Your best taxable investment opportunity has an EAR of 4%. Your best tax-free investment opportunity has an EAR of 3%. If your tax rate is 30%, which opportunity provides the higher after-tax interest rate?
To determine which opportunity provides the higher after-tax interest rate, we need to consider the effect of taxes on the returns.
Let's start by calculating the after-tax interest rate for the taxable investment opportunity:
Step 1: Calculate the tax-adjusted rate by subtracting the tax amount from the EAR of 4%:
Tax-adjusted rate = EAR - (tax rate * EAR)
Tax-adjusted rate = 4% - (30% * 4%)
Tax-adjusted rate = 0.04 - (0.30 * 0.04)
Tax-adjusted rate = 0.04 - 0.012
Tax-adjusted rate = 0.028 or 2.8%
Next, let's calculate the after-tax interest rate for the tax-free investment opportunity:
Since the tax-free investment opportunity has an EAR of 3%, there is no need to adjust it for taxes. Therefore, the after-tax interest rate for the tax-free investment opportunity is simply 3%.
Now, we can compare the two after-tax interest rates:
After-tax interest rate for taxable investment: 2.8%
After-tax interest rate for tax-free investment: 3%
Based on the calculations, the tax-free investment opportunity with an after-tax interest rate of 3% provides a higher return compared to the taxable investment opportunity with an after-tax interest rate of 2.8%.