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Difficulty: EasyGovernment, Municipal, and Corporate Bonds

An investor in the 30%30\% marginal federal income tax bracket is evaluating a qualifying municipal bond offering a yield of 3.50%3.50\%. What yield must a fully taxable corporate bond offer to provide the investor with an equivalent after-tax return?

  1. 5.00%5.00\%Answer
  2. B
    2.45%2.45\%
  3. C
    4.55%4.55\%
  4. D
    3.50%3.50\%

Answer

The taxable corporate bond must yield 5.00%5.00\% to match the after-tax yield of the 3.50%3.50\% municipal bond.
Interest income from qualifying municipal bonds is generally exempt from federal income taxation. To compare a tax-exempt municipal yield to a taxable corporate bond yield, investors calculate the Tax-Equivalent Yield using the formula Municipal Yield÷(1−Tax Bracket)\text{Municipal Yield} \div (1 - \text{Tax Bracket}). Dividing 3.50%3.50\% by 0.700.70 yields 5.00%5.00\%.

Step-by-Step Solution

1
Identify the formula for Tax-Equivalent Yield (TEY).
Tax-Equivalent Yield=Municipal Yield1−Investor’s Tax Bracket\text{Tax-Equivalent Yield} = \frac{\text{Municipal Yield}}{1 - \text{Investor's Tax Bracket}}
Since interest from qualifying municipal bonds is exempt from federal income tax, a taxable corporate bond must generate a higher pre-tax yield to match the municipal bond's net payout.
2
Substitute the given values into the formula.
TEY=3.50%1−0.30=3.50%0.70\text{TEY} = \frac{3.50\%}{1 - 0.30} = \frac{3.50\%}{0.70}
The investor retains 70%70\% of any taxable interest income after paying federal income taxes.
3
Calculate the required pre-tax corporate yield.
TEY=5.00%\text{TEY} = 5.00\%
A 5.00%5.00\% corporate yield taxed at 30%30\% leaves an after-tax yield of 5.00%×(1−0.30)=3.50%5.00\% \times (1 - 0.30) = 3.50\%, matching the municipal bond.

Key Concept

Tax-Equivalent Yield (TEY) calculation for municipal debt vs. taxable debt
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Topics

Government, Municipal, and Corporate Bonds

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