Tax Equivalent Yield Calculator
Compare tax-free and taxable bond yields
Taxable Investment Is Better
The after-tax yield on the taxable bond (3.80%) exceeds the tax-free yield (3.50%) by 0.30%.
4.61%
Taxable yield equivalent to 3.50% tax-free at 24.00% tax rate
3.80%
Net return on 5.00% taxable yield
$173.13
Tax-free benefit
Tax-Free Annual Income
$350.00
Taxable Annual Income (before tax)
$500.00
Annual Taxes Paid
$120.00
| Metric | Tax-Free | After-Tax Taxable |
|---|---|---|
| Initial Investment | $10,000.00 | $10,000.00 |
| Total Interest/Gains | $1,876.86 | $2,049.99 |
| Total Taxes Paid | $0.00 | $712.82 |
| Final Value | $11,876.86 | $12,049.99 |
What Is Tax Equivalent Yield and Why Does It Matter?
Tax Equivalent Yield (TEY) answers a simple but critical investment question: given a tax-free bond yielding X%, what yield would a taxable bond need to pay to put the same amount of money in your pocket after taxes? The answer depends entirely on your marginal federal income tax rate — and it makes a dramatic difference for investors in higher brackets.
The concept exists because municipal bonds — debt issued by states, cities, counties, and other local government entities — pay interest that is exempt from federal income tax and often from state and local taxes as well. Corporate bonds and U.S. Treasury notes pay interest that is fully taxable at your ordinary income rate. A naive comparison of the two yields (e.g., 3.5% muni vs. 5.0% corporate) is therefore misleading: you keep all 3.5% of the muni income, but only keep a fraction of the 5.0% corporate income after paying taxes.
TEY converts the tax-free yield to a taxable equivalent so you can compare apples to apples. A 3.5% tax-free yield is equivalent to a 5.30% taxable yield for someone in the 34% combined federal + state bracket — and 5.88% for someone in the 40.5% bracket. If a comparable taxable bond is yielding less than the TEY, the tax-free bond wins on an after-tax basis.
This calculator uses your federal marginal rate. For the full picture, add your state marginal income tax rate to the federal rate — especially if you live in a high-tax state like California (13.3%), New York (10.9%), or New Jersey (10.75%) and are comparing in-state municipal bonds, which are typically also state-tax-exempt.
The TEY Formula: Both Directions
There are two versions of the formula depending on which direction you are solving:
Tax Equivalent Yield — from a tax-free bond
TEY = Tax-Free Yield ÷ (1 − Marginal Tax Rate) Example: 3.5% muni at 24% federal tax rate TEY = 3.5% ÷ (1 − 0.24) = 3.5% ÷ 0.76 = 4.61% Interpretation: A taxable bond must yield at least 4.61% to match the 3.5% muni after tax at a 24% bracket.
Use this formula when you hold a tax-free bond and want to know what taxable yield would be equivalent. If the taxable bond you are comparing to yields less than the TEY, the muni wins.
After-Tax Yield — from a taxable bond
After-Tax Yield = Taxable Yield × (1 − Marginal Tax Rate) Example: 5.0% corporate bond at 24% federal tax rate After-Tax = 5.0% × (1 − 0.24) = 5.0% × 0.76 = 3.80% Interpretation: After paying 24% tax on interest, you net only 3.80%. Compare this directly to any tax-free yield to see which is better.
Use this formula when you hold a taxable bond and want to express its yield net of taxes for direct comparison to a tax-free alternative.
Break-Even Tax Rate
Break-Even Rate = 1 − (Tax-Free Yield ÷ Taxable Yield) Example: 3.5% muni vs. 5.0% corporate Break-Even = 1 − (3.5% ÷ 5.0%) = 1 − 0.70 = 30% Interpretation: If your marginal rate exceeds 30%, the muni wins. Below 30%, the corporate bond delivers more after-tax income.
The break-even tax rate is a quick screening tool: if your combined federal + state marginal rate exceeds this number, choose the tax-free bond without further calculation.
TEY Quick-Reference Table: Tax-Free Yield → Required Taxable Yield
| Tax-Free Yield | 22% bracket | 24% bracket | 32% bracket | 35% bracket | 37% bracket |
|---|---|---|---|---|---|
| 2.5% | 3.21% | 3.29% | 3.68% | 3.85% | 3.97% |
| 3.0% | 3.85% | 3.95% | 4.41% | 4.62% | 4.76% |
| 3.5% | 4.49% | 4.61% | 5.15% | 5.38% | 5.56% |
| 4.0% | 5.13% | 5.26% | 5.88% | 6.15% | 6.35% |
| 4.5% | 5.77% | 5.92% | 6.62% | 6.92% | 7.14% |
| 5.0% | 6.41% | 6.58% | 7.35% | 7.69% | 7.94% |
Federal brackets only. Add your state marginal rate to get a combined rate for comparing in-state munis that are also state-tax-exempt.
Municipal Bonds: Types, Tax Treatment, and Risks
Municipal bonds ("munis") are debt securities issued by state and local governments to finance public infrastructure: roads, schools, hospitals, water systems, and housing. They are the primary type of tax-free investment the TEY formula applies to. Understanding the varieties helps you apply the formula correctly.
General Obligation (GO) Bonds
Backed by the full faith, credit, and taxing power of the issuing government. The issuer can raise taxes to meet debt service. Considered among the safest municipal bonds because repayment does not depend on project revenue.
Tax treatment: Federal tax-exempt. Usually state-tax-exempt for in-state residents.
Risk: Low-to-moderate. Default risk is low but not zero (e.g., Detroit 2013, Puerto Rico 2016). GO bonds are typically rated investment grade.
Revenue Bonds
Backed solely by revenues from a specific project: toll roads, airports, utilities, hospitals, convention centers. If the revenue stream fails (e.g., a toll road with low traffic), there is no taxing authority backstop.
Tax treatment: Federal tax-exempt in most cases. State exemption varies.
Risk: Moderate-to-higher than GO bonds. Depends entirely on project revenue. Hospital and airport revenue bonds are common; rates reflect project risk.
Private Activity Bonds (PABs)
Issued to finance projects with significant private involvement: private universities, non-profit hospitals, affordable housing, airports. While federally tax-exempt for regular income tax purposes, PAB interest may be subject to the Alternative Minimum Tax (AMT).
Tax treatment: Federal tax-exempt for regular income tax. May be taxable under AMT. Check the bond's official statement.
Risk: Varies by issuer and project type. Non-profit hospital bonds carry healthcare sector risk.
Build America Bonds (BABs)
A special category issued in 2009–2010 under the American Recovery and Reinvestment Act. BABs pay taxable interest — not tax-free — but the issuer receives a federal subsidy. Investors cannot use TEY for these; they are priced as taxable bonds.
Tax treatment: Interest is fully taxable federally and at the state level. Do not apply the TEY formula to BABs.
Risk: Similar credit risk to comparable GO or revenue bonds from the same issuer.
In-State vs. Out-of-State Munis
Most states exempt interest from bonds issued within the state from state income tax for state residents. Interest from out-of-state bonds is usually subject to state income tax. This "in-state preference" amplifies the TEY advantage in high-state-tax jurisdictions.
Tax treatment: For in-state munis: federal-exempt + state-exempt. For out-of-state munis: federal-exempt + state-taxable. Use combined (federal + state) rate only for in-state munis in the TEY formula.
Risk: Credit quality varies by issuer, not by in-state vs. out-of-state status.
Muni Bond Funds and ETFs
Rather than buying individual bonds, most retail investors access the muni market through mutual funds or ETFs (iShares MUB, Vanguard VTEB, PIMCO MUNI). These provide diversification and daily liquidity but introduce fund-level expenses that reduce the effective after-tax yield.
Tax treatment: Dividends from muni bond funds are federally tax-exempt to the extent the underlying bonds are tax-exempt. Capital gain distributions are taxable. State exemption depends on the fund's state allocation.
Risk: Interest rate risk: prices fall when rates rise. Duration-matched funds reduce but do not eliminate this risk.
When Do Municipal Bonds Beat Taxable Bonds?
Tax-free bonds are not superior for every investor — their advantage depends on your tax bracket, the specific yield spread between taxable and tax-free bonds at a given maturity, and your account type. Here is a structured framework for deciding:
Munis Are Usually Better When...
- Your marginal federal rate is 32% or higher (the TEY advantage is largest in the top brackets — at 37%, a 3.5% muni equates to a 5.56% taxable yield)
- You add a high state income tax rate (e.g., California 13.3%) and the muni is in-state — combined rates of 40%+ make even modest muni yields extremely competitive
- The muni's TEY exceeds the yield on a comparable-maturity Treasury or investment-grade corporate bond — especially after adjusting for similar credit quality
- The investment is in a taxable brokerage account, not a tax-advantaged account (IRA, 401k) — the tax benefit of munis is redundant inside tax-deferred accounts
- You are in the top AMT bracket only for regular income tax, not for AMT — avoiding AMT PABs specifically
- You want to reduce your Modified Adjusted Gross Income (MAGI) to stay below ACA premium thresholds, Medicare IRMAA surcharge triggers, or other income-based phase-outs — muni interest is excluded from MAGI
Taxable Bonds Are Usually Better When...
- Your marginal rate is 22% or below — the after-tax yield on a 5% corporate bond (3.90%) often exceeds available muni yields in lower brackets
- The bond is inside a tax-advantaged account (traditional IRA, 401k, Roth IRA) — interest grows tax-deferred or tax-free anyway, so the muni exemption provides no additional benefit
- The yield spread is unusually wide — during periods of market stress, corporate bond spreads over munis can exceed the TEY threshold, making taxable bonds superior even at higher rates
- You need greater liquidity — the taxable bond market (Treasuries, investment-grade corporates) is significantly more liquid than the muni market, with tighter bid-ask spreads for smaller positions
- The muni is subject to AMT and you have significant AMT exposure — PAB interest is a preference item for AMT, potentially making the bond partially or fully taxable
- You expect your tax rate to decline significantly in future years (approaching retirement) — the muni advantage shrinks as your bracket drops
How Your Tax Rate Changes the TEY Calculation
The TEY advantage grows non-linearly with your tax rate. Moving from the 22% to the 37% bracket nearly doubles the TEY premium on the same tax-free yield. This is why munis are primarily marketed to high-net-worth investors — they provide the most benefit to those who need it most.
| Federal Bracket | 3.0% Muni TEY | 3.5% Muni TEY | 4.0% Muni TEY | 4.5% Muni TEY | Verdict at 5% taxable |
|---|---|---|---|---|---|
| 10% | 3.33% | 3.89% | 4.44% | 5.00% | Taxable wins on 3.0–3.5% munis |
| 12% | 3.41% | 3.98% | 4.55% | 5.11% | Taxable wins on most munis |
| 22% | 3.85% | 4.49% | 5.13% | 5.77% | Muni wins at 4.0%+ |
| 24% | 3.95% | 4.61% | 5.26% | 5.92% | Muni wins at 3.8%+ |
| 32% | 4.41% | 5.15% | 5.88% | 6.62% | Muni wins at 3.4%+ |
| 35% | 4.62% | 5.38% | 6.15% | 6.92% | Muni wins at 3.25%+ |
| 37% | 4.76% | 5.56% | 6.35% | 7.14% | Muni wins at 3.15%+ |
Green values indicate that the muni TEY exceeds 5.00% — meaning the muni beats a 5.00% taxable bond at that bracket. Federal rate only; add state rate for in-state munis.
Including State Tax: The Full TEY Calculation
The basic TEY formula uses only the federal tax rate. But for investors in high-income-tax states comparing an in-state municipal bond (which is typically exempt from state tax as well), the correct combined rate to use is:
Combined Rate = Federal Rate + State Rate × (1 − Federal Rate) (adjusts for the state tax deduction on federal returns for itemizers) Full TEY = Tax-Free Yield ÷ (1 − Combined Rate) Example: California resident in 37% federal + 13.3% state bracket Combined Rate = 0.37 + 0.133 × (1 − 0.37) = 0.37 + 0.0838 = 45.38% Full TEY = 3.5% ÷ (1 − 0.4538) = 3.5% ÷ 0.5462 = 6.41% The California in-state muni at 3.5% is equivalent to a 6.41% fully taxable bond.
Note: Only apply the combined rate when the muni is exempt from BOTH federal AND state tax. Out-of-state munis are generally state-taxable; use only the federal rate for those.
California
Top state rate: 13.3%
In-state CA munis are state-exempt
Combined rate (37% fed): 45.4%
TEY of 3.5% muni: 6.41%
New York
Top state rate: 10.9%
In-state NY munis are state-exempt
Combined rate (37% fed): 43.9%
TEY of 3.5% muni: 6.24%
New Jersey
Top state rate: 10.75%
In-state NJ munis are state-exempt
Combined rate (37% fed): 43.8%
TEY of 3.5% muni: 6.23%
Oregon
Top state rate: 9.9%
In-state OR munis are state-exempt
Combined rate (37% fed): 43.2%
TEY of 3.5% muni: 6.16%
Minnesota
Top state rate: 9.85%
In-state MN munis state-exempt
Combined rate (37% fed): 43.2%
TEY of 3.5% muni: 6.16%
Texas / Florida
Top state rate: 0%
No state income tax; federal only
Combined rate (37% fed): 37.0%
TEY of 3.5% muni: 5.56%
Advanced TEY Considerations
Alternative Minimum Tax (AMT)
Interest from Private Activity Bonds (PABs) is an AMT preference item. If you are subject to AMT, PAB interest may be partially or fully taxable under the AMT calculation. For investors with significant ISO stock options, accelerated depreciation, or other AMT items, always check whether a muni is an AMT bond before applying the standard TEY formula. Look for "subject to AMT" in the bond's official statement.
Social Security Taxation and MAGI
Municipal bond interest, while not itself taxable, is included in the Modified Adjusted Gross Income (MAGI) calculation that determines how much of your Social Security benefits are taxable (up to 85% at higher incomes). It also affects Medicare IRMAA surcharges ($97.10–$443.80/month added to Part B premiums in 2024) at higher income levels. For retirees near these thresholds, the true benefit of munis includes avoiding income that could trigger these surcharges.
Net Investment Income Tax (NIIT)
The 3.8% Net Investment Income Tax (Obamacare surtax) applies to interest, dividends, and capital gains for taxpayers with MAGI above $200,000 single or $250,000 MFJ. Municipal bond interest is exempt from the NIIT. For investors subject to the NIIT, the effective marginal rate on taxable bond income is effectively 37% + 3.8% = 40.8%, which makes the TEY premium for munis even larger.
De Minimis Rule on Discounted Munis
When a muni is purchased in the secondary market at a price below par, the discount may be taxable as ordinary income (not at capital gains rates) upon sale or maturity under the "de minimis rule" — if the discount exceeds 0.25% per year of remaining maturity. A muni purchased at $95 with 10 years to maturity has a $5 discount and a de minimis threshold of $2.50 (0.25% × 10 × $100). The remaining $2.50 discount is ordinary income. For deeply discounted munis, this erodes the tax advantage.
Duration and Interest Rate Risk
TEY analysis tells you about income return, but bonds also carry interest rate risk: when rates rise, bond prices fall. Longer-duration bonds fall more in price per unit of rate increase (modified duration ≈ years). A 10-year muni with duration 8.5 years loses approximately 8.5% in price for each 1% rise in yields. Always evaluate whether the TEY premium adequately compensates for the additional duration risk relative to a shorter-maturity taxable alternative.
Muni Bond Credit Risk
Municipal bonds are not risk-free. Puerto Rico's 2016 default on $70 billion in debt, Detroit's 2013 bankruptcy, and smaller issuer defaults demonstrate that credit risk is real. Investment-grade munis (rated BBB-/Baa3 or better) have very low historical default rates (~0.1% annually), but high-yield munis carry meaningful risk. The TEY advantage must be weighed against the extra credit risk of lower-rated munis relative to comparably-rated corporate or Treasury bonds.
Frequently Asked Questions
Are all municipal bonds free from federal tax?
Most are, but not all. The vast majority of municipal bonds qualify for federal income tax exemption under Section 103 of the Internal Revenue Code. The main exceptions are: (1) bonds issued for activities not deemed to be a valid public purpose (determined by IRS regulations); (2) Private Activity Bonds where more than 10% of proceeds benefit private businesses and more than 10% of debt service is secured by private entity payments — though many PABs still qualify for tax-exemption under specific authorized categories (airports, housing, student loans); (3) taxable municipal bonds, including Build America Bonds, which issuers chose to make taxable in exchange for a federal subsidy. Always verify a bond's tax status in its official statement before assuming it is federally tax-exempt.
Should I hold municipal bonds in my IRA or 401(k)?
Generally no. Tax-advantaged accounts (traditional IRA, Roth IRA, 401(k)) already shelter investment income from current taxes — either through deferral (traditional) or permanent exemption (Roth). Placing tax-exempt municipal bonds inside these accounts wastes the tax exemption because the tax benefit is redundant. Munis already pay lower yields than comparable taxable bonds to compensate for the tax benefit. The correct asset location strategy is: hold taxable bonds (corporates, Treasuries) inside tax-advantaged accounts (where the taxable income is sheltered), and hold municipal bonds in taxable brokerage accounts (where the tax exemption provides direct value).
What does "yield to maturity" mean and is it different from the coupon rate?
The coupon rate is the fixed annual interest payment as a percentage of the bond's face value ($1,000). A 3.5% coupon on a $1,000 bond pays $35 per year. The yield to maturity (YTM) is the total annualized return if you hold the bond to maturity, accounting for any difference between the purchase price and face value. If you buy a bond at a discount ($950 for a $1,000 face value bond), the YTM is higher than the coupon rate because you also gain $50 at maturity. The TEY calculator and this guide use yield to maturity as the relevant comparison figure — not just the coupon.
How do I find the current TEY on municipal bond ETFs?
Municipal bond ETFs report a "30-Day SEC Yield" (standardized by the SEC for comparability), which represents an annualized yield based on net investment income over the prior 30 days minus expenses. For muni ETFs, this yield is already expressed as the tax-free yield. To find the TEY, divide the 30-Day SEC Yield by (1 minus your marginal rate). For example, iShares MUB (National Muni ETF) with a 30-day SEC yield of 3.20% has a TEY of 5.08% at a 37% rate. Compare this to the 30-day SEC yield on a comparable taxable bond ETF (e.g., iShares LQD for investment-grade corporates) to determine which provides better after-tax income.
What is the "muni ratio" and what does it tell investors?
The muni ratio (also called the muni-to-Treasury ratio) expresses the yield of a tax-free municipal bond as a percentage of the yield on a comparable-maturity U.S. Treasury bond. A ratio of 70% means a 10-year AAA muni yields 70% of the 10-year Treasury yield. Since Treasuries are taxable and munis are not, a ratio well below 100% is normal — munis naturally yield less because of the tax advantage. When the ratio rises toward or above 100% (meaning munis yield as much as Treasuries before the tax benefit), munis are considered cheap relative to Treasuries and particularly attractive. During financial stress (COVID March 2020, 2022 rate spike), muni ratios can temporarily exceed 100%, creating exceptional TEY opportunities.
Related Calculators
Bond Yield Calculator
Yield to maturity, duration, and price
Investment Return
ROI, CAGR, and total return analysis
Income Tax Calculator
Find your marginal and effective rate
Dividend Yield
Stock dividend income and yield analysis
Rental Yield
Gross and net yield on rental property
Tax Refund Estimator
Estimate your 2024 federal refund