Question

Variable rate CD’s = $90 Treasury bills = $150 Discount Loans = $20 Treasury notes = $100 Fixed rate CDs = $160 Money Market deposit accts. = $140 Savings deposits = $90 Fed Funds borrowing = $40 Variable rate mortgage loans $140 Demand Deposits = $40 Primary Reserves = $50 Fixed rate loans = $210 Fed Funds Lending = $50 Equity Capital = $120 A. Develop a balance sheet from the above data. Be sure to divide your balance sheet into rate-sensitive assets and liabilities as we did in class and in the examples. B. Perform a Standard Gap Analysis and a Duration Analysis using the above data if you have a 1.15% decrease in interest rates and an average duration of assets of 5.4 years and an average duration of liabilities of 3.8 years. C. Indicate if this bank will remain solvent after the valuation changes. If so, indicate the new level of equity capital after the valuation changes. If not, indicate the amount of the shortage in equity capital.

Answer 1

1) option :1

$20,000 =Future value

given present value = $16,200

n is 6 years

pv(f/p,i,n)=fv

16,200(f/p,i,6)=20,000
(f/p,i,6)=20,000 / 16,200
1.2345 = (f/p,i,6)

solving i for trial and error we get i = 3.57442% (by solving values of i)

2) option:2
given,

Future value = $20,000 ,pv = $10,600

coupon rate = 5.5%

n is 6 years

coupon rate * future value=coupon payment = 5.5% * 20,000 = 1,100
present value(f/p,i,n) + coupon payment(f/a,i,n)= future value

10,600(f/p,i,6) + 1,100(f/a,i,6)=20,000

error we get i = 19.43568% ( by solving for values of i)

3)option:3

$15,000=Present value ,then given data

payment recieved in 5 years is $6,534.8

payment recieved in 10 years is $8,540.72

payment recieved in 15 years is $11,162.38

payment recieved in 5 years(p/f,i,n) + payment recieved in 10 years(p/f,i,n) + payment recieved in 15 years(p/f,i,n)=present value

6,534.8(p/f,i,5) + 8,540.72(p/f,i,10) + 11,162.38(p/f,i,15)=15,000

error we get i = 5.49999% ( by solving for values of i)