Chapter 11
10. Metrobank offers one-year loans with a 9 percent stated or ba rate, charges a 0.25 percent loan origination fee, impos a 10 percent compensating balance requirement, and must pay a 6 percent rerve requirement to the Federal Rerve. The loans typically are repaid at maturity.
a. If the risk premium for a given customer is 2.5 percent, what is the simple promid interest return on the loan?
The simple promid interest return on the loan is BR + m = 0.09 + 0.025 = 0.115 or 11.5 percent.
b. What is the contractually promid gross return on the loan per dollar lent?
c. Which of the fee items has the greatest impact on the gross return?
The compensating balance has the strongest effect on the gross return on the loan. Without the compensating balance, the gross return would equal 11.75 percent, a reduction of 1.22 percent. Without the origination fee, the gross return would be 12.69 percent, a reduction of only 0.28 percent. Eliminating the rerve requirement would cau the gross return to increa to 13.06 percent, an increa of 0.09 percent.
24. Assume a one-year T-Bill is currently yielding 5.5 percent, and a AAA-rated discount bond with similar maturity is yielding 8.5 percent.
a. If the expected recovery from collateral in the event of default is 50 percent of principal and interest, what is the probability of repayment of the AAA-rated bond? What is the probability of default?
p(1 + k) + (1 - p)(1 + k) = 1+I. Solve for the probability of repayment (p):
Therefore the probability of default is 1.0 - .9447 = 0.0553 or 5.53 percent.
b. What is the probability of repayment of the AAA-rated bond if the expected recovery from collateral in the ca of default is 94.47 percent of principal and interest? What is the probability of default?
Therefore the probability of default is 1.0 – 0.5000 = 0.5000 or 50.00 percent.
c. What is the relationship between the probability of default and the proportion of principal and interest that may be recovered in the ca of default on the loan?
The proportion of the loan’s principal and interest that is collectible on default is a perfect substitute for the probability of repayment should such defaults occur.
32. A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It ex
pects to charge a rvicing fee of 50 basis points. The loan has a maturity of 8 years and a duration of 7.5 years. The cost of funds (the RAROC benchmark) for the bank is 10 percent. Assume the bank has estimated the maximum change in the risk premium on the steel manufacturing ctor to be approximately 4.2 percent, bad on two years of historical data. The current market interest rate for loans in this ctor is 12 percent.
a. Using the RAROC model, determine whether the bank should make the loan?
RAROC = Fees and interest earned on loan/ Loan or capital risk
