24. The balance sheet for Gotbucks Bank Inc. (GBI) is presented below ($ millions). $ 30...

Ans a)

Five year loan(values in $ million)

Par Value = $ 65 Coupon rate = 12% Annual Payments =$ 65 * 12% = $ 7.8 YTM = 12% Maturity = 5 Years

Time	Cash Flow	PVIF	PV of cash flow	PV of cash flow * Time
1	$7.80	0.892857	$6.964	$6.964
2	$7.80	0.797194	$6.218	$12.436
3	$7.80	0.71178	$5.552	$16.656
4	$7.80	0.635518	$4.957	$19.828
5	$72.80	0.567427	$41.309	$206.543
			$65.000	$262.427

Duration of fixed rate loan = $ 262.427 / $ 65 = 4.0373

The duration is 4.037 years.

b)

Duration of GBI Asset = [30(0) + 20 (.36) + 105 (.36) + 65(4.037) ]/220 = 1.397 years

c)

Two-year core deposits (values in $ million)

Par value = $20 Coupon rate = 8% Annual payments R = 8% Maturity = 2 years

Time	Cash Flow	PVIF	PV of cash flow	PV of cash flow * Time
1	$1.60	0.92593	$1.481	$1.481
2	$21.60	0.85734	$18.519	$37.038
			$20.000	$38.519

Duration = $38.519/$20.000 = 1.9259

The duration of the core deposits is 1.9259 years.

d)

Duration of GBI Liabilities  = [20 × (1.9259) + 50 × (0.401) + 130 × (0.401)]/200 = 0.5535 years

e)

GBI’s leveraged adjusted duration gap is: 1.397 - 200/220 * (0.5535) =0.8938 years

f)

The duration gap of GBI is positive, so if the interest rate increase the net worth will decrease . For 1 percent increase in interest rate, the change in net worth is:

E = -0.8938 * (0.01) * $220 = -$1,966,360 (new net worth will be $ 20,000,000 - $ 1,966,360 = $18,033,640).

g)

The duration gap of GBI is positive,so if the interest rate decrease the net worth will increase. For a 0.5 percent decrease in interest rate, the change in net worth is:

E = -0.8938 * (-0.005) * $220 = $983,180 (new net worth will be $ 20,000,000 + $ 983,180 = $20,983,180)

h)

For Immunization the bank requires to have a leverage-adjusted duration gap of 0.0.

1. GBI use the combination of reduced asset duration and increased liability duration so that leverage-adjusted duration gap is attain 0.0 or,

2. GBI may reduce the duration of its assets to 0.5535 years by using more floating rate loans and fed funds .