Part 1.
Sunburn Sunscreen has a zero coupon bond issue outstanding with a $20,000 face value that matures in one year. The current market value of the firm's assets is $21,700. The standard deviation of the return on the firm's assets is 38 percent per year, and the annual risk-free rate is 5 percent per year, compounded continusously. Based on the Black-Scholes moel, what is the market value of the firm's equity and debt?
Part 2.
Suppose the firm in the previous problem is considering two mutually exclusive investments. Project A has an NPV of $1,200, and Project B has an NPV of $1,600. As a result of taking Project A, the standard deviation of the return on the firm's assets will increase to 55 percent per year. If Project B is taken, the standard deviation will fall to 34 percent per year.
A) What is the value of he firm's equity and debt if Project A is undertaken? If Project B is undertaken?
B) Which project would the stockholders prefer? Can you reconcile your anser with the NPV rule?
C) Suppose the stockholders and bondholders are, in fact, the same group of investors. Would this affect your answer to (B)?
D) What does this problem suggest to you about stockholders incentives?