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 enjoy 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

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Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

V. Risk and Return

14. Options and Corporate Finance

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Robert C. Merton on Applications of Options Analysis

Organized markets for trading options on stocks, fixed-income securities, currencies, financial futures, and a variety of commodities are among the most successful financial innovations of the past generation. Commercial success is not, however, the reason that option pricing analysis has become one of the cornerstones of finance theory. Instead, its central role derives from the fact that optionlike structures permeate virtually every part of the field.

From the first observation 30 years ago that leveraged equity has the same payoff structure as a call option, option pricing theory has provided an integrated approach to the pricing of corporate liabilities, including all types of debt, preferred stocks, warrants, and rights. The same methodology has been applied to the pricing of pension fund insurance, deposit insurance, and other government loan guarantees. It has also been used to evaluate various labor contract provisions such as wage floors and guaranteed employment including tenure.

A significant and recent extension of options analysis has been to the evaluation of operating or "real" options in capital budgeting decisions. For example, a facility that can use various inputs to produce various

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outputs provides the firm with operating options not available from a specialized facility that uses a fixed set of inputs to produce a single type of output. Similarly, choosing among technologies with different proportions of fixed and variable costs can be viewed as evaluating alternative options to change production levels, including abandonment of the project. Research and development projects are essentially options to either establish new markets, expand market share, or reduce production costs. As these examples suggest, options analysis is especially well suited to the task of evaluating the "flexibility" components of projects. These are precisely the components whose values are particularly difficult to estimate by using traditional capital budgeting techniques.

Robert C. Merton is the John and Natty McArthur University Professor at Harvard University. He was previously the J.C. Penney Professor of Management at MIT. He received the 1997 Nobel Prize in Economics for his work on pricing options and other contingent claims and for his work on risk and uncertainty.

sections, a portfolio that has the present value of $800 invested in a risk-free asset and ($1,200 - 800)/(200 - 0) = 2 call options exactly replicates the value of the assets of the firm.

The present value of $800 at the risk-free rate of 12.5 percent is $800/1.125 = $711.11. This amount, plus the value of the two call options, is equal to $950, the current value of the firm:

Because the call option in this case is actually the firm's equity, the value of the equity is $119.44. The value of the debt is thus $950 - 119.44 = $830.56.

Finally, because the debt has a $1,000 face value and a current value of $830.56, the interest rate is ($1,000/830.56) - 1 = 20.4%. This exceeds the risk-free rate, of course, because the debt is now risky.

EXAMPLE 14.3 |

Equity as a Call Option

Swenson Software has a pure discount debt issue with a face value of $100. The issue is due in a year. At that time, the assets of the firm will be worth either $55 or $160, depending on the sales success of Swenson's latest product. The assets of the firm are currently worth $110. If the risk-free rate is 10 percent, what is the value of the equity in Swenson? The value of the debt? The interest rate on the debt?

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

V. Risk and Return

14. Options and Corporate Finance

© The McGraw-Hill Companies, 2002

CHAPTER 14 Options and Corporate Finance

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