# Agency Costs & Expected Value of a Firm

Sheaves Corporation economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The manager 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 $8,000 payment to bondholders at the end of the year. The projects have the same systematic risk, but different volatities. Consider the following information pertaining to the two projects:

Economy Probability Low-Volatity Project Payoff High-Volatility Project Payoff

Bad .5 $8,000 $7,200

Good .5 8,600 9,200

a. What is the expected value of the firm if the low-volatility project is undertaken? What if the high-volatility project is undertaken? Which of the two strategies maximized value of the firm?

b. What is the expected value of the firm's equity if the low-volatility project is undertaken and the high-volatility project is undertaken?

c. Which project would the firm's stockholders prefer? explain

d. 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?

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The solution answers the following questions:

a. What is the expected value of the firm if the low-volatility project is undertaken? What if the high-volatility project is undertaken? Which of the two strategies maximized value of the firm?

b. What is the expected value of the firm's equity if the low-volatility project is undertaken and the high-volatility project is undertaken?

c. Which project would the firm's stockholders prefer? explain

d. 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?