Problem 22-9 (LG 22-3) Use the data provided for Gotbucks Bank, Inc., to answer

Question

Problem 22-9 (LG 22-3)

Use the data provided for Gotbucks Bank, Inc., to answer this question.

Notes to the balance sheet: Currently, the fed funds rate is 10.1 percent. Variable-rate loans are priced at 2 percent over LIBOR (currently at 12 percent). Fixed-rate loans are selling at par and have five-year maturities with 13 percent interest paid annually. Assume that fixed rate loans are non-amortizing. Core deposits are all fixed rate for two years at 9 percent paid annually. Euro CDs currently yield 10 percent.

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))

If the average duration of GBI’s floating-rate loans (including fed fund assets) is .52 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))

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))

If the duration of GBI’s Euro CDs and fed fund liabilities is .417 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))

What is GBI’s duration gap? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

What is the expected change in equity value if all yields increase by 200 basis points? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations.)

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.)

Use the data provided for Gotbucks Bank, Inc., to answer this question.

Explanation / Answer

a) Loan (fixed) = Par Value $81.00 Annual interest = Loans (fixed) x rate = $81 x 13% $10.53 Maturity 5 years t CF PV@ 13% PV of CF PV of CF x t 1 $10.53 $0.8850 $9.32 $9.32 2 $10.53 $0.7831 $8.25 $16.49 3 $10.53 $0.6931 $7.30 $21.89 4 $10.53 $0.6133 $6.46 $25.83 5 $91.53 $0.5428 $49.68 $248.39 $321.93 Duration = $321.93/$81 3.974 Years b) DA = [46(0) + 36(.52) + 121(.52)+ 81(3.974)]/284 1.4210 Years c) Loan (fixed) = Par Value $29.00 Annual interest = Loans (fixed) x rate = $29 x 9% $2.61 Maturity 2 years t CF PV@ 9% PV of CF PV of CF x t 1 $2.61 $0.9174 $2.39 $2.39 2 $31.61 $0.8417 $26.61 $53.21 $55.61 Duration = $55.61/$29 1.917 Years d) DL = [29*(1.917) + 66*(.417) + 146*(.417)]/(284 -43) = 0.5975 Years e) 1) GBI’s leveraged adjusted duration gap = DA - (TL - E)/TA) x DL GBI’s leveraged adjusted duration gap = 1.421-($284 -43/284) x .5975 0.9140 years 2) ?E = -0.9142 x $284,000,000 x (0.02) -$5,191,253.46 Expected change in equity value = -$5,191,253.46 3) New market value = $43,000,000 - $5,191,253.46 $37,808,746.54

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