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 $5,500 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: Economy Probability Low-Volatility Project Payoff High-Volatility Project Payoff Bad .50 $5,500 $4,900 Good .50 6,700 7,300 a. What is the expected value of the firm if the low-volatility project is undertaken? What if the high-volatility project is undertaken? (Do not round intermediate calculations and round your answers to the nearest whole dollar amount (e.g., 32).) Expected value of the firm Low-volatility project value $ High-volatility project value $ b. 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? (Do not round intermediate calculations and round your answers to the nearest whole dollar amount (e.g., 32).) Expected value of the firm's equity Low-volatility project value $ High-volatility project value $ c. Which project would the firm’s stockholders prefer? Low-volatility project High-volatility project 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? (Do not round intermediate calculations and round your answers to the nearest whole dollar amount (e.g., 32).)

Explanation / Answer

1. Expected value of the firm if low volatility project is undertaken:

Low volatility project value = .50($5,500)+.50($6,700)

=$2,750+$3,350 =$6,100

High volatility project value = .50($4,900)+.50($7,300)

=$2,450+$3,650 =$6,100

Expected value of the firm is same for both, low volatility and high volatility projects.

2. The value of equity is the residual value of the firm after the bondholders are paid off. If the low-volatility project is undertaken, the value of the firm's equity will be $0 if the ecomomy is bad and $1,200 if the economy is good. If the high-volatility project is undertaken, the value of the firm's equity will be $0 if the ecomomy is bad and $1,800 if the economy is good.

Expected value of equity with low volatility project =.50($0)+.50($1,200) = $600

Expected value of equity with high volatility project =.50($0)+.50($1,800) = $900

3. The firm's stockholders prefer the high-volatility project since it maximizes the expected value of the company's equity.

4. The payment to bondholders would make stockholders indifferent between the two projects:

In order to make stockholders indifferent between the low-volatility and high-volatiltiy project, the expected value of equity of high-volatity project should equal the expected value of equity of low-volatility project

Expected value of equity = $600 =.50($0)+.50($7,300-X)

X = $6,100

The payment to bondholders would make stockholders indifferent between the two projects = $ 6,100.

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