Question

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: LOADING.... Assume that for each​ strategy, firm value is zero in the event of failure.​ Also, suppose Petron Corp. has debt with a face value of $ 42 million outstanding. For simplicity assume all risk is​ idiosyncratic, the​ risk-free interest rate is​ zero, and there are no taxes. a. 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? b. Suppose Petron issues equity and buys back its​ debt, reducing the​ debt's face value to $ 5 million. If it does​ so, which strategy will it choose after the​ transaction? Will the total value of the firm​ increase? c. 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? d. Based on your answer to ​(c​), how much will Petron need to raise from equity holders in order to buy back the​ debt? e. 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?

Table

Strategy
	A	B	C	D
Probability of Success	100%	81%	62%	43%
Firm Value if Successful​ (in $​ million)	52	64	76	88

Answer 1

Given that all risks are idiosyncratic, that means both equity and debt have their own risks and not dependent on each other.

Answer (a):

The Expected Value of Equity = (Probability of Success * Equity Value if success) + (Probability of failure * Equity Value if failure)

Given Firm Value if successful for different strategy.

Also given that current Debt face value is $ 42 Million.

Hence, Equity Value if successful = Face value if successful – Debt

Given that, Equity Value if failure = 0

See below the Calculation of Expected value of Equity in all the 4 Stratergies

As above, once can see that Expected Value of Equity is Maximum in if the company chooses Strategy C.

The Expected Value of Equity is $ 21.08 Millions.

Total Firm Value in Strategy is $ 63.08 Millions.

Answer (b)

After Equity raise the Deb is reduced to $ 5 Million

After equity raise the Expected value of equity as indicated in the above image is maximum in Strategy B which the company will choose.

The Expected value of Equity and Firm value can bee observed in the above figure under the strategy B.

Answer (c)

Debt Seller can expect $ 42.79 Millions