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	$

c. Which project would the firm’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 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

Probability(P) Low High PX PY P(X-mean)2 P(Y-mean)2

volatility(X)   volatility(Y)

0.50 4900 4300 4900*0.50=2450 4300*0.50=2150 101250 551250   

0.50   5800   6400 5800*0.50=2900   6400*0.50=3200 101250 551250 PX=5350 PY=5350 =202500 =1102500

a. Expected value of the firm if low volatility project is undertaken=PX=$5350

Expected value of the firm if high volatility project is undertaken=PY=$5350

b.Vaue of equity= Value of firm- Value of bond

Expected value of the firm's equity if low volatility project is undertaken=$5350-$4900=400

Expected value of the firm's equity if high volatility project is undertaken=$5350-$4900=400

c.Since NPV of project is same.Now we need to calculate coefficient of variation.

Coefficient of variation= S.D./Mean *100

S.D.of project X===square root of 202500=450,Mean=PX=5350

S.D. of project Y=square root of 1102500=1050,Mean =PY=5350

Coefficient of variation of low volatilty project=450/5350*100=8.41%

Coefficient of variation of high volatilty project=1050/5350*100=19.62%

Project having lower coefficient of varaiation is better i.e.low volatility project.

d.$4900 is the payment to bondholders would make stockholders indifferent between the two projects