Tax-Equivalent Yield Calculator (TEY)
To compare a tax-free bond (US muni, UK ISA, HK iBond, etc.) against a regular taxable bond you need to compare after-tax yields. This tool uses the standard formula TEY = tax-free yield ⁄ (1 − marginal rate − state/local rate) to give the pre-tax yield a taxable bond must offer to match the tax-free one, and places the taxable bond's after-tax yield right next to it so the verdict is immediate.
Enter a non-negative tax-free yield and tax rates that together stay below 99.99 %.
Tax-equivalent yield (TEY)
4.61%
After-tax yield of a taxable bond at the same gross %
3.42%
Comparison
—
Formula
TEY = TaxFreeYield ⁄ (1 − marginalRate − stateRate) After-tax taxable yield = TaxableYield · (1 − marginalRate − stateRate) Verdict: TaxableYield > TEY → pick taxable; TaxableYield < TEY → pick tax-free.
- · References: Bogleheads wiki "Taxable equivalent yield"; SEC investor.gov bond-comparison guide.
- · Common tax-free wrappers: US municipal bonds (federal-exempt; in-state munis also state-exempt), UK ISA wrapper (interest tax-free up to the annual allowance), Canada TFSA, Singapore SRS/CPF, Hong Kong iBond / tax-free savings plans.
- · Marginal rate is your top bracket, not your average rate. US federal 2025: seven brackets 0/10/12/22/24/32/35/37 %.
- · State taxes stack with federal: a New York City resident at 24 % federal + 6.85 % state + 3.876 % city = 34.726 %, giving a TEY multiplier of about 1.531×. Out-of-state munis usually do not avoid your own state tax.
- · Limitations: TEY ignores AMT (Alternative Minimum Tax), the 3.8 % Net Investment Income Tax, credit-quality differences, liquidity, and call-feature risk. Compare ratings (Aaa vs A) and yield-to-call alongside TEY.
- · Inverse use: given a TEY target and tax rates you can derive the tax-free yield threshold: TaxFreeYield = TEY · (1 − combinedRate).
Frequently asked
I am not a US citizen — is TEY still relevant to me?
Yes — TEY is a generic formula and is not US-specific. Any pair of investments with asymmetric tax treatment can be compared this way: · UK residents: an ISA wrapper (£20k/yr limit) shields all interest, dividends and capital gains from tax; outside an ISA you pay marginal income tax of 0/20/40/45 %. To compare a 4 % gilt held inside an ISA against a 5 % gilt held outside, set TaxFreeYield = 4 and marginalRate = 40 → TEY ≈ 6.67 %, well above 5 %, so ISA wins. · Singapore residents: CPF SA/RA pays 4 % tax-free vs. a 3.5 % bank deposit taxed at the marginal 0–24 %. · Hong Kong has no interest or capital-gains tax for individuals, so TEY is most useful at the corporate / Profit Tax layer, or when comparing MPF mandatory contributions (tax-free) against private ORSO / IIPP funds taxed at the marginal salaries-tax rate. Fundamentally TEY is a "marginal-rate equaliser" and works in any country whenever two investments are taxed differently.
Can state taxes just be added to the federal rate inside the (1 − r) denominator?
For most cases yes, but there are two corrections to be aware of: (1) State tax deductibility: pre-2018 (US), state taxes were fully deductible as an itemised deduction, so the effective federal rate is federal × (1 − stateRate). Since 2018, the SALT cap limits state-and-local deductions to USD 10,000 per filing, so high-state-tax residents (CA, NY) lose most of this benefit. For exact treatment use combined = federal + state − federal × min(state, deductibleCap). (2) Multiple layers can stack on the same income — a NYC resident pays 24 % federal + 6.85 % NY state + 3.876 % NYC for a flat sum of 34.73 % (less a small SALT-cap adjustment to ~33 %). This tool adds stateRate to the federal marginalRate directly, which is correct for non-itemisers and a good approximation for itemisers above the SALT cap. If you itemise and stay below the cap, lower marginalRate by federal × stateRate before entering.
What risks should I still weigh after computing TEY?
TEY normalises tax only; four non-tax factors still need alignment before you can call a comparison fair: (1) Credit rating: US Treasury (AAA/risk-free) vs muni (Aaa to Baa) vs corporate (investment-grade AAA–BBB, junk below BB). Two bonds with the same TEY but different ratings are not equivalent. (2) Liquidity: muni secondary markets are thin with wide bid-ask spreads; Treasuries and large corporates are deeply liquid. TEY can hide this premium. (3) Call / prepayment risk: many munis are callable after ~10 years; when rates fall the issuer calls and your locked-in income window collapses. Compare using Yield-to-Worst (YTW), not Yield-to-Maturity. (4) Duration / interest-rate risk: two bonds with the same TEY but different durations differ enormously in price sensitivity — a 30-year muni vs. a 5-year Treasury can move 5× as much per 1 bp rate change. Bottom line: TEY is necessary but not sufficient. In practice match rating, duration and call profile first, then use TEY as the final tax adjustment.
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