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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 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.
Answer:
Interest income $1,000 $10,000 x 0.10
Interest expense 600 $10,000 x 0.06
Net interest income (NII) $400
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?
Answer:
Interest income $1,000 $10,000 x 0.10
Interest expense 700 $10,000 x 0.07
Net interest income (NII) $300
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. Note: this answer makes no assumption about reinvesting the first year’s interest income at the new higher rate.
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 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.
Answer:
Cash $1,000 Certificate of deposit $10,000
Bond $9,446 Equity $ 446
Total assets $10,446 Total liabilities and equity $10,446
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?
Answer:
The market value of the equity would be higher ($1,600) because the value of the bond would be higher ($10,600) and the value of the CD would remain unchanged.
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