Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionV. Risk and Return 14. Options and Corporate
Finance© The McGraw−Hill^497
Companies, 2002aged firm (one that has issued debt) is effectively a call option on the assets of the firm.
This is a remarkable observation, and we explore it next.
Looking at an example is the easiest way to get started. Suppose a firm has a single
debt issue outstanding. The face value is $1,000, and the debt is coming due in a year.
There are no coupon payments between now and then, so the debt is effectively a pure
discount bond. In addition, the current market value of the firm’s assets is $950, and the
risk-free rate is 12.5 percent.
In a year, the stockholders will have a choice. They can pay off the debt for $1,000
and thereby acquire the assets of the firm free and clear, or they can default on the debt.
If they default, the bondholders will own the assets of the firm.
In this situation, the stockholders essentially have a call option on the assets of the
firm with an exercise price of $1,000. They can exercise the option by paying the
$1,000, or they can choose not to exercise the option by defaulting. Whether or not they
will choose to exercise obviously depends on the value of the firm’s assets when the
debt becomes due.
If the value of the firm’s assets exceeds $1,000, then the option is in the money, and
the stockholders will exercise by paying off the debt. If the value of the firm’s assets is
less than $1,000, then the option is out of the money, and the stockholders will optimally
choose to default. What we now illustrate is that we can determine the values of the debt
and equity using our option pricing results.
Case I: The Debt Is Risk-Free
Suppose that in one year the firm’s assets will be worth either $1,100 or $1,200. What
is the value today of the equity in the firm? The value of the debt? What is the interest
rate on the debt?
To answer these questions, we first recognize that the option (the equity in the firm) is
certain to finish in the money because the value of the firm’s assets ($1,100 or $1,200) will
always exceed the face value of the debt. In this case, from our discussion in previous sec-
tions, we know that the option value is simply the difference between the value of the un-
derlying asset and the present value of the exercise price (calculated at the risk-free rate).
The present value of $1,000 in one year at 12.5 percent is $888.89. The current value of
the firm is $950, so the option (the firm’s equity) is worth $950 888.89 $61.11.
What we see is that the equity, which is effectively an option to purchase the firm’s as-
sets, must be worth $61.11. The debt must therefore actually be worth $888.89. In fact, we
really didn’t need to know about options to handle this example, because the debt is risk-
free. The reason is that the bondholders are certain to receive $1,000. Because the debt is
risk-free, the appropriate discount rate (and the interest rate on the debt) is the risk-free
rate, and we therefore know immediately that the current value of the debt is $1,000/1.125
$888.89. The equity is thus worth $950 888.89 $61.11, as we calculated.
Case II: The Debt Is Risky
Suppose now that the value of the firm’s assets in one year will be either $800 or $1,200.
This case is a little more difficult because the debt is no longer risk-free. If the value of
the assets turns out to be $800, then the stockholders will not exercise their option and
will thereby default. The stock is worth nothing in this case. If the assets are worth
$1,200, then the stockholders will exercise their option to pay off the debt and will en-
joy a profit of $1,200 1,000 $200.
What we see is that the option (the equity in the firm) will be worth either zero or $200.
The assets will be worth either $1,200 or $800. Based on our discussion in previous
CHAPTER 14 Options and Corporate Finance 469