Tax Equivalent Yield Calculator For Savings Bonds, Treasury Bills, and Tax-Exempt Money Market Funds

There are many investments out there that are exempt from certain taxes. For example, U.S. Savings Bonds and Treasury Bonds are exempt from state and local income taxes. In addition, there are money market funds available that are exempt from federal income tax and others that are even exempt from a specific state or city’s income taxes.

Therefore, it is desirable to know what the equivalent fully-taxable rate is for one of these investments. For example, is it more profitable to earn a federal tax-exempt interest rate of 3.8% or a fully taxable 5.0%? How about a Treasury Bill paying 4.8%? Several variables affect this rate, including your marginal tax brackets for each area, as well as if you itemize your state and local taxes on your federal tax return. I could not find a calculator that accurately captured all of this, so I made my own.

Tax Equivalent Yield Calculator
(You may need to be on the individual post page for it to work.)

Enter the interest rate: %
Enter your marginal federal income tax rate: %
Enter your marginal state income tax rate (if any): %
Enter your marginal city/local income tax rate (if any): %
Exempt?
Federal Tax-Exempt
State Tax-Exempt
City/Local Tax-Exempt
Itemize?
Do you itemize deductions? Yes
No
Your tax-equivalent rate:   %

Example
Let’s say you live in California, and your marginal federal tax rate is 25%, your state rate is 9.3%, and you have no local income taxes. You do not itemize your taxes. You are trying to compare the taxable Vanguard Prime Money Market Fund (VMMXX, yielding 5.08%), the federally exempt Vanguard Tax-Exempt Money Market Fund (VMSXX, yielding 3.48%), and the state and federal tax-exempt Vanguard California Tax-Exempt Money Market Fund (VCTXX, yielding 3.38%).

With that profile, the tax equivalent 7-day yields would be 4.804% for VMSXX, and 5.145% for VCTXX, making the California Tax-Exempt Fund the best bet currently for this specific situation.

How It Works (Warning: Math Ahead!)
The calculator computes the tax-equivalent rates by comparing after-tax returns. That is:

AfterTaxReturnEquivalentTaxableRate = AfterTaxReturnTaxAdvantagedRate

Using the California Tax-Exempt Fund example above:

EquivalentRate x (1 – FederalTaxes – StateTaxes) = 3.38%
EquivalentRate x (1 – 0.25 – 0.093) = 0.0338
EquivalentRate = 5.145%

So earning 3.38% free from federal and state taxes is the same as earning 5.145% in a fully taxable account.

Note that itemizing deductions means that you deduct your state income taxes from your federal taxable income. The effect is that your overall tax liability is reduced, which lowers the benefit of any tax-exemptions and thus the equivalent rates. That would change the previous equation to:

EquivalentRate x (1 – FederalTaxes – StateTaxes + (FederalTaxes x StateTaxes)) = 3.38%
EquivalentRate = 4.969%

The inclusion of this option may give different results from some of the other online calculators out there, but I believe it makes the results more complete. Another fully-worked-out example can be found here for savings bonds.

Finally, it may be handy to use this in conjunction with my Ultimate Interest Rate Chaser Calculator. Be sure to compare APRs to APRs and APYs to APYs.

Useful Resources
2007 Federal Tax Rates
State Income Tax Rates
Recent Treasury Bill Auction Results
Savings Bonds Rates

Comments

  1. Have you had to deal with how you handle these with your taxes yet? I have my 1099, but I am assuming somewhere on your state return you deal with this correct?

  2. I dealt with it last year, as I recall there are simply different portions of the 1099s that indicate in which areas they are exempt from taxes.

  3. Don you still have your T-bill ladder?

  4. Love the calculator, with one request: could you increase the size of the little windows? On my mac, I can only view about one digit at a time. It may be a Mac/PC text size thingy. Now if you could only help me know how much tax-free money I can earn without triggering AMT, I’d be eternally greatful. :-)

  5. Your calculator doesn’t seem to work for your example of 5.376apy, 28% fed, and 9% tax. The calculator gives 6.144% when it should be 5.908% (you were off by 1 basis pt in the example in your blog, perhaps from rounding). It should simply be Eqiv rate = Tbill rate/ (1- state tax). Since Tbills are subject to federal taxes, they don’t factor into the calculation at all. Am i missing something?

  6. I’ve seen that formula, but it really only works well if you are subject to, and exempt, from one tax (like federal tax). The effect of taxes also changes if you itemize and deduct your state income taxes paid from your income. Please see the “How It Works” section above for the derivation of the formula that I use.

    My example was 5.367 (not 5.376), 28% fed, 9% tax, plus “yes” on itemizing – which still gives me 5.898%.

  7. 5.367. You’re right. I did look at the how it works section, but even using 5.367 doesn’t get you the right number using the calculator.

    Btw, your formula simplifies to mine for Tbills.

    TR = ER x (1-F-S+FS)/(1-F)
    = ER x [(1-F)+(-S+FS)]/(1-F)
    = ER x [1 + S x (-1+F)/(1-F)]
    = ER x (1-S)

    hence, ER = TR/(1-S)

    Basically the Federal tax cancels out as it should.

    My real question is whether the calculator on this page is based on a different formula.

    Thanks.

  8. Yes, if you itemize, the state tax cancels out. If you don’t itemize, it doesn’t cancel out.

    Using your formula, which is the same as the calculator formula, you get

    5.367 / (1-.09) = 5.367 / .91 = 5.898%.

    I’m confused – doesn’t that agree with what I wrote previously?

  9. I guess I have the same question as rob. 5.898 is the correct equivalent yield using that formula, but that formula is for NON-itemized. If you were to itemize, wouldn’t it be:

    5.367 / (1-.09 +.28*.09) = 5.739

    Your calculator appears to give the non-itemized result when itemized is selected, and some other number (6.134) when non-itemized is selected. Perhaps you could explain how you are getting that number.

  10. Jonathan???

  11. Sorry, Jonathan. I looked at your javascript and found my mistake.

  12. the buttons are backwards for state and federal tax exemptions.

  13. backwards?

  14. FYI – you calculator is wrong. If you are subject to both State and Federal, you do not simply divide by 1- the sum of Fed and State. Who know how many people you haev mislead. Please correct

  15. What is the correct answer, Tim?

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