Question

A financial institution has the following market value balance sheet structure:

Assets				Liabilities and Equity
Cash	$	3,000		Certificate of deposit	$	12,000
Bond		10,300		Equity		1,300
Total assets	$	13,300		Total liabilities and equity	$	13,300

a. The bond has a 10-year maturity, a fixed-rate coupon of 9 percent paid at the end of each year, and a par value of $10,300. The certificate of deposit has a 1-year maturity and a 5 percent fixed rate of interest. The FI expects no additional asset growth. What will be the net interest income (NII) at the end of the first year? (Note: Net interest income equals interest income minus interest expense.)
b. If at the end of year 1 market interest rates have increased 100 basis points (1 percent), what will be the net interest income for the second year? Is the change in NII caused by reinvestment risk or refinancing risk?
c. Assuming that market interest rates increase 1 percent, the bond will have a value of $9,707 at the end of year 1. What will be the market value of the equity for the FI? Assume that all of the NII in part (a) is used to cover operating expenses or is distributed as dividends.
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 $1,300?
e. What factors have caused the changes in operating performance and market value for this FI?

Answer 1

Answer A

Bond : coupon rate = 9% , fave value = 10300

Interest amount to be rec'd = coupon rate * face value = 9% * 10300 = 927

Certificate of deposit: interest rate = 5% , value = 12000

Interest amount to be paid = 12000 *5% = 600

Net interest income = interest rec'd - interest paid = 927 - 600 = 327

Answer B:

There is no impact of market interest rates on a bond's coupon rate. The bond's coupon rate remains the same throughout the bond's holding. The market price of a bond can change owing the interest rate change. So there will be no reinvestment risk. However, the new interest rates will be applied on certificate of deposits for year 2 as the previous interest rate is valid for one year owing to the 1 year maturity term of CD. So there will be a fall in NII due to refinancing risk.

Bond: Interest amount to be rec'd from coupon = 927

Certificate of deposit: New Interest rate = 6%, value 12000

Interest amount to be paid = 12000 *6% = 720

Net interest income = interest rec'd - interest paid = 927 - 720 = 207

Answer C

Face Value = 9707

Net interest income = NIL as either it is given away as dividends or used to cover up expenses.

Cash	3000	Certificate of deposit	12000
Bond	9707	Equity	707
Total assets	12707	Total liabilities	12707

With Bond = 9707, total assets = 12707.

Revised Equity = Total liabilities - Certificate of deposit

= 12707 - 12000 = 707

Answer D

if interest rate went down by 1% in year 1, then the value of bonds would definately be higher than 10,300 on assets side thus increasing the value to total assets.

On liabilities side, the value of CD would remain unchanged and the market value of equity would increase as the value of total liabilities has increased owing to an increase in the value of bond on assets side. So the value of equity would definately be higher than 1300.

Answer E

The market value of the firm has changed because of the effect of the changing rates on the market value of the bond. The operating performance has been affected by the changes in the market interest rates that have caused the interest income, interest expense and net interest income to change. These changes took place because of the unique maturities of the fixed-rate assets and fixed-rate liabilities.

Hope this helps. Have a good day.