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You are evaluating a loan request of $2.5 million from Dubious Corp.The firm has an existing debt repayment obligation of $5 million.It has $2.6 million of equity.The firm has two projects, A and B.An investment in A will yield a payoff of $5 million with probability
0.8 and $2.5 million with probability 0.2.Project B will yield a payoff of $8 million with probability 0.4 and zero with probability 0.6.The firm has assets-in-place that generates $6 million with probability 0.8 and zero with probability 0.2.Assume that the distributions of payoff from projects A and B are common knowledge, and the payoff from A is statistically independent of the payoff from B.However, as a bank lending officer, you cannot observe the firm's project choice.
-Under the assumption that the firm doesn't have equity capital and the loan is priced assuming that A is chosen, what will be the expected value of equity if the firm switches to project B?
A)$4.16 million
B)$3.56 million
C)$2.36 million
D)$1.90 million
E)$1.88 million

Question

Use the following information for questions 
You are evaluating a loan request of $2.5 million from Dubious Corp.The firm has an existing debt repayment obligation of $5 million.It has $2.6 million of equity.The firm has two projects, A and B.An investment in A will yield a payoff of $5 million with probability
0.8 and $2.5 million with probability 0.2.Project B will yield a payoff of $8 million with probability 0.4 and zero with probability 0.6.The firm has assets-in-place that generates $6 million with probability 0.8 and zero with probability 0.2.Assume that the distributions of payoff from projects A and B are common knowledge, and the payoff from A is statistically independent of the payoff from B.However, as a bank lending officer, you cannot observe the firm's project choice.
-Under the assumption that the firm doesn't have equity capital and the loan is priced assuming that A is chosen, what will be the expected value of equity if the firm switches to project B?
A)$4.16 million
B)$3.56 million
C)$2.36 million
D)$1.90 million
E)$1.88 million

Quizplus · Accepted Answer

The expected payoff from project B is (0.4 * $8 million) + (0.6 * $0) = $3.2 million. The expected payoff from assets-in-place is (0.8 * $6 million) + (0.2 * $0) = $4.8 million. Total expected payoff = $3.2 million + $4.8 million = $8 million. The debt obligation is $5 million, so the expected value of equity is $8 million - $5 million = $3 million. However, since the loan is priced assuming project A is chosen, the expected value of equity is reduced by the difference in expected payoffs between projects A and B, which is $5 million (expected payoff from A) - $3.2 million (expected payoff from B) = $1.8 million. Therefore, the expected value of equity if the firm switches to project B is $3 million - $1.8 million = $1.88 million.

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