Inverse Relationship Between Default Probability and Expected Return

Calculating Expected Return on a Startup Loan Portfolio

A commercial bank issues a $50,000 loan to a company at an annual interest rate of 10%. The bank's analysts determine that there is a 92% probability the company will repay the loan in full, but an 8% probability of a complete default where nothing is recovered. What is the bank's expected percentage return on this loan?

Determining Minimum Interest Rate Based on Default Risk

A bank is considering two loans of the same principal amount. Loan A has a 15% interest rate and a 90% probability of full repayment. Loan B has a 10% interest rate and a 95% probability of full repayment. Assuming zero recovery in case of default, the bank's expected return is higher for Loan A than for Loan B.

A financial institution is evaluating a portfolio of similar loans. Each loan has a principal amount of $50,000, an interest rate of 12%, and a 90% probability of being fully repaid. In the event of non-repayment, the institution recovers nothing. Match each calculated value below to the concept it represents in the expected return analysis for a single loan.

Implied Repayment Probability from Expected Return

Critique of the Expected Loan Return Model

A bank's loan portfolio has an average interest rate of 10% and an average repayment probability of 95%, with zero recovery on defaulted loans. To improve profitability, management is debating two proposals. Proposal 1 is to increase the average interest rate to 11%. Proposal 2 is to implement a new screening process that increases the average repayment probability to 96%. Which proposal would lead to a higher expected return for the bank?

Evaluating Loan Viability

Calculating Expected Return with Collateral