1. Firm A considers to undertake a new project that will produce cash flows $180 next year if the economy is strong and $80 if the economy is weak. The economy will be strong with probability 50%. Firm A borrowed $90 by issuing debt with a face value $100. So, the firm will defaults when the economy is weak. Suppose the creditors will get only $16 in bankruptcy because of some bankruptcy costs. The tax rate is 30%. The risk-free rate is 5% and the market premium is 7%. The manager also issues equity and does not retain any equity ownership in the firm after equity issuance. For clarification, the creditors do not need to pay the tax on the abovementioned bankruptcy proceeds of $16. Put differently, $16 is the after-tax bankruptcy proceeds to the creditors.

(a) Calculate the equity payoffs for each of the economic outcomes.

(b) Calculate the total payments accrued to all the claim holders, that is, both equity holders and creditors, for each of the economic outcomes.

There is another firm, say, firm B, which has an identical project. That is, this project will produce $180 next year if the economy is strong and $80 if the economy is weak. But firm B issued only equity to finance this project.

(c) Calculate the total payments to all the claim holders (or, equivalently, to the equity holders in this case) for each of the economic outcomes.

(d) Which company between firm A and firm B can raise more funds? (Hint: If the total payments of firm A has a higher expected value and a lower variance than the total payments of firm B, then firm A can raise more funds, and vice versa.)

(e) Should an optimal level of face value be lower than 100 or higher than 100?