Tax-Equivalent Yield Calculator
Find the taxable yield that matches a tax-free yield after federal and state tax.
What it does
Tax-equivalent yield answers a simple comparison question: what taxable yield would leave you with the same after-tax return as a tax-free investment? It is most often used to compare municipal bonds with taxable bonds, CDs, or Treasuries.
The calculation grosses up the tax-free yield by the tax rate you avoid. With a 3.5% tax-free yield and a combined 29% rate, the equivalent taxable yield is 3.5% divided by 0.71, or 4.93%. A taxable investment would need to yield 4.93% to match the tax-free one after tax.
The combined rate is usually the sum of the federal marginal rate and the state marginal rate. That simple sum is an approximation. It ignores the federal deduction for state and local taxes, the 3.8% net investment income tax, alternative minimum tax, and any state-level subtleties. It also assumes the investment is fully exempt from both taxes.
The result is a break-even yield, not a recommendation. A taxable bond with a higher yield may still carry more credit risk, interest-rate risk, or liquidity risk. Tax-exempt bonds can also be subject to state tax if you live outside the issuer's state. Use the calculator to frame the comparison, then look at risk and tax details.
How to use
- Enter the tax-free yield as a percentage.
- Enter your federal marginal tax rate.
- Enter your state marginal tax rate, or 0 if the interest is state-tax-exempt for you.
- Enter the amount you plan to invest.
- Read the combined rate and the tax-equivalent yield.
- Compare that yield with the taxable yields available for similar risk and maturity.
- Check the federal-only result if the state tax treatment is uncertain.
Formula
- TEY
- Tax-equivalent taxable yield as a percentage.
- Y_tf
- Tax-free yield as a percentage.
- f
- Federal marginal tax rate as a decimal.
- s
- State marginal tax rate as a decimal.
- r
- Combined marginal tax rate, approximated as f + s.
- Investment
- Amount used to convert the yield into annual income.
The combined rate is a simple sum. A more precise federal calculation may account for the state tax deduction and other limitations. If the bond is exempt from federal tax but taxable by your state, use the federal-only yield or a state-adjusted version. The calculator does not know the issuer's state or your residency, so it cannot decide the state exemption for you.
Worked example
Example: 3.5% tax-free yield, 24% federal, 5% state
Defaults: 3.5% tax-free yield, 24% federal, 5% state, $10,000 invested.
- Combined rate: 24% + 5% = 29.0%, or 0.29.
- Tax-equivalent yield: 3.5% / (1 - 0.29) = 3.5% / 0.71 = 4.93%.
- Federal-only yield: 3.5% / (1 - 0.24) = 4.61%.
- Tax-free income on $10,000: 3.5% x $10,000 = $350.
- Equivalent taxable income: 4.93% x $10,000 = $492.96.
- The taxable investment must earn about $142.96 more before tax to leave the same after-tax income.
Reference table
| Tax-free yield | Federal-only, 24% | Combined, 29% |
|---|---|---|
| 2.5% | 3.29% | 3.52% |
| 3.0% | 3.95% | 4.23% |
| 3.5% | 4.61% | 4.93% |
| 4.0% | 5.26% | 5.63% |
| 4.5% | 5.92% | 6.34% |
| 5.0% | 6.58% | 7.04% |
Limits
- Assumes the investment is fully exempt from federal and state income tax.
- Uses a simple sum of federal and state rates, not the federal deduction for state and local taxes.
- Ignores the net investment income tax, alternative minimum tax, and local taxes.
- Does not compare credit risk, duration, liquidity, call features, or state residency rules.
- A marginal rate is not the same as an average rate. Use the rate on the next dollar of income.
Common mistakes
- Using your average tax rate instead of your marginal rate.
- Adding state tax when the bond is already exempt from state tax where you live.
- Comparing a long-term municipal bond with a short-term CD without adjusting for maturity and risk.
- Treating the tax-equivalent yield as a guaranteed return. Bond yields and prices change.
- Forgetting that municipal bond interest can affect other tax calculations, such as Social Security taxation.
Try it yourself
Quick checks. Answers sit tucked under each question.
A tax-free yield is 3.0%, the federal rate is 24%, and the state rate is 5%. What is the tax-equivalent yield?
Combined rate is 29%, so TEY = 3.0% / 0.71 = 4.23%.
A tax-free yield is 4.0% and the federal rate is 32%. What is the federal-only tax-equivalent yield?
TEY = 4.0% / (1 - 0.32) = 5.88%.
A 3.5% tax-free yield on $25,000 produces how much annual income?
0.035 x $25,000 = $875 per year.
Questions
What is tax-equivalent yield?
It is the taxable yield that would give you the same after-tax return as a tax-free investment at your tax rates.
Is a higher tax-equivalent yield always better?
No. It only makes the after-tax yields comparable. You still need to compare credit quality, maturity, liquidity, and other risks.
Should I include state tax?
Include it only if the interest is taxable by your state. Many municipal bonds are exempt from federal tax but may be taxable in another state.
Why is the combined rate not exactly federal plus state?
The simple sum ignores interactions such as the federal deduction for state and local taxes and other tax rules. It is a common approximation for a quick comparison.
Can I use this for a Treasury bond?
Treasury interest is exempt from state and local tax but taxable federally. Use the federal-only result, and check the state treatment for any other investment.
Does the calculator include the net investment income tax?
No. If the 3.8% NIIT applies to you, add it to the federal rate or calculate a separate scenario.