Tax-equivalent yield calculator

Published August 16, 2026

Tax-equivalent yield is the taxable yield that matches a tax-exempt yield after tax. A 3.50 percent municipal yield at a 32 percent federal rate equals a 5.15 percent taxable yield, because 5.15 percent times 0.68 is 3.50 percent.

Tax-equivalent yield

5.15%

A taxable yield of 5.15% leaves 3.50% after 32 percent tax, matching the tax-exempt quote.

Tax-exempt yield: 3.50%
Marginal tax rate: 32%
Tax-equivalent yield: 5.15%
Check: after-tax taxable yield: 3.50%

Tax-exempt yield

The yield on the municipal bond or other tax-exempt instrument.

Marginal tax rate

The federal rate that would apply to a taxable alternative. State tax is a separate adjustment.

The formula

y_{te} = \frac{y_{ex}}{1 - t}

$y_{ex}$ is the tax-exempt yield and $t$ is the marginal tax rate, both as decimals. The identity is just 'undo the tax': a taxable yield, after tax, should equal the exempt yield.

What the identity is matching

A tax-exempt yield and a taxable yield cannot be compared as printed, because one of them still has tax to pay. The tax-equivalent yield puts them on the same after-tax footing. At a 32 percent marginal rate, a 3.50 percent municipal yield is the same after-tax amount as a 5.15 percent taxable yield, because $0.051471 \times (1 - 0.32) = 0.035$ .

The rate in the formula is the marginal tax rate that would apply to the taxable alternative, not the average rate on all income. A municipal coupon that displaces income at the top of the schedule is saved at the top rate. Using the average rate understates the equivalent yield and makes the municipal look worse than the identity says.

At a 24 percent rate, a 4 percent tax-exempt yield is equivalent to 5.26 percent taxable: $0.04 / 0.76 = 0.052632$ . Lower brackets shrink the gap, which is why the same municipal quote is worth less, in equivalent-yield terms, to a holder who is not in the 32 percent band.

What the identity leaves out

State tax, the federal exemption for some Treasuries, and the alternative minimum tax are all local adjustments. A state that taxes Treasuries and exempts its own municipals widens the gap; a state that taxes both narrows it. This calculator is federal only, on purpose. Folding a guessed state rate into the one-line identity is how a 5.15 percent equivalent becomes a number nobody can audit.

Credit risk is also outside it. A 3.50 percent municipal yield is not 'the same' as a 5.15 percent Treasury yield just because the tax identity matches. One of them can default. The identity equalises tax treatment. It does not equalise issuers.

Holding period matters in a different way. The identity is about yield, a rate. Selling a municipal at a gain can produce taxable capital gain even when the coupons were exempt. That is a price-path fact, not a yield-identity fact, and it does not belong inside $1-t$ .

The check that the arithmetic is right

Multiply the tax-equivalent yield by one minus the tax rate. You must get the exempt yield back. On the default, $5.1471 \times 0.68 = 3.50$ . If you do not, the rate or the tax band was typed as a percent where a decimal belongs, or the other way around. 32 percent is 0.32 in the formula, not 32.

That check is also why a 0 percent tax rate returns the exempt yield unchanged, and why a 100 percent tax rate has no finite equivalent: there is no taxable yield that survives a tax that takes everything. The calculator will not print infinity there. It will refuse the band.

Where this sits next to APR and APY

APR against APY is a compounding conversion. Tax-equivalent yield is a tax conversion. They are both 'put these two quoted rates on the same footing' tools, and they are not interchangeable. A municipal APY still needs the tax identity on top if you are comparing it to a taxable APY. Do the compounding conversion first, so both yields are effective annual, then do this conversion so both are after tax.

The APR against APY calculator is the compounding step. The real return calculator is the inflation step. After-tax, after-inflation, after-compounding is three identities, not one.

Worked examples

A 3.50 percent municipal at a 32 percent federal rate

A municipal bond yields 3.50 percent. Your federal marginal rate is 32 percent. What taxable yield matches it after tax?

Divide the exempt yield by one minus the tax rate: $3.50 / (1 - 0.32) = 3.50 / 0.68$ .
$3.50 / 0.68 = 5.1471$ percent.
Check: $5.1471 \times 0.68 = 3.50$ .

The tax-equivalent yield is 5.15 percent. A taxable quote below 5.15 percent loses to the municipal on tax-adjusted yield at this band; a quote above it wins on that one measure, credit risk aside.

A 4 percent municipal at a 24 percent rate

The same identity at a 24 percent federal band, with a 4 percent tax-exempt yield.

$4 / (1 - 0.24) = 4 / 0.76 = 5.2632$ percent.
Check: $5.2632 \times 0.76 = 4$ .

The tax-equivalent yield is 5.26 percent. The lower band shrinks the gap: the same 4 percent municipal was worth more, in equivalent-yield terms, at 32 percent than it is at 24 percent.

A zero tax rate leaves the yield unchanged

A 3.50 percent tax-exempt yield at a 0 percent tax rate. What is the equivalent?

$3.50 / (1 - 0) = 3.50$ .
After-tax taxable yield is $3.50 \times 1 = 3.50$ .

The tax-equivalent yield is 3.50 percent, the exempt yield itself. With no tax to undo, the two quotes are already on the same footing.

The mistake that costs the most

Multiplying the municipal yield by one minus the tax rate, instead of dividing.

$3.50 \times (1 - 0.32) = 2.38$ percent, which is the after-tax leftover of a 3.50 percent taxable yield, not the equivalent of a 3.50 percent exempt yield. The identity that matches an exempt yield is division, $y / (1-t)$ . Multiplication goes the other way: it taxes a taxable yield. Mixing them understates the municipal by a wide margin and will make almost every exempt quote look worse than the arithmetic says.

Common questions

Does this include state tax?

No. The rate is a federal marginal rate. State tax, and whether the state exempts in-state municipals or Treasuries, is a separate adjustment that depends on where you file.

Is a higher equivalent yield always the better bond?

No. The identity equalises tax treatment. Credit risk, call risk, and duration still differ. A 5.15 percent equivalent municipal is not a 5.15 percent Treasury.

Should I use my average tax rate?

No. The coupon you are comparing displaces income at the margin, so the marginal rate is the one the identity needs. An average rate understates the equivalent yield.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.