Question

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

Assets Liabilities and Equity
Cash $ 1,000 Certificate of deposit $10,000
Bond 10,000 Equity 1,000
Total assets $11,000 Total liabilities and equity $11,000


a. The bond has a 10-year maturity, a fixed-rate coupon of 10 percent paid at the end of each year, and a par value of $10,000. The certificate of deposit has a one-year maturity and a 6 percent 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 this result caused by reinvestment risk or refinancing risk?
c. Assuming that market interest rates increase 1 percent, the bond will have a value of $9,446 at the end of year 1. What will be the market value of equity for the FI? Assume that all of the NII in part (a) is used to cover operating expenses or 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 $1,000? Why? e. What factors have caused the changes in operating performance and market value for this FI?

Answer 1

Answer and Explanation:

a. To calculate the net interest income (NII) at the end of the first year, we need to determine the interest income and interest expense.

For the bond:

The interest income is calculated as the fixed-rate coupon of 10 percent multiplied by the par value of $10,000, which equals $1,000.

For the certificate of deposit:

The interest expense is calculated as the rate of interest of 6 percent multiplied by the certificate of deposit amount of $10,000, which equals $600.

NII = Interest income - Interest expense

= $1,000 - $600

= $400

Therefore, the net interest income at the end of the first year is $400.

b. If market interest rates increase 100 basis points (1 percent) at the end of the first year, it will affect the interest income and interest expense for the second year. However, since we don't have specific information about the interest rates for the second year, we cannot determine the exact net interest income for that year.

The result of increased market interest rates causing changes in net interest income is primarily due to reinvestment risk. Reinvestment risk refers to the risk that the FI may have to reinvest its cash flows from maturing investments at lower interest rates, thereby reducing its interest income.

c. If the bond's market value is $9,446 at the end of the first year, the market value of equity for the FI can be calculated by subtracting the liabilities (certificate of deposit) from the total assets:

Market value of equity = Total assets - Liabilities

= $11,000 - $10,000

= $1,000

Therefore, the market value of equity for the FI is $1,000.

d. If market interest rates had decreased 100 basis points by the end of the first year, the market value of equity would be higher than $1,000. This is because a decrease in market interest rates would result in an increase in the value of fixed-rate bonds, such as the bond held by the FI. As a result, the market value of the bond would increase, leading to a higher market value of equity for the FI.

e. The changes in operating performance and market value for this FI are primarily influenced by factors such as changes in market interest rates, the maturity and coupon rate of the bond, the rate of interest on the certificate of deposit, and the reinvestment risk associated with the FI's investments. These factors can affect the interest income, interest expense, and the market value of assets and equity for the FI.