mcgraw-hill/irwin corporate finance, 7/e © 2005 the mcgraw-hill companies, inc. all rights...

22-1

McGraw-Hill/IrwinCorporate Finance, 7/e © 2005 The McGraw-Hill Companies, Inc. All Rights

Reserved.

CHAPTER

22Options and Corporate

Finance: Basic Concepts

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Chapter Outline22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An Option‑Pricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and Conclusions

22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An Option‑Pricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and Conclusions

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22.1 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.

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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Reserved.

22.1 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 PutsCall 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.

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 PutsCall 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.

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22.1 Options Contracts: Preliminaries

Exercising the OptionThe act of buying or selling the underlying asset through the option contract.

Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.

ExpiryThe maturity date of the option is referred to as the expiration date, or the expiry.

European versus American optionsEuropean options can be exercised only at expiry.

American options can be exercised at any time up to expiry.

Exercising the OptionThe act of buying or selling the underlying asset through the option contract.

Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.

ExpiryThe maturity date of the option is referred to as the expiration date, or the expiry.

European versus American optionsEuropean 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-MoneyThe exercise price is less than the spot price of the underlying asset.

At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.

Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.

In-the-MoneyThe exercise price is less than the spot price of the underlying asset.

At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.

Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.

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Options Contracts: Preliminaries

Intrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.

Speculative ValueThe difference between the option premium and the intrinsic value of the option.

Intrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.

Speculative ValueThe difference between the option premium and the intrinsic value of the option.

Option Premium =

Intrinsic Value

Speculative Value

+

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22.2 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.

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.

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Basic Call Option Pricing Relationshipsat 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

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

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Call Option Payoffs

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($) Buy

a ca

ll

Exercise price = $50

50

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Call Option Payoffs

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

Sell a call


50

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Call Option Profits

Exercise price = $50; option premium = $10

Sell a call

Buy a call

–20

12020 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

50–10

10

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22.3 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.

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.

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Basic Put Option Pricing Relationshipsat 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]

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]

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Put Option Payoffs

–20

0 20 40 60 80 100

–40

20

0

40

60

Stock price ($)

Op

tion

pay

offs

($)

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 ($)

Op

tion

pay

offs

($)

Sell a put


50

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Reserved.

Put Option Profits

–20

20 40 60 80 100

–40

20

40

60

Stock price ($)

Op

tion

pay

offs

($)

Buy a put

Exercise price = $50; option premium = $10

–10

10Sell a put

50

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22.4 Selling Options

Exercise price = $50; option premium = $10 Sell a call

Buy a call

50 6040 100

–40

40

Stock price ($)

Op

tion

pay

offs

($)

Buy a put

Sell a put

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

The purchaser of an option has an option.

–10

10

Buy a call

Sell a

put

Buy a put

Sell a call

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Reserved.

22.5 Reading The WallStreet Journal

Option/Strike Exp. Vol. Last Vol. LastIBM 130 Oct 364 15¼ 107 5¼138¼ 130 Jan 112 19½ 420 9¼138¼ 135 Jul 2365 4¾ 2431 13/16

138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

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22.5 Reading The Wall Street Journal


138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

This option has a strike price of $135;

a recent price for the stock is $138.25

July is the expiration month

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138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

This makes a call option with this exercise price in-the-money by $3.25 = $138¼ – $135.

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

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138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

On this day, 2,365 call options with thisexercise price were traded.

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138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

The CALL option with a strike priceof $135 is trading for $4.75.

Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions.

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138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

On this day, 2,431 put options with thisexercise price were traded.

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138¼ 135 Aug 1231 9¼ 94 5½138¼ 140 Jul 1826 1¾ 427 2¾138¼ 140 Aug 2193 6½ 58 7½

--Put----Call--

The PUT option with a strike price of $135 is trading for $.8125.

Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions.

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22.6 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.

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.

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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 protection and upside potential

$40

$0

-$40

$50

Value at expiry


-$10

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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


-$30

$10

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Reserved.

Long Straddle: Buy a Call and a Put

30 40 60 70

30

40

Stock price ($)

Op

tion

pay

offs

($)

Buy a put with exercise price 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

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Long Straddle: Buy a Call and a Put

–30

30 40 60 70

–40

Stock price ($)

Op

tion

pay

offs

($)

$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

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bond

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

25

25

Stock price ($)

Op

tion

pay

offs

($)

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)T

E

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Reserved.


25

25

Stock price ($)

Op

tion

pay

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

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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 ($)

Opt

ion

payo

ffs

($)

25

25

Stock price ($)

Opt

ion

payo

ffs

($) Portfolio value today

= p0 + S0

Portfolio value today

(1+ r)T

E= c0 +

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22.7 Valuing Options

The last section concerned itself with the value of an option 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.

This section considers the value of an option prior to the expiration date.

A much more interesting question.

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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.

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Market Value, Time Value and Intrinsic Valuefor an American Call

The value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.

25

Op

tion

pay

offs

($) Call

ST

loss

E

Profit

ST

Time value

Intrinsic value

Market Value

In-the-moneyOut-of-the-money

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Reserved.

22.8 An Option‑Pricing Formula

We will start with a binomial option pricing formula to build our intuition.

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.

Then we will graduate to the normal approximation to the binomial for some real-world option valuation.

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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?

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?

$25

$21.25 = $25×(1 –.15)

$28.75 = $25×(1.15)S1S0

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Binomial Option Pricing Model1. 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.

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

$28.75S1S0 C1

$3.75

$0

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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.

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.

$25

$21.25

$28.75S1S0 debt

– $21.25portfolio$7.50

$0

( – ) ==

=

C1

$3.75

$0– $21.25

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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:

The value today of the levered equity portfolio is today’s value of one share less the present value of a $21.25 debt:

)1(

25.21$25$

fr

$25

$21.25

$28.75S1S0 debt


$0

( – ) ==

=

C1

$3.75

$0– $21.25

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Reserved.


We can value the call option todayas half of the value of thelevered equity portfolio:

We can value the call option todayas half of the value of thelevered equity portfolio:

)1(

25.21$25$

2

10

frC

$25

$21.25

$28.75S1S0 debt


$0

( – ) ==

=

C1

$3.75

$0– $21.25

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Reserved.

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

$28.75S1S0 debt


$0

( – ) ==

=

C1

$3.75

$0– $21.25

$2.38

C0

22-45


Reserved.

the replicating portfolio intuition.the replicating portfolio intuition.the replicating portfolio intuition.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.

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

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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:

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$

Swing of callSwing of stock

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Reserved.

Delta

Determining the Amount of Borrowing:

Value of a call = Stock price × Delta – Amount borrowed

$2.38 = $25 × ½ – Amount borrowed

Amount borrowed = $10.12

Determining the Amount of Borrowing:

Value of a call = Stock price × Delta – Amount borrowed

$2.38 = $25 × ½ – Amount borrowed

Amount borrowed = $10.12

38.2$24.20$25$2

1

)05.1(

25.21$25$

2

10

C

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Reserved.

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

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)

S(D), V(D)

q

1- q

)1(

)()1()()0(

fr

DVqUVqV

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Reserved.


S(0) is the value of the underlying asset today.S(0) is the value of the underlying 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 in the next period following an up move and a down move, respectively.

q

1- q

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

q is the risk-neutral probability of an “up” move.

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The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):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), V(0)

S(U), V(U)

S(D), V(D)

q

1- q

A minor bit of algebra yields:)()(

)()0()1(

DSUS

DSSrq f

)1()()1()(

)0(fr

DSqUSqS

)1(

)()1()()0(

fr

DVqUVqV

22-51


Reserved.

Example of the Risk-Neutral Valuation of a Call:

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:

$21.25,C(D)

q

1- q

$25,C(0)

$28.75,C(D)

)15.1(25$75.28$

)15.1(25$25.21$

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Reserved.


$21.25,C(D)

2/3

1/3

The next step would be to compute the risk neutral probabilities

$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

22-53


Reserved.


$21.25, $0

2/3

1/3

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

$25,C(0)

$28.75, $3.75

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

25$75.28$)( UC

22-54


Reserved.


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

$21.25, $0

2/3

1/3

$25,C(0)

$28.75,$3.75

$25,$2.38

)1(

)()1()()0(

fr

DCqUCqC

)05.1(

0$)31(75.3$32)0(

C

38.2$)05.1(

50.2$)0( C

22-55


Reserved.

This risk-neutral result is consistent with valuing the call using a replicating portfolio.

This risk-neutral result is consistent with valuing the call using a replicating portfolio.

Risk-Neutral Valuationand the Replicating Portfolio

38.2$24.2025$2

1

)05.1(

25.21$25$

2

10

C

38.2$05.1

50.2$

)05.1(

0$)31(75.3$320

C

22-56


Reserved.

The Black-Scholes Model

The Black-Scholes Model isThe Black-Scholes Model is

Where

C0 = the value of a European option at time t = 0r = the risk-free interest rate.

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 2-state world.

)N()N( 210 dEedSC rT

T

Tσ

rESd

)2

()/ln(2

1

Tdd 12

22-57


Reserved.


Find the value of a six-month call option on the 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.

Find the value of a six-month call option on the 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.

22-58


Reserved.


Let’s try our hand at using the model. If you have a calculator handy, follow along.

Let’s try our hand at using the model. If you have a calculator handy, follow along.

Then,

First calculate d1 and d2

T

TσrESd

)5.()/ln( 2

1

5282.05.30.0

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

1 d

31602.05.30.052815.012 Tdd

22-59


Reserved.


N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401

)N()N( 210 dEedSC rT

5282.01 d

31602.02 d

92.20$

62401.01507013.0160$

0

5.05.0

C

eC

22-61


Reserved.

22.9 Stocks and Bonds as OptionsLevered Equity is a Call 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 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.

Levered Equity is a Call 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 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.

22-62


Reserved.

22.9 Stocks and Bonds as OptionsLevered 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.

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.

22-63


Reserved.

22.9 Stocks and Bonds as Options

It all comes down to put-call parity.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= + –

Stockholder’s position in terms of call options

Stockholder’s position in terms of put options

c0 = S0 + p0 – (1+ r)T

E

22-64


Reserved.

22.10 Capital-Structure Policyand 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.

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.

22-65


Reserved.

Balance Sheet for a Companyin 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?

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

22-66


Reserved.

Selfish Strategy 1: Take Large Risks

The Gamble Probability Payoff

Win Big 10% $1,000

Lose Big 90% $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

The Gamble Probability Payoff

Win Big 10% $1,000

Lose Big 90% $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

NPV = –$200 + $100

(1.10)

NPV = –$133

22-67


Reserved.

Selfish Stockholders Accept Negative NPV Project with Large Risks

Expected CF from the GambleTo 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

Expected CF from the GambleTo 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

$20 =$30

(1.50) PV of Bonds With the Gamble:

$47 =$70

(1.50) PV of Stocks With the Gamble:

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 of the firm is increased.

22-68


Reserved.

22.11 Mergers and Options

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.

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.

22-69


Reserved.


Cash payment to

newly issued shares

$0

Value of General Mills in 1 year

$42.55$38

$4.55

The contingent value rights paidthe difference between $42.55 andGeneral Mills’ stock price in oneyear up to a maximum of $4.55.

22-70


Reserved.


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

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

22-71


Reserved.


$38

$0


$42.55

$42.55

–$38

Own a putStrike $42.55

Sell a putStrike $38

– $38.00$4.55

$42.55

Cash payment to newly issued shares

22-72


Reserved.


Value of a share

$38

$4.55

$0

$42.55

Value of General

Mills in 1 year


Value of a share plus cash payment

$42.55

22-73


Reserved.

22.12 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.

Classic NPV calculations typically ignore the flexibility that real-world firms typically have.

The next chapter will take up this point.

22-74


Reserved.

22.13 Summary and Conclusions

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

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– (1+ r)T

E= S0 + p0

22-75


Reserved.

22.13 Summary and Conclusions

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.

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.

mcgraw-hill/irwin corporate finance, 7/e © 2005 the mcgraw-hill companies, inc. all rights...

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