Reference no: EM133492807

Question 1. A bank has the following balance sheet. The loans have a 6-year maturity and earn 6.5% annually. The interest is paid once a year and the principal will not be repaid until maturity. The securities do not earn interest. The certificates of deposit (CDs) have a 1-year maturity. The bank must pay 3.7% on the CDs. 

a) What is the net interest income (NII) for the bank at the end of the first year?  

b) Suppose that interest rates are expected to increase by 90 basis points (0.9%) at the end of the first year. What will the NII be at the end of the second year?  

c) If interest rates change as expected, the value of the bank's loans will decrease in value to $2,245,632.48. What 

will happen to the market value of the bank's equity? Why? 

Question 2- Given the following balance sheet, analyze the bank's interest rate risk by answering the questions below. Dollars are in millions. 

a) Calculate the bank's net interest income (NII).  

b) Calculate (i) the one-year repricing gap (CGAP) and (ii) the gap ratio for the bank.  

c) Use the repricing gap model to estimate the change in net interest income (ΔNII) if interest rates are expected to decrease by 40 basis points next year. Assume that the spread between rates on assets and liabilities remains constant.  

d) Estimate ΔNII if interest rates on rate-sensitive assets decrease by 60 basis points and interest rates on rate-sensitive liabilities increase 20 basis point.  

e) Why are the answers in c. and d. different? How do these estimates represent the CGAP effect and the spread effect? Explain.  

Question 3-Suppose a bank has financed a $9,000,000 3-year loan with a semiannual coupon rate of 7.48% with a 7-year $9,000,000 CD with an annual coupon rate of 5.96%. The yield on the loan is 7.80% and the yield on the CD is 5.50%. 

a) Calculate the (i) duration and (ii) modified duration for the loan.  

b) Calculate the (i) duration and (ii) modified duration for the CD.  

c) If market interest rates decrease 130 basis points, calculate the estimated effect on the market value of the bank's equity from this arrangement.  

Question 4-An insurance company owns a 20-year 6.4 percent Treasury bond. The bond has a $100,000 face value and pays its coupon semiannually. Its duration is 11.3557 years, current market price is $94,117.65 and its current yield to maturity is 6.8%. The insurance company is concerned that interest rates may increase by 75 basis points. Treasury bond futures are currently available with a price of 95.3. 

a) If interest rates rise by 75 basis points, what will be the impact on the insurance company's Treasury bond value? Support your answer with appropriate calculations.  

b) If the insurance company hedges its position in the Treasury bond with a Treasury future, what position should it take in the future? Why?  

c) Suppose interest rates rise by the expected 75 basis points and the insurance company has hedged its position as you recommend in b. Calculate the net value of the hedge after the increase in interest rates.  

Question 5- A financial institution currently uses a base rate of 5.6%, charges an origination fee of 0.73% and requires a compensating balance of 15%. The Federal Reserve imposes a 10% reserve requirement on the bank's demand deposits. For a customer with a 4.9% risk premium, calculate the bank's ROA on the loan.  

Question 6- A bank is considering a loan applicant for a $6,500,000 7-year loan. The servicing fee is expected to be 90 basis points and the bank's cost of funds, its RAROC benchmark, is 12%. The estimated maximum change in the borrower's risk premium is 4.2%. The loan's duration is 5.7435 years and the current market interest rate for similar loans is 13.4%. Based on the RAROC model, should the bank make the loan? Why or why not?