Question

4.4.

Gotbucks Bank, Inc. (in $millions) Assets Liabilities and Equity $ 41 Core deposits Cash Federal funds Loans (floating) 31 Federal funds 61 116 Euro CDs Loans (fixed) 76 Equity 17 Total assets S 264 Total liabilities and equity S 264 Notes to the balance sheet: Currently, the fed funds rate is 9.6 percent. Variable-rate loans are priced at 2 percent over LIBOR (currently at 10 percent). Fixed-rate loans are selling at par and have five-year maturities with 11 percent interest paid annually. Assume that fixed rate loans are non-amortizing. Core deposits are all fixed rate for two years at 7 percent paid annually. Euro CDs currently yield 8 percent. a. What is the duration of Gotbucks Bank's (GBI) fixed-rate loan portfolio if the loans are priced at par? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) Duration ears b. If the average duration of GBI's floating-rate loans (including fed fund assets) is 47 year, what is the duration of the bank's assets? (Note that the duration of cash is zero.) (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) Duration (assets) years c. What is the duration of GBI's core deposits if they are priced at par? (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)) Duration (deposits) ears d. If the duration of GBI's Euro CDs and fed fund liabilities is .412 years, what is the duration of the bank's liabilities? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616)) Duration (liabilities) years e-1. What is GBI's duration gap? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616)) Duration gap ears e-2. What is the expected change in equity value if all yields increase by 300 basis points? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.) Expected change in equity value e-3. Given the equity change in e-2. what is the expected new market value of equity after the interest rate change? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.) New market value

Answer 1

a) par $76 rate = 11%, Maturity 5 Years

Cash flow = Par Value * rate = 76* 11% = 8.6 , final year cash flow = 76 * (1+ 11%) = 82.36

Present Value , PV = Cash flow / (1 + rate) ^ t

t CF PV PV *t

1 8.36 7.532 7.532

2     8.36 6.785 13.570

3 8.36 6.113 18.338

4 8.36 5.507 22.028

5 82.36 50.064 250.318

76.000 311.786

Duration for fixed rate loan = 311.786/ 76 = 4.102 Years

b) Duration of floating rate loan (including fed fund asset) = 0.47 years

For Cash , there will be duration, hence duration = 0. Cash = 41, Federal fund = 31, floating rate = 116, fixed rate = 76

Total assets = 220

Duration of asset = [ 41 (0) + 31 (0.47) + 116 (0.47) + 76 (4.102) ]/ 264 = 1.443 Years.

c) Par value of core -deposit = 45, Maturity = 2 years, rate = 7%

similar to a)

t CF PV PV *t

1 3.15 2.944 2.944

2 48.15 42.056 84.112

45.000 87.056

Duration = 87.056/ 45 = 1.935

d) Duration of EURO CDs and Fed Funds liabilities is .412 years

Core deposits = 45, Federal funds = 61, EURO CDs = 141

Duration of Banks liabilities = [ 45 (1.935) + 61 (.412) + 141 (.412)] / 264 = 0.645 years.