Answer: 2.73%

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: 1. **Economic Capital**: This is 10% of the loan amount, which is JPY 4,200,000,000 * 0.10 = JPY 420,000,000. 2. **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. 3. **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. 4. **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. 5. **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. 6. **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. 7. **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%.

Author: LeetQuiz Editorial Team