Question

An FI is planning to give a loan of $5,000,000 to a firm in the steel industry. It expects to charge an up-front fee of 0.15 percent and a service fee of 5 basis points. The loan has a maturity of 8 years. The cost of funds for the FI is 10 percent. The FI has estimated the risk premium on the steel manufacturing sector to be approximately 0.20 percent, based on two years of historical data. The current market interest rate for loans in this sector is 10.20 percent. The 99th (extreme case) loss rate for borrowers of this type has historically run at 5 percent, and the dollar proportion of loans of this type that cannot be recaptured on default has historically been 85 percent. Using the RAROC model, should the FI make the loan if the bank ROE is 13%?

Answer 1

RAROC = One year net income per dollar earned/(unexpected default rate * proportion of loan lost on default)

Unexpected default rate = 5%

Proportion of loan lost on default = 85%

Loan income:	Interest rate (i)	Loan amount (a)	(r*a)
Expected interest	10.20%	5,000,000	510,000
Servicing fees	0.05%	5,000,000	2,500
Less: cost of funds	10%	5,000,000	500,000
		Net income	12,500

(Note: up-front fees is not taken into account for calculating the loan's income.)

One year net income per dollar = 12,500/5,000,000 = 0.0025

RAROC = 0.0025/(5%*85%) = 5.88%

The FI should not make the loan as the RAROC is less compared to the bank's ROE of 13%.