Sheaves Corporation economists estimate that a good business environment and a b

Question

Sheaves Corporation economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of Sheaves must choose between two mutually exclusive projects. Assume that the project Sheaves chooses will be the firm’s only activity and that the firm will close one year from today. Sheaves is obligated to make a $4,000 payment to bondholders at the end of the year. The projects have the same systematic risk, but different volatilities. Consider the following information pertaining to the two projects:

  

  

What is the expected value of the firm if the low-volatility project is undertaken? What if the high-volatility project is undertaken?

What is the expected value of the firm’s equity if the low-volatility project is undertaken? What is it if the high-volatility project is undertaken?

Suppose bondholders are fully aware that stockholders might choose to maximize equity value rather than total firm value and opt for the high-volatility project. To minimize this agency cost, the firm's bondholders decide to use a bond covenant to stipulate that the bondholders can demand a higher payment if the firm chooses to take on the high-volatility project. What payment to bondholders would make stockholders indifferent between the two projects?

  Economy Probability Low-Volatility
Project Payoff High-Volatility
Project Payoff   Bad .50 $4,000       $3,400           Good .50 4,450         5,050        

Explanation / Answer

In simple language, Expected Value = Possible Outcome X Probability of outcome.

If low volatility project is selected, expected value of firm is: (0.5 X $4000) + (0.5 X 4450) = $4225.

Sheaves has an obligation of $4000 to bondholders; therefore expected value of equity is: Expected value of firm - Obligation to bondholders: $4225 - $4000 = $225. Expected value of equity = $225.

If the stockholders choose to take the High Volatility Project, the expected value of the firm will be (0.5 X $3400) + (0.5 X 5050) = $4225. Which is same as the Low Volatility Project pay-off. Hence the bondholders are indifferent to two projects.

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