The duration of a soon to be approved loan of $10 million is four years.The 99^th percentile increase in risk premium for bonds belonging to the same risk category of the loan has been estimated to be 5.5 percent. If the minimum RAROC acceptable to the bank is 8 percent, what should be its expected percentage fee income in order for it to approve the loan?

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Quizplus · Accepted Answer

The expected percentage fee income can be calculated using the formula for RAROC (Risk-Adjusted Return on Capital), which is given by the return (in this case, the fee income) over the capital at risk (the loan amount) adjusted for the risk premium. The bank requires a minimum RAROC of 8%, and the risk premium increase is 5.5%. To find the fee income percentage that would satisfy the RAROC requirement, we set up the equation:$$ \text{RAROC} = \frac{\text{Fee Income}}{\text{Loan Amount} \times (1 + \text{Risk Premium Increase})} $$Given that the RAROC required is 8% (or 0.08 when expressed as a decimal), the loan amount is $10 million, and the risk premium increase is 5.5% (or 0.055 when expressed as a decimal), we can solve for the Fee Income percentage:$$ 0.08 = \frac{\text{Fee Income}}{10,000,000 \times (1 + 0.055)} $$$$ \text{Fee Income} = 0.08 \times 10,000,000 \times (1 + 0.055) $$$$ \text{Fee Income} = 800,000 \times 1.055 $$$$ \text{Fee Income} = 844,000 $$To find the fee income as a percentage of the loan amount:$$ \text{Fee Income Percentage} = \frac{844,000}{10,000,000} \times 100 $$$$ \text{Fee Income Percentage} = 8.44\% $$However, this calculation does not directly lead to the correct answer because the question seems to involve a more complex calculation or possibly a misunderstanding in the setup. The correct approach should consider the impact of the risk premium on the required return and how the fee income contributes to meeting the RAROC requirement. Given the options and the nature of the question, it seems there might be a mistake in the calculation or interpretation of the question as presented. The correct calculation should involve determining how much fee income is needed to achieve an 8% return over the risk-adjusted loan amount, taking into account the increase in risk premium. However, without the exact formula or additional details on how the fee income is expected to compensate for both the risk premium and achieve the RAROC, it's challenging to arrive at the options provided directly. The response assumes a straightforward calculation that does not match the provided options, indicating a need for clarification or a more detailed formula that incorporates the specifics of RAROC calculation in this context.

The Duration of a Soon to Be Approved Loan of $10