Final answer:
To estimate the effect of a 100 basis point decrease in interest rates on the market value of equity, the duration approximation formula can be used. However, without the initial market value or the duration of the bank's equity, the exact dollar effect cannot be calculated. Generally, the market value of a bank's equity increases when interest rates decrease.
Step-by-step explanation:
The effect of a 100 basis point decrease in interest rates on the market value of equity of a bank can be estimated using the duration approximation relationship. Given that R (the initial interest rate) equals 4%, we can calculate the percentage change in the value of equity using the formula:
ΔValue / Value = -Duration * ΔR / (1 + R)
However, since the exact duration of the bank's equity is not provided, we cannot compute the dollar change in market value. For illustrative purposes, if we assume a duration of 5 (without currency units), the formula will look like this:
ΔValue / Value = -5 * (-0.01) / (1 + 0.04) = 0.0481 or 4.81%
To get the change in dollar value, we would need the initial market value of the equity. We would then calculate:
ΔValue = Market Value * 0.0481
Without the initial market value, we are unable to provide the exact dollar effect. But it is certain that a decrease in interest rates typically increases the market value of a bank's equity due to the inverse relationship between interest rates and the value of financial assets.