Wintech Corp. has a zero coupon bond issue outstanding with a $$15,000$ face value that matures in one year. The current market value of the firm$$s assets is $$15,800.$ The standard deviation of the return on the firm$$s assets is $38$ percent per year, and the annual risk$-$free rate is $5$ percent per year, compounded continuously.

a$.$ Based on the Black$-$Scholes model, what is the market value of the firm$$s equity and debt?

Wintech 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 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.

b$.$ What is the value of the firm$$s equity and debt if Project A is undertaken? If Project B is undertaken?

c$.$ Which project would the stockholders prefer? Which project would make society as a whole better off? Can you reconcile your answer with the NPV rule?

d$.$ Suppose the stockholders and bondholders are, in fact, the same group of investors. Would this affect your answer to $($c$)?$

e$.$ What does this problem suggest to you about stockholder incentives?