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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.
-What is the interest rate for the secured loan?
A)120%
B)83.33%
C)57.33%
D)27.08%
E)15.75%

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.
-What is the interest rate for the secured loan?
A)120%
B)83.33%
C)57.33%
D)27.08%
E)15.75%

Quizplus · Accepted Answer

The interest rate for the secured loan can be calculated by considering the amount borrowed, the riskless interest rate, and the value of collateral. Given a $1.5 million loan and a riskless interest rate of 10%, the repayment amount without considering collateral would be $1.5 million * (1 + 10%) = $1.65 million. Since collateral is involved and it's worth 90 cents on the dollar to the bank, the bank would require collateral that, to the borrower, is worth the difference between the loan repayment amount and the loan amount, adjusted for the collateral's value to the bank. However, the question does not provide specific details on the amount of collateral required or its impact on the calculation of the interest rate directly. Therefore, without additional information on how the collateral affects the repayment amount or the calculation of the interest rate, we can't directly calculate the interest rate based on collateral value. The correct answer must be derived from the information given, which does not directly lead to a calculation involving collateral's depreciated value to the bank. The interest rate calculation typically involves the loan amount, the repayment amount, and the period, without directly adjusting the rate based on collateral's depreciated value.

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