Final answer:
To calculate the expected probability of repayment, one must consider the difference of the average loan rate and the risk-free rate, adjusted by the loss given default. For the given scenario, with an average loan rate of 3.8%, a risk-free rate of 1.2%, and a 25% loss given default, the expected probability of repayment is 89.6%.
Step-by-step explanation:
The student's question is asking to calculate the expected probability of repayment using the given risk-free rate, market risk premium, average loan rate, and loss given default. This involves understanding the risk and pricing of financial instruments, specifically loans and bonds. When it comes to a bond issued at a certain interest rate below the prevailing market rates, the price of the bond must typically be discounted to make it attractive to investors. If the market interest rates increase, the value of the bond will decrease accordingly, so investors are compensated for the lower interest income received compared to newer issues.
The expected probability of repayment (Credit Spread) can be calculated by taking the difference between the average loan rate and the risk-free rate, then adjusting for the loss given default (LGD). So, if the average loan rate is 3.8%, and the risk-free rate is 1.2%, the credit spread is 2.6%. Given a 25% LGD, the market-implied expected probability of default (EPD) can be estimated as Credit Spread / LGD, which in this case will be 2.6% / 25% = 10.4%. Therefore, the expected probability of repayment is 1 - EPD, which corresponds to 89.6%.