Taxable vs tax-exempt yield
A tax-exempt yield and a taxable yield are not in the same units until you undo the tax. A 3.50 percent municipal at a 32 percent federal marginal rate equals a 5.15 percent taxable yield. At 24 percent the same identity on a 4 percent municipal prints 5.26 percent. Credit risk is still a separate question.
| Tax-exempt yield | Tax-equivalent yield | |
|---|---|---|
| Formula | The municipal quote itself. | Exempt yield / (1 - marginal tax rate). |
| 3.50 percent at 32 percent federal | 3.50 percent after federal tax, on the teaching sheet. | 5.1471 percent taxable, because 5.1471 times 0.68 is 3.50. |
| 4 percent at 24 percent federal | 4 percent after federal tax. | 5.2632 percent taxable, because 5.2632 times 0.76 is 4. |
| Zero tax rate | 3.50 percent, unchanged. | 3.50 percent. With no tax to undo, the quotes already match. |
| Which rate to type | The exempt quote on the bond. | The federal marginal rate, not the average rate. |
| What it leaves out | State tax, AMT, and whether the state exempts in-state municipals. | Credit risk, call risk, and duration. A 5.15 percent equivalent is not a 5.15 percent Treasury. |
On this page
Undo the tax, then compare
A 3.50 percent municipal at a 32 percent federal marginal tax rate is 3.50 / 0.68 = 5.1471 percent taxable. That is tax-equivalent yield: the taxable quote that, after tax, matches the tax-exempt one.
A 4 percent municipal at 24 percent is 5.2632 percent equivalent. The lower band does less work. The same municipal is worth more, in equivalent-yield terms, to a 32 percent filer than to a 24 percent filer.
Equal tax treatment is not equal risk
The identity equalises tax. It does not equalise credit, call, or duration. On the first sheet, 5.15 percent is 3.50 percent divided by 0.68, nothing more.
How tax-equivalent yield works is the long form, with the calculator under the answer. How bond pricing works is the price at a yield once the yields are in the same units. 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
Should I use my average tax rate?
No. The coupon displaces income at the margin. An average rate understates the equivalent because 1 minus that rate is too large. On the first sheet the 32 percent is a marginal rate, and 3.50 / 0.68 is 5.1471 percent.
Does a higher equivalent mean a better bond?
No. It means the tax treatment has been equalised. A 5.15 percent equivalent municipal is not a 5.15 percent Treasury. Credit, call and duration still differ.
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.