Question

Use the following information to answer questions #3, #4, and #5

A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to charge a servicing fee of 50 basis points. The loan has a maturity of 8 years with a duration of 7.5 years. The return on equity (ROE) for the bank is 10 percent. The bank has estimated the maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2 percent, based on two years of historical data. The current market interest rate for loans in this sector less the cost of funds is 2 percent.

3. What is the Risk Adjusted Return on Capital (RAROC)? Should the bank make this loan?

4. What should the duration be in order to accept this loan?

5. Assuming duration cannot be changed, how much additional fee income will need to be charged?

Answer 1

3). RAROC = Net interest and fees earned on a loan/loan at risk

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

= -7.5*5,000,000*(4.2%/(1+12%)) = -1,406,250

Net interest and fees = annual interest + fees - cost of funds

= (12%*5,000,000) + (0.5%*5,000,000) - (10%*5,000,000) = 125,000

RAROC = 125,000/1,406,250 = 8.89%

RAROC < cost of funds (ROE for the bank) so it should not make the loan.

4). In order to accept the loan, RAROC should be atleast equal to the cost of funds i.e.10%, so

125,000/loan at risk = 10%

Loan at risk = 1,250,000

-duration*5,000,000*(4.2%/(1+12%)) = 1,250,000

duration = 6.67 years.

5). If duration remains 7.5 years then

minimum acceptable RAROC = 10%

Net interest and fees/loan at risk = 10%

Net interest and fees = 1,406,250*10% = 140,625

So, additional income required = 140,625 - 125,000 = 15,625