Tax-Equivalent Yield Calculator

Compare tax-exempt municipal bond yields with taxable corporate or treasury bond yields based on marginal tax rates.

Wealth & Investment

Standard: IRS Code Section 103 (Tax-Exempt Bonds)

Bond Parameters

Tax-Free Municipal Bond Stated Yield

Federal Marginal Tax Bracket

State Marginal Tax Bracket

Statutory Context (IRC § 103): Municipal bond interest is generally exempt from federal income taxation and from state income taxation if issued by the investor's resident state. Capital gains upon sale remain fully taxable.

Tax-Equivalent Yield

6.746%

Required gross yield on a taxable bond

Combined Marginal Tax

37.00%

Federal + State total

After-Tax Retained Ratio

63.0%

1 − Combined Tax Rate

Interactive Tax-Equivalent Yield Derivation

Tax adjustment formula reflecting current yield and marginal tax brackets

IRS Code Section 103 & Municipal Bond Yield Analysis

Design Scenario

Evaluating stated 4.25% bond yield under 32.00% federal and 5.00% state tax brackets.

Mathematical Solution

1Calculate Combined Marginal Tax Rate

Sum of highest marginal tax rates applicable to taxable interest income.

t_{\text{combined}} = 32.00\% + 5.00\% = 37.00\%

2Compute Retained Cash Fraction

The fraction of each dollar of taxable interest retained after income tax.

1 - 0.3700 = 0.6300

3Calculate Tax-Equivalent Yield

A fully taxable corporate or Treasury bond must pay this gross rate to deliver the same after-tax cash as the municipal bond.

Y_{\text{TEY}} = \frac{4.25\%}{0.6300} = 6.746\%

6.746% Tax-Equivalent Yield

Email Link Text/SMS WhatsApp

What is Municipal Bond Tax Mechanics?

Interest earned on Municipal Bonds is generally exempt from Federal income tax. If you buy a bond issued by your home state, it is often exempt from State income tax as well. To accurately compare a tax-free Municipal bond against a fully taxable Corporate bond, investors use the Tax-Equivalent Yield (TEY) formula. This indicates how high a corporate bond's gross yield must be to generate equivalent after-tax cash flow.

Mathematical Foundation

TEY = \frac{Y_{muni}}{1 - (t_{fed} + t_{state})}

TEY

= Tax-Equivalent Yield (the hurdle rate a corporate bond must beat).

Y_{muni}

= The stated interest rate of the tax-free municipal bond.

t_{fed}

= Your highest marginal Federal tax bracket.

t_{state}

= Your marginal State tax bracket (if applicable).

\text{After-Tax Yield} = Y_{corp} \times (1 - (t_{fed} + t_{state}))

Y_{corp}

= The gross yield of a fully taxable Corporate or Treasury bond.

Laws & Principles

Tax Bracket Sensitivity: Municipal bonds typically offer lower stated coupon yields than corporate bonds of similar maturity and credit rating. However, because municipal interest is tax-exempt, the effective yield advantage increases with an investor's marginal tax rate. Tax-exempt municipal bonds generally offer greater relative benefit in higher tax brackets, particularly for investors subject to high state and local income tax rates.
Capital Gains Warning: The tax exemption on muni bonds applies ONLY to the interest income. If you buy a muni bond on the secondary market at a discount and later sell it for a profit, that capital gain is fully taxable.
The AMT Trap: Interest from certain 'Private Activity' municipal bonds (like those funding stadiums or airports) may still be subject to the Alternative Minimum Tax (AMT). Standard 'General Obligation' munis are almost uniformly safe from AMT.

Step-by-Step Example Walkthrough

" An investor in the 37% Federal bracket and 10% State bracket is choosing between a 4.5% Municipal Bond and a 7.5% Corporate Bond. "

1. Determine Combined Bracket: 37% + 10% = 47%.
2. The investor only keeps 53 cents of every taxable dollar they earn (1 - 0.47).
3. Calculate TEY: 4.5% / 0.53 = 8.49%.
4. Compare: The Corporate bond yields 7.5%. The Muni's equivalent yield is 8.49%.

Final Result: Even though the corporate bond's gross yield is higher, the tax burden reduces net yield below the municipal bond's 4.50% after-tax payout.

Quick Answer: How does the Tax-Equivalent Yield Calculator work?

This tool compares tax-free Municipal Bonds against fully taxable Corporate or Treasury Bonds by converting yields into the same after-tax basis. Enter the tax-free municipal bond yield along with your Federal and State tax brackets, and the calculator shows the yield a taxable bond must provide to match. You can also switch to After-Tax Mode to determine after-tax yields on corporate debt securities. Results update automatically in your browser without requiring an account.

Tax-Equivalent Yield Formulas

Mode 1 — Muni → Taxable Equivalent

TEY = Muni Yield ÷ (1 − Combined Tax Rate)

Mode 2 — Taxable → After-Tax Yield

After-Tax Yield = Corporate Yield × (1 − Combined Tax Rate)

Combined Tax Rate

t_combined = t_federal + t_state

Muni Yield— The stated annual coupon rate on the tax-exempt municipal bond. This is the rate you receive with zero federal income tax owed.
Federal Rate— Your highest marginal Federal income tax bracket (e.g. 22%, 24%, 32%, 35%, 37%).
State Rate— Your State income tax bracket. Set to 0% if you live in a state with no income tax (TX, FL, NV, etc.) or if the muni is issued by your home state.

Real-World Scenarios

✓ High-Income Investor — Muni Wins

37% Federal + 10% CA State = 47% combined rate

Muni Bond Yield: 4.50% (tax-free, in-state CA GO bond)
TEY Calculation: 4.50% ÷ (1 − 0.47) = 4.50% ÷ 0.53
Tax-Equivalent Yield: 8.49%
Corporate Bond Available: 7.50% (fully taxable)
After-Tax Corporate: 7.50% × 0.53 = 3.98%

→ The 4.50% muni delivers $4,500 in tax-free income per $100k invested. The 7.50% corporate delivers only $3,975 after taxes. The muni wins by $525/year despite its lower headline yield.

✗ Lower-Bracket Investor — Corporate Wins

22% Federal + 0% State (TX) = 22% combined rate

Muni Bond Yield: 4.00% (tax-free)
TEY Calculation: 4.00% ÷ (1 − 0.22) = 4.00% ÷ 0.78
Tax-Equivalent Yield: 5.13%
Corporate Bond Available: 6.50% (fully taxable)
After-Tax Corporate: 6.50% × 0.78 = 5.07%

→ The corporate bond yields 5.07% after-tax vs the muni's 4.00%. Even after paying taxes, the higher corporate coupon delivers $1,070 more per $100k invested. At this low bracket, the tax shield isn't powerful enough to justify the yield sacrifice.

TEY by Tax Bracket — Quick Reference

Combined Tax Rate	Cash Retention	TEY Multiplier	TEY on a 4% Muni
12%	0.88	1.14x	4.55%
22%	0.78	1.28x	5.13%
24%	0.76	1.32x	5.26%
32%	0.68	1.47x	5.88%
35%	0.65	1.54x	6.15%
37% + 10% State	0.53	1.89x	7.55%

Pro Tips & Common Pitfalls

Do This

✓Consider account tax efficiency. Holding tax-exempt municipal bonds inside tax-deferred accounts such as IRAs provides no incremental tax sheltering and forfeits the yield spread typically available on taxable corporate debt. Tax-exempt securities generally align best with taxable investment accounts.
✓Re-run the calculation as tax brackets change. Variations in marginal federal or state tax brackets shift the relative attractiveness of tax-exempt versus taxable yields. Recalculate your TEY following significant changes in household taxable income.
✓Factor in your State tax for the full picture. A resident of California (13.3% top bracket) or New York (10.9%) gets a dramatically larger TEY multiplier than someone in a no-income-tax state like Texas or Florida.

Avoid This

✗Don't ignore the AMT trap on Private Activity munis. Interest from certain municipal bonds that fund private projects (stadiums, airports, industrial facilities) can trigger the Alternative Minimum Tax, completely voiding your expected tax exemption.
✗Don't confuse interest income with capital gains. The tax exemption applies exclusively to coupon interest payments. If you buy a muni bond at a discount and sell it for a profit, that capital gain is fully taxable at short-term or long-term rates just like any other security.

Frequently Asked Questions

Are municipal bonds completely tax-free?

Most municipal bonds are exempt from federal income taxes. Furthermore, if you purchase a municipal bond issued by the state in which you reside, the interest is typically exempt from state and local taxes as well — a status known as "Triple Tax-Free." However, capital gains on bond price appreciation and certain Private Activity bonds may still trigger taxes.

Why don't all investors buy municipal bonds?

Because of the supply and demand dynamics around tax exemptions, municipal bonds are priced at a premium, causing their base yields to be significantly lower than corporate bonds. For an investor in the 12% or 22% tax bracket, the math dictates that the higher yield of a corporate bond usually outpaces the tax savings of a municipal bond. Munis primarily benefit high-income earners.

What is the formula for Tax-Equivalent Yield?

To find the Tax-Equivalent Yield, divide the tax-free Municipal Bond yield by (1 minus your total marginal tax rate). For example, if the muni yields 4% and your combined federal + state tax rate is 35%, the TEY is 4% ÷ (1 − 0.35) = 4% ÷ 0.65 = 6.15%. A corporate bond must yield at least 6.15% to match the 4% muni after taxes.

Should I use Tax-Equivalent Yield or After-Tax Yield?

Both approaches give you the same conclusion — one just converts "up" and the other converts "down." Tax-Equivalent Yield converts the muni yield upward to see what a corporate bond would need to match it. After-Tax Yield converts the corporate yield downward to see what you actually keep. Use whichever feels more intuitive. This calculator supports both modes with a single toggle.

Related Calculators

Calculation Provenance & Validation Record

Method

Tax-Equivalent Yield and After-Tax Yield

Formula

TEY = \frac{Y_{muni}}{1 - (t_{fed} + t_{state})}, \quad Y_{after} = Y_{corp} \times (1 - (t_{fed} + t_{state}))

Assumptions

Municipal bond interest is exempt from Federal income tax under IRC Section 103
Marginal tax rate applies to incremental interest income without phaseout adjustments
Capital gains on bond market discounts remain fully taxable

References

Interest on State and Local Bonds Tax Exemption (IRC Section 103) (Current Internal Revenue Code) — IRC Section 103 & Municipal Bond Yield Comparison

Last substantive review: 2026-10-04

Automated test status: 4 golden test vectors passing (TEY-01, TEY-02, TEY-03, TEY-04)

Method & assumptions

Calculation Methodology

Financial modeling and scenario projections based on standard time-value-of-money and compounding formulas.

Governing Standard 26 U.S. Code § 103 (Interest on State and local bonds)

Standard:IRC Section 103 / MSRB Rules

Key Assumptions & Constraints

Municipal bond interest is exempt from Federal income tax under IRC Section 103
Marginal tax rate applies to incremental interest income without phaseout adjustments
Capital gains on bond market discounts remain fully taxable

Financial Disclaimer: Calculations are educational estimates based on constant mathematical models. They do not account for market fluctuations, taxes, fees, or individual underwriting approval. Consult a certified financial professional.