Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 14. Options and Corporate

Finance

© The McGraw−Hill^487

Companies, 2002

FUNDAMENTALS OF OPTION VALUATION

Now that we understand the basics of puts and calls, we can discuss what determines
their values. We will focus on call options in the discussion that follows, but the same
type of analysis can be applied to put options.

Value of a Call Option at Expiration

We have already described the payoffs from call options for different stock prices. In
continuing this discussion, the following notation will be useful:

S 1 Stock price at expiration (in one period)
S 0 Stock price today
C 1 Value of the call option on the expiration date (in one period)
C 0 Value of the call option today
EExercise price on the option
From our previous discussion, remember that, if the stock price (S 1 ) ends up below
the exercise price (E) on the expiration date, then the call option (C 1 ) is worth zero. In
other words:

C 1 0 if S 1 E

Or, equivalently:

C 1 0 if S 1 
 E 0 [14.1]

This is the case in which the option is out of the money when it expires.
If the option finishes in the money, then S 1 E, and the value of the option at expi-
ration is equal to the difference:

C 1 S 1 
 Eif S 1 E

Or, equivalently:

C 1 S 1
Eif S 1
E 0 [14.2]
For example, suppose we have a call option with an exercise price of $10. The option
is about to expire. If the stock is selling for $8, then we have the right to pay $10 for
something worth only $8. Our option is thus worth exactly zero because the stock price
is less than the exercise price on the option (S 1 E). If the stock is selling for $12, then
the option has value. Because we can buy the stock for $10, the option is worth S 1
E
$12
10 $2.
Figure 14.1 plots the value of a call option at expiration against the stock price. The
result looks something like a hockey stick. Notice that for every stock price less than E,
the value of the option is zero. For every stock price greater than E,the value of the call
option is S 1
E. Also, once the stock price exceeds the exercise price, the option’s value
goes up dollar for dollar with the stock price.

The Upper and Lower Bounds on a Call Option’s Value

Now that we know how to determine C 1 , the value of the call at expiration, we turn to a
somewhat more challenging question: How can we determine C 0 , the value sometime
beforeexpiration? We will be discussing this in the next several sections. For now, we
will establish the upper and lower bounds for the value of a call option.

CHAPTER 14 Options and Corporate Finance 459

14.2

To learn more about

options, visit http://www.

e-analytics.com.