An investor in a 40% marginal tax bracket purchased a stock for $45 and sold it for $52.20 at the end of the year. If inflation was 2.6% over the period, what is the investor’s real, after-tax rate of return?
Question
An investor in a 40% marginal tax bracket purchased a stock for 52.20 at the end of the year. If inflation was 2.6% over the period, what is the investor’s real, after-tax rate of return?
Solution
Step 1: Calculate the nominal return
The nominal return is the percentage change in the value of the investment. It can be calculated as follows:
Nominal Return = (Selling Price - Purchase Price) / Purchase Price
In this case, the selling price is 45.
Nominal Return = (45) / 7.20 / $45 = 0.16 or 16%
Step 2: Calculate the after-tax return
The after-tax return is the nominal return adjusted for taxes. It can be calculated as follows:
After-tax Return = Nominal Return * (1 - Tax Rate)
In this case, the tax rate is 40%.
After-tax Return = 16% * (1 - 0.40) = 16% * 0.60 = 9.6%
Step 3: Calculate the real return
The real return is the after-tax return adjusted for inflation. It can be calculated as follows:
Real Return = (1 + After-tax Return) / (1 + Inflation Rate) - 1
In this case, the inflation rate is 2.6%.
Real Return = (1 + 9.6%) / (1 + 2.6%) - 1 = 1.096 / 1.026 - 1 = 0.0682 or 6.82%
So, the investor’s real, after-tax rate of return is 6.82%.
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