Final answer:
To perform a standard gap analysis, we calculate the rate sensitive gap and multiply it by the change in interest rates to find the change in interest income. The duration analysis uses the average durations of assets and liabilities to find the duration gap, which helps in determining the effect on equity. Lastly, we calculate the new level of equity capital by subtracting the change in interest income from the current equity.
Step-by-step explanation:
To perform a standard gap analysis, we first need to calculate the gap which is the difference between rate sensitive assets and rate sensitive liabilities.
Rate Sensitive Gap (RSG) = Rate Sensitive Assets (RSA) - Rate Sensitive Liabilities (RSL)
RSG = $16.14m - $24.75m = -$8.61m
If there is a 1.45% increase in interest rates, the change in interest income can be calculated by multiplying the rate change by the gap:
Change in Interest Income = Rate Sensitive Gap × Change in Interest Rates
Change in Interest Income = -$8.61m × 1.45% = -$0.125m
The duration analysis would involve using the average duration of assets (D_A) and liabilities (D_L) to determine the impact on equity.
Duration Gap (DG) = (D_A × RSA) - (D_L × RSL)
DG = (6.6 × $16.14m) - (2.7 × $24.75m)
DG = $106.524m - $66.825m = $39.699m
Using the duration gap, we can calculate the change in equity value due to the interest rate change. First, we find the duration effect which is the product of the duration gap, the change in interest rates, and the total assets.
Duration Effect on Equity (DE) = Duration Gap × Change in Interest Rates × Total Assets
DE = $39.699m × 1.45% × ($16.14m + $50.66m)
DE = $39.699m × 1.45% × $66.8m = -$38.695m
The new level of equity capital will be the current equity less the change in interest income (since it's a loss):
New Equity Capital = Current Equity - Change in Interest Income
New Equity Capital = $9.09m - $0.125m = $8.965m