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There are two types of borrower, L low risk and H high risk. The bank can distinguish the types but cannot control the borrower’s project choice. The borrower has a choice of two mutually exclusive projects: S safe and R risky. The project requires $250 investment. For borrower L, project S can generate $315 for sure; while project R generates $320 with probability 0.8 and zero with probability 0.2. For borrower H, project S can generate $320 with probability 0.8 and zero with probability 0.2; while project R generates $337 with probability 0.6 and zero with probability 0.4. The riskless interest rate is 6%, and the bank thinks that it can charge an additional 1.5% before a customer switches to another bank.
-Suppose that the bank charges 7.593%.What is the bank's expected profit to L? What is the expected profit to H?

Question

Use the following information for problems 
There are two types of borrower, L low risk and H high risk. The bank can distinguish the types but cannot control the borrower’s project choice. The borrower has a choice of two mutually exclusive projects: S safe and R risky. The project requires $250 investment. For borrower L, project S can generate $315 for sure; while project R generates $320 with probability 0.8 and zero with probability 0.2. For borrower H, project S can generate $320 with probability 0.8 and zero with probability 0.2; while project R generates $337 with probability 0.6 and zero with probability 0.4. The riskless interest rate is 6%, and the bank thinks that it can charge an additional 1.5% before a customer switches to another bank.
-Suppose that the bank charges 7.593%.What is the bank's expected profit to L? What is the expected profit to H?

Quizplus · Accepted Answer

For borrower L choosing project S, the expected return is $315. The bank charges 7.593% on the $250 loan, which amounts to $250 * 1.07593 = $268.98. Thus, the bank's expected profit from L is $315 - $268.98 = $46.02. However, for borrower H choosing project R, the expected return is $337 * 0.6 + $0 * 0.4 = $202.2. The bank's expected repayment is still $268.98, leading to an expected loss of $268.98 - $202.2 = -$66.78. The correct answer must account for the correct calculation of expected profits or losses, which involves subtracting the expected repayment from the expected returns of the projects. The provided choices do not directly match these calculations, indicating a potential misunderstanding in the question's setup or a mistake in the calculation process.

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