Question

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

=(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.