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
o A financial option is a derivative security in
that its value is derived from the value of
another asset.
o The owner 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.
o The asset that the owner has a right to buy or
sell is known as the underlying asset.
Financial Options
o The last date on which an option can be
exercised is called the exercise date or
expiration date, and the price at which 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
o AMERICAN, EUROPEAN, AND BERMUDAN
OPTIONS
• Options that can only be exercised on the
expiration date are known as European options.
• American options can be exercised at any point
in time on or before the expiration date.
• Bermudan 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
o It is more 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
will change over time, and therefore we don’t
know if it will make sense to exercise the
option.
Option Valuation
o LIMITS ON OPTION VALUATION
• We know that the value of a call option can
never be less than zero, since the owner of the
option can always 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
would not make sense to pay more for the right
to buy an asset than you would 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 riskfree 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 Option
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
o VARIABLES THAT AFFECT OPTION VALUES
• The greater the time to maturity, the more the
value of the underlying asset is likely to change
by the time the option expires; this increases the
value of an option.
• The time until the expiration affects the value of
a call option through its effect on the volatility
of the value of the underlying asset.
• The value of a call option increases with the
risk-free rate.
Option Valuation
o VARIABLES THAT AFFECT OPTION VALUES
• Exercising a call option involves paying cash in
the future for the underlying asset.
• The higher the interest rate, the lower the
present value of the amount that the owner of a
call option will have to pay to exercise it, which
translates into value for the owner of the option.
Option Valuation
o THE BINOMIAL OPTION PRICING MODEL
• This simple model assumes that the underlying
asset will have one of only two possible values
when the option expires.
• The value of the underlying asset will either
increase to some value above the exercise price
or decrease to some 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
o THE BINOMIAL OPTION PRICING MODEL
• The relative investments in these two assets will
be selected so that the combination of the asset
and the loan have the same cash flows as the
call option when it expires, regardless of
whether the value of the underlying asset goes
up or down.
• This is called a replicating portfolio, since it
replicates the cash flows 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
o PUT-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 with the same maturity
and exercise price.
This relation is called the put-call parity.
Option Valuation
o PUT-CALL PARITY
P  C  Xert  V
(20.1)
where:
P is the value of the put option
C is the value of the call option
X is the exercise price
V is the current value of the underlying asset
e is the exponential function
Option Valuation
o Put-call parity example:
• What is the value of ABC 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 Valuation
o 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
o Real options are options on real assets.
o NPV analysis does not adequately reflect the
value of real options.
o It might 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
o OPTIONS TO DEFER INVESTMENT
• An example from the text is that of the Russian
government and an oil field development
project. The Russian government waited to see
what happened to the price of oil before
deciding to exercise its option to acquire an
ownership 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
o OPTIONS TO MAKE FOLLOW-ON
INVESTMENTS
• Some projects open the door to future business
opportunities that would not otherwise be
available. This type of real option is an option to
make follow-on investments.
• Options to make follow-on investments are
inherently difficult to value because, at the time
we are evaluating the original project, it may not
be obvious what the follow-on projects will be.
Real Options
o OPTIONS TO MAKE FOLLOW-ON
INVESTMENTS
• Even if we know what the projects will be, we
are unlikely to have enough information to
estimate what they are worth.
• Projects that lead to investment opportunities
that are consistent with a company’s overall
strategy are more valuable than otherwise
similar 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
o OPTIONS TO ABANDON PROJECTS
• An option to abandon a project is the ability to
choose to terminate a project by shutting it
down.
• Management will save money that would
otherwise be lost if the project kept going. The
amount saved represents the gain from
exercising this option.
Real Options
o CONCLUDING COMMENTS ON NPV ANALYSIS
AND REAL OPTIONS
• In order to use NPV analysis to value the option
to expand operations, we would not only have to
estimate all the cash flows associated with the
expansion but would also have to estimate the
probability that we would actually undertake the
expansion and determine the appropriate rate at
which to discount the value of the expansion
back to the present.
Agency Costs
o Agency conflicts between stockholders and
debt holders and between stockholders and
managers arise because the interests of
stockholders, lenders (creditors), and
managers are not perfectly aligned.
o One reason is that the claims that they have
against the cash flows produced by the firm
have payoff functions that look like different
types of options.
Agency Costs
o AGENCY COSTS OF DEBT
• The payoff functions for stockholders and
lenders (creditors) differ as do the payoff
functions for different options.
• The payoff function for the stockholders looks
exactly like that of the owner of a call option,
where the exercise price is the amount owed on
the loan and the underlying asset is the firm
itself.
Agency Costs
o AGENCY COSTS OF DEBT
• If the value of the firm exceeds the exercise
price, the stockholders will choose to exercise
their option; and if it does not exceed the
exercise price, they will let their option expire
unexercised.
• One 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
o AGENCY COSTS OF DEBT
• This option gives the stockholders the right to
“put” the assets to the lenders for an exercise
price that equals the amount they owe.
• When the value of the firm is less than the
exercise price, the stockholders will 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 positiveNPV projects when all of the benefits are likely to go to
the lenders. The problem arises from the differences in
the payoff functions.
Agency Costs
o 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 Management
o 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.