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Project A

Project B

Market value of equity

$ 5.938

$8.730

Market value of debt

$18.062

$13.27

There is a dramatic difference between the two projects. Project A benefits both the stockholders and the bondholders, but most of the gain goes to the bondholders. Project B has a huge impact on the value of the equity plus it reduces the value of the debt. Clearly, the stockholders prefer B.

What are the implications of our analysis? Basically, what we have discovered is two things. First, when the equity has a delta significantly smaller than 1.0, any value created

Ross et al.: Fundamentals VIII. Topics in Corporate 24. Option Valuation of Corporate Finance, Sixth Finance

Ross et al.: Fundamentals VIII. Topics in Corporate 24. Option Valuation of Corporate Finance, Sixth Finance Edition, Alternate Edition

832 PART EIGHT Topics in Corporate Finance 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:

Market value of assets

$20 million

Face value of pure discount debt

$100 million

Debt maturity

5 years

Asset return standard deviation

50 percent

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

Market value of equity

$2 million

Market value of debt

$18 million

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:

Project NPV

-$1 million

Market value of firm's assets ($20 million + NPV)

$19 million

Firm's asset return standard deviation

70 percent

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:

Market value of equity

$4.821 million

Market value of debt

$14.179 million

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 incentive to go for a long shot, even if that long shot has a negative NPV. It's a bit like using your very last dollar on a lottery ticket. It's a bad investment, but there aren't a lot of other options!

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