. (See also Applied research, Development.)
BC(X): Abbreviation for a random-expiration binary call option with a strike price of X.
Best response: In game theory, a move that gives Player A the highest expected payoff
against Strategy Z by Player B is called a best response by A against Z by B. (See also
Nash equilibrium.)
Beta: English pronunciation of the Greek letter, ?. Within the Capital Asset Pricing Model
(CAPM), the beta of an asset is the factor loading of that asset on the market portfolio.
In this model, beta is the regression coef?cient on an asset’s excess returns when it is
regressed on the market premium. Within multifactor models, beta is sometimes used
generically to refer to the loading on any factor. (See also Alpha.)
Binary call option: An option that pays a ?xed amount if the price of an underlying asset is
higher than a preset strike price on an exercise date.
Binomial trees: A decision tree with exactly two branches from each risk node and a ?xed
time period for each branch. Binomial trees are commonly used to value options.
Black-Scholes formula: A valuation formula for European call options.
Boom period: As used in this book, the period between 1995 and 2000, inclusive. (See also
Preboom, Postboom periods.)
GLOSSARY 513
Branch: In a tree, each possible move is represented by a branch.
Breakeven valuation: The total valuation of a company such that LP valuation 5 LP cost.
Broad-base formula: One of the methods used to compute the adjusted conversion price
under weighted average antidilution protections. The broad-base formula gives smaller
adjustments than does the narrow-base formula.
Burn rate: The speed with which a company is using up its cash.
Business plan: A summary document about the business that entrepreneurs show to investors.
Business risks: Risks faced by R&D investors that are correlated with the state of the
economy. These risks are best modeled using real options. (See also Competitive risks,
Technical risks.)
CA: Acronym for Cambridge Associates.
Call option: Gives the holder the right, but not the obligation, to purchase an underlying
security at a strike price.
Cambridge Associates (CA): A gatekeeper and a provider of a net-return index for the VC
industry.
Cap point: The level of proceeds where the liquidation return of PCPC stock is
maximized. (5 W
A
(cap))
Capital call: When the general partner of a fund requests capital from the limited
partners. (5 Drawdown, 5 Takedown)
Capital asset pricing model (CAPM): Model that expresses the expected return of an asset
as a function of the risk-free rate, the market premium, and beta.
Capitalization table: A table prepared as part of the term sheet that lists the stock ownership
of all investors, both before and after the current transaction.
CAPM: acronym for capital asset pricing model
Carried interest: The fund pro?ts paid to the general partner. (5 Carry)
Carried interest basis (5 carry basis): Fund pro?ts are de?ned as total proceeds minus the
carried interest basis. Typically, this basis is set to be either the committed capital or
the investment capital of the fund.
Carry: (5 Carried interest)
Carry basis: (5 Carried interest basis)
Carry%: The percentage level of carried interest. The most common carry% is 20 percent.
Cash distributions: The distribution of cash to limited partners. The alternative to a cash
distribution is an in-kind distribution.
Catch-up provision: When limited partners receive a hurdle return, the general partner
may have a catch-up provision that allows them to receive a share greater than carry%
for some range of pro?ts after the hurdle return is achieved.
CDF: Acronym for cumulative distribution function.
Certi?cate of incorporation: (5 Charter)
Charter: A legal document, setting out the main rules of corporate governance. Key
provisions from the charter are included as part of the term sheet. (5 Certi?cate of
incorporation) (See also Investor Rights Agreement.)
Clawback: If carried interest is received before the entire carried interest basis and hurdle
returns have been paid, and if later proceeds are insuf?cient to reach these thresholds,
514 GLOSSARY
then general partners may be subject to a clawback, where some of the earlier carried
interest must be transferred to the limited partners.
Cliff vesting: When all remaining options (or stock) becomes vested at the same time. (See
also Step vesting.)
Clinical trials: Drug tests in humans for safety and ef?cacy. (5 Human trials)
Closed: In raising a fund, general partners ask limited partners to commit to providing
capital. When the general partners have reached some desirable threshold of committed
capital, they publicly announce that the fund has closed. Despite the ?nality of this term,
some funds close multiple times, each time announcing a new level of committed capital.
(See also Raised.)
Closing: With respect to transactions in portfolio companies, the closing is the formal
signing of all necessary contracts and the transferring of the capital from the fund to the
company.
Commitment period: The time—usually the ?rst ?ve years of life—during which the fund
is permitted to make investments in new portfolio companies. (5 Investment period)
Committed capital: The total amount of capital promised to the fund by the limited
partners.
Common stock: Equity claims that are paid last upon any liquidation of the company. (See
also Preferred stock.)
Comparables analysis: The valuation of an asset by using data on similar assets. (5 Multi-
ples analysis, 5 Method of multiples, 5 Relative valuation)
Competitive advantage: Anything that allows a company to charge prices above marginal
costs.
Competitive risks: Risks faced by R&D investments that are caused by competition from
other entities. Competitive risks are modeled using game theory. (See also Business risks,
Technical risks.)
Compound interest: Interest that is paid on principal and on any interest accrued from
previous periods. (See also Simple interest.)
Compound return: A periodic return calculated by multiplying the subperiod returns.
Constant-sum games: A game where the sum of the payoffs to all players is a constant. (See
also Zero-sum games.)
Continuous random variables: A random variable de?ned on a continuous range, with an
in?nity of possible outcomes. (See also Discrete random variables.)
Continuously compounded returns: Returns with interest compounded at every instant.
(5 Log returns)
Contributed capital: At any given time in the life of the fund, contributed capital is equal to
the sum of invested capital plus all prior management fees.
Conversion condition: An inequality for convertible preferred stock that requires that
conversion value be greater than redemption value. The minimum value of proceeds that
satis?es the conversion condition is called the conversion point.
Conversion-order shortcut: When there are multiple rounds of convertible preferred share-
holders, they would choose to convert in the same order as the redemption value per share.
Conversion point (5 W
A
): The minimum level of proceeds such that the holder of
convertible preferred stock would choose to convert rather than to redeem. The
conversion point is the minimum solution to the conversion condition.
GLOSSARY 515
Convertible preferred (CP): Equity that can either be turned in for its redemption value or
converted to common stock.
Coordination games: Games with multiple pure-strategy Nash equilibria where all players
would prefer any of these equilibria to the nonequilibrium outcomes.
Corporate venture capital: VC investment by corporations. Although traditional VC seeks
to maximize ?nancial returns, corporate venture capital often mixes ?nancial and strategic
goals.
Cost of capital (r): The cost of capital is the risk-adjusted discount rate for an investment
project. In an equilibrium model like the CAPM, the cost of capital is equal to the
expected return.
Country beta: In the global CAPM, the country beta is the factor loading of a country on
the global market premium.
Country risk: The risk that an investment project in a foreign country will fail because of
some political or economic disaster in that country.
Covariance: Covariance measures the extent to which two variables tend to move together.
In ?nancial economics, assets earn excess returns because of the covariance of asset
returns with some price factor. (See also Variance.)
CP: Acronym for convertible preferred
Crossover investing: Investment in public companies by private equity ?rms.
CRR model: Acronym for Cox-Ross-Rubenstein Model, a speci?c method for constructing
binomial trees.
Cumulative distribution function (cdf): The cdf evaluated at point x gives the probability
that the random variable will be less than or equal to x. The cdf evaluated at x is the
integral of the pdf from negative in?nity to x.
Cumulative dividends: Dividends that accrue if not paid. (See also Noncumulative
dividends.)
DCF: Acronym for discounted cash ?ow analysis.
Deal ?ow: The investment opportunities available to a VC. In general, the better a VC ?rm’s
reputation, the better quality is their deal ?ow. (See also Sourcing, Proprietary deal ?ow.)
Decision nodes: The point in a tree where a player must make a decision.
Decision trees: Trees with two types of nodes, risk nodes and decision nodes. (See also
Event trees, Binomial trees, Game trees.)
Deemed liquidation event: (5 Liquidation) An event where certain preferred stock rights
come into force. These events are carefully de?ned in the term sheet. The most common
triggers for a deemed liquidation event are when a portfolio company is purchased or
shut down.
Demand registration rights: Rights that allow preferred stock holders to demand that their
shares be sold in a registered transaction. (See also Registration rights, S-3 registra-
tion rights, Piggyback registration rights.)
Derivative assets: Assets whose value is completely dependent on the value of other assets.
(See also underlying assets.)
Development: When used to describe a type of R&D project, development projects are
those designed to translate scienti?c research into marketable products. (See also Applied
research, Basic research.)
516 GLOSSARY
Discount rate: The rate that equates a $1 today with the expected value of $1 in some future
period.
Discounted cash ?ow (DCF) analysis: A method that values an asset as the sum of the
discounted value of all cash ?ows produced by that asset. DCF analysis is a form of
absolute valuation.
Discrete random variables: A random variable whose possible values are physically sep-
arated when plotted on a real line. (See also Continuous random variables.)
Distress investing: Investing in companies that have a signi?cant risk of going out of
business. (5 Special situations)
Diversi?able risk: Risk that has only a negligible impact on the whole economy (e.g.,
the risk that any speci?c house will burn down is diversi?able risk). (5 Idiosyncratic
risk)
Dividend preference: The restriction that dividends cannot be paid to common stock holders
unless they are ?rst paid to preferred stock holders.
Domestic beta: The regression coef?cient on an asset’s excess returns when it is regressed on
the market premium from its own country. (See also Domestic CAPM.)
Domestic CAPM: A CAPM that uses the market premium from any one country. In
contrast, the global CAPM uses the global market premium. (See also Domestic beta.)
Dominant strategy: In game theory, a strategy that does at least as well as every other
strategy, no matter what strategies are chosen by other players.
Down round: In term sheets, the technical de?nition that round Y is a down round
typically requires that the conversion price for preferred stock in round Y is lower than
the conversion price for preferred stock in Round X, where X ,Y. More generally, we can
also think of a down round occurring if the implied valuation for series X after round Y is
lower than the LP cost of series X.
Dragalong: A right of preferred stock holders to force other investors to sell their stake
in the company, provided that the preferred stock holder has found a buyer for all shares at
the same price. (See also Take-me-along, 5 Tagalong, 5 Right of ?rst offer, 5 Right
of ?rst refusal, 5 Transfer restrictions.)
Drawdown: (5 Capital call, 5 Takedown)
Due diligence: Careful study of all aspects of a potential investment.
Early stage: The de?nitions of early stage, midstage (5 Expansion stage), and later stage
are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that this stage “provides
?nancing to companies completing development where products are mostly in testing or
pilot production”.
Early stage fund: A fund that invests predominantly in early stage companies. (See also
Late-stage fund, Multistage fund.)
Earnings: (5 Net income, 5 Net pro?ts): The difference between revenue and expenses.
Earnings before Interest and Taxes (EBIT): Earnings plus interest expense plus taxes.
EBIT: Acronym for Earnings before Interest and Taxes.
Enterprise value: The market value of all securities issued by a company.
Entrepreneurial ecosystem: A regional community of entrepreneurs, venture capitalists,
technologists, and service providers.
GLOSSARY 517
Equilibrium concept: In game theory, a set of conditions necessary to de?ne an equilibrium.
For example, for the equilibrium concept of Nash equilibrium, the conditions require that
every player give a full menu of strategies at every decision node, with all these strategies
being a best response to the menu provided by all other players.
Equilibrium strategy: In game theory, the strategy for any given player that satis?es a
speci?c equilibrium concept.
Equity market value: (5 market cap, 5 market capitalization)
European call: Gives the holder the right, but not the obligation, to purchase an underlying
security at a strike price on a speci?c expiration date.
European put: Gives the holder the right, but not the obligation, to sell an underlying
security at a strike price on a speci?c expiration date.
Event trees: Trees without any decision nodes. (See also Binomial trees, Decision trees,
Game trees.)
Exercise price: (5 Strike price) (2X, 3X, 4X etc.) excess liquidation preference: The
multiple of aggregate purchase price that holders of preferred stock receive on
redemption. (See also Liquidation preference.)
Excess returns: The difference between the return on a speci?c asset and the risk-free rate
over the same time period.
Exit: This term has two related meanings. First, an exit refers to the sale or initial public
offering (IPO) of a portfolio company. Second, an exit refers to the sale of a VC’s stake
in a portfolio company. These two de?nitions are not always the same (e.g., a VC usually
must hold his stock for at least six months after an IPO). Then, we have the paradox of an
IPO “exit” followed by the VC “exit” six months later.
Exit diagram: On the x-axis, the market value of a company at exit; on the y-axis, the value
of a VC stake in that company at exit. An exit diagram differs from an expiration
diagram in that the former plots values at a VC exit at some unknown exit date, whereas
the latter plots values on a known expiration date.
Exit equation: The value of a VC stake in a company at exit, expressed as a portfolio of
random-expiration options. We obtain exit equations by reading the exit diagram.
Exit valuation: The expected value of a portfolio company, conditional on a successful exit.
Expansion stage: The de?nitions of early stage, midstage (5 Expansion stage), and later
stage are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that “this stage involves
applying working capital to the initial expansion of a company. The company is now
producing, is shipping, and has growing accounts receivables and inventories. It may or
may not be showing a pro?t”.
Expected holding period: The amount of time that a VC expects to hold an investment
before exit.
Expected retention percentage: Suppose a VC fund owns X percent of a company after
making its initial investment. Before an exit occurs, the fund expects that the company
will need to raise more capital by selling additional shares, which will reduce the initial
ownership to Y percent. Then, the expected retention percentage would be Y/X.
Expected return: From a mathematical perspective, the expected return on an investment
is computed by multiplying each possible return by the probability of that return.
In an equilibrium model like the CAPM, the expected return is equal to the cost of capital.
Expiration date: The last possible date that an option can be exercised.
518 GLOSSARY
Expiration diagram: On the x-axis, the market value of the underlying asset on the
expiration date; on the y-axis, the value of an option on that asset. An exit diagram
differs from an expiration diagram in that the former plots values at a VC exit at some
unknown exit date, whereas the latter plots values on a known expiration date.
Expropriation: A fancy way to say “stealing”. Minority investors (like VCs) must always be
on guard for subtle ways that managers and majority investors can expropriate resources
of the company. (5 Investor Expropriation, 5 Self-dealing, 5 Tunneling)
Extensive form: A decision tree with more than one player. In game theory, the normal
form lists all possible strategies for all players; the extensive form provides all the
information available in the normal form, and also shows the timing for all moves.
(5 Game tree)
Factor: A systematic risk in the economy. In the CAPM, the only factor is the market
premium. (5 Risk factor)
Factor model: A model where expected returns are determined by factor loadings on a set
of factors. The CAPM is an example of a factor model, where the market premium is
the factor and beta is the factor loading.
Factor loading: The amount that an asset’s return is related to a speci?c factor. In the
CAPM, the market premium is the factor and beta is the factor loading.
Fama-French Model (FFM): A multifactor model with three factors related to the market
premium, the size of the company, and the growth prospects of the company.
FDA: Acronym for the Food and Drug Administration, a unit of the U.S. government that is
responsible for the regulation of prescription drugs.
FDA approval: The ?nal step before a drug can be legally sold in the United States. (See also
Phase I, Phase II, Phase III, Preclinical.)
FFM: Acronym for the Fama-French Model.
Financial intermediary: Any economic actor that stands between a supplier of capital and
the real investment of that capital.
Financial options: Options on ?nancial assets. In contrast, real options are options on, you
guessed it, real assets.
Financing round: (5 Round) A discrete event where a young company receives capital
from investors. Financing rounds are often referred to sequentially as ?rst round
(5 Series A), second round (5 Series B), etc.
Finite games: A game with a ?nite number of moves for every player. Finite games can be
completely described using the normal form and the extensive form. (See also In?nite
games.)
Firm: In VC, a ?rm is the legal entity that serves as the general partner for a VC fund.
First Round (Series A): The ?rst round of investment by VCs. (See also Financing Round,
Second Round (Series B).)
FOF: Acronym for fund-of-funds.
Folk theorem: Loosely speaking, the folk theorem is that virtually any observed behavior in
an in?nite game can be supported as part of a subgame-perfect Nash equilibrium.
Follow-on investments: Investments made in Round Y by a VC investor in Round X, where
Y . X.
GLOSSARY 519
Full-ratchet antidilution: A strong version of antidilution protection, where the adjusted
conversion price is the lowest price paid by any later-round investor. (See also
Weighted-average antidilution.)
Fully diluted basis: Any computation that assumes the conversion of all preferred stock
and the exercise of all options.
Fully diluted share count: The total number of shares outstanding assuming the conversion
of all preferred stock and the exercise of all options.
Fund: (5 VC fund) A pool of capital used for VC investments. Typically, a VC fund is a
limited partnership with a ?xed lifetime, where the capital is provided by limited
partners and the fund is managed by a VC ?rm acting as the general partner.
Fund-of-funds (FOF): A fund that makes investments in other funds, rather than making
investment directly in portfolio companies.
Game tree: (5 Extensive form) (See alsoEvent trees, Decisiontrees, Binomial trees, Trees.)
Gatekeeper: A consultant who advises limited partners on their fund investments.
General partner (GP): The investment manager of a limited-partnership VC fund.
Geometric mean: For a series of N numbers, the geometric mean is the nth root of the
product of all N numbers.
Global beta: The beta in a global CAPM.
Global CAPM: The CAPM, with the global market premium used as the factor.
Global market premium: The expected excess return of the value-weighted global equity
market.
GP: Acronym for general partner.
GPvaluation: The valuation, using option pricing methods, of the GP’s stake in an investment.
GP%: The expected percentage of partial valuation that belongs to the VC. GP Valuation
5 GP% * partial valuation.
Graduation: In the reality-check DCF model, graduation marks the date where a company
moves from the rapid-growth period to the stable-growth period.
Graduation value: The discounted value of the company at graduation.
Gross investment: The gross amount added to a company’s capital stock in a period.
Gross investment multiple (5 Gross value multiple (GVM)): The total value of all
investments at exit, divided by investment capital.
Gross return: A return calculated before subtracting management fees, carried interest, or
any other investment costs.
Gross value multiple (GVM): (5 Gross investment multiple)
Growth capital: Capital used for VC investing beyond the early stage.
Growth factor: In a binomial tree, the growth factor is the risk-free rate measured over the
step size of the tree.
GVM: Acronym for gross value multiple (5 Gross investment multiple)
Harmonic mean: In a group of numbers, the harmonic mean is the reciprocal of the mean of
the reciprocals (i.e., for N numbers Xi, I 5 1, . . . N, the harmonic mean 5
N=
X
N
i51
1
X
i
Þ
520 GLOSSARY
Hedge funds: Hedge funds comprise a wide class of investment vehicles, with mandates that
include virtually any strategy that can be imagined. Hedge funds differ from mutual funds
in that the former has much lighter regulation. Hedge funds differ from private equity
funds in that the former tends to focus mostly on publicly traded securities, although the
distinctions between these types of funds has blurred somewhat in recent years. With
more liquid investments, hedge funds typically have much shorter lockup periods for
investors than do private equity funds.
Historical return: (5 Realized return) The past return for an asset, fund, or manager.
Hockey stick: (5 J-curve): On the x-axis, the number of years since a fund’s vintage year.
On the y-axis, the IRR of the fund up to that year. For successful funds, this curve takes
the form of a hockey stick, with negative IRRs reported for early years (when manage-
ment fees are paid but before any exits) and higher IRRs in later years (after the best exits
have occurred.)
Human trials: (5 Clinical trials)
Hurdle returns: (5 Preferred returns, 5 Priority returns) A preset level of returns that
the fund must pay to investors before the GP can begin to take any carried interest.
Idiosyncratic risk: (5 Diversi?able risk)
Implied GP valuation: The implied valuation of the GP stake in an investment, based on the
price paid in the most recent round. (See also Implied LP valuation, Implied partial
valuation.)
Implied LP valuation: The implied valuation of the LP stake in an investment, based on the
price paid in the most recent round. (See also Implied GP valuation, Implied partial
valuation.)
Implied partial valuation: The implied valuation of the fund’s stake in an investment, based
on the price paid in the most recent round. Implied partial valuation 5 Implied GP
valuation + Implied LP valuation.
Implied prevaluation (IV
pre
): The implied valuation of a company immediately prior to the
most recent round of investment.
Implied postvaluation (IV
post
): The market value of a company, as implied by the VCV
model, under the assumption that the most recent investors paid fair value, LP valuation
5 LP cost.
Implied valuation: For any piece of a company, the implied valuation of that piece is its
valuation, as implied by the VCV model, under the assumption that the most recent
investors paid fair value, LP valuation 5 LP cost.
In?nite games: Games with an in?nite number of decision nodes for at least one player. (See
also Finite games.)
Initial public offering (IPO): A company’s ?rst sale of securities in public markets.
Historically, IPOs have been the most lucrative exits for VCs.
In-kind distributions: (5 Stock distributions) The distribution of stock to limited
partners. The alternative to an in-kind distribution is a cash distribution.
Integrated markets: When all investors can make investments in any country, we say that
?nancial markets are integrated. (See also Segmented markets.)
Internal rate of return (IRR): Start with a stream of cash ?ows. Compute the NPV of these
cash ?ows as a function of the discount rate. The discount rate that makes this NPV equal
to zero is the IRR.
GLOSSARY 521
In the money: If the price of an underlying asset is above (below) the strike price for a call
(put) option, we say that the option is in the money. (See also Out of the money.)
Invested capital: At any point during the life of a fund, invested capital is equal to the total
amount of capital that has already been invested in portfolio companies. For a fund that
has reached the end of its life, invested capital is equal to investment capital.
Investment capital: The difference between committed capital and lifetime fees.
$investment: The amount of cash invested by the fund in a speci?c round of investment.
Investment multiple: (5 Absolute return, 5 Realization ratio, 5 Value multiple)
Investment period: (5 Commitment period)
Investment rate (IR): (5 Plowback ratio, 5 Reinvestment rate) The percentage of a
company’s earnings that is reinvested into the capital stock of the company.
Investor expropriation: (5 Expropriation, 5 Self-dealing, 5 Tunneling)
Investor Rights Agreement: The portion of the term sheet that lists any special rights of the
investors.
IPO: Acronym for initial public offering.
IR: Acronym for investment rate.
IRR: Acronym for internal rate of return.
IV
pre
: Abbreviation for implied pre-valuation.
IV
post
: Abbreviation for implied post-valuation.
J-curve: (5 Hockey stick).
Later-stage: The de?nitions of early stage, midstage (5 Expansion stage), and later stage
are imprecise. The NVCA de?nitions (Exhibit 1-5) indicate that “capital in this stage is
provided for companies that have reached a fairly stable growth rate; that is, companies
that are not growing as fast as the rates attained in the expansion stages”.
Late-stage fund: A fund that invests predominantly in late-stage companies. (See also
Early stage fund, Multistage fund.)
LBO: Acronym for leverage buyout.
Lead investor: In a round of investment, there may be multiple investors that form a
syndicate. In this case, one of the investors will typically take the lead in organizing the
syndicate and negotiating with the portfolio company. If the syndicate receives a single
board seat, then this seat will typically be ?lled by the lead investor.
Leader-follower games: A game where one player (the leader) would like to play the same
strategy as the other player (the follower), whereas the follower would like to play a
different strategy than the leader. Notwithstanding the temporal implications of its name,
leader-follower games are typically simultaneous games.
Least-squares regression: A statistical technique where the analyst attempts to ?nd the best
equation to explain a set of data.
Leveraged buyouts (LBOs): When a company is purchased using a signi?cant amount
of debt.
Levered beta: A beta estimated from a factor model regression using the returns of a
levered asset. If a company has any debt, then the stock of that company is a levered asset.
(See also Unlevered beta.)
License: (5 R&D licensing agreement) A contract between a technology provider
(licensor) and a user of that technology (licensee). The license agreement may be
522 GLOSSARY
exclusive (only the licensee can use the technology) or nonexclusive (the licensor is free
to license the technology to other users).
Licensee: The user of technology in a license.
Licensor: The technology provider in a license.
Lifetime fees: The total amount of management fees that will be paid by limited partners
over the lifetime of a fund.
Limited partner (LP): In a private equity fund, the limited partners provide the capital,
which is then invested by the general partner.
Linear model: A model without any nonlinear interactions between any of the input vari-
ables. For example, if X and Y are input variables that determine Z, then Z 5 2X + 2Y
would be a linear model, whereas Z 5 2X * 2Y would be a nonlinear model.
Liquidation: (5 Deemed liquidation event)
Liquidation preference: In its simplest meaning, a liquidation preference describes the order
in which different security holders are paid in the event of a liquidation. For example, if
we say that the Series B preferred stock has a liquidation preference to the Series A
preferred stock, which in turn has a liquidation preference to the common stock, we are
saying that B gets paid before A, which gets paid before the common stock holders. In a
more complex meaning of the term, some preferred stock holders may have an excess
liquidation preference, which provides a multiple of the aggregate purchase price in a
liquidation. Thus, we could say that Series B has a liquidation preference to Series A,
which has a 2X liquidation preference to the common stock. In this case, we are saying
that Series B gets paid back its aggregate purchase price before Series A, which then
receives two times its aggregate purchase price before the common stock holders get
anything.
Liquidation return: The return on preferred stock in the event of a deemed liquidation
event.
Liquidity risk: The systematic risk for an asset that corresponds with movements in a
liquidity factor. (See also the Pastor-Stambaugh model.)
Lockup: An agreement between the underwriter of an IPO and the prior investors in the
company that prevents these prior investors from selling any of their shares for some
lockup period that follows the IPO.
Log return: (5 Continuously compounded return) The natural logarithm of a periodic
return.
Long position: The ownership of a positive amount of an asset. (See also Short position,
Zero-cost long-short portfolio.)
LP: Acronym for limited partner.
LP cost: The all-inclusive cost to limited partners of a fund investment: LP cost 5
$investment * (committed capital/investment capital).
LP valuation: The valuation, using option pricing methods, of the LP’s stake in an
investment. (See also GP valuation, Partial valuation.)
LP valuation equation: The equation, expressed as a portfolio of options, for the LP
valuation.
Management carve out: At the time of an exit, the portion of proceeds reserved for current
management. Management carve outs are common in cases where managerial stock
options are out of the money at exit.
GLOSSARY 523
Management fees: Regular payments made by limited partners to general partners
intended to cover the ?xed costs of operating the fund.
Management test: “Does the current management have the capabilities to make this business
work?” Along with the market test, the management test is one of the two big-picture
questions about any potential investment.
Market cap: (5 Equity market value 5 Market capitalization) For public companies, the
market capitalization is equal to the total market value (price per share times shares
outstanding) of a company’s common stock.
Market capitalization: (5 Equity market value 5 Market cap).
Market portfolio: In theory, the market portfolio in the CAPM includes all risky assets in
every market around the world. In practice, most analysts include only the common
stocks in a single country (for a domestic CAPM) or in all major world markets (for a
global CAPM).
Market premium: The expected excess return on the market portfolio.
Market risk: (5 Nondiversi?able risk, 5 Systematic risk) Market risk is the component
of asset risk that cannot be diversi?ed away. In the CAPM, market risk is described by the
beta of the security.
Market test: “Does this venture have a large and addressable market?” Along with the
management test, the market test is one of the two big-picture questions about any
potential investment.
Market valuation: Any valuation method that relies on current market prices for a company’s
securities. The market cap is an example of a market valuation for a public company; the
implied valuation is an example of a market valuation for a private company.
Mean: The expected value of a random variable.
Methodof multiples: (5 Comparable analysis, 5 Multiples analysis, 5 Relative valuation)
Mezzanine: This has two meanings within private equity—in both cases the meanings rely
on a generic de?nition of mezzanine as “middle”. In the ?rst meaning, mezzanine refers to
the “middle of capital structure”, as in subordinated debt. This debt is typically
purchased by specialized mezzanine lenders in leveraged buyout transactions. In the
second meaning, mezzanine refers to the “middle of a company’s development”, as in
the last private ?nancing round before an IPO. This second meaning of mezzanine has
gone out of favor in recent years, with most investors substituting terms like growth
capital, expansion stage, or late stage.
Midstage: (5 Expansion stage) (See also Early-stage, Late-stage.)
Midyear correction: In many DCF models, analysts estimate a single cash ?ow at the end of
each year. Because these cash ?ows would in reality be spread across the year, many
analysts shift all cash ?ows back by six months. This can be accomplished by a single
multiplication of the uncorrected NPV by (1 + r)
1/2
, where r is the discount rate.
Milestone payments: Payments made to a licensor based on achievement of speci?c
milestones. In drug development, typical milestones are the achievement of Phase II,
Phase III, and FDA approval. (See also Royalty payments, Up-front payments.)
Minimax solution: In game theory, the solution method where one player seeks to minimize
the maximum payoff of the other player.
Mixed strategy: In game theory, a strategy that includes more than one pure strategy, with
each pure strategy played with positive probability.
524 GLOSSARY
Mixed-strategy NE: A Nash equilibrium where at least one player uses a mixed strategy.
(See also Pure-strategy NE.)
Modi?ed VC method: An adjustment to the standard VC method where the analyst explicitly
take account of management fees and carried interest.
Monitoring: The collection of VC activities to watch over and help portfolio companies.
Monte Carlo analysis: (5 Monte Carlo simulation) The estimation of expected value by
computing the average from a simulated sample of observations.
Monte Carlo simulation: (5 Monte Carlo analysis)
Multifactor models: A model where expected returns are determined by factor loadings
on a set of factors. The Fama-French Model is an example of a multifactor model, with
three factors related to the market premium, the size of the company, and the growth
prospects of the company. (See also Pastor-Stambaugh model (PSM).)
Multiples analysis: (5 Comparable analysis, 5 Method of multiples, 5 Relative
valuation)
Multiple of money: When multiple of money is used in regard to fund returns, it means the
same thing as absolute return, realization ratio, and times money. When a multiple of
money (5 X) is used in regard to the return on a speci?c VC investment, it means “for
every dollar we invested, we got back $X.”
Multistage fund: A VC fund that invests across all stages. (See also Early stage fund,
Late-stage fund.)
Narrow-base formula: One of the methods used to compute the adjusted conversion price
under weighted average antidilution protections. The narrow-base formula provides
larger adjustments than does the broad-base formula.
Nash equilibrium (NE): In game theory, where all players are choosing best responses to
the strategies of the other players. In a NE, no player can bene?t by changing his strategy.
National Venture Capital Association (NVCA): The main organization for venture
capitalists in the United States.
NE: Acronym for Nash equilibrium
Net contributed capital: At any given time in the life of the fund, net contributed capital is
equal to contributed capital, less the cost basis of all exited and written-off investments.
Net income: (5 Earnings, 5 Net pro?ts)
Net invested capital: At any given time in the life of the fund, net invested capital is equal to
invested capital, less the cost basis of all exited and written-off investments.
Net investment (NI): The net amount added to a company’s capital stock in a period: net
investment 5 gross investment À depreciation.
Net pro?ts: (5 Earnings, 5 Net income)
Net return: Return computed after taking account of management fees, carried interest,
and any other investment costs.
NI: Acronym for net investment.
Nodes: In a tree, decision nodes signify where a player must make a move and risk nodes
signify where uncertainty is resolved.
Noncumulative dividends: Dividends that do not accrue across periods. (See also
Cumulative dividends.)
Nondiversi?able risk: (5 Market risk, 5 Systematic risk)
GLOSSARY 525
Nonlinear model: A model with nonlinear interactions between any of the input variables.
For example, if X and Y are input variables that determine Z, then Z 5 2X + 2Y would be a
linear model, whereas Z 5 2X * 2Y would be a nonlinear model.
Normal form: A matrix representation of a game. In a two-player game, one player’s
strategies are represented in the columns and the other player’s strategies are represented
in the rows.
Normative analysis: Research about how things “should” be. In contrast, positive analysis
is research about how things actually are.
NVCA: Acronym for the National Venture Capital Association.
Operating assets: Company assets that are necessary for the production of goods and
services.
OPP: Acronym for original purchase price.
Option to abandon: A real option to abandon a project after it has been started.
Option to delay: A real option to begin a project at a later date.
Option to expand: A real option to expand a project at a later date.
Option to extend: A real option to extend a project at a later date.
Option to shrink: A real option to shrink a project at a later date.
Option to switch: A real option to switch the underlying production process.
Option tree: A type of binomial tree showing the values of an option at each point in time.
(See also Base tree.)
Original purchase price (OPP): The price per share paid in a transaction. (See also
Aggregate purchase price (APP).)
Out of the money: If the price of an underlying security is below (above) the strike price
for a call (put) option, then the option is out-of-the-money. (Also see In the money.)
Partial valuation: The valuation of the fund’s stake, using option-pricing methods. (See also
Total valuation.)
Participating convertible preferred (PCP): Convertible preferred stock that is entitled to
a liquidation return, which includes both its redemption value and as-if conversion into
common stock. PCP is forced to convert to common stock in the event of a quali?ed
public offering.
Participating convertible preferred with cap (PCPC): Identical to PCP, except that the
liquidation return is capped, even if there is no quali?ed public offering.
Pastor-Stambaugh Model (PSM): A multifactor model with four factors related to the
market premium, the size of the company, the growth prospects of the company, and
the liquidity risk of the company. (See also Fama-French Model (FFM).)
Payment-in-kind (PIK) dividends: (5 Stock dividends) Dividends that are paid in stock.
Payoffs: In a tree, we refer to all cash ?ows, positive and negative, as payoffs.
PCP: Acronym for participating convertible preferred.
PCPC: Acronym for participating convertible preferred with cap.
PDF: Acronym for probability density function. This acronym was around for a long time
before Adobe software.
Performance-evaluation regression: The estimation of a factor model on returns gener-
ated by an investment manager. The estimate of alpha—the abnormal return—is then
interpreted as the performance of the manager.
526 GLOSSARY
Periodic return: The return over a set time period from t 2 1 to t: R
t
5 (P
t
+ D
t
)/P
t 2 1
,
where R is the periodic return, P is the price, and D is the dividend (if any).
Perpetuity: A constant payment in every period, forever.
Personal valuation: An analyst’s opinion about the value of an asset. This personal valuation
may rely almost exclusively on the analyst’s forecasts (as in absolute valuation), or
it may use market information from similar assets (as in relative valuation). In contrast, a
market valuation relies exclusively on information embedded in the price of the actual
asset or derivative securities for the asset.
Phase I: The ?rst phase of clinical trials for a drug. Phase I trials test for the safety of the drug
using healthy volunteers. (See also FDA approval.)
Phase II: The second phase of clinical trials for a drug. Phase II trials test for ef?cacy and
safety of the drug using patients who have the relevant disorder. Phase II trials differ from
Phase III trials in that the latter are much larger, take longer, and are more expensive.
(See also FDA approval.)
Phase III: The third and ?nal phase of human trials for a drug. Phase III trials test for ef?cacy
and safety of the drug using patients who have the relevant disorder. Phase II trials differ
from Phase III trials in that the latter are much larger, take longer, and are more expensive.
(See also FDA approval.)
Piggyback registration rights: Rights that allow preferred stock holders to “piggyback”
and sell their shares in an already scheduled registered transaction. Piggyback registra-
tion rights are weaker than demand registration rights, because the former cannot create a
new transaction, but must rely on other investors obtaining a registered transaction. (See
also Registration rights, S-3 registration rights.)
PIK: Acronym for payment-in-kind
Pitch meeting: A meeting where entrepreneurs attempt to sell VCs on making an investment
in their company.
Plowback ratio: (5 Investment rate (IR), 5 Reinvestment rate)
Portfolio company: A company that has received VC investment and has not yet been
exited.
Positive analysis: Research about how things “actually are”. In contrast, normative analysis
is research about how things “should be”.
Postboom period: In this book, the period since 2001. (See also Preboom, boom.)
Postmoney valuation: The $investment divided by the proposed ownership percentage.
(See also Premoney valuation.)
Preboom: In this book, the period before 1995. (See also Boom, Postboom periods.)
Preclinical: The stage of drug testing that precedes clinical trials. (See also Phase I, Phase
II, Phase III, FDA approval.)
Preferred returns: (5 Hurdle returns, 5 Priority returns)
Preferred stock: Equity that is above common stock in the capital structure.
Premoney valuation: The post-money valuation minus the $investment.
Priority returns: (5 Hurdle returns, 5 Preferred returns)
Prisoner’s dilemma: A famous game used to illustrate an arms race.
Private equity: In its broadest meaning, private equity includes all investments that cannot
be resold in public markets. In its more narrow meaning, private equity refers to a class of
GLOSSARY 527
investments, managed by private equity ?rms, which make investments in VC, leveraged
buyouts, mezzanine, or distress.
Probability density function (pdf): For a discrete random variable, the pdf evaluated at
point x is the probability that the random variable is exactly equal to x. For a continuous
random variable, the de?nition is more subtle. In standard continuous distributions, there
are an in?nity of possible outcomes, so the probability of any one outcome is vanishingly
small. To obtain probabilities from continuous functions, we need to integrate that
function over some range. The pdf is the function that we integrate: its inputs are not
exactly probabilities, but are equivalent to probabilities if integrated over a unit interval.
Proceeds: The amount of value (in cash and stock) that is received in an exit.
Proposed%: The shorthand we use in equations to represent the proposed ownership
percentage.
Proposed ownership percentage (5 Proposed%): In any given transaction, the proposed
ownership percentage represents the percentage of fully diluted shares that the VC is
proposing to buy.
Proprietary deal ?ow: When a private equity investor receives investment opportunities
that are not offered to anyone else, we say that he has proprietary deal ?ow. (See also Deal
?ow, Sourcing.)
PSM: Acronym for Pastor-Stambaugh model.
Pure strategy: In game theory, if a player chooses the same move every time, we say that he
is playing a pure strategy. In contrast, a mixed strategy is a combination of several
moves, each with a positive probability of being played.
Pure-strategy NE: A Nash equilibrium where all players choose pure strategies.
QIBs: Acronym for quali?ed institutional buyers.
QPO: Acronym for quali?ed public offering.
QREs: Acronym for quali?ed research expenses.
Quali?ed Institutional Buyers (QIBs): Large institutional investors, who are permitted to
purchases securities under exceptions to the SEC’s registration rules. The main class of
QIBs are institutions that manage more than $100M.
Quali?ed public offering (QPO): An IPO above a minimum size and above a minimum
per-share price. These minimums are speci?ed in the term sheet.
Quali?ed Research Expenses (QREs): R&D expenses that qualify for the R&D tax credit
in the United States.
r: Symbol for the cost of capital.
R: Symbol for the return on capital
R&D: Acronym for research and development.
R&D licensing agreement: (5 License)
R&D tax credit: A program by a government to reduce the tax liability of companies in
some proportion to their R&D expenses. In the United States, the federal government
provides the largest tax credit, and many states and municipalities have smaller programs.
Raised: (5 Closed)
Random-expiration (RE) option: An option with a random and unknown expiration date.
Random-expiration binary call option (BC(X)): A binary call option with a random and
unknown expiration date.
528 GLOSSARY
Rapid-growth period: In the reality-check DCF model, the rapid-growth period is between
exit and graduation.
RE option: Abbreviation for random-expiration option.
Reading the exit diagram: The translation of an exit diagram into a portfolio of random-
expiration options.
Real options: An option on a real asset. In contrast, ?nancial options are options on ?nancial
assets.
Reality-check DCF: A model that uses aggressive data-driven assumptions for growth,
margins, and capital ef?ciency in order to get an absolute valuation for the exit value.
Realization ratio: (5 Investment multiple, 5 Absolute return, 5 Value multiple)
Realized return: This term has two meanings: The ?rst meaning, which is generic for all
?nance, is a synonym for historical returns. The second meaning, specialized for private
equity, refers to a fund’s returns from all exited investments. (See also Unrealized
returns.)
Recombine: If a binomial tree recombines, then each additional step in the tree only
adds one additional branch. In a nonrecombining tree, each additional step doubles the
number of branches. In the CRR model, the up moves and down moves are reciprocals of
each other. Thus, from any starting price, if an underlying asset follows an up move with a
down move, the base tree recombines at the starting price. If the underlying asset pays a
dividend that is proportional to the stock price, then the tree will recombine at a price
slightly below the starting price. If the underlying asset pays a ?xed cash dividend, then
the tree does not recombine.
Redeemable preferred (RP): Preferred stock that pays a redemption value on liquida-
tion, but does not offer the holder the option of conversion to common stock.
Redemption: The act of turning in preferred stock in return for the redemption value.
Redemption rights: The right of preferred stock holders to redeem their stock outside of a
deemed liquidation event. This right is usually less powerful in practice than it is on
paper because preferred stock holders, as equity investors, do not have the power to force
a company into bankruptcy if the company cannot pay the redemption.
Redemption value (RV): The amount paid to the holder of preferred stock on redemption. In
the absence of dividends or excess liquidation preferences, the redemption value is equal
to the aggregate purchase price.
Redemption Value per Share (RVPS): The redemption value of for a speci?c class of
convertible preferred stock divided by the number of shares of common stock on
conversion of that class.
Registration rights: As speci?ed in the term sheet, registration rights give the holders the
power to sell some of their shares in a registered transaction. These rights come in
several different strengths, with demand registration rights being the strongest. (See
also S-3 registration rights, Piggyback registration rights.)
Registered transaction: A transaction on a public exchange that has been approved by the
Securities and Exchange Commission. Restricted stock becomes unrestricted after it is
sold in a registered transaction.
Reinvestment rate: (5 Investment rate (IR), 5 Plowback ratio)
Relative valuation: The valuation of an asset based on the market values of similar assets.
(See also Absolute valuation.)
GLOSSARY 529
Replicating portfolio: A combination of risk-free bonds and risky assets that provides
exactly the same payoffs as a derivative asset.
Required investment: The amount of capital needed for a round of VC investment.
Research and development (R&D): Investment made in basic research, applied research,
or development projects.
Restricted stock: Stock that cannot be sold in a public market, except through a registered
transaction or through a Rule 144 exception to the registration rules. Once a stock has
been sold in a registered or Rule 144 transaction, it becomes unrestricted stock.
Restrictive covenants: Contractual terms in limited partnership agreements that restrict the
activities of the general partner.
Return on capital (R): For a company, the return on capital is an (adjusted) operating pro?t
divided by operating assets. For an investment manager, the return on capital is the
periodic return on the assets under management.
Return on investment (ROI): For a company, ROI is de?ned the same way as R, except that
the pro?ts and assets are measured only for the newly invested capital.
Right of ?rst offer: If Investor X has a right of ?rst offer for investor Y’s shares, then Y must
give X the option to bid on Y’s shares before those shares are offered to anyone else. If Y
turns down X’s offer, then she can sell her shares to other investors, but only if she obtains
a price above X’s initial offer. (See also Take-me-along 5 Tagalong, 5 Right of ?rst
refusal, 5 Dragalong, 5 Transfer restrictions.)
Right of ?rst refusal: The right of ?rst refusal is more powerful than the right of ?rst offer.
If Investor X has a right of ?rst refusal for investor Y’s shares, then Y must give X the
option to buy on Y’s shares at any price that Y has negotiated with an outside bidder. In
this case, few outside bidders are likely to make an offer because they know that X can
just come in and take away the deal. (See also Take-me-along 5 Tagalong, 5 Right of
?rst offer, 5 Dragalong, 5 Transfer restrictions.)
Risk-free rate: The rate of return on securities that have no systematic risk. In the United
States, federal government debt is often considered to be risk free (5 riskless rate).
Riskless rate: (5 risk-free rate).
Risk-neutral: We say that an investor is risk-neutral if her utility function in wealth is a
straight line.
Risk-neutral probabilities: The probabilities that would have to exist if all investors were
risk-neutral and asset prices were the same as in the real world.
Risk factor: (5 Factor)
Risk node: The point in a tree where uncertainty is resolved along multiple branches.
ROI: Acronym for return on investment
Round: (5 Financing round)
Royalty payments: When a product is sold as part of a license agreement, the licensee will
sometimes pay a percentage of sales or gross pro?t to the licensor. (See also Milestone
payments, Up-front payments.)
RP: Acronym for redeemable preferred.
Rule 144: A Securities and Exchange Commission rule that provides exceptions that allow
the public sale of (otherwise) restricted stock.
530 GLOSSARY
Rule 144A: A Securities and Exchange Commission rule that allows the private sale of
restricted stock to quali?ed institutional buyers.
RV: Acronym for redemption value.
RVPS: Acronym for redemption value per share.
S-3 registration rights: A type of demand registration right that only takes effect once the
company is already public. S-3 rights are weaker than regular demand registration rights
because the former cannot be used to force a private company to go public. (See also
Demand registration rights, Piggyback registration rights, Registration rights.)
Sand Hill Econometrics (SHE): A company that produces the Sand Hill Index
s
and its
successor (DowJones Index of Venture Capital), a gross-return index for the VC industry.
Sand Hill Road: The street in Menlo Park, California, that is home to many of the world’s
top VC ?rms.
Screening: The activities of analyzing companies, performing due diligence, and making
investment decisions.
Second Round (Series B): The second occurrence of VC investment. (See also Financing
Round, First Round (Series A).)
Seed stage: An investment in an idea that has not yet become a company. Seed-stage
investments are typically made by angels, not by VCs.
Segmented markets: When investors in countries A and B are unable to make investments in
the other country, we say that these two markets are segmented (See also Integrated
markets.)
Self-dealing: (5 Expropriation, 5 Investor expropriation, 5 Tunneling).
Sequential game: A game where players take turns making moves. (See also Simultaneous
game.)
Series: In VC transactions, preferred stock is referred to by a series letter: Series A, Series
B, etc. The letter usually refers to the round of investment, with Series A referring to ?rst
round and Series B referring to second round, etc. Most of the time that a VC refers to a
“Series A” investment, they mean this as a synonym for “?rst round”. Nevertheless, in
some cases, a VC round will include multiple series, so it is possible for the ?rst round of
investment to include shares labeled as Series A and as Series B.
SHE: Acronym for Sand Hill Econometrics.
Short position: The ownership of a negative amount of an asset. (See also Long position,
Zero-cost long-short portfolio.)
Simple interest: Interest that does not compound (i.e., 5 percent simple interest on $100
would pay $5 every year, even if the previous payments were accrued to the face value).
(See also Compound interest.)
Simultaneous game: A game where players make moves at the same time. (See also
Sequential game.)
Sourcing: The activities performed by VCs to generate deal ?ow.
Special situations: (5 Distress investing)
SPNE: Acronym for subgame-perfect Nash equilibrium.
Stable-growth period: In the reality-check DCF model, the stable-growth period follows
graduation.
GLOSSARY 531
Stale values: When live VC funds report their performance, active investments are usually
reported at the postmoney valuation of their most recent round. Because many of these
companies have had material changes since the last round, we say that these values are
stale. When evaluating the performance of the VC industry using a factor model, we
adjust for stale values by including past observations of the factors in the regression.
Standard VC method: The name for the group of techniques used by VCs to make invest-
ment decisions. The main idea of the standard VC method is to estimate a value for the
company conditional on a successful exit, and then discount that value back to the present
using a high target rate of return. (See also Modi?ed VC method.)
Star fund: A VC fund with committed capital of at least $50M and a value multiple of ?ve
or greater.
Startup stage: A pre-marketing stage of company development that may involve product
development, market research, building a management team, and developing a business
plan.
Step vesting: When some set percentage of options (or stock) becomes vested on a speci?c
date (e.g., if options are 25 percent step vested each year, then the vesting increases from
25 percent to 50 percent to 75 percent to 100 percent over a four-year period). (See also
cliff vesting.)
Stock dividends: (5 Payment-in-kind (PIK) dividends)
Strategic alliance: A long-term contract between two companies that facilitates work toward
a common goal.
Strategic investing: Investing with goals beyond the maximization of ?nancial returns.
Strategy: A complete description of a player’s choices at every decision node.
Strategy pair: The strategies of both players in a two-player game.
Strike price: (5 Exercise price) The price that is paid (received) to purchase (sell) stock
when a call (put) option is exercised.
Style adjustments: Adjustments made to the CAPM to re?ect differential risks for various
classes of stocks. The style adjustments in the Pastor-Stambaugh model are for size,
value, growth, and liquidity.
Subgame-perfect Nash equilibrium (SPNE): A set of strategies that represent Nash equi-
libria on all subgames.
Subgames: A subgame includes any collection of decision nodes that can be “snipped” from
the extensive form without cutting a closed curve around those nodes.
Successful exit: An exit where the company has executed on optimistic (but reasonable)
expectation from the time of the VC investment. Most successful exits end with an IPO or
high-value acquisition.
Superstar fund: A VC fund with committed capital of at least $50M and a value multiple
of ten or greater.
Survivor bias: A statistical bias caused when the data sample includes a disproportionate
number of entries from surviving entities. For example, there would be survivor bias if a
database of VC funds was more likely to include historical data from long-lived VC
?rms.
Syndicate: When multiple VCs invest in the same round, we call this group a syndicate.
Systematic risk: (5 Market risk, 5 Nondiversi?able risk)
532 GLOSSARY
Tagalong: (5 Take-me-along) If shareholder A has a tagalong right relative to shareholder
B, then A can force B to include A in any sale of shares made by B. Typically, this right
gives A a pro rata claim on any stock sales. (See also Right of ?rst offer, Right of ?rst
refusal, Dragalong, Transfer restrictions.)
Takedown: (5 Capital call, 5 Drawdown)
Take-me-along: (5 Tagalong) (See also Right of ?rst offer, Right of ?rst refusal,
Dragalong, Transfer restrictions.)
Target multiple of money: The average multiple of money that a VC expects in a
successful exit. The target multiple of money is a key input in the venture capital
method of valuation.
Target return: Similar to the target multiple of money, but expressed as an annual return.
Technical risks: In R&D investment, the risks that the project will fail for nonmarket
reasons, usually scienti?c or engineering failures. (See also Business risks, Competitive
risks.)
Term Sheet: The summary document describing the key terms of a proposed VC investment.
(See also Charter, Investor Rights Agreement.)
Terminal node: A ?nal point on a game tree. (See also Decision node, Risk node.)
Times money: (5 Absolute return, 5 Value multiple, 5 Multiple of money)
Top-quartile fund: A fund with an IRR among the top 25 percent of all funds in the same
vintage year.
Top-tier ?rm: A generic industry term meant to denote a high reputation ?rm. In this book,
we classify six Tier A ?rms and nine Tier B ?rms in Exhibit 5-2 of Chapter 5.
Total valuation: An analyst’s personal valuation for an entire company. (See also Partial
valuation.)
Tranche: Generically, within ?nance a tranche refers to a slice of the capital structure of a
company or security offering. Within VC, a tranche refers to a slice of a ?nancing round,
with different tranches delivered to the portfolio company at different times.
Transfer restrictions: Any restriction that prevents a shareholder from selling any part of
her shares. (See also Take-me-along 5 Tagalong, 5 Right of ?rst offer, 5 Right of
?rst refusal, 5 Dragalong.)
Trees: Generically, a perennial woody plant with a main trunk. Within economics, a
graphical representation of decisions and risks. (See also Event trees, Decision trees,
Binomial trees, Game trees.)
Tunneling: (5 Investor expropriation, 5 Self-dealing)
Two-by-two games: Games with two players each with two possible strategies.
Underlying asset: An asset on which an option has been written. (See also Derivative
assets.)
Underwriter: Financial intermediary that takes possession of an asset or a risk. In capital
markets, this possession is of a very short duration, with the assets transferred to the
ultimate investors. In these markets, the underwriter’s main job is to identify and sell to
these ultimate investors.
Unlevered beta: A beta estimated from a factor model regression for an unlevered asset.
The equity in an all-equity company is an unlevered asset.
GLOSSARY 533
Unrealized returns: In a VC fund, the unrealized returns are the estimated returns from
investments that have not yet been exited. (See also Realized returns.)
Unrestricted stock: Stock that can be sold to any investor in a public market.
Upfront payments: Payments from a licensee to a licensor made at the beginning of a
license agreement. (See also Milestone payments, Royalty payments.)
Value multiple: (5 Investment multiple, 5 Realization ratio, 5 Absolute return)
Variance: A measure of the dispersion of a random variable. (See also Covariance.)
VC: Acronym for venture capital and for venture capitalist.
VCs: Acronym for venture capitalists.
VC ?rm: (5 Firm)
VC fund: (5 Fund)
VCV model: A Web-based model, developed as a companion to Part III of this book, which
can be used to estimate partial valuation, LP valuation, GP valuation, and implied
valuation.
Venture capital (VC): Capital used by specialized ?nancial intermediaries for investment in
private companies with the intention of helping these companies to grow.
Venture capitalists (VCs): Financial intermediaries who invest in and monitor private
companies with the intention of helping these companies to grow.
Venture capital method of valuation: The name for the group of techniques used by VCs to
make investment decisions. The two versions studied in this book are the standard VC
method and the modi?ed VC method.
Venture period: In the reality-check DCF model, the period that precedes the exit.
Vesting: In VC transactions, managerial stock ownership and option claims are typically
granted over time, in a process called vesting. For speci?c rules of vesting, see the entries
for cliff vesting and step vesting.
Vintage year: Typically de?ned as the calendar year that a VC fund began investing. Fund
performance is often compared with other funds with the same vintage year.
W
A
(cap): Equation shorthand for the cap point.
Weighted-average antidilution: A version of antidilution protection, where the adjusted
conversion price is a weighted average of prices paid by all investors. (See also Broad-
base formula, Narrow-base formula, Full-ratchet antidilution.)
Zero-cost long-short portfolio: A portfolio with an equal amount of investment on both
long and short positions. These zero-cost portfolios are used to construct factors.
Zero-sum games: A game where the sum of the payoffs to all players is zero. (See also
Constant-sum games.)
534 GLOSSARY
INDEX
Abnormal returns, 68, 512
negative, 68
positive, 68
Absolute return, 55, 512
Absolute valuation, 179, 512
Accel Partners, 89
Accrued cash dividends, 153,
282À284, 512
Adjusted conversion price, 173, 513
Adjusted conversion rate, 173, 513
Aggregate purchase price (APP),
149, 252, 513
Alpha, 67, 74, 79, 513
Alternative investments, 5, 7À8
American option pricing, 242À243, 513
American Research and Development
Corporation (ARD), 10
Americanization, 87
Am-tree worksheet, 416
Analysis
normative, 431
positive, 431
Angel investors/angels, 4, 513
Angel shares, exit diagram for, 309,
Annualized returns, 47, 513
Antidilution provisions, 152, 154,
173À176
adjusted conversion price, 173
adjusted conversion rate, 173
full-ratchet, 173
weighted-average, 173
Applied research, 342, 513
Arbitrage, 237
Arms races, 424, 513
As-if conversion, 513
Assets
derivative, 232, 516
underlying, 232, 533
At the money, 242, 513
AUTO Calculator, 255, 484
Banana utility
with bird risk, 70
with weather risk, 72
Barriers to entry, 205, 513
Base trees, 403, 513
base-tree worksheet, 407, 412
Base-case option-pricing assumptions,
253À254
Basic research, 342, 513
Battery Ventures, 91
BC(X) , 513
Benchmark Capital, 89, 126, 138
Best response, 423, 513
Best VCs, 83À98. See also Portfolio ?rms
Group A, 89À91
Accel Partners, 89
Benchmark Capital, 89
Charles River Ventures, 90
Kleiner Perkins Cau?eld & Byers
(KPCB), 90
Matrix Partners, 91
Sequoia Capital, 91
Group B, 91À95
Battery Ventures, 91
Doll Capital Management (DCM), 92
Draper Fisher Jurvetson (DFJ), 92
Institutional Venture Partners, 93
InterWest Partners, 93
Menlo Ventures, 93
New Enterprise Associates (NEA),
93À94
Summit Partners, 94
Technology Crossover Ventures
(TCV), 94
Beta, 66, 74, 79, 513
Binary options, 291À292, 386, 513
Binomial trees, 355, 400À418, 513. See also
Black-Scholes equation; Dividends
base tree, 403
CRR model, 406
535
Binomial trees (continued)
dividends, 411À417
multiple strike prices and early exercise,
409À411
warrants, 409
option tree, 403À404
recombine feature, 403
Bintree.xls spreadsheet, 406À410
Black-Scholes equation/formula, 231,
238À242, 244, 250À251, 368,
400À408, 513
binomial trees and, 400À408
Board of Directors, 160
Board representation, 95À96, 157
Bond values, 235
Boom period, 12À13, 513
Branches, event tree, 358, 514
Breakeven valuation, 252, 514
Broad-base formula, 174, 514
Burn rate, 143, 514
Business plan, 137, 514
Business risks, 347, 514
Busy boards, 96
Buyout, 99
California Public Employee Retirement
System (CALPERS), 61
Californization, 88
Call option, 40, 232, 514
in a decision tree, 401
delay, 381
expand, 381
extend, 381
Cambridge Associates (CA), 50, 59, 112, 118,
124, 514
Cap point, 169, 514
Capital
calls, 21, 514
contributed, 35, 515
cost of, 224À226, 516
net contributed, 35, 525
net invested, 32, 525
Capital asset pricing model (CAPM), 65À69,
514. See also Global CAPM
domestic CAPM, 112
least-squares regression, 67
market risk, 67
nondiversi?able risk, 67
performance evaluation regression, 68
re?ecting covariance of asset’s returns, 67
Capitalization, 150
capitalization table, 148, 514
Carried interest, 11, 32À39, 247À248, 514
carried interest basis, 33, 514
clawbacks, 33, 515
contributed capital, 35, 515
net contributed capital, 35, 525
percentage level of, 33
priority returns, 33, 35, 527
refund of, 37
timing of, 34À35
write downs (partial losses), 36
Carry basis, 514
Cash distributions, 514
Cash ?ow (CF), 200
Catch-up provision, priority returns,
35À36, 514
Certi?cate of Incorporation. See Charter
Channels, 142À143
Charles River Ventures, 90
Charter, 151À155, 514
anti-dilution provisions, 152
deemed liquidation event, 151, 516
dividends, 151, 153
liquidation preference, 151, 153À154, 523
mandatory conversion, 152, 154
optional conversion, 152
protective provisions, 151
redemption rights, 152, 154À155
voting rights, 151, 154
Clawbacks, 33, 514À515
Cli vesting, 159, 515
Clinical trials, 345, 515
Closing, 135, 515
Coase, Ronald, 14
Collateralized debt obligations (CDOs), 352
Collateralized loan obligations (CLOs), 352
Commitment period, 21, 515
Committed capital, 21, 515
by limited partners, 28
Common stock, 150, 167, 515
exit diagram for, 167
Comparables analysis, 214À228, 515
choice of comparable companies, 214
choice of valuation measures, 214
choosing comparable companies, 219À224
cost of capital estimation, 224À226
EV/EBIT, 215
EV/EBITDA, 216
EV/Employees, 217
536 INDEX
EV/Revenue, 216
Price/Book, 217
Price/Earnings, 216
Compensation, venture capital, 32
Competition, 142
Competitive advantage, 205, 515
Competitive risks in drug development,
347, 515
Complex structures, 320À336. See also
Management carve-outs
dealing with partners, 327À329
Series F, exit diagram for, 332
Compound interest, 153, 515
Compound return, 46, 515
Comps. See Comparables analysis
Constant-sum games, 422, 515
Continuous probability distributions
simulation with, 362À373
Continuous random variables, 357, 362, 515
Continuously compounded returns, 238, 515
Contributed capital, 35, 515
Conversion condition, 163À164, 515
Conversion-order shortcut, 278, 515
Conversion point, 163, 515
Convertible preferred (CP) stock, 163, 516
conversion condition, 163À164
exit diagram, 164À165
participating convertible preferred (PCP),
165
participating convertible preferred with cap
(PCPC), 166
Series A CP, 172
Convertible preferred (CP) valuation, 261À263
combining RP and CP, 266À268
comparing RP and CP, 268À269
with excess liquidation preferences or
dividends, 263À266
Coordination games, 431, 516
Corporate Governance, 96
Corporate venture capital, 6, 516
Cost basis, 32
Cost of capital estimation, 224À226, 516
Cost of capital for VC, 65À82. See also Beta
and the banana birds; Capital asset
pricing model (CAPM)
estimating, 74À79
CAPM estimations for VC indices, 74
liquidity risk, 75, 77
SIZE factor, 76
stale values, 75, 78
style adjustments, 75À77
VALUE factor, 76
Country beta, 113, 516
Country risk, 108, 516
global CAPM, 116À117
Covariance, 516
Crossover investing, 94, 516
CRR model (Cox-Ross-Rubenstein),
406, 516
Crystal ball
s
, guide to, 487À511
cumulative frequency chart, 497
decision tables, de?ning, 506À511
decision variables, de?ning, 506À511
dynamic assumptions, de?ning,
505À506
spreadsheet setup for, 489
distribution gallery, 490
forecast, de?ning (Step 2), 491À492, 495,
499, 502
random number assumptions, de?ning
(Step 1), 489À490, 495, 498, 500
results analysis (Step 5), 493, 496,
499, 502
simulation, running (Step 4), 493,
496, 499, 502
simulation run preferences, setting (Step 3),
492À493, 496, 499, 502
toolbar, 488
Cultural dierences, in VC activity 108
Cumulative distribution function (cdf),
362, 516
log-normal CDF, 369
normal CDF, 368
triangular CDF, 372
uniform CDF, 363
Cumulative dividend rights, 153, 516
Currency risk, global CAPM, 115À116
Customers, 141
Dark Side of Valuation, The, 195
Deal ?ow, 137, 516
proprietary deal ?ow, 137
Decision nodes, 379, 516
Decision trees, 355, 379À381, 516
commuting options, 379
with exit, 380
pruned, 380
decision nodes, 379
Deemed liquidation event, 151, 153, 516
Demand registration, 155, 158, 516
INDEX 537
Demand side, 83
Derivative assets, 232, 516
Discounted cash ?ow (DCF) analysis, 180,
195À213, 517. See also Graduation
value; Reality-check model DCF
model
concepts, 196À198
graduation, 196
leverage of VC-backed ?rms, 199
mechanics, 198À203
phases of growth, 196
rapid-growth period, 196
stable-growth period, 196
venture period, 196
Discrete random variables, 357, 362, 517
Distress investing, 8, 517
Diversi?able risk, 66, 517
Dividend preference, 153, 517
Dividends, 151, 153, 259À261, 411À417
am-tree worksheet, 416
base tree, 412
Fuelco’s problem, 416À417
in later rounds, 282À285. See also under
Later-round investments
option tree, 413
Doll Capital Management (DCM), 92
Dollar-denominated bonds, sovereign spread
of, 109
Domestic beta, 113, 517
Domestic CAPM, 112, 517
Dominant strategy, simultaneous game,
424, 517
Doriot, George, 10
Dow Jones Report, 146À148
Down round, 154, 517
Down rounds, question of, 314À317
Series C, exit diagram for, 315À316
Dragalong, 517
Draper Fisher Jurvetson (DFJ), 92
Drawdowns, 21, 517
Drug development, 345À348, 445À455
Investigational New Drug (IND), 346
risks
business, 347À348
competitive, 347À348
technical, 347
stages, 345
FDA approval, 345
Phase I, 345À346
Phase II, 345À346
Phase III, 345
preclinical, 345
Drugco, 395À397
newdrug
DCF model for, 397
decision tree for, 396
Due diligence, 9, 135, 140, 517
Early stage, 517
EarlyBird Ventures (EBV), 22À23, 43À44
Early-stage fund, 21, 517
Earnings before Interest and Taxes (EBIT),
200, 517
Earnings before interest, taxes, depreciation,
and amortization (EBITDA), 215
eBay, 138À139
Economic pro?ts, 84
Economics of VC, 83À86
demand side, 83
supply side, 83À85
Employee stock options, 157À159
Energy innovation, 348À349
fuel cell project, 349
Energy, 455À464
Enterprise value (EV), 199, 215, 517
Entrepreneurial ecosystem, 103À104, 517
Entrepreneurial self-con?dence, 110
Entry game, 433
extensive form, 434
normal form, 435
Equilibrium concepts, 423, 518
Equilibrium strategy, 423, 518
Equity betas, 225
Equity market capitalization, 215
Equity market value, 518
European Call-Option Calculator, 240
European options, 232À234, 518
call option, 232
European put, 233
expiration diagram, 233
put option, 234
European put, 233, 518
Event trees, 355, 357À362, 518
branches, 358
?rst ten draws, 359, 361
risk node, 358
with three risk nodes, 361
terminal node, 358
Excess liquidation preferences, 154, 257À259
Excess returns, 518
538 INDEX
Exercise price, 518
Exit diagram, 164À165, 518
reading, 245À247
Exit diagrams, 518
for angel shares, 309
for carried interest, 247
for common stock, 167
for employees’ shares, 310
for management carve-out, 322, 325
for participating convertible preferred
(PCP), 169
for participating convertible preferred with
cap (PCPC), 170
reading, 245À47
for redeemable preferred (RP), 168
for remaining shares, 323, 326
for Series A, 172, 255, 258, 260, 262,
264À265, 267
for Series B, 274, 275, 313
for Series C, 315
for Series E, 322, 326
for Series F, 302
Exit valuation, 178À180, 518
absolute valuation, 179
relative valuation, 179
Expansion stage, 6, 518
Expected holding period, 518
Expected retention percentage, 178,
182À183, 518
Expected returns, 48, 518
Expected terminal value, 367
Expenses, 155
Expiration date, 232, 518
Expiration diagram, 233, 519
Expiration, 160
Expropriation, 104, 519
Extensive form, game theory,
420À421, 519
Factor loadings, 75, 519
Factor model, 519
Factors, 75, 519
SIZE factor, 76
VALUE factor, 76
Fama-French model (FFM), 75, 519
Fees
lifetime, 30, 523
management, 11, 30À32, 43À45, 524
Financial intermediary, 3, 519
Financial options, 232, 519
Financing round, 15, 519
?rst round (or Series A), 15
second round (or Series B), 15
Finite games, 438, 519
Firms, 21À27, 519
First Round (Series A), 519
FLEX Calculator, 256, 484
Folk theorem, 438, 519
Follow-on investments, 21, 519
Food and Drug Administration (FDA),
345, 519
Founders’ stock, 160À161
Freedom of Information Act (FOIA), 61
Full-ratchet anti-dilution protection,
173, 520
Fully diluted basis, 148, 520
Fully diluted share count, 148, 520
Fund returns, 53À62
de?nitions, 53À59
evidence, 59À62
gross value multiple (GVM), 57À58, 520
internal rate of return (IRR), 54, 521
J-curve, 55À56, 522
top-quartile fund, 60
Venture Economics (VE), 59
VE median and top-quartile returns by
vintage year, 60
Fund-of-funds (FOF), 29, 520
Funds, 21À27, 520
EarlyBird Ventures (EBV), 22À23
early-stage fund, 21
general partner (GP) for, 21
late-stage fund, 21
limited partners (LPs), 21, 27À30. See also
individual entry
multistage fund, 22
Game theory, 419À444
coordination game, 431
description, 419À422
extensive form, 420À421
normal form, 420
normative analysis, 431
odds-and evens-game, extensive
form, 422
odds-and-evens game, normal form, 422
payos, 420
positive analysis, 431
prisoner’s dilemma, 419À421
and real options, 438À443
INDEX 539
Game theory (continued)
sequential games, 420, 433À438. See also
individual entry
simultaneous games, 420, 423À433. See
also individual entry
standards game
extensive form, 432
normal form, 433
strategies, 420
zero-sum games, 422
Game trees, 355, 520
Gatekeeper, 50, 520
General partners (GP), 3, 21À41, 520
income sources, 26À27
carried interest, 26
management fees, 26
restrictions on activities of, 39, 41
Geometric mean, 218, 520
Global beta, 520
Global CAPM, 112À114, 520
extensions to, 114À117
country risk, 116À117
currency risk, 115À116
segmented markets, 117
style adjustments, 114
objective, 114À117
Global distribution of VC investing, 99À111
continental Europe and Asia lagging in,
reasons for, 101À102
country risk, 108
cultural dierences, 108
entrepreneurial ecosystem, 103À104
exits, 101
law and corporate governance, 104À108
dollar-denominated bonds, sovereign spread
of, 109
entrepreneurial self-con?dence, 110
high-tech private-equity investment,
100À101
Asia-Paci?c region, 100
European GDP, 100
Israel, 100
Sweden, 100
United Kingdom, 100
United States, 100
Global Entrepreneurship Monitor, 109À111
Global market premium, 520
Global multifactor model for VC, 118À119
Global Private Equity Report (GPER), 99
Google, 138À139
Graduation, 196, 520
Graduation value, 204À207, 520
barriers to entry, 205
competitive advantage, 205
return on capital as a function of NI, 205
Gross investment, 520
Gross-Return Index, 48À50
Gross returns, 47, 520
Gross value multiple (GVM), 57À58,
125, 520
for ?rst-round investments, 127À128
acquisitions, 127
IPOS, 127
for second-round investments, 130À131
acquisitions, 130
IPOS, 130
for third-round investments, 133À134
acquisitions, 133
IPOS, 133
Growth capital, 7, 520
Growth companies, discounted-cash-?ow
analysis, 195À212
Growth factor, 520
Hamilton Lane Advisors, 59
Harmonic mean, 218, 520
Health care, investment pattern in, 15
Hedge funds, 6, 521
private enquiry and, 7
High-tech private-equity investment, 100
Historical returns, 48, 521
History of venture capital, 10À14
boom period, 12À13
limited partnerships, 11
pension funds, 12
postboom period, 12À13
preboom period, 12
pro?t sharing, 11
Hockey stick pattern of returns, 55, 521
Human Resources, 97
Human trials, 521
Hurdle returns. See Priority returns
Idiosyncratic risk, 66, 521
Implied GP valuation, 311, 521
Implied LP valuation, 311, 521
Implied partial valuation, 311, 521
Implied post-valuation (IV
post
),
305À306, 521
Implied pre-valuation (IV
pre
), 311, 521
540 INDEX
Implied valuation, 305À319, 521. See also
Portfolio value, measurement; Post-
money valuation
confusion, avoiding, 317À318
In the money, 242, 522
Index
gross-return, 48À50
net-return, 50À53
Industry, investments by, 15À18
Industry, venture capital (VC), 3À20
funds ?ow in, 4
Industry returns, 46À53
annualized returns, 47
compound return, 46
de?nitions, 46À48
expected returns, 48
gross returns, 47, 48À50
historical returns, 48
net-return index, 50À53
net returns, 47
periodic return, 46À48
realized returns, 48
Industry Statistics, 198
In?nite games, 438, 521
Information technology (IT), investment
pattern in, 15
Initial public oering (IPO), 3, 101À102, 521
In-kind distributions, 158, 521
Inputs sheet, example of, 408, 416
Inputs tree, example of, 410
Inputs worksheet, 406À408, 410
Institutional Venture Partners, 93
Integrated markets, 111, 521
Interest
carried, 247À248
compound, 153, 515
simple, 153, 531
Internal corporate funds for R&D, 350
Internal growth, 6
Internal rate of return (IRR), 54, 521
International VC, 111À119
baseline model, 112À114
country beta, 113
domestic beta, 113
global CAPM, 112À114. See also
individual entry
cost of capital for, 111À119
global multifactor model, 118À119
InterWest Partners, 93
Invested capital, 32, 522
Investigational New Drug (IND), 346
$Investment, 148, 522
Investment Benchmark Reports (IBR), 59
Investment capital, 30, 522
Investment multiple, 522
Investment period, 21, 522
Investment process, 135À144. See also
Analysis of VC investments
channels, 142À143
closing, 135
competition, 142
customers, 141
due diligence, 135, 140
management test, 137À139, 141
market test, 137À139, 141
money, 143
partners, 143
pitch meeting, 140
post-term-sheet step, 140
preterm-sheet step, 140
product, 142
projections, 142
screening, 135, 137, 140
technology, 142
term sheet, 135
terrible things, 144
themes, 136
transaction terms, 143
Investment rate (IR), 200, 522
Investment recommendation, 183
Investor director approval, matters requiring,
156, 158
Investor expropriation, 104, 522
Investor Rights Agreement, 146,
155À159, 522
board matters, 157
demand registration, 155
employee stock options, 157, 158À159
expenses, 155
key person insurance, 157
lockup, 155
management and information rights, 156
matters requiring investor director
approval, 156, 158
non-competition and non-solicitation and
agreements, 157
non-disclosure and developments
agreement, 157
piggyback registration, 155
registrable securities, 155
INDEX 541
Investor Rights Agreement (continued)
registration on form S-3, 155
registration rights, 155, 158
right to maintain proportionate
ownership, 156
Investors, 148À149
Israel, 100
Japan, 100
J-curve, 55À56, 522
Key person insurance, 157
Kleiner, Perkins Cau?eld & Byers
(KPCB), 61, 90
Later stages, 16
Later-round investments, 272À289
conversion order shortcut, 277À278, 515
dividends in later rounds, 282À285
accrued cash dividends, 282À284
payment-in-kind (PIK) dividends,
284À285, 515
Series B, 272À276
Series C, 278À282
beyond Series C, 285À288
Late-stage fund, 21, 522
Latin America, 104
Law, corporate governance and, 104À108
Lead investor, 91, 522
Leader-follower game, 428, 522
extensive form, 429
normal form, 430
Least-squares regression, 67, 522
Leveraged buyout (LBO) transactions,
7À8, 522
Levered betas, 224, 522
License, R&D, 353, 522
licensee, 523
licensing agreement, 353
licensor, 523
Lifetime fees, 30, 523
Limited partners (LPs), 3, 21, 27À30, 523
committed capital by, 28
corporations, 29
endowments, 28
?nancial institutions, 28
foundations, 28
individuals and families, 29
pension funds, 27
intermediaries in, 29
Linear model, 523
Monte Carlo simulation, 366
Liquidation preference, 151, 153À154, 523
Liquidation return, 523
Liquidity risk, 75, 77, 523
Lockup, 155, 159, 523
Log-normal distribution, 370
Log returns, 238, 523
Long position, 523
Major Investor, 156
Management and information rights, 156
Management carve-outs, 320À327, 523
exit diagram for, 322, 325, 333
remaining shares, exit diagram for,
323, 326
Series E, exit diagram for, 322, 326
Management fees, 11, 30À32, 524
coverage by, 32
investment capital, 30
lifetime fees, 30
realized investments, 32
unrealized investments, 32
Management test, 137À139, 141, 524
Mandatory conversion, 152, 154
Market cap, 215, 524
Market capitalization, 215, 524
Market portfolio, 524
Market premium, 66, 524
Market risk, 67, 524
Market test, 137À139, 524
Market valuation, 317, 524
Matchmaking, 97
Matrix Partners, 91
Mean, 363, 524
geometric, 218
harmonic, 218
Menlo Ventures, 93
Method of multiples, 214, 524
Mezzanine, 7À8, 524
Midstage, 15, 524
Midyear correction, 201, 524
Milestone payments, R&D, 353, 524
Minimax solution, 427, 524
Minority investors, 106
Mixed-strategy NE, 426, 525
Models. See individual entries
Modi?ed VC method, 185À191, 525
11 steps, 187
GP valuation, 186
542 INDEX
LP cost, 186
LP valuation, 186
Monitoring, of venture capital (VC)
board representation, 95
corporate governance, 96
human resources, 97
matchmaking, 97
strategy, 97
Monte Carlo simulation, 357À377, 525.
See also Continuous probability
distributions; Event trees
linear model, 366
nonlinear model, 366
Multifactor models, 525
Multiple of money, 55, 525
Multiple sources of uncertainty,
373À376
simulation with, 373À376
Multiple strike prices and early exercise,
409À411
Multiples analysis, 214À228, 525
Multistage fund, 22, 525
Narrow-base formula, 174, 525
NASDAQ, 5, 92, 222
versus CA Index, 51
versus Sand Hill Index, 49
Nash Equilibrium (NE), 423, 525
National Science Foundation (NSF), 339
research & development de?nitions
from, 343
National Venture Capital Association
(NVCA), 146, 525
Net contributed capital, 35, 525
Net income (= earnings), 525
Net invested capital, 32, 525
Net investment (NI), 200, 525
Net pro?ts, 525
Net-return index, 50À53
Cambridge Associates (CA), 50
CA index
s
versus NASDAQ, 51
Net returns, 47, 525
Netscape, 138
New Enterprise Associates (NEA), 93À94
No shop/con?dentiality, 160
Nodes, 448, 455, 515
decision, 380
Non-competition and non-solicitation and
agreements, 157
Noncumulative dividends, 153, 525
Non-disclosure and developments
agreement, 157
Nondiversi?able risk, 67, 525
Nonlinear model, 526
Monte Carlo simulation, 366
Non-solicitation agreement, 17
Normal form, game theory, 420, 526
Normative analysis, game theory, 431, 526
Odds-and evens-game, extensive form, 422
Odds-and-evens game, normal form, 422
Operating assets, 199, 526
Option pricing, 231À251
American options, 241À243
carried interest as an option, 247À248
European options, 232À234
exit diagrams, reading, 245À247
random-expiration (RE) options,
243À245
using replicating portfolio, 234À237
bond values, 235
option values, 236
replicating portfolio, 234
stock values, 235
Option to abandon, 382, 526
Option to delay, 381, 526
Option to expand, 381, 526
Option to extend, 381, 526
Option to shrink, 382, 526
Option to switch, 382, 526
Option tree, 403À404, 526
Option values, 236
Optional conversion, 152
Option-tree worksheet, 406À408, 410
Organization for Economic Co-operation and
Development (OECD), 340
Original purchase price (OPP), 149, 526.
See also Price per share
Out of the money, 242, 526
Paci?c Corporate Group, 59
Pari passu, 153
Partial implied valuation, 311, 521
Partial valuation, 183, 526
Participating convertible preferred stock
(PCP), 165, 252À271, 290À304, 526
binary options, 291À292
exit diagram for, 291
exit diagram for, 169
Series B and beyond, 296À303
INDEX 543
Participating convertible preferred stock
(PCP) (continued)
exit diagram, 297À298
Series D, 301
Series F, 302
valuation of, 292À294
breakeven valuation, sensitivity
analysis, 293
Series A, exit diagram for, 293
Participating convertible preferred
with cap (PCPC), 166, 252À271,
290, 526
exit diagram for, 170
valuation of, 294À296
Series A, exit diagram for, 295
voluntary conversion for, 170
Partners, dealing with, 143, 327À329
Techco options, exit diagram for, 328
Partnership agreements, 30À41. See also
Restrictive covenants
carried interest, 32À39. See also
individual entry
management fees, 30À32. See also
individual entry
Pastor-Stambaugh model (PSM), 77, 79,
118, 526
Payment-in-kind (PIK) dividends, 153,
284À285, 526
Payments
milestones, 353
royalty, 353
upfront, 353
Payos, game theory, 420, 526
Performance evaluation regression, 68, 526
Periodic return, 46À48, 527
Periods
rapid-growth, 196, 529
stable-growth, 196, 531
venture, 196, 534
Perpetuity, 201, 527
Personal valuation, 317, 527
Piggyback registration, 155, 158, 527
Pitch meeting, 140, 527
post-term-sheet step, 140
pre-term-sheet step, 140
Plowback ratio, 201, 527
Portfolio companies, 3, 527
early-stage, 6
late-stage, 6
mid-stage, 6
Portfolio company status over time,
125À126, 129
assuming no private companies after 10 years
all ?rst-round investments, 126
all second-round investments, 131
all third-round investments, 132
Portfolio ?rms, 95À98
value added and the monitoring of, 95À98
corporate governance, 96
human resources, 97
matchmaking, 97
strategy, 97
Portfolio value, measurement, 310À314
implied GP valuation, 311
implied LP valuation, 311
implied partial valuation, 311
implied prevaluation, 311
Series B, exit diagram for, 313
value division after Series B investment,
311
Positive analysis, game theory, 431, 527
Postboom period, 12À13, 527
Post-money valuation, 149À150, 306À310,
318, 527
angel shares, exit diagram for, 309
employees’ shares, exit diagram, 310
Series A investment
exit diagram for, 308
value division after, 307
Preboom period, 12, 527
Preclinical stage, development, 345, 527
Preferred returns. See Priority returns
Preferred stock valuation, 252À271. See also
Convertible preferred (CP) valuation;
Redeemable preferred (RP) valuation,
254À256
Preferred stock, 150, 163À177, 527
types of, 163À173. See also Antidilution
provisions; Common stock;
Convertible preferred (CP) stock;
Redeemable preferred (RP) stock
Pre-money valuation, 149À150, 527
Price per share, 149
PricewaterhouseCoopers, 99
Pricing options. See Option pricing
Priority returns, 33, 35, 527
catch-up provision, 35À36
Prisoner’s dilemma, 420, 527
Private Equity Analyst, 87
Private Equity International (PEI), 61À62
544 INDEX
Private Equity Performance Monitor, 87
Private equity, 5, 527
and hedge funds, 7
Probabilities, risk-neutral, 461
Probability density function (pdf), 362, 528
log-normal PDF, 369
normal PDF, 367
triangular PDF, 372
uniform PDF, 362
Proceeds, 528
Product, role in investment, 142
Pro?ts, economic, 84
Projections, role in investment, 142
Proposed ownership percentage, 148, 528
Proprietary deal ?ow, 94, 137, 528
Protective provisions, 151
Pure strategy NE, 426, 528
Put option, 234
Quali?ed Institutional Buyers (QIBs),
158, 528
Quali?ed public oering (QPO), 154, 528
Quali?ed Research Expenses (QREs),
350, 528
R&D ?nance, 339À356, 528, 530
applied research, 343À344
basic research, 343À344
development, 343À344
expenditure by source and performer, 343
global stance, 339À345
spending, 340
by industry and industry group, 344
options in, 349À354
banks, 351
government, 349
internal corporate funds, 350
large companies, 353
license, 353
milestone payments, 353
public debt markets, 351
public equity markets, 352
royalty payments, 353
strategic alliance, 353
upfront payment, 353
venture capital, 353
Quali?ed Research Expenses (QREs), 350
R&D share of GDP, 2004À08, 341
R&D tax credit, 350
sources, 354À355
touchstones, 345À349. See also Drug
development; Energy innovation
U.S. R&D funding, 342
R&D licensing agreement, 528
R&D tax credit, 528
R&D valuation, 445À465
drug development, 445À455
energy, 455À464
Fuelco’s decision tree, 457À461
node 10, expanded, 462
node 11, expanded, 462
node 12, expanded, 463
forest and the trees, 464
Random-expiration (RE) options,
243À245, 484, 528
Random-expiration binary call option
(BC(X)), 528
Rapid-growth period, 196, 529
Reading the exit diagram, 529
Real options, 378À399, 529. See also
Decision trees; Risk-neutral
probabilities
Drugco, 395À397
game theory and, 438À443
in R&D, 381À382
call options, 381À382
combinations of options, 382
option to abandon, 382
option to delay, 381
option to expand, 381
option to extend, 381
option to shrink, 382
option to switch, 382
put options, 382
spotting options, 378
valuation of, 382À387
Fuelco Project, 383À387
valuing options, 378
Reality-check model DCF model,
207À212, 529
baseline assumptions for, 207À212
Realization ratio, 55, 529
Realized investments, 32
Realized returns, 48, 529
Realized value multiple, 55
Redeemable preferred (RP) stock/valuation,
165, 254À257, 529
AUTO Calculator, 256
combining RP and CP, 266À268
comparing RP and CP, 268À269
INDEX 545
Redeemable preferred (RP) stock/valuation
(continued)
exit diagram for, 168
FLEX Calculator, 256
Series A RP, 171
Redemption rights, 152, 154À155, 529
Redemption value (RV), 252À271, 529
Redemption value per share (RVPS),
277À289, 529
Regional distribution of VC investment,
18À19
Registered transaction, 529
Registrable securities, 155
Registration on form S-3, 155
Registration rights, 155, 158, 529
demand, 158
in-kind distributions, 158
Piggyback, 158
Rule 144, 158
Rule 144A, 158
S-3, 158
Regression
equation for, 78
least-squares, 67
performance evaluation, 68
Reinvestment rate, 201, 529
Relative valuation, 529
Replicating portfolio, 234À237, 530.
See also under Option pricing
Reputation, of venture capital, 97
Required investment, 179, 530
Research and development (R&D). See R&D
?nance; R&D valuation
Restrictions, 160, 530
transfer restrictions, 160
Restrictive covenants, 39À41, 530
restrictions on fund management, 39À40
restrictions on GP activities, 39, 41
restrictions on investment type,
39, 41
Retention percentage, 182
Return on capital (R), 84, 530
Return on investment (ROI), 84, 530
Returns, VC, 46À64. See also Fund returns;
Industry returns
Right of ?rst oer, 160, 530
Right of ?rst refusal/co-sale agreement and
voting agreement, 159, 530
Board of Directors, 160
Lockup, 159
Right of First Refusal/Co-Sale Agreement,
159À160
Rights, 160
to maintain proportionate ownership, 156
right of ?rst oer, 160
right of ?rst refusal, 160
Risk factor, 530
Risk-free rate, 530
Riskless rate, 530
Risk node, event tree, 358, 530
Risk-neutral probabilities, 388À394, 530
Fuelco Project, 389À391
decision tree, 391
decision tree, pruned, 392
event tree, after node 3, 394
Rounds, 15, 147, 530
Royalty payments, R&D, 353, 530
Rule 144, 158, 530
Rule 144A, 158, 531
S-3 registration rights, 158, 531
Sample term sheet. See Term sheet, sample
Sand Hill Econometrics (SHE), 123, 531
Sand Hill Index
s
, 48À52, 531
San Hill index
s
versus NASDAQ, 49
survivor bias, 52
Screening, 135, 137, 140, 531
Securities and Exchange Commission
(SEC), 5
Seed stage, 15, 531
Segmented markets, 111, 531
global CAPM, 117
Self-dealing, 104, 531
Sensitivity analysis, 190, 191
for breakeven valuation, 256, 258,
261, 263
Sequential games, 420, 433À438, 531
entry game, 433
with commitment extensive form, 437
extensive form, 434, 436
normal form, 435
?nite games, 438
in?nite games, 438
subgames, 435
Sequoia Capital, 91
Series, 16, 531
Series B investment, 272À276
conversion condition, 277
exit diagram for, 274À275
valuation of LP, 274
546 INDEX
Series C investment, 278À282
exit diagram for, 281, 287
Short position, 531
Silicon Valley, location of ?rms in, 87, 103
Simple interest, 153, 531
Simulation, with multiple sources of
uncertainty, 373À376
Simultaneous games, 420, 423À433, 531
advertising game
extensive form, 425
mixed-strategy NE, 426
normal form, 426
pure strategy NE, 426
two-by-two games, 426
arms races, 424
best responses, 423
dominant strategy, 424
equilibrium concepts, 423
equilibrium strategy, 423
leader-follower game, 428
minimax solution, 427
Nash Equilibrium (NE), 423
odds-and-evens game, normal form, with
best responses, 427
SIZE factor, 76
Small Business Act of 1958, 11
Small Business Investment Companies
(SBICs), 11
Sourcing, 137, 531
Special situations, 531
Spotting options, 378
Stable-growth period, 196, 531
Stale values, 75, 78, 532
Standard VC method, 184À185, 532
Standards game, 432, 433
Star fund, 86, 532
Step vesting, 158, 532
Stock
common, 150, 515
preferred, 150, 527
values, 235
Stock dividends, 153, 532
Stock Purchase Agreement, 159
conditions to closing, 159
counsel and expenses, 159
representations and warranties, 159
Stock values, 235
Strategies, 532
game theory, 420, 532
portfolio ?rms, 97
strategic alliance, R&D, 353, 532
strategic investing, 532
Strike price, 232, 532
Style adjustments, 75À77, 532
global CAPM, 114
Subgame perfect Nash equilibrium (SPNE),
435, 532
Subgames, 435, 532
Successful exit, 178, 532
Summit Partners, 94
Superstar fund, 86, 532
Supply side, 83À85
Survivor bias, 52, 532
Syndication, 91, 532
Systematic risk, 67, 532
Tag-along rights, 160, 533
Takedown, 21, 533
Take-me-along rights, 160, 533
Talltree Ventures IV, 44À45
Target multiple of money, 178, 181, 533
Target returns, 178, 180À182, 533
Tax credit, 350
Technical risks in drug development, 347, 533
Technology Crossover Ventures (TCV), 94
Technology, 142
Term sheet, sample, 466À483
existing preferred stock, 482
Founders’ stock, 482
investor rights agreement, 475
Board matters, 479
demand registration, 476
employee stock options, 480
expenses, 476
key person insurance, 480
lock-up, 477
management and information rights, 477
matters requiring investor director
approval, 478
non-competition and non-solicitation and
agreements, 479
non-disclosure and developments
agreement, 479
piggyback registration, 476
registrable securities, 475
registration on Form S-3, 476
registration rights, 475
right to maintain proportionate
ownership, 477
no shop/con?dentiality, 482
INDEX 547
Term sheet, sample (continued)
pre and post-?nancing capitalization, 468
anti-dilution provisions, 472
capitalization, 468
dividends, 468
liquidation preference, 469
mandatory conversion, 473
optional conversion, 471
pay-to-play, 473
pre-money valuation, 468
protective provisions, 470
redemption rights, 474
voting rights, 470
right of ?rst refusal/co-sale agreement, 480
lock-up, 481
right of ?rst refusal/right of co-sale (take-
me-along), 480
stock purchase agreement, 474À475
conditions to closing, 475
counsel and expenses, 475
representations and warranties, 474
voting agreement, 481
Board of Directors, 481
drag along, 481
Term sheets, 9, 135À136, 146À162, 533. See
also Charter; Investor rights agreement
aggregate purchase price (APP), 149
basics, 147À150
capitalization, 150
common stock, 150
expiration, 160
founders’ stock, 160À161
investors, 148À149
no shop/con?dentiality, 160
original purchase price (OPP), 149
post-money valuation, 149À150
preferred stock, 150
pre-money valuation, 149À150
price per share, 149
right of ?rst refusal/co-sale agreement and
voting agreement, 159
rights and restrictions, 160
stock purchase agreement, 159
Terminal node, event tree, 358, 533
Termination, 156
Terrible things, 144
Times money, 533
Top-quartile fund, 60, 533
Top-tier ?rms, 89À95, 533
Total valuation, 179, 317, 533
Tranches, 148, 533
Transaction terms, 143
Transfer restrictions, 160, 533
Trees, 355, 533. See also Event trees
binomial, 355
decision, 355
game, 355
Triangular distribution, 373
Tunneling expropriation, 104, 533
Two-by-two games, 426, 533
Unbiased approximation, 240À241
Underlying asset, 232, 533
Underwriter, 533
Uniform CDF, 363
Uniform PDF, 362
United Kingdom, 99
United States, VC investment patterns in,
14À19
growth stages, 16
early stage ?nancing, 16À17
expansion (mid) stage ?nancing, 16À17
later stage ?nancing, 16À17
seed/startup stage ?nancing, 16À17
investments by industry, 15À18
boom period, 17À18
health care, 15
information technology (IT), 15
postboom period, 17À18
preboom period, 17À18
investments by region, 18À19
Unlevered betas, 224, 533
Unrealized investments, 32
Unrealized returns, 534
Unrealized value multiple, 55
Unrestricted stock, 534
Valuation, 195
VALUE factors, 76
Value multiple, 55, 534
Valuing options, 378
Variables
continuous random, 357, 362
discrete random, 357, 362
Variance, 66, 534
VC method, 178À194, 534
exit valuation, 178À180
expected retention, 178, 182À183
investment recommendation, 183
modi?ed VC method, 185À191
548 INDEX
spreadsheet, 189
standard VC method, 184À185
target returns, 180À182
VCV model, 484À486, 534
AUTO calculator, 484
Euro-option calculator, 484
FLEX calculator, 484
Random-Expiration (RE) option
calculator, 484
Venture capital (VC), 3, 534
characteristics, 3À5
as ?nancial intermediary, 3
helping in companies portfolio, 5
investing in internal growth, 6
investing in private companies, 5
maximizing ?nancial return, 5
Venture capitalists (VCs), 534
exiting, 9À10
investing, 9
monitoring, 9
work of, 9À10
top-tier, 89-95
Venture Economics (VE), 59
Venture period, 196, 534
VentureExpert, 123
VentureSource database, 253
Vesting, 158, 534
cli vesting, 159
step vesting, 158
Vintage year, 22, 534
Volatility ratios, selected countries, 115
Voluntary conversion for the PCPC, 170
Voting agreement, 159À160
Voting rights, 151, 154
Warrants, 409
Weighted-average antidilution protection,
173, 534
Woodward, Susan, 48
Worldwide investments, 99À119. See also
Global distribution of VC investing;
International VC
Write downs, 36
Yahoo!, 138
Zero-cost long-short portfolios, 76, 534
Zero-pro?t curve, 452, 455
Zero-sum games, 422, 534
INDEX 549
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