An investor in the 32\% federal marginal income tax bracket resides in a state with a 5\% … — FINRA SIE (Securities Industry Essentials)

An investor in the $32\%$ federal marginal income tax bracket resides in a state with a $5\%$ state marginal income tax rate. The investor is evaluating a qualifying in-state municipal bond offering a yield of $4.41\%$ . What is the tax-equivalent yield (TEY) that a fully taxable corporate bond must offer to provide the investor with an equivalent after-tax return? Express your answer as a percentage rounded to two decimal places.

Answer: 7 %

Answer

7.00%

To determine the tax-equivalent yield of an in-state municipal bond, the combined federal and state tax rate must be used because the interest is exempt from both federal (

32\%

) and state (

5\%

) income taxes, resulting in a total tax rate of

37\%

. Applying the formula

\text{TEY} = \frac{\text{Municipal Yield}}{1 - \text{Marginal Tax Rate}}

gives

\frac{4.41\%}{1 - 0.37} = \frac{4.41\%}{0.63} = 7.00\%

. A fully taxable corporate bond must yield

7.00\%

to provide the same net after-tax income.

Step-by-Step Solution

Determine the combined marginal tax rate

Combined tax rate is 37% (0.37)

In-state municipal bond interest is triple-tax-exempt (exempt at both federal and state levels for state residents), so both federal (32%) and state (5%) tax rates apply when calculating tax equivalence against fully taxable corporate bonds.

Set up the Tax-Equivalent Yield formula

TEY = Municipal Yield / (1 - Combined Tax Rate)

This standard formula adjusts the tax-exempt yield upward to represent the yield a fully taxable security must pay to equal the tax-free return.

Perform the calculation

4.41% / (1 - 0.37) = 4.41% / 0.63 = 7.00%

Dividing the municipal yield by 0.63 provides the exact taxable yield needed to match the net after-tax return.

Key Concept

Tax-Equivalent Yield (TEY) for In-State Municipal Debt

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