Question

11 and 12. Please show work. thank you!

Use the following information for questions 11 and 12 A bank is planning to make a loan of $2,000,000. It expects to charge a loan application processing fee of 0.75 %. The loan has a maturity of 12 years with duration of 9.15 years. The cost of funds (the RAROC benchmark) for the bank is 7.75%. Historically, the bank has estimated a maximum change in the risk premium for similar risk customers to be approximately 5.65%. The current market interest rate for loans to similar risk customers is 119% 11. Should the bank make this loan? Why? A. Yes, because the market rate of interest of 11 % is greater than the cost of funds of 7.75%. B. Yes, because RAROC of 7.92% is greater than the RAROC benchmark of 7.75% C. Yes, because RAROC of 8.59% is greater than the RAROC benchmark of 7.75% D. No, because the loan at risk is almost half the proposed loan amount E. None of the above 12. What should be the minimum duration in order for this loan to be approved? A. 12 years B.9.15 years C. 11.23 years D. 10.56 years E. None of the above

Answer 1

11). RAROC = net interest and fees income/loan at risk

Loan at risk = -duration*loan amount*(expected change in risk premium/(1+ loan interest rate))

= -9.15*2,000,000*(5.65%/(1+11%)) = 931,486.49

Net interest and fees income = (interest rate + processing fees %age - cost of funds)*loan amount

= (11%+0.75%-7.75%)*2,000,000 = 80,000

RAROC = 80,000/931,486.49 = 8.59%

Option C is correct. RAOC of 8.59% is higher than the benchmark RAROC so the loan can be made.

12). For the minimum duration, RAROC = benchmark RAROC of 7.75%

Duration*loan amount*(expected change in risk premium/(1+ loan interest rate)) = Net interest and fees income/7.75%

Duration*2,000,000*(5.65%/(1+11%)) = 80,000/7.75%

Duration = 10.14 years (option E - none of the above)