Description
understand the influence of taxes, corporate and personal, on the choice of capital structure, to understand the phenomenon of financial distress and its consequences, to discuss other factors that affect the debt-equity choice in practice. It also covers pecking order theory, classical theory of interest, exchange rate relationships
? Corporate Taxes and Value
? Corporate and Personal Taxes
? Cost of Financial Distress
? Pecking Order of Financial Choices
? To understand the influence of taxes,
corporate and personal, on the choice of
capital structure
? To understand the phenomenon of financial
distress and its consequences
? To discuss other factors that affect the debt-
equity choice in practice
Financial Risk - Risk to shareholders
resulting from the use of debt. Financial
risk increases with an increase in the
debt-equity ratio.
Financial Leverage - Increase in the
variability of shareholder returns that
comes from the use of debt.
Interest Tax Shield- Tax savings resulting
from deductibility of interest payments.
Interest tax shield: (Tc)(Interest expense),
where Tc is the corporate tax rate.
Example - You own all the equity of Space
Babies Diaper Co.. The company has no
debt. The company’s annual cash flow is
$1,000, before interest and taxes. The
corporate tax rate is 40%. You have the
option to exchange 1/2 of your equity
position for 10% bonds with a face value of
$1,000.
Should you do this and why?
All Equity 1/2 Debt
EBIT 1,000 1,000
Interest Pmt 0 100
Pretax Income 1,000 900
Taxes @ 40% 400 360
Net Cash Flow $600 $540
Example - You own all the equity of Space Babies Diaper Co..
The company has no debt. The company’s annual cash flow
is $1,000, before interest and taxes. The corporate tax rate
is 40%. You have the option to exchange 1/2 of your equity
position for 10% bonds with a face value of $1,000. Should
you do this and why?
All Equity 1/2 Debt
EBIT 1,000 1,000
Interest Pmt 0 100
Pretax Income 1,000 900
Taxes @ 40% 400 360
Net Cash Flow 600 $540
Example - You own all the equity of Space Babies Diaper Co.. The
company has no debt. The company’s annual cash flow is
$1,000, before interest and taxes. The corporate tax rate is
40%. You have the option to exchange 1/2 of your equity
position for 10% bonds with a face value of $1,000. Should you
do this and why?
Total Cash Flow
All Equity = 600
*1/2 Debt = 640
(540 + 100)
PV of Tax Shield =
(assume perpetuity)
D x r
D
x Tc
r
D
= D x Tc
Example:
Tax benefit = 1000 x (.10) x (.40) = $40
PV of 40 perpetuity = 40 / .10 = $400
PV Tax Shield = D x Tc = 1000 x .4 = $400
Firm Value =
Value of All Equity Firm + PV Tax Shield
Example
All Equity Value = 600 / .10 = 6,000
PV Tax Shield = 400
Firm Value with 1/2 Debt = $6,400
The increase in the value of the firm due to the debt is the present value of
the tax shield.
Relative Advantage Formula (RAF)
( Debt vs Equity )
1-TP
(1-TPE) (1-TC)
RAF > 1 Debt
RAF < 1 Equity
Advantage
If TP = TPE; i.e. if equity income comes entirely as
dividend; the RAF would depend only on Corporate tax
rate:
1
(1-TC)
RAF > 1 Debt
RAF < 1 Equity
Advantage
Example 1
All Debt All Equity
Income BTCP 1.00 1.00
less TC=.46 0.00 0.46
Income BTP 1.00 0.54
Taxes TP =.5 TPE=0 0.50 0.00
After Tax Income 0.50 0.54
RAF = .926
Advantage Equity
Example 2
All Debt All Equity
Income BTCP 1.00 1.00
less TC=.34 0.00 0.34
Income BTP 1.00 0.66
Taxes TP =.28 TPE=.21 0.28 0.139
After Tax Income 0.72 0.521
RAF = 1.381
Advantage Debt
? Today’s RAF & Debt vs Equity preference.
1 - .33
(1 - .16) (1 - .35)
= 1.23
RAF =
Why are companies not all debt?
Structure of Bond Yield Rates
D
E
Bond
Yield
r
Traditional view, as the debt-equity ratio increases, the interest rate on debt
increases because of an increase in the probability of default (Bankruptcy risk).
Weighted Average Cost of Capital
without taxes (traditional view)
r
D
V
r
D
r
E
Includes
Bankruptcy Risk
WACC
This shows the weighted average cost of capital vs. D/V
Costs of Financial Distress - Costs arising from
bankruptcy or distorted business decisions
before bankruptcy.
? At higher levels of debt, costs of financial distress have to be
considered.
? Financial distress occurs when promises to creditors are broken or
honored with difficulty.
? Financial distress includes failure to pay interest or principal or
both.
? Formally, financial distress is defined as events preceding and
including bankruptcy, such as violation of a loan or bond contract.
? Financial distress has both direct and indirect costs.
Costs of Financial Distress - Costs arising
from bankruptcy or distorted business
decisions before bankruptcy.
Market Value = Value if all Equity Financed
+ PV Tax Shield
- PV Costs of Financial Distress
Debt
M
a
r
k
e
t
V
a
l
u
e
o
f
T
h
e
F
i
r
m
Value of
unlevered
firm
PV of interest
tax shields
Costs of
financial distress
Value of levered firm
Optimal amount
of debt
Maximum value of firm
? Cash In and Run – Stockholders may be reluctant to
put money into a form in financial distress’ but are
happy to take out the money in the form of
dividend– “refusing to contribute equity capital
? Playing for Time – When firm is in distress, creditors
would like to salvage what they can by forcing the
firm to settle; Stockholders want to delay –
accounting changes, encouraging false hopes,
cutting corners to make results look better
? Bait and Switch – Quick way to get into distress –
you start with issuance of limited amount of
relatively safe debt and then suddenly issue lot
more – thus imposing capital loss on old bond
holders
Trade-off Theory - Theory that capital
structure is based on a trade-off between
tax savings and distress costs of debt.
Pecking Order Theory - Theory stating that
firms prefer to issue debt rather than equity
if internal finance is insufficient.
1. Stock-for-debt Stock price
exchange offers falls
Debt-for-stock Stock price
exchange offers rises
2. Issuing common stock drives down stock prices;
repurchase increases stock prices.
3. Issuing straight debt has a small negative impact.
? Why does security issues affect stock
price? The demand for a firm’s
securities ought to be flat. Security
issues should not affect stock prices.
This leads us to the pecking order
theory.
? Any firm is a drop in the bucket.
? Plenty of close substitutes.
? Large debt issues don’t significantly
depress the stock price.
Some Implications:
?Internal equity may be better than external
equity.
?Financial slack is valuable.
?If external capital is required, debt is better.
(There is less room for difference in
opinions about what debt is worth).
? Compute Present value of interest tax shields,
marginal tax at 35%.
? A Rs. 1000 one year loan at 8%
? A 5 yr loan of Rs. 1000 at 8%, with no repayment till
maturity
? A Rs. 1000 perpetuity at 7%
? What are costs of bankruptcy?
? What type of firms are likely to incur high
costs in the event of bankruptcy or financial
distress? What would have relatively low
costs? Give examples
? After Tax WACC
? Tricks of the Trade
? Capital Structure and WACC
? Adjusted Present Value
? Discounting Safe, Nominal Cash Flows
? The tax benefit from interest expense
deductibility must be included in the cost
of funds.
? This tax benefit reduces the effective cost
of debt by a factor of the marginal tax
rate.
|
.
|
\
|
× +
|
.
|
\
|
× =
E D
r
V
E
r
V
D
WACC
rD is the after-tax cost of debt. This is also used when taxes are not considered.
Old Formula
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
Tax Adjusted Formula
rD is the before-tax cost of debt. (1-Tc)rD is the after-tax cost
of debt. In this formula corporate taxes are taken into account.
Example - Sangria Corporation
The firm has a marginal tax rate of 35%.
The cost of equity is 14.6% and the pretax
cost of debt is 8%. Given the book and
market value balance sheets, what is the
tax adjusted WACC?
Always use the market values for calculating WACC.
Example - Sangria Corporation -
continued
Balance Sheet (Book Value, millions)
Assets 100 50 Debt
50 Equity
Total assets 100 100 Total liabilities
Many times, market to book ratios are available, and then we
can convert these book values to market values
Example - Sangria Corporation -
continued
Balance Sheet (Market Value, millions)
Assets 125 50 Debt
75 Equity
Total assets 125 125 Total liabilities
Example - Sangria Corporation -
continued
Debt ratio = (D/V) = 50/125 = .4 or 40%
Equity ratio = (E/V) = 75/125 = .6 or 60%
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
Example - Sangria Corporation -
continued
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
% 84 . 10
1084 .
146 .
125
75
08 .
125
50
) 35 . 1 (
=
=
|
.
|
\
|
× +
|
.
|
\
|
× ÷ = WACC
Example - Sangria Corporation -
continued
The company would like to invest in a
perpetual crushing machine with cash
flows of $2.085 million per year pre-
tax.
Given an initial investment of $12.5
million, what is the value of the
machine?
This problem assumes that the project
has the same risk as the firm
Example - Sangria Corporation -
continued
The company would like to invest in a perpetual crushing
machine with cash flows of $2.085 million per year pre-tax.
Given an initial investment of $12.5 million, what is the value
of the machine?
Cash Flows
Pretax cash flow 2.085
Tax @ 35% 0.73
After-tax cash flow $1.355 million
After tax cash flows are the relevant cash flows for calculating the NPV.
Example - Sangria Corporation -
continued
The company would like to invest in a perpetual crushing
machine with cash flows of $2.085 million per year pre-tax.
Given an initial investment of $12.5 million, what is the value
of the machine?
0
1084 .
355 . 1
5 . 12
1
0
=
+ ÷ =
÷
+ =
g r
C
C NPV
? Preferred stock and other forms of financing
must be included in the formula
|
.
|
\
|
× +
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E P D
r
V
E
r
V
P
r
V
D
Tc WACC ) 1 (
V = D + E + P
Example - Sangria Corporation -
continued
Calculate WACC given preferred stock is $25 mil of total
equity and yields 10%.
Balance Sheet (Market Value, millions)
Assets 125 50 Debt
25 Preferred Equity
50 Common Equity
Total assets 125 125 Total liabilities
% 04 . 11
1104 .
146 .
125
50
10 .
125
25
08 .
125
50
) 35 . 1 (
=
=
|
.
|
\
|
× +
|
.
|
\
|
× +
|
.
|
\
|
× ÷ = WACC
? What should be included with debt?
? Long-term debt?
? Short-term debt?
? Cash (netted off?)
? Receivables?
? Deferred tax?
? How are costs of financing determined?
? Return on equity can be derived from market data
Return on equity can be derived using CAPM or DCF.
CAPM = rE + rf + b(rm - rf);
DCF = rE = [D1/Po ] + g.
? Cost of debt is set by the market given the specific
rating of a firm’s debt
It is the yield to maturity or the effective interest rate on
debt
? Preferred stock often has a preset dividend rate
Cost of preferred equity: rP = D/Po.
? If you discount at WACC, cash flows have to be
projected just as you would for a capital
investment project. Do not deduct interest.
Calculate taxes as if the company were all-
equity financed. The value of interest tax
shields is picked up in the WACC formula.
Normally rE > WACC > rD
? The company's cash flows will probably not be forecasted to
infinity.
? Financial managers usually forecast to a medium-term
horizon -- ten years, say -- and add a terminal value to the
cash flows in the horizon year.
? The terminal value is the present value at the horizon of
post-horizon flows.
? Estimating the terminal value requires careful attention,
because it often accounts for the majority of the value of the
company.
? After tax cash flows are calculated as EBIT (1-Tc).
? Discounting at WACC the values of the
assets and operations of the company.
? If the object is to value the company's
equity, that is, its common stock, don't
forget to subtract the value of the company's
outstanding debt.
? Discounting at WACC gives the total value of
the firm (V).
? The flow-to-equity approach gives the value
of the common equity in that case:
E = [EBIT – rDD](1 - Tc) / rE
where rE is the cost of levered equity.
Example continued: Sangria and the Perpetual
Crusher project at 20% D/V
Step 1 – r at current debt of 40%
Step 2 – D/V changes to 20%
Step 3 – New WACC
12 . ) 6 (. 146 . ) 4 (. 08 . = + = r
13 . ) 25 )(. 08 . 12 (. 12 . = ÷ + =
E
r
114 . ) 8 (. 13 . ) 2 )(. 35 . 1 ( 08 . = + ÷ = WACC
If the debt ratio changes, then the cost of equity should be adjusted
to reflect the new debt ratio. Equity becomes more risky when debt
increases.
APV = Base Case NPV + PV Impact
? Base Case = All equity finance firm NPV
? PV Impact = all costs/benefits directly
resulting from project
? A conceptually appealing and a general approach
to valuation
? It applies the value additivity property.
example:
Project A has an NPV of $150,000. In order to
finance the project we must issue stock, with
a brokerage cost of $200,000.
example:
Project A has an NPV of $150,000. In order to
finance the project we must issue stock, with a
brokerage cost of $200,000.
Project NPV = 150,000
Stock issue cost = -200,000
Adjusted NPV = - 50,000
Don’t do the project
Financing costs outweigh the NPV of the project
example:
Project B has a NPV of -$20,000. We can
issue debt at 8% to finance the project. The
new debt has a PV Tax Shield of $60,000.
Assume that Project B is your only option.
example:
Project B has a NPV of -$20,000. We can
issue debt at 8% to finance the project.
The new debt has a PV Tax Shield of
$60,000. Assume that Project B is your
only option.
Project NPV = - 20,000
Stock issue cost = 60,000
Adjusted NPV = 40,000
Do the project
PV Tax Shield is like a subsidy from the
government
|
|
.
|
\
|
+
+
÷ =
D
c D
r
r
T Lr r WACC
1
1
This formula assumes that debt is rebalanced each year.
Debt to project value ratios are held constant where L = D / V.
debt) for avail CF ( loan Equivalent PV =
Equivalent loan is the present value of cash flows
available to pay for debt
? Calculate the WACC for A Ltd. Having Rs. 7.5
crores debt. The debt is trading at 90% of
par. Its YTM is 9%. It has 25 lac shares
trading at Rs. 42 per share. Assume the tax
rate to be 35% and the expected return by
the shareholders to be 18%.
? What are your key assumptions?
? For what type of project would WACC be the right
discount rate?
? Y Ltd is 100% equity financed. The expected
rate of return on its shares is 12%.
? What is the opportunity cost of capital for an average
risk investment?
? Suppose the company issues debt and repurchases
equity resulting in debt ratio of 30%. What will the
WACC, if the borrowing rate is 7.5% and tax rate 35%?
56
? The Classical Theory of Interest
? Duration and Volatility
? The Term Structure and YTM
? Explaining the Term Structure
? Allowing for the Risk of Default
N
N
r
C
r
C
r
C
PV
) 1 (
000 , 1
...
) 1 ( ) 1 (
2
2
1
1
+
+
+ +
+
+
+
=
Example
? If today is October 2002, what is the value of the
following bond? An IBM Bond pays $115 every Sept
for 5 years. In Sept 2007 it pays an additional $1000
and retires the bond. The bond is rated AAA (WSJ
AAA YTM is 7.5%)
Cash Flows
Sept 03 04 05 06 07
115 115 115 115 1115
Example continued
? If today is October 2002, what is the value of the following bond? An
IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an
additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA
YTM is 7.5%)
( ) ( ) ( ) ( )
84 . 161 , 1 $
075 . 1
115 , 1
075 . 1
115
075 . 1
115
075 . 1
115
075 . 1
115
5 4 3 2
=
+ + + + = PV
0
200
400
600
800
1000
1200
1400
1600
0 2 4 6 8 10 12 14
5 Year 9% Bond 1 Year 9% Bond
Yield
P
r
i
c
e
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Nominal Interest Rate = The rate you actually
pay when you borrow money
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Nominal Interest Rate = The rate you actually pay
when you borrow money
Real Interest Rate = The theoretical rate you pay
when you borrow money, as determined by
supply and demand
Supply
Demand
$ Qty
r
Real r
Nominal r = Real r + expected inflation
Real r is theoretically somewhat stable
Inflation is a large variable
Q: Why do we care?
A: This theory allows us to understand the Term
Structure of Interest Rates.
Q: So What?
A: The Term Structure tells us the cost of debt.
Example (Bond 1)
Calculate the duration of our 6 7/8 % bond @ 4.9
% YTM
Year CF PV@YTM % of Total PV % x Year
1 68.75 65.54 .060 0.060
2 68.75 62.48 .058 0.115
3 68.75 59.56 .055 0.165
4 68.75 56.78 .052 0.209
5 68.75 841.39 .775 3.875
1085.74 1.00 Duration 4.424
Example (Bond 2)
Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM,
what is this bond’s duration?
Year CF PV@YTM % of Total PV % x Year
1 90 82.95 .081 0.081
2 90 76.45 .075 0.150
3 90 70.46 .069 0.207
4 90 64.94 .064 0.256
5 1090 724.90 .711 3.555
1019.70 1.00 Duration= 4.249
example
1000 = 1000
(1+R
3
)
3
(1+f
1
)(1+f
2
)(1+f
3
)
Forward Rate Computations
(1+ r
n
)
n
= (1+ r
1
)(1+f
2
)(1+f
3
)....(1+f
n
)
Example
What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660
? Example
What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660
Answer
FV of principal @ YTM
2 yr 1000 x (1.08995)
2
= 1187.99
3 yr 1000 x (1.09660)
3
= 1318.70
IRR of (FV1318.70 & PV=1187.99) = 11%
Example
Two years from now, you intend to begin a
project that will last for 5 years. What
discount rate should be used when evaluating
the project?
2 year spot rate = 5%
7 year spot rate = 7.05%
coupons paying bonds to derive rates
Bond Value = C
1
+ C
2
(1+r) (1+r)
2
Bond Value = C
1
+ C
2
(1+R
1
) (1+f
1
)(1+f
2
)
d1 = C
1
d2 = C
2
(1+R
1
) (1+f
1
)(1+f
2
)
example
8% 2 yr bond YTM = 9.43%
10% 2 yr bond YTM = 9.43%
What is the forward rate?
Step 1
value bonds 8% = 975
10%= 1010
Step 2
975 = 80d1 + 1080 d2 -------> solve for d1
1010 =100d1 + 1100d2 -------> insert d1 &
solve for d2
example continued
Step 3 solve algebraic equations
d1 = [975-(1080)d2] / 80
insert d1 & solve = d2 = .8350
insert d2 and solve for d1 = d1 = .9150
Step 4
Insert d1 & d2 and Solve for f
1
& f
2
.
.9150 = 1/(1+f
1
) .8350 = 1 /
(1.0929)(1+f
2
)
f
1
= 9.29% f
2
= 9.58%
Spot Rate - The actual interest rate today (t=0)
Forward Rate - The interest rate, fixed today, on a
loan made in the future at a fixed time.
Future Rate - The spot rate that is expected in the
future
Yield To Maturity (YTM) - The IRR on an interest
bearing instrument
YTM (r)
Year
1981
1987 & Normal
1976
1 5 10 20 30
What Determines the Shape of the TS?
1 - Unbiased Expectations Theory
2 - Liquidity Premium Theory
3 - Market Segmentation Hypothesis
Term Structure & Capital Budgeting
? CF should be discounted using Term Structure
info
? Since the spot rate incorporates all forward
rates, then you should use the spot rate that
equals the term of your project.
? If you believe in other theories take advantage of
the arbitrage.
? All interest bearing instruments are priced
to fit the term structure
? This is accomplished by modifying the
asset price
? The modified price creates a New Yield,
which fits the Term Structure
? The new yield is called the Yield To
Maturity (YTM)
Example
? A $1000 treasury bond expires in 5 years. It
pays a coupon rate of 10.5%. If the market
price of this bond is 1078.8, what is the YTM?
Example
? A $1000 treasury bond expires in 5 years.
It pays a coupon rate of 10.5%. If the
market price of this bond is 107-88, what is
the YTM?
C0 C1 C2 C3 C4 C5
-1078.80 105 105 105 105 1105
Calculate IRR = 8.5%
The risk of default changes the price of a bond and the YTM.
Example
We have a 9% 1 year bond. The built in price is $1000. But,
there is a 20% chance the company will go into bankruptcy
and not be able to pay. What is the bond’s value?
A:
Example
We have a 9% 1 year bond. The built in price is $1000. But, there
is a 20% chance the company will go into bankruptcy and not be
able to pay. What is the bond’s value?
A: Bond Value Prob
1090 .80 = 872.00
0 .20 = 0 .
872.00 =expected CF
Value
YTM
= =
= =
872
109
1090
800
36 3%
.
$800
.
Conversely - If on top of default risk, investors require an additional 2
percent market risk premium, the price and YTM is as follows:
Value
YTM
= =
= =
872
111
59
1090
78559
388%
.
$785.
.
.
? Insurance
? Hedging With Futures
? Forward Contracts
? SWAPS
? How to Set Up A Hedge
? Most businesses face the possibility of a
hazard that can bankrupt the company in an
instant.
? These risks are neither financial or business
and can not be diversified.
? The cost and risk of a loss due to a hazard,
however, can be shared by others who share
the same risk.
Example
An offshore oil platform is valued at
$1 billion. Expert meteorologist
reports indicate that a 1 in 10,000
chance exists that the platform may
be destroyed by a storm over the
course of the next year.
How can the cost of this hazard
be shared?
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm
over the course of the next year.
? How can the cost of this hazard be shared
Answer
A large number of companies with similar risks
can each contribute pay into a fund that is set
aside to pay the cost should a member of this
risk sharing group experience the 1 in 10,000
loss. The other 9,999 firms may not
experience a loss, but also avoided the risk of
not being compensated should a loss have
occurred.
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm over
the course of the next year.
? What would the cost to each group member be for
this protection.
Answer
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm over
the course of the next year.
? What would the cost to each group member be for
this protection.
Answer
000 , 100 $
000 , 10
000 , 000 , 000 , 1
=
? Why would an insurance company not offer
a policy on this oil platform for $100,000?
? Why would an insurance company not offer
a policy on this oil platform for $100,000?
? Administrative costs
? Adverse selection
? Moral hazard
? The loss of an oil platform by a storm
may be 1 in 10,000. The risk, however,
is larger for an insurance company since
all the platforms in the same area may be
insured, thus if a storm damages one in
may damage all in the same area. The
result is a much larger risk to the insurer
? Catastrophe Bonds - (CAT Bonds) Allow
insurers to transfer their risk to bond
holders by selling bonds whose cash flow
payments depend on the level of
insurable losses NOT occurring.
Business has risk
Business Risk - variable costs
Financial Risk - Interest rate changes
Goal - Eliminate risk
HOW?
Hedging & Futures Contracts
Ex - Kellogg produces cereal. A major component and
cost factor is sugar.
? Forecasted income & sales volume is set by using a
fixed selling price.
? Changes in cost can impact these forecasts.
? To fix your sugar costs, you would ideally like to
purchase all your sugar today, since you like today’s
price, and made your forecasts based on it. But, you
can not.
? You can, however, sign a contract to purchase sugar at
various points in the future for a price negotiated
today.
? This contract is called a “Futures Contract.”
? This technique of managing your sugar costs is called
“Hedging.”
1- Spot Contract - A contract for immediate sale &
delivery of an asset.
2- Forward Contract - A contract between two people
for the delivery of an asset at a negotiated price on a
set date in the future.
3- Futures Contract - A contract similar to a forward
contract, except there is an intermediary that creates a
standardized contract. Thus, the two parties do not
have to negotiate the terms of the contract.
Commodity Futures
-Sugar -Corn -OJ
-Wheat -Soy beans -Pork bellies
Financial Futures
-Tbills -Yen -GNMA
-Stocks -Eurodollars
Index Futures
-S&P 500 -Value Line Index
-Vanguard Index
SUGAR
Not an actual sale
Always a winner & a loser (unlike stocks)
K are “settled” every day. (Marked to Market)
Hedge - K used to eliminate risk by locking in
prices
Speculation - K used to gamble
Margin - not a sale - post partial amount
Hog K = 30,000 lbs
Tbill K = $1.0 mil
Value line Index K = $index x 500
birth 1981
Definition - An agreement between two firms, in
which each firm agrees to exchange the “interest
rate characteristics” of two different financial
instruments of identical principal
Key points
Spread inefficiencies
Same notation principal
Only interest exchanged
? “Plain Vanilla Swap” - (generic swap)
? fixed rate payer
? floating rate payer
? counterparties
? settlement date
? trade date
? effective date
? terms
? Swap Gain = fixed spread - floating spread
example (vanilla/annually settled)
XYZ ABC
fixed rate 10% 11.5%
floating rate libor + .25 libor + .50
Q: if libor = 7%, what swap can be made 7 what is the profit
(assume $1mil face value loans)
A:
XYZ borrows $1mil @ 10% fixed
ABC borrows $1mil @ 7.5% floating
XYZ pays floating @ 7.25%
ABC pays fixed @ 10.50%
example - cont
Benefit to XYZ Net position
floating +7.25 -7.25 0
fixed +10.50 -10.00 +.50
Net gain +.50%
Benefit ABC Net Position
floating +7.25 - 7.50 -.25
fixed -10.50 + 11.50 +1.00
net gain +.75%
example - cont
Settlement date
ABC pmt 10.50 x 1mil = 105,000
XYZ pmt 7.25 x 1mil = 72,500
net cash pmt by ABC = 32,500
if libor rises to 9%
settlement date
ABC pmt 10.50 x 1mil = 105,000
XYZ pmt 9.25 x 1mil = 92,500
net cash pmt by ABC = 12,500
? transactions
? rarely done direct
? banks - middleman
? bank profit - part of “swap gain”
example - same continued
XYZ & ABC go to bank separately
XYZ term = SWAP floating @ libor + .25 for fixed @
10.50
ABC terms = swap floating libor + .25 for fixed 10.75
example - cont
settlement date - XYZ
Bank pmt 10.50 x 1mil = 105,000
XYZ pmt 7.25 x 1mil = 72,500
net Bank pmt to XYZ = 32,500
settlement date - ABC
Bank pmt 7.25 x 1mil = 72,500
ABC pmt 10.75 x 1mil = 107,500
net ABC pmt to bank = 35,000
bank “swap gain” = +35,000 - 32,500 = +2,500
example - cont
benefit to XYZ
floating 7.25 - 7.25 = 0
fixed 10.50 - 10.00 = +.50 net gain
.50
benefit to ABC
floating 7.25 - 7.50 = - .25
fixed -10.75 + 11.50 = + .75 net gain .50
benefit to bank
floating +7.25 - 7.25 = 0
fixed 10.75 - 10.50 = +.25 net gain +.25
total benefit = 12,500 (same as w/o bank)
Example - You are speculating in Hog Futures. You
think that the Spot Price of hogs will rise in the
future. Thus, you go Long on 10 Hog Futures. If the
price drops .17 cents per pound ($.0017) what is
total change in your position?
Example - You are speculating in Hog Futures. You
think that the Spot Price of hogs will rise in the
future. Thus, you go Long on 10 Hog Futures. If the
price drops .17 cents per pound ($.0017) what is
total change in your position?
30,000 lbs x $.0017 loss x 10 Ks = $510.00 loss
Since you must settle your account every day, you must give your
broker $510.00
50.63
50.80
-$510
cents
per lbs
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month
of August. In June, the September corn
futures are selling for $2.94 per bushel (1K
= 5,000 bushels). Farmer Smith wishes to
lock in this price.
Show the transactions if the Sept spot price
drops to $2.80.
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month of
August. In June, the September corn futures are
selling for $2.94 per bushel (1K = 5,000 bushels).
Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price drops to
$2.80.
Revenue from Crop: 10,000 x 2.80 28,000
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 2.80 = 28,000 .
Gain on Position------------------------------- 1,400
Total Revenue $ 29,400
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month
of August. In June, the September corn
futures are selling for $2.94 per bushel (1K
= 5,000 bushels). Farmer Smith wishes to
lock in this price.
Show the transactions if the Sept spot price
rises to $3.05.
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month of
August. In June, the September corn futures are
selling for $2.94 per bushel (1K = 5,000 bushels).
Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price rises to
$3.05.
Revenue from Crop: 10,000 x 3.05 30,500
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 3.05 = 30,500 .
Loss on Position------------------------------- ( 1,100 )
Total Revenue $ 29,400
You have lived in NYC your whole life and are independently wealthy. You
think you know everything there is to know about pork bellies (uncurred bacon)
because your butler fixes it for you every morning. Because you have decided
to go on a diet, you think the price will drop over the next few months. On the
CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @
44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to
close your position. What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290
Loss of 10.23 % = - 5,130
You have lived in NYC your whole life and are independently wealthy. You
think you know everything there is to know about pork bellies (uncurred bacon)
because your butler fixes it for you every morning. Because you have decided
to go on a diet, you think the price will drop over the next few months. On the
CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @
44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to
close your position. What is your gain/loss?
? The amount (percentage) of a Futures Contract
Value that must be on deposit with a broker.
? Since a Futures Contract is not an actual sale, you
need only pay a fraction of the asset value to
open a position = margin.
? CME margin requirements are 15%
? Thus, you can control $100,000 of assets with
only $15,000.
You have lived in NYC your whole life and are independently wealthy.
You think you know everything there is to know about pork bellies
(uncurred bacon) because your butler fixes it for you every morning.
Because you have decided to go on a diet, you think the price will drop
over the next few months. On the CME, each PB K is 38,000 lbs.
Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb,
the price rises to 48.5 cents and you decide to close your position.
What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290
Loss = - 5,130
Loss 5130 5130
Margin 50160 x.15 7524
------------ = -------------------- = ------------ = 68% loss
You have lived in NYC your whole life and are independently wealthy.
You think you know everything there is to know about pork bellies
(uncurred bacon) because your butler fixes it for you every morning.
Because you have decided to go on a diet, you think the price will drop
over the next few months. On the CME, each PB K is 38,000 lbs.
Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb,
the price rises to 48.5 cents and you decide to close your position.
What is your gain/loss?
? Foreign Exchange Markets
? Some Basic Relationships
? Hedging Currency Risk
? Exchange Risk and International Investment
Decisions
? Political Risk
Exchange Rate - Amount of one currency
needed to purchase one unit of another.
Spot Rate of Exchange - Exchange rate
for an immediate transaction.
Forward Exchange Rate - Exchange rate
for a forward transaction.
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen
per dollar and the 3 month forward rate is
119.660 yen per dollar, what is the
premium and discount relationship?
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen per
dollar and the 3 month forward rate is 119.660 yen
per dollar, what is the premium and discount
relationship?
3.5% = 1 -
119.66
120.700
4
) (-Discount or Premium = 1 -
Price Forward
Price Spot
×
× T
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen per
dollar and the 3 month forward rate is 119.660 yen
per dollar, what is the premium and discount
relationship?
Answer - The dollar is selling at a 3.5% discount,
relative to the yen. The yen is selling at a 3.5%
premium, relative to the dollar.
? Basic Relationships
1 + r
1 + r
foreign
$
1 + i
1 + i
foreign
$
f
S
foreign / $
foreign / $
E(s
S
foreign / $
foreign / $
)
equals
equals
equals equals
1) Interest Rate Parity Theory
? The ratio between the risk free interest
rates in two different countries is equal
to the ratio between the forward and
spot exchange rates.
1 + r
1 + r
=
foreign
$
f
S
foreign / $
foreign / $
Example - You have the opportunity to invest
$1,000,000 for one year. All other things being
equal, you have the opportunity to obtain a 1
year Japanese bond (in yen) @ 0.06 % or a 1
year US bond (in dollars) @ 3.65%. The spot
rate is 120.700 yen:$1 The 1 year forward rate
is 116.535 yen:$1
Which bond will you prefer and why?
Ignore transaction costs
Value of US bond = $1,000,000 x 1.0365 = $1,036,500
Value of Japan bond = $1,000,000 x 120.700 = 120,700,000 yen exchange
120,700,000 yen x 1.0006 = 120,772,420 yen bond pmt
120,772,420 yen / 116.535 = $1,036,400 exchange
Example - You have the opportunity to invest $1,000,000 for one
year. All other things being equal, you have the opportunity to obtain
a 1 year Japanese bond (in yen) @ 0.06 % or a 1 year US bond (in
dollars) @ 3.65%. The spot rate is 120.700 yen:$1 The 1 year
forward rate is 116.535 yen:$1
Which bond will you prefer and why? Ignore transaction costs
2) Expectations Theory of Exchange Rates
Theory that the expected spot exchange rate equals the forward
rate.
f
S
foreign / $
foreign / $
=
E(s
S
foreign / $
foreign / $
)
3) Purchasing Power Parity
The expected change in the spot rate equals the expected
difference in inflation between the two countries.
1 + i
1 + i
=
foreign
$
E(s
S
foreign / $
foreign / $
)
Example
If inflation in the US is forecasted at 2.0%
this year and Japan is forecasted to fall
1.5%, what do we know about the
expected spot rate?
Given a spot rate of 120.700 yen:$1
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
120.700
E(s )
=
.02 + 1
.015 - 1
foreign/$
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
solve for Es
Es = 116.558
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
120.700
E(s )
=
.02 + 1
.015 - 1
foreign/$
4) International Fisher effect
The expected difference in inflation rates equals the difference in
current interest rates.
Also called common real interest rates
1 + r
1 + r
=
foreign
$
1 + i
1 + i
foreign
$
Example - The real interest rate in each
country is about the same
1.016 =
.985
1.0006
=
i + 1
r + 1
) (
foreign
foreign
= real r
1.016 =
1.02
1.0365
=
i + 1
r + 1
) (
$
$
= real r
Example - Honda builds a new car in Japan for a cost + profit of
1,715,000 yen. At an exchange rate of 120.700Y:$1 the car sells for
$14,209 in Indianapolis. If the dollar rises in value, against the yen, to
an exchange rate of 134Y:$1, what will be the price of the car?
1,715,000 = $12,799
134
Conversely, if the yen is trading at a
forward discount, Japan will
experience a decrease in
purchasing power.
Example - Harley Davidson builds a motorcycle for a cost plus profit of
$12,000. At an exchange rate of 120.700Y:$1, the motorcycle sells
for 1,448,400 yen in Japan. If the dollar rises in value and the
exchange rate is 134Y:$1, what will the motorcycle cost in Japan?
$12,000 x 134 = 1,608,000 yen
? Currency Risk can be reduced by using
various financial instruments
? Currency forward contracts, futures contracts,
and even options on these contracts are
available to control the risk
1) Exchange to Rs. and analyze
2) Discount using foreign cash
flows and interest rates, then
exchange to Rs.
3) Choose a currency standard (Rs.)
and hedge all non Rupee CF.
Techniques
Political Risk Scores
A B C D E F G H I J K L Total
Maximum Score 12 12 12 12 12 6 6 6 6 6 6 4 100
Netherlands 9 10 10 12 12 6 6 6 6 6 6 4 93
USA 11 10 11 11 8 4 6 6 6 5 6 4 88
Germany 10 8 9 12 11 5 6 6 6 5 5 4 87
UK 11 10 11 9 9 5 6 6 6 4 6 4 87
France 10 7 9 10 11 3 5 6 5 5 5 4 80
Japan 10 6 6 12 10 2 6 5 6 6 5 4 78
Brazil 9 4 5 9 11 3 4 6 2 4 4 2 63
China 11 4 6 10 9 2 2 5 5 4 1 2 61
India 5 5 5 8 5 3 5 2 4 2 5 3 52
Russia 7 2 3 8 10 1 4 5 3 3 2 1 49
Indonesia 10 3 5 4 9 1 1 2 2 2 2 3 44
Iraq 8 3 4 3 4 1 0 5 2 2 0 0 32
A = Govt stability G = Military in politics
B = Socioeonmic conditions H = Religious tensions
C = Investment profile I = Law and order
D = Internal conflict J = Ethnic tensions
E = External conflict K = Democratic accountability
F = Corruption L = Bureaucracy quality
14
1
? Calls, Puts and Shares
? Financial Alchemy with Options
? What Determines Option Value
? Option Valuation
14
2
Put Option
Right to sell an asset at a specified exercise
price on or before the exercise date.
14
3
Call Option
Right to buy an asset at a specified exercise
price on or before the exercise date.
14
4
Buyer Seller
Call option Right to buy asset Obligation to sell asset
Put option Right to sell asset Obligation to buy asset
? The value of an option at expiration is a
function of the stock price and the
exercise price.
14
5
? The value of an option at expiration is a
function of the stock price and the
exercise price.
Example - Option values given a exercise
price of $55
14
6
0 0 0 5 15 25 Value Put
25 15 5 0 0 0 Value Call
80 70 60 50 40 $30 Price Stock
14
7
Call option value (graphic) given a $55 exercise price.
Share Price
C
a
l
l
o
p
t
i
o
n
v
a
l
u
e
55 75
$20
14
8
Put option value (graphic) given a $55 exercise price.
Share Price
P
u
t
o
p
t
i
o
n
v
a
l
u
e
50 55
$5
14
9
Call option payoff (to seller) given a $55 exercise price.
Share Price
C
a
l
l
o
p
t
i
o
n
$
p
a
y
o
f
f
55
15
0
Put option payoff (to seller) given a $55 exercise price.
Share Price
P
u
t
o
p
t
i
o
n
$
p
a
y
o
f
f
55
Protective Put - Long stock and long put
15
1
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long Stock
Protective Put - Long stock and long put
15
2
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long Put
Protective Put - Long stock and long put
15
3
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Protective Put
Long Put
Long Stock
Protective Put - Long stock and long put
15
4
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Protective Put
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
5
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long call
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
6
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long put
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
7
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Straddle
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
8
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Straddle
15
9
Upper Limit
Stock Price
16
0
Upper Limit
Stock Price
Lower Limit
(Stock price - exercise price) or 0
which ever is higher
Time Decay Chart
Option Price
Stock Price
16
1
16
2
? Simple Valuation Model
? Binomial Model
? Black-Scholes Model
? Black Scholes vs. Binomial
16
3
Probability Up = p = (a - d) Prob Down = 1 - p
(u - d)
a = e
rD t
d =e
-s [D t]
.5
u =e
s [D t]
.5
Dt =
time intervals as % of year
16
4
Binomial Pricing
Example
Price = 36 s = .40 t = 90/365 D t = 30/365
Strike = 40 r = 10%
a = 1.0083
u = 1.1215
d = .8917
Pu = .5075
Pd = .4925
16
5
Binomial Pricing
40.37
32.10
36
37 . 40 1215 . 1 36
1 0
= ×
= ×
U
P U P
Binomial Pricing
16
6
40.37
32.10
36
37 . 40 1215 . 1 36
1 0
= ×
= ×
U
P U P
10 . 32 8917 . 36
1 0
= ×
= ×
D
P D P
Binomial Pricing
16
7
50.78 = price
40.37
32.10
25.52
45.28
36
28.62
40.37
32.10
36
1 +
= ×
t t
P U P
Binomial Pricing
16
8
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
36
28.62
36
40.37
32.10
Binomial Pricing
16
9
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
28.62
40.37
32.10
36
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
The greater of
Binomial Pricing
17
0
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
.19
28.62
0
40.37
2.91
32.10
.10
36
1.51
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
Binomial Pricing
17
1
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
.19
28.62
0
40.37
2.91
32.10
.10
36
1.51
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
Binomial Pricing
17
2
Components of the Option Price
1 - Underlying stock price
2 - Striking or Exercise price
3 - Volatility of the stock returns (standard deviation
of annual returns)
4 - Time to option expiration
5 - Time value of money (discount rate)
17
3
17
4
Black-Scholes Option Pricing Model
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
- Call Option Price
P
s
- Stock Price
N(d
1
) - Cumulative normal density function of (d
1
)
S - Strike or Exercise price
N(d
2
) - Cumulative normal density function of (d
2
)
r - discount rate (90 day comm paper rate or risk free rate)
t - time to maturity of option (as % of year)
v - volatility - annualized standard deviation of daily returns
Black-Scholes Option Pricing Model
17
5
(d
1
)=
ln + ( r + ) t
P
s
S
v
2
2
v t
32 34 36 38 40
N(d
1
)=
Black-Scholes Option Pricing Model
17
6
(d
1
)=
ln + ( r + ) t
P
s
S
v
2
2
v t
Cumulative Normal Density Function
(d
2
) = d
1
- v t
17
7
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
17
8
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
17
9
(d
1
) =
ln + ( r + ) t
P
s
S
v
2
2
v t
(d
1
) = - .3070 N(d
1
) = 1 - .6206 = .3794
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
18
0
(d
2
) = - .5056
N(d
2
) = 1 - .6935 = .3065
(d
2
) = d
1
- v t
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
18
1
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
= 36[.3794] - 40[.3065]e
- (.10)(.2466)
O
C
= $ 1.70
Put Price = Oc + S - P - Carrying Cost +
Div.
18
2
Carrying cost = r x S x t
Example
ABC is selling at $41 a share. A six
month May 40 Call is selling for
$4.00. If a May $ .50 dividend is
expected and r=10%, what is the put
price?
18
3
18
4
1 step 2 steps 4 steps
(2 outcomes) (3 outcomes) (5 outcomes)
etc. etc.
Binomial vs. Black Scholes
18
5
No. of steps Estimated value
1 48.1
2 41.0
3 42.1
5 41.8
10 41.4
50 40.3
100 40.6
Black-Scholes 40.5
Binomial vs. Black Scholes
? Many corporate securities are
similar to the stock options that
are traded on organized
exchanges.
? Almost every issue of corporate
stocks and bonds has option
features.
? In addition, capital structure and
capital budgeting decisions can be
viewed in terms of options.
18
6
? An option gives the holder the right, but not
the obligation, to buy or sell a given quantity
of an asset on (or perhaps before) a given
date, at prices agreed upon today.
? Calls versus Puts
? Call options gives the holder the right, but not the
obligation, to buy a given quantity of some asset at
some time in the future, at prices agreed upon
today. When exercising a call option, you “call in”
the asset.
? Put options gives the holder the right, but not the
obligation, to sell a given quantity of an asset at
some time in the future, at prices agreed upon
today. When exercising a put, you “put” the asset to
someone.
18
7
? Exercising the Option
? The act of buying or selling the underlying asset
through the option contract.
? Strike Price or Exercise Price
? Refers to the fixed price in the option contract at
which the holder can buy or sell the underlying
asset.
? Expiry
? The maturity date of the option is referred to as
the expiration date, or the expiry.
? Spot Price
? The Price at which an option is currently valued
(either in the market or privately)
18
8
? In-the-Money
? The exercise price is less than the spot price of
the underlying asset.
? At-the-Money
? The exercise price is equal to the spot price of the
underlying asset.
? Out-of-the-Money
? The exercise price is more than the spot price of
the underlying asset.
18
9
? Intrinsic Value
? The difference between the exercise price of the
option and the spot price of the underlying asset.
? Speculative Value
? The difference between the option premium and
the intrinsic value of the option.
19
0
Option
Premium
=
Intrinsic
Value
Speculative
Value
+
19
1
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Buy a call
Exercise price = $50
19
2
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Write a call
Exercise price = $50
19
3
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Write a call
Buy a call
Exercise price = $50; option premium = $10
19
4
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Buy a put
Exercise price = $50
19
5
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
write a put
Exercise price = $50
Stock price ($)
19
6
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Buy a put
Write a put
Exercise price = $50; option premium = $10
10
-10
? The seller (or writer)
of an option has an
obligation.
? The purchaser of an
option has an option.
19
7
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Buy a put
Write a put
10
-10
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Write a call
Buy a call
? Puts and calls can serve as the
building blocks for more complex
option contracts.
? If you understand this, you can
become a financial engineer,
tailoring the risk-return profile to
meet your client’s needs.
19
8
19
9
Buy a put with an
exercise price of $50
Buy
the
stock
Protective Put
strategy has downside
protection and upside
potential
$50
$0
$50
Value at
expiry
Value of
stock at
expiry
20
0
Buy a put with
exercise price
of $50 for $10
Buy the stock at $40
$40
Protective Put
strategy has
downside
protection and
upside potential
$40
$0
-$40
$50
Value at
expiry
Value of
stock at
expiry
20
1
Sell a call with
exercise price
of $50 for $10
Buy the stock at $40
$4
0
Covered call
$40
$0
-$40
$10
-$30
$30 $5
0
Value of stock at
expiry
Value at
expiry
20
2
Buy a put with
an exercise price
of $50 for $10
$40
A Long Straddle only makes money if
the stock price moves $20 away
from $50.
$40
$0
-$20
$50
Buy a call with
an exercise
price of $50 for
$10
-$10
$30
$60 $30 $70
Value of
stock at
expiry
Value at
expiry
20
3
Sell a put with an
exercise price of $40
Buy the stock at $40
financed with some
debt: FV = $X
Buy a call option with
an exercise price of $40
$0
-$40
$40-P
0
rT
Xe
÷
÷ 40 $
$40
Buy the
stock at $40
0
40 $ C +
) 40 ($
rT
Xe
÷
÷ ÷
-[$40-P
0
]
0
C ÷
0
P
In market equilibrium, it mast be the case that option prices
are set such that: Value of stock + Value of put - Value of call =
Present value of strike price discounted at r
F
Otherwise, riskless portfolios with positive payoffs exist.
Value of
stock at
expiry
Value at
expiry
? The last section
concerned itself
with the value of
an option at
expiry.
? This section
considers the
value of an
option prior to
the expiration
date.
? A much more
interesting
question.
20
4
20
5
Call Put
1. Stock price + –
2. Exercise price – +
3. Interest rate +
–
4. Volatility in the stock price + +
5. Expiration date + +
The value of a call option must fall within
max (stock price – exercise price, 0) < value of the option
< value of the stock.
The precise position will depend on these factors.
? The binomial
option pricing
formula is used
to value options
that have two
potential future
values – an up-
state and a
down-state
? The Black-
Scholes model
provides a
normalized
approximation
to the binomial
for some real-
world option
valuation.
20
6
Suppose a stock is worth $25 today and in one
period will either be worth 15% more or 15% less.
S
0
= $25 today and in one year S
1
is either $28.75
or $21.25. The risk-free rate is 5%. What is the
value of an at-the-money call option?
20
7
$25
$21.25
$28.75
S
1
S
0
1. A call option on this stock with exercise
price of $25 will have the following payoffs.
2. We can replicate the payoffs of the call
option. With a levered position in the stock.
20
8
$25
$21.25
$28.75
S
1
S
0
C
1
$3.75
$0
? The most familiar options are puts and calls.
? Put options give the holder the right to sell stock at
a set price for a given amount of time.
? Call options give the holder the right to buy stock
at a set price for a given amount of time.
20
9
? The value of a stock option depends on six
factors:
1. Current price of underlying stock.
2. Dividend yield of the underlying stock.
3. Strike price specified in the option contract.
4. Risk-free interest rate over the life of the contract.
5. Time remaining until the option contract expires.
6. Price volatility of the underlying stock.
? Much of corporate financial theory can be
presented in terms of options.
1. Common stock in a levered firm can be viewed as a call
option on the assets of the firm.
2. Real projects often have hidden option that enhance value.
Classic NPV calculations typically ignore the flexibility that
real-world firms typically have.
21
0
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
211
212
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
213
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
a
b
c
Forward sale Receivable
Hedged
receivable
214
-10
-5
0
5
10
15
20
25
30
35
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Premium
215
-20
-10
0
10
20
30
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Premium
216
-60
-50
-40
-30
-20
-10
0
10
20
30
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Put Receivable
Hedged receivable
21
7
? Follow Up Investments
? Abandon
? Wait
? Vary Output or Production
21
8
4 types of “Real Options”
1 - The opportunity to make follow-up
investments.
2 - The opportunity to abandon a project
3 - The opportunity to “wait” and invest later.
4 - The opportunity to vary the firm’s output
or
production methods.
Value “Real Option” = NPV with option
- NPV w/o option
21
9
Intrinsic Value
22
0
Option
Price
Stock Price
Intrinsic Value + Time Premium = Option
Value
Time Premium = Vale of being able to wait
22
1
Option
Price
Stock Price
More time = More value
22
2
Option
Price
Stock Price
Example - Abandon
Mrs. Mulla gives you a non-retractable
offer to buy your company for $150 mil
at anytime within the next year. Given
the following decision tree of possible
outcomes, what is the value of the offer
(i.e. the put option) and what is the most
Mrs. Mulla could charge for the option?
Use a discount rate of 10%
22
3
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your
company for $150 mil at anytime within the next year. Given the
following decision tree of possible outcomes, what is the value of
the offer (i.e. the put option) and what is the most Mrs. Mulla
could charge for the option?
22
4
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 145
70 (.6)
50 (.4)
40 (.4)
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your
company for $150 mil at anytime within the next year. Given the
following decision tree of possible outcomes, what is the value of
the offer (i.e. the put option) and what is the most Mrs. Mulla
could charge for the option?
22
5
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 162
150 (.4)
Option Value =
162 - 145 =
$17 mil
Reality
? Decision trees for valuing “real
options” in a corporate setting can
not be practically done by hand.
? We must introduce binomial theory &
B-S models
22
6
By
Girish Naravane
[email protected]
22
7
? What is a Warrant?
? What is a Convertible Bond?
? The Difference Between Warrants and
Convertibles
? Why do Companies Issue Warrants and
Convertibles?
Example:
BJ Services warrants, April 2000
Exercise price $ 15
Warrant Value $110
Share price $ 70
BJ Services share price
15
Warrant price at maturity
Value of
warrant
Exercise price = $15
Actual warrant value prior
to expiration
Theoretical value
(warrant lower limit)
Stock price
? # shares outstanding = 1 mil
? Current stock price = $12
? Number of shares issued per share outstanding =
.10
? Total number of warrants issued = 100,000
? Exercise price of warrants = $10
? Time to expiration of warrants = 4 years
? Annualized standard deviation of stock daily
returns = .40
? Rate of return = 10 percent
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
warrant each of Cost
100,000
500,000
$5
1,500,000 - 2,000,000 500,000
warrants w/o loans of value - financing total warrants of Cost
=
=
=
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
(d
1
) = 1.104
N(d
1
) = .865
(d
2
) = .304
N(d
2
) = .620
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
Warrant
= 12[.865] - [.620]{10/1.1
4
]
= $6.15
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
loans of value -
assets total
s United' of Value
firm e alternativ
of ue equity val Current
= =V
million V 5 . 12 $ 5 . 5 18 = ÷ =
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
$12.50
1
million 12.5
firm e alternativ
of price share Current
= = =
million N
V
64 . 6 $ value gives formula Scholes Black =
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
03 . 6 $ 64 . 6
10 . 1
1
firm e alternativ on call of value
1
1
= ×
×
+ q
? Amazon
? 4.75% Convertible 2009
? Convertible into 6.41 shares
? Conversion ratio 6.41
? Conversion price = 1000/6.41 = $156.05
? Market price of shares = $120
? Lower bound of value
? Bond value
? Conversion value = 6.41 x 120 = $768.00
? How bond value varies with firm value at maturity
0
1
2
3
0 1 2 3 4 5
Value of firm ($ million)
default
bond repaid in full
Bond value ($ thousands)
? How conversion value at maturity varies with firm
value
0
1
2
3
0 0.5 1 1.5 2 2.5 3 3.5 4
Value of firm ($ million)
Conversion value ($ thousands)
? How value of convertible at maturity varies with firm
value
0
1
2
3
0 1 2 3 4
Value of firm ($ million)
default
bond repaid in full
convert
Value of convertible ($ thousands)
doc_802198541.pptx
understand the influence of taxes, corporate and personal, on the choice of capital structure, to understand the phenomenon of financial distress and its consequences, to discuss other factors that affect the debt-equity choice in practice. It also covers pecking order theory, classical theory of interest, exchange rate relationships
? Corporate Taxes and Value
? Corporate and Personal Taxes
? Cost of Financial Distress
? Pecking Order of Financial Choices
? To understand the influence of taxes,
corporate and personal, on the choice of
capital structure
? To understand the phenomenon of financial
distress and its consequences
? To discuss other factors that affect the debt-
equity choice in practice
Financial Risk - Risk to shareholders
resulting from the use of debt. Financial
risk increases with an increase in the
debt-equity ratio.
Financial Leverage - Increase in the
variability of shareholder returns that
comes from the use of debt.
Interest Tax Shield- Tax savings resulting
from deductibility of interest payments.
Interest tax shield: (Tc)(Interest expense),
where Tc is the corporate tax rate.
Example - You own all the equity of Space
Babies Diaper Co.. The company has no
debt. The company’s annual cash flow is
$1,000, before interest and taxes. The
corporate tax rate is 40%. You have the
option to exchange 1/2 of your equity
position for 10% bonds with a face value of
$1,000.
Should you do this and why?
All Equity 1/2 Debt
EBIT 1,000 1,000
Interest Pmt 0 100
Pretax Income 1,000 900
Taxes @ 40% 400 360
Net Cash Flow $600 $540
Example - You own all the equity of Space Babies Diaper Co..
The company has no debt. The company’s annual cash flow
is $1,000, before interest and taxes. The corporate tax rate
is 40%. You have the option to exchange 1/2 of your equity
position for 10% bonds with a face value of $1,000. Should
you do this and why?
All Equity 1/2 Debt
EBIT 1,000 1,000
Interest Pmt 0 100
Pretax Income 1,000 900
Taxes @ 40% 400 360
Net Cash Flow 600 $540
Example - You own all the equity of Space Babies Diaper Co.. The
company has no debt. The company’s annual cash flow is
$1,000, before interest and taxes. The corporate tax rate is
40%. You have the option to exchange 1/2 of your equity
position for 10% bonds with a face value of $1,000. Should you
do this and why?
Total Cash Flow
All Equity = 600
*1/2 Debt = 640
(540 + 100)
PV of Tax Shield =
(assume perpetuity)
D x r
D
x Tc
r
D
= D x Tc
Example:
Tax benefit = 1000 x (.10) x (.40) = $40
PV of 40 perpetuity = 40 / .10 = $400
PV Tax Shield = D x Tc = 1000 x .4 = $400
Firm Value =
Value of All Equity Firm + PV Tax Shield
Example
All Equity Value = 600 / .10 = 6,000
PV Tax Shield = 400
Firm Value with 1/2 Debt = $6,400
The increase in the value of the firm due to the debt is the present value of
the tax shield.
Relative Advantage Formula (RAF)
( Debt vs Equity )
1-TP
(1-TPE) (1-TC)
RAF > 1 Debt
RAF < 1 Equity
Advantage
If TP = TPE; i.e. if equity income comes entirely as
dividend; the RAF would depend only on Corporate tax
rate:
1
(1-TC)
RAF > 1 Debt
RAF < 1 Equity
Advantage
Example 1
All Debt All Equity
Income BTCP 1.00 1.00
less TC=.46 0.00 0.46
Income BTP 1.00 0.54
Taxes TP =.5 TPE=0 0.50 0.00
After Tax Income 0.50 0.54
RAF = .926
Advantage Equity
Example 2
All Debt All Equity
Income BTCP 1.00 1.00
less TC=.34 0.00 0.34
Income BTP 1.00 0.66
Taxes TP =.28 TPE=.21 0.28 0.139
After Tax Income 0.72 0.521
RAF = 1.381
Advantage Debt
? Today’s RAF & Debt vs Equity preference.
1 - .33
(1 - .16) (1 - .35)
= 1.23
RAF =
Why are companies not all debt?
Structure of Bond Yield Rates
D
E
Bond
Yield
r
Traditional view, as the debt-equity ratio increases, the interest rate on debt
increases because of an increase in the probability of default (Bankruptcy risk).
Weighted Average Cost of Capital
without taxes (traditional view)
r
D
V
r
D
r
E
Includes
Bankruptcy Risk
WACC
This shows the weighted average cost of capital vs. D/V
Costs of Financial Distress - Costs arising from
bankruptcy or distorted business decisions
before bankruptcy.
? At higher levels of debt, costs of financial distress have to be
considered.
? Financial distress occurs when promises to creditors are broken or
honored with difficulty.
? Financial distress includes failure to pay interest or principal or
both.
? Formally, financial distress is defined as events preceding and
including bankruptcy, such as violation of a loan or bond contract.
? Financial distress has both direct and indirect costs.
Costs of Financial Distress - Costs arising
from bankruptcy or distorted business
decisions before bankruptcy.
Market Value = Value if all Equity Financed
+ PV Tax Shield
- PV Costs of Financial Distress
Debt
M
a
r
k
e
t
V
a
l
u
e
o
f
T
h
e
F
i
r
m
Value of
unlevered
firm
PV of interest
tax shields
Costs of
financial distress
Value of levered firm
Optimal amount
of debt
Maximum value of firm
? Cash In and Run – Stockholders may be reluctant to
put money into a form in financial distress’ but are
happy to take out the money in the form of
dividend– “refusing to contribute equity capital
? Playing for Time – When firm is in distress, creditors
would like to salvage what they can by forcing the
firm to settle; Stockholders want to delay –
accounting changes, encouraging false hopes,
cutting corners to make results look better
? Bait and Switch – Quick way to get into distress –
you start with issuance of limited amount of
relatively safe debt and then suddenly issue lot
more – thus imposing capital loss on old bond
holders
Trade-off Theory - Theory that capital
structure is based on a trade-off between
tax savings and distress costs of debt.
Pecking Order Theory - Theory stating that
firms prefer to issue debt rather than equity
if internal finance is insufficient.
1. Stock-for-debt Stock price
exchange offers falls
Debt-for-stock Stock price
exchange offers rises
2. Issuing common stock drives down stock prices;
repurchase increases stock prices.
3. Issuing straight debt has a small negative impact.
? Why does security issues affect stock
price? The demand for a firm’s
securities ought to be flat. Security
issues should not affect stock prices.
This leads us to the pecking order
theory.
? Any firm is a drop in the bucket.
? Plenty of close substitutes.
? Large debt issues don’t significantly
depress the stock price.
Some Implications:
?Internal equity may be better than external
equity.
?Financial slack is valuable.
?If external capital is required, debt is better.
(There is less room for difference in
opinions about what debt is worth).
? Compute Present value of interest tax shields,
marginal tax at 35%.
? A Rs. 1000 one year loan at 8%
? A 5 yr loan of Rs. 1000 at 8%, with no repayment till
maturity
? A Rs. 1000 perpetuity at 7%
? What are costs of bankruptcy?
? What type of firms are likely to incur high
costs in the event of bankruptcy or financial
distress? What would have relatively low
costs? Give examples
? After Tax WACC
? Tricks of the Trade
? Capital Structure and WACC
? Adjusted Present Value
? Discounting Safe, Nominal Cash Flows
? The tax benefit from interest expense
deductibility must be included in the cost
of funds.
? This tax benefit reduces the effective cost
of debt by a factor of the marginal tax
rate.
|
.
|
\
|
× +
|
.
|
\
|
× =
E D
r
V
E
r
V
D
WACC
rD is the after-tax cost of debt. This is also used when taxes are not considered.
Old Formula
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
Tax Adjusted Formula
rD is the before-tax cost of debt. (1-Tc)rD is the after-tax cost
of debt. In this formula corporate taxes are taken into account.
Example - Sangria Corporation
The firm has a marginal tax rate of 35%.
The cost of equity is 14.6% and the pretax
cost of debt is 8%. Given the book and
market value balance sheets, what is the
tax adjusted WACC?
Always use the market values for calculating WACC.
Example - Sangria Corporation -
continued
Balance Sheet (Book Value, millions)
Assets 100 50 Debt
50 Equity
Total assets 100 100 Total liabilities
Many times, market to book ratios are available, and then we
can convert these book values to market values
Example - Sangria Corporation -
continued
Balance Sheet (Market Value, millions)
Assets 125 50 Debt
75 Equity
Total assets 125 125 Total liabilities
Example - Sangria Corporation -
continued
Debt ratio = (D/V) = 50/125 = .4 or 40%
Equity ratio = (E/V) = 75/125 = .6 or 60%
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
Example - Sangria Corporation -
continued
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E D
r
V
E
r
V
D
Tc WACC ) 1 (
% 84 . 10
1084 .
146 .
125
75
08 .
125
50
) 35 . 1 (
=
=
|
.
|
\
|
× +
|
.
|
\
|
× ÷ = WACC
Example - Sangria Corporation -
continued
The company would like to invest in a
perpetual crushing machine with cash
flows of $2.085 million per year pre-
tax.
Given an initial investment of $12.5
million, what is the value of the
machine?
This problem assumes that the project
has the same risk as the firm
Example - Sangria Corporation -
continued
The company would like to invest in a perpetual crushing
machine with cash flows of $2.085 million per year pre-tax.
Given an initial investment of $12.5 million, what is the value
of the machine?
Cash Flows
Pretax cash flow 2.085
Tax @ 35% 0.73
After-tax cash flow $1.355 million
After tax cash flows are the relevant cash flows for calculating the NPV.
Example - Sangria Corporation -
continued
The company would like to invest in a perpetual crushing
machine with cash flows of $2.085 million per year pre-tax.
Given an initial investment of $12.5 million, what is the value
of the machine?
0
1084 .
355 . 1
5 . 12
1
0
=
+ ÷ =
÷
+ =
g r
C
C NPV
? Preferred stock and other forms of financing
must be included in the formula
|
.
|
\
|
× +
|
.
|
\
|
× +
|
.
|
\
|
× ÷ =
E P D
r
V
E
r
V
P
r
V
D
Tc WACC ) 1 (
V = D + E + P
Example - Sangria Corporation -
continued
Calculate WACC given preferred stock is $25 mil of total
equity and yields 10%.
Balance Sheet (Market Value, millions)
Assets 125 50 Debt
25 Preferred Equity
50 Common Equity
Total assets 125 125 Total liabilities
% 04 . 11
1104 .
146 .
125
50
10 .
125
25
08 .
125
50
) 35 . 1 (
=
=
|
.
|
\
|
× +
|
.
|
\
|
× +
|
.
|
\
|
× ÷ = WACC
? What should be included with debt?
? Long-term debt?
? Short-term debt?
? Cash (netted off?)
? Receivables?
? Deferred tax?
? How are costs of financing determined?
? Return on equity can be derived from market data
Return on equity can be derived using CAPM or DCF.
CAPM = rE + rf + b(rm - rf);
DCF = rE = [D1/Po ] + g.
? Cost of debt is set by the market given the specific
rating of a firm’s debt
It is the yield to maturity or the effective interest rate on
debt
? Preferred stock often has a preset dividend rate
Cost of preferred equity: rP = D/Po.
? If you discount at WACC, cash flows have to be
projected just as you would for a capital
investment project. Do not deduct interest.
Calculate taxes as if the company were all-
equity financed. The value of interest tax
shields is picked up in the WACC formula.
Normally rE > WACC > rD
? The company's cash flows will probably not be forecasted to
infinity.
? Financial managers usually forecast to a medium-term
horizon -- ten years, say -- and add a terminal value to the
cash flows in the horizon year.
? The terminal value is the present value at the horizon of
post-horizon flows.
? Estimating the terminal value requires careful attention,
because it often accounts for the majority of the value of the
company.
? After tax cash flows are calculated as EBIT (1-Tc).
? Discounting at WACC the values of the
assets and operations of the company.
? If the object is to value the company's
equity, that is, its common stock, don't
forget to subtract the value of the company's
outstanding debt.
? Discounting at WACC gives the total value of
the firm (V).
? The flow-to-equity approach gives the value
of the common equity in that case:
E = [EBIT – rDD](1 - Tc) / rE
where rE is the cost of levered equity.
Example continued: Sangria and the Perpetual
Crusher project at 20% D/V
Step 1 – r at current debt of 40%
Step 2 – D/V changes to 20%
Step 3 – New WACC
12 . ) 6 (. 146 . ) 4 (. 08 . = + = r
13 . ) 25 )(. 08 . 12 (. 12 . = ÷ + =
E
r
114 . ) 8 (. 13 . ) 2 )(. 35 . 1 ( 08 . = + ÷ = WACC
If the debt ratio changes, then the cost of equity should be adjusted
to reflect the new debt ratio. Equity becomes more risky when debt
increases.
APV = Base Case NPV + PV Impact
? Base Case = All equity finance firm NPV
? PV Impact = all costs/benefits directly
resulting from project
? A conceptually appealing and a general approach
to valuation
? It applies the value additivity property.
example:
Project A has an NPV of $150,000. In order to
finance the project we must issue stock, with
a brokerage cost of $200,000.
example:
Project A has an NPV of $150,000. In order to
finance the project we must issue stock, with a
brokerage cost of $200,000.
Project NPV = 150,000
Stock issue cost = -200,000
Adjusted NPV = - 50,000
Don’t do the project
Financing costs outweigh the NPV of the project
example:
Project B has a NPV of -$20,000. We can
issue debt at 8% to finance the project. The
new debt has a PV Tax Shield of $60,000.
Assume that Project B is your only option.
example:
Project B has a NPV of -$20,000. We can
issue debt at 8% to finance the project.
The new debt has a PV Tax Shield of
$60,000. Assume that Project B is your
only option.
Project NPV = - 20,000
Stock issue cost = 60,000
Adjusted NPV = 40,000
Do the project
PV Tax Shield is like a subsidy from the
government
|
|
.
|
\
|
+
+
÷ =
D
c D
r
r
T Lr r WACC
1
1
This formula assumes that debt is rebalanced each year.
Debt to project value ratios are held constant where L = D / V.
debt) for avail CF ( loan Equivalent PV =
Equivalent loan is the present value of cash flows
available to pay for debt
? Calculate the WACC for A Ltd. Having Rs. 7.5
crores debt. The debt is trading at 90% of
par. Its YTM is 9%. It has 25 lac shares
trading at Rs. 42 per share. Assume the tax
rate to be 35% and the expected return by
the shareholders to be 18%.
? What are your key assumptions?
? For what type of project would WACC be the right
discount rate?
? Y Ltd is 100% equity financed. The expected
rate of return on its shares is 12%.
? What is the opportunity cost of capital for an average
risk investment?
? Suppose the company issues debt and repurchases
equity resulting in debt ratio of 30%. What will the
WACC, if the borrowing rate is 7.5% and tax rate 35%?
56
? The Classical Theory of Interest
? Duration and Volatility
? The Term Structure and YTM
? Explaining the Term Structure
? Allowing for the Risk of Default
N
N
r
C
r
C
r
C
PV
) 1 (
000 , 1
...
) 1 ( ) 1 (
2
2
1
1
+
+
+ +
+
+
+
=
Example
? If today is October 2002, what is the value of the
following bond? An IBM Bond pays $115 every Sept
for 5 years. In Sept 2007 it pays an additional $1000
and retires the bond. The bond is rated AAA (WSJ
AAA YTM is 7.5%)
Cash Flows
Sept 03 04 05 06 07
115 115 115 115 1115
Example continued
? If today is October 2002, what is the value of the following bond? An
IBM Bond pays $115 every Sept for 5 years. In Sept 2007 it pays an
additional $1000 and retires the bond. The bond is rated AAA (WSJ AAA
YTM is 7.5%)
( ) ( ) ( ) ( )
84 . 161 , 1 $
075 . 1
115 , 1
075 . 1
115
075 . 1
115
075 . 1
115
075 . 1
115
5 4 3 2
=
+ + + + = PV
0
200
400
600
800
1000
1200
1400
1600
0 2 4 6 8 10 12 14
5 Year 9% Bond 1 Year 9% Bond
Yield
P
r
i
c
e
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Nominal Interest Rate = The rate you actually
pay when you borrow money
Classical Theory of Interest Rates (Economics)
? developed by Irving Fisher
Nominal Interest Rate = The rate you actually pay
when you borrow money
Real Interest Rate = The theoretical rate you pay
when you borrow money, as determined by
supply and demand
Supply
Demand
$ Qty
r
Real r
Nominal r = Real r + expected inflation
Real r is theoretically somewhat stable
Inflation is a large variable
Q: Why do we care?
A: This theory allows us to understand the Term
Structure of Interest Rates.
Q: So What?
A: The Term Structure tells us the cost of debt.
Example (Bond 1)
Calculate the duration of our 6 7/8 % bond @ 4.9
% YTM
Year CF PV@YTM % of Total PV % x Year
1 68.75 65.54 .060 0.060
2 68.75 62.48 .058 0.115
3 68.75 59.56 .055 0.165
4 68.75 56.78 .052 0.209
5 68.75 841.39 .775 3.875
1085.74 1.00 Duration 4.424
Example (Bond 2)
Given a 5 year, 9.0%, $1000 bond, with a 8.5% YTM,
what is this bond’s duration?
Year CF PV@YTM % of Total PV % x Year
1 90 82.95 .081 0.081
2 90 76.45 .075 0.150
3 90 70.46 .069 0.207
4 90 64.94 .064 0.256
5 1090 724.90 .711 3.555
1019.70 1.00 Duration= 4.249
example
1000 = 1000
(1+R
3
)
3
(1+f
1
)(1+f
2
)(1+f
3
)
Forward Rate Computations
(1+ r
n
)
n
= (1+ r
1
)(1+f
2
)(1+f
3
)....(1+f
n
)
Example
What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660
? Example
What is the 3rd year forward rate?
2 year zero treasury YTM = 8.995
3 year zero treasury YTM = 9.660
Answer
FV of principal @ YTM
2 yr 1000 x (1.08995)
2
= 1187.99
3 yr 1000 x (1.09660)
3
= 1318.70
IRR of (FV1318.70 & PV=1187.99) = 11%
Example
Two years from now, you intend to begin a
project that will last for 5 years. What
discount rate should be used when evaluating
the project?
2 year spot rate = 5%
7 year spot rate = 7.05%
coupons paying bonds to derive rates
Bond Value = C
1
+ C
2
(1+r) (1+r)
2
Bond Value = C
1
+ C
2
(1+R
1
) (1+f
1
)(1+f
2
)
d1 = C
1
d2 = C
2
(1+R
1
) (1+f
1
)(1+f
2
)
example
8% 2 yr bond YTM = 9.43%
10% 2 yr bond YTM = 9.43%
What is the forward rate?
Step 1
value bonds 8% = 975
10%= 1010
Step 2
975 = 80d1 + 1080 d2 -------> solve for d1
1010 =100d1 + 1100d2 -------> insert d1 &
solve for d2
example continued
Step 3 solve algebraic equations
d1 = [975-(1080)d2] / 80
insert d1 & solve = d2 = .8350
insert d2 and solve for d1 = d1 = .9150
Step 4
Insert d1 & d2 and Solve for f
1
& f
2
.
.9150 = 1/(1+f
1
) .8350 = 1 /
(1.0929)(1+f
2
)
f
1
= 9.29% f
2
= 9.58%
Spot Rate - The actual interest rate today (t=0)
Forward Rate - The interest rate, fixed today, on a
loan made in the future at a fixed time.
Future Rate - The spot rate that is expected in the
future
Yield To Maturity (YTM) - The IRR on an interest
bearing instrument
YTM (r)
Year
1981
1987 & Normal
1976
1 5 10 20 30
What Determines the Shape of the TS?
1 - Unbiased Expectations Theory
2 - Liquidity Premium Theory
3 - Market Segmentation Hypothesis
Term Structure & Capital Budgeting
? CF should be discounted using Term Structure
info
? Since the spot rate incorporates all forward
rates, then you should use the spot rate that
equals the term of your project.
? If you believe in other theories take advantage of
the arbitrage.
? All interest bearing instruments are priced
to fit the term structure
? This is accomplished by modifying the
asset price
? The modified price creates a New Yield,
which fits the Term Structure
? The new yield is called the Yield To
Maturity (YTM)
Example
? A $1000 treasury bond expires in 5 years. It
pays a coupon rate of 10.5%. If the market
price of this bond is 1078.8, what is the YTM?
Example
? A $1000 treasury bond expires in 5 years.
It pays a coupon rate of 10.5%. If the
market price of this bond is 107-88, what is
the YTM?
C0 C1 C2 C3 C4 C5
-1078.80 105 105 105 105 1105
Calculate IRR = 8.5%
The risk of default changes the price of a bond and the YTM.
Example
We have a 9% 1 year bond. The built in price is $1000. But,
there is a 20% chance the company will go into bankruptcy
and not be able to pay. What is the bond’s value?
A:
Example
We have a 9% 1 year bond. The built in price is $1000. But, there
is a 20% chance the company will go into bankruptcy and not be
able to pay. What is the bond’s value?
A: Bond Value Prob
1090 .80 = 872.00
0 .20 = 0 .
872.00 =expected CF
Value
YTM
= =
= =
872
109
1090
800
36 3%
.
$800
.
Conversely - If on top of default risk, investors require an additional 2
percent market risk premium, the price and YTM is as follows:
Value
YTM
= =
= =
872
111
59
1090
78559
388%
.
$785.
.
.
? Insurance
? Hedging With Futures
? Forward Contracts
? SWAPS
? How to Set Up A Hedge
? Most businesses face the possibility of a
hazard that can bankrupt the company in an
instant.
? These risks are neither financial or business
and can not be diversified.
? The cost and risk of a loss due to a hazard,
however, can be shared by others who share
the same risk.
Example
An offshore oil platform is valued at
$1 billion. Expert meteorologist
reports indicate that a 1 in 10,000
chance exists that the platform may
be destroyed by a storm over the
course of the next year.
How can the cost of this hazard
be shared?
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm
over the course of the next year.
? How can the cost of this hazard be shared
Answer
A large number of companies with similar risks
can each contribute pay into a fund that is set
aside to pay the cost should a member of this
risk sharing group experience the 1 in 10,000
loss. The other 9,999 firms may not
experience a loss, but also avoided the risk of
not being compensated should a loss have
occurred.
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm over
the course of the next year.
? What would the cost to each group member be for
this protection.
Answer
Example - cont
An offshore oil platform is valued at $1 billion. Expert
meteorologist reports indicate that a 1 in 10,000 chance
exists that the platform may be destroyed by a storm over
the course of the next year.
? What would the cost to each group member be for
this protection.
Answer
000 , 100 $
000 , 10
000 , 000 , 000 , 1
=
? Why would an insurance company not offer
a policy on this oil platform for $100,000?
? Why would an insurance company not offer
a policy on this oil platform for $100,000?
? Administrative costs
? Adverse selection
? Moral hazard
? The loss of an oil platform by a storm
may be 1 in 10,000. The risk, however,
is larger for an insurance company since
all the platforms in the same area may be
insured, thus if a storm damages one in
may damage all in the same area. The
result is a much larger risk to the insurer
? Catastrophe Bonds - (CAT Bonds) Allow
insurers to transfer their risk to bond
holders by selling bonds whose cash flow
payments depend on the level of
insurable losses NOT occurring.
Business has risk
Business Risk - variable costs
Financial Risk - Interest rate changes
Goal - Eliminate risk
HOW?
Hedging & Futures Contracts
Ex - Kellogg produces cereal. A major component and
cost factor is sugar.
? Forecasted income & sales volume is set by using a
fixed selling price.
? Changes in cost can impact these forecasts.
? To fix your sugar costs, you would ideally like to
purchase all your sugar today, since you like today’s
price, and made your forecasts based on it. But, you
can not.
? You can, however, sign a contract to purchase sugar at
various points in the future for a price negotiated
today.
? This contract is called a “Futures Contract.”
? This technique of managing your sugar costs is called
“Hedging.”
1- Spot Contract - A contract for immediate sale &
delivery of an asset.
2- Forward Contract - A contract between two people
for the delivery of an asset at a negotiated price on a
set date in the future.
3- Futures Contract - A contract similar to a forward
contract, except there is an intermediary that creates a
standardized contract. Thus, the two parties do not
have to negotiate the terms of the contract.
Commodity Futures
-Sugar -Corn -OJ
-Wheat -Soy beans -Pork bellies
Financial Futures
-Tbills -Yen -GNMA
-Stocks -Eurodollars
Index Futures
-S&P 500 -Value Line Index
-Vanguard Index
SUGAR
Not an actual sale
Always a winner & a loser (unlike stocks)
K are “settled” every day. (Marked to Market)
Hedge - K used to eliminate risk by locking in
prices
Speculation - K used to gamble
Margin - not a sale - post partial amount
Hog K = 30,000 lbs
Tbill K = $1.0 mil
Value line Index K = $index x 500
birth 1981
Definition - An agreement between two firms, in
which each firm agrees to exchange the “interest
rate characteristics” of two different financial
instruments of identical principal
Key points
Spread inefficiencies
Same notation principal
Only interest exchanged
? “Plain Vanilla Swap” - (generic swap)
? fixed rate payer
? floating rate payer
? counterparties
? settlement date
? trade date
? effective date
? terms
? Swap Gain = fixed spread - floating spread
example (vanilla/annually settled)
XYZ ABC
fixed rate 10% 11.5%
floating rate libor + .25 libor + .50
Q: if libor = 7%, what swap can be made 7 what is the profit
(assume $1mil face value loans)
A:
XYZ borrows $1mil @ 10% fixed
ABC borrows $1mil @ 7.5% floating
XYZ pays floating @ 7.25%
ABC pays fixed @ 10.50%
example - cont
Benefit to XYZ Net position
floating +7.25 -7.25 0
fixed +10.50 -10.00 +.50
Net gain +.50%
Benefit ABC Net Position
floating +7.25 - 7.50 -.25
fixed -10.50 + 11.50 +1.00
net gain +.75%
example - cont
Settlement date
ABC pmt 10.50 x 1mil = 105,000
XYZ pmt 7.25 x 1mil = 72,500
net cash pmt by ABC = 32,500
if libor rises to 9%
settlement date
ABC pmt 10.50 x 1mil = 105,000
XYZ pmt 9.25 x 1mil = 92,500
net cash pmt by ABC = 12,500
? transactions
? rarely done direct
? banks - middleman
? bank profit - part of “swap gain”
example - same continued
XYZ & ABC go to bank separately
XYZ term = SWAP floating @ libor + .25 for fixed @
10.50
ABC terms = swap floating libor + .25 for fixed 10.75
example - cont
settlement date - XYZ
Bank pmt 10.50 x 1mil = 105,000
XYZ pmt 7.25 x 1mil = 72,500
net Bank pmt to XYZ = 32,500
settlement date - ABC
Bank pmt 7.25 x 1mil = 72,500
ABC pmt 10.75 x 1mil = 107,500
net ABC pmt to bank = 35,000
bank “swap gain” = +35,000 - 32,500 = +2,500
example - cont
benefit to XYZ
floating 7.25 - 7.25 = 0
fixed 10.50 - 10.00 = +.50 net gain
.50
benefit to ABC
floating 7.25 - 7.50 = - .25
fixed -10.75 + 11.50 = + .75 net gain .50
benefit to bank
floating +7.25 - 7.25 = 0
fixed 10.75 - 10.50 = +.25 net gain +.25
total benefit = 12,500 (same as w/o bank)
Example - You are speculating in Hog Futures. You
think that the Spot Price of hogs will rise in the
future. Thus, you go Long on 10 Hog Futures. If the
price drops .17 cents per pound ($.0017) what is
total change in your position?
Example - You are speculating in Hog Futures. You
think that the Spot Price of hogs will rise in the
future. Thus, you go Long on 10 Hog Futures. If the
price drops .17 cents per pound ($.0017) what is
total change in your position?
30,000 lbs x $.0017 loss x 10 Ks = $510.00 loss
Since you must settle your account every day, you must give your
broker $510.00
50.63
50.80
-$510
cents
per lbs
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month
of August. In June, the September corn
futures are selling for $2.94 per bushel (1K
= 5,000 bushels). Farmer Smith wishes to
lock in this price.
Show the transactions if the Sept spot price
drops to $2.80.
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month of
August. In June, the September corn futures are
selling for $2.94 per bushel (1K = 5,000 bushels).
Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price drops to
$2.80.
Revenue from Crop: 10,000 x 2.80 28,000
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 2.80 = 28,000 .
Gain on Position------------------------------- 1,400
Total Revenue $ 29,400
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month
of August. In June, the September corn
futures are selling for $2.94 per bushel (1K
= 5,000 bushels). Farmer Smith wishes to
lock in this price.
Show the transactions if the Sept spot price
rises to $3.05.
In June, farmer John Smith expects to harvest
10,000 bushels of corn during the month of
August. In June, the September corn futures are
selling for $2.94 per bushel (1K = 5,000 bushels).
Farmer Smith wishes to lock in this price.
Show the transactions if the Sept spot price rises to
$3.05.
Revenue from Crop: 10,000 x 3.05 30,500
June: Short 2K @ 2.94 = 29,400
Sept: Long 2K @ 3.05 = 30,500 .
Loss on Position------------------------------- ( 1,100 )
Total Revenue $ 29,400
You have lived in NYC your whole life and are independently wealthy. You
think you know everything there is to know about pork bellies (uncurred bacon)
because your butler fixes it for you every morning. Because you have decided
to go on a diet, you think the price will drop over the next few months. On the
CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @
44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to
close your position. What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290
Loss of 10.23 % = - 5,130
You have lived in NYC your whole life and are independently wealthy. You
think you know everything there is to know about pork bellies (uncurred bacon)
because your butler fixes it for you every morning. Because you have decided
to go on a diet, you think the price will drop over the next few months. On the
CME, each PB K is 38,000 lbs. Today, you decide to short three May Ks @
44.00 cents per lbs. In Feb, the price rises to 48.5 cents and you decide to
close your position. What is your gain/loss?
? The amount (percentage) of a Futures Contract
Value that must be on deposit with a broker.
? Since a Futures Contract is not an actual sale, you
need only pay a fraction of the asset value to
open a position = margin.
? CME margin requirements are 15%
? Thus, you can control $100,000 of assets with
only $15,000.
You have lived in NYC your whole life and are independently wealthy.
You think you know everything there is to know about pork bellies
(uncurred bacon) because your butler fixes it for you every morning.
Because you have decided to go on a diet, you think the price will drop
over the next few months. On the CME, each PB K is 38,000 lbs.
Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb,
the price rises to 48.5 cents and you decide to close your position.
What is your gain/loss?
Nov: Short 3 May K (.4400 x 38,000 x 3 ) = + 50,160
Feb: Long 3 May K (.4850 x 38,000 x 3 ) = - 55,290
Loss = - 5,130
Loss 5130 5130
Margin 50160 x.15 7524
------------ = -------------------- = ------------ = 68% loss
You have lived in NYC your whole life and are independently wealthy.
You think you know everything there is to know about pork bellies
(uncurred bacon) because your butler fixes it for you every morning.
Because you have decided to go on a diet, you think the price will drop
over the next few months. On the CME, each PB K is 38,000 lbs.
Today, you decide to short three May Ks @ 44.00 cents per lbs. In Feb,
the price rises to 48.5 cents and you decide to close your position.
What is your gain/loss?
? Foreign Exchange Markets
? Some Basic Relationships
? Hedging Currency Risk
? Exchange Risk and International Investment
Decisions
? Political Risk
Exchange Rate - Amount of one currency
needed to purchase one unit of another.
Spot Rate of Exchange - Exchange rate
for an immediate transaction.
Forward Exchange Rate - Exchange rate
for a forward transaction.
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen
per dollar and the 3 month forward rate is
119.660 yen per dollar, what is the
premium and discount relationship?
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen per
dollar and the 3 month forward rate is 119.660 yen
per dollar, what is the premium and discount
relationship?
3.5% = 1 -
119.66
120.700
4
) (-Discount or Premium = 1 -
Price Forward
Price Spot
×
× T
Forward Premiums and Forward Discounts
Example - The yen spot price is 120.700 yen per
dollar and the 3 month forward rate is 119.660 yen
per dollar, what is the premium and discount
relationship?
Answer - The dollar is selling at a 3.5% discount,
relative to the yen. The yen is selling at a 3.5%
premium, relative to the dollar.
? Basic Relationships
1 + r
1 + r
foreign
$
1 + i
1 + i
foreign
$
f
S
foreign / $
foreign / $
E(s
S
foreign / $
foreign / $
)
equals
equals
equals equals
1) Interest Rate Parity Theory
? The ratio between the risk free interest
rates in two different countries is equal
to the ratio between the forward and
spot exchange rates.
1 + r
1 + r
=
foreign
$
f
S
foreign / $
foreign / $
Example - You have the opportunity to invest
$1,000,000 for one year. All other things being
equal, you have the opportunity to obtain a 1
year Japanese bond (in yen) @ 0.06 % or a 1
year US bond (in dollars) @ 3.65%. The spot
rate is 120.700 yen:$1 The 1 year forward rate
is 116.535 yen:$1
Which bond will you prefer and why?
Ignore transaction costs
Value of US bond = $1,000,000 x 1.0365 = $1,036,500
Value of Japan bond = $1,000,000 x 120.700 = 120,700,000 yen exchange
120,700,000 yen x 1.0006 = 120,772,420 yen bond pmt
120,772,420 yen / 116.535 = $1,036,400 exchange
Example - You have the opportunity to invest $1,000,000 for one
year. All other things being equal, you have the opportunity to obtain
a 1 year Japanese bond (in yen) @ 0.06 % or a 1 year US bond (in
dollars) @ 3.65%. The spot rate is 120.700 yen:$1 The 1 year
forward rate is 116.535 yen:$1
Which bond will you prefer and why? Ignore transaction costs
2) Expectations Theory of Exchange Rates
Theory that the expected spot exchange rate equals the forward
rate.
f
S
foreign / $
foreign / $
=
E(s
S
foreign / $
foreign / $
)
3) Purchasing Power Parity
The expected change in the spot rate equals the expected
difference in inflation between the two countries.
1 + i
1 + i
=
foreign
$
E(s
S
foreign / $
foreign / $
)
Example
If inflation in the US is forecasted at 2.0%
this year and Japan is forecasted to fall
1.5%, what do we know about the
expected spot rate?
Given a spot rate of 120.700 yen:$1
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
120.700
E(s )
=
.02 + 1
.015 - 1
foreign/$
Example - If inflation in the US is
forecasted at 2.0% this year and Japan is
forecasted to fall 1.5%, what do we
know about the expected spot rate?
Given a spot rate of 120.700 yen:$1
solve for Es
Es = 116.558
foreign/$
foreign/$
$
foreign
)
=
i + 1
i + 1
S
E(s
120.700
E(s )
=
.02 + 1
.015 - 1
foreign/$
4) International Fisher effect
The expected difference in inflation rates equals the difference in
current interest rates.
Also called common real interest rates
1 + r
1 + r
=
foreign
$
1 + i
1 + i
foreign
$
Example - The real interest rate in each
country is about the same
1.016 =
.985
1.0006
=
i + 1
r + 1
) (
foreign
foreign
= real r
1.016 =
1.02
1.0365
=
i + 1
r + 1
) (
$
$
= real r
Example - Honda builds a new car in Japan for a cost + profit of
1,715,000 yen. At an exchange rate of 120.700Y:$1 the car sells for
$14,209 in Indianapolis. If the dollar rises in value, against the yen, to
an exchange rate of 134Y:$1, what will be the price of the car?
1,715,000 = $12,799
134
Conversely, if the yen is trading at a
forward discount, Japan will
experience a decrease in
purchasing power.
Example - Harley Davidson builds a motorcycle for a cost plus profit of
$12,000. At an exchange rate of 120.700Y:$1, the motorcycle sells
for 1,448,400 yen in Japan. If the dollar rises in value and the
exchange rate is 134Y:$1, what will the motorcycle cost in Japan?
$12,000 x 134 = 1,608,000 yen
? Currency Risk can be reduced by using
various financial instruments
? Currency forward contracts, futures contracts,
and even options on these contracts are
available to control the risk
1) Exchange to Rs. and analyze
2) Discount using foreign cash
flows and interest rates, then
exchange to Rs.
3) Choose a currency standard (Rs.)
and hedge all non Rupee CF.
Techniques
Political Risk Scores
A B C D E F G H I J K L Total
Maximum Score 12 12 12 12 12 6 6 6 6 6 6 4 100
Netherlands 9 10 10 12 12 6 6 6 6 6 6 4 93
USA 11 10 11 11 8 4 6 6 6 5 6 4 88
Germany 10 8 9 12 11 5 6 6 6 5 5 4 87
UK 11 10 11 9 9 5 6 6 6 4 6 4 87
France 10 7 9 10 11 3 5 6 5 5 5 4 80
Japan 10 6 6 12 10 2 6 5 6 6 5 4 78
Brazil 9 4 5 9 11 3 4 6 2 4 4 2 63
China 11 4 6 10 9 2 2 5 5 4 1 2 61
India 5 5 5 8 5 3 5 2 4 2 5 3 52
Russia 7 2 3 8 10 1 4 5 3 3 2 1 49
Indonesia 10 3 5 4 9 1 1 2 2 2 2 3 44
Iraq 8 3 4 3 4 1 0 5 2 2 0 0 32
A = Govt stability G = Military in politics
B = Socioeonmic conditions H = Religious tensions
C = Investment profile I = Law and order
D = Internal conflict J = Ethnic tensions
E = External conflict K = Democratic accountability
F = Corruption L = Bureaucracy quality
14
1
? Calls, Puts and Shares
? Financial Alchemy with Options
? What Determines Option Value
? Option Valuation
14
2
Put Option
Right to sell an asset at a specified exercise
price on or before the exercise date.
14
3
Call Option
Right to buy an asset at a specified exercise
price on or before the exercise date.
14
4
Buyer Seller
Call option Right to buy asset Obligation to sell asset
Put option Right to sell asset Obligation to buy asset
? The value of an option at expiration is a
function of the stock price and the
exercise price.
14
5
? The value of an option at expiration is a
function of the stock price and the
exercise price.
Example - Option values given a exercise
price of $55
14
6
0 0 0 5 15 25 Value Put
25 15 5 0 0 0 Value Call
80 70 60 50 40 $30 Price Stock
14
7
Call option value (graphic) given a $55 exercise price.
Share Price
C
a
l
l
o
p
t
i
o
n
v
a
l
u
e
55 75
$20
14
8
Put option value (graphic) given a $55 exercise price.
Share Price
P
u
t
o
p
t
i
o
n
v
a
l
u
e
50 55
$5
14
9
Call option payoff (to seller) given a $55 exercise price.
Share Price
C
a
l
l
o
p
t
i
o
n
$
p
a
y
o
f
f
55
15
0
Put option payoff (to seller) given a $55 exercise price.
Share Price
P
u
t
o
p
t
i
o
n
$
p
a
y
o
f
f
55
Protective Put - Long stock and long put
15
1
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long Stock
Protective Put - Long stock and long put
15
2
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long Put
Protective Put - Long stock and long put
15
3
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Protective Put
Long Put
Long Stock
Protective Put - Long stock and long put
15
4
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Protective Put
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
5
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long call
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
6
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Long put
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
7
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Straddle
Straddle - Long call and long put
- Strategy for profiting from high volatility
15
8
Share Price
P
o
s
i
t
i
o
n
V
a
l
u
e
Straddle
15
9
Upper Limit
Stock Price
16
0
Upper Limit
Stock Price
Lower Limit
(Stock price - exercise price) or 0
which ever is higher
Time Decay Chart
Option Price
Stock Price
16
1
16
2
? Simple Valuation Model
? Binomial Model
? Black-Scholes Model
? Black Scholes vs. Binomial
16
3
Probability Up = p = (a - d) Prob Down = 1 - p
(u - d)
a = e
rD t
d =e
-s [D t]
.5
u =e
s [D t]
.5
Dt =
time intervals as % of year
16
4
Binomial Pricing
Example
Price = 36 s = .40 t = 90/365 D t = 30/365
Strike = 40 r = 10%
a = 1.0083
u = 1.1215
d = .8917
Pu = .5075
Pd = .4925
16
5
Binomial Pricing
40.37
32.10
36
37 . 40 1215 . 1 36
1 0
= ×
= ×
U
P U P
Binomial Pricing
16
6
40.37
32.10
36
37 . 40 1215 . 1 36
1 0
= ×
= ×
U
P U P
10 . 32 8917 . 36
1 0
= ×
= ×
D
P D P
Binomial Pricing
16
7
50.78 = price
40.37
32.10
25.52
45.28
36
28.62
40.37
32.10
36
1 +
= ×
t t
P U P
Binomial Pricing
16
8
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
36
28.62
36
40.37
32.10
Binomial Pricing
16
9
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
28.62
40.37
32.10
36
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
The greater of
Binomial Pricing
17
0
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
.19
28.62
0
40.37
2.91
32.10
.10
36
1.51
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
Binomial Pricing
17
1
50.78 = price
10.78 = intrinsic value
40.37
.37
32.10
0
25.52
0
45.28
5.60
36
.19
28.62
0
40.37
2.91
32.10
.10
36
1.51
( ) ( ) | | ( )
t r
d d u u
e P U P O
A ÷
× × + ×
Binomial Pricing
17
2
Components of the Option Price
1 - Underlying stock price
2 - Striking or Exercise price
3 - Volatility of the stock returns (standard deviation
of annual returns)
4 - Time to option expiration
5 - Time value of money (discount rate)
17
3
17
4
Black-Scholes Option Pricing Model
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
- Call Option Price
P
s
- Stock Price
N(d
1
) - Cumulative normal density function of (d
1
)
S - Strike or Exercise price
N(d
2
) - Cumulative normal density function of (d
2
)
r - discount rate (90 day comm paper rate or risk free rate)
t - time to maturity of option (as % of year)
v - volatility - annualized standard deviation of daily returns
Black-Scholes Option Pricing Model
17
5
(d
1
)=
ln + ( r + ) t
P
s
S
v
2
2
v t
32 34 36 38 40
N(d
1
)=
Black-Scholes Option Pricing Model
17
6
(d
1
)=
ln + ( r + ) t
P
s
S
v
2
2
v t
Cumulative Normal Density Function
(d
2
) = d
1
- v t
17
7
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
17
8
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
17
9
(d
1
) =
ln + ( r + ) t
P
s
S
v
2
2
v t
(d
1
) = - .3070 N(d
1
) = 1 - .6206 = .3794
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
18
0
(d
2
) = - .5056
N(d
2
) = 1 - .6935 = .3065
(d
2
) = d
1
- v t
Example
What is the price of a call option given the
following?
P = 36 r = 10% v = .40
S = 40 t = 90 days / 365
18
1
O
C
= P
s
[N(d
1
)] - S[N(d
2
)]e
-rt
O
C
= 36[.3794] - 40[.3065]e
- (.10)(.2466)
O
C
= $ 1.70
Put Price = Oc + S - P - Carrying Cost +
Div.
18
2
Carrying cost = r x S x t
Example
ABC is selling at $41 a share. A six
month May 40 Call is selling for
$4.00. If a May $ .50 dividend is
expected and r=10%, what is the put
price?
18
3
18
4
1 step 2 steps 4 steps
(2 outcomes) (3 outcomes) (5 outcomes)
etc. etc.
Binomial vs. Black Scholes
18
5
No. of steps Estimated value
1 48.1
2 41.0
3 42.1
5 41.8
10 41.4
50 40.3
100 40.6
Black-Scholes 40.5
Binomial vs. Black Scholes
? Many corporate securities are
similar to the stock options that
are traded on organized
exchanges.
? Almost every issue of corporate
stocks and bonds has option
features.
? In addition, capital structure and
capital budgeting decisions can be
viewed in terms of options.
18
6
? An option gives the holder the right, but not
the obligation, to buy or sell a given quantity
of an asset on (or perhaps before) a given
date, at prices agreed upon today.
? Calls versus Puts
? Call options gives the holder the right, but not the
obligation, to buy a given quantity of some asset at
some time in the future, at prices agreed upon
today. When exercising a call option, you “call in”
the asset.
? Put options gives the holder the right, but not the
obligation, to sell a given quantity of an asset at
some time in the future, at prices agreed upon
today. When exercising a put, you “put” the asset to
someone.
18
7
? Exercising the Option
? The act of buying or selling the underlying asset
through the option contract.
? Strike Price or Exercise Price
? Refers to the fixed price in the option contract at
which the holder can buy or sell the underlying
asset.
? Expiry
? The maturity date of the option is referred to as
the expiration date, or the expiry.
? Spot Price
? The Price at which an option is currently valued
(either in the market or privately)
18
8
? In-the-Money
? The exercise price is less than the spot price of
the underlying asset.
? At-the-Money
? The exercise price is equal to the spot price of the
underlying asset.
? Out-of-the-Money
? The exercise price is more than the spot price of
the underlying asset.
18
9
? Intrinsic Value
? The difference between the exercise price of the
option and the spot price of the underlying asset.
? Speculative Value
? The difference between the option premium and
the intrinsic value of the option.
19
0
Option
Premium
=
Intrinsic
Value
Speculative
Value
+
19
1
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Buy a call
Exercise price = $50
19
2
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Write a call
Exercise price = $50
19
3
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Write a call
Buy a call
Exercise price = $50; option premium = $10
19
4
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
Buy a put
Exercise price = $50
19
5
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
O
p
t
i
o
n
p
a
y
o
f
f
s
(
$
)
write a put
Exercise price = $50
Stock price ($)
19
6
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Buy a put
Write a put
Exercise price = $50; option premium = $10
10
-10
? The seller (or writer)
of an option has an
obligation.
? The purchaser of an
option has an option.
19
7
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Buy a put
Write a put
10
-10
-20
100 90 80 70 60 0 10 20 30 40 50
-40
20
0
-60
40
60
Stock price ($)
O
p
t
i
o
n
p
r
o
f
i
t
s
(
$
)
Write a call
Buy a call
? Puts and calls can serve as the
building blocks for more complex
option contracts.
? If you understand this, you can
become a financial engineer,
tailoring the risk-return profile to
meet your client’s needs.
19
8
19
9
Buy a put with an
exercise price of $50
Buy
the
stock
Protective Put
strategy has downside
protection and upside
potential
$50
$0
$50
Value at
expiry
Value of
stock at
expiry
20
0
Buy a put with
exercise price
of $50 for $10
Buy the stock at $40
$40
Protective Put
strategy has
downside
protection and
upside potential
$40
$0
-$40
$50
Value at
expiry
Value of
stock at
expiry
20
1
Sell a call with
exercise price
of $50 for $10
Buy the stock at $40
$4
0
Covered call
$40
$0
-$40
$10
-$30
$30 $5
0
Value of stock at
expiry
Value at
expiry
20
2
Buy a put with
an exercise price
of $50 for $10
$40
A Long Straddle only makes money if
the stock price moves $20 away
from $50.
$40
$0
-$20
$50
Buy a call with
an exercise
price of $50 for
$10
-$10
$30
$60 $30 $70
Value of
stock at
expiry
Value at
expiry
20
3
Sell a put with an
exercise price of $40
Buy the stock at $40
financed with some
debt: FV = $X
Buy a call option with
an exercise price of $40
$0
-$40
$40-P
0
rT
Xe
÷
÷ 40 $
$40
Buy the
stock at $40
0
40 $ C +
) 40 ($
rT
Xe
÷
÷ ÷
-[$40-P
0
]
0
C ÷
0
P
In market equilibrium, it mast be the case that option prices
are set such that: Value of stock + Value of put - Value of call =
Present value of strike price discounted at r
F
Otherwise, riskless portfolios with positive payoffs exist.
Value of
stock at
expiry
Value at
expiry
? The last section
concerned itself
with the value of
an option at
expiry.
? This section
considers the
value of an
option prior to
the expiration
date.
? A much more
interesting
question.
20
4
20
5
Call Put
1. Stock price + –
2. Exercise price – +
3. Interest rate +
–
4. Volatility in the stock price + +
5. Expiration date + +
The value of a call option must fall within
max (stock price – exercise price, 0) < value of the option
< value of the stock.
The precise position will depend on these factors.
? The binomial
option pricing
formula is used
to value options
that have two
potential future
values – an up-
state and a
down-state
? The Black-
Scholes model
provides a
normalized
approximation
to the binomial
for some real-
world option
valuation.
20
6
Suppose a stock is worth $25 today and in one
period will either be worth 15% more or 15% less.
S
0
= $25 today and in one year S
1
is either $28.75
or $21.25. The risk-free rate is 5%. What is the
value of an at-the-money call option?
20
7
$25
$21.25
$28.75
S
1
S
0
1. A call option on this stock with exercise
price of $25 will have the following payoffs.
2. We can replicate the payoffs of the call
option. With a levered position in the stock.
20
8
$25
$21.25
$28.75
S
1
S
0
C
1
$3.75
$0
? The most familiar options are puts and calls.
? Put options give the holder the right to sell stock at
a set price for a given amount of time.
? Call options give the holder the right to buy stock
at a set price for a given amount of time.
20
9
? The value of a stock option depends on six
factors:
1. Current price of underlying stock.
2. Dividend yield of the underlying stock.
3. Strike price specified in the option contract.
4. Risk-free interest rate over the life of the contract.
5. Time remaining until the option contract expires.
6. Price volatility of the underlying stock.
? Much of corporate financial theory can be
presented in terms of options.
1. Common stock in a levered firm can be viewed as a call
option on the assets of the firm.
2. Real projects often have hidden option that enhance value.
Classic NPV calculations typically ignore the flexibility that
real-world firms typically have.
21
0
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
211
212
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
213
-60
-40
-20
0
20
40
60
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
a
b
c
Forward sale Receivable
Hedged
receivable
214
-10
-5
0
5
10
15
20
25
30
35
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Premium
215
-20
-10
0
10
20
30
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Premium
216
-60
-50
-40
-30
-20
-10
0
10
20
30
40
0.58 0.6 0.62 0.64 0.66 0.68
Exchange rate ($/DM)
G
a
i
n
o
r
l
o
s
s
i
n
d
o
l
l
a
r
s
(
0
0
0
s
)
Put Receivable
Hedged receivable
21
7
? Follow Up Investments
? Abandon
? Wait
? Vary Output or Production
21
8
4 types of “Real Options”
1 - The opportunity to make follow-up
investments.
2 - The opportunity to abandon a project
3 - The opportunity to “wait” and invest later.
4 - The opportunity to vary the firm’s output
or
production methods.
Value “Real Option” = NPV with option
- NPV w/o option
21
9
Intrinsic Value
22
0
Option
Price
Stock Price
Intrinsic Value + Time Premium = Option
Value
Time Premium = Vale of being able to wait
22
1
Option
Price
Stock Price
More time = More value
22
2
Option
Price
Stock Price
Example - Abandon
Mrs. Mulla gives you a non-retractable
offer to buy your company for $150 mil
at anytime within the next year. Given
the following decision tree of possible
outcomes, what is the value of the offer
(i.e. the put option) and what is the most
Mrs. Mulla could charge for the option?
Use a discount rate of 10%
22
3
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your
company for $150 mil at anytime within the next year. Given the
following decision tree of possible outcomes, what is the value of
the offer (i.e. the put option) and what is the most Mrs. Mulla
could charge for the option?
22
4
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 145
70 (.6)
50 (.4)
40 (.4)
Example - Abandon
Mrs. Mulla gives you a non-retractable offer to buy your
company for $150 mil at anytime within the next year. Given the
following decision tree of possible outcomes, what is the value of
the offer (i.e. the put option) and what is the most Mrs. Mulla
could charge for the option?
22
5
Year 0 Year 1 Year 2
120 (.6)
100 (.6)
90 (.4)
NPV = 162
150 (.4)
Option Value =
162 - 145 =
$17 mil
Reality
? Decision trees for valuing “real
options” in a corporate setting can
not be practically done by hand.
? We must introduce binomial theory &
B-S models
22
6
By
Girish Naravane
[email protected]
22
7
? What is a Warrant?
? What is a Convertible Bond?
? The Difference Between Warrants and
Convertibles
? Why do Companies Issue Warrants and
Convertibles?
Example:
BJ Services warrants, April 2000
Exercise price $ 15
Warrant Value $110
Share price $ 70
BJ Services share price
15
Warrant price at maturity
Value of
warrant
Exercise price = $15
Actual warrant value prior
to expiration
Theoretical value
(warrant lower limit)
Stock price
? # shares outstanding = 1 mil
? Current stock price = $12
? Number of shares issued per share outstanding =
.10
? Total number of warrants issued = 100,000
? Exercise price of warrants = $10
? Time to expiration of warrants = 4 years
? Annualized standard deviation of stock daily
returns = .40
? Rate of return = 10 percent
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
warrant each of Cost
100,000
500,000
$5
1,500,000 - 2,000,000 500,000
warrants w/o loans of value - financing total warrants of Cost
=
=
=
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
(d
1
) = 1.104
N(d
1
) = .865
(d
2
) = .304
N(d
2
) = .620
? United glue has just issued $2 million package
of debt and warrants. Using the following data,
calculate the warrant value.
Warrant
= 12[.865] - [.620]{10/1.1
4
]
= $6.15
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
loans of value -
assets total
s United' of Value
firm e alternativ
of ue equity val Current
= =V
million V 5 . 12 $ 5 . 5 18 = ÷ =
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
$12.50
1
million 12.5
firm e alternativ
of price share Current
= = =
million N
V
64 . 6 $ value gives formula Scholes Black =
? United glue has just issued $2 million package of debt and
warrants. Using the following data, calculate the warrant value.
? Value of warrant with dilution
03 . 6 $ 64 . 6
10 . 1
1
firm e alternativ on call of value
1
1
= ×
×
+ q
? Amazon
? 4.75% Convertible 2009
? Convertible into 6.41 shares
? Conversion ratio 6.41
? Conversion price = 1000/6.41 = $156.05
? Market price of shares = $120
? Lower bound of value
? Bond value
? Conversion value = 6.41 x 120 = $768.00
? How bond value varies with firm value at maturity
0
1
2
3
0 1 2 3 4 5
Value of firm ($ million)
default
bond repaid in full
Bond value ($ thousands)
? How conversion value at maturity varies with firm
value
0
1
2
3
0 0.5 1 1.5 2 2.5 3 3.5 4
Value of firm ($ million)
Conversion value ($ thousands)
? How value of convertible at maturity varies with firm
value
0
1
2
3
0 1 2 3 4
Value of firm ($ million)
default
bond repaid in full
convert
Value of convertible ($ thousands)
doc_802198541.pptx