Question

9. A financial institution is considering a customer’s request for a 12-year $15 million loan, with annual interest payments and the principal due at maturity. The financial institution requires a 22.5% risk adjusted return on capital for this loan. Its cost of funds is 3.875% for this loan and it will charge a 2% risk premium. Historically, the worst 1% of comparable loans experience a 125 basis point increase in the credit risk premium. The financial institution’s typical origination fee for this type of loan is 0.25% and similar loans yield 6.125%. The loan has a duration of 8.9.

a. If the financial institution charges its standard origination fee and the uses the yield on similar loans as the coupon rate, what risk adjusted return on capital will the loan generate?

Answer 1

RAROC = one year net income on a loan/loan at risk.

One year net income = (spread %age + fees)*loan amount

spread %age = yield on similar loans - cost of funds = 6.125%-(3.875%+2%) = 0.25%

One year net income = (0.25%+0.25%)*15 = 0.075 million

Loan at risk = duration*loan amount*(change in credit risk premium)/(1+yield)

= 8.9*15*1.25%/(1+6.125%) = 1.572 million

RAROC = 0.075/1.572 = 4.77%

Required RAROC is 22.5% so this loan has much lower RAROC.

(Note: If the additional 2% risk premium is not charged on the cost of funds, then RAROC is 23.85%)