## Question

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

## Answers

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 .