Question

20. A bank has the following balance sheet: Assets Rate sensitive $225,000 Fixed rate 550.000 Nonearning 120,000 $895,000 Avg. Rate 6.35% 7.55 Liabilities/Equity Rate sensitive $300,000 Fixed rate 505,000 Nonpaying 90,000 Total $895,000 Avg. Rate 4.25% 6.15 Total Suppose interest rates rise such that the average yield on rate-sensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points. a. Calculate the bank's repricing GAP. b. Assuming the bank does not change the composition of its balance sheet, cal culate the net interest income for the bank before and after the interest rate changes. What is the resulting change in net interest income! c. Explain how the CGAP and spread effects influenced this increase in net interest income.

Answer 1

1. Repricing GAP    = Rate-sensitive assets (RSA) - Rate-sensitive liabilities (RSL)

                                   = $225000 * (6.80%) - $300000 * (4.60%)

                                   = $1500

2. Net Interest Income (Before Interest Rate Change) =

                                   = ($225,000(.0635) +$550,000(.0755)) – ($300,000(.0425) + $505,000(.0615))

                                   = $12005

              Net Interest Income (After Interest Rate Change) =

                                   = ($225,000(.068) +$550,000(.0755)) – ($300,000(.046) + $505,000(.0615))

                                   = $11967.50

3. The CGAP affect worked to decrease net interest income. That is, the CGAP was negative while interest rates increased. Thus, interest income increased by more than interest expense. The result is a decrease in NII. In contrast, the spread effect worked to increase net interest income. The spread increased by 10 basis points. According to the spread affect, as spread increases, so does net interest income. However, in this case, the increase in NII due to the spread effect was dominated by the decrease in NII due to the CGAP effect.