Apex Corporation's economic unit estimates that the probability of a good business environment next year is equal to the probability of a bad environment. Knowing that, the managers of Apex must choose between two mutually exclusive projects, project A and project B, which will provide the only assets of the firm. Apex has outstanding a zero coupon bond with a face value of $300m, maturing next year, when the project chosen will have its only payoff. The firm has currently available cash of $200m. Project A requires an initial investment of $100m, while project B requires $200m; final payoffs one year from now are: State of the economy: Good Bad Probability: 1/2 1/2 Project A $400m $300m Project B $800m $50m The appropriate discount rate for these projects is the risk-free rate, which is assumed to be equal to zero. There are no taxes.

a) Which project maximizes the market value of the firm? 

b) Which project maximizes the market value of equity? 

c) Explain your results. 

d) Discuss how the use of a convertible bond may have been preferable in this case.