Question

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

Gotbucks Bank, Inc. (in $ millions)
Assets   Liabilities and Equity
Cash   $   48     Core deposits   $   43
Federal funds      38     Federal funds      68
Loans (floating)      123     Euro CDs      148
Loans (fixed)      83     Equity      33
   
   
Total assets   $   292     Total liabilities and equity   $   292
   
   

Notes to the balance sheet: Currently, the fed funds rate is 10.3 percent. Variable-rate loans are priced at 4 percent over LIBOR (currently at 11 percent). Fixed-rate loans are selling at par and have five-year maturities with 12 percent interest paid annually. Assume that fixed rate loans are non-amortizing. Core deposits are all fixed rate for two years at 8 percent paid annually. Euro CDs currently yield 9 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 .54 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 .419 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)
Loan (fixed) = Par Value	$83.00
Annual interest = Loans (fixed) x rate = $83 x 12%	$9.96
Maturity	5	years
t	CF	PV@ 12%	PV of CF	PV of CF x t
1	$9.96	$0.8929	$8.89	$8.89
2	$9.96	$0.7972	$7.94	$15.88
3	$9.96	$0.7118	$7.09	$21.27
4	$9.96	$0.6355	$6.33	$25.32
5	$92.96	$0.5674	$52.75	$263.74
				$335.10
Duration = $282.76/$74	4.037	Years
b)
DA = [48(0) + 38(.54) + 123(.54)+ 83(4.037)]/292	1.4453	Years
c)
Loan (fixed) = Par Value	$43.00
Annual interest = Loans (fixed) x rate = $43 x 8%	$3.44
Maturity	2	years
t	CF	PV@ 8%	PV of CF	PV of CF x t
1	$3.44	$0.9259	$3.19	$3.19
2	$46.44	$0.8573	$39.81	$79.63
				$82.81
Duration = $82.81/$43	1.926	Years
d)
DL = [43*(1.9126)/($68+$148+$43) + ($68+ $148) *(.419)/($68+$148+$43) =	0.6692	Years
e)
1) GBI’s leveraged adjusted duration gap = DA - (TL - E)/TA) x DL
GBI’s leveraged adjusted duration gap = 1.45-($292 - 33/292) x .6692	0.8518	years
2)
ΔE = -0.8518 x $292,000,000 x (0.01)	-$2,487,211.81
Expected change in equity value =	-$2,487,211.81
3) New market value = $33,000,000 - $2,487,211.81	$35,487,211.81