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How to Calculate Tax-Equivalent Yield

By JLP | October 20, 2006

Let’s say you have the choice between two fixed-income options:

A 5.00% taxable yield or a 4.50% tax-free yield.

We’ll also assume that you are in the 28% tax bracket.

So, how do you know what option is best for you?

Well, there’s a really simple formula that you can use to calculate a tax-equivalent yield so that you can compare the yields on an equal basis. The formula is:

Tax-Equivalent Yield = Tax-Free Interest Rate &#247 (1 – tax rate)

So, for this example, the formula would like this:

4.50 &#247 (1 – .28)

4.50 &#247 .72

6.25% tax-equivalent yield

So, this tells us is that if you are in the 28% tax bracket, you need to find a fixed income investment that yields AT LEAST 6.25% BEFORE TAX in order to get the same after-tax yield of a 4.50% tax-free. In this case you would be much better purchasing the tax-free option. Make sense? If not, let’s look at it another way to test our math.

Again, we will assume that you are in the 28% tax bracket and you find an investment with a taxable yield of 6.25%. Since this yield is taxable, you won’t get to keep it all. So, you want to calculate how much of that yield is going to be left after taxes. So, you can perform the following calculation, which is an alteration of the formula used above:

After Tax Yield = Taxable Interest Rate &#215 (1 – tax rate)

6.25 × (1 – .28)

6.25 × .72

4.50%

See, it works!

We can also calculate what the after-tax yield is on the 5.00% yield:

5.00 × (1 – .28)

5.00 × .72

3.60%

Which would you rather have 4.50% tax-free or 3.60% tax-free? I think it is a pretty easy choice.

A couple of things to understand about tax-free yields:

1. The higher your tax bracket, the more advantageous a tax-free yield becomes. Take a look at the graphic I put together:

Tax-Equivalent Yields

So, what may be good for a high-income doctor may not necessarily be good for you. Also, what the heck are you doing getting investment advice from a doctor?

2. Just because a bond is tax-free DOES NOT mean you will never owe taxes on it. Say what? Capital gains from bonds (even tax-free bonds) are taxable. So, if you purchase a bond and then interest rates fall, the value of your bond will go up. If you SELL that bond for more than you purchased it, you will owe capital gains on the difference. The only way to avoid taxation on the bond is to hold it until maturity at which time you will get your original investment back (no capital gains). This is a whole post by itself.

Okay, now it’s your turn to weigh in. Did this post make sense? Did I miss anything?

Topics: Basics, Bonds, Financial Math Basics, Financial Planning | 19 Comments »


19 Responses to “How to Calculate Tax-Equivalent Yield”

  1. Foobarista Says:
    October 20th, 2006 at 2:51 pm

    Only quibble: don’t forget your state income tax – which those of us outside of Texas have to deal with. (From what I’ve seen, Texas makes up the revenue with relatively high property taxes.)

    Also, there are boundary cases if the taxable bond income would push you up a bracket – in those cases, your formula understates the value of the tax-free bond if you use the income tax bracket without the bond’s income as the basis.

  2. JLP Says:
    October 20th, 2006 at 2:55 pm

    Foobarista,

    Good points.

    All of this stuff makes me realize just how crazy our tax code is.

  3. D Says:
    October 20th, 2006 at 3:44 pm

    Wow, you explained it perfect!

    I knew to add in my state for my tax rate, but excellent to include for those who don’t!

  4. Mike Says:
    October 20th, 2006 at 9:43 pm

    I would also point out that tax-free interest would not necessarily be truly tax-free for a retiree drawing social security. Yes, the retiree would not pay tax directly on $1 of tax-free income but might have to pay taxes on $.50 or $.85 of social security income, so indirectly it wouldn’t really be tax-free income. While there is an exemption amount before social security is taxed, this exemption amount is not indexed for inflation and will affect more and more people.

  5. Daniel Says:
    October 21st, 2006 at 9:32 am

    Great post. Foobarista makes a great point. For those of us in California, state taxes can be as high as 9.3% bringing the total tax almost as high as 45% in some cases.

    You did say it right though. Our tax code is crazy! For example, you can buy a muni bond in California to earn interest tax free, however if you are required to pay “Alternative Minimum Tax” these may not be tax free. What is “Alternative Minimum Tax”? Who knows! But it could probably be explained in about 5 pages! Haha

  6. thc Says:
    October 21st, 2006 at 10:02 am

    Great post and some very astute comments as well. Now shall we throw AMT into the mix?

  7. » Weekly Roundup on Blueprint for Financial Prosperity Says:
    October 21st, 2006 at 6:55 pm

    […] JLP’s math lesson of the week is How to Calculate Tax-Equivalent Yield. […]

  8. Carnival of Personal Finance #71 - Fat Pitch Financials Says:
    October 23rd, 2006 at 2:29 pm

    […] How to Calculate Tax-Equivalent Yield at AllFinancialMatters * Editor’s Choice * A good post on how to determine if a tax free investment is as good as a taxable bond investment. […]

  9. Nagel Says:
    October 27th, 2006 at 6:53 am

    AMT screws up the entire formula. AMT is becoming more and more widespread. Hopefully if the tax code is changed they will rid us of this or fix it so it does what is was proposed in the LBJ administration.

  10. samerwriter » Samerwriter’s Saturday Says:
    October 28th, 2006 at 2:28 pm

    […] It’s pretty easy to figure out if you’re best off in the Tax Exempt fund or the taxable fund. You just need to know your tax bracket. There are online calculators, or JLP shows the algorithm here. I keep a table next to my computer showing the tax-equivalent yield at 1%, then just multiply that yield by the actual tax-exempt yield I’m looking at to decide if I’m better off in a tax-exempt fund or a taxable fund: […]

  11. Send Money Online » Carnival of Personal Finance #71 Says:
    November 6th, 2006 at 12:08 pm

    […] How to Calculate Tax-Equivalent Yield at AllFinancialMatters * Editor’s Choice * A good post on how to determine if a tax free investment is as good as a taxable bond investment. […]

  12. FIRE Finance Says:
    November 11th, 2006 at 1:40 pm

    We Catch Up With Carnival Of Personal Finance #71

    We are almost always up to date with our readings of Carnivals and Festivals on Personal finance. However due to a movie festival at our place over a weekend we had missed reading Carnival Of Personal Finance #71 hosted at FatPitchFinancials. This wa…

  13. Phyllis Michaux Says:
    January 19th, 2008 at 10:07 am

    Bernie and Pam Britten are a young married couple beginning careers and establishing a household. They will each make about $50,000 next year and will have accumulated about $40,000 to invest. They now rent an apartment but are considering purchasing a condominium for $100,000. If they do, a down payment of $10,000 will be required.

    They have discussed their situation with Lew McCarthy, an investment advisor and personal friend, and he has recommended the following investments:

    The condominium – expected annual increase in market value = 5%.
    Municipal bonds – expected annual yield = 5%.
    High-yield corporate stocks – expected dividend yield = 8%.
    Savings account in a commercial bank-expected annual yield = 3%.
    High-growth common stocks – expected annual increase in market value = 10%; expected dividend yield = 0.
    Calculate the after-tax yields on the foregoing investments, assuming the Brittens have a 28% marginal tax rate (based on Public Law 108-27, The Jobs and Growth Tax Relief Reconciliation Act of 2003).
    How would you recommend the Brittens invest their $40,000? Explain your answer.

  14. Bob Says:
    February 24th, 2008 at 12:57 pm

    How do you calculate a tax-quivalent rate of return for an annuity with a exclusion ratio? In other words part of the return is taxable and the rest isn’t (excluded).

  15. Martha Says:
    April 1st, 2008 at 11:26 am

    Did anybody have an answer to Phyllis Michaux (#13) posting on January 19th, 2008 on calculating the after-tax yields on certain investments? I have a similar homework problem. I think the 2003 Act lowered the tax rates on stock dividends and capital gains.

  16. crystal kingsbury Says:
    June 22nd, 2008 at 3:19 pm

    did anyone have the answer to question of Phyllis Michaux (#13)

  17. Andy Says:
    June 25th, 2008 at 3:50 pm

    Answer to #13… they should put the minimum down on the condo and take out a 30 year fixed mortgage. The rest of the money should be put in the market with a pretty aggresive Asset Allocation.

    Here is why: the first several years, their mortgage payments will be mostly interest… which is tax deductible. Also, think about inflation, what seems like a big payment now will not be so big toward the end of the mortgage. There money is much better off in a properly allocated portfolio, especially with a 6.5% or less mortgage. Investing in bonds and other fixed income would be foolish. If you had a 30 year time frame for investing… you would have an allocation closer to 80/20 stocks/bonds.

  18. Andy Says:
    June 25th, 2008 at 3:56 pm

    Here is more info to back up what I’ve said about #13.

    http://ricedelman.com/cs/education/article?articleId=232

  19. tariq Says:
    November 5th, 2009 at 2:15 pm

    so good bu explane withe more detail that understand every one easily.thanks

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