Chapter 17
Options and Corporate Finance
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Key Concepts and Skills





Understand option terminology
Be able to determine option payoffs and profits
Understand the major determinants of option
prices
Understand and apply put-call parity
Be able to determine option prices using the
binomial and Black-Scholes models
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Outline
17.1 Options
17.2 Call Options
17.3 Put Options
17.4 Selling Options
17.5 Option Quotes
17.6 Combinations of Options
17.7 Valuing Options
17.8 An Option Pricing Formula
17.9 Stocks and Bonds as Options
17.10 Options and Corporate Decisions: Some Applications
17.11 Investment in Real Projects and Options
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.1 Options


An option gives the holder the right, but not the
obligation, to buy or sell a given quantity of an asset on
(or before) a given date, at prices agreed upon today.
Exercising the Option


Strike Price or Exercise Price


The act of buying or selling the underlying asset
Refers to the fixed price in the option contract at which the
holder can buy or sell the underlying asset.
Expiry (Expiration Date)

The maturity date of the option
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Options

European versus American options



In-the-Money


Exercising the option would result in a positive payoff.
At-the-Money


European options can be exercised only at expiry.
American options can be exercised at any time up to expiry.
Exercising the option would result in a zero payoff (i.e.,
exercise price equal to spot price).
Out-of-the-Money

Exercising the option would result in a negative payoff.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.2 Call Options


Call options gives the holder the right,
but not the obligation, to buy a given
quantity of some asset on or before
some time in the future, at prices
agreed upon today.
When exercising a call option, you
“call in” the asset.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Call Option Pricing at Expiry

At expiry, an American call option is worth the
same as a European option with the same
characteristics.


If the call is in-the-money, it is worth ST – E.
If the call is out-of-the-money, it is worthless:
C = Max[ST – E, 0]
Where
ST is the value of the stock at expiry (time T)
E is the exercise price.
C is the value of the call option at expiry
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Call Option Payoffs
Option payoffs ($)
60
40
20
20
40
50
60
80
100
120
Stock price ($)
–20
McGraw-Hill/Irwin
–40
Copyright © 2007
by The McGraw-Hill
Exercise
price
= $50 Companies, Inc. All rights reserved.
Call Option Profits
Option payoffs ($)
60
Buy a call
40
20
10
20
–10
40
50
60
80
100
120
Stock price ($)
–20
McGraw-Hill/Irwin
–40
Exercise price = $50; option premium = $10
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.3 Put Options


Put options gives the holder the right,
but not the obligation, to sell a given
quantity of an asset on or before some
time in the future, at prices agreed
upon today.
When exercising a put, you “put” the
asset to someone.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Put Option Pricing at Expiry



At expiry, an American put option is
worth the same as a European option
with the same characteristics.
If the put is in-the-money, it is worth
E – ST.
If the put is out-of-the-money, it is
worthless.
P = Max[E – ST, 0]
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Put Option Payoffs
Option payoffs ($)
60
50
40
20
0
Buy a put
0
20
40
50
60
80
100
Stock price ($)
–20
McGraw-Hill/Irwin
–40
Copyright © 2007
by The McGraw-Hill
Exercise
price
= $50 Companies, Inc. All rights reserved.
Put Option Profits
Option payoffs ($)
60
40
20
10
Stock price ($)
–10
20
40 50 60
80
100
Buy a put
–20
–40
McGraw-Hill/Irwin
© 2007
by The McGraw-Hill
Companies,
Inc. All rights reserved.
Exercise priceCopyright
= $50;
option
premium
= $10
Option Value
 Intrinsic
Value
Call: Max[ST – E, 0]
 Put: Max[E – ST , 0]

 Speculative

Value
The difference between the option premium and
the intrinsic value of the option.
Option
Premium
McGraw-Hill/Irwin
=
Intrinsic
Value
+ Speculative
Value
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.4 Selling Options


The seller (or writer) of an option has an
obligation.
The seller receives the option premium in
exchange.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Call Option Payoffs
Option payoffs ($)
60
40
20
20
40
50
60
80
100
120
Stock price ($)
–20
McGraw-Hill/Irwin
–40
Copyright=
© 2007
Exercise price
$50by The McGraw-Hill Companies, Inc. All rights reserved.
Put Option Payoffs
Option payoffs ($)
40
20
0
Sell a put
0
20
40
50
60
80
100
Stock price ($)
–20
–40
Exercise price = $50
–50
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option payoffs ($)
Option Diagrams Revisited
Buy a call
40
10
–10
–40
McGraw-Hill/Irwin
Sell a call
Buy a call
Sell a put
40
50 60
Stock price ($)
100
Buy a put
Exercise price = $50;
option premium = $10
Sell a call
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.5 Option Quotes
Option/Strike Exp.
IBM
130 Oct
138¼
130 Jan
138¼
135 Jul
138¼
135 Aug
138¼
140 Jul
138¼
140 Aug
McGraw-Hill/Irwin
--Call---Put-Vol. Last Vol. Last
364 15¼
107
5¼
112 19½
420
9¼
2365
4¾ 2431 13/16
1231
9¼
94
5½
1826
1¾
427
2¾
2193
6½
58
7½
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
This option has a strike price of $135;
Option/Strike Exp.
130 Oct
IBM
130 Jan
138¼
135 Jul
138¼
135 Aug
138¼
140 Jul
138¼
140 Aug
138¼
--Put---Call-Vol. Last Vol. Last
5¼
107
364 15¼
9¼
420
112 19½
4¾ 2431 13/16
2365
5½
94
9¼
1231
2¾
427
1¾
1826
7½
58
6½
2193
a recent price for the stock is $138.25;
July is the expiration month.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
This makes a call option with this exercise price in-themoney by $3.25 = $138¼ – $135.
Option/Strike Exp.
130 Oct
IBM
130 Jan
138¼
135 Jul
138¼
135 Aug
138¼
140 Jul
138¼
140 Aug
138¼
--Put---Call-Vol. Last Vol. Last
5¼
107
364 15¼
9¼
420
112 19½
4¾ 2431 13/16
2365
5½
94
9¼
1231
2¾
427
1¾
1826
7½
58
6½
2193
Puts with this exercise price are out-of-the-money.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
Option/Strike Exp.
IBM
130 Oct
138¼
130 Jan
138¼
135 Jul
138¼
135 Aug
138¼
140 Jul
138¼
140 Aug
--Call---Put-Vol. Last Vol. Last
364 15¼
107
5¼
112 19½
420
9¼
2365
4¾ 2431 13/16
1231
9¼
94
5½
1826
1¾
427
2¾
2193
6½
58
7½
On this day, 2,365 call options with this exercise price were
traded.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
The CALL option with a strike price of $135 is trading for $4.75.
--Call---Put-Option/Strike Exp. Vol. Last Vol. Last
IBM
130 Oct
364 15¼
107
5¼
138¼
130 Jan
112 19½
420
9¼
138¼
135 Jul
2365
4¾ 2431 13/16
138¼
135 Aug 1231
9¼
94
5½
138¼
140 Jul
1826
1¾
427
2¾
138¼
140 Aug 2193
6½
58
7½
Since the option is on 100 shares of stock, buying this option
would cost $475 plus commissions.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
Option/Strike Exp.
IBM
130 Oct
138¼
130 Jan
138¼
135 Jul
138¼
135 Aug
138¼
140 Jul
138¼
140 Aug
--Call---Put-Vol. Last Vol. Last
364 15¼
107
5¼
112 19½
420
9¼
2365
4¾ 2431 13/16
1231
9¼
94
5½
1826
1¾
427
2¾
2193
6½
58
7½
On this day, 2,431 put options with this exercise price were
traded.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Quotes
The PUT option with a strike price of $135 is trading for $.8125.
--Put---Call-Option/Strike Exp. Vol. Last Vol. Last
5¼
107
364 15¼
130 Oct
IBM
9¼
420
112 19½
130 Jan
138¼
4¾ 2431 13/16
2365
135 Jul
138¼
5½
94
9¼
135 Aug 1231
138¼
2¾
427
1¾
1826
140 Jul
138¼
7½
58
6½
140 Aug 2193
138¼
Since the option is on 100 shares of stock, buying this
option would cost $81.25 plus commissions.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.6 Combinations of Options


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.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Protective Put Strategy (Payoffs)
Value at
expiry
Protective Put payoffs
$50
Buy the
stock
Buy a put with an exercise
price of $50
$0
$50
McGraw-Hill/Irwin
Value of stock at
expiry
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Protective Put Strategy (Profits)
Value at
expiry
Buy the stock at $40
$40
Protective Put
strategy has
downside protection
and upside potential
$0
-$10
-$40
McGraw-Hill/Irwin
$40 $50
Buy a put with exercise price of $50
for $10
Value of
stock at
expiry
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Covered Call Strategy
Value at
expiry
Buy the stock at $40
$10
Covered Call strategy
$0
Value of stock at expiry
$40 $50
-$30
Sell a call with exercise price
of $50 for $10
-$40
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option payoffs ($)
Long Straddle
Buy a call with exercise
price of $50 for $10
40
30
Stock price ($)
30
–20
McGraw-Hill/Irwin
40
60
70
Buy a put with exercise
price of $50 for $10
$50
A Long Straddle only makes money if the stock price moves
$20 away from $50.Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option payoffs ($)
Short Straddle
This Short Straddle only loses money if the stock
price moves $20 away from $50.
20
Sell a put with exercise price of
$50 for $10
Stock price ($)
30
–30
McGraw-Hill/Irwin
–40
40
$50
60
70
Sell a call with an
exercise price of $50 for $10
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
Option payoffs ($)
Portfolio value today = c0 +
E
(1+ r)T
Portfolio payoff
Call
bond
25
25
McGraw-Hill/Irwin
Stock price ($)
Consider the payoffs from holding a portfolio consisting
of a call with a strike price of $25 and a bond with a future
value of $25.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Put-Call Parity
Portfolio payoff
Option payoffs ($)
Portfolio value today = p0 + S0
25
Stock price ($)
25
McGraw-Hill/Irwin
Consider the payoffs from holding a portfolio consisting of a
share of stock and a put with a $25 strike.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Portfolio value today
E
= c0 +
(1+ r)T
25
Option payoffs ($)
Option payoffs ($)
Put-Call Parity
Portfolio value today
= p0 + S0
25
25
Stock price ($)
25
Stock price ($)
Since these portfolios have identical payoffs, they must have
the same value today: hence
T=p +S
Put-Call
Parity:
c
+
E/(1+r)
0 © 2007 by The McGraw-Hill
0 Companies,
0
McGraw-Hill/Irwin
Copyright
Inc. All rights reserved.
17.7 Valuing Options

The last section
concerned itself
with the value of
an option at
expiry.

This section
considers the
value of an option
prior to the
expiration date.

McGraw-Hill/Irwin
A much more
interesting
question.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
American Call
ST
Option payoffs ($)
Profit
Call
25
Market Value
Time value
Intrinsic value
ST
E
Out-of-the-money
loss
McGraw-Hill/Irwin
In-the-money
C0 must fall within max (S0 – E, 0) < C0 < S0.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Option Value Determinants
1.
2.
3.
4.
5.
Stock price
Exercise price
Interest rate
Volatility in the stock price
Expiration date
Call
+
–
+
+
+
Put
–
+
–
+
+
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
The precise position will depend on these factors.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.8 An Option Pricing Formula

We will start with
a binomial option
pricing formula to
build our
intuition.
McGraw-Hill/Irwin

Then we will
graduate to the
normal
approximation to
the binomial for
some real-world
option valuation.
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
Suppose a stock is worth $25 today and in one period will either
be worth 15% more or 15% less. S0= $25 today and in one year
S1is either $28.75 or $21.25. The risk-free rate is 5%. What is the
value of an at-the-money call option?
S0
S1
$28.75 = $25×(1.15)
$25
$21.25 = $25×(1 –.15)
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
1.
2.
A call option on this stock with exercise price of $25 will
have the following payoffs.
We can replicate the payoffs of the call option with a levered
position in the stock.
S0
S1
C1
$28.75
$3.75
$21.25
$0
$25
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
Borrow the present value of $21.25 today and buy 1 share.
The net payoff for this levered equity portfolio in one period is either
$7.50 or $0.
The levered equity portfolio has twice the option’s payoff, so the
portfolio is worth twice the call option value.
S0
( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50
$3.75
$25
McGraw-Hill/Irwin
$21.25 – $21.25 =
$0
$0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
The value today of the levered equity
portfolio is today’s value of one share
less the present value of a $21.25 debt:
S0
$21.25
$25 
(1  rf )
( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50
$3.75
$25
$21.25 – $21.25 =
McGraw-Hill/Irwin
$0
$0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
We can value the call option today
as half of the value of the levered
equity portfolio:
S0
1 
$21.25 
C0  $25 
2 
(1  rf ) 
( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50
$3.75
$25
$21.25 – $21.25 =
McGraw-Hill/Irwin
$0
$0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
If the interest rate is 5%, the call is worth:
1
$21.25  1
  $25  20.24  $2.38
C0   $25 
2
(1.05)  2
C0
S0
( S1 – debt ) = portfolio C1
$28.75 – $21.25 = $7.50
$2.38
$25
$21.25 – $21.25 =
McGraw-Hill/Irwin
$3.75
$0
$0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Binomial Option Pricing Model
The most important lesson (so far) from the
binomial option pricing model is:
the replicating portfolio intuition.
Many derivative securities can be valued by
valuing portfolios of primitive securities when
those portfolios have the same payoffs as the
derivative securities.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Delta


This practice of the construction of a
riskless hedge is called delta hedging.
The delta of a call option is positive.

Recall from the example:
Swing of call
$3.75  0
$3.75 1



D
Swing of stock
$28.75  $21.25 $7.5 2
• The delta of a put option is negative.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Delta

Determining the Amount of Borrowing:
1
$21.25  1
  $25  $20.24  $2.38
C0   $25 
2
(1.05)  2
Value of a call = Stock price × Delta
– Amount borrowed
$2.38 = $25 × ½ – Amount borrowed
Amount borrowed = $10.12
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Risk-Neutral Approach
S(U), V(U)
q
S(0), V(0)
1- q
S(D), V(D)
We could value the option, V(0), as the value of the
replicating portfolio. An equivalent method is risk-neutral
valuation:
q  V (U )  (1  q)  V ( D)
V (0) 
McGraw-Hill/Irwin
(1  r )
Copyright © 2007 by The McGraw-Hill Companies, Inc. fAll rights reserved.
The Risk-Neutral Approach
S(U), V(U)
q
S(0), V(0)
q is the risk-neutral
probability of an
“up” move.
1- q
S(0) is the value of the underlying
S(D), V(D)
asset today.
S(U) and S(D) are the values of the asset in the next period
following an up move and a down move, respectively.
V(U) and V(D) are the values of the option in the next period
following an up move and aCopyright
down© 2007
move,
respectively.
McGraw-Hill/Irwin
by The McGraw-Hill Companies, Inc. All rights reserved.
The Risk-Neutral Approach
S(U), V(U)
q
q  V (U )  (1  q)  V ( D)
V (0) 
(1  rf )
S(0), V(0)
1- q
S(D), V(D)

The key to finding q is to note that it is already impounded
into an observable security price: the value of S(0):
S (0) 
q  S (U )  (1  q)  S ( D)
(1  rf )
A minor bit of algebra yields: q 
McGraw-Hill/Irwin
(1  rf )  S (0)  S ( D)
S (U )  S ( D)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example of Risk-Neutral Valuation
Suppose a stock is worth $25 today and in one period will
either be worth 15% more or 15% less. The risk-free rate is
5%. What is the value of an at-the-money call option?
The binomial tree would look like this:
$28.75  $25  (1.15)
q
$25,C(0)
$21.25  $25  (1  .15)
1- q
McGraw-Hill/Irwin
$28.75,C(U)
$21.25,C(D)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example of Risk-Neutral Valuation
The next step would be to compute the risk neutral
probabilities
q
q
(1  rf )  S (0)  S ( D)
S (U )  S ( D)
(1.05)  $25  $21.25
$5

2 3
$28.75  $21.25
$7.50
2/3
$28.75,C(U)
$25,C(0)
1/3
McGraw-Hill/Irwin
$21.25,C(D)
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example of Risk-Neutral Valuation
After that, find the value of the call in the up
state and down state.
C (U )  $28.75  $25
2/3
C ( D)  max[$ 25  $28.75,0]
$25,C(0)
1/3
McGraw-Hill/Irwin
$28.75, $3.75
$21.25, $0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example of Risk-Neutral Valuation
Finally, find the value of the call at time 0:
C (0) 
q  C (U )  (1  q)  C ( D)
(1  rf )
C (0) 
2 3  $3.75  (1 3)  $0
(1.05)
C (0) 
$2.50
 $2.38
(1.05)
2/3
$28.75,$3.75
$25,$2.38
$25,C(0)
1/3
McGraw-Hill/Irwin
$21.25, $0
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Risk-Neutral Valuation and the
Replicating Portfolio
This risk-neutral result is consistent with valuing the
call using a replicating portfolio.
2 3  $3.75  (1 3)  $0 $2.50
C0 

 $2.38
(1.05)
1.05
1
$21.25  1
  $25  20.24  $2.38
C0   $25 
2
(1.05)  2
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Black-Scholes Model
C0  S  N(d1 )  Ee
 rT
 N(d 2 )
Where
C0 = the value of a European option at time t = 0
r = the risk-free interest rate.
σ2
N(d) = Probability that a
ln( S / E )  (r  )T
standardized, normally
2
d1 
distributed, random
 T
d 2  d1   T
variable will be less than
or equal to d.
The Black-Scholes Model allows us to value options in the
real world just as we have done in the 2-state world.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Black-Scholes Model
Find the value of a six-month call option on Microsoft
with an exercise price of $150.
The current value of a share of Microsoft is $160.
The interest rate available in the U.S. is r = 5%.
The option maturity is 6 months (half of a year).
The volatility of the underlying asset is 30% per annum.
Before we start, note that the intrinsic value of the
option is $10—our answer must be at least that
amount.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Black-Scholes Model
Let’s try our hand at using the model. If you
have a calculator handy, follow along.
First calculate d1 and d2
ln( S / E )  (r  .5σ 2 )T
d1 
 T
ln( 160 / 150)  (.05  .5(0.30) 2 ).5
d1 
 0.52815
0.30 .5
Then,
d 2  d1   T  0.52815  0.30 .5  0.31602
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
The Black-Scholes Model
C0  S  N(d1 )  Ee
d1  0.52815
d 2  0.31602
 rT
 N(d 2 )
N(d1) = N(0.52815) = 0.7013
N(d2) = N(0.31602) = 0.62401
C0  $160  0.7013  150e .05.5  0.62401
C0  $20.92
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.9 Stocks and Bonds as Options

Levered equity is a call option.




The underlying asset comprises the assets of the firm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the
firm are greater in value than the debt, the
shareholders have an in-the-money call. They will
pay the bondholders and “call in” the assets of the
firm.
If at the maturity of the debt the shareholders have
an out-of-the-money call, they will not pay the
bondholders (i.e. the shareholders will declare
bankruptcy) and let the call expire.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Stocks and Bonds as Options

Levered equity is a put option.





The underlying asset comprises the assets of the firm.
The strike price is the payoff of the bond.
If at the maturity of their debt, the assets of the firm
are less in value than the debt, shareholders have an
in-the-money put.
They will put the firm to the bondholders.
If at the maturity of the debt the shareholders have an
out-of-the-money put, they will not exercise the option
(i.e. NOT declare bankruptcy) and let the put expire.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Stocks and Bonds as Options

It all comes down to put-call parity.
E
c0 = S0 + p0 –
(1+ r)T
Value of a
call on the
firm
Value of a
Value of
= the firm + put on the –
firm
Stockholder’s
position in terms
of call options
McGraw-Hill/Irwin
Value of a
risk-free
bond
Stockholder’s
position in terms
of put options
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Mergers and Diversification




Diversification is a frequently mentioned reason for
mergers.
Diversification reduces risk and, therefore, volatility.
Decreasing volatility decreases the value of an option.
Assume diversification is the only benefit to a merger:



Since equity can be viewed as a call option, should the merger
increase or decrease the value of the equity?
Since risky debt can be viewed as risk-free debt minus a put
option, what happens to the value of the risky debt?
Overall, what has happened with the merger and is it a good
decision in view of the goal of stockholder wealth
maximization?
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example



Consider the following two merger candidates.
The merger is for diversification purposes only with no
synergies involved.
Risk-free rate is 4%.
Market value of assets
Face value of zero coupon
debt
Debt maturity
Asset return standard
deviation
McGraw-Hill/Irwin
Company A
$40 million
$18 million
Company B
$15 million
$7 million
4 years
40%
4 years
50%
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example


Use the Black and Scholes OPM (or an options
calculator) to compute the value of the equity.
Value of the debt = value of assets – value of equity
Company A Company B
Market Value of Equity
25.72
9.88
Market Value of Debt
14.28
5.12
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example



The asset return standard deviation for the combined firm is 30%
Market value assets (combined) = 40 + 15 = 55
Face value debt (combined) = 18 + 7 = 25
Combined Firm
Market value of equity
34.18
Market value of debt
20.82
Total MV of equity of separate firms = 25.72 + 9.88 = 35.60
Wealth transfer from stockholders to bondholders = 35.60 – 34.18 = 1.42
(exact increase in MV of debt)
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
M&A Conclusions
Mergers for diversification only transfer
wealth from the stockholders to the
bondholders.
 The standard deviation of returns on the assets
is reduced, thereby reducing the option value
of the equity.
 If management’s goal is to maximize
stockholder wealth, then mergers for reasons
of diversification should not occur.

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Options and Capital Budgeting


Stockholders may prefer low NPV projects to high
NPV projects if the firm is highly leveraged and the
low NPV project increases volatility.
Consider a company with the following
characteristics:





MV assets = 40 million
Face Value debt = 25 million
Debt maturity = 5 years
Asset return standard deviation = 40%
Risk-free rate = 4%
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example: Low NPV


Current market value of equity = $22.706 million
Current market value of debt = $17.294 million
NPV
MV of assets
Asset return standard
deviation
MV of equity
MV of debt
McGraw-Hill/Irwin
Project I
$3
$43
30%
Project II
$1
$41
50%
$23.831
$19.169
$25.381
$15.169
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example: Low NPV
Which project should management take?
 Even though project B has a lower NPV, it is
better for stockholders.
 The firm has a relatively high amount of
leverage:

With project A, the bondholders share in the NPV
because it reduces the risk of bankruptcy.
 With project B, the stockholders actually
appropriate additional wealth from the
bondholders for a larger gain in value.

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example: Negative NPV
We’ve seen that stockholders might prefer a
low NPV to a high one, but would they ever
prefer a negative NPV?
 Under certain circumstances, they might.
 If the firm is highly leveraged, stockholders
have nothing to lose if a project fails, and
everything to gain if it succeeds.
 Consequently, they may prefer a very risky
project with a negative NPV but high potential
rewards.

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example: Negative NPV
Consider the previous firm.
 They have one additional project they are
considering with the following characteristics

Project NPV = -$2 million
 MV of assets = $38 million
 Asset return standard deviation = 65%


Estimate the value of the debt and equity
MV equity = $25.453 million
 MV debt = $12.547 million

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Example: Negative NPV
In this case, stockholders would actually prefer
the negative NPV project to either of the
positive NPV projects.
 The stockholders benefit from the increased
volatility associated with the project even if
the expected NPV is negative.
 This happens because of the large levels of
leverage.

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Options and Capital Budgeting
As a general rule, managers should not accept
low or negative NPV projects and pass up high
NPV projects.
 Under certain circumstances, however, this
may benefit stockholders:

The firm is highly leveraged
 The low or negative NPV project causes a
substantial increase in the standard deviation of
asset returns

McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
17.12 Investment in Real Projects and Options

Classic NPV calculations generally ignore
the flexibility that real-world firms typically
have.
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Quick Quiz







What is the difference between call and put options?
What are the major determinants of option prices?
What is put-call parity? What would happen if it
doesn’t hold?
What is the Black-Scholes option pricing model?
How can equity be viewed as a call option?
Should a firm do a merger for diversification
purposes only? Why or why not?
Should management ever accept a negative NPV
project? If yes, under what circumstances?
McGraw-Hill/Irwin
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.