Tax Equivalent Yield Calculator

What this tax equivalent yield calculator does

A municipal bond yielding 3.5 percent and a corporate bond yielding 4.8 percent. The corporate looks obviously better, and if the municipal interest is tax free and you are in a high bracket, it may not be.

Tax equivalent yield settles that. It converts a tax free yield into the taxable yield you would need to end up with the same money after tax, so the two become directly comparable.

Two inputs, one answer. Give it the tax free yield and your marginal tax rate, and it returns what that yield is worth on a taxable basis.

It is a small calculation that changes a lot of decisions, and the reason municipal bonds can offer visibly lower headline yields than corporates and still be the better buy for some people and not others.

Everything runs in your browser. Nothing typed here is stored or sent anywhere.

How to use it

1. Bond yield. The tax free yield, as a percentage. This is the municipal bond's yield, exactly as quoted.
2. Marginal tax rate. The rate on your next dollar of income, not your average rate across everything you earn. This is the number people most often get wrong, and using an average rate understates the value of the exemption.

Press Calculate. Press Reset to clear it.

If your municipal bond is exempt from state tax as well as federal, and you want the full picture, the combined rate is not simply the two added together and there is a short calculation below.

The formula

Tax equivalent yield = tax free yield ÷ (1 − marginal tax rate)

The logic is worth seeing rather than memorising. A taxable bond hands you a yield and then the tax authority takes a slice, so what you keep is the yield times (1 minus your rate). A tax free bond hands you the whole thing.

To find the taxable yield that survives down to your tax free yield, you divide by that same (1 minus rate) factor. It is the same adjustment run in reverse.

Which is why the value of an exemption rises with your tax rate. At a zero rate the two are identical and the formula does nothing. At 37 percent you are dividing by 0.63, which lifts the yield by nearly sixty percent.

A worked example

A municipal bond yielding 3.5 percent, and a marginal federal rate of 32 percent.

3.5 ÷ (1 − 0.32) = 3.5 ÷ 0.68 = 5.15 percent

So that 3.5 percent tax free bond is worth the same to you as a taxable bond yielding 5.15 percent. If the best comparable corporate bond you can find pays 4.8 percent, the municipal wins, despite looking worse by more than a point on the headline.

Check it the long way round. On 10,000 invested, the municipal pays 350 and you keep all of it. The corporate at 5.15 percent pays 515, of which 32 percent goes in tax, leaving 350.20. The same money.

Now change one thing. Same bond, but you are in the 12 percent bracket:

3.5 ÷ 0.88 = 3.98 percent

Now the 4.8 percent corporate is comfortably better. Identical bond, opposite conclusion, decided entirely by who is holding it. That is the whole point of the calculation.

What a tax free yield is worth at each bracket

The same 3.5 percent tax free yield, across the range of marginal rates:

Two things fall out of that column.

The first is how much the exemption is worth at the top. Between the 12 percent bracket and the 37 percent bracket, the same bond goes from being worth 3.98 to 5.56, a difference of more than a point and a half of yield, for doing nothing at all.

The second is why the municipal bond market is shaped the way it is. Because the benefit is concentrated among high earners, municipal issuers can pay visibly less than corporate issuers and still attract buyers. Investor.gov puts it plainly: given the tax benefits, tax exempt municipal yields are usually lower than taxable securities of similar maturity and credit quality. The lower yield is not a worse deal, it is the exemption being priced in.

Which also means that if you are in a low bracket, or investing through a retirement account where nothing is currently taxable anyway, municipal bonds are usually the wrong instrument. You would be accepting the lower yield without collecting the benefit that justifies it.

The break even, running it backwards

Often the more useful question is the reverse. You have a taxable bond in front of you, and you want to know what tax free yield would beat it.

Break even tax free yield = taxable yield × (1 − marginal rate)

Against a 5 percent taxable bond:

This is the version to carry around when you are actually shopping. It gives you a single threshold number: at 32 percent, any tax free yield above 3.40 percent beats the 5 percent taxable alternative. Below it, take the taxable bond.

Worth doing this before you look at any municipal offerings rather than after, because it turns a comparison into a filter.

Adding state tax, and why it is not simple addition

Municipal bond interest is generally exempt from federal income tax, and may also be exempt from state and local tax if you live in the state that issued it. A bond that clears both is often called double exempt, and it is worth more than the calculator above will tell you if you only enter your federal rate.

The temptation is to add the two rates together. That overstates it, because state income tax may itself be deductible against federal tax, so the two do not stack cleanly.

Combined rate = federal rate + state rate × (1 − federal rate)

At a 35 percent federal rate and a 5 percent state rate, the combined figure is 35 + (5 × 0.65) = 38.25 percent, not 40.

What that does to a 3.5 percent double exempt bond:

Nearly three tenths of a point of extra value from the state exemption, which is real and worth capturing in the comparison.

Two conditions on that formula. It assumes you itemise deductions and can actually deduct your state income tax, which many taxpayers cannot because of limits on the deduction. If you cannot deduct it, the combined rate is simply the two added together. And it only applies if the bond is genuinely exempt in your state, which normally means it was issued there.

Given the number of ways that can go, the honest advice is to work out your own combined rate carefully, or ask whoever does your tax return, and then enter that single figure.

Where the simple comparison stops working

Tax equivalent yield answers one question cleanly. Several things sit outside it.

Not every municipal bond is fully tax free. Some are subject to the federal alternative minimum tax, which means the interest is taxable for anyone the AMT applies to. Private activity bonds are the usual culprit. If your bond is AMT subject and you are an AMT payer, the exemption you are pricing does not exist for you.

Taxable municipal bonds exist. The category name is misleading. Some municipal issues are federally taxable, and they generally pay higher yields precisely because of it. Check the specific bond rather than assuming the sector.

Capital gains are still taxable. The exemption covers interest. If you buy a municipal bond at a discount and sell it higher, or hold it to maturity from below par, that gain can be taxable even though the coupons were not.

Credit quality has to match. Comparing a municipal bond against a corporate bond is only meaningful if the two carry similar credit risk and similar maturity. A high yield corporate paying more than a AAA rated municipal is not evidence that the tax comparison failed. It is evidence that you are comparing different risks.

Your bracket is not permanent. The calculation uses today's marginal rate on a bond you may hold for twenty years. Retirement, a change in income, or a change in the law all move it.

Municipal bonds in a retirement account. Nothing in a tax deferred account is currently taxable, so the exemption buys you nothing and you have accepted a lower yield for it. That is the single most common mistake with this asset class.

Questions people ask

How do I calculate tax equivalent yield?

Divide the tax free yield by one minus your marginal tax rate. A 3.5 percent yield at a 32 percent rate is 3.5 divided by 0.68, which is 5.15 percent.

Should I use my marginal or my effective tax rate?

Marginal, meaning the rate on your next dollar of income. Using your average rate understates the value of the exemption, sometimes substantially.

Is a municipal bond worth it for me?

Work out the break even instead. Multiply the taxable yield you could get by one minus your marginal rate. If a municipal bond pays more than that, it wins. See the reverse table.

How do I include state tax?

Combined rate is federal plus state times one minus federal, if you can deduct state tax against federal. At 35 percent federal and 5 percent state that is 38.25 percent, not 40.

Should I hold municipal bonds in my retirement account?

Generally not. Nothing in there is currently taxed anyway, so you would be taking the lower municipal yield without collecting the exemption that justifies it.

Are all municipal bonds tax free?

No. Some are subject to the alternative minimum tax, and some municipal bonds are federally taxable outright. Check the individual bond.

Why does 100 percent tax break the calculator?

Because the formula divides by one minus the rate, and at 100 percent that is zero. Mathematically the answer is infinite, which is the arithmetic pointing out that no taxable yield could ever survive a full confiscation.

References

A note on sourcing. The federal tax exemption for most municipal bond interest, the possible additional exemption from state and local tax for residents of the issuing state, and the exceptions including alternative minimum tax treatment and taxable municipal issues are described by the Securities and Exchange Commission's investor education service and by the Municipal Securities Rulemaking Board. Marginal tax rates and deductibility rules change, so anyone acting on a figure from this page should confirm their own position with a tax professional.

1. U.S. Securities and Exchange Commission, Municipal Bonds, Investor.gov. https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds-or-fixed-income-products-0
2. Municipal Securities Rulemaking Board, Understanding Taxable Municipal Bonds. https://www.msrb.org/Understanding-Taxable-Municipal-Bonds
3. Municipal Securities Rulemaking Board, Municipal Bond Basics. https://www.msrb.org/Education/Municipal-Bond-Basics-0
4. Internal Revenue Service, Topic No. 409, Capital Gains and Losses. https://www.irs.gov/taxtopics/tc409