Tax Equivalent Yield Calculator

Understanding Tax Equivalent Yield

Introduction

When you compare a municipal bond with a taxable bond, the stated yields do not tell the whole story. A municipal bond often pays interest that is exempt from federal income tax and may also be exempt from state income tax, depending on where you live and which bond you own. A corporate bond, Treasury security, certificate of deposit, or bond fund may show a higher headline yield, but part of that income can be lost to taxes. The purpose of a tax equivalent yield calculation is to convert the tax-free yield into a taxable equivalent so you can make a more realistic side-by-side comparison.

This calculator is designed for that exact decision. You enter the yield on the municipal investment, your marginal federal tax rate, your marginal state tax rate, and the taxable yield you are comparing against. The calculator then estimates the taxable yield an alternative investment would need to offer in order to leave you with the same after-tax income. In other words, it answers a practical question: if a municipal bond yields a certain percentage tax free, how high would a taxable bond's yield need to be before it truly matches it?

This matters most for investors in moderate or high tax brackets, because taxes can materially reduce the value of taxable interest income. It also matters when comparing individual bonds, bond funds, or cash alternatives. A taxable bond that looks better at first glance may not actually be superior once taxes are considered. By translating the municipal yield into a taxable equivalent, the calculator gives you a cleaner benchmark for evaluating income options.

How to Use

Using the calculator is straightforward. Start with the yield on the tax-free investment, usually the municipal bond or municipal bond fund you are considering. Enter that figure as a percentage, such as 3.25 for a 3.25% yield. Then enter your marginal federal tax rate. This is the tax rate that applies to your next dollar of ordinary income, not necessarily your average tax rate across all income. If your state taxes interest income, enter your marginal state tax rate as well. If your state does not tax that income, or if the bond is exempt in your state and you want a simplified comparison, you can enter 0 for the state rate.

After you run the calculation, the result area shows the tax-equivalent yield, the after-tax yield from the taxable investment you entered, and a short interpretation. For a quick in-state municipal comparison, leave the municipal state-tax setting as exempt and enter your state tax rate so taxable alternatives are still penalized correctly. For an out-of-state municipal bond that your state taxes, change the municipal state-tax setting to taxed.

Once you have the result, compare it with the yield on the taxable bond or fund you are evaluating. If the taxable investment yields more than the tax-equivalent yield, it may provide a better after-tax return. If it yields less, the municipal bond may still be the stronger choice from an income perspective. That does not automatically make one investment better overall, but it gives you a more informed starting point.

Formula

The default combined tax rate treats federal and state taxes as separate marginal taxes on ordinary taxable interest:

combined tax rate = federal rate + state rate

If you choose the state-tax deductible option, the calculator uses a reduced state-tax effect because a deductible state tax can offset federal taxable income:

combined tax rate = federal rate + state rate × (1 - federal rate)

For a municipal bond that is state-taxable, the calculator reduces the municipal yield before converting it to a taxable equivalent. The general method is:

municipal after-tax yield = municipal yield × (1 - municipal state tax rate)

tax-equivalent yield = municipal after-tax yield / (1 - combined tax rate)

The older shortcut below is the deductible-state-tax version, not the right default for every household. Use the select box in the form to match the assumption you want to model. In MathML form, the deductible-state-tax combined rate is $t=t\_f+t\_s-t\_ft\_s$, where $t\_f$ and $t\_s$ represent the federal and state tax rates respectively. Use that version only when state tax deductibility is a reasonable assumption for the comparison you are making.

The tax equivalent yield is then expressed through the following MathML equation:

Formula: TEY = r / (1 - t)

$\mathrm{TEY}=\frac{r}{1-t}$

Here, $r$ denotes the municipal bond's after-tax yield after any state tax on the municipal bond itself and $t$ is the combined tax rate. The denominator represents the portion of the taxable bond's yield you would keep after taxes. Dividing the municipal after-tax yield by this value inflates it to a comparable taxable rate. In plain language, the formula asks: if you only keep a fraction of taxable interest after taxes, how large must the taxable yield be so that the amount left over equals the municipal bond's after-tax yield?

For example, if your combined tax rate is 35%, you keep 65% of the interest from a taxable bond. A municipal bond yielding 3.00% tax free would therefore be equivalent to a taxable bond yielding about 4.62%, because 4.62% multiplied by 65% leaves roughly 3.00%. That is the core logic behind the calculator's output.

Worked Example

Suppose you are considering an in-state municipal bond that yields 3.00%. Your marginal federal tax rate is 32%, and your state tax rate is 5%. With the default non-deductible state-tax assumption, the taxable interest tax burden is 37.0%. That means you would keep 63.0% of the interest from a taxable bond after taxes.

Next, the calculator divides the municipal after-tax yield by the after-tax share of taxable income. In this case, 3.00% divided by 0.630 gives a tax-equivalent yield of about 4.76%. That means a taxable bond would need to yield approximately 4.76% just to match the municipal bond's after-tax income. If a corporate bond you are considering yields 4.50%, it would still fall short on an after-tax basis. If another taxable bond yields 5.10%, it may be more attractive from a pure income standpoint, assuming similar risk and other features.

This kind of example shows why tax-equivalent yield is especially useful in higher tax brackets. The higher your tax rate, the more valuable tax-free income becomes. A municipal bond with a modest stated yield can compete surprisingly well once taxes are taken into account.

The table makes the pattern easy to see. As tax rates rise, the taxable bond must offer a meaningfully higher yield to keep pace with the tax-free municipal bond. That is why municipal bonds often appeal most to investors with higher taxable income and why a simple nominal-yield comparison can be misleading.

Interpreting the Result

The result is best understood as a break-even threshold, not a prediction. If the calculator returns 4.76%, that does not mean every taxable bond yielding more than 4.76% is automatically better. It means that 4.76% is the approximate point where the taxable bond's after-tax income matches the municipal bond's after-tax income. Above that level, the taxable bond may produce more after-tax income. Below that level, the municipal bond may produce more.

You can use this threshold in several ways. It can help you compare individual municipal bonds with corporate bonds, compare municipal bond funds with taxable bond funds, or evaluate whether a tax-free investment still makes sense after a change in your income or tax bracket. It can also help with account placement decisions. In a taxable brokerage account, municipal bonds may be more compelling. In a tax-advantaged account such as an IRA or 401(k), the tax-free feature of municipal bonds is often less valuable because the account itself already changes the tax treatment.

It is also useful to remember that the calculator focuses on yield, not total return. Bond prices can rise or fall, and a bond's maturity, duration, call features, and credit quality all affect the investment outcome. The tax-equivalent yield is a comparison tool, not a complete investment analysis.

Limitations and Assumptions

Like any financial calculator, this one relies on simplifying assumptions. It uses your marginal federal and state tax rates as inputs, which is usually the right approach for comparing the tax effect of additional investment income. However, real tax situations can be more complicated. Some municipal bonds are exempt from federal tax but not from state tax. Some are exempt from both only if you live in the issuing state. Certain private activity bonds may have Alternative Minimum Tax treatment, and state-tax deductibility may be limited or unavailable in practice.

The calculator also assumes that the taxable bond's interest is taxed at ordinary income rates. That is often appropriate for many bond investments, but not every income-producing asset is taxed the same way. Treasury securities, corporate bonds, municipal bonds, bond funds, preferred securities, and other income products can have different tax characteristics. If you are comparing investments with unusual tax treatment, the result should be treated as a rough guide rather than a final answer.

Another limitation is that the tool does not measure risk. A municipal bond and a taxable corporate bond may have very different credit quality, liquidity, call risk, and maturity structure. A taxable bond with a higher yield may be compensating you for taking on more default risk or more price volatility. Likewise, a municipal bond with a lower yield may still be attractive because of stronger credit quality or more favorable tax treatment. The calculator isolates the tax question so you can answer that part clearly, but it does not replace broader due diligence.

Finally, tax laws change and personal circumstances change. A move to a different state, a change in income, retirement, or new tax legislation can all alter the comparison. For that reason, it is wise to revisit the calculation periodically rather than relying on an old estimate. Used properly, the calculator is a practical screening tool that helps you think in after-tax terms, which is often the most meaningful way to compare income investments.