Ch22 Options and Corporate Finance Basic Concepts

5/25/2018 Ch22 Options and Corporate Finance Basic Concepts

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McGraw-Hill Ryerson 2003 McGrawHi ll Ryerson Limited

Corporate FinanceRoss Westerfield Jaffe

Sixth Edition

22

Chapter Twenty Two

Options and Corporate

Finance: Basic Concepts

Instructor: AJAB KHAN BURKI

For Download: tinyurl.com/burki09

http://www.theoptionsguide.com


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Chapter Outline

22.1 Options

22.2 Call Options

22.3 Put Options

22.4 Selling Options

22.5 Stock Option Quotations

22.6 Combinations of Options

22.7 Valuing Options

22.8 An Option-Pricing Formula

22.9 Stocks and Bonds as Options

22.10 Capital-Structure Policy and Options

22.11 Mergers and Options

22.12 Investment in Real Projects and Options

22.13 Summary and Conclusions


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22.1 Options

Many corporate securities are similar to the stockoptions 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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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 theobligation, tobuya 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 sella 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 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 theholder 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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In The Money

1. For a call option, when the option's strike price isbelow the market price of the underlying asset.

2. For a put option, when the strike price is above

the market price of the underlying asset.

Being in the money does not mean you will profit, it

just means the option is worth exercising. This is

because the option costs money to buy.


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In The Money (Con)

In the money means that your stock option is worthmoney and you can turn around and sell or exercise

it. For example, if John buys a call option on ABC

stock with a strike price of $12, and the price of the

stock is sitting at $15, the option is considered to be

in the money. This is because the option gives John

the right to buy the stock for $12 but he could

immediately sell the stock for $15, a gain of $3. If

John paid $3.50 for the call, then he wouldn't

actually profit from the total trade, but it is still

considered in the money.


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Out Of The Money - OTM

A call option with a strike price that is higher thanthe market price of the underlying asset, or a put

option with a strike price that is lower than the

market price of the underlying asset. An out of the

money option has no intrinsic value, but only

possesses extrinsic or time value. As a result, the

value of an out of the money option erodes quickly

with time as it gets closer to expiry. If it still out of

the money at expiry, the option will expire

worthless.


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At The Money

A situation where an option's strike price is identicalto the price of the underlying security. Both call and

put options will be simultaneously "at the money."

For example, if XYZ stock is trading at 75, then the

XYZ 75 call option is at the money and so is theXYZ 75 put option. An at-the-money option has no

intrinsic value, but may still have time value.

Options trading activity tends to be high when

options are at the money.


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At The Money (Con)

"At the money" is one of three terms used todescribe the relationship between an option's strike

price and the underlying security's price, or option

"moneyness." The other two are "in the money,"

meaning the option has some intrinsic value, and"out of the money," meaning the option has no

intrinsic value. Also, sometimes the term "near the

money" is used to describe an option that is within

50 cents of being at the money


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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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22.2 Call Options

Call options gives the holder the right, but not theobligation, tobuya 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 Relationships at Expiry

At expiry, an American call option is worth the same asa 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)

E is the exercise price.

CaTis the value of an American call at expiry

CeT is the value of a European call at expiry


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Call Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionpayoffs($)

Buy a call

Exercise price = $50


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Call Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionpayoffs($)

Write a call



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Call Option Profits

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionprofits

($)

Write a call

Buy a call

Exercise price = $50; option premium = $10


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22.3 Put Options

Put options give the holder the right, but not theobligation, to sella 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 thesame 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

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionpayoffs($)

Buy a put



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22-20


Put Option Payoffs

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Optionpayoffs($)

write a put


Stock price ($)


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Put Option Profits

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionprofits(

$)

Buy a put

Write a put

Exercise price = $50; option premium = $10

10

-10


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22.4 Selling Options

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

The purchaser of an option hasan option.

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Option

profits($)

Buy a put

Write a put

10

-10

-20

100908070600 10 20 30 40 50

-40

20

0

-60

40

60

Stock price ($)

Optionprofits($)

Write a call

Buy a call


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Stk Exp P/C Vol Bid Ask Opint

Nortel Networks (NT) 9.35

9 Mar C 446 0.50 0.55 24619 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 1.25 459

11 Sept P 5 2.65 2.80 279


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9 Mar C 446 0.50 0.55 24619 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 1.25 459

11 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 24619 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 1.25 459

11 Sept P 5 2.65 2.80 279

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9 Mar C 446 0.50 0.55 24619 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.

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9 Mar C 446 0.50 0.55 24619 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.

22 28


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9 Mar C 446 0.50 0.55 24619 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.

22 29


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9 Mar C 446 0.50 0.55 24619 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.

22 30


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22.6 Combinations of Options

Puts and calls can serve as the building blocksfor more complex option contracts.

If you understand this, you can become a

financial engineer, tailoring the risk-return

profile to meet your clients needs.

22 31 P i P S B P d B


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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 strategy has

downside protection and

upside potential

$50

$0

$50

Value atexpiry

Value of

stock at

expiry

22 32


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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

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Covered Call Strategy

Sell a call withexercise price of

$50 for $10


$40

Coveredcall

$40

$0

-$40

$10

-$30

$30 $50

Value of stock at expiry

Value at

expiry

22 34ddl ll d


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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 of

stock at

expiry

Value at

expiry

22 35


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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 of stock at

expiry

Value at

expiry

22 36


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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 of

stock at

expiry

Value atexpiry

22-37


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Put-Call Parity

Sell a put with an

exercise price of $40


financed with somedebt: FV = $XBuy a call option with

an exercise price of $40

$0

-$40

$40-P0rT

Xe40$

$40

Buy the

stock at $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 of

stock at

expiry

Value at

expiry

22-38


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22.7 Valuing Options

The last sectionconcerned itself with the

value of an option at

expiry.

This section considersthe value of an option

prior to the expiration

date.

A much moreinteresting question.

22-39


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Option Value Determinants

Call Put

1. Stock price +

2. Exercise price +

3. Interest rate +

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

The value of a call option C0must fall within

max (S0E,0) < C0 < S0.

The precise position will depend on these factors.

22-40 M k t V l Ti V l d I t i i


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Market Value, Time Value, and Intrinsic

Value for an American Call

CaT>Max[ST- E, 0]

Profit

lossE ST

Market Value

Intrinsic valueTime value

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

The value of a call option C0must fallwithin max (S0E,0) < C0 < S0.

22-41


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22 41


22.8 An Option-Pricing Formula

We will start with abinomial option pricing

formula to build our

intuition.

Then we will graduateto the normal

approximation to the

binomial for some real-

world option valuation.

22-42


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22 42


Binomial Option Pricing Model

Suppose a stock is worth $25 today and in one period willeither 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

22-43


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1. A call option on this stock with exercise price of $25 willhave 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

22-44


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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

22-45


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

)1(

25.21$25$

fr

$25

$21.25

$28.75

S1S0 debt- $21.25

portfolio$7.50

$0

( - ) ==

=

C1$3.75

$0- $21.25

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We can value the option today ashalf 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

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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

22-48


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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

22-49


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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:

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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 r isk-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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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 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.

qis the risk-neutral

probability of an

up move.

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The key to finding qis 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(

frDSqUSqS

A minor bit of algebra yields:)()(

)()0()1(

DSUS

DSSrq

f

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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 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$25.21$

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$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

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$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

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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

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This risk-neutral result is consistent with valuing the callusing 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$320 C

22-58


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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

)2

()/ln(2

1

Tdd 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.

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Find the value of a six-month call option on Microsoft with anexercise 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 intrinsicvalueof the option is

$10our answer must be at least that amount.

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Lets try our hand at using the model. If you have a calculatorhandy, follow along.

Then,

T

TrES

d

)5.()/ln( 2

1

First calculate d1and d2

31602.05.30.052815.012 Tdd

5282.05.30.0

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

1

d

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N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401

5282.01d

31602.02d

)N()N( 210 dEedSC rT

92.20$

62401.01507013.0160$

0

5.05.

0

C

eC

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Levered Equity is a Call Option.

The underlying asset comprises the assets of thefirm.

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

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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 the

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

put expire.

22-65

22 9 S k d d O i


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It all comes down to put-call parity.

Value of acall on the

firm

Value of aput on the

firm

Value of arisk-free

bond

Value of

the firm= +

TreXPSC 00

Stockholders

position in terms

of call options

Stockholders

position in terms

of put options

22-66

22 10 C i l S P li d O i


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22.10 Capital-Structure Policy and Options

Recall some of the agency costs of debt: they canall be seen in terms of options.

For example, recall the incentive shareholders in

a levered firm have to take large risks.

22-67

B l Sh f C i Di


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Balance Sheet for a Company in Distress

Assets BV MV Liabilities BV MVCash $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.

22-68 Selfish Strategy 1: Take Large Risks


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Selfish Strategy 1: Take Large Risks

(Think of a Call Option)

The Gamble Probability PayoffWin 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

133$

50.1

100$200$

NPV

NPV

22-69 Selfish Stockholders Accept Negative


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p g

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.

22-70

22 11 M d O ti


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22.11 Mergers and Options

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

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22.12 Investment in Real Projects & Options

Classic NPV calculations typically ignore theflexibility 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 stock

at 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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Ch22 Options and Corporate Finance Basic Concepts

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