Yield Equivalence

Tax-Equivalent Yield

Overview

Tax-equivalent yield (TEY) is the taxable yield a bond must offer to match the after-tax return of a comparable tax-exempt investment, typically a municipal bond. Investors use TEY to compare tax-exempt and taxable fixed-income options on an apples-to-apples basis. The result depends on an investor’s marginal tax rate (including applicable state taxes).

Formula

TEY = (Tax-exempt yield) / (1 − t)

Where:
– TEY = tax-equivalent yield (the taxable yield required)
– Tax-exempt yield = yield on the municipal (tax-free) bond
– t = investor’s marginal tax rate (federal plus any relevant state tax)

You can reverse the formula to find the tax-free yield equivalent of a given taxable yield.

Tip: Include state income taxes (if applicable) when calculating t.

How to use it

• Calculate TEY for the municipal yield using your marginal tax rate.
• Compare that TEY to the yield on a taxable bond.
• If the taxable bond’s yield > TEY, the taxable bond offers the higher after-tax return.
• If the taxable bond’s yield < TEY, the municipal bond offers the higher after-tax return.

Examples

1) Comparing a 7% tax-free bond across marginal tax brackets:
– 10% bracket: TEY = 7% / (1 − 0.10) = 7.78%
– 12% bracket: TEY = 7% / (1 − 0.12) = 7.95%
– 22% bracket: TEY = 7% / (1 − 0.22) = 8.97%
– 24% bracket: TEY = 7% / (1 − 0.24) = 9.21%
– 32% bracket: TEY = 7% / (1 − 0.32) = 10.29%
– 35% bracket: TEY = 7% / (1 − 0.35) = 10.77%
– 37% bracket: TEY = 7% / (1 − 0.37) = 11.11%

If a taxable bond yields 9.75%, investors in the 10%, 12%, 22%, and 24% brackets would earn more after tax from the taxable bond; those in the top three brackets might prefer the 7% tax-free bond.

2) Specific calculation:
– Investor in 22% bracket owns an 8% municipal bond:
TEY = 8% / (1 − 0.22) = 10.26%
A taxable bond must yield at least 10.26% to match the municipal bond’s after-tax return.
– In the 37% bracket, the same 8% muni requires:
TEY = 8% / (1 − 0.37) = 12.70%

Tax treatment and other considerations

• Municipal bond interest is generally exempt from federal income tax. State tax treatment varies: some states exempt interest from in-state municipal bonds but tax out-of-state munis.
• U.S. Treasury interest is subject to federal income tax but typically exempt from state and local taxes.
• Capital gains on tax-free investments (for example, selling a municipal bond for a profit or mutual funds holding tax-free bonds) are taxable.
• The IRS may tax bond interest differently if a bond is bought at a significant discount to par.
• Taxable municipal bonds do exist (issued for certain projects or circumstances) but are less common.

Key takeaways

• TEY lets you compare a tax-exempt bond’s return to taxable alternatives by adjusting for taxes.
• Use TEY = tax-exempt yield / (1 − marginal tax rate), including state taxes when relevant.
• Choose the instrument (taxable vs. tax-exempt) based on whether the taxable yield exceeds the TEY given your tax situation.