Tax-Equivalent Yield Calculator

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 tells you exactly how high a corporate bond's gross yield would have to be to put the same amount of net cash in your pocket.

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

The Wealth Effect: Municipal bonds typically pay dramatically lower interest rates than corporate bonds. However, the higher your personal income tax bracket, the more mathematically valuable the tax exemption becomes. Munis make the most sense for ultra-high-net-worth individuals in high-tax states like California or New York.
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 3% higher, the massive tax burden kills the return. The investor mathematically walks away with more cash by choosing the 4.5% Muni bond.

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 instantly shows the exact yield a taxable bond would need to match. You can also switch to After-Tax Mode to see how much cash a corporate bond actually delivers after the IRS takes its cut. Results update instantly 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

✓Always hold municipal bonds in taxable brokerage accounts. Holding a tax-exempt bond inside a tax-sheltered account like a Roth IRA or 401(k) wastes the entire tax exemption — you're already tax-free inside those accounts.
✓Re-run the calculation every time your income bracket changes. What made sense at 24% Federal may no longer make sense at 32%. If you get a raise, promotion, or large bonus, recalculate your TEY to see if munis now beat corporates for you.
✓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.