Question

Provide your answers in the space provided.

Any quantitative questions require showing your work for full credit.

Round all $ problems to the nearest cent.

All other calculations must be to at least the fifth decimal place.

Given the following information: (all numbers are in millions)

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:

Future value = $20,000

Present value = $16,200

n = 6 years

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

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

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

1.2345 = (f/p,i,6)

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

2) Option 2:

Future value = $20,000

pv = $10,600

coupon rate = 5.5%

n = 6 years

coupon payment = coupon rate * future value = 5.5% * 20,000 = 1,100

future value = present value(f/p,i,n) + coupon payment(f/a,i,n)

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

solving for i via trial and error we get i = 19.43568% ( by solving for various values of i)

3) Option 3:

Present value = $15,000

payment recieved in 5 years = $6,534.8

payment recieved in 10 years = $8,540.72

payment recieved in 15 years = $11,162.38

present value = 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)

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

solving for i via trial and error we get i = 5.49999% ( by solving for various values of i)

Based on the yield , option 2 is th