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XYZ Bank Balance Sheet (in AUD millions) (as of June 30, 2022) Assets: 1. Cash ...
May 14, 2024
Solution by Steps
step 1
Identify the one-year rate-sensitive assets (RSA) and rate-sensitive liabilities (RSL) from the balance sheet
step 2
Calculate the total RSA: RSA=Short-term Treasury Bonds+Maturity within 6 months+Maturity within 6-12 months+Checking Accounts+Savings Accounts+Short-Term Borrowings \text{RSA} = \text{Short-term Treasury Bonds} + \text{Maturity within 6 months} + \text{Maturity within 6-12 months} + \text{Checking Accounts} + \text{Savings Accounts} + \text{Short-Term Borrowings} RSA=120+80+40+350+400+100=1090 million AUD \text{RSA} = 120 + 80 + 40 + 350 + 400 + 100 = 1090 \text{ million AUD}
step 3
Calculate the total RSL: RSL=Checking Accounts+Savings Accounts+Short-Term Borrowings \text{RSL} = \text{Checking Accounts} + \text{Savings Accounts} + \text{Short-Term Borrowings} RSL=350+400+100=850 million AUD \text{RSL} = 350 + 400 + 100 = 850 \text{ million AUD}
step 4
Calculate the cumulative repricing gap: Cumulative Repricing Gap=RSA−RSL \text{Cumulative Repricing Gap} = \text{RSA} - \text{RSL} Cumulative Repricing Gap=1090−850=240 million AUD \text{Cumulative Repricing Gap} = 1090 - 850 = 240 \text{ million AUD}
Answer
The one-year rate-sensitive assets are 1090 million AUD, the rate-sensitive liabilities are 850 million AUD, and the cumulative repricing gap is 240 million AUD.
Key Concept
Rate-sensitive assets and liabilities
Explanation
Rate-sensitive assets and liabilities are those that will reprice or mature within one year. The cumulative repricing gap is the difference between these assets and liabilities.
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Solution by Steps
step 1
Identify the interest rate formulas for assets and liabilities: Interest rate on assets=Cash rate+0.02 \text{Interest rate on assets} = \text{Cash rate} + 0.02 Interest rate on liabilities=0.4×Cash rate+0.01 \text{Interest rate on liabilities} = 0.4 \times \text{Cash rate} + 0.01
step 2
Find the change in the cash rate from June 30, 2022, to June 30, 2023, using the RBA's website. Assume the cash rate increased by 1% (for example purposes)
step 3
Calculate the new interest rates: New interest rate on assets=(Cash rate+0.01)+0.02=Cash rate+0.03 \text{New interest rate on assets} = (\text{Cash rate} + 0.01) + 0.02 = \text{Cash rate} + 0.03 New interest rate on liabilities=0.4×(Cash rate+0.01)+0.01=0.4×Cash rate+0.004+0.01=0.4×Cash rate+0.014 \text{New interest rate on liabilities} = 0.4 \times (\text{Cash rate} + 0.01) + 0.01 = 0.4 \times \text{Cash rate} + 0.004 + 0.01 = 0.4 \times \text{Cash rate} + 0.014
step 4
Calculate the impact on net interest income using the repricing model: Change in net interest income=(New interest rate on assets−New interest rate on liabilities)×Cumulative Repricing Gap \text{Change in net interest income} = (\text{New interest rate on assets} - \text{New interest rate on liabilities}) \times \text{Cumulative Repricing Gap} Change in net interest income=((Cash rate+0.03)−(0.4×Cash rate+0.014))×240 \text{Change in net interest income} = ((\text{Cash rate} + 0.03) - (0.4 \times \text{Cash rate} + 0.014)) \times 240 =(0.6×Cash rate+0.016)×240 = (0.6 \times \text{Cash rate} + 0.016) \times 240 =0.6×1%×240+0.016×240 = 0.6 \times 1\% \times 240 + 0.016 \times 240 =1.44+3.84=5.28 million AUD = 1.44 + 3.84 = 5.28 \text{ million AUD}
Answer
The impact on the bank's net interest income due to the increase in cash rates is an increase of 5.28 million AUD.
Key Concept
Net interest income
Explanation
Net interest income is the difference between the interest income generated by banks and the amount of interest paid out to their lenders. The repricing model helps in understanding the impact of interest rate changes on this income.
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