Tax Equivalent Yield Calculator

What Is the Tax Equivalent Yield?

The tax equivalent yield (TEY) is the pretax yield a taxable bond must offer to match the after-tax return of a tax-exempt investment, such as a municipal bond. Because tax-free income is not subject to federal (and sometimes state) income tax, comparing it directly to a taxable yield is misleading. The TEY calculation adjusts for your tax bracket, giving you an apples-to-apples comparison.

For example, a municipal bond yielding 3.5% might seem low compared to a corporate bond yielding 4.5%. But if you are in a high tax bracket, the municipal bond's after-tax return could actually be higher. The tax equivalent yield tells you exactly what taxable yield you would need to beat that tax-free return.

How the Tax Equivalent Yield Is Calculated

The formula depends on whether you are comparing federal tax-exempt bonds or bonds that are also exempt from state and local taxes.

Basic Formula (Federal Tax Only)

Tax Equivalent Yield = Tax-Free Yield ÷ (1 − Federal Tax Rate)

The federal tax rate is expressed as a decimal. For example, if your marginal federal tax rate is 32% (0.32) and the tax-free yield is 3.5%:

TEY = 3.5% ÷ (1 − 0.32) = 3.5% ÷ 0.68 ≈ 5.15%

This means a taxable bond would need to yield at least 5.15% to provide the same after-tax income as the 3.5% tax-free bond.

Formula Including State Tax

If the bond is also exempt from state income tax, the formula adjusts to account for the state tax deduction on federal returns:

TEY = Tax-Free Yield ÷ (1 − Federal Rate − [State Rate × (1 − Federal Rate)])

This is relevant for investors in high-tax states like California or New York who hold in-state municipal bonds.

How to Use This Calculator

1. Enter the tax-free yield of the municipal bond or tax-exempt investment you are considering.
2. Enter your marginal federal tax rate (the rate applied to your highest dollar of income).
3. Optionally, enter your state tax rate if the bond is exempt from state income tax and you want a more precise comparison.
4. The calculator will display the tax equivalent yield — the taxable yield you would need to match the tax-free return.

You can also reverse the calculation: enter a taxable yield to see what tax-free yield would be equivalent.

Example: Comparing a Municipal Bond to a Corporate Bond

Suppose you are choosing between:

• A municipal bond yielding 3.2% (federal tax-free)
• A corporate bond yielding 4.5% (taxable)

Your marginal federal tax rate is 35%.

TEY = 3.2% ÷ (1 − 0.35) = 3.2% ÷ 0.65 ≈ 4.92%

The municipal bond's tax equivalent yield is 4.92%, which is higher than the corporate bond's 4.5%. Despite the lower nominal yield, the municipal bond provides a better after-tax return in your tax bracket.

Understanding Your Results

The tax equivalent yield is a comparison tool, not a prediction of future returns. It tells you the minimum taxable yield you would need to match the after-tax income of a tax-free investment.

• If the TEY is higher than available taxable yields, the tax-free bond is likely the better choice for your tax situation.
• If the TEY is lower than available taxable yields, a taxable bond may offer a higher after-tax return.
• The higher your tax bracket, the more valuable tax-free income becomes, and the higher the TEY will be.

Remember that this calculation does not account for credit risk, liquidity, or maturity differences between bonds. A municipal bond may carry lower credit risk than some corporate bonds, but that is a separate consideration.

Common Mistakes When Using Tax Equivalent Yield

• Using the wrong tax rate. Use your marginal federal tax rate, not your effective tax rate. The marginal rate determines the tax impact on additional investment income.
• Ignoring state taxes. If you live in a state with income tax and the bond is state-tax-exempt, include your state rate for an accurate comparison.
• Forgetting the Alternative Minimum Tax (AMT). Some municipal bonds are subject to AMT. If you are subject to AMT, the tax-free yield may be partially taxable, reducing the effective benefit.
• Comparing bonds with different risk profiles. The TEY calculation assumes equal risk. A high-yield corporate bond carries more default risk than a general obligation municipal bond. Adjust your comparison accordingly.

Limitations of the Tax Equivalent Yield

The tax equivalent yield is a useful screening tool, but it has limitations:

• It does not account for capital gains taxes. If you sell a bond before maturity, any price appreciation may be taxed differently than interest income.
• It assumes a constant tax rate. If your income changes significantly, your marginal rate may change, altering the comparison.
• It does not consider the time value of money. A bond's yield to maturity assumes reinvestment at the same rate, which may not be realistic.
• It ignores transaction costs and bid-ask spreads that can reduce actual returns.

Use the TEY as one input in a broader investment decision, not as the sole determining factor.

Practical Use Cases

• Portfolio allocation: Decide whether to hold municipal bonds or taxable bonds in taxable accounts versus tax-advantaged accounts.
• Bond ladder construction: Compare tax-free and taxable bonds across different maturities to optimize after-tax income.
• High-income investors: Determine whether tax-free municipal bonds are more advantageous than corporate bonds or Treasury securities.
• Retirement planning: Evaluate bond investments in taxable brokerage accounts versus tax-deferred accounts like IRAs.