Task #3 (The Agency Costs of Leverage). Petron Corporation's management team is meeting to decide on a new corporate strategy. There are four options, each with a different probability of success and total firm value in the event of success, as shown below: C B 100% 80% 60% 40% 60 70 80 Strategy A Probability of success Firm value if successful (in $ million) 50 Assume that for each strategy, firm value is zero in the event of failure. a) Which strategy has the highest expected payoff? b) Suppose Petron's management team will choose the strategy that leads to the highest expected value of Petron's equity. Which strategy will management choose if Petron currently has (i) No debt? (ii) Debt with a face value of $20 million? (iii) Debt with a face value of $40 million? c) What agency cost of debt is illustrated in your answer to part (b)? Now suppose Petron Corp. has debt with a face value of $40 million outstanding. For simplicity assume all risk is idiosyncratic, the risk-free interest rate is zero, and there are no taxes. d) What is the expected value of equity, assuming Petron will choose the strategy that maximizes the value of its equity? What is the total expected value of the firm? e) Suppose Petron issues equity and buys back its debt, reducing the debt's face value to $5 million. If it does so, what strategy will it choose after the transaction? Will the total value of the firm increase? f) Suppose you are a debt holder, deciding whether to sell your debt back to the firm. If you expect the firm to reduce its debt to $5 million, what price would you demand to sell your debt? g) Based on your answer to f), how much will Petron need to raise from equity holders in order to buy back the debt? h) How much will equity holders gain or lose by recapitalizing to reduce leverage? How much will debt holders gain or lose? Would you expect Petron's management to choose to reduce its leverage? 5