Equity As A Call Option On The Firms Assets

Now that we understand the basic determinants of an option's value, we turn to examining some of the many ways that options appear in corporate finance. One of the most important insights we gain from studying options is that the common stock in a lever-

Ross et al.: Fundamentals V. Risk and Return 14. Options and Corporate of Corporate Finance, Sixth Finance

Edition, Alternate Edition aged 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.

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