How this instrument works
Taxable-equivalent yield answers a specific question: if this municipal bond's interest were taxed like ordinary income, how much would a fully taxable bond have to pay to hand you the same amount after the IRS takes its share? The arithmetic behind it is a rearrangement, not a guess. A taxable bond keeps only (1 − rate) of what it pays; setting that kept portion equal to the muni's tax-free yield and solving for the taxable rate is exactly why the formula divides by (1 − marginal tax rate) rather than multiplying the tax-free yield by the rate itself, which is the shortcut that trips up a lot of first attempts at this comparison.
The rate that belongs in this formula is the marginal rate, not an average or effective rate pulled from a pay stub or a prior year's return. Municipal interest, were it taxable, would stack on top of your existing income and get taxed at the rate applying to that next dollar — the top slice of your bracket, not a blended figure across every dollar you earned. Using an effective rate instead of the marginal one understates the taxable-equivalent yield and can make a municipal bond look worse than it actually performs against the alternative.
A retail investor or their advisor reaches for this number when a muni bond and a corporate bond or CD sit side by side with different headline yields and different tax treatment, and a straight comparison of the two percentages would be comparing different things. The formula's blind spot is what it does not know about you: it takes one marginal rate at face value, so it says nothing about state tax exemption on in-state munis, the alternative minimum tax that can claw back the exemption on certain private-activity bonds, or how your bracket might shift once the extra taxable income is added.
- Enter the bond's quoted rate in Tax-free yield, % — the interest rate the municipal bond actually pays, before any tax adjustment.
- Enter your top tax rate in Marginal tax rate, % — the rate on your next dollar of ordinary income, not your average rate across all income.
- Read Taxable-equivalent yield, % — the yield a fully taxable bond would need to match the muni's after-tax return.
- Raise the marginal tax rate and watch the taxable-equivalent yield climb — the same tax-free yield is worth more the higher the bracket it shelters.
Worked example — a 3% muni at the 32% bracket
Take a municipal bond quoted at a 3% tax-free yield, held by an investor in the 32% marginal federal tax bracket. Dividing 3 by (1 − 0.32) gives 4.41176…%, so a taxable bond would need to pay about 4.41% to leave this investor with exactly the same after-tax income the muni already delivers tax-free.
That 4.41% only means something next to an actual alternative: a similarly rated taxable bond paying 4.2% would leave this investor worse off than the muni, since 4.41% beats 4.2%. Move the same 3% muni to a 0% bracket and the taxable-equivalent yield falls to exactly 3%, because an exemption is worth nothing to someone with no tax bill to reduce. Move it to the top 37% bracket instead and it climbs to roughly 4.76%, since the higher the bracket, the more valuable the exemption becomes.
Questions
Why does the formula divide by (1 − rate) instead of multiplying by the rate?
Because a taxable bond only keeps a (1 − rate) fraction of what it pays after tax. Setting that kept fraction equal to the tax-free yield and solving for the taxable rate produces a division, not a multiplication. Multiplying the tax-free yield by the tax rate instead is a common shortcut, and it understates the true taxable-equivalent yield rather than calculating it.
Should I use my marginal tax rate or my effective tax rate here?
Marginal. Municipal interest, if it were taxed like ordinary income, would stack on top of what you already earn and be taxed at the rate applying to that last dollar — your marginal bracket — not the blended average rate across your whole income. Entering an effective rate instead of a marginal one understates the taxable-equivalent yield the calculator returns.
Does this account for state income tax exemption too?
No — it takes a single marginal rate as given. Many municipal bonds are also exempt from state and local tax for residents of the issuing state, which is a separate, additional benefit this sheet does not model on its own. To approximate a double-exempt bond, combine your federal and state marginal rates before entering a figure, since the true taxable-equivalent yield is higher than the federal-only version shown here.
What happens if I enter a marginal tax rate of 100% or more?
The instrument stops and shows an error instead of a number. Dividing by (1 − rate) when the rate reaches 100% means dividing by zero, which has no finite answer, so a rate at or above 100% is rejected rather than displayed as an infinite or nonsensical yield.
Is the bond with the higher taxable-equivalent yield always the better buy?
Not on this number alone. Taxable-equivalent yield is a tax-adjusted comparison of income only — it says nothing about the issuer's credit quality, whether the bond can be called early, how easily it trades, or whether its maturity matches the taxable bond you are weighing it against. A higher figure means better after-tax income today, not a lower-risk instrument.
Does the calculator account for the alternative minimum tax?
No. Interest from certain municipal bonds — private-activity bonds in particular — is exempt from regular federal tax but added back when calculating the alternative minimum tax. An investor who owes AMT and holds one of those bonds keeps less of the interest than this formula assumes, since a portion of the supposedly tax-free yield gets taxed after all.
References
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.