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 $5,400 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	$ 5,400	$ 4,800
Good	.50	6,550	7,150

  

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?
	Low-volatility project High-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

Answer-A Expected Value of the Firm

As the chosen project will be the only activity of the company, the expected value of the project would be the expected value of the firm. To calculate the expected value of the project multiply the probability of each state of economy with the value in that state and add up all values as under;

                Value with Low Volatility Project = (5400 * 0.50) + (6550 * 0.50) = $5,975

                Value with High Volatility Project = (4800 * 0.50) + (7150 * 0.50) = $5,975

Answer-B Expected Value of the Company’s Equity

The value of the company’s equity is the value of the company after payment to the bondholders. To calculate the value of the equity, multiply the probability of each state of economy with the value in that state after deducting bondholder’s payment as under;

       Value with Low Volatility Project = 0.50 (5400 – 5400) + 0.50 (6550 – 5400) = (0.50 * 0) + (0.50 * 1150) = $575

       Value with High Volatility Project = 0.50 (4800 – 5400) + 0.50 (7150 – 5400) = (0.50 * 0) + (0.50 * 1750) = $875

(Note: In case of high volatility project, payoff in bad state of economy ($4800) would not be sufficient to cover payment to bondholders ($5400), therefore payoff to equity holders would be 0.

Answer-C: High volatility project offers maximum value to equity holder i.e. $875 that is more than the equity value from low volatility project. Therefore, the company’s stockholders will prefer the high volatility project.

Answer-D:

Let assume that payment to be made to bondholder in case of high volatility project is X,

Stockholder will be indifferent between two projects when both project will offer same equity value, i.e.

Value of equity in case High Volatility Project = Value of Equity in Case Low volatility Project

(Here, Value of equity in case of low volatility project is $575 as calculated above, and

(Value of equity in case of high volatility project will be calculate assuming payment to be made to bondholder is X)

(0.50 * 0) + (0.50 * (7150 – X) = 575

0 + 3575 – 0.50X = 575

0.50X = 3000

X = 6000