Question

Sheaves Corporation economists estimate that a good business environment and a bad business environment are equally likely for the coming year. Management must choose between two mutually exclusive projects. Assume that the project chosen will be the firm’s only activity and that the firm will close one year from today. The firm is obligated to make a $5,100 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		$	5,100			$	4,500
Good		.50			6,100				6,700

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, 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, 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?

High-volatility project

Low-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, e.g., 32.)

Payment to bondholders

Answer 1

a.

Value of firm - low volatility project	Value of firm - high volatility project
0.5*5100 + 0.5*6100 = $5600	0.5*4500 + 0.5*6700 = $5600

b.

Value of debt is given to be 5100, value of equity in both projects is given below:

Value of equity - low volatility project	Value of equity - high volatility project
0.5*0 + 0.5*(6100-5100) = $500	0.5*0 + 0.5*(6700-5100) = $800

The value of equity will be 0 when the economy is in bad shape as all the value of the firm belongs the debt.

c. Equity holder will choose high volatility project because they only have the possibility of having a share in the profit when the economy is in good shape and in the high volatility project the amount of profit they would get is much higher.

d. If the firm chooses the high volatility project the bondholders may lose an amount equal to $600 when the economy is in bad shape. So a payment of $600 to bondholders would make them indifferent between the two projects.