Question

9. A proposed loan of $8m has total annual interest rate 5.875% and fees of 0.25%. The loan’s duration is 6.14 years. The lender’s cost of funds is 5.525%. Comparable loans have a yield of 5.875%. The expected maximum change in the loan rate due to a change in the credit risk premium for the loan is 0.85%. (This value is based on actual change in credit risk premium for the worst 1% of comparable loans over some prior period.)

a. What is the risk adjusted return on capital (RAROC) on this loan?

b. If the lender requires RAROC to exceed 25%, how could the terms of the loan be changed to make this loan acceptable?

Answer 1

a) RAROC (Revenues - Cost - Expected Loss)/ Risk Capital Revenues (5.875% + 0.25%)* 8,000,000 6.125% * 8,000,000 = $490,000 Costs 5.525% * 8,000,000 = $442,000 Risk capital will be calculated by using the duration of loan 6.14 years Capital risk premium 0.85% Discount factor 5.875% So, capital risk premium to be discounted 0.85% / (1+0.05875) = 0.80283353% Risk adjusted capital 0.8028% * 6.14 * 8,000,000 = $394,351.83 RAROC (Revenues - Cost - Expected Loss)/ Risk Capital E(490,000 442,000) / 394,351.83 0.12171872 Or 12.17% RAROC 12.17%

b) RAROC to exceed 25% 25% Net Income / 394,352 Net income 98,588 Let x be the new rate of loan including fee to achieve this So, (x%-5.525%)* 8,000,000 98,588 x%-5.525% = 98,588/8,000,000 x 5.525% 1.23235% = 6.757% So, loan annual interest rate and fee should be charged more than 6.757% to achieve the required RAROC.