Tax-Equivalent Yield: What It Is and How It Works

What Is Tax-Equivalent Yield?

The tax-equivalent yield is the return a taxable bond needs to equal the yield on a comparable tax-exempt municipal bond. Investors use this calculation to compare the returns between a tax-free investment and a taxable alternative.

Tax-Equivalent Yield Formula

The tax-equivalent yield is the yield on a taxable bond that an investor would have to earn to match the return on a comparable tax-free investment. Depending on an investor's tax bracket, a tax-free vehicle like a municipal bond may not be the best investment decision for their portfolio.

An investor's tax bracket depends on their filing status and income. The federal income tax brackets for 2024 and 2025 are 10%, 12%, 22%, 24%, 32%, 35%, and 37%. To calculate the taxable equivalent yield of a tax-free municipal bond:

Return (TEY) = Return (TX) / (1 - t)

Where:

• Return (TEY) = Return on fully taxable equivalent yield
• Return (TX) = Return on tax-exempt investment
• t = Investor's marginal tax rate

This formula can be reversed to determine the tax-free equivalent yield of a municipal bond that would match the return on a taxable bond.

Tax Rate Implications

An investor's tax bracket and rate affect the resulting tax-equivalent yields. For example, assume there is a tax-free bond yielding 7%. Investing in this bond or any of the many taxable choices available greatly depends on the investor's marginal tax bracket. In 2024, the tax-equivalent yield calculations for these brackets are:

• 10% Bracket: R(te) = 7% / (1 - 10%) = 7.78%
• 12% Bracket: R(te) = 7% / (1 - 12%) = 7.95%
• 22% Bracket: R(te) = 7% / (1 - 22%) = 8.97%
• 24% Bracket: R(te) = 7% / (1 - 24%) = 9.21%
• 32% Bracket: R(te) = 7% / (1 - 32%) = 10.29%
• 35% Bracket: R(te) = 7% / (1 - 35%) = 10.77%
• 37% Bracket: R(te) = 7% / (1 - 37%) = 11.11%

Given this information, assume a taxable bond yields 9.75%. Investors in the first four marginal tax brackets would be better off investing in the taxable bond because they would still earn more than a 7% non-taxable bond after tax liability. Investors in the highest three brackets may choose the tax-free bond.

Examples

An investor in the 22% federal income tax bracket with no state taxes owns a tax-exempt municipal bond with an 8% coupon rate. To calculate the fully taxable equivalent yield that a taxable bond would have to earn to match the municipal bond's yield:

Return (TEY) = 0.08 / (1 - 0.22) = 10.26%

A taxable bond would have to earn an equivalent yield of 10.26%. After taxes are deducted this bond would match the 8% return of the tax-free municipal bond.

If the marginal tax rate is higher, the required fully taxable equivalent yield will also be higher than 10.26%. If the investor is in the 37% tax bracket, the fully taxable equivalent yield would have to be:

Return (TEY) = 0.08 / (1 - 0.37) = 12.70%

The Bottom Line

The tax-equivalent yield is the return a taxable bond needs to equal the yield on a comparable tax-exempt bond, such as a municipal bond. A bond's interest income, called coupon payments, is taxed according to the type of bond and where it's issued. Coupon payments from a U.S. Treasury bond are free from state and local taxes. Coupon payments from municipal bonds are also exempt from regular federal income tax.