Chapter Options)

8/2/2019 Chapter Options)

1/92

23-0

McGraw-Hill Ryerson 2005 McGrawHill Ryerson Limited

Sixth Edition

23

Chapter Twenty Three

Options and Corporate

Finance: Basic Concepts

Prepared by

Gady Jacoby

University of Manitoba



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23-1


Chapter Outline

23.1 Options23.2 Call Options

23.3 Put Options

23.4 Selling Options

23.5 Stock Option Quotations23.6 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


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23.1 Options

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.


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23.1 Options Contracts: Preliminaries

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, tobuy 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 theobligation, 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.


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23.1 Options Contracts: Preliminaries

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.


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Options Contracts: Preliminaries

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 theunderlying asset.


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Options Contracts: Preliminaries

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+


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23-7


23.2 Call Options

Call options gives the holder the right, but not the

obligation, tobuy 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.


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23-8


Basic Call Option Pricing Relationships 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.

CaT= CeT=Max[ST- E, 0]

Where

STis the value of the stock at expiry (time T)

Eis the exercise price.

CaTis the value of an American call at expiry

CeTis the value of a European call at expiry


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Call Option Payoffs

20

12020 40 60 80 100

40

20

40

60

Stock price ($)

Option

payoffs($)

Exercise price = $50

50


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23-10


Call Option Payoffs

20

12020 40 60 80 100

40

20

40

60

Stock price ($)

Option

payoffs($)


50


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Call Option Profits

Exercise price = $50;

option premium = $10Sell a call

Buy a call

20

12020 40 60 80 100

40

20

40

60

Stock price ($)

Option

payoffs($)

50

10

10


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23.3 Put Options

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.


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Basic Put Option Pricing Relationships 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 worthE - ST. If the put is out-of-the-money, it is worthless.

PaT=PeT=Max[E - ST, 0]


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Put Option Payoffs

20

0 20 40 60 80 100

40

20

0

40

60

Stock price ($)

Option

payoffs($)

Buy a put


50

50


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Put Option Payoffs

20

0 20 40 60 80 100

40

20

0

40

50

Stock price ($)

Optionpayoffs($)

Sell a put


50


17/92

23-16


Put Option Profits

20

20 40 60 80 100

40

20

40

60

Stock price ($)

Option

payoffs($)

Buy a put

Exercise price = $50; option premium = $10

10

10Sell a put

50


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23-17


23.4 Selling Options

Exercise price = $50;

option premium = $10Sell a call

Buy a call

50 6040 100

40

40

Stock price ($)

Option

profits($)

Buy a put

Sell a put

The seller (or writer) of an option has an obligation.

The purchaser of an option has an option (right).

10

10

Buy a call

Sell a call


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23.5 Stock Option Quotations

Stk Exp P/C Vol Bid Ask Opint

Nortel Networks (NT) 9.35

9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


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9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


This option has a strike price of $8;

A recent price for the stock is $9.35

June is the expiration month


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This makes a call option with this exercise price in-the-

money by $1.35 = $9.35 $8.

Puts with this exercise price are out-of-the-money.



9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


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9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


On this day, 15 call options with this exercise price were traded.


23/92

23-22

McGraw-Hill Ryerson 2005 McGraw

Hill Ryerson Limited



9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


The holder of this CALL option can sell it for $1.95.

Since the option is on 100 shares of stock, selling this option

would yield $195.


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23-23





9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


Buying this CALL option costs $2.10.

Since the option is on 100 shares of stock, buying this option

would cost $210.


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9 Mar C 446 0.50 0.55 2461

9 Mar P 155 0.20 0.30 841

8 June C 15 1.95 2.10 660

8 June P 35 0.55 0.65 1310

11 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279


On this day, there were 660 call options with this exercise

outstanding in the market.


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23.6 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-returnprofile to meet your clients needs.


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23-26



Protective Put Strategy: Buy a Put and Buy

the Underlying Stock: Payoffs at Expiry

Buy a put with an exercise

price of $50

Buy the

stock

Protective Put payoffs

$50

$0

$50

Value at

expiry

Value of

stock at

expiry


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Protective Put Strategy Profits

Buy a put with exercise price of $50

for $10

Buy the stock at $40

$40

Protective Put

strategy has

downside protectionand upside potential

$40

$0

-$40

$50

Value at

expiry

Value of

stock at

expiry

-$10


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23-28



Covered Call Strategy

Sell a call with exercise price

of $50 for $10

Buy the stock at $40

$40

Covered Call strategy

$0

-$40

$50

Value at

expiry

Value of stock at expiry

-$30

$10


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23-29



Long Straddle: Buy a Call and a Put

30 40 60 70

30

40

Stock price ($)

Buy a put with exerciseprice of $50 for $10

Buy a call with exercise

price of $50 for $10

A Long Straddle only makes money if the stock price moves

$20 away from $50.

$50

20

Value atexpiry


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23-30



Long Straddle: Buy a Call and a Put

30

30 40 60 70

40

Stock price ($)

$50

This Short Straddle only loses money if the stock

price moves $20 away from $50.

Sell a put with exercise price of

$50 for $10

Sell a call with an

exercise price of $50 for

$10

20

Value atexpiry


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23-31



Long Call Spread


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23-32



Sell a call with exercise

price of $55 for $5

$55

long call spread$5

$0

$50

Buy a call with an

exercise price of

$50 for $10

-$10-$5

$60

Value of

stock at

expiry

Value at

expiry

Long Call Spread


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23-33



Call options and Slope


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23-34



Option Combo


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23-35



Bond

Put-Call Parity:p0 + S0 = c0 +E/(1+ r)T

25

25

Stock price ($)

Optionpayoffs($)

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.

Call

Portfolio payoffPortfolio value today = c0 +

(1+ r)TE


37/92

23-36




25

25

Stock price ($)

Optionpay

offs($)

Consider the payoffs from holding a portfolio

consisting of a share of stock and a put with a $25

strike.

Portfolio value today =p0 + S0

Portfolio payoff

Put

Stock


38/92

23-37




Since these portfolios have identical payoffs, they must have

the same value today: hence

Put-Call Parity: c0 +E/(1+r)T=p0 + S0

25

25

Stock price ($)

Optionpayoffs($)

25

25

Stock price ($)

Optionpayoffs($) Portfolio value today

=p0 + S0

Portfolio value today

(1+ r)T

E= c0 +


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23.7 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.

A much more

interesting question.


40/92

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American Option Value Determinants

Call Put1. Stock price +

2. Exercise price +

3. Interest rate +

4. Volatility in the stock price + +5. Expiration date + +

The value of a call option C0 must fall within

max (S0 E, 0) < C0 < S0.

The precise position will depend on these factors.


41/92

23-40



Market Value, Time Value and Intrinsic

Value for an American Call

The value of a call option C0 must fall within

max (S0 E, 0) < C0 < S0.

25

Call

ST

loss

E

$

ST

Time value

Intrinsic value

Market Value

In-the-moneyOut-of-the-money


42/92

23-41



23.8 An Option-Pricing Formula

We will start with a

binomial option pricing

formula to build our

intuition.

Then we will graduate

to the normal

approximation to the

binomial for some real-

world option valuation.


43/92

23-42



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 yearS1 is either $28.75 or $21.25. The risk-free rate is

5%. What is the value of an at-the-money call option?

$25

$21.25

$28.75

S1S0


44/92

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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.

$25

$21.25

$28.75

S1S0 C1

$3.75

$0


45/92

23-44




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 options payoff so

the portfolio is worth twice the call option value.

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25


46/92

23-45




The levered equity portfolio value today istodays value of one share less the present valueof a $21.25 debt:

)1(

25.21$25$

f

r+-

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25


47/92

23-46




We can value the option today as

half of the value of the levered

equity portfolio:

+-=

)1(

25.21$25$

2

10

frC

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25


48/92

23-47



If the interest rate is 5%, the call is worth:

The Binomial Option Pricing Model

( ) 38.2$24.2025$2

1

)05.1(

25.21$25$

2

10 =-=

-=C

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25


49/92

23-48



If the interest rate is 5%, the call is worth:

The Binomial Option Pricing Model

( ) 38.2$24.2025$2

1

)05.1(

25.21$25$

2

10 =-=

-=C

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25

$2.38

C0


50/92

23-49




the replicating portfolio intuition.the replicating portfolio intuition.

Many derivative securities can be valued by

valuing portfolios of primitive securitieswhen those portfolios have the same

payoffs as the derivative securities.

The most important lesson (so far) from the binomialoption pricing model is:


51/92

23-50



Delta and the Hedge Ratio

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:

The delta of a put option is negative.

2

1

5.7$

75.3$

25.21$75.28$

075.3$==

-

-=D =

Swing of call

Swing of stock


52/92

23-51



Delta

Determining the Amount of Borrowing:

( ) 38.2$24.20$25$2

1

)05.1(

25.21$25$

2

10 =-=

-=C

Value of a call = Stock price DeltaAmount borrowed

$2.38 = $25 Amount borrowed

Amount borrowed = $10.12


53/92

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The Risk-Neutral Approach to Valuation

We could value V(0) as the value of the replicating portfolio.

An equivalent method is risk-neutral valuation

S(0), V(0)

S(U), V(U)

q

S(D), V(D)

1- q

)1(

)()1()()0(

fr

DVqUVqV

+

-+=


54/92

23-53




S(0) is the value of theunderlying asset today.

S(0), V(0)

S(U), V(U)

S(D), V(D)

S(U) and S(D) are the values of the asset inthe next period following an up move and adown move, respectively.

q

1- q

V(U) and V(D) are the values of the asset in the next periodfollowing an up move and a down move, respectively.

q is the risk-neutral

probability of an

up move.


55/92

23-54




The key to finding q is to note that it is already impounded

into an observable security price: the value ofS(0):

S(0), V(0)

S(U), V(U)

S(D), V(D)

q

1- q

)1(

)()1()()0(

fr

DVqUVqV

+

-+=

)1(

)()1()()0(

fr

DSqUSqS +

-+

=

A minor bit of algebra yields:)()(

)()0()1(

DSUS

DSSrq

f

-

-+=


56/92

23-55



Example of the Risk-Neutral Valuation of a Call:

$21.25,C(D)

q

1- q

Suppose a stock is worth $25 today and in one period willeither be worth 15% more or 15% less. The risk-free rate is5%. What is the value of an at-the-money call option?

The binomial tree would look like this:

$25,C(0)

$28.75,C(D)

)15.1(25$75.28$ =

)15.1(25$25.21$ -=


57/92

23-56




$21.25,C(D)

2/3

1/3

The next step would be to compute the risk neutralprobabilities

$25,C(0)

$28.75,C(D)

)()(

)()0()1(

DSUS

DSSrq

f

-

-+=

3250.7$5$

25.21$75.28$25.21$25$)05.1( ==-

-=q


58/92

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$21.25, $0

2/3

1/3

After that, find the value of the call in the up state and downstate.

$25,C(0)

$28.75, $3.75

25$75.28$)( -=UC

]0,75.28$25max[$)( -=DC


59/92

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Finally, find the value of the call at time 0:

$21.25, $0

2/3

1/3

$25,C(0)

$28.75,$3.75

)1(

)()1()()0(

fr

DCqUCqC

+

-+=

)05.1(0$)31(75.3$32)0(

+=C

38.2$)05.1(

50.2$)0( ==C

$25,$2.38


60/92

23-59



This risk-neutral result is consistent with valuing the call

using a replicating portfolio.

Risk-Neutral Valuation and the Replicating Portfolio

( ) 38.2$24.2025$2

1

)05.1(

25.21$25$

2

10 =-=

-=C

38.2$05.150.2$

)05.1(0$)31(75.3$32

0 ==+=C


61/92

23-60



The Black-Scholes Model

The Black-Scholes Model is)N()N( 210 dEedSC

rT -= -

Where

C0 = the value of a European option at time t= 0

r= the risk-free interest rate.

T

T

rESd

s

)2

()/ln(2

1

++=

Tdd s-= 12

N(d) = Probability that a

standardized, normally

distributed, random

variable will be less thanor 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.


62/92

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Find the value of a six-month call option onMicrosoft 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 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 $10our answer must be at least that

amount.


63/92

23-62




Lets try our hand at using the model. If you have acalculator handy, follow along.

Then,

T

TrESd s

)5.()/ln( 2

1

++=

First calculate d1 and d2

31602.05.30.052815.012 =-=-= Tdd s

5282.05.30.0

5).)30.0(5.05(.)150/160ln( 2

1 =++

=d


64/92

23-63




N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401

5282.01 =d

31602.02 =d

)N()N( 210 dEedSCrT -= -

92.20$

62401.01507013.0160$

0

5.05.

0

=

-= -

C

eC


65/92

23-64



Assume S= $50,X= $45, T= 6 months, r= 10%,and s = 28%, calculate the value of a call and a put.

125.1$45$50$32.8$ )50.0(10.0 =+-= -eP

32.8$)754.0(45)812.0(50 )50.0(10.0)5.0(0 =-= -- eeC

( )884.0

50.028.0

50.02

28.0010.0

4550ln

2

1 =

+-+

=d

686.050.028.0884.02 =-=d

From a standard normal probability table, look upN(d1) =

0.812 andN(d2) = 0.754 (or use Excels normsdist function)

Another Black-Scholes Example


66/92

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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 firmare greater in value than the debt, the shareholdershave 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 havean out-of-the-money call, they will not pay the

bondholders (i.e., the shareholders will declarebankruptcy), and let the call expire.


67/92

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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 havean 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 theoption (i.e.,NOT declare bankruptcy) and let the

put expire.


68/92

23-67




It all comes down to put-call parity.

Value of a

call on the

firm

Value of a

put on the

firm

Value of a

risk-free

bond

Value of

the firm= +

Stockholders

position in terms

of call options

Stockholders

position in terms

of put options

c0 = S0 +p0 (1+ r)TE


69/92

23-68


23.10 Capital-Structure Policy and Options

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.

23 69


70/92

23-69


Balance Sheet for a Company in Distress

Assets BV MV Liabilities BV MV

Cash $200 $200 LT bonds $300

Fixed Asset $400 $0 Equity $300

Total $600 $200 Total $600 $200

What happens if the firm is liquidated today?

The bondholders get $200; the shareholders get nothing.

$200

$0

23 70


71/92

23-70


Selfish Strategy 1: Take Large Risks

(Think of a Call Option)

The Gamble Probability Payoff

Win Big 10% $1,000

Lose Big 90% $0

Cost of investment is $200 (all the firms cash)

Required return is 50%

Expected CF from the Gamble = $1000 0.10 + $0 = $100

NPV =$200 +$100

(1.10)

NPV =$133

23 71


72/92

23-71


Selfish Stockholders Accept Negative

NPV Project with Large Risks

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.

23 72


73/92

23-72



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 Diageos stockholders

received 141 million shares of General Mills stock

(then valued at $42.55) plus contingent value rights

of $4.55 per share.

23 73


74/92

23-73



The contingent value rights paid the difference

between $42.55 and General Mills stock price in

one year up to a maximum of $4.55.

Cash

payment tonewly

issued

shares

$0

Value of General

Mills in 1 year$42.55$38

$4.55

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The contingent value plan can be viewed in terms of

puts:

Each newly issued share of General Mills given

to Diageos 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

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$38

$0

Value of General

Mills in 1 year$42.55

$42.55

$38

Own a put

Strike $42.55

Sell a put

Strike $38

$38.00

$4.55

$42.55

Cash payment to newly issued shares

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Value of a share

$38

$4.55

$0

$42.55

Value of

GeneralMills in 1

year

Value of General

Mills in 1 year

Value of a share

plus cash

payment

$42.55

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23.12 Investment in Real Projects & Options

Classic NPV calculations typically ignore the

flexibility that real-world firms typically have.

The next chapter will take up this point.

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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 stockat a set price for a given amount of time.

Put-Call parity

00 PSeXC Tr +=+ -

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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.

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Binomial Option Pricing Model Example

European Call Option Example

European Call Option that at t = 1 matures and has a strike price of $27

Future Call Value

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B.O.P.M Example Cont.

Replicating Portfolio for the call option involving the

underlying stock and risk-free debt.

Scale down by 3/10 so as to make a replicating portfolio of

the same future call value.

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B.O.P.M Example Cont.

Co = Price of this portfolio =

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B.O.P.M Example Cont

European Put Option Example

European Put Option that at t = 1 matures with a strike price of $27

Future Put Value

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Replicating Portfolio for the put involving the underlying

stock and risk-free debt

Scale down by 7/10 so as to make a replicating portfolio

of the same future put value.

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Po = Price of this portfolio =

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McGraw-Hill Ryerson

2005 McGrawHill Ryerson Limited


Remember

26.59 = 26.59

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B.O.P.M Example Cont/ Risk-Neutral Pricing

Risk-Neutral Pricing

Example

American call option with strike price $18 and r = 10%

What is the price of the call?

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We know that by using Binomial Option pricing

For American call, PV of exercising at t=0 is $2

PV of not exercising is $4.45

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Is there another way of pricing this option?

Fact. Option pricing depends on price of stock, not (directly)

on Beta (), the discount factor, or probabilities of high-vs-

low state.

Price of call option should be the same for all (, )combinations such that S0 is constant

Idea: Assume = 0 compute compute value of call

option

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Solve for S0 = (option payoff in good state) + (1- )

(option payoff in bad state)

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Documents

Chapter Options)