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 $4,000 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	$ 4,000	$ 3,400
Good	.50	4,450	5,050

  

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?
	High-volatility project 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

Economy	Probability	Low volatility project payoff	High volatility project payoff
Bad	0.50	4000	3400
Good	0.50	4450	5050

a) Expected value:

• Low volatility project payoff = (0.50 * 4000) + (0.50 * 4450) = $4225
• High volatility project payoff = (0.50 * 3400) + (0.50 * 5050) = $4225

b) Expected value of company's equity:

Payment to bondholders= 4000

• Low volatility project payoff = 0.50 * (4000- 4000) + 0.50 * (4450- 4000) = $225
• High volatility project payoff = 0.50 * 0 + 0.50 * (5050- 4000) = $525

c) The company's managers will choose High volatility project when risk neutral as its payoff is more .

d) Payment to bondholders = 5050- (225/ 0.50) = $5050 - $450 = $4600