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Calculating Tax-equivalent Yield for Muni bonds and bond funds
Old 06-25-2018, 03:49 PM   #1
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Calculating Tax-equivalent Yield for Muni bonds and bond funds

After the 2017 tax legislation, our marginal tax rate has dropped significantly in 2018 because AMT went away for us - due to the much higher thresholds.

So, I was looking at some muni bond funds we own and realized I needed to calculate our marginal rate again.

I also notice that the ratio of muni bond rates to the equivalent duration treasury have dropped quite a bit on the short end due to the recent rapid rise in treasury rates. After some confusion in late 2017, it seems like muni bonds are more fully valued compared to treasuries. For years muni bonds were paying higher rates in spite of their tax advantage. No longer. So definitely a good time to compare again.

This article provides the basic formula: https://www.thebalance.com/calculati...t-yield-417147
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Calculating Tax Equivalent Yield

The good news: the calculation's not difficult. The following shows how to calculate the tax equivalent yield in a few steps:
  1. Find the reciprocal of your tax rate, or in other words, use (1 Ė your tax rate). If you pay 25 percent, your reciprocal would be (1 - .25) = .75, or 75 percent.
  2. Divide this into the yield on the tax-free bond to find out the tax-equivalent yield. If the bond in question yields 3 percent, use the equation (3.0 / .75) = 4 percent.
If you plug different tax rates into the equation above, you will see that the higher your tax rate, the higher the tax-equivalent yield, illustrating how tax-free bonds are best suited to those investors in the higher tax brackets.
Our ordinary income falls in the 12% bracket, but, since we have a lot of long-term capital gains income taxed at 0%, any additional ordinary income from taxable bonds will push the same amount of capital gains income into the fixed income bracket. So for estimating the tax equivalent yield I have to add 15% for a total of a 27% tax bracket.
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Old 06-25-2018, 04:01 PM   #2
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Originally Posted by audreyh1 View Post
This article provides the basic formula:
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Find the reciprocal of your tax rate, or in other words, use (1 Ė your tax rate). If you pay 25 percent, your reciprocal would be (1 - .25) = .75, or 75 percent.
I had to do a double take when I read that.

Back in Paleozoic times when i went to school, a reciprocal was 1 divided by X, not 1 minus X.
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Old 06-25-2018, 04:04 PM   #3
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I like calculating the after-tax yield of non-tax-exempt bonds instead.

I like calculating the after-tax yield of dividend paying funds, too.

I think this "tax-equivalent yield" idea was invented to make financial sales reps look smarter than they are.
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Old 06-25-2018, 04:05 PM   #4
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I had to do a double take when I read that.

Back in Paleozoic times when i went to school, a reciprocal was 1 divided by X, not 1 minus X.
He simply means the result of 1-x is the reciprocal you use to calculate your tax equivalent yield.

25% tax bracket.
1-25% = 75%
tax equivalent yield = muni yield/.75 so a 3% muni yield gives you a 4% tax equivalent yield.

That's all.
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Old 06-25-2018, 04:06 PM   #5
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Originally Posted by LOL! View Post
I like calculating the after-tax yield of non-tax-exempt bonds instead.

I like calculating the after-tax yield of dividend paying funds, too.

I think this "tax-equivalent yield" idea was invented to make financial sales reps look smarter than they are.
I find it useful as that shows directly how it will reduce my taxes.
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Old 06-25-2018, 04:23 PM   #6
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He simply means the result of 1-x is the reciprocal you use to calculate your tax equivalent yield.

25% tax bracket.
1-25% = 75%
tax equivalent yield = muni yield/.75 so a 3% muni yield gives you a 4% tax equivalent yield.

That's all.
He should just say take 1-x and skip using the incorrect term "reciprocal" then. Before you call this pedantic, I was very confused reading this, trying to figure out what the calculation would be since I was trying to figure out how to do it with reciprocals.
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Old 06-25-2018, 04:39 PM   #7
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Originally Posted by audreyh1 View Post
Our ordinary income falls in the 12% bracket, but, since we have a lot of long-term capital gains income taxed at 0%, any additional ordinary income from taxable bonds will push the same amount of capital gains income into the fixed income bracket. So for estimating the tax equivalent yield I have to add 15% for a total of a 27% tax bracket.
OK, now that weíve heard from all the accountants and English majors, Iíd like to hear what Audrey has decided to do based on the tax-equivalent yield.

Also, pls address state taxes in your plan.
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Old 06-25-2018, 05:11 PM   #8
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OK, now that we’ve heard from all the accountants and English majors, I’d like to hear what Audrey has decided to do based on the tax-equivalent yield.

Also, pls address state taxes in your plan.
I haven’t finished reviewing my calcs yet. Also, I don’t pay state taxes. The article discusses them brokerage briefly.

Yeah, tough crowd today, lol!
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Old 06-25-2018, 05:34 PM   #9
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I havenít finished reviewing my calcs yet. Also, I donít pay state taxes. The article discusses them brokerage briefly.

Yeah, tough crowd today, lol!
Right...Republic of Texas; I forgot.

Well, Iím interested in your findings when you have done the calcs. Iím interested because part of our plan is to keep a certain amount of cash-ish assets on hand, and weíve decided to keep part of it in a Muni-Bond fund in out taxable account. So, Iím interested in what another member thinks.
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Old 06-25-2018, 05:43 PM   #10
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I too, was immediately distracted by the incorrect use of the term reciprocal......what were we talking about?
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Old 06-25-2018, 06:02 PM   #11
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I too, was immediately distracted by the incorrect use of the term reciprocal......what were we talking about?
LOL - he was simply talking about what goes in the denominator, so it didnít confuse me.
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Old 06-25-2018, 06:05 PM   #12
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Right...Republic of Texas; I forgot.

Well, Iím interested in your findings when you have done the calcs. Iím interested because part of our plan is to keep a certain amount of cash-ish assets on hand, and weíve decided to keep part of it in a Muni-Bond fund in out taxable account. So, Iím interested in what another member thinks.
Well - at first pass quick figuring I determined that the tax equivalent rates my muni bonds were paying were not too far off the mark, whereas at first they looked paultry.

But I do want to do a more thorough review and put things in a spreadsheet.
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Old 06-25-2018, 06:46 PM   #13
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After the 2017 tax legislation, our marginal tax rate has dropped significantly in 2018 because AMT went away for us - due to the much higher thresholds.

.....

Our ordinary income falls in the 12% bracket, but, since we have a lot of long-term capital gains income taxed at 0%, any additional ordinary income from taxable bonds will push the same amount of capital gains income into the fixed income bracket. So for estimating the tax equivalent yield I have to add 15% for a total of a 27% tax bracket.
So I'm just going to be stupid and blunt (after a glass of wine) and say you are wrong.
But don't take offense as I understand the reason why you think this.

Pretend you have $101K as ordinary income, top of the 12% bracket.
Now add in $40K as capital gains.
They will be taxed at 15%
Add another $20K capital gains and you will still be taxed at 15% for that.

No way you will be taxed at 27%

Yes, I get that with say $1,000 space under the 12% top, the capital gain is tax free, and when interest of $1,000 bumps it out, so the interest is taxes at 12% and the capital gain is now taxed at 15% you add them up to claim 27%.
However, since it is for $2,000 difference in taxation and the tax is $120 + $150 = $270, it should at best be divided to be 13.5% avg increase.

But since this is below the 15% rate, for comparing muni's to regular bonds, I'd use the 15%
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Old 06-25-2018, 06:55 PM   #14
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So I'm just going to be stupid and blunt (after a glass of wine) and say you are wrong.
But don't take offense as I understand the reason why you think this.

Pretend you have $101K as ordinary income, top of the 12% bracket.
Now add in $40K as capital gains.
They will be taxed at 15%
Add another $20K capital gains and you will still be taxed at 15% for that.

No way you will be taxed at 27%

Yes, I get that with say $1,000 space under the 12% top, the capital gain is tax free, and when interest of $1,000 bumps it out, so the interest is taxes at 12% and the capital gain is now taxed at 15% you add them up to claim 27%.
However, since it is for $2,000 difference in taxation and the tax is $120 + $150 = $270, it should at best be divided to be 13.5% avg increase.

But since this is below the 15% rate, for comparing muni's to regular bonds, I'd use the 15%
Put down the glass of wine. Quite simply, you add $1000 taxable interest, you get taxed an extra $270 of taxes, or 27% for the marginal rate.

It is not a $2000 difference of taxable income. You already had that $1000 of capital gains, and it was taxable, but it happened that the tax rate of 0%. The new bond income changed the tax rate of that bond income to 15%. It didn't create $1000 of new bond income, it just changed the tax rate on that existing bond income.
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Old 06-25-2018, 06:58 PM   #15
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So I'm just going to be stupid and blunt (after a glass of wine) and say you are wrong.
But don't take offense as I understand the reason why you think this.

Pretend you have $101K as ordinary income, top of the 12% bracket.
Now add in $40K as capital gains.
They will be taxed at 15%
Add another $20K capital gains and you will still be taxed at 15% for that.

No way you will be taxed at 27%

Yes, I get that with say $1,000 space under the 12% top, the capital gain is tax free, and when interest of $1,000 bumps it out, so the interest is taxes at 12% and the capital gain is now taxed at 15% you add them up to claim 27%.
However, since it is for $2,000 difference in taxation and the tax is $120 + $150 = $270, it should at best be divided to be 13.5% avg increase.

But since this is below the 15% rate, for comparing muni's to regular bonds, I'd use the 15%
But I’m not at the top of the 12% bracket in terms of ordinary income, I’m well under it, and the additional taxable income is still not enough to push me to the top of the 12% bracket. Yet I have plenty of capital gains (well above the 0% threshold). So the total effect is that the additional ordinary income from taxable interest has me paying 12% on it, plus 15% on the capital gains income it displaces (no additional income - it’s simply pushed up to a higher tax bracket). Plenty of discussions here on the high marginal tax rate of ordinary income until you reach the 15% cap gains threshold.

As RunningBum so elegantly pointed out, you are paying $270 on an additional $1000 of income, NOT $2000 of income.
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Old 06-25-2018, 07:08 PM   #16
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LOL - he was simply talking about what goes in the denominator, so it didnít confuse me.


Oh, I KNEW what he was talking about, but someone in that position using inaccurate terminology loses credibility in my eyes. I'm all too familiar with this particular calculation so no chance of me screwing it up but without the example a newbie might mess it up. Too sensitive, I suppose. Article does a decent job explaining how to handle state taxes and Treasuries.
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Old 06-25-2018, 07:10 PM   #17
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The 27% marginal rate is right if you are at the top of the 12% tax bracket for additional income equal to your preferenced income, and then it reverts to 22%.

For example, let's say one has $77,400 of taxable income; $67,400 of ordinary income and $10,000 of preferenced income (qualified dividends and/or LTCG). Add $11,000 of ordinary income... the first $10,000 is taxed at 27%, the next $1,000 is taxed at 22%.

If you are not quite to the top of the 12% tax bracket, then you'll have 3 marginal rates... 12% until your ordinary income reaches the top of the 12% tax bracket, then 27% to the extent of your capital gains and then 22% (this assumes that your ordinary income was in the 12% tax bracket to begin with).
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Old 06-25-2018, 07:11 PM   #18
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Oh, I KNEW what he was talking about, but someone in that position using inaccurate terminology loses credibility in my eyes. I'm all too familiar with this particular calculation so no chance of me screwing it up but without the example a newbie might mess it up. Too sensitive, I suppose. Article does a decent job explaining how to handle state taxes and Treasuries.
Whatever - it was the quickest way for me to get the right formula. So I guess the terminology flew right past me.....
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Old 06-25-2018, 07:14 PM   #19
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Oh, I KNEW what he was talking about, but someone in that position using inaccurate terminology loses credibility in my eyes. I'm all too familiar with this particular calculation so no chance of me screwing it up but without the example a newbie might mess it up. Too sensitive, I suppose. Article does a decent job explaining how to handle state taxes and Treasuries.
Yeah, not to beat a dead horse (OK, we are doing it, but it's par for the course around here), but it's like saying you add two numbers, but what you're really doing is multiplying. The only difference is that most people really aren't as certain, or just don't know, what a reciprocal is, so they see the term, and how it's being (incorrectly) used, and they accept the bad usage. It's just as wrong, and for me too that loses some credibility.
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Old 06-25-2018, 11:51 PM   #20
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Put down the glass of wine. Quite simply, you add $1000 taxable interest, you get taxed an extra $270 of taxes, or 27% for the marginal rate.

It is not a $2000 difference of taxable income. You already had that $1000 of capital gains, and it was taxable, but it happened that the tax rate of 0%. The new bond income changed the tax rate of that bond income to 15%. It didn't create $1000 of new bond income, it just changed the tax rate on that existing bond income.
Nice explanation.

So if I have 50K of income and 50K of dividends, when I think to my self I'd like to convert 50K of IRA to ROTH, I'm really shooting myself in the foot.

I go from 50K taxed money (ignoring the deduction in all cases) to 150K taxed by adding only 50K to the pot.

Because the 50K of dividends will now be taxed at 15%. and the conversion money will be taxed at 12% too.
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