1. A financial institution has the following market value balance sheet structure: (LG 19-1)
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, 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 1-year maturity at 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 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 of refinancing risk?
c. Assuming the market interest rates increase 1 percent, the bond will have a value of $9,446 at the end o year 1. What will be e 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 $1,000? Why?
a. To calculate the net interest income (NII) at the end of the first year, we need to calculate the interest income and interest expense.
Interest income from the bond can be calculated by multiplying the bond's par value ($10,000) by its fixed-rate coupon (10%):
Interest income from bond = ($10,000) x (10%) = $1,000
Interest income from the certificate of deposit can be calculated by multiplying the certificate of deposit's value ($10,000) by its fixed rate of interest (6%):
Interest income from certificate of deposit = ($10,000) x (6%) = $600
The net interest income (NII) is the difference between interest income and interest expense:
NII = Interest income from bond + Interest income from certificate of deposit - Interest expense
NII = $1,000 + $600 - Interest expense
However, we are not given the interest expense, so we cannot determine the exact NII without additional information.
b. To calculate the net interest income for the second year, we need to consider the change in market interest rates and the impact on interest income and interest expense.
Since the bond has a fixed-rate coupon, the interest income from the bond will not change. So, the change in net interest income will be primarily driven by the change in interest expense from the certificate of deposit.
If market interest rates have increased by 100 basis points (1%), the new interest expense from the certificate of deposit can be calculated by multiplying the increased market rate (6% + 1% = 7%) by the certificate of deposit value ($10,000):
New interest expense = ($10,000) x (7%) = $700
The net interest income for the second year will be:
NII = Interest income from bond + Interest income from certificate of deposit - New interest expense
NII = $1,000 + $600 - $700
The change in NII is caused by the reinvestment risk, as the interest expense increases due to higher market interest rates.
c. To calculate the value of equity for the financial institution (FI) at the end of year 1, we need to subtract the liabilities from the total assets.
The value of equity for the FI is equal to the total assets minus the total liabilities:
Equity = Total assets - Total liabilities
Equity = $11,000 - $11,000
Equity = $0
However, we are given that the equity value is $1,000. This means that the NII in part (a) is used to cover operating expenses or is distributed as dividends. Therefore, the value of the equity for the FI will remain $1,000.
d. If market interest rates had decreased by 100 basis points (1%) by the end of year 1, the market value of the bond would increase. As a result, the market value of the equity for the FI would also increase.
The market value of equity would be higher than $1,000 because a decrease in interest rates leads to an increase in bond prices. This increase in bond prices would positively impact the market value of the bond held by the FI, resulting in a higher market value of equity for the FI.