Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

VIII. Topics in Corporate

Finance

24. Option Valuation © The McGraw−Hill^857
    Companies, 2002

will go partially to bondholders. Second, stockholders have a strong incentive to increase

the variance of the return on the firm’s assets. More specifically, stockholders will have

a strong preference for variance-increasing projects as opposed to variance-decreasing

ones, even if that means a lower NPV.

Let’s do one final example. Here is a different set of numbers:

The risk-free rate is 4 percent, so the equity and debt values are:

Notice that the change from our previous example is the face value of the debt is $100

million, so the option is far out of the money. The delta is only .24, so most of any value

created will go to the bondholders.

The firm has an investment under consideration, which must be taken now or never.

The project affects both the market value of the firm’s assets and the firm’s asset return

standard deviation as follows:

Thus, the project has a negative NPV, but it increases the standard deviation of the

firm’s return on assets. If the firm takes the project, here is the result:

This project more than doubles the value of the equity! Once again, what we are seeing

is that stockholders have a strong incentive to increase volatility, particularly when the

option is far out of the money. What is happening is that the shareholders have relatively

little to lose because bankruptcy is the likely outcome. As a result, there is a strong in-

centive to go for a long shot, even if that long shot has a negative NPV. It’s a bit like us-

ing your very last dollar on a lottery ticket. It’s a bad investment, but there aren’t a lot

of other options!

CONCEPT QUESTIONS

24.5a What is a pure financial merger?

24.5bWhy might stockholders in a leveraged firm prefer a low NPV project over a

higher NPV project?

Market value of equity $4.821 million

Market value of debt $14.179 million

Project NPV 
$1 million

Market value of firm’s assets ($20 million NPV) $19 million

Firm’s asset return standard deviation 70 percent

Market value of equity $2 million

Market value of debt $18 million

Market value of assets $20 million

Face value of pure discount debt $100 million

Debt maturity 5 years

Asset return standard deviation 50 percent

832 PART EIGHT Topics in Corporate Finance