Question

Fountain Corporation’s economists estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of the company must choose between two mutually exclusive projects. Assume that the project the company chooses will be the company’s only activity and that the company will close one year from today. The company is obligated to make a $5,000 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	$ 5,000	$ 4,400
Good	.50	5,950	6,550

  

a.	What is the expected value of the company if the low-volatility project is undertaken? The high-volatility project? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)

  

Expected value of the company
Low-volatility project	$
High-volatility project	$

  

b.	What is the expected value of the company’s equity if the low-volatility project is undertaken? The high-volatility project? (Do not round intermediate calculations and round your answers to the nearest whole number, e.g., 32.)

  

Expected value of the company's equity
Low-volatility project	$
High-volatility project	$

   

c.	Which project would the company’s stockholders prefer?
	a - High-volatility project b - Low-volatility project

  

d.

Suppose bondholders are fully aware that stockholders might choose to maximize equity value rather than total company value and opt for the high-volatility project. To minimize this agency cost, the company's bondholders decide to use a bond covenant to stipulate that the bondholders can demand a higher payment if the company 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 answer to the nearest whole number, e.g., 32.)

  

Payment to bondholders

$

Answer 1

a. Given Information

Probability of bad economy (P_B) = 0.5

Probability of good economy (P_G) = 0.5

Expected Value of Company (CV_L) if Low volatility project is chosen –

CV_L = P_B * Payoff when economy bad + P_G * Payoff when economy good

CV_L = 0.5 * 5000 + 0.5 * 5950 = $5,475

Expected Value of Company (CV_H) if High volatility project is chosen –

CV_H = P_B * Payoff when economy bad + P_G * Payoff when economy good

CV_H = 0.5 * 4400 + 0.5 * 6550 = $5,475

b. Payoff to company’s equity are as follows –

Economy	Probability	Low Volatility Project Payoff to equity	High Volatility Project Payoff to equity
Bad	0.5	Max(0, (5000 – 5000) =0	Max(0, (4400 – 5000) =0
Good	0.5	Max(0, (5950 – 5000) =950	Max(0, (6550 – 5000) =1550

Payoff to company’s equity is calculated by deducting 5,000 from the total payoffs. Minimum payoff is limited to zero for equity.

So, Expected Value of equity (Low Volatility Project) = 0.5*0 + 0.5*950 =$475

Expected Value of equity (High Volatility Project) = 0.5*0 + 0.5*1550 =$775

c. Company’s stockholder would prefer High Volatility Project because the expected value to equity of $775 is higher than that from Low Volatility Project (i.e. $475)

d. To make stockholders indifferent between the two projects, the expected value to equity from High Volatility project needs to be equal to expected value to equity from Low Volatility project.

As the payoffs to equity in bad economy from both projects is equal to zero. So, the payoffs to equity from both projects in good economy needs to be equal.

Let’s assume the higher payment required by bondholders in case of high volatility project be H.

So, 950 = 1550 – H

=> H = $600 (higher payment required by bondholders in case of high volatility project)