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 here:

Strategy

A B C D

Probability of Success 95% 83% 71% 59%

Firm Value if Successful (in $ million) 54 66 78 90

Assume that for each strategy, firm value is zero in the event of failure. Also, suppose Petron Corp. must pay a 25% tax rate on the amount of the final payoff that is paid to equity holders. It pays no tax on payments to, or capital raised from, debt holders.

a. Which strategy will Petron choose with no debt? Which will it choose with a face value of $9 million, $31 million, or $34 million in debt? (Assume management maximizes the value of equity, and in the case of ties, will choose the safer strategy.)

b. Given your answer to (a), show that the total combined value of Petron's equity and debt is maximized with a face value of $53 million in debt.

c. Show that if Petron has $31 million in debt outstanding, shareholders can gain by increasing the face value of debt to $53 million, even though this will reduce the total value of the firm

.

d. Show that if Petron has $53 million in debt outstanding, shareholders will lose by buying back debt to reduce the face value of debt to $31 million, even though that will increase the total value of the firm.

Equity Value

Debt Face Value A B C D

$0 $ $ $ $

Debt Face Value A B C D

$9 $ $ $ $

Debt Face Value A B C D

$31 $ $ $ $

Debt Face Value A B C D

$53 $ $ $ $

b. Given your answer to (a), show that the total combined value of Petron's equity and debt is maximized with a face value of $53 million in debt.

Calculate the total value of the firm:

Deface Face Value $0

Debt Value ?

Equity Value ?

Firm Value ?

Deface Face Value $9

Debt Value ?

Equity Value ?

Firm Value ?

Deface Face Value $31

Debt Value ?

Equity Value ?

Firm Value ?

Deface Face Value $53

Debt Value ?

Equity Value ?

Firm Value ?