financial institution

financial institution

Question 1: A financial institution has the following balance sheet structure:

Asserts Liabilities and

equhy

Cash $1 000 Certificate of deposit $10 0000

Bond 10 000 quity

1 000

Total asserts $11 000 Total liabilities and equity $11 000

The bond has a ten- year maturity and a

fixed- rate coupon of 10 per cent. The certificate of deposit has a one- year maturity and a 6 per cent fixed rate of interest. The Fl
expects no additional asset growth.

a) What will be the net interest income at the end ofthe first year? (Note: Net interest income equals

interest income minus interest expense.

b) If at the end of year1 market interest rates have increased 100 basis points (1 per cent), what

will be the net interest income for the second year? Is this result caused by reinvestment risk or refinancing risk?

c) Assuming that

market interest rate increase 1 per cent, the bond will have a value of $9446 at the end of year 1. What will be the market value of equity
for the FI?

d) If market interest rates had decreased 100 basis points by the end of year 1 , would the market value of equity be higher or
lower than $1000? Why?

e) What factors have caused the changes in operating performance and market value for this firm?

Question 2:

bank invested $50 million in a two- year asset paying 10 per cent interest per annum and simultaneously issued a $50 million, one-year
liability paying 8 per cent interest per annum. What will be the impact on the bank’s net interest income if at the end ofthe first year
all interest rates have increased by 1 per cent (100 basis points)?

Question 3:

Evaluate the price ofthe following pure discount (zero-

coupon) bonds:

a) $ 1000 face value received in five years yielding an annual rate of8 per cent.

b) $1000 face value received in three

years yielding an annual rate of6 per cent.

c) $100 000 face value received in 10 years yielding an annual rate of 13 per cent.

d) $1000

000 face value received in two years yielding an annual rate of7 per cent.

e) $1000 000 face value received in six months yielding an

annual rate of7 per cent.

f) Calculate the value of each ofthe bonds if all yields increased by 1 per cent.

g) Calculate the percentage

price changes for each the bonds if all yields increased 1 per cent.

Question 4: Consider the following Fl balance sheet:

M.Match Ltd (in

thousands of dollars)

Assets Liabilities

Two- year Treasury bond $ 175 one-year CD

$135

15-year corporate bond $165 Five-year deposit $160

Notes: All securities are selling at par (equal to book

value). The two-year Treasure bonds yields 5 per cent; the 15-year corporate bonds yield 9 per cent; the one-year CD issue pay4.5 per cent;
and the five-year deposit pays 8 per cent. Assume that all instruments have annual coupon payments.

a) What is the value if M. Match

Ltd’s equity?

b) What is the weighted average maturity ofthe Fl’s assets?

c) What us the weighted average maturity ofthe Fl’s

liabilities?

d) What is the Fl’s maturity gap?

e) What does your answer to part(d) imply about the interest rate risk exposure of M.Match

Ltd?

f) Calculate the values of all four securities on M. Match Ltd’s balance sheet if all interest rates increase by 2 per cnet
g) What

is the impact on the equity of M. Match Ltd? Calculate the percentage change in the value of equity.

h) What would be the impact on M.Match

Ltd’s interest rate risk exposure if its liabilities paid interest semi- annually as opposed to annually?

Question 5:

What is the price

of a newly tendered five- year Treasury bond with a coupon of7 per cent and a yield of 7.05 per cent? (Hints: all Treasury notes and bonds
pay interest semi-annually)

Question 6:

a) What are all ofthe promised cash flows on a $1000 one -year loan yielding 10 per cent

p.a. that pays interest and principal quarterly?

b) What is the present value ofthe loan if interest rates are 10 per cent p.a.?

c) What is

the present value ofthe loan if interest rates are 8 per cent p.a.?

Question 7:

Calculate the duration of a two-year Euro-note with $100

000 par value and an annual coupon rate of 10 per cent iftoday’s yield to maturity is 11.5 per cent. What would the duration be if
today’s yield was 5.5 per cent? (Hint: interest is to be paid annually)

Question 8:

Use the following information about a hypothetical

government security dealer named J.P. Mersal Citover to answer parts(a) through (e). (Market yields are in parentheses.)
J.P.Mersal

Citover( in million of dollars)

Assets Liabilties

Cash $10

Overnight interbank

borrowing (7.00%) $170

T-notes: 30-day(7.05%) 75 Subordinated debt:

T-notes:

91-day(7.25%) 75 Seven-year, fixed at (8.55%) 150

T-bonds: two- year (7.5%) 50

Equity

T-bonds: 10-year (8.96%) 100

Corporate bonds? 25

5-year quarterly floating rate (8.20%)

a) What is the

repricing or funding gap ifthe planning period is 30 days? 91days? Two years? (Recall that cash is a non- interest earning asset.)
b) What

is the impact over the next 30 days on net interest income if all interest rates rise by 50 basis points?

c) lfthe duration of assets is

3.41 years and the duration of liabilities is 3.5years, what is J.P. Mersal Citover’s duration gap?

d) What conclusions regarding

J.P.Mersal Citover’s interest rate risk exposure can you draw from the duration gap in your answer to part(c)? From the repricing or
funding gap (30 days’ planning period) in your answer to part (a)?
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