17 Use the following data to answer parts (a) to (c) Assets Rate-sensitive Fixed

Question

17 Use the following data to answer parts (a) to (c) Assets Rate-sensitive Fixed-rate Givebucks Bank, Inc. $m 50 50 Liabilities Rate-sensitive Fixed-rate Equity $m 70 20 10 Notes All rate-senstive assets cumently eam 10 per cent interest per annum. All fixed-rate assets eam 7 per cent per annum. Rate-senstive liabilities cumently pay 6 per cent per annum, while fixed-rate liabilities offer 6 per cent annual interest. a What is Givebucks Bank's current net interest income? b What will the net interest income be if interest rates increase by 2 per cent? c What is Givebucks' repricing or funding gap? Use it to check your answer to part (b). LO 5.3, 5.4

Explanation / Answer

a. Current net interest income = Interest earned on Assets - Interest paid on liabilities

Interest earned on Assets = Interest Earned on Rate Sensitive Assets + Interest Earned on Fixed rate Assets

Interest Earned on Rate Sensitive Assets = ($50 mil * 10%) = $5 mil

Interest Earned on Fixed Rate Assets = ($50 mil * 7%) = $3.5 mil

Hence, Interest earned on assets = $8.5 mil

Interest paid on Liabilities = Interest paid on Rate Sensitive Liabilities + Interest paid on Fixed rate Liabiltiies

Interest Paid on Rate Sensitive Liabilities = ($70 mil * 6%) = $4.2 mil

Interest Paid on Fixed Rate Liabilties = ($20 mil * 6%) = $1.2 mil

Hence, Interest paid on liabilities = $5.4 mil

Net Interest Income = $8.5 mil - $5.4 mil = $3.1mil

b. When interest rates rise by 2%, interest income on fixed rate assets and liabilities would remain same, but that on rate sensitive assets and liabilities would increase.

Interest earned on Assets = Interest Earned on Rate Sensitive Assets + Interest Earned on Fixed rate Assets

Interest Earned on Rate Sensitive Assets = ($50 mil * 12%) = $6 mil

Interest Earned on Fixed Rate Assets = ($50 mil * 7%) = $3.5 mil

Hence, Interest earned on assets = $9.5 mil

Interest paid on Liabilities = Interest paid on Rate Sensitive Liabilities + Interest paid on Fixed rate Liabiltiies

Interest Paid on Rate Sensitive Liabilities = ($70 mil * 8%) = $5.6 mil

Interest Paid on Fixed Rate Liabilties = ($20 mil * 6%) = $1.2 mil

Hence, Interest paid on liabilities = $6.8 mil

Net Interest Income = $9.5 mil - $6.8 mil = $2.7mil

c. Repricing gap focuses on change in net interest income when the interest rate changes by 1%.

Repricing Gap = Rate Sensitive Assets - Rate Sensitive Liabilities = $50 mil - $70 mil = - $20 mil

Change in Net Interest Income = Repricing Gap * 1% = - $20 mil * 1% = -$0.2 mil.

Hence, for every 1% increase in interest rate, interest income declines by $0.2 mil.

Now, let us check if this remains valid in part b. The interest rates there increase by 2%.

This means, from the calculation we just did, the net interest income should decline by 2 * 0.2mil = 0.4 mil.

Difference in Net Interest Income in Part (b) and Part (a) is $0.4 mil, where net interest income is lower when interest rate rise.

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