Question

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

  

Gotbucks Bank, Inc. (in $ millions)
Assets			Liabilities and Equity
Cash	$	38	Core deposits	$	42
Federal funds		28	Federal funds		58
Loans (floating)		113	Euro CDs		138
Loans (fixed)		73	Equity		14
Total assets	$	252	Total liabilities and equity	$	252

  

Notes to the balance sheet: Currently, the fed funds rate is 9.3 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 .44 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 .409 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

Soln : a) As the Fixed rate loans are being sold at par the price = fixed loan value and also the discount rate = 12%

accordingly we have calculated here the duration in the table with the help of cash flow and period.

Year	1	2	3	4	5
Cash Flows	8.76	8.76	8.76	8.76	81.76
Period* cash flows (CF)	8.76	17.52	26.28	35.04	408.8
Discounted CF (DCF)	7.82	13.97	18.71	22.27	231.96
Duration = sum(DCF)/price	4.037

Duration = 4.037 years

(b) Duration of floating rate fund and fed fund = 0.44 years, For cash , duration = 0

weighted duration of floating rate fund & fed fund = 0.44 *(113+28)/252 = 0.246

weighted duration of fixed loan fund = 4.037*73/252 = 1.17 years (as for cash duration is 0)

c) As it is given that core deposits is at Par , so as calculated in (a) the par value = $42 = price and discount rate = 8%. Please refer here the table :

Year	1	2
Cash Flows	3.36	45.36
Period* cash flows (CF)	3.36	90.72
Discounted CF (DCF)	3.11	77.78
Duration = sum(DCF)/price	1.926

Duration of core deposits = 1.926 years

d) Again like part (b) , duration of Euro CDs and fed fund liabilities is .409 years

weighted duration of euro CDs and fed fund liabilities = 0.409 *(138+58)/(252-14) = 0.337

weighted duration of cored deposits = 42*1.926/238 = 0.34 years

duration of liabilities = 0.337 + 0.34 = 0.677 years