How tax-equivalent yield works
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. State tax is a separate adjustment.
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%
The yield on the municipal bond or other tax-exempt instrument.
The federal rate that would apply to a taxable alternative. State tax is a separate adjustment.
On this page
In short
- Tax-equivalent yield is . A 3.50 percent tax-exempt yield at a 32 percent marginal tax rate is 3.50 / 0.68 = 5.1471 percent.
- The check is the other direction: 5.1471 percent times 0.68 is 3.50 percent. A taxable quote below 5.15 percent loses to the municipal on this one measure, credit risk aside.
- A 4 percent municipal at a 24 percent rate is 4 / 0.76 = 5.2632 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: 3.50 / 1 = 3.50 percent. With no tax to undo, the two quotes are already on the same footing.
- Use the marginal rate, not the average rate. The coupon you are comparing displaces income at the margin.
Undo the tax, then compare
A tax-exempt yield and a taxable yield are not in the same units until you put them there. Tax-equivalent yield asks what taxable yield, after tax, matches the exempt one:
A 3.50 percent municipal at a 32 percent federal marginal tax rate: percent, which prints as 5.15 percent. Check: .
The tax-equivalent yield calculator on this page is that division. It equalises tax treatment. It does not equalise credit risk, call risk, or duration. A 5.15 percent equivalent municipal is not a 5.15 percent Treasury.
How bond pricing works is the price of a coupon at a market yield. This page is the tax adjustment before you compare two yields.
The identity on this page is the row that equalises two quotes. Taxable against tax-exempt yield is the rest of the comparison: credit risk, call risk and state tax, which the division does not equalise.
A lower band shrinks the gap
A 4 percent municipal at a 24 percent federal band: percent. Check: .
The exempt yield is higher than 3.50 percent and the tax rate is lower than 32 percent. The equivalent is 5.26 percent, not far from the first sheet's 5.15 percent. The lower band does less work: there is less tax to undo. That is why the same municipal is worth more, in equivalent-yield terms, to a 32 percent filer than to a 24 percent filer.
No tax, nothing to undo
A 3.50 percent tax-exempt yield at a 0 percent tax rate is 3.50 percent. After-tax taxable yield is 3.50 percent times 1. The two quotes are already on the same footing.
This is the identity's floor. It is also why an average tax rate understates the equivalent: an average rate is lower than the marginal rate on the next dollar of coupon, so is too large and comes out too small.
What this page is not doing
It is not a state-tax adjustment, not an AMT screen, and not a credit comparison. Whether a state exempts in-state municipals or Treasuries depends on where you file. The three sheets are 3.50 percent at 32 percent (5.1471 percent equivalent), 4 percent at 24 percent (5.2632), and 3.50 percent at 0 percent (3.50). This is educational material, not financial advice.
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: .
- percent.
- Check: .
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.
- percent.
- Check: .
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?
- .
- After-tax taxable yield is .
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.
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. On the first sheet, 5.1471 percent is 3.50 percent divided by 0.68, nothing more.
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 because 1 minus that rate is too large.
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.