Question

Economists at The Wells Corporation estimate that a good business environment and a bad business environment are equally likely for the coming year. The managers of Wells must choose between two mutually exclusive projects. Assume that the project Wells chooses will be the firm’s only activity and that the firm will close one year from today. Wells is obligated to make a $4,500 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 Payoff	High Volatility Payoff
Bad	0.5	4023	3627
Good	0.5	5235	5511

What is the expected value of the firm if the low volatility project is undertaken? (Round answer to 0 decimal places. Do not round intermediate calculations)

What is the expected value of the firm if the high volatility project is undertaken? (Round answer to 0 decimal places. Do not round intermediate calculations)

What is the expected value of the firm’s equity if the low volatility project is undertaken? (Round answer to 0 decimal places. Do not round intermediate calculations)

What is the expected value of the firm’s equity if the high volatility project is undertaken? (Round answer to 0 decimal places. Do not round intermediate calculations)

*This is an indirect agency cost issue. Note which project adds the most value to the firm vs. which project is more likely to be undertaken by the firm’s equity holders.

Answer 1

The expected value of each project/firm is the sum of the probability of each state of the economy times the value in that state of the economy.

Low-volatility project value = 0.50($4,023) + 0.50($5,235 )

Expected Value of firm if low volatility project is undertaken = $4,629

High-volatility project value = 0.50($3,627) + 0.50($5,511)

Expected value of the firm if the high volatility project is undertaken = $4,569

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 $735 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 firm's equity with low-volatility project = 0.50($0) + 0.50($5,235 - 4,500)

Expected value of equity with low-volatility project = $367.5 or $367(Rounded off)

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

Expected value of equity with high-volatility project = 0.50($0) + 0.50($5,511- $4,500)

Expected value of equity with high-volatility project = $505.5 or $505(Rounded off)