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There are two types of borrowers, low risk L and high risk H.As a lending officer, you cannot distinguish between the two types of borrowers.You believe, however, that there is a 0.5 probability that a randomly chosen borrower is L, and 0.5 that it is H.There are 500 potential loan applicants, each requiring $150.Type L will invest this loan in a single-period project that pays $250 with probability 0.8 or zero with probability 0.2.Type H will invest the loan in a single-period project that pays $275 with probability 0.5 and zero with probability 0.5.Your bank is a monopolist to these borrowers.The riskless interest rate is 6%, and a borrower must have at least $2 of net profit in the successful state in order to apply for the loan.Everybody is risk neutral and suppose that you have $75,000 to lend.
-Suppose that you have decided to charge 65% interest rate.What would be the type L's net profit in the successful state?

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There are two types of borrowers, low risk L and high risk H.As a lending officer, you cannot distinguish between the two types of borrowers.You believe, however, that there is a 0.5 probability that a randomly chosen borrower is L, and 0.5 that it is H.There are 500 potential loan applicants, each requiring $150.Type L will invest this loan in a single-period project that pays $250 with probability 0.8 or zero with probability 0.2.Type H will invest the loan in a single-period project that pays $275 with probability 0.5 and zero with probability 0.5.Your bank is a monopolist to these borrowers.The riskless interest rate is 6%, and a borrower must have at least $2 of net profit in the successful state in order to apply for the loan.Everybody is risk neutral and suppose that you have $75,000 to lend.
-Suppose that you have decided to charge 65% interest rate.What would be the type L's net profit in the successful state?

Quizplus · Accepted Answer

For type L borrowers, the expected return on the investment is:

Expected Return = (0.8 x $250) + (0.2 x $0) = $200

The cost of the loan at 65% interest rate is:

Cost of Loan = $150 * (1 + 0.65) = $247.50

So, the net profit in the successful state for type L borrowers is:

Net Profit = $200 - $247.50 = -$47.50

However, since the borrower must have at least $2 of net profit in the successful state, the net profit is $0.

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