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^489

Companies, 2002

If we put our two conditions together, we have:

C 0  0 if S 0 
 E  0 [14.4]

C 0 S 0 
 Eif S 0 
 E 0

These conditions simply say that the lower bound on the call’s value is either zero or
S 0
E, whichever is bigger.
Our lower bound is called the intrinsic valueof the option, and it is simply what the
option would be worth if it were about to expire. With this definition, our discussion
thus far can be restated as follows: at expiration, an option is worth its intrinsic value; it
will generally be worth more than that anytime before expiration.
Figure 14.2 displays the upper and lower bounds on the value of a call option. Also
plotted is a curve representing typical call option values for different stock prices prior
to maturity. The exact shape and location of this curve depends on a number of factors.
We begin our discussion of these factors in the next section.

A Simple Model: Part I

Option pricing can be a complex subject, and we defer a detailed discussion to a later
chapter. Fortunately, as is often the case, many of the key insights can be illustrated with
a simple example. Suppose we are looking at a call option with one year to expiration
and an exercise price of $105. The stock currently sells for $100, and the risk-free rate,
Rf, is 20 percent.
The value of the stock in one year is uncertain, of course. To keep things simple, sup-
pose we know that the stock price will be either $110or $130. It is important to note that

CHAPTER 14 Options and Corporate Finance 461

FIGURE 14.2

Value of a Call Option

Before Expiration for

Different Stock Prices

Slide14.9

Call price

(C 0 )

Stock price

(S 0 )

Exercise price

(E)

Upper bound

C 0  S 0

45 o

Lower bound

C 0  S 0 – E

C 0  0

Typical call

option values

As shown, the upper bound on a call's value is given by the value

of the stock (C 0  S 0 ). The lower bound is either S 0 – E or zero,

whichever is larger. The highlighted curve illustrates the value of

a call option prior to maturity for different stock prices.

intrinsic value

The lower bound of an

option’s value, or what

the option would be

worth if it were about to

expire.