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 $4,900 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		$	4,900			$	4,300
Good		.50			5,800				6,400

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	$

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). Low-volatility project value = 0.50($4,900) + 0.50($5,800) = $2,450 + $2,900 = $5,350

High-volatility project value = 0.50($4,300) + 0.50($6,400) = $2,150 + $3,200 = $5,350

b). The value of the equity is the residual value of the company after the bondholders are paid off. If the low-volatility project is undertaken, the firm’s equity will be worth $0 if the economy is bad and $900 if the economy is good. Since each of these two scenarios is equally probable, the expected value of the firm’s equity is:

Expected value of equity with low-volatility project = .50($0) + .50($900) = $450

And the value of the company if the high-volatility project is undertaken will be:

Expected value of equity with high-volatility project = .50($0) + .50($1,500) = $750

d). In order to make stockholders indifferent between the low-volatility project and the high-volatility project, the bondholders will need to raise their required debt payment so that the expected value of equity if the high-volatility project is undertaken is equal to the expected value of equity if the low-volatility project is undertaken. As shown in part b, the expected value of equity if the low-volatility project is undertaken is $450. If the high-volatility project is undertaken, the value of the firm will be $4,300 if the economy is bad and $6,400 if the economy is good.If the economy is bad, the entire $4,300 will go to the bondholders and stockholders will receive nothing. If the economy is good, stockholders will receive the difference between $6,400, the total value of the firm, and the required debt payment. Let X be the debt payment that bondholders will require if the high-volatility project is undertaken. In order for stockholders to be indifferent between the two projects, the expected value of equity if the high-volatility project is undertaken must be equal to $300, so:

Expected value of equity = $450 = 0.50($0) + 0.50($6,400 – X)

$450 = $3,200 - 0.50X

0.5X = $2,750

x = $2,750/0.5 = $5,500