Consider an economy with two states. Suppose that a firm produces 1 unit of a single output with no cost. The output will be sold in 1 year, and the price of the output will be (10, 40) depending on the states. It has a liability of R to the debt holders of the firm. Furthermore, suppose that the prices of the basic (Arrow-Debreu) securities for both states are 0.5 (i.e., 1 = 2 = 0.5). Not that, if cash flow is above R, the debt holder receives R and if the cash flow is below R, the debt holder receives the entire cash flow.

a. Show that the firm can hedge its cash-flow by trading options on its output, so that its cash-flow becomes 25 in both states. What type of options should the firm trade and how does it achieve the cash flow of 25? Explain with supporting calculations.

b. If there is no tax nor default (bankruptcy) cost, what is the market value of the firm before and after hedging using the strategy in part 1 (assuming cost of hedging is borne by the equity holders? Does the value of the firm depend on the level of debt (i.e., value of R)?

c. Suppose that R=20 and that before the debt payment is due and after the firms cash-flow is realized, the firm is given an investment opportunity such that investment of 10 will generate a payoff of 15 for certain. If the firms equity holder makes decision on whether to undertake this investment opportunity, will the investment be undertaken? Consider the cases with and without hedging to eliminate uncertainty. Calculate the market value of the firm in both cases. Should the firm undertake the investment? Explain briefly