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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.
-Suppose that the firm doesn't have equity capital.As a lending officer, what is the repayment obligation that you require to break-even, assuming that project A will be undertaken?
A)$2.5 million
B)$2.6 million
C)$3.125 million
D)$3.765 million
E)$4.125 million

Question

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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.
-Suppose that the firm doesn't have equity capital.As a lending officer, what is the repayment obligation that you require to break-even, assuming that project A will be undertaken?
A)$2.5 million
B)$2.6 million
C)$3.125 million
D)$3.765 million
E)$4.125 million

Quizplus · Accepted Answer

If project A is undertaken, the expected payoff is $5 million * 0.8 + $2.5 million * 0.2 = $4.5 million. The firm will still need to repay its existing debt of $5 million, leaving a deficit of $0.5 million. To break-even, the lending officer should require a repayment obligation of $4.5 million / 0.72 (the probability of the assets-in-place generating cashflow) = $6.25 million. However, since the firm only has $2.6 million of equity, the maximum repayment obligation it can afford is $6.25 million - $2.6 million = $3.65 million. Adding the deficit of $0.5 million, the required repayment obligation is $3.65 million + $0.5 million = $3.125 million. Therefore, the correct answer is C.

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