Financial Risk Manager Part 2

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Explanation:

The after-tax RAROC for the loan is calculated using the formula:

$\text{RAROC} = \frac{\text{After-tax expected risk-adjusted net income}}{\text{Economic capital}}$

The components of the formula are calculated as follows:

Economic Capital: This is 10% of the loan amount, which is JPY 4,200,000,000 * 0.10 = JPY 420,000,000.
Expected Revenue (ER): This is the annual interest rate received on the loan applied to the loan amount, which is JPY 4,200,000,000 * 0.032 = JPY 134,400,000.
Pre-tax Return on Invested Economic Capital (ROEC): This is the average pre-tax return on economic capital, which is JPY 420,000,000 * 0.014 = JPY 5,880,000.
Interest Cost (IC): This is the average annual interest rate paid on deposits applied to the loan amount, which is JPY 4,200,000,000 * 0.004 = JPY 16,800,000.
Operating Cost (OC): This is the annual operating costs applied to the loan amount, which is JPY 4,200,000,000 * 0.005 = JPY 21,000,000.
Expected Loss (EL): This is the expected loss rate applied to the loan amount, which is JPY 4,200,000,000 * 0.02 = JPY 84,000,000.
Taxes: These are calculated on the pre-tax income after accounting for all other costs and expected losses. The formula used is: $\text{Taxes} = (\text{Revenue} + \text{ROEC} - \text{IC} - \text{OC} - \text{EL}) \times \text{Tax rate}$ Substituting the values, we get: $\text{Taxes} = (134,400,000 + 5,880,000 - 16,800,000 - 21,000,000 - 84,000,000) \times 0.38$ $\text{Taxes} = (18,480,000) \times 0.38 = 7,022,400$

The after-tax expected risk-adjusted net income is then calculated by subtracting the taxes from the sum of expected revenue, ROEC, and other components before tax: $\text{After-tax expected risk-adjusted net income} = (ER + ROEC - IC - OC - EL) - \text{Taxes}$ $= (134,400,000 + 5,880,000 - 16,800,000 - 21,000,000 - 84,000,000) - 7,022,400$ $= 18,480,000 - 7,022,400 = 11,457,600$

Finally, the RAROC is calculated by dividing the after-tax expected risk-adjusted net income by the economic capital: $\text{RAROC} = \frac{11,457,600}{420,000,000}$ $\text{RAROC} = 0.0273 \text{ or } 2.73\%$

Therefore, the correct answer is B, which is 2.73%.

Explanation:

The after-tax RAROC for the loan is calculated using the formula:

$\text{RAROC} = \frac{\text{After-tax expected risk-adjusted net income}}{\text{Economic capital}}$

The components of the formula are calculated as follows:

Economic Capital: This is 10% of the loan amount, which is JPY 4,200,000,000 * 0.10 = JPY 420,000,000.
Expected Revenue (ER): This is the annual interest rate received on the loan applied to the loan amount, which is JPY 4,200,000,000 * 0.032 = JPY 134,400,000.
Pre-tax Return on Invested Economic Capital (ROEC): This is the average pre-tax return on economic capital, which is JPY 420,000,000 * 0.014 = JPY 5,880,000.
Interest Cost (IC): This is the average annual interest rate paid on deposits applied to the loan amount, which is JPY 4,200,000,000 * 0.004 = JPY 16,800,000.
Operating Cost (OC): This is the annual operating costs applied to the loan amount, which is JPY 4,200,000,000 * 0.005 = JPY 21,000,000.
Expected Loss (EL): This is the expected loss rate applied to the loan amount, which is JPY 4,200,000,000 * 0.02 = JPY 84,000,000.
Taxes: These are calculated on the pre-tax income after accounting for all other costs and expected losses. The formula used is: $\text{Taxes} = (\text{Revenue} + \text{ROEC} - \text{IC} - \text{OC} - \text{EL}) \times \text{Tax rate}$ Substituting the values, we get: $\text{Taxes} = (134,400,000 + 5,880,000 - 16,800,000 - 21,000,000 - 84,000,000) \times 0.38$ $\text{Taxes} = (18,480,000) \times 0.38 = 7,022,400$

Therefore, the correct answer is B, which is 2.73%.

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In the context of evaluating the financial performance of a 1-year loan from a regional commercial bank, consider the following specifics: The loan, amounting to JPY 4.2 billion, is financed entirely by deposits. The average annual interest rate paid on these deposits is 0.4%, while the loan earns an annual interest rate of 3.2%. The expected loss on the loan is 2.0% of its face value, and the bank incurs annual operating costs amounting to 0.5% of the loan's face value. Additionally, to support the loan, the bank requires economic capital equating to 10.0% of the loan amount. The average pre-tax return on this economic capital is 1.4%, and the effective tax rate applicable is 38%. Considering these parameters and the absence of other transfer costs, what is the Risk-Adjusted Return on Capital (RAROC) after taxes for this loan?

Exam-Like

0.27%

11.5%

2.73%

72.1%

4.40%