Chapter Twenty Three
Options and Corporate
Finance: Basic Concepts
Prepared by
Professor Wei Wang
Queen’s University
© 2011 McGraw–Hill Ryerson Limited
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Chapter Outline
23.1 Options
23.2 Call Options
23.3 Put Options
23.4 Selling Options
23.5 Stock Option Quotations
23.6 Combinations of Options
23.7 Valuing Options
23.8 An Option-Pricing Formula
23.9 Stocks and Bonds as Options
23.10 Capital-Structure Policy and Options
23.11 Mergers and Options
23.12 Investment in Real Projects and Options
23.13 Summary and Conclusions
© 2011 McGraw–Hill Ryerson Limited
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Options
LO23.1
• 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.
© 2011 McGraw–Hill Ryerson Limited
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Options Contracts: Preliminaries
LO23.1
• 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.
© 2011 McGraw–Hill Ryerson Limited
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Options Contracts: Preliminaries
LO23.1
• 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.
• European versus American options
– European options can be exercised only at expiry.
– American options can be exercised at any time up to expiry.
© 2011 McGraw–Hill Ryerson Limited
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Options Contracts: Preliminaries
LO23.1
• 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.
© 2011 McGraw–Hill Ryerson Limited
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Options Contracts: Preliminaries
LO23.1
• 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.
Option
Premium
=
Intrinsic
Value
+ Speculative
Value
© 2011 McGraw–Hill Ryerson Limited
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Call Options
LO23.2
• Call options give 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.
© 2011 McGraw–Hill Ryerson Limited
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Basic Call Option Pricing Relationships at Expiry
LO23.2
• 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.
CaT = CeT = Max[ST - E, 0]
where
ST is the value of the stock at expiry (time T)
E is the exercise price.
CaT is the value of an American call at expiry
CeT is the value of a European call at expiry
© 2011 McGraw–Hill Ryerson Limited
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Call Option Payoffs
LO23.2
Option payoffs ($)
60
40
20
20
40
50
60
80
100
120
Stock price ($)
–20
–40
Exercise price = $50
© 2011 McGraw–Hill Ryerson Limited
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Call Option Payoffs
LO23.2
Option payoffs ($)
60
40
20
20
40
50
60
80
100
120
Stock price ($)
–20
–40
Exercise price = $50
© 2011 McGraw–Hill Ryerson Limited
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Call Option Profits
LO23.2
Option payoffs ($)
60
Buy a call
40
20
10
20
40
50
60
–10
80
100
120
Stock price ($)
–20
–40
Exercise price = $50;
option premium = $10
Sell a call
© 2011 McGraw–Hill Ryerson Limited
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Put Options
LO23.3
• Put options give the holder the right, but
not the obligation, to sell a given quantity
of an asset on or before some time in the
future, at prices agreed upon today.
• When exercising a put, you “put” the asset
to someone.
© 2011 McGraw–Hill Ryerson Limited
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Basic Put Option Pricing Relationships at Expiry
LO23.3
• At expiry, an American put option is worth the
same as a European option with the same
characteristics.
• If the put is in-the-money, it is worth E - ST.
• If the put is out-of-the-money, it is worthless.
PaT = PeT = Max[E - ST, 0]
where
PaT is the value of an American call at expiry
PeT is the value of a European call at expiry
© 2011 McGraw–Hill Ryerson Limited
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Put Option Payoffs
LO23.3
Option payoffs ($)
60
50
40
20
0
Buy a put
0
20
40
50
60
80
100
Stock price ($)
–20
–40
Exercise price = $50
© 2011 McGraw–Hill Ryerson Limited
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Option payoffs ($)
Put Option Payoffs
LO23.3
40
20
0
Sell a put
0
20
40
50
60
80
100
Stock price ($)
–20
–40
Exercise price = $50
–50
© 2011 McGraw–Hill Ryerson Limited
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Put Option Profits
LO23.3
Option payoffs ($)
60
40
20
Sell a put
10
Stock price ($)
–10
20
40
50
60
80
100
Buy a put
–20
–40
Exercise price = $50; option premium = $10
© 2011 McGraw–Hill Ryerson Limited
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Option profits ($)
Selling Options
LO23.4
• The seller (or writer) of an option has an obligation.
• The purchaser of an option has an option (right).
Buy a call
40
10
–10
–40
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
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
Stk
Exp
P/C
Vol
Nortel Networks (NT)
9
Mar
C
446
9
Mar
P
155
8
June
C
15
8
June
P
35
11 Sept
C
11
11 Sept
P
5
LO23.5
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
LO23.5
A recent price for the stock is $9.35
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
This option has a strike price of $8;
June is the expiration month
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
LO23.5
This makes a call option with this exercise price in-themoney by $1.35 = $9.35 – $8.
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
Puts with this exercise price are out-of-the-money.
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
LO23.5
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
On this day, 15 call options with this exercise price were traded.
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
LO23.5
The holder of this CALL option can sell it for $1.95.
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
Since the option is on 100 shares of stock, selling this option
would yield $195.
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
LO23.5
Buying this CALL option costs $2.10.
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
Since the option is on 100 shares of stock, buying this option
would cost $210.
© 2011 McGraw–Hill Ryerson Limited
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Stock Option Quotations
Vol
P/C
Exp
Stk
Nortel Networks (NT)
446
C
Mar
9
155
P
Mar
9
15
C
June
8
35
P
June
8
11
C
11 Sept
5
P
11 Sept
LO23.5
Bid
0.50
0.20
1.95
0.55
1.10
2.65
Ask
0.55
0.30
2.10
0.65
1.25
2.80
Opint
9.35
2461
841
660
1310
459
279
On this day, there were 660 call options with this exercise
outstanding in the market.
© 2011 McGraw–Hill Ryerson Limited
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Combinations of Options
LO23.6
• 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 riskreturn profile to meet your client’s needs.
© 2011 McGraw–Hill Ryerson Limited
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Protective Put Strategy: Buy a Put and Buy the
Underlying Stock: Payoffs at Expiry (Figure 23.4)
Value at
expiry
LO23.6
Protective Put payoffs
$50
Buy the
stock
Buy a put with an exercise
price of $50
$0
$50
Value of
stock at
expiry
© 2011 McGraw–Hill Ryerson Limited
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Protective Put Strategy Profits
Value at
expiry
LO23.6
Buy the stock at $40
$40
Protective Put
strategy has
downside protection
and upside potential
$0
-$10
-$40
$40 $50
Buy a put with exercise price of $50
for $10
Value of
stock at
expiry
© 2011 McGraw–Hill Ryerson Limited
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Covered Call Strategy Profits
Value at
expiry
Buy the stock at $40
$10
Covered Call strategy
$0
Value of stock at expiry
$40 $50
-$30
LO23.6
Sell a call with exercise price
of $50 for $10
-$40
© 2011 McGraw–Hill Ryerson Limited
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Long Straddle: Buy a Call and a Put
LO23.6
Value at
expiry
Buy a call with exercise
price of $50 for $10
40
30
Stock price ($)
30
–20
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.
© 2011 McGraw–Hill Ryerson Limited
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Short Straddle: Sell a Call and a Put
Value at
expiry
LO23.6
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
–40
40
$50
60
70
Sell a call with an
exercise price of $50 for $10
© 2011 McGraw–Hill Ryerson Limited
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Long Call Spread
LO23.6
Value at
expiry
Buy a call with an
exercise price of
$50 for $10
$5
$0
-$5
-$10
long call spread
$50 $60
Value of
stock at
expiry
$55
Sell a call with exercise
price of $55 for $5
© 2011 McGraw–Hill Ryerson Limited
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E
Portfolio value today = c0 +
(1+ r)T
Portfolio payoff
Option payoffs ($)
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
Call
LO23.6
25
Bond
25
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 $25.
© 2011 McGraw–Hill Ryerson Limited
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Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
LO23.6
Portfolio payoff
Option payoffs ($)
Portfolio value today = p0 + S0
Stock
25
Put
Stock price ($)
25
Consider the payoffs from holding a portfolio
consisting of a share of stock and a put with a $25
strike.
© 2011 McGraw–Hill Ryerson Limited
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Portfolio value today
E
= c0 +
(1+ r)T
25
Option payoffs ($)
Option payoffs ($)
Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T
LO23.6
Portfolio value today
= p0 + S0
25
25
Stock price ($)
25
Stock price ($)
Since these portfolios have identical payoffs, they must have
the same value today: hence
Put-Call Parity: c0 + E/(1+r)T = p0 + S0
© 2011 McGraw–Hill Ryerson Limited
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Valuing Options
• The last section
concerned itself
with the value of an
option at expiry.
LO23.7
• This section
considers the value
of an option prior to
the expiration date.
• A much more
interesting question.
© 2011 McGraw–Hill Ryerson Limited
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American Option Value Determinants
1.
2.
3.
4.
5.
Stock price
Exercise price
Interest rate
Volatility in the stock price
Expiration date
Call
+
–
+
+
+
LO23.7
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.
© 2011 McGraw–Hill Ryerson Limited
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Market Value, Time Value and Intrinsic
Value for an American Call
LO23.7
$
ST
Call
Market Value
Time value
Intrinsic value
ST
E
Out-of-the-money
loss
In-the-money
The value of a call option C0 must fall within
max (S0 – E, 0) < C0 < S0.
© 2011 McGraw–Hill Ryerson Limited
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An Option-Pricing Formula
• We will start with a
binomial option
pricing formula to
build our intuition.
LO23.8
• Then we will
graduate to the
normal
approximation to the
binomial for some
real-world option
valuation.
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
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 S1 is 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)
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
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.
S0
S1
C1
$28.75
$3.75
$21.25
$0
$25
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
Borrow the present value of $21.25 today and buy one 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
$21.25 - $21.25 =
$0
$0
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
The levered equity portfolio value today is
today’s value of one share less the present value
of a $21.25 debt:
$21.25
$25 
(1  rf )
S0
( S1 - debt ) = portfolio C1
$28.75 - $21.25 = $7.50
$3.75
$25
$21.25 - $21.25 =
$0
$0
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
We can value the option today
as half of the value of the
levered equity portfolio:
S0
LO23.8
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 =
$0
$0
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
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
S0
( S1 - debt ) = portfolio C1
$28.75 - $21.25 = $7.50
$3.75
$25
$21.25 - $21.25 =
$0
$0
© 2011 McGraw–Hill Ryerson Limited
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Binomial Option Pricing Model
LO23.8
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.
© 2011 McGraw–Hill Ryerson Limited
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Delta and the Hedge Ratio
LO23.8
• 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:
$3.75  0
$3.75 1
Swing of call



D
Swing of stock
$28.75  $21.25 $7.5 2
• The delta of a put option is negative.
© 2011 McGraw–Hill Ryerson Limited
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Delta
LO23.8
• 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
© 2011 McGraw–Hill Ryerson Limited
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The Risk-Neutral Approach to Valuation
LO23.8
S(U), V(U)
q
S(0), V(0)
1- q
S(D), V(D)
We could value 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) 
(1  rf )
© 2011 McGraw–Hill Ryerson Limited
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The Risk-Neutral Approach to Valuation
LO23.8
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
S(D), V(D)
underlying 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 asset in the next period
following an up move and a down move, respectively.
© 2011 McGraw–Hill Ryerson Limited
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The Risk-Neutral Approach to Valuation
LO23.8
S(U), V(U)
q
V (0) 
S(0), V(0)
q  V (U )  (1  q)  V ( D)
(1  rf )
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):
q  S (U )  (1  q )  S ( D)
S (0) 
(1  rf )
A minor bit of algebra yields: q 
(1  rf )  S (0)  S ( D)
S (U )  S ( D)
© 2011 McGraw–Hill Ryerson Limited
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Example of the Risk-Neutral Valuation of a Call:
LO23.8
• 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)
$28.75,C(D)
$21.25  $25  (1  .15)
1- q
$21.25,C(D)
© 2011 McGraw–Hill Ryerson Limited
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Example of the Risk-Neutral Valuation of a Call:
LO23.8
• 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(D)
$25,C(0)
1/3
$21.25,C(D)
© 2011 McGraw–Hill Ryerson Limited
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Example of the Risk-Neutral Valuation of a Call:
LO23.8
• After that, find the value of the call in the up state and down
state.
C (U )  $28.75  $25
2/3
$28.75, $3.75
C ( D)  max[$25  $28.75,0]
$25,C(0)
1/3
$21.25, $0
© 2011 McGraw–Hill Ryerson Limited
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Example of the Risk-Neutral Valuation of a Call:
LO23.8
• Finally, find the value of the call at time 0:
q  C (U )  (1  q )  C ( D)
C (0) 
(1  rf )
C (0) 
2 3  $3.75  (1 3)  $0
(1.05)
$2.50
C (0) 
 $2.38
(1.05)
2/3
$28.75,$3.75
$25,$2.38
$25,C(0)
1/3
$21.25, $0
© 2011 McGraw–Hill Ryerson Limited
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Risk-Neutral Valuation and the Replicating Portfolio LO23.8
• 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
© 2011 McGraw–Hill Ryerson Limited
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The Black-Scholes Model
LO23.8
The Black-Scholes Option Pricing Model:
C0  S  N(d1 )  Ee  rT  N(d 2 )
Where
C0 = the value of a European option at time t = 0
r = the continuously-compounded risk-free interest rate.
σ2
ln(S / E )  (r  )T
2
d1 
 T
d 2  d1   T
N(d) = Probability that a
standardized, normally
distributed, random
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 two-state world.
© 2011 McGraw–Hill Ryerson Limited
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The Black-Scholes Model
LO23.8
• 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 continuously-compounded interest rate
available in the U.S. is r = 5%.
• The option maturity is six 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.
© 2011 McGraw–Hill Ryerson Limited
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The Black-Scholes Model
LO23.8
• 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 
 0.5282
0.30 .5
Then,
d 2  d1   T  0.52815  0.30 .5  0.31602
© 2011 McGraw–Hill Ryerson Limited
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The Black-Scholes Model
LO23.8
C0  S  N(d1 )  Ee rT  N(d 2 )
d1  0.5282
d 2  0.31602
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
© 2011 McGraw–Hill Ryerson Limited
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Stocks and Bonds as Options
LO23.9
• 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.
© 2011 McGraw–Hill Ryerson Limited
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Stocks and Bonds as Options
LO23.9
• Levered Equity is a Put Option.
– The underlying asset comprise 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.
© 2011 McGraw–Hill Ryerson Limited
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Stocks and Bonds as Options
LO23.9
• 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
Value of a
risk-free
bond
Stockholder’s
position in terms
of put options
© 2011 McGraw–Hill Ryerson Limited
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Capital-Structure Policy and Options
LO23.10
• Recall some of the agency costs of debt:
they can all be seen in terms of options.
• For example, recall the incentive
shareholders in a levered firm have to take
large risks.
© 2011 McGraw–Hill Ryerson Limited
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Balance Sheet for a Company in Distress
•Assets
•Cash
•Fixed Asset
•Total
BV MV
$200 $200
$400
$0
$600 $200
Liabilities
LT bonds
Equity
Total
BV
$300
$300
$600
LO23.10
MV
$200
$0
$200
•What happens if the firm is liquidated today?
The bondholders get $200; the shareholders get nothing.
© 2011 McGraw–Hill Ryerson Limited
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Selfish Strategy 1: Take Large Risks
(Think of a Call Option)
• The Gamble
• Win Big
• Lose Big
Probability
10%
90%
LO23.10
Payoff
$1,000
$0
• Cost of investment is $200 (all the firm’s cash)
• Required return is 50%
• Expected CF from the Gamble = $1000 × 0.10 + $0 = $100
$100
NPV = –$200 +
(1.10)
NPV = –$133
© 2011 McGraw–Hill Ryerson Limited
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Selfish Stockholders Accept Negative NPV
Project with Large Risks
LO23.10
• Expected cash flow from the Gamble
– To Bondholders = $300 × 0.10 + $0 = $30
– To Stockholders = ($1000 - $300) × 0.10 + $0 = $70
•
•
•
•
PV of Bonds Without the Gamble = $200
PV of Stocks Without the Gamble = $0
PV of Bonds With the Gamble = $30 / 1.5 = $20
PV of Stocks With the Gamble = $70 / 1.5 = $47
The stocks are worth more with the high risk project because
the call option that the shareholders of the levered firm hold
is worth more when the volatility is increased.
© 2011 McGraw–Hill Ryerson Limited
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Mergers and Options
LO23.11
• This is an area rich with optionality, both in the
structuring of the deals and in their execution.
• In the first half of 2000, General Mills was
attempting to acquire the Pillsbury division of
Diageo PLC.
• The structure of the deal was Diageo’s stockholders
received 141 million shares of General Mills stock
(then valued at $42.55) plus contingent value rights
of $4.55 per share.
© 2011 McGraw–Hill Ryerson Limited
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Mergers and Options
LO23.11
Cash
payment to • The contingent value rights paid the difference
newly
between $42.55 and General Mills’ stock price in
issued
one year up to a maximum of $4.55.
shares
$4.55
$0
$38 $42.55
Value of General
Mills in 1 year
© 2011 McGraw–Hill Ryerson Limited
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Mergers and Options
LO23.11
• The contingent value plan can be viewed in
terms of puts:
– Each newly issued share of General Mills given
to Diageo’s shareholders came with a put option
with an exercise price of $42.55.
– But the shareholders of Diageo sold a put with an
exercise price of $38
© 2011 McGraw–Hill Ryerson Limited
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Mergers and Options
LO23.11
Cash payment to newly issued shares
Own a put
Strike $42.55
$42.55
$42.55
– $38.00
$4.55
$0
$38 $42.55
–$38
Value of General
Mills in 1 year
Sell a put
Strike $38
© 2011 McGraw–Hill Ryerson Limited
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Mergers and Options
Value of
General
Mills in 1
year
Value of a share
plus cash
payment
LO23.11
Value of a share
$42.55
$4.55
$0
$38 $42.55
Value of General
Mills in 1 year
© 2011 McGraw–Hill Ryerson Limited
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Investment in Real Projects & Options
LO23.12
• Classic NPV calculations typically ignore
the flexibility that real-world firms
typically have.
• The next chapter will take up this point.
© 2011 McGraw–Hill Ryerson Limited
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Summary and Conclusions
LO23.13
• 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.
• Put-Call parity
C0  X e
rT
 S  P0
© 2011 McGraw–Hill Ryerson Limited
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Summary and Conclusions
•
•
LO23.13
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 options that enhance
value.
© 2011 McGraw–Hill Ryerson Limited
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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
does not hold?
• What is the Black-Scholes option pricing model?
• How can equity be viewed as a call option?
• Should management ever accept a negative NPV
project? If yes, under what circumstances?
© 2011 McGraw–Hill Ryerson Limited