Use the data provided for Gotbucks Bank, Inc., to answer this question. 22-4 Not

Question

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

22-4

Notes to the balance sheet: Currently, the fed funds rate is 9 percent. Variable-rate loans are priced at 3 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.

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 .41 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 .406 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. Duration = 4.10 years

Since the loan was selling at par, the YTM = interest rate.

Bond price = sum of PVs

Duration = sum of all (PVs * t) / Bond price

b. Duration of bank's assets = [ (25+110)*0.41 + 70*04.1 + 35*0 ] / (25+110+70+35) = 1.43 years

c. Duration of core deposits = 1.93 years

d. Duration of the bank’s liabilities = [ 36 *1.93 + (55+135)*0.406) / (36+55+135) = 0.65 years

e.1. Duration gap = duration of assets - duation of liabilities = 1.43 - 0.65 = 0.78 years

e.2. Yield increase will lower the book value of both the floating rate loans and core deposits by 4.9 and 1.3 respectively result in a net decrease of 3.6 (= 4.9 - 1.3) in assets. This will lead to a reduction of 3.6 in equity.

.e.3. New market value of equity = 14 -3.6 = 10.4

YTM 11% interest rate 11% Loan size 70 Period (t) 1 2 3 4 5 cash flow 7.7 7.7 7.7 7.7 77.7 PV 6.9 6.2 5.6 5.1 46.1 Bond Price 70.0 PV * t 6.9 12.5 16.9 20.3 230.6 Duration (years) 4.10

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