Question

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

Assets				Liabilities and Equity
Cash	$	2,400		Certificate of deposit	$	11,400
Bond		10,200		Equity		1,200
Total assets	$	12,600		Total liabilities and equity	$	12,600

a. The bond has a 10-year maturity, a fixed-rate coupon of 12 percent paid at the end of each year, and a par value of $10,200. The certificate of deposit has a 1-year maturity and a 6 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 $9,677 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 $1,200?
e. What factors have caused the changes in operating performance and market value for this FI?

Answer 1

a). Net Interest Income = Interest Income - Interest Expense

= [$10,200 * 0.12] - [$10,200 * 0.06] = $1,224 - $612 = $612

b). Net Interest Income = Interest Income - Interest Expense

= [$10,200 * 0.12] - [$10,200 * 0.07] = $1,224 - $714 = $510

The decrease in net interest income is caused by the increase in financing cost without a corresponding increase in the earnings rate. Thus, the change in NII is caused by refinancing risk. The increase in market interest rates does not affect the interest income because the bond has a fixed-rate coupon for ten years.

c). Remember after one year, there are 9 years left;
find price of bond with PMT = 1200, N = 9, FV = 10,200, R (interest rate) = 13%; find PV = $9,553.41
Cash	$2,400	Certificate of Deposit	$11,400
Bond	$9,553	Equity	$553
Total Assets	$11,953	Total Liabilities and equity	$11,953
Market value of equity falls to $553 due to lower market value of the bond.

d). The market value of equity would be higher because value of the bond would be higher. The CD would be the same, meaning that the equity had to be higher because liabilities + Equity and assets must balance.

find price of bond with PMT = 1200, N = 9, FV = 10,200, R (interest rate) = 11%; find PV = $10,631.89

Cash	$2,400	Certificate of Deposit	$11,400
Bond	$10,632	Equity	$1,632
Total Assets	$13,032	Total Liabilities and equity	$13,032

Market value of equity raises to $1632 due to lower market interest rate and higher market value of the bond.

e). The decrease of net interest income was caused by the increase of market rates by 100 basis points. This increase in market rates decreased interest income, increased interest expense, and decreased the value of the FI’s bonds, which in turn decreased the market value of the firm.