Case 1
- Tax-free yield
- 3.5%
- Marginal tax rate
- 32%
5.147%
Open with these valuesTax-Equivalent Yield Calculator
5.147%
Result: 5.147 %Divide the tax-free yield by what is left of a euro after tax. In the 32 % bracket you keep 68 %, so a 3.5 % tax-free yield is worth the same as 5.147 % taxable. The higher the bracket, the further apart the two numbers move — which is why tax-free bonds favour high earners.
Worked examples
Case 2
- Tax-free yield
- 3%
- Marginal tax rate
- 37%
4.762%
Open with these valuesCase 3
- Tax-free yield
- 2.5%
- Marginal tax rate
- 12%
2.841%
Open with these valuesHow it's calculated
TEY = tax-free yield ÷ (1 − tax rate)
- StepEnter the yield on the tax-exempt investment, before any tax.
- StepAdd your marginal rate — the rate on your next euro of income.
- StepWhere two exemptions apply, add both marginal rates together.
- ResultCompare the result with the yield of a taxable bond of similar risk.
What this number means
Municipal bond interest is usually exempt from federal income tax, so you keep every cent of it. A taxable bond hands part of its interest to the tax collector, which makes the two impossible to compare on headline yields alone. Tax-equivalent yield levels the field: it is the yield a taxable bond would have to pay to leave you just as well off after tax. The arithmetic is a single division — the tax-free yield divided by the share of income you keep, which is one minus your marginal rate. A 3.5 percent tax-free yield for someone in the 32 percent bracket comes out at 5.147 percent, because only 68 percent of every taxable unit of interest actually reaches you. Read the result as a break-even. A taxable bond of similar risk yielding more than that beats the tax-free one for you; anything yielding less loses to it. Because the denominator shrinks as the bracket rises, the same bond is worth wildly different amounts to different people: that 3.5 percent yield is equivalent to 3.98 percent in the 12 percent bracket but 5.56 percent in the 37 percent one, which is why tax-free income rewards high earners most. The caveat that matters most is which rate you type in — your marginal rate, the rate on your next unit of income, never your average rate. Credit risk, duration and liquidity are not in this number at all.
Marginal rate, never the average one
The divisor is the rate on your next unit of income, not the share of your whole income that goes in tax. Entering the average rate understates the result.
The same bond is worth different amounts
A 3.5 percent tax-free yield equals 3.98 percent in the 12 percent bracket and 5.56 percent in the 37 percent one. Tax-free income rewards high earners most.
Read it as a break-even
A taxable bond of similar risk yielding more than the figure shown beats the tax-free one for you. Anything below it loses to it.
Commonly misread
A higher tax-equivalent yield means the better bond.
It only means better after tax at your rate. Credit risk, duration and liquidity are not in this number at all.
State tax is in here too.
The figure uses the single rate you entered. A bond exempt from state tax as well leaves your true break-even higher than this shows.
Reference table
| Tax-free yield, tax rate | Yield pickup | Tax-equivalent yield |
|---|---|---|
| 3.5, 32 | 1.647 | 5.147 |
| 4, 24 | 1.263 | 5.263 |
| 3, 12 | 0.409 | 3.409 |
| 3, 37 | 1.762 | 4.762 |
| 2.5, 12 | 0.341 | 2.841 |
| 5, 0 | 0.000 | 5.000 |
Questions
What is tax-equivalent yield?
It is the yield a taxable investment would need to offer to leave you with the same return after tax as a tax-free one. Because municipal bond interest is usually exempt from federal and sometimes state tax, a 3.5 % muni can beat a higher-yielding taxable bond once tax is counted. This calculator finds that break-even taxable yield.
What is the formula?
TEY = tax-free yield ÷ (1 − marginal tax rate). A 3.5 % tax-free yield in the 32 % bracket is 3.5 ÷ 0.68 = 5.147 %. Note the division: multiplying instead is the classic mistake, and it would give 2.38 %, which is lower than the tax-free yield and therefore nonsense.
Why do higher brackets benefit more?
Tax-free income is worth more when you would otherwise lose more to tax. Someone in the 12 % bracket keeps 88 % of taxable interest, so the exemption is worth 12 %; someone in the 37 % bracket keeps only 63 %. That is why the same 3 % muni is worth 3.409 % to the first and 4.762 % to the second.
Which tax rate should I enter?
Your marginal rate — the rate on your next euro of income, not your average rate, because the interest sits on top of everything else you earn. If the bond is exempt from two taxes at once, add the two marginal rates and enter the combined figure. The calculator simply uses whatever rate you give it.
When is a tax-free bond worth it?
Compare the tax-equivalent yield with what a taxable bond of similar risk actually pays. If the tax-equivalent yield is higher, the tax-free bond wins for you. Because it rises with your bracket, tax-free bonds tend to favour high earners, while low-bracket investors often do better with a higher-yielding taxable bond in a tax-sheltered account.
Is this a substitute for tax advice?
No. The formula ignores surtaxes such as the US alternative minimum tax and the net investment income tax, any allowance that shelters part of your interest, and everything else about your situation. Confirm the figures with a qualified tax professional before deciding.
Sources and last check
Information, not financial advice.