Fundamentals of Corporate Finance, 2/e

Fundamentals of Corporate Finance, 2/e

ROBERT PARRINO, PH.D.DAVID S. KIDWELL, PH.D.THOMAS W. BATES, PH.D.

Chapter 20: Options and Corporate Finance

Learning Objectives

1. DEFINE A CALL OPTION AND A PUT OPTION, AND DESCRIBE THE PAYOFF FUNCTION FOR EACH OF THESE OPTIONS.

2. LIST AND DESCRIBE THE VARIABLES THAT AFFECT THE VALUE OF AN OPTION. CALCULATE THE VALUE OF A CALL OPTION AND OF A PUT OPTION.

Learning Objectives

4. NAME SOME OF THE REAL OPTIONS THAT OCCUR IN BUSINESS AND EXPLAIN WHY TRADITIONAL NPV ANALYSIS DOES NOT ACCURATELY INCORPORATE THEIR VALUES.

5. DESCRIBE HOW THE AGENCY COSTS OF DEBT AND EQUITY ARE RELATED TO OPTIONS.

6. EXPLAIN HOW OPTIONS CAN BE USED TO MANAGE A FIRM’S EXPOSURE TO RISK.

Financial Options

oA financial option is a derivative security in that its value is derived from

the value of another asset.

oThe ow

ner of a financial option has the right, but not the obligation, to buy or sell an asset on or before a specified date for a specified price.

oThe asset that the ow

ner has a right to buy or sell is know

n as the underlying asset.

Financial Options

oThe last date on w

hich an option can be exercised is called the exercise date or expiration date, and the price at w

hich the option holder can buy or sell the asset is called the exercise price or strike price.

Financial Options

o CALL OPTIONS• A call option gives the owner the right to buy,

or “call,” the underlying asset.• Once the asset price goes above the exercise

price, the value of the call option at exercise increases dollar for dollar with the price of the underlying asset.

• The buyer pays the seller a fee to purchase the option.

• This fee, which is known as the call premium, makes the total return to the seller positive when the price of the underlying asset is near or below the exercise price.

Exhibit 20.1: Payoff Functions

Financial Options

o PUT OPTIONS• The owner of a put option has

the right to sell the underlying asset at a pre-specified price.

• The payoff function for the owner of a put option is similar to that of a call option, but it is the reverse in the sense that the owner of a put option profits if the price of the underlying asset is below the exercise price.

• The owner of a put option will not want to exercise the option if the price of the underlying asset is above the exercise price.

Financial Options

o PUT OPTIONS• When the value of the

underlying asset is below the exercise price, however, the owner of the put option will find it profitable to exercise the option.

• The payoff for the seller of the put option is negative when the price of the underlying asset is below the exercise price.

• The seller of a put option hopes to profit from the fee, or put premium, that he or she receives from the buyer of the put option.

Exhibit 20.2: Payoff Functions

Financial Options

oAM

ERICAN, EU

ROPEAN

, AND

BERMU

DAN O

PTION

S•

Options that can only be

exercised on the expiration date are know

n as European options.

•A

merican options can

be exercised at any point in tim

e on or before the expiration date.

•B

ermudan options can

be exercised only on specific dates during the life of the option.

Financial Options

o MORE ON THE SHAPES OF OPTION PAYOFF FUNCTIONS• The payoff functions for

options are not straight lines for all possible values of the underlying asset.

• Each payoff function has a “kink” at the exercise price which exists because the owner of the option has a right, but not the obligation, to buy or sell the underlying asset. If it is not in the owner’s interest to exercise the option, he or she can simply let it expire.

Option Valuation

oIt is m

ore complicated to

determine the value of an

option at a point in time before

the expiration date because we

don’t know exactly how

the value of the underlying asset w

ill change over time, and

therefore we don’t know

if it w

ill make sense to exercise the

option.

Option Valuation

oLIM

ITS ON

OPTIO

N

VALUATION

•W

e know that the

value of a call option can never be less than zero, since the ow

ner of the option can alw

ays decide not to exercise it if doing so is not beneficial.

•The value of a call option can never be greater than the value of the underlying asset since it w

ould not make

sense to pay more

for the right to buy an asset than you w

ould pay for the asset itself.

Option Valuation

o LIMITS ON OPTION VALUATION• The value of a call option

prior to expiration will never be less than the value of that option at expiration because there is always a possibility that the value of the underlying asset will be greater than it is today at some time before the option expires.

Option Valuation

o LIMITS ON OPTION VALUATION• When we consider the value of a call

option at some point prior to expiration, we must compare the current value of the underlying asset with the present value of the exercise price, discounted at the risk-free rate.

• The present value of the exercise price is the amount an investor would have to invest in risk-free securities at any point prior to the expiration date to ensure that he or she would have enough money to exercise the option when it expires.

Exhibit 20.3: Values of a Call O

ption

Option Valuation

o VARIABLES THAT AFFECT OPTION VALUES• The higher the current

value of the underlying asset, the more likely it is that the value of the asset will be above the exercise price when the call option expires.

The opposite relation applies to the exercise price. The lower the exercise price, the more likely that the value of the underlying asset will be higher than the exercise price when the option nears expiration.

Option Valuation

o VARIABLES THAT AFFECT OPTION VALUES• The higher the current value of the

asset, the greater the likely difference between the value of the asset and the exercise price when the option expires.

In addition, the lower the exercise price, the more valuable the option is likely to be at expiration.

Option Valuation

o VARIABLES THAT AFFECT OPTION VALUES• The greater the volatility of the

underlying asset value, the higher the value of a call option on the asset prior to valuation.

• The intuition here is that the value of an option will increase more when the value of the underlying asset goes up than it will decrease when the value of the underlying asset goes down; this means that a greater potential change in the underlying price will be more beneficial to the value of the option.

Option Valuation

oVARIABLES THAT AFFECT O

PTION

VALUES

•The greater the tim

e to m

aturity, the more the

value of the underlying asset is likely to change by the tim

e the option expires; this increases the value of an option.

•The tim

e until the expiration aff

ects the value of a call option through its eff

ect on the volatility of the value of the underlying asset.

•The value of a call option increases w

ith the risk-free rate.

Option Valuation

oVARIABLES THAT AFFECT O

PTION

VALUES

•Exercising a call option involves paying cash in the future for the underlying asset.

•The higher the interest rate, the low

er the present value of the am

ount that the owner

of a call option will have

to pay to exercise it, w

hich translates into value for the ow

ner of the option.

Option Valuation

oTHE BIN

OM

IAL OPTIO

N PRICIN

G M

ODEL

•This sim

ple model

assumes that the

underlying asset will

have one of only two

possible values when

the option expires.•

The value of the underlying asset w

ill either increase to som

e value above the exercise price or decrease to som

e value below the

exercise price.

Option Valuation

o THE BINOMIAL OPTION PRICING MODEL• To solve for the value of the call

option using this model, we must assume that investors have no arbitrage opportunities with regard to this option.

• Arbitrage is the act of buying and selling assets in a way that yields a return above that suggested by the Security Market Line (SML).

• To value the call option in our simple model, we will first create a portfolio that consists of the asset underlying the call option and a risk-free loan.

Option Valuation

oTHE BIN

OM

IAL OPTIO

N PRICIN

G M

ODEL

•The relative investm

ents in these tw

o assets will

be selected so that the com

bination of the asset and the loan have the sam

e cash flows as the

call option when it

expires, regardless of w

hether the value of the underlying asset goes up or dow

n.•

This is called a replicating portfolio, since it replicates the cash flow

s of the option.

Option Valuation

o THE BINOMIAL OPTION PRICING MODEL• The replicating portfolio

will consist of:“x” shares of the underlying stock;a risk-free loan with a face value of “y”.

• The value of the call option can be calculated as follows:

Solve for the values of “x” and “y”.Multiply the current cost of the underlying stock by “x”.Subtracting “y” from the above amount will yield the value of the call option.

Option Valuation

oPU

T-CALL PARITY•

Although there are

other methods, the

value of a put option can be calculated by the relationship of a put to a call option w

ith the sam

e maturity and

exercise price.This relation is called the put-call

parity.

Option Valuation

oPU

T-CALL PARITY

where:

P is the value of the put optionC is the value of the call optionX is the exercise priceV is the current value of the

underlying assete is the exponential function

rtP C Xe V (20.1)

Option Valuation

oPut-call parity exam

ple:•

What is the value of

AB

C corporation put

option if C=

$5.95, X

=$55, r=

0.05, t=1, and

V=

$50?P = $5.95 + $55e-(0.05)(1) - $50 = $5.95 + $52.32 - $50 = $8.27

Option Valuationo VALUING OPTIONS ASSOCIATED WITH THE FINANCIAL

SECURITIES THAT FIRMS ISSUE• Financial options are often included in

the financial securities that firms issue and they make the valuation of those securities more complicated.

• The key principle that is used in valuing securities with options is known as the principle of value additivity.

It states that if two independent assets are bundled together, the total value of both assets equals the sum of their individual values.

Real Options

oReal options are options on real assets.

oN

PV analysis does not adequately reflect the value of real options.

oIt m

ight not always be possible

to directly estimate the value of

the real options associated with

a project, it is important to

recognize that they exist when

we perform

a project analysis.

Real Options

oO

PTION

S TO DEFER

INVESTM

ENT

•A

n example from

the text is that of the R

ussian government

and an oil field developm

ent project. The R

ussian governm

ent waited to

see what happened to

the price of oil before deciding to exercise its option to acquire an ow

nership interest in the Sakhalin II project.

Real Options

o OPTIONS TO DEFER INVESTMENT• The underlying asset in this

option is the stream of cash flows that the developed oil field would produce, while the exercise price is the amount of money that the company would have to spend to develop it (drill the well and build any necessary infrastructure).

• The value of an option to defer investment is not reflected in a NPV analysis as it does not allow for the possibility of deferring an investment decision.

Real Options

oO

PTION

S TO M

AKE FOLLO

W-O

N

INVESTM

ENTS

•Som

e projects open the door to future business opportunities that w

ould not otherwise be

available. This type of real option is an option to m

ake follow-on

investments.

•O

ptions to make follow

-on investm

ents are inherently diff

icult to value because, at the tim

e we are evaluating

the original project, it m

ay not be obvious what

the follow-on projects

will be.

Real Options

oO

PTION

S TO M

AKE FOLLO

W-O

N

INVESTM

ENTS

•Even if w

e know w

hat the projects w

ill be, we

are unlikely to have enough inform

ation to estim

ate what they are

worth.

•Projects that lead to investm

ent opportunities that are consistent w

ith a com

pany’s overall strategy are m

ore valuable than otherw

ise sim

ilar projects that do not.

Real Options

o OPTIONS TO CHANGE OPERATIONS• Are related to the flexibility that managers

have once an investment decision has been made.

• These include the option to change operations and to abandon a project; they affect the NPV of a project and must be taken into account at the time the investment decision is made.

• The changes that managers might make can involve something as simple as reducing output if prices decline or increasing output if prices increase.

Real Options

oO

PTION

S TO ABAN

DON

PRO

JECTS•

An option to abandon a

project is the ability to choose to term

inate a project by shutting it dow

n. •

Managem

ent will save

money that w

ould otherw

ise be lost if the project kept going. The am

ount saved represents the gain from

exercising this option.

Real Options

oCO

NCLU

DING CO

MM

ENTS O

N

NPV AN

ALYSIS AND REAL

OPTIO

NS

•In order to use N

PV

analysis to value the option to expand operations, w

e would

not only have to estim

ate all the cash flow

s associated with

the expansion but would

also have to estimate

the probability that we

would actually

undertake the expansion and determ

ine the appropriate rate at w

hich to discount the value of the expansion back to the present.

Agency Costs

oAgency conflicts betw

een stockholders and debt holders and betw

een stockholders and m

anagers arise because the interests of stockholders, lenders (creditors), and m

anagers are not perfectly aligned.

oO

ne reason is that the claims

that they have against the cash flow

s produced by the firm have

payoff functions that look like different types of options.

Agency Costso

AGENCY CO

STS OF DEBT

•The payoff

functions for stockholders and lenders (creditors) diff

er as do the payoff

functions for different

options.•

The payoff function for

the stockholders looks exactly like that of the ow

ner of a call option, w

here the exercise price is the am

ount owed on

the loan and the underlying asset is the firm

itself.

Agency Costso

AGENCY CO

STS OF DEBT

•If the value of the firm

exceeds the exercise price, the stockholders w

ill choose to exercise their option; and if it does not exceed the exercise price, they w

ill let their option expire unexercised.

•O

ne way to think about

the payoff function for

the lenders is that when

they lend money to the

firm, they are

essentially selling a put option to the stockholders.

Agency Costs

oAGEN

CY COSTS O

F DEBT•

This option gives the stockholders the right to “put” the assets to the lenders for an exercise price that equals the am

ount they ow

e.•

When the value of the

firm is less than the

exercise price, the stockholders w

ill exercise their option by defaulting.

Exhibit 20.4: Payoff Function

Agency Costs

o AGENCY COSTS OF DEBT• The Dividend Payout Problem

The incentives that stockholders of a leveraged firm have to pay themselves dividends arise because of their option to default.If a company faces some realistic risk of going bankrupt, the stockholders might decide that they are better off taking money out of the firm by paying themselves dividends.This situation can arise because the stockholders know that the bankruptcy laws limit their possible losses.

Agency Costs

o AGENCY COSTS OF DEBT• The Asset-Substitution Problem

When bankruptcy is possible, stockholders have an incentive to invest in very risky projects, some of which might even have negative NPVs.Stockholders have this incentive because they receive all of the benefits if things turn out well but do not bear all of the costs if things turn out poorly.

Agency Costs

o AGENCY COSTS OF DEBT• The Underinvestment Problem

Stockholders have incentives to turn down positive-NPV projects when all of the benefits are likely to go to the lenders. The problem arises from the differences in the payoff functions.

Agency Costso AGENCY COSTS OF EQUITY

• Managers are hired to manage the firm on behalf of the stockholders but managers do not always act in the stockholders’ best interest.

• The payoff function for a manager can be quite different from that for stockholders. In fact, it can look a lot like that of a lender.

• If a company gets into financial difficulty and a manager is viewed as responsible, that manager could lose his or her job and find it difficult to obtain a similar job at another company.

Agency Costs

o AGENCY COSTS OF EQUITY• The most obvious way for a company

to get into financial difficulty is to default on its debt.

• So, as long as a company is able to avoid defaulting on its debt, a manager has a reasonable chance of retaining his or her job.

Agency Costs

o AGENCY COSTS OF EQUITY• The fact that the payoff function for

a manager resembles that of a lender means that managers, like lenders, have incentives to invest in less risky assets and to distribute less value through dividends and stock repurchases than the stockholders would like them to.

Exhibit 20.5: Payoff Function

Options and Risk Management

o Risk management typically involves hedging, or reducing the financial risks faced by a firm.

o Options, along with other derivative instruments, such as forwards, futures, and swaps, are commonly used to reduce risks associated with commodity prices, interest rates, foreign exchange rates, and equity prices.

Options and Risk Managemento One interesting benefit of using options in this way is

that they provide downside protection but do not limit the upside.• This is just like buying insurance.

Many insurance contracts are really little more than specialized put options.

o Options and other derivative instruments can be used to manage commodity price risks, large swings in interest rates, risks associated with foreign exchange rates, as well as to manage risks associated with equity prices as occurs within defined benefit pension plans.