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 $4,300 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? (Do not round intermediate calculations and round your answers to the nearest whole dollar amount (e.g., 32).)

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).)

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).)

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 $4,300 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:

Explanation / Answer

a. Expected value

Low volatility firm = 0.5*4300 + 0.5*4900 = $4600

High volatility firm = 0.5*3700 + 0.5*5500 = $4600

b. Expected value of equity in low volatility firm will be 4300-4300 = 0 if economy is bad and 4900-4300 = 600 if economy is good. In case of high volatility firm, the expected value of equity will be 0 if economy is bad and 5500-4300= 1200 if the economy is good. Combining with the probabilities, the expected value of equity will be

Low volatility firm = 0.5*(0)+ 0.5*600 = $300

High volatility firm = 0.5*0+0.5*1200 = $600

c. The risk averse investors will prefer the low volatility firm while the risk neutral investors will prefer the high volatility firm since it will yield a higher value of equity.

d. Let the amount of payment to bondholders be X

The expected value of the equity if low volatility project is undertaken = 300. Thisshould be equal to the equity value of high volatility firm. Hence

300 = 0.5*(3700-3700) + 0.5*(5500-x)

300= 2750-0.5X

X= 2450/0.5 = 4900

Hence amount payable to bondholders will be $4900

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