Question

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

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.

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. Duration = 4.10 years

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

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

YTM	7%
Interest rate	7%
Loan size	36
Period (t)	1	2
cash flow	2.52	38.52
PV	2.4	33.6
Bond Price	36.0
PV * t	2.4	67.3
Duration (years)	1.93

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