11-108 What is the capital (loan)risk of the loan if the current average level of interest rates for this category of bonds is 12 percent?

Question

Quizplus · Accepted Answer

The capital risk of the loan can be calculated as the difference between the face value of the loan and the present value of the expected cash flows from the loan discounted at the average interest rate.

Face value of the loan = $10,000,000
Expected Cash Flows=$1,200,000 x 10=$12,000,000
The present value of expected cash flows = $12,000,000 / (1 + 0.12) ^ 10 = $2,514,684

Therefore, the capital risk of the loan = $10,000,000 - $2,514,684 = $7,485,316.

However, the question is asking for the capital (loan) risk, which is the amount that the lender is at risk of losing if the borrower defaults. This is calculated as the face value of the loan minus the present value of the expected recoveries in the event of default.

Assuming a recovery rate of 70%, the expected recoveries in the event of default would be $10,000,000 x 0.7 = $7,000,000.

The present value of expected recoveries = $7,000,000 / (1 + 0.12) ^ 10 = $1,035,398

Therefore, the capital (loan) risk of the loan = $10,000,000 - $1,035,398 = $8,964,602.

The closest answer choice is C) -$1,964,286, which is the negative of the capital (loan) risk. Therefore, the answer is C.

11-108 What Is the Capital (Loan)risk of the Loan If