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Example of a Bank's Expected Return Calculation with Default Probability
Calculating Required Interest Rate with Default Risk
A commercial bank is structuring a portfolio of many identical small business loans. The bank's goal is to achieve an overall expected return of 4% on the total amount loaned out. Based on historical data, the bank anticipates that 12% of these borrowers will default and be unable to repay any amount. To compensate for this risk and meet its goal, what is the minimum interest rate the bank must charge on the loans that are successfully repaid? Provide the final interest rate and a brief outline of your calculation.
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Formula for Expected Return on a Loan Portfolio with Default Risk
A financial institution provides 200 separate small business loans, each for $5,000. The institution charges an interest rate of 15% on each loan. Based on its risk assessment model, the institution projects that 6% of these businesses will fail and be unable to repay any portion of their loan. The remaining businesses are expected to repay their loans in full, including interest. What is the total amount of money the institution can expect to receive back from this entire portfolio of 200 loans?
Loan Portfolio Profitability Analysis
Calculating Required Interest Rate with Default Risk
A commercial bank issues 1,000 identical loans of $10,000 each. The bank charges an annual interest rate of 12% on these loans. Based on historical data, the bank anticipates that 8% of the borrowers will be unable to repay any amount, while the remaining borrowers will repay their loans in full with interest. Which statement best analyzes the financial outcome for the bank from this portfolio?
A bank has a large, diversified portfolio of loans. It currently charges an 18% interest rate and anticipates that 5% of its borrowers will default, repaying nothing. The remaining 95% are expected to repay in full. Which of the following independent changes to its lending model would result in the largest increase in the bank's expected return per dollar loaned?
A bank issues a large number of identical loans. It expects 5% of these loans to default, with the borrowers paying back nothing. To break even on its entire loan portfolio (i.e., to have an expected return of 0%), the bank must charge an interest rate of exactly 5% on the loans that are repaid.
A financial institution is deciding between two strategies for a loan portfolio valued at $100,000.
- Strategy A: Offer loans at a 20% interest rate, anticipating that 10% of borrowers will default and repay nothing.
- Strategy B: Offer loans at a 15% interest rate, anticipating that only 5% of borrowers will default and repay nothing.
By calculating the total expected monetary return for each strategy, determine which one is more profitable and by how much.
A bank issues a portfolio of 100 loans, each for $1,000, at an interest rate of 22%. The bank projects that 10% of the loans will default, with nothing being repaid. The remaining 90% of loans will be repaid in full with interest. Which of the following statements accurately breaks down the bank's expected net profit from this entire portfolio?
Bank Lending Strategy Evaluation
A bank has a loan portfolio totaling $1,000,000. The bank charges a 15% interest rate on all loans. Based on its analysis, the bank anticipates that 95% of the loans will be repaid in full (principal plus interest), while the remaining 5% will default, resulting in a complete loss of the principal for those loans. Match each financial component with its correct calculated value based on this scenario.