Tax-Equivalent Yield Calculator
The formula
What the tax-equivalent yield tells you
The classic bracket-arbitrage calculation: what a Treasury or corporate would have to pay to match a muni's after-tax income. At high brackets munis routinely win by 20–40 basis points of pretax yield.
Calculation: TEY = muni ÷ (1 − combined tax rate). Enter your inputs and every substitution is shown below the result.
Reading the result
Inverted-muni screens — where munis yield less than Treasuries after tax-equivalence — mark the top of municipal demand cycles.
Rules of thumb: TEY comparisons flip at the 35% federal bracket; below 24% treasuries often win
Limitations and best practice
Assumes you can use the exemption (AMT, NICRA rules, out-of-state double taxation and NIIT on some munis all break the math). The 3.8% net investment income tax applies to muni income for high earners — subtract that too.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Do munis beat Treasuries for me?
Do Treasuries get the same tax treatment?
Source & methodology
IRS §103 treatment; MSRB investor education materials.
How Tax-Equivalent Yield works — and what your result really means
Capital decisions deserve better than a gut feeling — this page gives you the arithmetic to defend one. Tax-Equivalent Yield is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Taxable-equivalent yield in real time, and see every substitution printed below.
There is a habit that separates people who get useful answers from Fixed Income numbers: they decide what question the figure answers before they compute it. Tax-Equivalent Yield answers “Taxable-equivalent yield?” — and nothing else, which is precisely why the result is trustworthy.
In Investing & Markets the same quantity is often quoted under two or three different conventions. The formula printed above fixes one convention and applies it consistently, which is what makes results from this page comparable with each other.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to taxable-equivalent yield = 5.58% on the default inputs, and the sensitivity section ranks the inputs that move the result — Tax-exempt yield first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
How Tax-Equivalent Yield is computed, line by line
Here is the complete model this tool runs — TEY = muni ÷ (1 − combined tax rate) — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Tax-exempt yield (%) (example value 3) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Federal marginal rate (%) (example value 34) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Enter it exactly as your document states it — quoted annual, monthly and effective rates are three different numbers.
State marginal rate (%) (example value 6) is a numeric input whose unit is fixed by the label; a wrong unit is a wrong answer wearing a plausible disguise. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Tax-Equivalent Yield with real numbers, step by step
Rather than describe the calculation, here it is end to end — every substitution in order, starting from the inputs above. Starting figures: Tax-exempt yield (%), Federal marginal rate (%), State marginal rate (%). Run to the end, the taxable-equivalent yield resolves to 5.58% — A corporate bond must pay 5.58% to beat this muni on the bands this tool uses.
- Combined rate = 1 − (1−0.34)(1−0.06) = 38.0%
- TEY = 3.46% ÷ (1 − 0.3796) = 5.58%
Combined marginal rate — 38.0 %. This is the number experienced users quote when the headline alone would mislead.
Federal-only equivalent — 5.24 %. This is the number experienced users quote when the headline alone would mislead.
After-tax value of a 5.2% taxable bond — 3.23 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
Re-running with your own figures is instant; re-running by hand once is the best way to know the tool is telling you the truth.
Scenario table: Tax-Equivalent Yield at ±10 % and ±20 % of the key input
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Tax-exempt yield setting | Taxable-equivalent yield |
|---|---|
| 80 % of the example value | 4.46% |
| 90 % of the example value | 5.02% |
| example inputs | 5.58% |
| 110 % of the example value | 6.13% |
| 120 % of the example value | 6.69% |
That spread — 4.46% at the low end, 6.69% at the high — is what a careful read of Tax-Equivalent Yield looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Tax-exempt yield alone; the substitution steps will follow your figures exactly.
The levers behind Tax-Equivalent Yield, ranked by effect
Nobody should have to guess which input matters. The engine was re-run once per field below — ten percent up, ten percent down, everything else frozen — and the results ranked by how far they moved the taxable-equivalent yield. It is the fastest honest answer to “what matters most in Tax-Equivalent Yield?” — and it is specific to these defaults, because sensitivity moves with the starting point.
- Tax-exempt yield: ten percent up gives 6.13%, ten percent down gives 5.02% — ≈10.0 % of the taxable-equivalent yield either way
- Federal marginal rate: ten percent up gives 5.88%, ten percent down gives 5.30% — ≈5.4 % of the taxable-equivalent yield either way
- Nudge State marginal rate by ±10 % and Tax-Equivalent Yield lands between 5.54% and 5.61% (sensitivity ≈0.6 %)
Tax-exempt yield is the dominant lever here: ten percent either way moves the result by about 10.0 %, from 5.02% to 6.13%. Spend your verification effort there first, and treat Federal marginal rate as the second priority (≈5.4 % per ten percent). The remaining fields can sit at safe defaults without materially changing the answer — knowing which is which is what separates a careful calculation from an anxious one.
What a Tax-Equivalent Yield of 5.58% means in practice
The value above only becomes useful the moment you know what it is being measured against. The default case lands in the “A corporate bond must pay 5.58% to beat this muni” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Tax-exempt yield already spans 5.02% to 6.13%. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Where Tax-Equivalent Yield sits next to similar measures: this tool answers “how much is the Tax-Equivalent Yield”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
Common mistakes with Tax-Equivalent Yield (and the fix)
Assumes you can use the exemption (AMT, NICRA rules, out-of-state double taxation and NIIT on some munis all break the math). The 3.8% net investment income tax applies to muni income for high earners — subtract that too. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Stopping at the first plausible answer. If the result surprises you, the productive question is which input would have to be wrong for the surprise to disappear — then go check that input.
Attention is also misallocated between fields. Having measured this engine, we can say where it belongs: Tax-exempt yield first, everything else second.
A final trap is presentation: reporting Tax-Equivalent Yield to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
A quick check for any Tax-Equivalent Yield figure
- Compare the result with one independent method or published benchmark.
- Verify each input against its original source document, not memory.
- Re-verify Tax-exempt yield against a source document — ten percent of error there moves the headline by ≈10.0 %.
- Confirm the example values are plausible for your own situation before replacing them.
- Note the date and the inputs beside the number so the figure can be audited later.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
Five steps from raw inputs to a figure you can defend
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — one document, one pass. Open the statement, label or record that holds tax-exempt yield (%), federal marginal rate (%), state marginal rate (%) and transcribe straight into the form. Transcription from a single source removes the mismatch errors that appear when figures are assembled from three different places. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 2 — start from the case you can defend. Enter pessimistic-but-honest figures first; the optimistic run is a ceiling, not a plan. A conclusion that holds on conservative inputs holds everywhere. Half of a good calculation is knowing which input you would hate to be wrong about.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. When two sources disagree, it is almost never the arithmetic that differs.
Step 4 — compute a corridor, not a point. Three runs — worst, likely, best — turn Tax-Equivalent Yield from a snapshot into a range. Plan against the pessimistic end and treat the optimistic end as the upside story. Write the figure down before moving on; memory flatters whichever number you saw last.
Step 5 — schedule the next run. In Investing & Markets the inputs drift quietly. Put a reminder a quarter out, re-enter the same fields, and read the change rather than the level. Most surprises in numbers are surprises about inputs, not about formulas.
The real-world conversations Tax-Equivalent Yield settles
Most Fixed Income disagreements are arithmetic disagreements in disguise. When Taxable-equivalent yield of 5.58% sits on the table with its working shown, the conversation stops being about who sounds more confident and starts being about which input is wrong. Precision is a promise you make about your data; make sure your inputs can keep it.
The companion outputs — Combined marginal rate and Federal-only equivalent — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
There is a personal-administration use people overlook: periodic self-checking. Tax-Equivalent Yield quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
The questions that come up most about Tax-Equivalent Yield
What affects Tax-Equivalent Yield the most?
Tax-Equivalent Yield is driven above all by Tax-exempt yield. Perturbing only that field by ten percent either way produced 6.13% against the 5.58% baseline — a ≈10.0 % response, while Federal marginal rate manages ≈5.4 %.
Which matters more: federal marginal rate or tax-exempt yield?
By the numbers, Tax-exempt yield: a ten-percent change in it moves the result ≈10.0 %, versus ≈5.4 % for Federal marginal rate. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Tax-Equivalent Yield?
On the worked example above Tax-Equivalent Yield comes out at 5.58%. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Tax-Equivalent Yield by hand?
TEY = muni ÷ (1 − combined tax rate) is the entire method. Work the inputs in that order — Combined rate = 1 − (1−0.34)(1−0.06) = 38.0% — and you will reach 5.58% on the default figures, the same number this tool prints.
What happens to Tax-Equivalent Yield if tax-exempt yield changes by 10 %?
The engine was re-run with that field moved by ten percent while everything else stayed fixed: the taxable-equivalent yield goes across 5.02% to 6.13%, a swing of roughly 10.0 % around the 5.58% baseline. That ratio is the practical definition of how much this input matters.
Is the Tax-Equivalent Yield result of 5.58% good or bad?
Neither, on its own — the label “A corporate bond must pay 5.58% to beat this muni” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Tax-exempt yield alone moves it by ≈10.0 %.
Is Tax-Equivalent Yield accurate?
The arithmetic is exact: TEY = muni ÷ (1 − combined tax rate) is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 5.58% result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Does Tax-Equivalent Yield account for fees and taxes?
Only what you put in. Fees belong inside Tax-exempt yield (%) where they shrink returns before compounding touches them; taxes are outside the scope of a pre-tax Tax-Equivalent Yield and should be layered on top before decisions.
Do munis beat Treasuries for me?
At 32%+ combined marginal rate, usually yes by TEY math; at 22% or below, Treasuries are simpler and more liquid. Run the numbers annually — spreads move.
Do Treasuries get the same tax treatment?
Treasuries are exempt from state and local tax but fully taxable federally. Compare them to munis by running TEY with the state rate only.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
Glossary for Tax-Equivalent Yield
- Combined marginal rate
- 38.0 % in the default Tax-Equivalent Yield calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Federal-only equivalent
- 5.24 % in the default Tax-Equivalent Yield calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- After-tax value of a 5.2% taxable bond
- 3.23 % on the example inputs — a companion figure printed beside the headline of Tax-Equivalent Yield so that no result is read in isolation.
- Taxable-equivalent yield
- The primary output of this tool: 5.58% for the default inputs, computed exactly from TEY = muni ÷ (1 − combined tax rate).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“A corporate bond must pay 5.58% to beat this muni” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Tax-Equivalent Yield moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Tax-Equivalent Yield calculation
The model is published arithmetic implemented exactly as written: TEY = muni ÷ (1 − combined tax rate). Source of record: IRS §103 treatment; MSRB investor education materials. Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
Treat the output as a precise answer to the question you typed: exact arithmetic, transparent formula, published source, no hidden rounding. What that buys you is reproducibility — two people, two browsers, the same arithmetic, and a printed trail from inputs to result that either of them can audit.
Next steps after the calculation
Run the pessimistic case before the optimistic one; an opportunity that survives the pessimistic inputs is the only kind worth pursuing.
The audience here is investors and founders comparing opportunities on equal terms. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.