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National Cleaner Corp.needs a $1.5 million loan to finance a project that pays off next period.There are two projects available, A and B.You are a lending officer and know about the projects but cannot control the borrower's project choice.A will yield a payoff of $6.75 million with probability 0.6 or zero with probability 0.4.B will pay off $8 million with probability 0.5 or zero with probability 0.5.Everybody is risk neutral and the riskless interest rate is 10%.You consider designing a loan contract that involves the use of collateral However, collateral is costly and $1 of the borrower's collateral is worth only 90 cents to your bank.
-Suppose you assume that A will be chosen, and offer an unsecured loan.What project will the firm choose and what is the interest rate?
A)Project A with net expected payoff $6.75 million, interest rate 10%
B)Project A with net expected payoff $2.4 million, interest rate 83.33%
C)Project A with net expected payoff $2.25 million, interest rate 57%
D)Project B with net expected payoff $2.625 million, interest rate 83.33%
E)Project B with net expected payoff $4 million, interest rate 57%

Question

Use the following information for questions 
National Cleaner Corp.needs a $1.5 million loan to finance a project that pays off next period.There are two projects available, A and B.You are a lending officer and know about the projects but cannot control the borrower's project choice.A will yield a payoff of $6.75 million with probability 0.6 or zero with probability 0.4.B will pay off $8 million with probability 0.5 or zero with probability 0.5.Everybody is risk neutral and the riskless interest rate is 10%.You consider designing a loan contract that involves the use of collateral However, collateral is costly and $1 of the borrower's collateral is worth only 90 cents to your bank.
-Suppose you assume that A will be chosen, and offer an unsecured loan.What project will the firm choose and what is the interest rate?
A)Project A with net expected payoff $6.75 million, interest rate 10%
B)Project A with net expected payoff $2.4 million, interest rate 83.33%
C)Project A with net expected payoff $2.25 million, interest rate 57%
D)Project B with net expected payoff $2.625 million, interest rate 83.33%
E)Project B with net expected payoff $4 million, interest rate 57%

Quizplus · Accepted Answer

Given the risk-neutral assumption and the inability to control the borrower's project choice, the firm will choose the project with the highest net expected payoff. For Project A, the expected payoff is $6.75 million * 0.6 = $4.05 million. For Project B, it's $8 million * 0.5 = $4 million. However, considering the loan amount ($1.5 million) and the interest rate (10%), the net expected payoff calculation changes. The interest on the loan is $1.5 million * 10% = $0.15 million, so the total repayment is $1.5 million + $0.15 million = $1.65 million. Subtracting the repayment from the expected payoffs: For Project A, $4.05 million - $1.65 million = $2.4 million. For Project B, $4 million - $1.65 million = $2.35 million. However, the firm will choose the project based on the contract designed assuming Project A will be chosen, which might alter the expected payoffs due to the structure of the loan (interest rates, collateral requirements, etc.). The correct choice involves understanding that the firm will opt for the project that maximizes its net expected payoff under the loan terms provided, which, based on the information given, aligns with Project B due to the higher initial expected payoff despite the equal probability of zero return. The interest rate calculation seems to be misunderstood in the question setup, as it directly asks for the project choice and interest rate without providing a clear mechanism for how the interest rate affects the project choice or how it's calculated based on the project's expected payoffs.

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