Description
This is a presentation about various valuation models.
VALUATION
Group 3
A Notion of Value
?“Value is in the eye of the beholder”
? Value is a relative notion.
• Is it what something is worth ?
• Is it what the market thinks it’s worth ?
• Is it what a strategic or motivated buyer think
it’s worth ?
?Differentiate “Price” from Value
Valuation by Replication
• How do you estimate the price of a 7 room
apartment on Park Ave if someone tells you
the price of a 2 room apartment in Battery
Park City?
• Yield to Maturity in Bond Pricing!
• Black-Scholes is all about: it tells you the
price of an option in terms of the price of a
stock and a bond.
Valuation Models
Asset Based
Valuation
Discounted Cashflow
Models
Relative Valuation Contingent Claim
Models
Liquidation
Value
Replacement
Cost
Equity Valuation
Models
Firm Valuation
Models
Cost of capital
approach
APV
approach
Excess Return
Models
Stable
Two-stage
Three-stage
or n-stage
Current
Normalized
Equity
Firm
Earnings Book
Value
Revenues Sector
specific
Sector
Market
Option to
delay
Option to
expand
Option to
liquidate
Patent Undeveloped
Reserves
Young
firms
Undeveloped
land
Equity in
troubled
firm
Dividends
Free Cashflow
to Firm
Approaches to Valuation
• Discounted cash flow valuation, relates the value of an
asset to the present value of expected future cash flows
on that asset
• Relative valuation, estimates the value of an asset by
looking at the pricing of 'comparable' assets relative to a
common variable like earnings, cash flows, book value or
sales
• Contingent claim valuation, uses option pricing models to
measure the value of assets that share option
characteristics
Which approach should you use?
Mature businesses
Separable & marketable assets
Growth businesses
Linked and non-marketable assets
Liquidation &
Replacement cost
valuation
Other valuation models
Asset Marketability and Valuation Approaches
Cashflows currently or
expected in near future
Assets that will never
generate cashflows
Discounted cashflow
or relative valuation
models
Relative valuation models
Cash Flows and Valuation Approaches
Cashflows if a contingency
occurs
Option pricing models
Unique asset or business
Large number of similar
assets that are priced
Discounted cashflow
or option pricing
models
Relative valuation models
Uniqueness of Asset and Valuation Approaches
Depends upon the asset being valued..
And the analyst doing the valuation
Very short time horizon Long Time Horizon
Liquidation value Discounted Cashflow value
I nvestor Time Horizon and Valuation Approaches
Option pricing
models
Relative valuation
Markets are correct on
average but make mistakes
on individual assets
Discounted Cashflow value
Views on market and Valuation Approaches
Option pricing models
Relative valuation
Markets make mistakes but
correct them over time
Asset markets and financial
markets may diverge
Liquidation value
Basis for all valuation approaches
• The use of valuation models in investment decisions (i.e., in
decisions on which assets are under valued and which are over
valued) are based upon
– a perception that markets are inefficient and make mistakes in assessing
value
– an assumption about how and when these inefficiencies will get corrected
• In an efficient market, the market price is the best estimate of value
• The purpose of any valuation model is then the justification of this
value
DISCOUNTED CASH FLOW VALUATION
Just 5 baby steps
? Single cash flow:
PV = CF
1
/(1+r)
? Single cash flow in “n” years from now:
PV = CF
n
/(1+r)
n
? Multiple cash flows in future:
PV = CF
1
/(1+r)+CF
2
/(1+r)
2
+CF
3
/(1+r)
3
+…
? Perpetuity of fixed cash flows:
PV = CF/r (1
st
CF is at the end of year 1)
? Growing Perpetuity:
PV = CF/(r-g) (1
st
CF at end of year 1, then grow at g)
Can you estimate cash flows?
Yes No
Use dividend
discount model
Is leverage stable or
likely to change over
time?
Stable
leverage
Unstable
leverage
Are the current earnings
positive & normal?
Yes
Use current
earnings as
base
No
Is the cause
temporary?
Yes No
Replace current
earnings with
normalized
earnings
Is the firm
likely to
survive?
Yes No
Adjust
margins over
time to nurse
firm to financial
health
Does the firm
have a lot of
debt?
Yes
No
Value Equity
as an option
to liquidate
Estimate
liquidation
value
What rate is the firm growing
at currently?
< Growth rate
of economy
Stable growth
model
> Growth rate of
economy
Are the firm’s
competitive
advantges time
limited?
Yes No
2-stage
model
3-stage or
n-stage
model
FCFE FCFF
Choosing the appropriate model
The flow in DCF analysis
=
Weighted average cost
of capital
Weighted by current share
of firm value
Cost of equity
Firm value
Minorities
Debt
All market value
Preference stock
Market values
Cash equity
investments Equity
value
- +
Cost of debt
10 years explicit and
perpetuity
Projected income statement
10 years explicit and
perpetuity
Projected balance sheet
DCF = valuation of firm’s or asset’s projected
free cash flows in perpetuity using its risk-
adjusted weighted average cost of capital
(WACC)
Projected free cash
flows
Predictable cash flows
The process of DCF analysis
? Project the operating results and free cash flows of the business over the
forecast period (typically 10 years, but can be 5–20 years depending on the
profitability horizon)
? Estimate the exit multiple and/or growth rate in perpetuity of the business
at the end of the forecast period
? Estimate the company’s weighted-average cost of capital to determine the
appropriate discount rate range
? Determine a range of values for the enterprise by discounting the
projected free cash flows and terminal value to the present
? Adjust the resulting valuation for all assets and liabilities not accounted for
in cash flow projections
Projections/FCF
Terminal value
Discount rate
Present value
Adjustments
2 basic DCF approaches should be kept independent
? DCF of unlevered cash flows
? Projected income and cash-flow streams are free of the effects of debt, net of
excess cash
? Present value obtained is the value of assets, assuming no debt or excess cash
(?firm value? or ?enterprise value?)
? Debt associated with the business is subtracted (and excess cash balances are
added) to determine the present value of the equity (?equity value?)
? Cash flows are discounted at the weighted-average cost of capital
? DCF of levered cash flows (most common in valuation of financial institutions)
? Projected income and cash-flow streams are after interest expense and net of any
interest income
? Present value obtained is the value of equity
? Cash flows are discounted at the cost of equity
The first step in DCF analysis is projection of
unlevered free cash flows
? Calculation of unlevered free cash flow begins with financial projections
? Comprehensive projections (i.e., fully-integrated income statement, balance sheet
and statement of cash flows) typically provide all the necessary elements
? Quality of DCF analysis is a function of the quality of projections
? Often required to ?fill in the gaps?
? Confirm and validate key assumptions underlying projections
? Sensitize variables that drive projections
? Sources of projections include
? Target company’s management
? Acquiring company’s management
? Research analysts
? Bankers
Projecting cash flows requires in-depth
understanding of the business
Accurate
cash flow
estimate
Anticipated industry growth
Major opportunities/risks
Pricing flexibility
Possible market share changes
Cost structure
Expansion opportunities
New product/stores/format
Development costs
Economies of scale
Reinvestment needs
Working capital
Required capital expenditures
Discretionary investments
Competitive position Industry outlook
Capital expenditure and working capital
Capital expenditures should include
•Research and development expenses, once they have been re-categorized as
capital expenses
•Acquisitions of other firms, whether paid for with cash or stock
•Working capital should be defined not as the difference between current assets
and current liabilities but as the difference between non-cash current assets and
non-debt current liabilities
•On both items, start with what the company did in the most recent year but do
look at the company’s history and at industry averages
Projecting financial statements
? Ideally projections should go out as far into the future as can reasonably be estimated to
reduce dependence on the terminal value
? Most important assumptions
? Sales growth: Use divisional, product-line or location-by-location build-up or simple growth
assumptions
? Operating margins: Evaluate improvement over time, competitive factors, SG&A costs
? Synergies: Estimate dollars in Year 1 and evaluate margin impact over time
? Depreciation: Should conform with historic and projected capex
? Capital expenditures: Consider both maintenance and expansion capex
? Changes in net working capital: Should correspond to historical patterns and grow as the
business grows
? Should show historical financial performance and sanity check projections against past results.
Be prepared to articulate why projections may or may not be similar to past results (e.g.
reasons behind margin improvements, increased sales growth, etc.)
? Analyze projections for consistency
? Sales increases usually require working capital increases
? CAPEX and depreciation should converge over time
Free cash flow is the cash that remains for creditors and
owners after taxes and reinvestment
? Unlevered free cash flows can be forecast from a firm’s financial projections, even
if those projections include the effects of debt
? To do this, simply start your calculation with EBIT (earnings before interest and
taxes)
? EBIT (from the income statement)
Plus: Non-tax-deductible goodwill amortization
Less: Taxes (at the marginal tax rate)
? Equals: Tax-effected EBITA (NOPAT)
Plus: Deferred taxes
1
Plus: Depreciation and any tax-deductible amortization
Less: Capital expenditures
Plus/(less): Decrease/(increase) in net working investment
? Equals: Unlevered free cash flow
1
One should only include actual cash taxes paid in the DCF. Depending on the firm and industry, you may want to adjust for the non-cash (or deferred) portion of a firm’s tax provision. The tax
footnote in the financial statements will give you a good idea of whether this is a meaningful issue for your analysis
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working
capital
10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Example: Calculating unlevered free cash flows
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Stand-alone DCF analysis of Company X
$ millions
Once unlevered free cash flows are calculated,
they must be discounted to the present
? The standard present value calculation takes into account the cost of capital by attributing greater
value to cash flows generated earlier in the projection period than later cash flows
? Since most businesses do not generate all of their free cash flows on the last day of the year, but
rather more-or-less continuously during the year, DCF analyses often use the so-called “mid-year
convention,” which takes into account the fact that free cash flows occur during the year
? This approach moves each cash flow from the end of the applicable period to the middle of the same
period (i.e., cash flows are moved closer to the present)
FCF
1
FCF
2
FCF
3
FCF
n
Present value =
(1+r)
1
+
(1+r)
2
+
(1+r)
3
+
. . .
+
(1+r)
n
FCF
1
FCF
2
FCF
3
FCF
n
Present value =
(1+r)
0.5
+
(1+r)
1.5
+
(1+r)
2.5
+
. . .
+
(1+r)
n-0.5
Mid year
standard
It is important to differentiate between the
transaction date and the mid-year convention
Year
0 1 2 3 0.5 1.5 2.5 3.5
First cash flow,
mid-year 1
Second cash flow,
mid-year 2
Third cash flow,
mid-year 3
Discounting =
CF
1
(1+r)
0.5
+
CF
2
(1+r)
1.5
+
CF
3
(1+r)
2.5
+ ….
Year
0 1 2 3 0.75 1.5 2.5 3.5
First cash flow,
mid-period 1
Second cash flow,
mid-year 2
Third cash flow,
mid-year 3
Discounting =
CF
1
(1+r)
(0.75-0.5)
+ +
CF
3
(1+r)
(2.5-0.5)
+ ….
0.5
Period 1 CF to buyer
CF
2
(1+r)
(1.5-0.5)
Transaction date: 01/01
Transaction date: 06/30
Stand-alone DCF analysis of Company X
$ millions
Example: Discounting free cash flows
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Discount rate = 10%
$189.6 =
$46.8
(1+.10)
0.5
$53.8
(1+.10)
1.5
$61.4
(1+.10)
2.5
$69.6
(1+.10)
3.5
+ + +
Formula
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Terminal value can account for a significant
portion of value in a DCF analysis
? Terminal value represents the business’s value at the end of the projection period; i.e., the
portion of the company’s total value attributable to cash flows expected after the projection
period
? Terminal value is typically based on some measure of the performance of the business in the
terminal year of the projection (which should depict the business operating in a steady-
state/normalized manner)
? Growth in perpetuity method
— Assumes that the business is held in perpetuity and that free cash flows continue to
grow at an assumed rate
? Terminal (or “Exit”) multiple method
— Assumes that the business is valued/sold at the end of the terminal year at a multiple of
some financial metric (typically EBITDA)
? A terminal multiple will have an implied growth rate and vice versa. It is essential to
review the implied multiple/growth rate for sanity check purposes
? Once calculated, the terminal value is discounted back to the appropriate date using the
relevant rate
? Attempt to reduce dependence on the terminal value
? What is appropriate projection time frame?
? What percentage of total value comes from the terminal value?
Terminal multiple method
? This method assumes that the business will be valued at the end of the last year of the
projected period
? The terminal value is generally determined as a multiple of EBIT, EBITDA or EBITDAR; this
value is then discounted to the present, as were the interim free cash flows
? The terminal value should be an asset (firm) value; remember that not all multiples
produce an asset value
? Note that in the exit multiple method terminal value is always assumed to be calculated at
the end of the final projected year, irrespective of whether you are using the mid-year
convention
? Should the terminal multiple be an LTM multiple or a forward multiple?
? If the terminal value is based on the last year of your projection then the multiple should
be based on an LTM multiple (most common)
? There are circumstances where you will project an additional year of EBITDA and apply a
forward multiple
Most common error: The final year is not
normalized
? Consider adding a year to the projections which represents a normalized year
? A steady-state, long-term industry multiple should be used rather than a current multiple,
which can be distorted by contemporaneous industry or economic factors
? Treat the terminal value cash flow as a separate, critical forecast
? Growth rate
— Consistent with long-term economic assumptions
? Reinvestment rate
— Net working investment consistent with projected growth
— Capital expenditures needed to fuel estimated growth
— Depreciation consistent with capital expenditures
? Margins
— Adjusted to reflect long-term estimated profitability
? Normalized tax rate
Growth in perpetuity method
? This method assumes that the business will be owned in perpetuity and that the
business will grow at approximately the long-term macroeconomic growth rate
? Few businesses can be expected to have cash flows that truly grow forever; be
conservative when estimating growth rates in perpetuity
? Take free cash flow in the last year of the projection period, n, and grow it one
more year to n+1;
1
this free cash flow is then capitalized at a rate equal to the
discount rate minus the growth rate in perpetuity
? To ensure that the terminal year is normalized, models are set up to project one
year past the projection year and allow for normalizing adjustments; this FCFn+1 is
then discounted by the perpetuity formula
Terminal value = (FCF
n+1
)/(WACC — g)
where FCF
n+1
= FCF in year after projections
g = growth rate in perpetuity
WACC = weighted-avg. cost of capital
PV of terminal value = terminal value/(1+WACC)
n-0.5
Recommended method Academic formula
Terminal value = (FCF
n
* (1 + g))/(WACC — g)
where FCF
n
= FCF in final projected period
g = growth rate in perpetuity
WACC = weighted-avg. cost of capital
PV of terminal value = terminal value/(1+WACC)
n-0.5
1
This step is taken because the perpetuity growth formula is based on the principle that the terminal value of a business is the value of its next cash flow, divided by the
difference between the discount rate and a perpetual growth rate
Growth in perpetuity method (cont’d)
? Note that when using the mid-year convention, terminal value is discounted as if
cash flows occur in the middle of the final projection period
? Here the growth-in-perpetuity method differs from the exit-multiple method
? Typical adjustments to normalize free cash flow in Year n include revising the
relationship between revenues, EBIT and capital spending, which in turn affects
CAPEX and depreciation
? Working capital may also need to be adjusted
? Often CAPEX and depreciation are assumed to be equal
Example: Growth in perpetuity method
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Discount rate = 10%
Perpetuity growth rate = 3%
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Discounted value of unlevered FCF $0.0 $44.6 $46.7 $48.4 $49.9
Discounted value of FCF 2005P–2008P 189.6
PV of Terminal Value 733.7
Total present value to acquirer $923.3
$733.6 =
$69.6 * (1 + .03)
(.10 - .03)*(1+.10)
3.5
Formula
Stand-alone DCF analysis of Company X
$ millions
Example: Terminal multiple method
Key assumptions:
Deal/valuation date = 12/31/04
Marginal tax rate = 40%
Discount rate = 10%
Exit multiple of EBITDA = 7.0x
$745.4 =
($155.9 * 7.0x)
(1+.10)
4
Formula
Fiscal year ending December 31,
2001 2001 2003 2004P 2005P 2006P 2007P 2008P
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes — — — — —
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Discounted value of unlevered FCF $0.0 $44.6 $46.7 $48.4 $49.9
Discounted value of FCF 2005P–2008P 189.6
EBITDA in 2008P $155.9
Exit multiple 7.0x
Firm value at exit 1,091.3
Discounted terminal value 745.4
Total present value to acquirer $934.9
Stand-alone DCF analysis of Company X
$ millions
Terminal multiples and perpetuity growth rates
are often considered side-by-side
? Assumptions regarding exit multiples are often checked for reasonableness by calculating
the growth rates in perpetuity that they imply (and vice versa)
? To go from the exit-multiple approach to an implied perpetuity growth rate:
g = [(WACC*terminal value) / (1+WACC)
0.5
- FCF
n
] / [FCF
n
+ (terminal value / (1 +
WACC)
0.5
)]
? To go from the growth-in-perpetuity approach to an implied exit multiple:
multiple = [FCF
n
* (1 + g)(1 + WACC)
0.5
] / [EBITDA
n
* (WACC - g)]
? These formulas adjust for the different approaches to discounting terminal value when
using the mid-year convention
Discount free cash flows at market cost of capital to get
enterprise value, minus net debt = equity value
? Value to closest year—value here is at
December 31, 2003
? Refine if necessary, including shifting
free cash flows to mid-year
? Terminal value calculated using
perpetuity growth rate of inflation only
? Enterprise value = value of cash flows to
be shared between net debt, minorities
and equity
? Option expense = Black-Scholes value of
outstanding options plus future
issuance assumed at 1.3% of NOSH
? Divide equity value by number of shares
(1,076mm) to get value per share
? Should coincide with share price
? Derive key multiples and check with
comps
Example
DCF-WACC valuation Base
WACC—taxed 7.13%
NPV FCF F2004—2013 26,100
NPV terminal value 49,400
Enterprise value 75,500
Cash 2,985
Investments 3,688
Debt (5,518)
Minority interests 0
Convertible preferred debt 0
Options outstanding (1,299)
Option grant NPV (4,856)
Equity value 70,500
Equity value per share 65.50
Share price 65.53
DCF % share price 100%
Firm value/EBITDA F2004 15.6
Choosing the discount rate is a critical step in
DCF analysis
? The discount rate represents the required rate of return given the risks inherent in
the business, its industry, and thus the uncertainty regarding its future cash flows,
as well as its optimal capital structure
? Typically the weighted average cost of capital (WACC) will be used as a foundation
for setting the discount rate
? The WACC is always forward-looking and is predicted based on the expectations of
an investment's future performance; an investor contributes capital with the
expectation that the riskiness of cash flows will be offset by an appropriate return
? The WACC is typically estimated by studying capital costs for existing investment
opportunities that are similar in nature and risk to the one being analyzed
? The WACC is related to the risk of the investment, not the risk or creditworthiness
of the investor¹
1
In valuing a company, always use the riskiness of its cash flows or comparable companies in estimating a weighted average cost of capital. Never use the acquirer’s cost capital unless, by some chance, it is engaged in an
extremely similar line of business. However, if a business is small relative to an acquiror’s, sometimes it may be appropriate to consider the use of the acquiror’s WACC in performing the valuation. The additional value
created by using the acquiror’s WACC can be viewed as a synergy to the acquiror in the context of the transaction.
Cost
of
equity
Mix of debt
and equity
Cost
of
debt
Three variables are relevant to determine weighted
average cost of capital
Derived using capital asset pricing model
(“CAPM”)
Cost of equity = RF + [B * (ERM - RF)]
? Risk free rate (“RF”)
? T-Bill
? 10-yr Treasury
? 30-yr Treasury
? Beta (“B”)
? Predicted, adjusted
? Historical
? Industry
? Expected Return on Market (“ERM”)
? Dividend Discount Model
? Arithmetic average
? Other various methodologies
Weighted by market value
? Medium term net debt and
current equity
value
? Current mix
? Target mix
? Industry mix
Market value of debt
? After tax basis
? Based on cost of
medium-term debt
CAPM approach to determine a firm’s cost of
equity
? Many companies use arbitrary discount rates
? Some investors and many advisors use arbitrary equity risk premiums (often 5%—7%)
Capital asset pricing model (CAPM)
E(r
i
) = r
f
+ ß
i
x [E(r
m
) - r
f
]
Expected return
on stock i
Risk-free rate
10-year government
bond yield
Beta of stock i
Investor judgment of
stock’s relative risk
Expected return
on market
Quantified from
various market
models
Risk-free rate
10-year government
bond yield
Equity risk premium
Derived as difference
between E(r
m
) and r
f
Most contentious/
difficult parts
The cost of equity is the major component of the
WACC
? The cost of equity reflects the long-term return expected by the market (dividend yield plus
share appreciation)
? Risk-free rate based on the 10 year bond yield
? Incorporates the undiversifiable risk of an investment (beta)
? Equity risk premium reflects expectations of today’s market
? The market risk premium (r
m
- r
f
; i.e., the spread of market return over the risk-free rate) is
periodically estimated
Cost of equity = Risk free rate + Beta x Equity risk premium
Long-term return on
equity investment in
today’s market
=
Long-term risk-free rate
of return (beta=0)
+
Adjustment for
correlation to
stock market
returns
x
Appropriate “extra”
return above risk free
rate
= 10-year bond yield
(annual average)
+ Predicted betas x Estimated using various
techniques
For market average = 4.97% + 1.00 x 5.00%
= 9.97%
Beta
? Beta provides a method to estimate an asset's systematic (non-diversifiable) risk
? Beta equals the covariance between expected returns on the asset and on the
stock market, divided by the variance of expected returns on the stock market
? A company whose equity has a beta of 1.0 is “as risky” as the overall stock market
and should therefore be expected to provide returns to investors that rise and fall
as fast as the stock market; a company with an equity beta of 2.0 should see
returns on its equity rise twice as fast or drop twice as fast as the overall market
? Returning to our CAPM formula, the beta determines how much of the market risk
premium will be added to or subtracted from the risk-free rate
? Since the cost of capital is an expected value, the beta value should be an
expected value as well
“Beta” is the most subjective part of DCF—
attempts to estimate undiversifiable risk relative
to market
Size/market cap.
Decreasing size = more risk
Multiples relative to
growth
Lower multiples/
higher yields
Stock price momentum
Higher excess return = more risk
Unexplained
volatility
Higher unknown risks
Leverage
Increasing leverage = more financial risk
Higher expected return =
higher cost of equity
= more risk
Industry
Some industries have higher returns
0
200
400
600
800
(1.5) (1.0) (0.5) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Beta
#
o
f
c
o
m
p
a
n
i
e
s
Historical Beta Predicted Beta
Predicted betas to calculate the cost of equity
0
200
400
600
800
(0.5) 0.2 1.0 1.9 2.6
Beta
#
o
f
c
o
m
p
a
n
i
e
s
Predicted betas
Supermarkets
0.78
Utilities
0.43
Food
0.52
Internet
2.09
Cellular
1.62
Distribution of predicted and historical betas for 5,600 publicly-traded companies
? Predicted betas are constructed to adjust for many risk factors, incorporating firms’ earnings volatility, size,
industry exposure, and leverage
? Predicted betas are more consistent and less volatile than historical betas
? Historical betas only measure the past relationship between a firm’s return and market returns and are
often distorted
? Projected betas can be obtained from an online database
? Note that Bloomberg betas are based on historic prices and are therefore not forward-looking
? Impute unlevered beta for private company from public comparables
Calculate risk premium
? Consider relevant time frame and use AM or GM
? Generally, geometric averages provide better estimates of risk premiums in valuation
? The risk premiums will vary across markets, depending upon their riskiness. While historical data can be
used to estimate premiums outside the United States, it is not very reliable. An alternative way of
estimating premiums is to use country bond ratings to estimate these premiums relative to the U.S.
premium
Country Rating Risk Premium
Argentina BBB
5.5% + 1.75%
= 7.25%
Brazil BB
5.5% + 2% =
7.5%
Chile AA
5.5% + 0.75%
= 6.25%
Columbia A+
5.5% + 1.25%
= 6.75
Using APM to calculate the cost of equity
? The arbitrage pricing model relates expected returns to economic factors, with a beta specific to each
factor. If these factor-specific betas and the factor risk premia can be estimated, the cost of equity can also
be estimated.
where,
Rf = Riskfree rate
bj = Beta specific to factor j
E(Rj) - Rf = Risk premium per unit of factor j risk
k = Number of factors
\
Using Dividend growth model to calculate the cost
of equity
? ke = DPS1 / P0 + g
= Expected Dividend Yield + Growth rate in earnings/dividends
where,
P0 = Price of the stock today
DPS1 = Expected dividends per share next year
ke = Cost of Equity
g = Growth rate in dividends (steady state)
? Since the current price is a key input to the model, it is inappropriate to use this approach to value stock in
a firm
? There is a strong element of circular reasoning involved that will lead the analyst to conclude, using this
cost of equity, that equity is fairly valued
43
Use long-term cost of debt in estimating WACC
? The long-term cost of debt is used because the cost of capital is normally
applied to long-term cash flows
? Using the long-term cost of debt removes any refinancing costs/risks
from the valuation analysis
? To the extent a company can fund its investments at a lower cost of
debt (with the same risk), this value should be attributed to the
finance staff
? Use the company’s normalized cash tax rate
45
Cost of equity
Cost of capital
10-year T-bond (Avg) 4.97%
Market risk premium 5.00%
(x) Beta (current predicted) 0.62
Adjusted market premium 3.10%
Cost of equity = 8.07%
Cost of debt
Cost of debt 6.25%
(-) Tax shield
1
2.19%
After-tax cost of debt 4.06%
The cost of equity and debt are blended together
based on a target capital structure
? The target capital structure reflects the company’s rating objective
? Firms generally try to minimize the cost of capital through the appropriate use of leverage
? The percentage weighting of debt and equity is usually based on the market value of a firm’s equity and debt position
? Most firms are at their target capital structure
? Adjustments should be made for seasonal or cyclical swings, as well as for firms moving toward a target
? Using a weighted average cost of capital assumes that all investments are funded with the same mix of equity and debt as
the target capital structure
Target capital structure
(Assumes current = optimal)
Debt/total capital
2
= 6.1%
Nominal WACC = 7. 82%
WACC = r
d
* [D *(1-T)] + r
e
* E
D+E D+E
Where:
E = Market value of equity
D = Market value of debt
T = Marginal tax rate
r
e
= Return on equity
r
d
= Return on debt
Illustrative weighted average cost of capital calculation
WACC formula
1
Assumes 35% marginal tax rate
2
Total capital = debt + market value of equity
Most common errors in calculating WACC
Cost of equity
? Equity risk premium based on very long time frame
? Substitute hurdle rate (goal) for cost of capital
? Use of historical (or predicted) betas that are clearly wrong
? Investment specific risk not fully incorporated (e.g., country risk premiums)
? Incorrect releveraging of the cost of equity
? Cost of equity based on book returns, not market expectations
Capital structure
? A target (possibly unrealistic) capital structure is used vs. actual
? Valuing a tax shield that may not exist
? WACC calculated based on book weights (should be market value, if available, book if not)
VALUATION MODELS IN A NUTSHELL
Cash in DCF valuation: Separated from other assets
? The simplest and most direct way of dealing with cash and marketable securities is to keep
it out of the valuation
? Once the firm has been valued, we generally add back the value of cash and marketable
securities and subtract out gross debt. (This is also equivalent to subtracting out net debt)
? Estimating how much cash is wasting cash…
? There are two solutions.
? No cash (or at least a negligible amount) will be wasting cash.
? Divide the interest income earned by the average cash balance during the year and to
compare this rate to the rate on a short-term government security (T-bill).
? Interest income for year = $ 3 million
? Average cash balance = $ 150 million
? Interest rate earned = 3/ 150 = 2%
? Treasury bill rate during year = 3%
? Wasting cash for year = ({3% - 2%} / 3%)* 150 = $ 50 million
Incorporating Cash into the DCF valuation
? When you value equity and use net income, you are valuing cash (because the interest
income from cash is part of net income). The cost of equity used then has to allow for the
firm’s cash holdings - the unlevered beta used should be the weighted beta of operating
assets and the beta of cash (zero)
? The danger with this approach is that it is built on the assumption that cash as a percent of
value will remain unchanged over time
Value of Holdings in other firms
Holdings in other firms can be categorized into
? Minority passive holdings, in which case only the dividend from the holdings is shown in
the balance sheet
? Minority active holdings, in which case the share of equity income is shown in the
income statements
? Majority active holdings, in which case the financial statements are consolidated
? After valuing the operating assets of a firm, using consolidated statements, it is common
to add on the balance sheet value of minority holdings (which are in book value terms)
and subtract out the minority interests (again in book value terms), representing the
portion of the consolidated company that does not belong to the parent company
? In a perfect world, we would strip the parent company from its subsidiaries and value
each one separately
? The value of the combined firm will be Value of parent company + Proportion of value of
each subsidiary
? To do this right, one will need to be provided with detailed information on each
subsidiary to estimated cash flows and discount rates
WHAT ARE INTANGIBLE ASSETS
? An asset that we can neither see nor feel. E.g. Goodwill of a firm or individual
? List of such assets include:
? Franchises, Copyrights & trademarks.
? Patents
? Brand names
? Some invisible assets include:
? Top notch management
? Loyal & well trained workforce
? Technical Know how's
CATEGORIZING INTANGIBLES
Independent and Cash flow
generating intangibles
Not independent and cash flow
generating to the firm
No cash flows now but potential
for cashflows in future
Examples Copyrights, trademarks, licenses,
franchises, professional practices
(medical, dental)
Brand names, Quality and Morale
of work force, Technological
expertise, Corporate reputation
Undeveloped patents, operating or
financial flexibili ty (to expand into
new products/markets or abandon
existing ones)
Valuation approach Estimate expected cashflows from
the product or service and discount
back at appropriate discount rate.
- Compare DCF value of firm
with intangible with firm
without (if you can find one)
- Assume that all excessreturns
of firm are due to intangible.
- Compare multiples at which
firm trades to sector averages.
Option valuation
- Value the undeveloped patent
as an option to develop the
underlying product.
- Value expansion options as call
options
- Value abandonment options as
put options.
Challenges - Life is usually finite and
terminal value may be small.
- Cashflows and value may be
person dependent (for
professional practices)
With multiple intangibles (brand
name and reputation for service), it
becomes difficult to break down
individual components.
- Need exclusivity.
- Difficult to replicate and
arbitrage (making option
pricing models dicey)
WAYS OF VALUING INTAGIBLES
? Capital Invested: We can estimate the book value of an asset by looking at what a
firm has invested in that asset over time. With brand name, for instance, this
would require looking at advertising expenditures over time, capitalizing these
expenses and looking at the balance that remains unamortized of these expenses
today.
? Discounted Cash Flow Valuation: We can discount the expected incremental cash
flows generated by the intangible asset in question to the firm. This will require
separating out the portion of the aggregate cash flows of a firm that can be
attributed to brand name or technological expertise and discounting back these
cash flows at a reasonable discount rate.
? Relative Valuation: One way to isolate the effect of an intangible asset such as
brand name is compare how the market values the firm (with the intangible) with
how it values otherwise similar companies without the intangible asset. The
difference can be attributed to the intangible asset.
VALUING COCA COLA BRAND NAME- CAPITAL INVESTED
Year
Total Selling
and Advertising
Brand Name
Relat ed
Expense
Amortization this
year
Unamortized
Expense
1980 $1,121 $561 $22.43 $0.00
1981 $1,189 $594 $23.77 $23.77
1982 $1,221 $610 $24.41 $48.83
1983 $1,376 $688 $27.52 $82.56
1984 $1,543 $771 $30.85 $123.41
1985 $1,579 $789 $31.57 $157.87
1986 $1,631 $815 $32.61 $195.68
1987 $1,777 $888 $35.53 $248.73
1988 $2,025 $1,013 $40.51 $324.05
1989 $2,232 $1,116 $44.64 $401.76
1990 $2,717 $1,359 $54.35 $543.47
1991 $3,069 $1,535 $61.39 $675.25
1992 $3,499 $1,750 $69.99 $839.84
1993 $3,797 $1,898 $75.93 $987.13
1994 $4,198 $2,099 $83.96 $1,175.44
1995 $4,657 $2,329 $93.15 $1,397.20
1996 $5,347 $2,673 $106.93 $1,710.93
1997 $5,235 $2,617 $104.69 $1,779.79
1998 $5,523 $2,761 $110.45 $1,988.16
1999 $6,543 $3,271 $130.85 $2,486.21
2000 $5,701 $2,850 $114.01 $2,280.27
2001 $4,099 $2,050 $81.99 $1,721.72
2002 $4,667 $2,334 $93.35 $2,053.63
2003 $4,992 $2,496 $99.84 $2,296.32
2004 $5,431 $2,715 $108.61 $2,606.72
$1,703.35 $26,148.75
Estimating brand value
? If we just accumulate the advertising expenses over time, assuming that 50% is
attributable to building up brand name, we get a value of $ 26 billion.
? If we adjust the expenses for inflation, the value that we obtain for the brand
name value is close to 50%.
? The two key problems with this approach are
? Estimating the proportion of advertising that can be attributed to brand name
building
? Estimating the life of brand name as an asset
GENERIC COMPARISON
Coca Cola With Cott Margins
Current Revenues = $21,962.00 $21,962.00
Length of high-growth period 10 10
Reinvestment Rate = 50% 50%
Operating Margin (after-tax) 15.57% 5.28%
Sales/Capital (Turnover ratio) 1.34 1.34
Return on capital (after-tax) 20.84% 7.06%
Growth rate during period (g) = 10.42% 3.53%
Cost of Capital during period = 7.65% 7.65%
Stable Growth Period
Growth rate in steady state = 4.00% 4.00%
Return on capital = 7.65% 7.65%
Reinvestment Rate = 52.28% 52.28%
Cost of Capital = 7.65% 7.65%
Value of Firm = $79,611.25 $15,371.24
Value of brand name = $79, 611 million - $15,371 million = $ 64,240 million
RELATIVE VALUATION
? Value of brand name = 16,406 (6.01 – 1.63) = $71,821 million
Coca Cola Cott
Market value of Equity $98,160 $949
Debt $7,178 $345
Cash $6,707 $27
Enterprise Value $98,631 $1,267
Sales $21,962 $1,646
EBITDA $7,760 $186
Capital Invested $16,406 $775
EV Multiples
EV/Sales 4.49 0.77
EV/EBITDA 12.71 6.81
EV/Capital Invested 6.01 1.63
INTANGIBLES GENERATING CASH FLOW IN FUTURE (not now)
? Assets to value are those that have the potential to create cash flows in the future but
do not right now.
? Assets are difficult to value on a discounted cash flow valuation basis and often
impossible to evaluate on a relative basis, they do have option characteristics and are
best valued using option pricing models.
? REAL OPTION PREMIUM
? Real option premium should be tacked to DCF.
Bad Investment ……………………….Becomes a good one.
3 basic questions
? When is there a real option embedded in a decision or an asset?
? When does that real option have significant economic value?
? Can that value be estimated using an option pricing model?
? An option provides the holder with the right to buy or sell a specified quantity of an underlying asset
at a fixed price (called a strike price or an exercise price) at or before the expiration date of the
option.
? There has to be a clearly defined underlying asset whose value changes over time in unpredictable
ways.
? The payoffs on this asset (real option) have to be contingent on an specified event occurring within a
finite period.
When option is embedded in an option
Product Patent as an Option
Present Value of Expected
Cash Flows on Product
PV of Cash Flows
from Project
Initial Investment in
Project
Project has negative
NPV in this section
Project's NPV turns
positive in this section
Expansion of existing project as an option
Present Value of Expected
Cash Flows on Expansion
PV of Cash Flows
from Expansion
Additional Investment
to Expand
Firm will not expand in
this section
Expansion becomes
attractive in this section
Determinants of option value
? Variables Relating to Underlying Asset
? Value of Underlying Asset; as this value increases, the right to buy at a fixed price (calls) will become
more valuable and the right to sell at a fixed price (puts) will become less valuable.
? Variance in that value; as the variance increases, both calls and puts will become more valuable
because all options have limited downside and depend upon price volatility for upside.
? Expected dividends on the asset, which are likely to reduce the price appreciation component of the
asset, reducing the value of calls and increasing the value of puts.
? Variables Relating to Option
? Strike Price of Options; the right to buy (sell) at a fixed price becomes more (less) valuable at a lower
price.
? Life of the Option; both calls and puts benefit from a longer life.
? Level of Interest Rates; as rates increase, the right to buy (sell) at a fixed price in the future becomes
more (less) valuable.
Sources of Synergy
Valuing synergies
? When two businesses are combined, the term “synergies” refers to the changes in their
aggregate operating and/or financial results attributable to their being operated as a
combined enterprise. Synergies can take many forms
? Revenue enhancements
? Cost savings
— Raw material discounts/purchasing power
— Sales and marketing overlap, Corporate overhead reductions
— Distribution cost reductions, Facilities consolidation
— Tax savings
? Merger related expenses (restructuring, additional CAPEX, integration expenses)
? The value of achievable synergies is often a key element in whether to proceed with a
proposed transaction
? Calculate synergies for both the acquiring company and the target
? Remember incremental cash flow
? Synergies are generally valued by toggling pre-tax changes to various financial statement line
items into a DCF model of the combined enterprise and simply measuring the incremental
impact
Sources of Financial Synergy
? Diversification: Acquiring another firm as a way of reducing risk cannot create
wealth for two publicly traded firms, with diversified stockholders, but it could
create wealth for private firms or closely held publicly traded firms
? Cash Slack: When a firm with significant excess cash acquires a firm, with great
projects but insufficient capital, the combination can create value
? Tax Benefits: The tax paid by two firms combined together may be lower than the
taxes paid by them as individual firms
? Debt Capacity: By combining two firms, each of which has little or no capacity to
carry debt, it is possible to create a firm that may have the capacity to borrow
money and create value
Valuing synergies
? Sources of synergy projections
? Management
? Research
? Estimates from comparable transaction (% of sales, increase in EBITDA
margin etc.)
? DCF with synergies
? Valued separately from standalone DCF
? Run sensitivity on synergy valuations
? Other considerations
? Timeline for achieving synergies
? Run as sensitivity various cases of realization e.g., 25%, 50%, 75%, 100%
realization
? Tax impact
? Costs incurred to achieve synergies
52
Value of Control
? The value of the control premium that will be paid to acquire a block of equity will depend
upon two factors
? Probability that control of firm will change: This refers to the probability that incumbent
management will be replaced. this can be either through acquisition or through existing
stockholders exercising their muscle
? Value of Gaining Control of the Company: The value of gaining control of a company arises
from two sources - the increase in value that can be wrought by changes in the way the
company is managed and run, and the side benefits and perquisites of being in control
? Value of Gaining Control = Present Value (Value of Company with change in control - Value of
company without change in control) + Side Benefits of Control
Minority Discounts and Voting Shares
Assume that a firm has a value of $ 100 million run by incumbent managers and US$
150 million run optimally
? Proposition 1: The market price will reflect the expected value of control
• The firm has 10 million voting shares outstanding
• Since the potential for changing management is created by this offering, the
value per share will fall between $10 and $15, depending upon the probability
that is attached to the management change. Thus, if the probability of the
management change is 60%, the value per share will be $13.00
Value/Share = (150*.6+100*.4)/10 = $13
? Proposition 2: If you have shares with different voting rights, the voting shares will
get a disproportionate share of the value of control
Distress and the Going Concern Assumption
? Traditional valuation techniques are built on the assumption of a going concern,
i.e., a firm that has continuing operations and there is no significant threat to
these operations
? In discounted cash flow valuation, this going concern assumption finds its place
most prominently in the terminal value calculation, which usually is based upon an
infinite life and ever-growing cash flows
? In relative valuation, this going concern assumption often shows up implicitly
because a firm is valued based upon how other firms - most of which are healthy -
are priced by the market today
? When there is a significant likelihood that a firm will not survive the immediate
future (next few years), traditional valuation models may yield an over-optimistic
estimate of value
Equity to Employees: Effect on Value
? In recent years, firms have turned to giving employees (and especially top
managers) equity option packages as part of compensation. These options are
usually
• Long term
• At-the-money when issued
• On volatile stocks
? Two key issues with employee options:
• How do options granted in the past affect equity value per share today?
• How do expected future option grants affect equity value today?
Options-Impact on value
Options outstanding
• Step 1: List all options outstanding, with maturity, exercise price and vesting status
• Step 2: Value the options, taking into accounting dilution, vesting and early
exercise considerations
• Step 3: Subtract from the value of equity and divide by the actual number of shares
outstanding (not diluted or partially diluted)
Expected future option and restricted stock issues
• Step 1: Forecast value of options that will be granted each year as percent of
revenues that year. (As firm gets larger, this should decrease)
• Step 2: Treat as operating expense and reduce operating income and cash flows
• Step 3: Take present value of cash flows to value operations or equity
Sensitivity analysis is vital when presenting the
results of DCF analysis
? Recall that DCF valuation is highly sensitive to projections and assumptions
? So-called “sensitivity tables” chart the output based on ranges of input variables
? Since DCF results are by their nature approximate, depicting sensitivity tables enables users of
DCF output to assess the degree of “fuzziness” in the results
? It is better to use DCF analysis using exit multiples and perpetuity growth rates generally show
sensitivities for the method used to calculate terminal value and a range of discount rates
? Sensitivities can be shown for any variable in the model (including financial projections)
? Judge which sensitivities would be useful to decision makers
Other considerations
Reliability of projections
? DCF results are generally more sensitive to cash flows (and terminal value) than to small
changes in the discount rate. Care should be taken that assumptions driving cash flows are
reasonable. Generally, we try to use estimates provided by analysts from reputable Wall
Street firms if the client has not provided projections
Sensitivity analysis
? Remember that DCF valuations are based on assumptions and are therefore approximate.
Use several scenarios to bound the target’s value. Generally, the best variables to sensitize
are sales, EBITDA margin, WACC and exit multiples or perpetuity growth rate
Always remember…
? Three key drivers
? Projections and incremental cash flows (unlevered free cash flow)
? Residual value at end of the projection period (terminal value)
? Weighted-average cost of capital (discount rate)
? Avoid pitfalls
? Validate and test projection assumptions
? Determine appropriate cash flow stream
? Thoughtfully consider terminal value methodology
? Use appropriate cost of capital approach
? Carefully consider all variables in calculation of the discount rate
? Sensitize appropriately (base projection variables, synergies, discount rates, terminal
values, etc.)
? Footnote assumptions in detail
? Think about other value enhancers and detractors
Other common mistakes
Value v. price
Many believe transaction multiples and premiums determine value of a
business
Synergy calculation
Valuing like a standalone company with normal growth: overvalues synergy
Preferable to use zero nominal growth rate for cost savings
No checks between
methods
Should run DCF and multiples side-by-side and resolve any differences
= only one value range
Historical Management estimates JPM extrapolation
YE Dec, €mm 2003A 2004A 2005A 2006E 2007E 2008E 2009E 2010E 2011E 2012E 2013E 2014E 2015E TP
Sales 132.1 134.2 134.0 135.2 146.2 155.0 161.2 166.0 170.2 173.6 177.1 180.6 184.2 187.0
% growth 1.6% (0.1)% 0.9% 8.1% 6.0% 4.0% 3.0% 2.5% 2.0% 2.0% 2.0% 2.0% 1.5%
EBITDA 14.0 11.7 11.7 11.6 16.1 21.0 20.2 19.9 20.4 20.8 21.2 21.7 22.1 22.4
% margin 10.6% 8.7% 8.7% 8.6% 11.0% 13.5% 12.5% 12.0% 12.0% 12.0% 12.0% 12.0% 12.0% 12.0%
EBITA 6.3 4.5 6.3 6.4 12.2 17.1 15.3 14.9 15.3 15.2 15.5 14.9 14.7 15.0
% margin 4.8% 3.4% 4.7% 4.7% 8.3% 11.0% 9.5% 9.0% 9.0% 8.8% 8.8% 8.3% 8.0% 8.0%
- Taxes (2.1) (1.5) (2.1) (2.1) (4.1) (5.8) (5.2) (5.1) (5.2) (5.2) (5.3) (5.0) (5.0) (5.1)
% tax rate 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8%
= NOPAT 4.2 3.0 4.2 4.2 8.0 11.3 10.1 9.9 10.1 10.1 10.3 9.9 9.8 9.9
+ Depreciation 7.7 7.2 5.4 5.2 4.0 3.9 4.8 5.0 5.1 5.6 5.7 6.8 7.4 7.5
% of capex 159.2% 106.2% 235.4% 210.0% 68.6% 54.2% 66.7% 75.0% 75.0% 80.5% 80.5% 93.8% 100.0% 100.0%
- Capex (4.8) (6.7) (2.3) (2.5) (5.8) (7.2) (7.3) (6.6) (6.8) (6.9) (7.1) (7.2) (7.4) (7.5)
% of Sales 3.7% 5.0% 1.7% 1.8% 4.0% 4.6% 4.5% 4.0% 4.0% 4.0% 4.0% 4.0% 4.0% 4.0%
? working capital¹ (4.0) (0.5) (0.8) 0.4 (1.1) (1.3) (1.1) (1.0) (0.8) (0.8) (0.8) (0.8) (0.8)
= Free cash-flow (0.5) 6.7 6.2 6.6 6.9 6.4 7.1 7.5 7.9 8.1 8.6 8.9 9.1
Company X DCF analysis
DCF assumptions (€mm)
¹ Working capital includes: inventories, trade receivables and trade payables
Firm value (€mm) Firm value (€mm)
Terminal growth %
1.0% 1.3% 1.5% 1.8% 2.0%
8.0% 114 116 119 122 125
8.5% 106 108 110 113 116
9.0% 99 101 103 105 107
9.5% 93 95 96 98 100
W
A
C
C
%
10.0% 88 89 91 92 94
EBITDA margin variance %
(1.0%) (0.5%) (0%) (0.5%) (1.0%)
8.0% 103 111 119 127 135
8.5% 95 103 110 118 126
9.0% 89 96 103 110 117
9.5% 83 90 96 103 110
W
A
C
C
%
10.0% 78 84 91 97 103
68
Capex is a key driver in DCF analysis; if possible, forecasts should
be based on maintaining relatively stable Net PPE % sales
? Common to forecast CAPEX based on % of sales (and depreciation % of capex)
? Required if we don’t have any balance sheet information (e.g., private company or division of larger company),
but…
? Can result in incorrect DCF valuation outcomes if strong future sales growth is not supported by necessary capital
expenditure
? Capex should be the plug after setting Net PPE % sales, depreciation as % Net PPE
? Example
? Forecasting business performance and capex for their business units to feed into a DCF valuation model
? Issue:
? The major division of the business was very capital intensive and therefore had a relatively low ROCE (NOPAT /
(Net PPE + NWI))
? Capex assumptions over time appeared reasonable at face value (as a % of sales), however on closer inspection,
ROCE employed increased dramatically, indicating that insufficient capital was being injected into the business to
support the forecast sales growth (given high Capital intensity)
? Analysis of ROCE and Capital Intensity benchmarks shows that CAPEX was underestimated
? Key Learning
? Analysis of Capex intensity and return on capital employed should be conducted when forecasting for DCF’s –
need balance sheet info and view of what appropriate level of capital for the business is
— If ROCE increases too much and capital intensity (Net PPE % sales) declines substantially versus peers then this
should be challenged and corrected.
Why do trading values differ from DCF?
? Market may view the firm’s outlook differently (different implied forecast)
? Due diligence in an M&A transaction may yield material private information that
affects DCF value but not public trading valuation
? Discounts
? Lack of liquidity
? IPO/spin-off
? Conglomerate
? Supply/demand imbalance
? Difference in capital structure
? Company doesn’t distribute all of its free cash flow to shareholders
? Option value
? Acquisition speculation
? Event risk
Why do transaction values differ from DCF?
? Control premium
? Cost of capital differences
? Buyer may assign a different cost of capital to target due to different view of risk
? High level of synergies
? Revenue enhancements
? Cost and capex savings
? Cross-border
? Differences in capital costs, tax rules, repatriation levels, etc.
? Differences in view of the future
? Buyer may have a dramatically different view of the future than the market
? Other strategic reasons
? Buy versus build
? Platform for other investments
? Defensive acquisition/strategic imperative
Relative Valuation
The Essence of relative valuation
? In relative valuation, the value of an asset is compared to the values assessed by the
market for similar or comparable assets.
? To do relative valuation then we need to identify comparable assets and obtain
market values for these assets
? Convert these market values into standardized values, since the absolute prices
cannot be compared This process of standardizing creates price multiples.
? Compare the standardized value or multiple for the asset being analyzed to the
standardized values for comparable asset, controlling for any differences between
the firms that might affect the multiple, to judge whether the asset is under or over
valued
Relative valuation is pervasive
? Almost 85% of equity research reports are based upon a multiple and comparables.
? More than 50% of all acquisition valuations are based upon multiples
? Rules of thumb based on multiples are not only common but are often the basis for
final valuation judgments.
? While there are more discounted cashflow valuations in consulting and corporate
finance, they are often relative valuations masquerading as discounted cash flow
valuations.
? The objective in many discounted cashflow valuations is to back into a number that
has been obtained by using a multiple.
? The terminal value in a significant number of discounted cashflow valuations is
estimated using a multiple.
The Market Imperative
? Relative valuation is much more likely to reflect market perceptions and moods than
discounted cash flow valuation. This can be an advantage when it is important that
the price reflect these perceptions as is the case when
? The objective is to sell a security at that price today (as in the case of an IPO)
? With relative valuation, there will always be a significant proportion of securities
that are under valued and over valued.
? Since portfolio managers are judged based upon how they perform on a relative basis
(to the market and other money managers), relative valuation is more tailored to
their needs
? Relative valuation generally requires less information than discounted cash flow
valuation (especially when multiples are used as screens)
The Four Steps to Deconstructing Multiples
? Define the multiple
? In use, the same multiple can be defined in different ways by different users. When
comparing and using multiples, estimated by someone else, it is critical that we
understand how the multiples have been estimated
? Describe the multiple
? Too many people who use a multiple have no idea what its cross sectional
distribution is. If you do not know what the cross sectional distribution of a multiple
is, it is difficult to look at a number and pass judgment on whether it is too high or
low
? Analyze the multiple
? It is critical that we understand the fundamentals that drive each multiple, and the
nature of the relationship between the multiple and each variable
? Apply the multiple
? Defining the comparable universe and controlling for differences is far more difficult
in practice than it is in theory
Definitional Tests
? Is the multiple consistently defined?
? Key Rule: Both the value (the numerator) and the standardizing variable ( the
denominator) should be to the same claimholders in the firm. In other words, the
value of equity should be divided by equity earnings or equity book value, and
firm value should be divided by firm earnings or book value
? Is the multiple uniformly estimated?
? The variables used in defining the multiple should be estimated uniformly across
assets in the ?comparable firm? list
? If earnings-based multiples are used, the accounting rules to measure earnings
should be applied consistently across assets. The same rule applies with book-value
based multiples
An Example: Price Earnings Ratio: Definition
PE = Market Price per Share / Earnings per Share
? There are a number of variants on the basic PE ratio in use. They are based upon
how the price and the earnings are defined
? Price: is usually the current price
is sometimes the average price for the year
? EPS: earnings per share in most recent financial year
earnings per share in trailing 12 months (Trailing PE)
forecasted earnings per share next year (Forward PE)
forecasted earnings per share in future year
Enterprise Value /EBITDA Multiple
? The enterprise value to EBITDA multiple is obtained by netting cash out against
debt to arrive at enterprise value and dividing by EBITDA.
? Net out cash from firm value
Enterprise Value
EBITDA
=
Market Value of Equity + Market Value of Debt - Cash
Earnings before Interest,Taxes and Depreciation
Descriptive Tests
? The average and standard deviation for this multiple, across the universe (market)
? The median for this multiple
? The median for this multiple is often a more reliable comparison point.
? Outliers
? Size of the outliers
? Throwing out the outliers may seem like an obvious solution, but if the outliers all lie
on one side of the distribution (they usually are large positive numbers), this can
lead to a biased estimate.
? Special cases for multiple estimation
? Change in multiple over time
PE Ratio: Descriptive Statistics for US
0
100
200
300
400
500
600
700
800
0-4 4-8 8-12 12-16 16-20 20- 25 25-30 35-40 40-50 50-100 >100
PE Range
Current, Trailing and Forward PE_ January 2003
Current PE
Trailing PE
Forward PE
PE: Deciphering the Distribution
Current PE Trailing PE Forward PE
Mean 33.36 32.75 24.46
Standard Error 2.02 2.21 1.20
Median 16.68 15.42 15.29
Skewness 23.78 18.98 15.42
Minimum 0.81 0.92 2.72
Maximum 4382.00 4008.00 1364.00
Count 3721 2973 2035
100th largest 135.33 119.41 55.88
100th smallest 2.18 0.03 7.45
Analytical Tests
? The fundamentals that determine and drive these multiples
? Key rule: Both Embedded in every multiple are all of the variables that drive
every discounted cash flow valuation - growth, risk and cash flow patterns.
? In fact, using a simple discounted cash flow model and basic algebra should yield the
fundamentals that drive a multiple
? Changes in these fundamentals change the multiple
? The relationship between a fundamental (like growth) and a multiple (such as PE) is
seldom linear.
? For example, if firm A has twice the growth rate of firm B, it will generally not trade
at twice its PE ratio
? Key rule: It is impossible to properly compare firms on a multiple, if we do not
know the nature of the relationship between fundamentals and the multiple.
Relative Value and Fundamentals: Equity Multiples
? Gordon Growth Model:
? Dividing both sides by the earnings,
? Dividing both sides by the book value of equity,
? Dividing by the Sales per share,
P
0
=
DPS
1
r ÷ g
n
P
0
EPS
0
= PE=
Payout Ratio*(1+ g
n
)
r-g
n
n
n
0
0
-g r
) g (1 * Ratio Payout * ROE
= PBV
BV
P +
=
P
0
Sales
0
= PS=
Profit Margin*Payout Ratio*(1+ g
n
)
r-g
n
The Determinants of Multiples
Value of Stock = DPS
1
/(k
e
- g)
PE=Payout Ratio
(1+g)/(r-g)
PEG=Payout ratio
(1+g)/g(r-g)
PBV=ROE (Payout ratio)
(1+g)/(r-g)
PS= Net Margin (Payout ratio)
(1+g)/(r-g)
Value of Firm = FCFF
1
/(WACC -g)
Value/FCFF=(1+g)/
(WACC-g)
Value/EBIT(1-t) = (1+g)
(1- RIR)/(WACC-g)
Value/EBIT=(1+g)(1-
RIR)(1-t)/(WACC-g)
VS= Oper Margin (1-t)
(1-RIR) (1+g)/(WACC-g)
Equity Multiples
Firm Multiples
PE=f(g, payout, risk) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS=f(Net Mgn, payout, g, risk)
V/FCFF=f(g, WACC) V/EBIT(1-t)=f(g, RIR, WACC) V/EBIT=f(g, RIR, WACC, t) VS=f(Oper Mgn, RIR, g, WACC)
Using the Fundamental Model to Estimate PE For a High Growth
Firm
? The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of
the two-stage dividend discount model, this relationship can be made explicit fairly simply:
? For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout
ratio.
? Dividing both sides by the earnings per share:
P
0
=
EPS
0
* Payout Ratio*(1+ g)* 1 ÷
(1+ g)
n
(1+ r)
n
|
\
|
.
r - g
+
EPS
0
* Payout Ratio
n
*(1+ g)
n
*(1+ g
n
)
(r -g
n
)(1+ r)
n
P
0
EPS
0
=
Payout Ratio* (1 + g) * 1 ÷
(1 + g)
n
(1+ r)
n
|
\
|
.
|
r - g
+
Payout Ratio
n
*(1+ g)
n
* (1 + g
n
)
(r - g
n
)(1+ r)
n
A Simple Example
? Assume that you have been asked to estimate the PE ratio for a firm which has the
following characteristics:
Variable High Growth Phase Stable Growth
Phase
Expected Growth Rate 25% 8%
Payout Ratio 20% 50%
Beta 1.00 1.00
Number of years 5 years Forever after
? Riskfree rate = T.Bond Rate = 6%
? Required rate of return = 6% + 1(5.5%)= 11.5%
PE =
0.2 * (1.25) * 1÷
(1.25)
5
(1.115)
5
|
\
|
.
|
(.115 - .25)
+
0.5 * (1.25)
5
*(1.08)
(.115- .08) (1.115)
5
= 28.75
PE and Growth: Firm grows at x% for 5 years, 8%
thereafter
PE Ratios and Expected Growth: Interest Rate Scenarios
0
20
40
60
80
100
120
140
160
180
5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Expected Growth Rate
P
E
R
a
t
i
o
r=4%
r=6%
r=8%
r=10%
PE Ratios and Length of High Growth: 25% growth
for n years; 8% thereafter
PE Ratios and Length of High Growth Period
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10
Length of High Growth Period
P
E
R
a
t
i
o
g=25%
g=20%
g=15%
g=10%
PE and Payout
PE Ratios and Payout Ratios: Growth Scenarios
0
5
10
15
20
25
30
35
0% 20% 40% 60% 80% 100%
Payout Ratio
P
E
g=25%
g=20%
g=15%
g=10%
Application Tests
? Given the firm that we are valuing, defining the comparable? firm
? While traditional analysis is built on the premise that firms in the same sector are
comparable firms, valuation theory would suggest that a comparable firm is one
which is similar to the one being analyzed in terms of fundamentals.
? Key Rule: There is no reason why a firm cannot be compared with another firm in
a very different business, if the two firms have the same risk, growth and cash
flow characteristics.
? Given the comparable firms, adjusting for differences across firms on the
fundamentals
? Key Rule: It is impossible to find an exactly identical firm to the one you are
valuing.
An example from the power sector
Name PE
Indowind Energy 22.1
Jaiprakash Hydro 14.39
Neyveli Lignite 12.34
NTPC 22.26
Energy Devlop.Co 17.59
Average 17.74
Standard Deviation 4.47
Torrent Power
Torrent
Power Expected Actual Error in %
PE 17.74 20.52 13.57
EPS 4.97 4.97 -
Share Price 88.15 101.98 13.57
Multiple accuracy
Companies considered Expected Actual Error in %
Indowind Energy 22.1 17.74 24.61
Jaiprakash Hydro 14.39 17.74 18.87
Neyveli Lignite 12.34 17.74 30.42
NTPC 22.26 17.74 25.51
Energy Devlop.Co 17.59 17.74 0.82
DCF base case Trading multiples
DCF synergy case Trading value with synergies
M&A value
Market value
Synergies +
Transaction multiples
Synergies
=
x
Transaction price
–
Part of
synergies
+
Premiums
Valuation is complex, requires experience and checks
between methods—should give same answers
? Market assumptions
? Market WACC
? Management deliverable
synergy assumptions
? Market WACC
? Exit financials
? Comparable transaction
multiples
? Current trading value
? Comparable transaction
premiums
? Market assumptions
? Comparable trading multiples
? Synergy multiples x after-tax
cost savings
Thank You
doc_927215592.pptx
This is a presentation about various valuation models.
VALUATION
Group 3
A Notion of Value
?“Value is in the eye of the beholder”
? Value is a relative notion.
• Is it what something is worth ?
• Is it what the market thinks it’s worth ?
• Is it what a strategic or motivated buyer think
it’s worth ?
?Differentiate “Price” from Value
Valuation by Replication
• How do you estimate the price of a 7 room
apartment on Park Ave if someone tells you
the price of a 2 room apartment in Battery
Park City?
• Yield to Maturity in Bond Pricing!
• Black-Scholes is all about: it tells you the
price of an option in terms of the price of a
stock and a bond.
Valuation Models
Asset Based
Valuation
Discounted Cashflow
Models
Relative Valuation Contingent Claim
Models
Liquidation
Value
Replacement
Cost
Equity Valuation
Models
Firm Valuation
Models
Cost of capital
approach
APV
approach
Excess Return
Models
Stable
Two-stage
Three-stage
or n-stage
Current
Normalized
Equity
Firm
Earnings Book
Value
Revenues Sector
specific
Sector
Market
Option to
delay
Option to
expand
Option to
liquidate
Patent Undeveloped
Reserves
Young
firms
Undeveloped
land
Equity in
troubled
firm
Dividends
Free Cashflow
to Firm
Approaches to Valuation
• Discounted cash flow valuation, relates the value of an
asset to the present value of expected future cash flows
on that asset
• Relative valuation, estimates the value of an asset by
looking at the pricing of 'comparable' assets relative to a
common variable like earnings, cash flows, book value or
sales
• Contingent claim valuation, uses option pricing models to
measure the value of assets that share option
characteristics
Which approach should you use?
Mature businesses
Separable & marketable assets
Growth businesses
Linked and non-marketable assets
Liquidation &
Replacement cost
valuation
Other valuation models
Asset Marketability and Valuation Approaches
Cashflows currently or
expected in near future
Assets that will never
generate cashflows
Discounted cashflow
or relative valuation
models
Relative valuation models
Cash Flows and Valuation Approaches
Cashflows if a contingency
occurs
Option pricing models
Unique asset or business
Large number of similar
assets that are priced
Discounted cashflow
or option pricing
models
Relative valuation models
Uniqueness of Asset and Valuation Approaches
Depends upon the asset being valued..
And the analyst doing the valuation
Very short time horizon Long Time Horizon
Liquidation value Discounted Cashflow value
I nvestor Time Horizon and Valuation Approaches
Option pricing
models
Relative valuation
Markets are correct on
average but make mistakes
on individual assets
Discounted Cashflow value
Views on market and Valuation Approaches
Option pricing models
Relative valuation
Markets make mistakes but
correct them over time
Asset markets and financial
markets may diverge
Liquidation value
Basis for all valuation approaches
• The use of valuation models in investment decisions (i.e., in
decisions on which assets are under valued and which are over
valued) are based upon
– a perception that markets are inefficient and make mistakes in assessing
value
– an assumption about how and when these inefficiencies will get corrected
• In an efficient market, the market price is the best estimate of value
• The purpose of any valuation model is then the justification of this
value
DISCOUNTED CASH FLOW VALUATION
Just 5 baby steps
? Single cash flow:
PV = CF
1
/(1+r)
? Single cash flow in “n” years from now:
PV = CF
n
/(1+r)
n
? Multiple cash flows in future:
PV = CF
1
/(1+r)+CF
2
/(1+r)
2
+CF
3
/(1+r)
3
+…
? Perpetuity of fixed cash flows:
PV = CF/r (1
st
CF is at the end of year 1)
? Growing Perpetuity:
PV = CF/(r-g) (1
st
CF at end of year 1, then grow at g)
Can you estimate cash flows?
Yes No
Use dividend
discount model
Is leverage stable or
likely to change over
time?
Stable
leverage
Unstable
leverage
Are the current earnings
positive & normal?
Yes
Use current
earnings as
base
No
Is the cause
temporary?
Yes No
Replace current
earnings with
normalized
earnings
Is the firm
likely to
survive?
Yes No
Adjust
margins over
time to nurse
firm to financial
health
Does the firm
have a lot of
debt?
Yes
No
Value Equity
as an option
to liquidate
Estimate
liquidation
value
What rate is the firm growing
at currently?
< Growth rate
of economy
Stable growth
model
> Growth rate of
economy
Are the firm’s
competitive
advantges time
limited?
Yes No
2-stage
model
3-stage or
n-stage
model
FCFE FCFF
Choosing the appropriate model
The flow in DCF analysis
=
Weighted average cost
of capital
Weighted by current share
of firm value
Cost of equity
Firm value
Minorities
Debt
All market value
Preference stock
Market values
Cash equity
investments Equity
value
- +
Cost of debt
10 years explicit and
perpetuity
Projected income statement
10 years explicit and
perpetuity
Projected balance sheet
DCF = valuation of firm’s or asset’s projected
free cash flows in perpetuity using its risk-
adjusted weighted average cost of capital
(WACC)
Projected free cash
flows
Predictable cash flows
The process of DCF analysis
? Project the operating results and free cash flows of the business over the
forecast period (typically 10 years, but can be 5–20 years depending on the
profitability horizon)
? Estimate the exit multiple and/or growth rate in perpetuity of the business
at the end of the forecast period
? Estimate the company’s weighted-average cost of capital to determine the
appropriate discount rate range
? Determine a range of values for the enterprise by discounting the
projected free cash flows and terminal value to the present
? Adjust the resulting valuation for all assets and liabilities not accounted for
in cash flow projections
Projections/FCF
Terminal value
Discount rate
Present value
Adjustments
2 basic DCF approaches should be kept independent
? DCF of unlevered cash flows
? Projected income and cash-flow streams are free of the effects of debt, net of
excess cash
? Present value obtained is the value of assets, assuming no debt or excess cash
(?firm value? or ?enterprise value?)
? Debt associated with the business is subtracted (and excess cash balances are
added) to determine the present value of the equity (?equity value?)
? Cash flows are discounted at the weighted-average cost of capital
? DCF of levered cash flows (most common in valuation of financial institutions)
? Projected income and cash-flow streams are after interest expense and net of any
interest income
? Present value obtained is the value of equity
? Cash flows are discounted at the cost of equity
The first step in DCF analysis is projection of
unlevered free cash flows
? Calculation of unlevered free cash flow begins with financial projections
? Comprehensive projections (i.e., fully-integrated income statement, balance sheet
and statement of cash flows) typically provide all the necessary elements
? Quality of DCF analysis is a function of the quality of projections
? Often required to ?fill in the gaps?
? Confirm and validate key assumptions underlying projections
? Sensitize variables that drive projections
? Sources of projections include
? Target company’s management
? Acquiring company’s management
? Research analysts
? Bankers
Projecting cash flows requires in-depth
understanding of the business
Accurate
cash flow
estimate
Anticipated industry growth
Major opportunities/risks
Pricing flexibility
Possible market share changes
Cost structure
Expansion opportunities
New product/stores/format
Development costs
Economies of scale
Reinvestment needs
Working capital
Required capital expenditures
Discretionary investments
Competitive position Industry outlook
Capital expenditure and working capital
Capital expenditures should include
•Research and development expenses, once they have been re-categorized as
capital expenses
•Acquisitions of other firms, whether paid for with cash or stock
•Working capital should be defined not as the difference between current assets
and current liabilities but as the difference between non-cash current assets and
non-debt current liabilities
•On both items, start with what the company did in the most recent year but do
look at the company’s history and at industry averages
Projecting financial statements
? Ideally projections should go out as far into the future as can reasonably be estimated to
reduce dependence on the terminal value
? Most important assumptions
? Sales growth: Use divisional, product-line or location-by-location build-up or simple growth
assumptions
? Operating margins: Evaluate improvement over time, competitive factors, SG&A costs
? Synergies: Estimate dollars in Year 1 and evaluate margin impact over time
? Depreciation: Should conform with historic and projected capex
? Capital expenditures: Consider both maintenance and expansion capex
? Changes in net working capital: Should correspond to historical patterns and grow as the
business grows
? Should show historical financial performance and sanity check projections against past results.
Be prepared to articulate why projections may or may not be similar to past results (e.g.
reasons behind margin improvements, increased sales growth, etc.)
? Analyze projections for consistency
? Sales increases usually require working capital increases
? CAPEX and depreciation should converge over time
Free cash flow is the cash that remains for creditors and
owners after taxes and reinvestment
? Unlevered free cash flows can be forecast from a firm’s financial projections, even
if those projections include the effects of debt
? To do this, simply start your calculation with EBIT (earnings before interest and
taxes)
? EBIT (from the income statement)
Plus: Non-tax-deductible goodwill amortization
Less: Taxes (at the marginal tax rate)
? Equals: Tax-effected EBITA (NOPAT)
Plus: Deferred taxes
1
Plus: Depreciation and any tax-deductible amortization
Less: Capital expenditures
Plus/(less): Decrease/(increase) in net working investment
? Equals: Unlevered free cash flow
1
One should only include actual cash taxes paid in the DCF. Depending on the firm and industry, you may want to adjust for the non-cash (or deferred) portion of a firm’s tax provision. The tax
footnote in the financial statements will give you a good idea of whether this is a meaningful issue for your analysis
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working
capital
10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Example: Calculating unlevered free cash flows
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Stand-alone DCF analysis of Company X
$ millions
Once unlevered free cash flows are calculated,
they must be discounted to the present
? The standard present value calculation takes into account the cost of capital by attributing greater
value to cash flows generated earlier in the projection period than later cash flows
? Since most businesses do not generate all of their free cash flows on the last day of the year, but
rather more-or-less continuously during the year, DCF analyses often use the so-called “mid-year
convention,” which takes into account the fact that free cash flows occur during the year
? This approach moves each cash flow from the end of the applicable period to the middle of the same
period (i.e., cash flows are moved closer to the present)
FCF
1
FCF
2
FCF
3
FCF
n
Present value =
(1+r)
1
+
(1+r)
2
+
(1+r)
3
+
. . .
+
(1+r)
n
FCF
1
FCF
2
FCF
3
FCF
n
Present value =
(1+r)
0.5
+
(1+r)
1.5
+
(1+r)
2.5
+
. . .
+
(1+r)
n-0.5
Mid year
standard
It is important to differentiate between the
transaction date and the mid-year convention
Year
0 1 2 3 0.5 1.5 2.5 3.5
First cash flow,
mid-year 1
Second cash flow,
mid-year 2
Third cash flow,
mid-year 3
Discounting =
CF
1
(1+r)
0.5
+
CF
2
(1+r)
1.5
+
CF
3
(1+r)
2.5
+ ….
Year
0 1 2 3 0.75 1.5 2.5 3.5
First cash flow,
mid-period 1
Second cash flow,
mid-year 2
Third cash flow,
mid-year 3
Discounting =
CF
1
(1+r)
(0.75-0.5)
+ +
CF
3
(1+r)
(2.5-0.5)
+ ….
0.5
Period 1 CF to buyer
CF
2
(1+r)
(1.5-0.5)
Transaction date: 01/01
Transaction date: 06/30
Stand-alone DCF analysis of Company X
$ millions
Example: Discounting free cash flows
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Discount rate = 10%
$189.6 =
$46.8
(1+.10)
0.5
$53.8
(1+.10)
1.5
$61.4
(1+.10)
2.5
$69.6
(1+.10)
3.5
+ + +
Formula
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Terminal value can account for a significant
portion of value in a DCF analysis
? Terminal value represents the business’s value at the end of the projection period; i.e., the
portion of the company’s total value attributable to cash flows expected after the projection
period
? Terminal value is typically based on some measure of the performance of the business in the
terminal year of the projection (which should depict the business operating in a steady-
state/normalized manner)
? Growth in perpetuity method
— Assumes that the business is held in perpetuity and that free cash flows continue to
grow at an assumed rate
? Terminal (or “Exit”) multiple method
— Assumes that the business is valued/sold at the end of the terminal year at a multiple of
some financial metric (typically EBITDA)
? A terminal multiple will have an implied growth rate and vice versa. It is essential to
review the implied multiple/growth rate for sanity check purposes
? Once calculated, the terminal value is discounted back to the appropriate date using the
relevant rate
? Attempt to reduce dependence on the terminal value
? What is appropriate projection time frame?
? What percentage of total value comes from the terminal value?
Terminal multiple method
? This method assumes that the business will be valued at the end of the last year of the
projected period
? The terminal value is generally determined as a multiple of EBIT, EBITDA or EBITDAR; this
value is then discounted to the present, as were the interim free cash flows
? The terminal value should be an asset (firm) value; remember that not all multiples
produce an asset value
? Note that in the exit multiple method terminal value is always assumed to be calculated at
the end of the final projected year, irrespective of whether you are using the mid-year
convention
? Should the terminal multiple be an LTM multiple or a forward multiple?
? If the terminal value is based on the last year of your projection then the multiple should
be based on an LTM multiple (most common)
? There are circumstances where you will project an additional year of EBITDA and apply a
forward multiple
Most common error: The final year is not
normalized
? Consider adding a year to the projections which represents a normalized year
? A steady-state, long-term industry multiple should be used rather than a current multiple,
which can be distorted by contemporaneous industry or economic factors
? Treat the terminal value cash flow as a separate, critical forecast
? Growth rate
— Consistent with long-term economic assumptions
? Reinvestment rate
— Net working investment consistent with projected growth
— Capital expenditures needed to fuel estimated growth
— Depreciation consistent with capital expenditures
? Margins
— Adjusted to reflect long-term estimated profitability
? Normalized tax rate
Growth in perpetuity method
? This method assumes that the business will be owned in perpetuity and that the
business will grow at approximately the long-term macroeconomic growth rate
? Few businesses can be expected to have cash flows that truly grow forever; be
conservative when estimating growth rates in perpetuity
? Take free cash flow in the last year of the projection period, n, and grow it one
more year to n+1;
1
this free cash flow is then capitalized at a rate equal to the
discount rate minus the growth rate in perpetuity
? To ensure that the terminal year is normalized, models are set up to project one
year past the projection year and allow for normalizing adjustments; this FCFn+1 is
then discounted by the perpetuity formula
Terminal value = (FCF
n+1
)/(WACC — g)
where FCF
n+1
= FCF in year after projections
g = growth rate in perpetuity
WACC = weighted-avg. cost of capital
PV of terminal value = terminal value/(1+WACC)
n-0.5
Recommended method Academic formula
Terminal value = (FCF
n
* (1 + g))/(WACC — g)
where FCF
n
= FCF in final projected period
g = growth rate in perpetuity
WACC = weighted-avg. cost of capital
PV of terminal value = terminal value/(1+WACC)
n-0.5
1
This step is taken because the perpetuity growth formula is based on the principle that the terminal value of a business is the value of its next cash flow, divided by the
difference between the discount rate and a perpetual growth rate
Growth in perpetuity method (cont’d)
? Note that when using the mid-year convention, terminal value is discounted as if
cash flows occur in the middle of the final projection period
? Here the growth-in-perpetuity method differs from the exit-multiple method
? Typical adjustments to normalize free cash flow in Year n include revising the
relationship between revenues, EBIT and capital spending, which in turn affects
CAPEX and depreciation
? Working capital may also need to be adjusted
? Often CAPEX and depreciation are assumed to be equal
Example: Growth in perpetuity method
Key assumptions:
Deal/valuation date = 31/12/07
Marginal tax rate = 40%
Discount rate = 10%
Perpetuity growth rate = 3%
Fiscal year ending December 31,
2004 2005 2006 2007E 2008E 2009E 2010E 2011E
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes – – – – –
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Discounted value of unlevered FCF $0.0 $44.6 $46.7 $48.4 $49.9
Discounted value of FCF 2005P–2008P 189.6
PV of Terminal Value 733.7
Total present value to acquirer $923.3
$733.6 =
$69.6 * (1 + .03)
(.10 - .03)*(1+.10)
3.5
Formula
Stand-alone DCF analysis of Company X
$ millions
Example: Terminal multiple method
Key assumptions:
Deal/valuation date = 12/31/04
Marginal tax rate = 40%
Discount rate = 10%
Exit multiple of EBITDA = 7.0x
$745.4 =
($155.9 * 7.0x)
(1+.10)
4
Formula
Fiscal year ending December 31,
2001 2001 2003 2004P 2005P 2006P 2007P 2008P
Net sales $400.0 $440.0 $484.0 $532.4 $585.6 $644.2 $708.6 $779.5
EBITDA 80.0 88.0 96.8 106.5 117.1 128.8 141.7 155.9
Less: Depreciation 12.0 13.2 14.5 16.0 17.6 19.3 21.3 23.4
EBITA 68.0 74.8 82.3 90.5 99.6 109.5 120.5 132.5
Less: Taxes at marginal rate 27.2 29.9 32.9 36.2 39.8 43.8 48.2 53.0
Tax-effected EBITA $40.8 $44.9 $49.4 $54.3 $59.7 $65.7 $72.3 $79.5
Plus: Depreciation 16.0 17.6 19.3 21.3 23.4
Plus: Deferred taxes — — — — —
Less: Capital expenditures 20.0 22.0 24.2 26.6 29.3
Less: Incr./(decr.) in working capital 10.0 8.5 7.0 5.5 4.0
Unlevered free cash flow 40.3 46.8 53.8 61.4 69.6
Adjustment for deal date (40.3) — — — —
Unlevered FCF to acquirer $0.0 $46.8 $53.8 $61.4 $69.6
Memo: Discounting factor 0.0 0.5 1.5 2.5 3.5
Discounted value of unlevered FCF $0.0 $44.6 $46.7 $48.4 $49.9
Discounted value of FCF 2005P–2008P 189.6
EBITDA in 2008P $155.9
Exit multiple 7.0x
Firm value at exit 1,091.3
Discounted terminal value 745.4
Total present value to acquirer $934.9
Stand-alone DCF analysis of Company X
$ millions
Terminal multiples and perpetuity growth rates
are often considered side-by-side
? Assumptions regarding exit multiples are often checked for reasonableness by calculating
the growth rates in perpetuity that they imply (and vice versa)
? To go from the exit-multiple approach to an implied perpetuity growth rate:
g = [(WACC*terminal value) / (1+WACC)
0.5
- FCF
n
] / [FCF
n
+ (terminal value / (1 +
WACC)
0.5
)]
? To go from the growth-in-perpetuity approach to an implied exit multiple:
multiple = [FCF
n
* (1 + g)(1 + WACC)
0.5
] / [EBITDA
n
* (WACC - g)]
? These formulas adjust for the different approaches to discounting terminal value when
using the mid-year convention
Discount free cash flows at market cost of capital to get
enterprise value, minus net debt = equity value
? Value to closest year—value here is at
December 31, 2003
? Refine if necessary, including shifting
free cash flows to mid-year
? Terminal value calculated using
perpetuity growth rate of inflation only
? Enterprise value = value of cash flows to
be shared between net debt, minorities
and equity
? Option expense = Black-Scholes value of
outstanding options plus future
issuance assumed at 1.3% of NOSH
? Divide equity value by number of shares
(1,076mm) to get value per share
? Should coincide with share price
? Derive key multiples and check with
comps
Example
DCF-WACC valuation Base
WACC—taxed 7.13%
NPV FCF F2004—2013 26,100
NPV terminal value 49,400
Enterprise value 75,500
Cash 2,985
Investments 3,688
Debt (5,518)
Minority interests 0
Convertible preferred debt 0
Options outstanding (1,299)
Option grant NPV (4,856)
Equity value 70,500
Equity value per share 65.50
Share price 65.53
DCF % share price 100%
Firm value/EBITDA F2004 15.6
Choosing the discount rate is a critical step in
DCF analysis
? The discount rate represents the required rate of return given the risks inherent in
the business, its industry, and thus the uncertainty regarding its future cash flows,
as well as its optimal capital structure
? Typically the weighted average cost of capital (WACC) will be used as a foundation
for setting the discount rate
? The WACC is always forward-looking and is predicted based on the expectations of
an investment's future performance; an investor contributes capital with the
expectation that the riskiness of cash flows will be offset by an appropriate return
? The WACC is typically estimated by studying capital costs for existing investment
opportunities that are similar in nature and risk to the one being analyzed
? The WACC is related to the risk of the investment, not the risk or creditworthiness
of the investor¹
1
In valuing a company, always use the riskiness of its cash flows or comparable companies in estimating a weighted average cost of capital. Never use the acquirer’s cost capital unless, by some chance, it is engaged in an
extremely similar line of business. However, if a business is small relative to an acquiror’s, sometimes it may be appropriate to consider the use of the acquiror’s WACC in performing the valuation. The additional value
created by using the acquiror’s WACC can be viewed as a synergy to the acquiror in the context of the transaction.
Cost
of
equity
Mix of debt
and equity
Cost
of
debt
Three variables are relevant to determine weighted
average cost of capital
Derived using capital asset pricing model
(“CAPM”)
Cost of equity = RF + [B * (ERM - RF)]
? Risk free rate (“RF”)
? T-Bill
? 10-yr Treasury
? 30-yr Treasury
? Beta (“B”)
? Predicted, adjusted
? Historical
? Industry
? Expected Return on Market (“ERM”)
? Dividend Discount Model
? Arithmetic average
? Other various methodologies
Weighted by market value
? Medium term net debt and
current equity
value
? Current mix
? Target mix
? Industry mix
Market value of debt
? After tax basis
? Based on cost of
medium-term debt
CAPM approach to determine a firm’s cost of
equity
? Many companies use arbitrary discount rates
? Some investors and many advisors use arbitrary equity risk premiums (often 5%—7%)
Capital asset pricing model (CAPM)
E(r
i
) = r
f
+ ß
i
x [E(r
m
) - r
f
]
Expected return
on stock i
Risk-free rate
10-year government
bond yield
Beta of stock i
Investor judgment of
stock’s relative risk
Expected return
on market
Quantified from
various market
models
Risk-free rate
10-year government
bond yield
Equity risk premium
Derived as difference
between E(r
m
) and r
f
Most contentious/
difficult parts
The cost of equity is the major component of the
WACC
? The cost of equity reflects the long-term return expected by the market (dividend yield plus
share appreciation)
? Risk-free rate based on the 10 year bond yield
? Incorporates the undiversifiable risk of an investment (beta)
? Equity risk premium reflects expectations of today’s market
? The market risk premium (r
m
- r
f
; i.e., the spread of market return over the risk-free rate) is
periodically estimated
Cost of equity = Risk free rate + Beta x Equity risk premium
Long-term return on
equity investment in
today’s market
=
Long-term risk-free rate
of return (beta=0)
+
Adjustment for
correlation to
stock market
returns
x
Appropriate “extra”
return above risk free
rate
= 10-year bond yield
(annual average)
+ Predicted betas x Estimated using various
techniques
For market average = 4.97% + 1.00 x 5.00%
= 9.97%
Beta
? Beta provides a method to estimate an asset's systematic (non-diversifiable) risk
? Beta equals the covariance between expected returns on the asset and on the
stock market, divided by the variance of expected returns on the stock market
? A company whose equity has a beta of 1.0 is “as risky” as the overall stock market
and should therefore be expected to provide returns to investors that rise and fall
as fast as the stock market; a company with an equity beta of 2.0 should see
returns on its equity rise twice as fast or drop twice as fast as the overall market
? Returning to our CAPM formula, the beta determines how much of the market risk
premium will be added to or subtracted from the risk-free rate
? Since the cost of capital is an expected value, the beta value should be an
expected value as well
“Beta” is the most subjective part of DCF—
attempts to estimate undiversifiable risk relative
to market
Size/market cap.
Decreasing size = more risk
Multiples relative to
growth
Lower multiples/
higher yields
Stock price momentum
Higher excess return = more risk
Unexplained
volatility
Higher unknown risks
Leverage
Increasing leverage = more financial risk
Higher expected return =
higher cost of equity
= more risk
Industry
Some industries have higher returns
0
200
400
600
800
(1.5) (1.0) (0.5) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
Beta
#
o
f
c
o
m
p
a
n
i
e
s
Historical Beta Predicted Beta
Predicted betas to calculate the cost of equity
0
200
400
600
800
(0.5) 0.2 1.0 1.9 2.6
Beta
#
o
f
c
o
m
p
a
n
i
e
s
Predicted betas
Supermarkets
0.78
Utilities
0.43
Food
0.52
Internet
2.09
Cellular
1.62
Distribution of predicted and historical betas for 5,600 publicly-traded companies
? Predicted betas are constructed to adjust for many risk factors, incorporating firms’ earnings volatility, size,
industry exposure, and leverage
? Predicted betas are more consistent and less volatile than historical betas
? Historical betas only measure the past relationship between a firm’s return and market returns and are
often distorted
? Projected betas can be obtained from an online database
? Note that Bloomberg betas are based on historic prices and are therefore not forward-looking
? Impute unlevered beta for private company from public comparables
Calculate risk premium
? Consider relevant time frame and use AM or GM
? Generally, geometric averages provide better estimates of risk premiums in valuation
? The risk premiums will vary across markets, depending upon their riskiness. While historical data can be
used to estimate premiums outside the United States, it is not very reliable. An alternative way of
estimating premiums is to use country bond ratings to estimate these premiums relative to the U.S.
premium
Country Rating Risk Premium
Argentina BBB
5.5% + 1.75%
= 7.25%
Brazil BB
5.5% + 2% =
7.5%
Chile AA
5.5% + 0.75%
= 6.25%
Columbia A+
5.5% + 1.25%
= 6.75
Using APM to calculate the cost of equity
? The arbitrage pricing model relates expected returns to economic factors, with a beta specific to each
factor. If these factor-specific betas and the factor risk premia can be estimated, the cost of equity can also
be estimated.
where,
Rf = Riskfree rate
bj = Beta specific to factor j
E(Rj) - Rf = Risk premium per unit of factor j risk
k = Number of factors
\
Using Dividend growth model to calculate the cost
of equity
? ke = DPS1 / P0 + g
= Expected Dividend Yield + Growth rate in earnings/dividends
where,
P0 = Price of the stock today
DPS1 = Expected dividends per share next year
ke = Cost of Equity
g = Growth rate in dividends (steady state)
? Since the current price is a key input to the model, it is inappropriate to use this approach to value stock in
a firm
? There is a strong element of circular reasoning involved that will lead the analyst to conclude, using this
cost of equity, that equity is fairly valued
43
Use long-term cost of debt in estimating WACC
? The long-term cost of debt is used because the cost of capital is normally
applied to long-term cash flows
? Using the long-term cost of debt removes any refinancing costs/risks
from the valuation analysis
? To the extent a company can fund its investments at a lower cost of
debt (with the same risk), this value should be attributed to the
finance staff
? Use the company’s normalized cash tax rate
45
Cost of equity
Cost of capital
10-year T-bond (Avg) 4.97%
Market risk premium 5.00%
(x) Beta (current predicted) 0.62
Adjusted market premium 3.10%
Cost of equity = 8.07%
Cost of debt
Cost of debt 6.25%
(-) Tax shield
1
2.19%
After-tax cost of debt 4.06%
The cost of equity and debt are blended together
based on a target capital structure
? The target capital structure reflects the company’s rating objective
? Firms generally try to minimize the cost of capital through the appropriate use of leverage
? The percentage weighting of debt and equity is usually based on the market value of a firm’s equity and debt position
? Most firms are at their target capital structure
? Adjustments should be made for seasonal or cyclical swings, as well as for firms moving toward a target
? Using a weighted average cost of capital assumes that all investments are funded with the same mix of equity and debt as
the target capital structure
Target capital structure
(Assumes current = optimal)
Debt/total capital
2
= 6.1%
Nominal WACC = 7. 82%
WACC = r
d
* [D *(1-T)] + r
e
* E
D+E D+E
Where:
E = Market value of equity
D = Market value of debt
T = Marginal tax rate
r
e
= Return on equity
r
d
= Return on debt
Illustrative weighted average cost of capital calculation
WACC formula
1
Assumes 35% marginal tax rate
2
Total capital = debt + market value of equity
Most common errors in calculating WACC
Cost of equity
? Equity risk premium based on very long time frame
? Substitute hurdle rate (goal) for cost of capital
? Use of historical (or predicted) betas that are clearly wrong
? Investment specific risk not fully incorporated (e.g., country risk premiums)
? Incorrect releveraging of the cost of equity
? Cost of equity based on book returns, not market expectations
Capital structure
? A target (possibly unrealistic) capital structure is used vs. actual
? Valuing a tax shield that may not exist
? WACC calculated based on book weights (should be market value, if available, book if not)
VALUATION MODELS IN A NUTSHELL
Cash in DCF valuation: Separated from other assets
? The simplest and most direct way of dealing with cash and marketable securities is to keep
it out of the valuation
? Once the firm has been valued, we generally add back the value of cash and marketable
securities and subtract out gross debt. (This is also equivalent to subtracting out net debt)
? Estimating how much cash is wasting cash…
? There are two solutions.
? No cash (or at least a negligible amount) will be wasting cash.
? Divide the interest income earned by the average cash balance during the year and to
compare this rate to the rate on a short-term government security (T-bill).
? Interest income for year = $ 3 million
? Average cash balance = $ 150 million
? Interest rate earned = 3/ 150 = 2%
? Treasury bill rate during year = 3%
? Wasting cash for year = ({3% - 2%} / 3%)* 150 = $ 50 million
Incorporating Cash into the DCF valuation
? When you value equity and use net income, you are valuing cash (because the interest
income from cash is part of net income). The cost of equity used then has to allow for the
firm’s cash holdings - the unlevered beta used should be the weighted beta of operating
assets and the beta of cash (zero)
? The danger with this approach is that it is built on the assumption that cash as a percent of
value will remain unchanged over time
Value of Holdings in other firms
Holdings in other firms can be categorized into
? Minority passive holdings, in which case only the dividend from the holdings is shown in
the balance sheet
? Minority active holdings, in which case the share of equity income is shown in the
income statements
? Majority active holdings, in which case the financial statements are consolidated
? After valuing the operating assets of a firm, using consolidated statements, it is common
to add on the balance sheet value of minority holdings (which are in book value terms)
and subtract out the minority interests (again in book value terms), representing the
portion of the consolidated company that does not belong to the parent company
? In a perfect world, we would strip the parent company from its subsidiaries and value
each one separately
? The value of the combined firm will be Value of parent company + Proportion of value of
each subsidiary
? To do this right, one will need to be provided with detailed information on each
subsidiary to estimated cash flows and discount rates
WHAT ARE INTANGIBLE ASSETS
? An asset that we can neither see nor feel. E.g. Goodwill of a firm or individual
? List of such assets include:
? Franchises, Copyrights & trademarks.
? Patents
? Brand names
? Some invisible assets include:
? Top notch management
? Loyal & well trained workforce
? Technical Know how's
CATEGORIZING INTANGIBLES
Independent and Cash flow
generating intangibles
Not independent and cash flow
generating to the firm
No cash flows now but potential
for cashflows in future
Examples Copyrights, trademarks, licenses,
franchises, professional practices
(medical, dental)
Brand names, Quality and Morale
of work force, Technological
expertise, Corporate reputation
Undeveloped patents, operating or
financial flexibili ty (to expand into
new products/markets or abandon
existing ones)
Valuation approach Estimate expected cashflows from
the product or service and discount
back at appropriate discount rate.
- Compare DCF value of firm
with intangible with firm
without (if you can find one)
- Assume that all excessreturns
of firm are due to intangible.
- Compare multiples at which
firm trades to sector averages.
Option valuation
- Value the undeveloped patent
as an option to develop the
underlying product.
- Value expansion options as call
options
- Value abandonment options as
put options.
Challenges - Life is usually finite and
terminal value may be small.
- Cashflows and value may be
person dependent (for
professional practices)
With multiple intangibles (brand
name and reputation for service), it
becomes difficult to break down
individual components.
- Need exclusivity.
- Difficult to replicate and
arbitrage (making option
pricing models dicey)
WAYS OF VALUING INTAGIBLES
? Capital Invested: We can estimate the book value of an asset by looking at what a
firm has invested in that asset over time. With brand name, for instance, this
would require looking at advertising expenditures over time, capitalizing these
expenses and looking at the balance that remains unamortized of these expenses
today.
? Discounted Cash Flow Valuation: We can discount the expected incremental cash
flows generated by the intangible asset in question to the firm. This will require
separating out the portion of the aggregate cash flows of a firm that can be
attributed to brand name or technological expertise and discounting back these
cash flows at a reasonable discount rate.
? Relative Valuation: One way to isolate the effect of an intangible asset such as
brand name is compare how the market values the firm (with the intangible) with
how it values otherwise similar companies without the intangible asset. The
difference can be attributed to the intangible asset.
VALUING COCA COLA BRAND NAME- CAPITAL INVESTED
Year
Total Selling
and Advertising
Brand Name
Relat ed
Expense
Amortization this
year
Unamortized
Expense
1980 $1,121 $561 $22.43 $0.00
1981 $1,189 $594 $23.77 $23.77
1982 $1,221 $610 $24.41 $48.83
1983 $1,376 $688 $27.52 $82.56
1984 $1,543 $771 $30.85 $123.41
1985 $1,579 $789 $31.57 $157.87
1986 $1,631 $815 $32.61 $195.68
1987 $1,777 $888 $35.53 $248.73
1988 $2,025 $1,013 $40.51 $324.05
1989 $2,232 $1,116 $44.64 $401.76
1990 $2,717 $1,359 $54.35 $543.47
1991 $3,069 $1,535 $61.39 $675.25
1992 $3,499 $1,750 $69.99 $839.84
1993 $3,797 $1,898 $75.93 $987.13
1994 $4,198 $2,099 $83.96 $1,175.44
1995 $4,657 $2,329 $93.15 $1,397.20
1996 $5,347 $2,673 $106.93 $1,710.93
1997 $5,235 $2,617 $104.69 $1,779.79
1998 $5,523 $2,761 $110.45 $1,988.16
1999 $6,543 $3,271 $130.85 $2,486.21
2000 $5,701 $2,850 $114.01 $2,280.27
2001 $4,099 $2,050 $81.99 $1,721.72
2002 $4,667 $2,334 $93.35 $2,053.63
2003 $4,992 $2,496 $99.84 $2,296.32
2004 $5,431 $2,715 $108.61 $2,606.72
$1,703.35 $26,148.75
Estimating brand value
? If we just accumulate the advertising expenses over time, assuming that 50% is
attributable to building up brand name, we get a value of $ 26 billion.
? If we adjust the expenses for inflation, the value that we obtain for the brand
name value is close to 50%.
? The two key problems with this approach are
? Estimating the proportion of advertising that can be attributed to brand name
building
? Estimating the life of brand name as an asset
GENERIC COMPARISON
Coca Cola With Cott Margins
Current Revenues = $21,962.00 $21,962.00
Length of high-growth period 10 10
Reinvestment Rate = 50% 50%
Operating Margin (after-tax) 15.57% 5.28%
Sales/Capital (Turnover ratio) 1.34 1.34
Return on capital (after-tax) 20.84% 7.06%
Growth rate during period (g) = 10.42% 3.53%
Cost of Capital during period = 7.65% 7.65%
Stable Growth Period
Growth rate in steady state = 4.00% 4.00%
Return on capital = 7.65% 7.65%
Reinvestment Rate = 52.28% 52.28%
Cost of Capital = 7.65% 7.65%
Value of Firm = $79,611.25 $15,371.24
Value of brand name = $79, 611 million - $15,371 million = $ 64,240 million
RELATIVE VALUATION
? Value of brand name = 16,406 (6.01 – 1.63) = $71,821 million
Coca Cola Cott
Market value of Equity $98,160 $949
Debt $7,178 $345
Cash $6,707 $27
Enterprise Value $98,631 $1,267
Sales $21,962 $1,646
EBITDA $7,760 $186
Capital Invested $16,406 $775
EV Multiples
EV/Sales 4.49 0.77
EV/EBITDA 12.71 6.81
EV/Capital Invested 6.01 1.63
INTANGIBLES GENERATING CASH FLOW IN FUTURE (not now)
? Assets to value are those that have the potential to create cash flows in the future but
do not right now.
? Assets are difficult to value on a discounted cash flow valuation basis and often
impossible to evaluate on a relative basis, they do have option characteristics and are
best valued using option pricing models.
? REAL OPTION PREMIUM
? Real option premium should be tacked to DCF.
Bad Investment ……………………….Becomes a good one.
3 basic questions
? When is there a real option embedded in a decision or an asset?
? When does that real option have significant economic value?
? Can that value be estimated using an option pricing model?
? An option provides the holder with the right to buy or sell a specified quantity of an underlying asset
at a fixed price (called a strike price or an exercise price) at or before the expiration date of the
option.
? There has to be a clearly defined underlying asset whose value changes over time in unpredictable
ways.
? The payoffs on this asset (real option) have to be contingent on an specified event occurring within a
finite period.
When option is embedded in an option
Product Patent as an Option
Present Value of Expected
Cash Flows on Product
PV of Cash Flows
from Project
Initial Investment in
Project
Project has negative
NPV in this section
Project's NPV turns
positive in this section
Expansion of existing project as an option
Present Value of Expected
Cash Flows on Expansion
PV of Cash Flows
from Expansion
Additional Investment
to Expand
Firm will not expand in
this section
Expansion becomes
attractive in this section
Determinants of option value
? Variables Relating to Underlying Asset
? Value of Underlying Asset; as this value increases, the right to buy at a fixed price (calls) will become
more valuable and the right to sell at a fixed price (puts) will become less valuable.
? Variance in that value; as the variance increases, both calls and puts will become more valuable
because all options have limited downside and depend upon price volatility for upside.
? Expected dividends on the asset, which are likely to reduce the price appreciation component of the
asset, reducing the value of calls and increasing the value of puts.
? Variables Relating to Option
? Strike Price of Options; the right to buy (sell) at a fixed price becomes more (less) valuable at a lower
price.
? Life of the Option; both calls and puts benefit from a longer life.
? Level of Interest Rates; as rates increase, the right to buy (sell) at a fixed price in the future becomes
more (less) valuable.
Sources of Synergy
Valuing synergies
? When two businesses are combined, the term “synergies” refers to the changes in their
aggregate operating and/or financial results attributable to their being operated as a
combined enterprise. Synergies can take many forms
? Revenue enhancements
? Cost savings
— Raw material discounts/purchasing power
— Sales and marketing overlap, Corporate overhead reductions
— Distribution cost reductions, Facilities consolidation
— Tax savings
? Merger related expenses (restructuring, additional CAPEX, integration expenses)
? The value of achievable synergies is often a key element in whether to proceed with a
proposed transaction
? Calculate synergies for both the acquiring company and the target
? Remember incremental cash flow
? Synergies are generally valued by toggling pre-tax changes to various financial statement line
items into a DCF model of the combined enterprise and simply measuring the incremental
impact
Sources of Financial Synergy
? Diversification: Acquiring another firm as a way of reducing risk cannot create
wealth for two publicly traded firms, with diversified stockholders, but it could
create wealth for private firms or closely held publicly traded firms
? Cash Slack: When a firm with significant excess cash acquires a firm, with great
projects but insufficient capital, the combination can create value
? Tax Benefits: The tax paid by two firms combined together may be lower than the
taxes paid by them as individual firms
? Debt Capacity: By combining two firms, each of which has little or no capacity to
carry debt, it is possible to create a firm that may have the capacity to borrow
money and create value
Valuing synergies
? Sources of synergy projections
? Management
? Research
? Estimates from comparable transaction (% of sales, increase in EBITDA
margin etc.)
? DCF with synergies
? Valued separately from standalone DCF
? Run sensitivity on synergy valuations
? Other considerations
? Timeline for achieving synergies
? Run as sensitivity various cases of realization e.g., 25%, 50%, 75%, 100%
realization
? Tax impact
? Costs incurred to achieve synergies
52
Value of Control
? The value of the control premium that will be paid to acquire a block of equity will depend
upon two factors
? Probability that control of firm will change: This refers to the probability that incumbent
management will be replaced. this can be either through acquisition or through existing
stockholders exercising their muscle
? Value of Gaining Control of the Company: The value of gaining control of a company arises
from two sources - the increase in value that can be wrought by changes in the way the
company is managed and run, and the side benefits and perquisites of being in control
? Value of Gaining Control = Present Value (Value of Company with change in control - Value of
company without change in control) + Side Benefits of Control
Minority Discounts and Voting Shares
Assume that a firm has a value of $ 100 million run by incumbent managers and US$
150 million run optimally
? Proposition 1: The market price will reflect the expected value of control
• The firm has 10 million voting shares outstanding
• Since the potential for changing management is created by this offering, the
value per share will fall between $10 and $15, depending upon the probability
that is attached to the management change. Thus, if the probability of the
management change is 60%, the value per share will be $13.00
Value/Share = (150*.6+100*.4)/10 = $13
? Proposition 2: If you have shares with different voting rights, the voting shares will
get a disproportionate share of the value of control
Distress and the Going Concern Assumption
? Traditional valuation techniques are built on the assumption of a going concern,
i.e., a firm that has continuing operations and there is no significant threat to
these operations
? In discounted cash flow valuation, this going concern assumption finds its place
most prominently in the terminal value calculation, which usually is based upon an
infinite life and ever-growing cash flows
? In relative valuation, this going concern assumption often shows up implicitly
because a firm is valued based upon how other firms - most of which are healthy -
are priced by the market today
? When there is a significant likelihood that a firm will not survive the immediate
future (next few years), traditional valuation models may yield an over-optimistic
estimate of value
Equity to Employees: Effect on Value
? In recent years, firms have turned to giving employees (and especially top
managers) equity option packages as part of compensation. These options are
usually
• Long term
• At-the-money when issued
• On volatile stocks
? Two key issues with employee options:
• How do options granted in the past affect equity value per share today?
• How do expected future option grants affect equity value today?
Options-Impact on value
Options outstanding
• Step 1: List all options outstanding, with maturity, exercise price and vesting status
• Step 2: Value the options, taking into accounting dilution, vesting and early
exercise considerations
• Step 3: Subtract from the value of equity and divide by the actual number of shares
outstanding (not diluted or partially diluted)
Expected future option and restricted stock issues
• Step 1: Forecast value of options that will be granted each year as percent of
revenues that year. (As firm gets larger, this should decrease)
• Step 2: Treat as operating expense and reduce operating income and cash flows
• Step 3: Take present value of cash flows to value operations or equity
Sensitivity analysis is vital when presenting the
results of DCF analysis
? Recall that DCF valuation is highly sensitive to projections and assumptions
? So-called “sensitivity tables” chart the output based on ranges of input variables
? Since DCF results are by their nature approximate, depicting sensitivity tables enables users of
DCF output to assess the degree of “fuzziness” in the results
? It is better to use DCF analysis using exit multiples and perpetuity growth rates generally show
sensitivities for the method used to calculate terminal value and a range of discount rates
? Sensitivities can be shown for any variable in the model (including financial projections)
? Judge which sensitivities would be useful to decision makers
Other considerations
Reliability of projections
? DCF results are generally more sensitive to cash flows (and terminal value) than to small
changes in the discount rate. Care should be taken that assumptions driving cash flows are
reasonable. Generally, we try to use estimates provided by analysts from reputable Wall
Street firms if the client has not provided projections
Sensitivity analysis
? Remember that DCF valuations are based on assumptions and are therefore approximate.
Use several scenarios to bound the target’s value. Generally, the best variables to sensitize
are sales, EBITDA margin, WACC and exit multiples or perpetuity growth rate
Always remember…
? Three key drivers
? Projections and incremental cash flows (unlevered free cash flow)
? Residual value at end of the projection period (terminal value)
? Weighted-average cost of capital (discount rate)
? Avoid pitfalls
? Validate and test projection assumptions
? Determine appropriate cash flow stream
? Thoughtfully consider terminal value methodology
? Use appropriate cost of capital approach
? Carefully consider all variables in calculation of the discount rate
? Sensitize appropriately (base projection variables, synergies, discount rates, terminal
values, etc.)
? Footnote assumptions in detail
? Think about other value enhancers and detractors
Other common mistakes
Value v. price
Many believe transaction multiples and premiums determine value of a
business
Synergy calculation
Valuing like a standalone company with normal growth: overvalues synergy
Preferable to use zero nominal growth rate for cost savings
No checks between
methods
Should run DCF and multiples side-by-side and resolve any differences
= only one value range
Historical Management estimates JPM extrapolation
YE Dec, €mm 2003A 2004A 2005A 2006E 2007E 2008E 2009E 2010E 2011E 2012E 2013E 2014E 2015E TP
Sales 132.1 134.2 134.0 135.2 146.2 155.0 161.2 166.0 170.2 173.6 177.1 180.6 184.2 187.0
% growth 1.6% (0.1)% 0.9% 8.1% 6.0% 4.0% 3.0% 2.5% 2.0% 2.0% 2.0% 2.0% 1.5%
EBITDA 14.0 11.7 11.7 11.6 16.1 21.0 20.2 19.9 20.4 20.8 21.2 21.7 22.1 22.4
% margin 10.6% 8.7% 8.7% 8.6% 11.0% 13.5% 12.5% 12.0% 12.0% 12.0% 12.0% 12.0% 12.0% 12.0%
EBITA 6.3 4.5 6.3 6.4 12.2 17.1 15.3 14.9 15.3 15.2 15.5 14.9 14.7 15.0
% margin 4.8% 3.4% 4.7% 4.7% 8.3% 11.0% 9.5% 9.0% 9.0% 8.8% 8.8% 8.3% 8.0% 8.0%
- Taxes (2.1) (1.5) (2.1) (2.1) (4.1) (5.8) (5.2) (5.1) (5.2) (5.2) (5.3) (5.0) (5.0) (5.1)
% tax rate 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8% 33.8%
= NOPAT 4.2 3.0 4.2 4.2 8.0 11.3 10.1 9.9 10.1 10.1 10.3 9.9 9.8 9.9
+ Depreciation 7.7 7.2 5.4 5.2 4.0 3.9 4.8 5.0 5.1 5.6 5.7 6.8 7.4 7.5
% of capex 159.2% 106.2% 235.4% 210.0% 68.6% 54.2% 66.7% 75.0% 75.0% 80.5% 80.5% 93.8% 100.0% 100.0%
- Capex (4.8) (6.7) (2.3) (2.5) (5.8) (7.2) (7.3) (6.6) (6.8) (6.9) (7.1) (7.2) (7.4) (7.5)
% of Sales 3.7% 5.0% 1.7% 1.8% 4.0% 4.6% 4.5% 4.0% 4.0% 4.0% 4.0% 4.0% 4.0% 4.0%
? working capital¹ (4.0) (0.5) (0.8) 0.4 (1.1) (1.3) (1.1) (1.0) (0.8) (0.8) (0.8) (0.8) (0.8)
= Free cash-flow (0.5) 6.7 6.2 6.6 6.9 6.4 7.1 7.5 7.9 8.1 8.6 8.9 9.1
Company X DCF analysis
DCF assumptions (€mm)
¹ Working capital includes: inventories, trade receivables and trade payables
Firm value (€mm) Firm value (€mm)
Terminal growth %
1.0% 1.3% 1.5% 1.8% 2.0%
8.0% 114 116 119 122 125
8.5% 106 108 110 113 116
9.0% 99 101 103 105 107
9.5% 93 95 96 98 100
W
A
C
C
%
10.0% 88 89 91 92 94
EBITDA margin variance %
(1.0%) (0.5%) (0%) (0.5%) (1.0%)
8.0% 103 111 119 127 135
8.5% 95 103 110 118 126
9.0% 89 96 103 110 117
9.5% 83 90 96 103 110
W
A
C
C
%
10.0% 78 84 91 97 103
68
Capex is a key driver in DCF analysis; if possible, forecasts should
be based on maintaining relatively stable Net PPE % sales
? Common to forecast CAPEX based on % of sales (and depreciation % of capex)
? Required if we don’t have any balance sheet information (e.g., private company or division of larger company),
but…
? Can result in incorrect DCF valuation outcomes if strong future sales growth is not supported by necessary capital
expenditure
? Capex should be the plug after setting Net PPE % sales, depreciation as % Net PPE
? Example
? Forecasting business performance and capex for their business units to feed into a DCF valuation model
? Issue:
? The major division of the business was very capital intensive and therefore had a relatively low ROCE (NOPAT /
(Net PPE + NWI))
? Capex assumptions over time appeared reasonable at face value (as a % of sales), however on closer inspection,
ROCE employed increased dramatically, indicating that insufficient capital was being injected into the business to
support the forecast sales growth (given high Capital intensity)
? Analysis of ROCE and Capital Intensity benchmarks shows that CAPEX was underestimated
? Key Learning
? Analysis of Capex intensity and return on capital employed should be conducted when forecasting for DCF’s –
need balance sheet info and view of what appropriate level of capital for the business is
— If ROCE increases too much and capital intensity (Net PPE % sales) declines substantially versus peers then this
should be challenged and corrected.
Why do trading values differ from DCF?
? Market may view the firm’s outlook differently (different implied forecast)
? Due diligence in an M&A transaction may yield material private information that
affects DCF value but not public trading valuation
? Discounts
? Lack of liquidity
? IPO/spin-off
? Conglomerate
? Supply/demand imbalance
? Difference in capital structure
? Company doesn’t distribute all of its free cash flow to shareholders
? Option value
? Acquisition speculation
? Event risk
Why do transaction values differ from DCF?
? Control premium
? Cost of capital differences
? Buyer may assign a different cost of capital to target due to different view of risk
? High level of synergies
? Revenue enhancements
? Cost and capex savings
? Cross-border
? Differences in capital costs, tax rules, repatriation levels, etc.
? Differences in view of the future
? Buyer may have a dramatically different view of the future than the market
? Other strategic reasons
? Buy versus build
? Platform for other investments
? Defensive acquisition/strategic imperative
Relative Valuation
The Essence of relative valuation
? In relative valuation, the value of an asset is compared to the values assessed by the
market for similar or comparable assets.
? To do relative valuation then we need to identify comparable assets and obtain
market values for these assets
? Convert these market values into standardized values, since the absolute prices
cannot be compared This process of standardizing creates price multiples.
? Compare the standardized value or multiple for the asset being analyzed to the
standardized values for comparable asset, controlling for any differences between
the firms that might affect the multiple, to judge whether the asset is under or over
valued
Relative valuation is pervasive
? Almost 85% of equity research reports are based upon a multiple and comparables.
? More than 50% of all acquisition valuations are based upon multiples
? Rules of thumb based on multiples are not only common but are often the basis for
final valuation judgments.
? While there are more discounted cashflow valuations in consulting and corporate
finance, they are often relative valuations masquerading as discounted cash flow
valuations.
? The objective in many discounted cashflow valuations is to back into a number that
has been obtained by using a multiple.
? The terminal value in a significant number of discounted cashflow valuations is
estimated using a multiple.
The Market Imperative
? Relative valuation is much more likely to reflect market perceptions and moods than
discounted cash flow valuation. This can be an advantage when it is important that
the price reflect these perceptions as is the case when
? The objective is to sell a security at that price today (as in the case of an IPO)
? With relative valuation, there will always be a significant proportion of securities
that are under valued and over valued.
? Since portfolio managers are judged based upon how they perform on a relative basis
(to the market and other money managers), relative valuation is more tailored to
their needs
? Relative valuation generally requires less information than discounted cash flow
valuation (especially when multiples are used as screens)
The Four Steps to Deconstructing Multiples
? Define the multiple
? In use, the same multiple can be defined in different ways by different users. When
comparing and using multiples, estimated by someone else, it is critical that we
understand how the multiples have been estimated
? Describe the multiple
? Too many people who use a multiple have no idea what its cross sectional
distribution is. If you do not know what the cross sectional distribution of a multiple
is, it is difficult to look at a number and pass judgment on whether it is too high or
low
? Analyze the multiple
? It is critical that we understand the fundamentals that drive each multiple, and the
nature of the relationship between the multiple and each variable
? Apply the multiple
? Defining the comparable universe and controlling for differences is far more difficult
in practice than it is in theory
Definitional Tests
? Is the multiple consistently defined?
? Key Rule: Both the value (the numerator) and the standardizing variable ( the
denominator) should be to the same claimholders in the firm. In other words, the
value of equity should be divided by equity earnings or equity book value, and
firm value should be divided by firm earnings or book value
? Is the multiple uniformly estimated?
? The variables used in defining the multiple should be estimated uniformly across
assets in the ?comparable firm? list
? If earnings-based multiples are used, the accounting rules to measure earnings
should be applied consistently across assets. The same rule applies with book-value
based multiples
An Example: Price Earnings Ratio: Definition
PE = Market Price per Share / Earnings per Share
? There are a number of variants on the basic PE ratio in use. They are based upon
how the price and the earnings are defined
? Price: is usually the current price
is sometimes the average price for the year
? EPS: earnings per share in most recent financial year
earnings per share in trailing 12 months (Trailing PE)
forecasted earnings per share next year (Forward PE)
forecasted earnings per share in future year
Enterprise Value /EBITDA Multiple
? The enterprise value to EBITDA multiple is obtained by netting cash out against
debt to arrive at enterprise value and dividing by EBITDA.
? Net out cash from firm value
Enterprise Value
EBITDA
=
Market Value of Equity + Market Value of Debt - Cash
Earnings before Interest,Taxes and Depreciation
Descriptive Tests
? The average and standard deviation for this multiple, across the universe (market)
? The median for this multiple
? The median for this multiple is often a more reliable comparison point.
? Outliers
? Size of the outliers
? Throwing out the outliers may seem like an obvious solution, but if the outliers all lie
on one side of the distribution (they usually are large positive numbers), this can
lead to a biased estimate.
? Special cases for multiple estimation
? Change in multiple over time
PE Ratio: Descriptive Statistics for US
0
100
200
300
400
500
600
700
800
0-4 4-8 8-12 12-16 16-20 20- 25 25-30 35-40 40-50 50-100 >100
PE Range
Current, Trailing and Forward PE_ January 2003
Current PE
Trailing PE
Forward PE
PE: Deciphering the Distribution
Current PE Trailing PE Forward PE
Mean 33.36 32.75 24.46
Standard Error 2.02 2.21 1.20
Median 16.68 15.42 15.29
Skewness 23.78 18.98 15.42
Minimum 0.81 0.92 2.72
Maximum 4382.00 4008.00 1364.00
Count 3721 2973 2035
100th largest 135.33 119.41 55.88
100th smallest 2.18 0.03 7.45
Analytical Tests
? The fundamentals that determine and drive these multiples
? Key rule: Both Embedded in every multiple are all of the variables that drive
every discounted cash flow valuation - growth, risk and cash flow patterns.
? In fact, using a simple discounted cash flow model and basic algebra should yield the
fundamentals that drive a multiple
? Changes in these fundamentals change the multiple
? The relationship between a fundamental (like growth) and a multiple (such as PE) is
seldom linear.
? For example, if firm A has twice the growth rate of firm B, it will generally not trade
at twice its PE ratio
? Key rule: It is impossible to properly compare firms on a multiple, if we do not
know the nature of the relationship between fundamentals and the multiple.
Relative Value and Fundamentals: Equity Multiples
? Gordon Growth Model:
? Dividing both sides by the earnings,
? Dividing both sides by the book value of equity,
? Dividing by the Sales per share,
P
0
=
DPS
1
r ÷ g
n
P
0
EPS
0
= PE=
Payout Ratio*(1+ g
n
)
r-g
n
n
n
0
0
-g r
) g (1 * Ratio Payout * ROE
= PBV
BV
P +
=
P
0
Sales
0
= PS=
Profit Margin*Payout Ratio*(1+ g
n
)
r-g
n
The Determinants of Multiples
Value of Stock = DPS
1
/(k
e
- g)
PE=Payout Ratio
(1+g)/(r-g)
PEG=Payout ratio
(1+g)/g(r-g)
PBV=ROE (Payout ratio)
(1+g)/(r-g)
PS= Net Margin (Payout ratio)
(1+g)/(r-g)
Value of Firm = FCFF
1
/(WACC -g)
Value/FCFF=(1+g)/
(WACC-g)
Value/EBIT(1-t) = (1+g)
(1- RIR)/(WACC-g)
Value/EBIT=(1+g)(1-
RIR)(1-t)/(WACC-g)
VS= Oper Margin (1-t)
(1-RIR) (1+g)/(WACC-g)
Equity Multiples
Firm Multiples
PE=f(g, payout, risk) PEG=f(g, payout, risk) PBV=f(ROE,payout, g, risk) PS=f(Net Mgn, payout, g, risk)
V/FCFF=f(g, WACC) V/EBIT(1-t)=f(g, RIR, WACC) V/EBIT=f(g, RIR, WACC, t) VS=f(Oper Mgn, RIR, g, WACC)
Using the Fundamental Model to Estimate PE For a High Growth
Firm
? The price-earnings ratio for a high growth firm can also be related to fundamentals. In the special case of
the two-stage dividend discount model, this relationship can be made explicit fairly simply:
? For a firm that does not pay what it can afford to in dividends, substitute FCFE/Earnings for the payout
ratio.
? Dividing both sides by the earnings per share:
P
0
=
EPS
0
* Payout Ratio*(1+ g)* 1 ÷
(1+ g)
n
(1+ r)
n
|
\
|
.
r - g
+
EPS
0
* Payout Ratio
n
*(1+ g)
n
*(1+ g
n
)
(r -g
n
)(1+ r)
n
P
0
EPS
0
=
Payout Ratio* (1 + g) * 1 ÷
(1 + g)
n
(1+ r)
n
|
\
|
.
|
r - g
+
Payout Ratio
n
*(1+ g)
n
* (1 + g
n
)
(r - g
n
)(1+ r)
n
A Simple Example
? Assume that you have been asked to estimate the PE ratio for a firm which has the
following characteristics:
Variable High Growth Phase Stable Growth
Phase
Expected Growth Rate 25% 8%
Payout Ratio 20% 50%
Beta 1.00 1.00
Number of years 5 years Forever after
? Riskfree rate = T.Bond Rate = 6%
? Required rate of return = 6% + 1(5.5%)= 11.5%
PE =
0.2 * (1.25) * 1÷
(1.25)
5
(1.115)
5
|
\
|
.
|
(.115 - .25)
+
0.5 * (1.25)
5
*(1.08)
(.115- .08) (1.115)
5
= 28.75
PE and Growth: Firm grows at x% for 5 years, 8%
thereafter
PE Ratios and Expected Growth: Interest Rate Scenarios
0
20
40
60
80
100
120
140
160
180
5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
Expected Growth Rate
P
E
R
a
t
i
o
r=4%
r=6%
r=8%
r=10%
PE Ratios and Length of High Growth: 25% growth
for n years; 8% thereafter
PE Ratios and Length of High Growth Period
0
10
20
30
40
50
60
0 1 2 3 4 5 6 7 8 9 10
Length of High Growth Period
P
E
R
a
t
i
o
g=25%
g=20%
g=15%
g=10%
PE and Payout
PE Ratios and Payout Ratios: Growth Scenarios
0
5
10
15
20
25
30
35
0% 20% 40% 60% 80% 100%
Payout Ratio
P
E
g=25%
g=20%
g=15%
g=10%
Application Tests
? Given the firm that we are valuing, defining the comparable? firm
? While traditional analysis is built on the premise that firms in the same sector are
comparable firms, valuation theory would suggest that a comparable firm is one
which is similar to the one being analyzed in terms of fundamentals.
? Key Rule: There is no reason why a firm cannot be compared with another firm in
a very different business, if the two firms have the same risk, growth and cash
flow characteristics.
? Given the comparable firms, adjusting for differences across firms on the
fundamentals
? Key Rule: It is impossible to find an exactly identical firm to the one you are
valuing.
An example from the power sector
Name PE
Indowind Energy 22.1
Jaiprakash Hydro 14.39
Neyveli Lignite 12.34
NTPC 22.26
Energy Devlop.Co 17.59
Average 17.74
Standard Deviation 4.47
Torrent Power
Torrent
Power Expected Actual Error in %
PE 17.74 20.52 13.57
EPS 4.97 4.97 -
Share Price 88.15 101.98 13.57
Multiple accuracy
Companies considered Expected Actual Error in %
Indowind Energy 22.1 17.74 24.61
Jaiprakash Hydro 14.39 17.74 18.87
Neyveli Lignite 12.34 17.74 30.42
NTPC 22.26 17.74 25.51
Energy Devlop.Co 17.59 17.74 0.82
DCF base case Trading multiples
DCF synergy case Trading value with synergies
M&A value
Market value
Synergies +
Transaction multiples
Synergies
=
x
Transaction price
–
Part of
synergies
+
Premiums
Valuation is complex, requires experience and checks
between methods—should give same answers
? Market assumptions
? Market WACC
? Management deliverable
synergy assumptions
? Market WACC
? Exit financials
? Comparable transaction
multiples
? Current trading value
? Comparable transaction
premiums
? Market assumptions
? Comparable trading multiples
? Synergy multiples x after-tax
cost savings
Thank You
doc_927215592.pptx