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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.
-What is the interest rate charged assuming that A is chosen and the firm has no equity?
A)0%
B)4%
C)25%
D)51%
E)65%

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.
-What is the interest rate charged assuming that A is chosen and the firm has no equity?
A)0%
B)4%
C)25%
D)51%
E)65%

Quizplus · Accepted Answer

The expected payoff from project A is $4.4 million. With assets-in-place, the total expected payoff is $10.4 million. The firm needs to repay $7.5 million ($5 million existing debt + $2.5 million new loan). The interest rate is calculated as (10.4 - 7.5) / 2.5 = 1.16 or 116%, but since the firm has no equity, the interest rate is based on the loan amount, leading to a 25% interest rate.

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