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Difficulty: MediumGovernment, Municipal, and Corporate Bonds

An investor in a 25%25\% federal marginal income tax bracket is evaluating a tax-exempt municipal bond offering a yield of 4.20%4.20\%. What taxable corporate bond yield would provide this investor with an equivalent after-tax return?

Answer: 5.6 %

Answer

The required corporate bond yield to achieve an equivalent after-tax return is 5.6%5.6\%.
To determine the taxable corporate bond yield required to match a tax-exempt municipal yield, divide the municipal yield by (1−marginal tax rate)(1 - \text{marginal tax rate}). Dividing 4.20%4.20\% by (1−0.25)=0.75(1 - 0.25) = 0.75 yields 5.60%5.60\%. An investor in the 25%25\% federal tax bracket earning 5.60%5.60\% on a corporate bond retains 75%75\% of that yield after taxes (5.60%×0.75=4.20%5.60\% \times 0.75 = 4.20\%), which equals the tax-free yield of the municipal bond.

Step-by-Step Solution

1
State the Tax-Equivalent Yield (TEY) formula
Tax-Equivalent Yield=Tax-Free Yield1−Marginal Tax Rate\text{Tax-Equivalent Yield} = \frac{\text{Tax-Free Yield}}{1 - \text{Marginal Tax Rate}}
Municipal bond interest is exempt from federal income tax. To compare it to taxable corporate debt, the tax-free yield must be adjusted upward to reflect what a taxable bond would need to earn before taxes.
2
Substitute the investor's tax bracket and municipal yield into the equation
TEY=4.20%1−0.25=4.20%0.75\text{TEY} = \frac{4.20\%}{1 - 0.25} = \frac{4.20\%}{0.75}
Subtracting the marginal tax rate from 100%100\% (1.001.00) identifies the proportion of income the investor retains after federal taxes.
3
Perform the division to calculate the equivalent taxable yield
5.60%5.60\%
An investor earning 5.60%5.60\% on a taxable bond would pay 25%25\% in taxes (1.40%1.40\%), resulting in a net after-tax yield of 4.20%4.20\% (5.60%−1.40%=4.20%5.60\% - 1.40\% = 4.20\%).

Key Concept

Tax-Equivalent Yield (TEY)
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Topics

Government, Municipal, and Corporate Bonds

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