Wondering whether a 3.42% municipal bond really beats a 5.31% corporate bond once taxes are paid? The tax-equivalent yield calculator converts a tax-exempt yield into the yield a taxable investment would have to pay to leave you with the same after-tax income. Enter the tax-free yield and your marginal tax bracket, and the tax-equivalent yield (TEY) shows the number a taxable bond must beat. Below you will find the formula, a full worked example, a bracket-by-bracket table and the traps that change the answer. If you want to see how the figures change, the cd calculator online gives you an instant result you can adjust as you go.
What Is My Tax-Equivalent Yield? The Formula Behind the Result
The tax equivalent yield is the return a taxable bond must offer so that, after you pay tax on its interest, you keep as much as you would from a tax-exempt bond. Interest from a municipal bond is not subject to federal income tax, so its stated yield is already your take-home yield. A taxable bond's stated yield is not, which makes a direct comparison misleading. The equivalent yield puts both on the same footing. The free cash and equities questionnaire uses the same plain-English approach, so you can compare results side by side.
$$\text{TEY} = \frac{\text{Tax-Free Yield}}{1 - \text{Marginal Tax Rate}}$$
The denominator is the share of each dollar of interest you keep after tax. At a 32% marginal tax rate you keep 68 cents, so a tax-free 3.42% has to be divided by 0.68 to find the taxable yield that delivers the same cash. The higher your bracket, the smaller the denominator and the larger the equivalent yield.
Why your bracket matters more than the yield
Two investors holding the same bond see different results. Someone in the 12% bracket gains little from tax-free interest, while someone in the 35% bracket gains a lot. That is why a tax bracket is the one input you should never guess.
How the Tax-Equivalent Yield Calculator Works
A good tax equivalent yield calculator needs only three inputs, and no other calculator input is required, and each maps onto a piece of the formula: The credit union certificate ladder calculator online is free to use with no sign-up, and works on desktop and mobile.
- Tax-free yield: the stated yield on the tax-exempt bond, such as 3.42%.
- Federal marginal tax rate: the bracket applied to your next dollar of interest income.
- State marginal tax rate: the state rate, relevant only when the bond is exempt from state tax too.
Press the Calculate button and the calculator adds the two rates, applies the formula and returns the taxable-equivalent return; a good calculator also lets you reset and try another bond in seconds. Read it as a hurdle: any taxable bond of similar quality yielding less than that number loses to the muni.
Entering your marginal tax bracket
Use your marginal tax bracket in the calculator, not your average rate. Your marginal rate is the one that applies to additional interest, and it comes from your taxable income, which is gross income less adjustments and deductions.
Adding state taxes to federal income tax
When you buy a bond issued in the state where you live, interest is usually exempt from state taxes as well. In that case the calculator needs the state rate added to the federal income tax rate to get the combined rate. Some calculators assume state taxes are fully deductible on your federal return; if they are not deductible for you, folding the state rate into the combined rate is the safer approach. An out-of-state muni gets only the federal exemption.
Comparing the result with a taxable bond
Once the calculator returns the equivalent yield, set it against the yield on a comparable taxable bond. If the equivalent yield is higher, the tax-exempt bond pays more after tax. If it is lower, the taxable bond wins.
Checking your after-tax income
For a second opinion beyond the calculator, multiply each bond's yield by what you invest, then by the share you keep after tax. The result is your after-tax income in dollars, which is often easier to judge than a gap of a fraction of a percentage point.
Municipal Bond Tax Equivalent Yield: A Worked Example
Suppose you live in a state with a 5.2% income tax rate and sit in the 32% federal bracket. You are choosing between an in-state municipal bond yielding 3.42% and a corporate bond yielding 5.31%, each with $50,000 invested and similar credit quality.
Because the muni is an in-state issue, the calculator's combined rate is 32% + 5.2% = 37.2%:
$$\text{TEY} = \frac{3.42\%}{1 - 0.372} = \frac{3.42\%}{0.628} \approx 5.45\%$$
| Measure | In-state municipal bond | Corporate bond |
|---|
| Stated yield | 3.42% | 5.31% |
| Tax rate on interest | 0% (federal and state) | 37.2% combined |
| Annual interest on $50,000 | $1,710.00 | $2,655.00 |
| Income kept after tax | $1,710.00 | $1,667.34 |
| Tax-equivalent yield | 5.45% | 5.31% |
The muni's 5.45% equivalent yield tops the corporate bond's 5.31% by 0.14 percentage points, which is $42.66 a year of extra income on $50,000. Change one assumption and the answer flips: if the same bond were issued out of state, only the federal 32% applies, the tax-equivalent yield drops to 3.42% ÷ 0.68 = 5.03%, and the corporate bond wins.
Pricing an $80,000 Muni Purchase With the Tax-Equivalent Yield Calculator
Imran, a dentist in Austin, has $80,000 from a matured CD and two offers on his broker's screen: a Texas school-district bond paying 4.12% and an A-rated corporate bond paying 6.05%. Texas levies no personal income tax, so the state rate is 0%. His taxable income of $268,000 puts him in the 35% federal bracket.
He types 4.12 into the tax-free yield field, 35 into the federal rate and 0 into the state rate, then clicks the button. The calculator returns a tax-equivalent yield of 4.12% ÷ 0.65 = 6.34%. That already beats the corporate bond's 6.05%, but only by 0.29 points, which feels thin for taking on a single issuer.
Then he remembers that his modified adjusted gross income sits above the $200,000 threshold for single filers, so the 3.8% Net Investment Income Tax applies to the corporate bond's interest and never touches the muni's. He reruns the figures with 38.8% as the federal rate: 4.12% ÷ 0.612 = 6.73%, now 0.68 points ahead of the 6.05% bond.
In dollars, the muni pays $3,296 a year, all kept. The corporate bond pays $4,840 before tax and $2,962.08 after the 38.8% rate, so the muni leaves him $333.92 more each year. The result decides it: he buys the Texas bond, and as a next step he asks his broker whether the issue carries an AA rating, since only a matching credit quality makes the comparison fair.
Equivalent Yield by Federal Tax Bracket
The table below holds the tax-free yield at 3.42% and varies only the marginal rate. The first column uses the federal rate alone; the second adds a 5.2% state rate for an in-state bond.
| Federal tax bracket | TEY, federal only | TEY, federal plus 5.2% state |
|---|
| 10% | 3.80% | 4.03% |
| 12% | 3.89% | 4.13% |
| 22% | 4.38% | 4.70% |
| 24% | 4.50% | 4.83% |
| 32% | 5.03% | 5.45% |
| 35% | 5.26% | 5.72% |
| 37% | 5.43% | 5.92% |
Run the calculator for each bracket and read down either column, and the pattern is plain: moving from the 12% bracket to the 37% bracket lifts the equivalent yield by about 1.5 percentage points. For investors in the lowest brackets, a tax-free bond rarely makes up for its lower coupon payments. For investors in the top brackets, it often does.
When a Taxable Bond Beats a Tax-Exempt Bond: Equivalent Yield and Risk
A high equivalent yield is not an automatic buy signal. Fixed income securities carry risk in proportion to their return, and the comparison only works between bonds of similar quality.
- Credit rating: agencies rate borrowers from AAA down through investment grade to speculative. Compare bonds with the same rating, or the higher yield simply reflects a higher chance of default.
- Alternative minimum tax: interest on some private activity bonds can be pulled back into the alternative minimum tax, which erodes the exemption.
- Capital gains: selling a bond before maturity at a profit creates capital gains tax, even when the coupon interest was tax-free; the result covers interest only, so a gain on sale sits outside it.
- Tax treatment of the issuer: Treasury bonds are taxed federally but exempt from state tax, so their tax treatment differs from both corporate bonds and munis; against a Treasury, enter only the federal rate on the taxable side.
Whenever the calculator's equivalent yield looks too good, check whether the municipal bond is lower rated, callable or subject to tax in your situation before you commit money.
Using Tax Equivalent Yield in Financial Planning
In financial planning, the tax-equivalent yield is a quick screen rather than the final verdict, and the calculator is only as good as the rates you feed it. A few details change what the number means for you:
- If you are a high earner, the 3.8% net investment income tax applies to taxable interest but not to municipal interest, so your real combined rate can be higher than your bracket alone suggests.
- Tax-free bonds make little sense inside an IRA or 401(k), where interest is already sheltered; the exemption is wasted there.
- Rates change. Recheck the figure whenever a bracket, deduction or state rate moves.
Every investor should also remember that this calculator ignores fees, bond prices and reinvestment of coupons. It answers one question well: which bond pays more after tax today. Use it alongside your own judgment about interest rate exposure and how long you intend to hold.
The tax-free label describes the interest, not the whole investment, and neither a muni nor a corporate bond is guaranteed. Treat the equivalent yield as a way to compare income, with return and risk weighed separately, and deductible state taxes or a changing bracket always worth a second pass through the tax equivalent yield calculator.