Your best taxable investment opportunity has an EAR of 4%. You best tax-free investment opportunity has and 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 compare the after-tax rates of return for both taxable and tax-free investments.
Let's start by calculating the after-tax rate of return for the taxable investment opportunity.
Given:
- Taxable investment opportunity EAR: 4%
- Tax rate: 30%
Step 1: Calculate the taxable interest rate by dividing the EAR by (1 - tax rate):
Taxable interest rate = 4% / (1 - 0.30) = 4% / 0.70 = 5.7143%
Step 2: Subtract the tax rate from the taxable interest rate to get the after-tax interest rate:
After-tax interest rate (for taxable investment) = Taxable interest rate - tax rate
= 5.7143% - 30% = 5.7143% - 1.4286% = 4.2857%
Hence, the after-tax interest rate for the taxable investment opportunity is 4.2857%.
Now, let's calculate the after-tax rate of return for the tax-free investment opportunity.
Given:
- Tax-free investment opportunity EAR: 3%
- Tax rate: 30%
Since the tax-free investment is, as the name suggests, tax-free, we do not need to adjust the rate of return for taxes.
Therefore, the after-tax interest rate for the tax-free investment opportunity is simply equal to the EAR, which is 3%.
Comparing the after-tax interest rates of the two options:
- Taxable investment after-tax interest rate: 4.2857%
- Tax-free investment after-tax interest rate: 3%
The taxable investment opportunity provides a higher after-tax interest rate than the tax-free investment opportunity.