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Lender's Break-Even Condition for a Risky Loan
The break-even condition for a risky loan occurs when a lender's expected payoff is exactly zero, meaning the expected repayment equals the loan's principal (). For a loan with interest rate and probability of repayment , this condition is satisfied when the expected repayment, , equals , which simplifies to . Under this condition, the lender expects to neither gain nor lose money on average.
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- Loan Alpha offers a 15% interest rate, but the borrower has a profile that suggests an 85% probability of full repayment.
- Loan Beta offers a 10% interest rate, and this borrower's profile suggests a 95% probability of full repayment.
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Break-Even Analysis for a Risky Loan
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Lender's Break-Even Condition for a Risky Loan