Question

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

Gotbucks Bank, Inc. (in $ millions)
Assets			Liabilities and Equity
Cash	$	32	Core deposits	$	25
Federal funds		22	Federal funds		52
Loans (floating)		107	Euro CDs		132
Loans (fixed)		67	Equity		19
Total assets	$	228	Total liabilities and equity	$	228

Notes to the balance sheet: Currently, the fed funds rate is 8.7 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 .38 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 .403 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 100 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 = Present value of a loan's cash flows, weighted by length of time to receipt and interest by the loan's current market value.

For calculating the duration we will go through below table for Fixed Rate Loan

Period	Cash Flow	Period x Cash flow	PV of $1 at 11%	PV of cash flow
1	$7.37	$7.37	$0.90	$6.64
2	$7.37	$14.74	$0.81	$11.96
3	$7.37	$22.11	$0.73	$16.17
4	$7.37	$29.48	$0.66	$19.42
5	$74.37	$371.85	$0.59	$220.67

Here we can see different cash flows (Interest rate) with the period.

Duration = Sum of all the Present Value of cash flows / Initial value

= 274.86 / 67

= 4.10 years

b)

Here first we will calculate weightage of each asset.

Weightage of cash = 32 / 228 = 0.14

Weightage of Federal Funds & Loans Floating is = (22+107) / 228 = 0.57

Weightage of Loans Fixed = 0.29

So the duration of total asset will be=

= 0.14 * 0 + 0.57 * 0.38 + 0.29 * 4.1

= 1.41 years

c)

For core deposit table of cash flows shall be as below:-

Period	Cash Flow	Period x Cash flow	PV of $1 at 7%	PV of cash flow
1	$1.75	$1.75	$0.93	$1.64
2	$26.75	$53.50	$0.87	$46.73

So duration = 48.36 / 25 = 1.93 years

d)

Bank liabilities weightage is given as below:-

Weightage of Core deposit = 25 / 209 = 0.12

Weightage of other liabilities = 1-0.12 = 0.88

So duration of liabilities will be:-

=0.12 * 1.93 + 0.88 * 0.403

= 0.59 years

e1)

Duration Gap is given as follows:-

D(gap) = D(Asset)-D(Lib.) * ( Lib / Asset)

So here

D(gap) = 1.41 - 0.59 * (209 / 228)

D(gap) = 0.87 years

e2)

As we know that economic value of equity is given by:-

EVE = MVA - MVL

MVA = Market value of asset

MVL = Market value of liability

and

duration gap (DGAP) = DA - DL * (MVL/MVA)

So

EVE = -DGAP (Change in interest rate / (1 + Average interest rate of assets) * MVA

So=

Change in EVE = -0.87 * ( 0.01 / (1+.109) * 228

Change in EVE = -$1.78 million

e3)

Current market value of equity = 19

Expected new market value of equity = 19 - 1.78 = $17.22 million

Thank You!!