Assume gold price risk is diversifiable, and the riskless rate is 5%. A firm produces a unit of gold a year from today. Assume all interest is compounded annually and is tax deductible. The price of gold is either $500 or $200, with probability 0.7 and 0.3, respectively.. Suppose the firm pays taxes at a rate of 40% for all its cash ow in excess of $300. The value of the firm is the expected discounted value of its cash flow less the expected discounted value of bankruptcy costs and taxes that it pays. The firm can hedge by buying/selling forward contracts on gold. Use this information to answer the below five questions c, d, e, f).

c) Find the value of the unhedged firm if it issues an optimally chosen quantity of safe debt.

(Hint: In both high and low income state, the tax payment and debt payment cannot exceed the pre-tax cash flow, or the price of gold)

d) Find the value of the hedged firm if it issues an optimally chosen quantity of safe debt.

In the remaining 2 questions ( e) and f) ) assume that bankruptcy costs are $20 per unit of gold.

e) If the firm issues $220 of risky debt, find the yield on the risky debt (x) and the value of the unhedged firm (V).

x=0.1948; V=340.1905

x=0.1494; V=340.1905

x=0.3594; V=337.1505

x=0.1494; V=355.69

f) Now suppose that the unhedged firm chooses the face value of risky debt optimally. Find the face value of debt (F) and the yield on the risky debt (x).

x=0.1578; F=340.1905

x=0.8619; F=340.1905

x=0.2849; F=358.68

x=0.3823; F=378.96