Question

22-4

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

Gotbucks Bank, Inc. (in $ millions)
Assets			Liabilities and Equity
Cash	$	35	Core deposits	$	36
Federal funds		25	Federal funds		55
Loans (floating)		110	Euro CDs		135
Loans (fixed)		70	Equity		14
Total assets	$	240	Total liabilities and equity	$	240

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.

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

years

b.	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))

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)

years

d.	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))

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

years

e-2.	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.)

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. Fixed rate loans are at par i.e. market value is same as book value shown at $ 70 million. Rate is 11% and tenure is 5 years. The duration will be as below:

(b) Duration of Assets = weighted average of duration of constituents, as below:

Duration of cash = 0; Duration of Fed funds & Floating Loans = 0.41 :

Duration of Assets = (25+110)/240 * 0.41 + 70/240 * 4.102 = 1.427 years

(c) Core deposit duration :

(d) Duration of Bank Liabilities = 36/240 * 1.935 + (55+135)/240 * 0.406 = 0.612

e1. Duration gap = 1.427 - 0.612 = 0.815 years

e2. If the yields increase by 200 bps, the value of assets & liabilities will change by -2% * duration.

Value of assets : Cash = 35; Fed fund & floating loans = (1 -2% * 0.41) * 135 = 133.893 ; Fixed Loans = (1-2%*4.102) * 70 = 64.257

Total assets = 233.150

Value of Liabilities : Core Deposits = (1-2% * 1.935) * 36 = 34.607; Fed funds & CDs = (1=2%*0.406)*190 = 188.457

Total Liab (without equity) = 223.064

Equity value = 10.086; Hence expected change in equity value = (14 - 10.086) = 3.914

e3. 10.086