The after-tax real rate of return is a financial metric that takes into account both inflation and taxes to provide a more accurate measure of the actual return on an investment after adjusting for the effects of these factors. It reflects the real purchasing power gained or lost on an investment after considering the impact of both inflation and taxes.

Here’s how you can calculate the after-tax real rate of return:

1. **Calculate the Nominal Rate of Return:**
– Begin by determining the nominal rate of return, which is the rate of return on an investment before adjusting for inflation or taxes. This rate is typically expressed as a percentage.

2. **Deduct Taxes:**
– Subtract any applicable taxes from the nominal rate of return. Taxes can significantly impact the actual returns on an investment, so it’s essential to account for them in the calculation.

3. **Adjust for Inflation:**
– Adjust the after-tax return for inflation by subtracting the inflation rate from the after-tax rate of return. This adjustment reflects the impact of inflation on the purchasing power of the investment returns.

The formula for calculating the after-tax real rate of return is as follows:

\[ \text{After-Tax Real Rate of Return} = \left( \frac{\text{1 + Nominal Rate of Return}}{\text{1 + Inflation Rate}} – 1 \right) \times (1 – \text{Tax Rate}) \]

In this formula:

– **Nominal Rate of Return:** The rate of return on the investment before adjusting for inflation or taxes.

– **Inflation Rate:** The rate at which the general level of prices for goods and services is rising, representing the reduction in the purchasing power of money.

– **Tax Rate:** The percentage of investment returns that is paid in taxes.

The after-tax real rate of return is expressed as a percentage, and it provides a more meaningful measure of an investment’s performance by accounting for the erosion of purchasing power due to inflation and the impact of taxes on returns.

Investors and financial analysts use the after-tax real rate of return to assess the actual growth or decline in wealth after considering the effects of inflation and taxes. This metric is particularly important for long-term investors who want to gauge the real value of their investments over time.