22-0 mcgraw-hill ryerson © 2003 mcgraw–hill ryerson limited corporate finance ross westerfield ...

22-1

McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited

Corporate Finance Ross Westerfield Jaffe Sixth Edition

22Chapter Twenty Two

Options and Corporate Finance: Basic Concepts

Prepared by

Gady JacobyUniversity of Manitoba

and

Sebouh AintablianAmerican University of Beirut

22-2


Chapter Outline22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Stock Option Quotations22.6 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

22-3


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.

22-4


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 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.

22-5


22.1 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.

22-6


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 the

underlying asset.

22-7


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

+

22-8


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.

22-9


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

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

22-10


Call Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

ayo

ffs

($)

Buy a call

Exercise price = $50

22-11


Call Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

ayo

ffs

($)

Write a call


22-12


Call Option Profits

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

rofi

ts (

$)

Write a call

Buy a call

Exercise price = $50; option premium = $10

22-13


22.3 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.

22-14


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 worth E - ST.

• If the put is out-of-the-money, it is worthless.

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

22-15


Put Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

ayo

ffs

($)

Buy a put


22-16


Put Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Op

tio

n p

ayo

ffs

($)

write a put


Stock price ($)

22-17


Put Option Profits

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

rofi

ts (

$)

Buy a put

Write a put

Exercise price = $50; option premium = $10

10

-10

22-18


22.4 Selling Options

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

• The purchaser of an option has an option.

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

rofi

ts (

$)

Buy a put

Write a put

10

-10

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Op

tio

n p

rofi

ts (

$)

Write a call

Buy a call

22-19


22.5 Stock Option Quotations

Stk Exp P/C Vol Bid Ask OpintNortel Networks (NT) 9.359 Mar C 446 0.50 0.55 24619 Mar P 155 0.20 0.30 8418 June C 15 1.95 2.10 6608 June P 35 0.55 0.65 131011 Sept C 11 1.10 1.25 45911 Sept P 5 2.65 2.80 279

22-20




This option has a strike price of $8;

A recent price for the stock is $9.35

June is the expiration month

22-21



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.


22-22




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

22-23




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.

22-24




Buying this CALL option costs $2.10.

Since the option is on 100 shares of stock, buying this option would cost $210.

22-25




On this day, there were 660 call options with this exercise outstanding in the market.

22-26


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.

22-27


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 strategy has downside protection and upside potential

$50

$0

$50

Value at expiry

Value of stock at expiry

22-28


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


22-29


Covered Call Strategy

Sell a call with exercise price of $50 for $10


$40

Covered call

$40

$0

-$40

$10

-$30

$30 $50


Value at expiry

22-30


Long Straddle: Buy a Call and a Put

Buy a put with an exercise price of

$50 for $10$40

A Long Straddle only makes money if the stock price moves $20 away from $50.

$40

$0

-$20$50

Buy a call with an exercise price of $50 for $10

-$10

$30

$60$30 $70


Value at expiry

22-31


Short Straddle: Sell a Call and a Put

Sell a put with exercise price of$50 for $10

$40

A Short Straddle only loses money if the stock price moves $20 away from $50.

-$40

$0

-$30$50

Sell a call with an exercise price of $50 for $10

$10

$20

$60$30 $70


Value at expiry

22-32


Long Call Spread

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 at expiry

22-33


Put-Call Parity

Sell a put with an exercise price of $40

Buy the stock at $40 financed with some debt: FV = $XBuy a call option with

an exercise price of $40

$0

-$40

$40-P0

rTXe40$

$40


040$ C)40($ rTXe

-[$40-P0]0C

0P

In market equilibrium, it mast be the case that option prices are set such that: 000 SPXeC rT

Otherwise, riskless portfolios with positive payoffs exist.


Value at expiry

22-34


22.7 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.

22-35


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.

22-36


Market Value, Time Value, and Intrinsic Value for an American Call

CaT > Max[ST - E, 0]

Profit

loss E ST

Market Value

Intrinsic value

S T - E

Time value

Out-of-the-money In-the-money

S T

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

22-37


22.8 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.

22-38


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 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?

$25

$21.25

$28.75

S1S0

22-39



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

22-40



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.

$25

$21.25

$28.75S1S0 debt

- $21.25portfolio$7.50

$0

( - ) ==

=

C1

$3.75

$0- $21.25

22-41



The levered equity portfolio value today 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

22-42



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

$28.75S1S0 debt


$0

( - ) ==

=

C1

$3.75

$0- $21.25

22-43


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

22-44


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



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:

22-46


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)

S(D), V(D)

q

1- q

)1(

)()1()()0(

fr

DVqUVqV

22-47



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.

22-48



• 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

)1(

)()1()()0(

fr

DVqUVqV

)1(

)()1()()0(

fr

DSqUSqS

A minor bit of algebra yields:)()(

)()0()1(

DSUS

DSSrq f

22-49


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 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:

$25,C(0)

$28.75,C(D)

)15.1(25$75.28$

)15.1(25$25.21$

22-50



$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

22-51



$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

25$75.28$)( UC

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

22-52



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

22-53


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$05.1

50.2$

)05.1(

0$)31(75.3$320

C

22-54


The Black-Scholes ModelThe Black-Scholes Model is

)N()N( 210 dEedSC rT

Where

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

T

Tσ

rESd

)2

()/ln(2

1

Tdd 12

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.

22-55


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 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.

22-56



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

Then,

T

TσrESd

)5.()/ln( 2

1

First calculate d1 and d2

31602.05.30.052815.012 Tdd

5282.05.30.0

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

1

d

22-57



N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401

5282.01 d

31602.02 d

)N()N( 210 dEedSC rT

92.20$

62401.01507013.0160$

0

5.05.0

C

eC

22-59


22.9 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.

22-60


22.9 Stocks and Bonds as Options

• 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.

22-61


22.9 Stocks and Bonds as Options

• 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= + –

TreXPSC 00

Stockholder’s position in terms of call options

Stockholder’s position in terms of put options

22-62


22.10 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.

22-63


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.

22-64


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 firm’s cash)

Required return is 50%

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

133$50.1

100$200$

NPV

NPV

22-65


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.

22-66


22.11 Mergers and Options

• This is an area rich with optionality, both in the structuring of the deals and in their execution.

22-67


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.

22-68


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

00 PSeXC Tr

22-69


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 options that enhance

value.

22-0 mcgraw-hill ryerson © 2003 mcgraw–hill ryerson limited corporate finance ross westerfield ...

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