Assume that you and your bank agree that the probability that you will default on a loan and repay nothing is 15% and that the appropriate interest rate is 6%. What interest rate would
You have to promise to pay in order to get a loan, assuming risk-neutrality? What is your cost
Of capital?

Question

Quizplus · Accepted Answer

The correct interest rate to promise, accounting for the default risk, can be calculated by dividing the desired interest rate (6%) by the probability of not defaulting (1 - 0.15 = 0.85), which gives 6% / 0.85 = 7.06%. However, this calculation does not match any of the provided options, indicating a misunderstanding in the question's interpretation. Typically, to find the rate that compensates for the risk of default, one would adjust the interest rate upwards to ensure the expected return equals the risk-free return. The cost of capital remains at the risk-free rate (6%) from the lender's perspective, assuming risk neutrality. However, without the correct calculations aligning with the provided options, the explanation intended here is to illustrate the general approach to adjusting for default risk, which seems to have been misapplied. The correct approach involves ensuring the expected return (accounting for the probability of default and the higher interest rate charged to offset this risk) equals the lender's required return. The options given do not accurately reflect this calculation, suggesting a possible error in the question or a misunderstanding in the explanation provided.

Assume That You and Your Bank Agree That the Probability