Effective Tax Rate [How to Calculate?]

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Effective Tax Rate [How to Calculate?]

Postby Middle » Wed Mar 13, 2013 7:12 pm

One thing I've never been clear on is the tax rate. For 2012 my AGI was $78,587 and my taxable income came to $53,079 (filed jointly) and according to my turbotax summary sheet my taxes are $5,546 for an effective tax rate of 7.06%. But how do you get $5546 as a tax rate on $53,079? I thought that $53k puts you into the 15% tax rate schedule.....wait a minute....I might be remembering something....it's a graduated tax rate right? So the 15% only applies to the portion above $17,400 and below $70k but that would still make my tax about $7k? Sorry, I'm kind of typing out loud here cuz I just went back to my tax return and it shows that the tax was $6619, which is closer to $7k, and then there was a foreign tax credit (73) along with the child tax credit ($1000)which got it down to $5546.

Mind you I'm not complaining why this works out better for me, but I would like to understand it. [Political comment removed by admin LadyGeek]
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Re: Effective Tax Rate [How to Calculate?]

Postby scubadiver » Wed Mar 13, 2013 9:49 pm

Keeping this discussion apolitical with a thread title that just begs for political discussion could be a challenge but I will do my part to stay on track.

Your observation regarding the effective tax rate, while pleasantly surprising, does not necessarily suggest that you have made an error [political reference removed by admin LadyGeek]. Our 2012 effective tax rate was 6.7% and, truth be known, we had a higher AGI. The child tax credit (we have two) and mortgage interest deduction (we're in year 3 of 30) are substantial and can dramatically reduce your effective tax rate as you have observed. Unfortunately we are probably transients in a tax law sweet spot with a moderate income but not one that is high enough to really feel the bite of multiple phase outs. I got a raise and a bonus this year and will probably begin to feel the effects of child tax credit phase out in 2013. :(

Obviously I can't speak to the accuracy of your own return, but on the surface there does not appear to be anything all that unusual.

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Re: Effective Tax Rate [How to Calculate?]

Postby NYBoglehead » Wed Mar 13, 2013 9:56 pm

I'm going to be apolitical as possible because I have run afoul of forum rules before.

The bottom line is most people (media included) fail to recognize the bracket they are in from their effective tax rate. Just because you are in the 15% bracket does not mean your effective tax rate is 15%.

Of course the important thing to remember is the total tax picture. You had to pay 7.65% of your gross income in FICA taxes, the overwhelming majority of states have income taxes and you pay property taxes if you are a homeowner. So while you might have an effective low federal rate, your overall level of taxation is undoubtedly higher than that.
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Re: Effective Tax Rate [How to Calculate?]

Postby LadyGeek » Wed Mar 13, 2013 10:04 pm

As a reminder:

In order to avoid the inevitable frictions that arise from these topics, political or religious posts and comments are prohibited.

I removed the political content and retitled the thread so the question can be answered.
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Re: Effective Tax Rate [How to Calculate?]

Postby etarini » Wed Mar 13, 2013 10:27 pm

AGI itself is an artificial construct, which can vary by the current state of the tax laws.

Here's what we do to get a sense of our effective federal tax rate:

1. Add up ALLincome, including 401k contributions, tax-exempt municipal bond fund dividends, employee healthcare contributions not taxed, etc. Add it all up, even if it doesn't show up on our W-2's. This number is everything we got that year, no matter where we ended up putting it, no matter whether or not the government considers it taxable.

2. Use TurboTax to file our returns.

3. Divide federal tax owed by the all-income number. THAT'S your effective tax rate. No politics necessary.

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Re: Effective Tax Rate [How to Calculate?]

Postby LadyGeek » Wed Mar 13, 2013 10:39 pm

Let's get the definitions right. Be sure that the concept of marginal tax rate is understood: Marginal Tax Rate (also explained - progressive tax)

Effective and marginal rates are used for different purposes. Read the referenced forum thread: Important to know Marginal Tax Rate? Effective Tax Rate?
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Re: Effective Tax Rate [How to Calculate?]

Postby Middle » Thu Mar 14, 2013 12:33 pm

Thanks LadyGeek and thanks for amending my post title to keep out the politics. I admit I was only trying to think of a clever subject title and did NOT want to get into politics. I will be more careful.

Also thanks for the links to discussions on marginal vs. effective tax rates. That's good clarification for me. I still can't quite get the math to work out.
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Re: Effective Tax Rate [How to Calculate?]

Postby retiredjg » Thu Mar 14, 2013 12:44 pm

There was a thread awhile back (probably tax time last year) that discussed how to calculate the effective tax rate. As I recall, there were at least three interpretations:

    -tax divided by total income

    -tax divided by taxable income

    -tax divided by AGI or some other number which I don't remember
There might have even been some more ideas on what "effective tax rate" is.


I don't know what the "right" answer is. I'm not sure it matters a lot because it is your marginal rate that you need to know to make decisions. Effective tax rate may be an interesting number, but I can't think of any decision that you would make based on it.
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Thu Mar 14, 2013 1:15 pm

LadyGeek wrote:Let's get the definitions right. Be sure that the concept of marginal tax rate is understood: Marginal Tax Rate (also explained - progressive tax)

Effective and marginal rates are used for different purposes. Read the referenced forum thread: Important to know Marginal Tax Rate? Effective Tax Rate?

I read the wiki and notice the following idea is missing. It could be under "using marginal rate for investment decisions"

The marginal tax rate can be different for different types of income. Clearly it is different for capital gains than for ordinary income, but in many case it is different for SS income, earned income (e.g. EITC), municipal bond income etc. When making a decision you need to use the marginal rate for the type of income you are thinking of changing. When making a decision involving many different types of income sometimes "marginal tax rate" is not helpful and it is better to just calculate the taxes for the two situations and pick the lower.

It probably would not be helpful to point out the "marginal tax rate" is really a partial derivative. :D
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Re: Effective Tax Rate [How to Calculate?]

Postby grabiner » Thu Mar 14, 2013 9:18 pm

Epsilon Delta wrote:I read the wiki and notice the following idea is missing. It could be under "using marginal rate for investment decisions"

The marginal tax rate can be different for different types of income. Clearly it is different for capital gains than for ordinary income, but in many case it is different for SS income, earned income (e.g. EITC), municipal bond income etc. When making a decision you need to use the marginal rate for the type of income you are thinking of changing. When making a decision involving many different types of income sometimes "marginal tax rate" is not helpful and it is better to just calculate the taxes for the two situations and pick the lower.


Thanks for this suggestion; I updated it on the wiki.
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Re: Effective Tax Rate [How to Calculate?]

Postby LadyGeek » Thu Mar 14, 2013 9:50 pm

I updated the wiki to show how the percentages were calculated. See: Marginal Tax Rate. For the last example, I got 23% instead of 21%. Can you please double-check?

Epsilon Delta wrote:It probably would not be helpful to point out the "marginal tax rate" is really a partial derivative. :D

I'm also partial to derivatives, care to expand? :D
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Re: Effective Tax Rate [How to Calculate?]

Postby grabiner » Thu Mar 14, 2013 10:57 pm

LadyGeek wrote:I updated the wiki to show how the percentages were calculated. See: Marginal Tax Rate. For the last example, I got 23% instead of 21%. Can you please double-check?


Clarified; 21% is correct because you still get the full federal deduction on your state tax/
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Fri Mar 15, 2013 8:26 am

LadyGeek wrote:
Epsilon Delta wrote:It probably would not be helpful to point out the "marginal tax rate" is really a partial derivative. :D

I'm also partial to derivatives, care to expand? :D

I'll try to explain, but it can be tricky because I'm not sure what you already understand. I'm going to assume you already know some calculus and have read some economics but never put them together.

The first point is that when a economist says "marginal" he means a derivative of some sort. If you know calculus this can give insight into concepts like marginal demand and marginal supply. You can bring what you learned about derivatives to bear and skip over the pages of the economics text that derive differential calculus from first principles.

The equivalence of marginal and derivatives is just a matter of definition. Going from words to symbols to the rigor of calculus.
Code: Select all
Increase your income from say $20,000 to $20,100 you have $100 in extra income and pay $15 in extra tax the marginal rate is $15/$100 or 15%.   So your marginal tax rate at an income of $20,000 is 15%.
 
 
                                         tax(20,000 + 100) - tax(20,000)
marginal tax rate at income of $20,000 = -------------------------------
                                            (20,000 + 100) -    (20,000)



                       tax( I + Δ ) - tax( I )
marginal tax rate(I) = -----------------------
                                 Δ
                                 

df(x)        f(x+δ) - f(x)
----- = lim  -------------
 dx     δ→∞       δ



Now to the partial derivative. This just says that tax is not simply a function of total income, you have to consider the different types of income, lets consider just wages and capital gains. So we have not a function of one variable tax(income) but a function of two variables tax(wage,gain).

A partial derivative of a function of two or more variables is just the derivative if we change one variable and leave the others constant. This is how we usually calculate marginal tax rates. For example at an income of about $50,000 the marginal tax rate on wages is 15% because an extra $100 of wages increase taxes by $15 while the marginal tax rate on gains is 0% because an extra $100 of capital gains results in $0 extra tax.

Now lets consider a hedge fund employee who can choose to convert some of his wages into gains. Both wages and gains are a function of yet another variable, the proportion he chooses to allocate to gains, call it x. So we have tax(wage(x),gain(x)). If we look at how his tax changes as he changes his allocation we have a full derivative in this case of tax with respect to x. (formally d tax(x)/dx)

I will now wish a good day to my one remaining reader.
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Fri Mar 15, 2013 8:40 am

grabiner wrote:
Thanks for this suggestion; I updated it on the wiki.


A nice write up, much clearer than I could have managed. :beer
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Re: Effective Tax Rate [How to Calculate?]

Postby porcupine » Fri Mar 15, 2013 9:21 am

Epsilon Delta wrote:[...]I will now wish a good day to my one remaining reader.

It appears that I am the chosen one ;-)

Let me see if I understand it right. The basic interpretation is that the effective tax rate is the extra tax that one would pay if one made a buck more (in the income bucket).

What you are adding to that interpretation is that that extra tax rate would vary depending on what it is that resulted in the extra buck being added to income, right? In other words, from a basic rise (in taxes, on the y-axis) over run (in income, on the x-axis) in a two-dimensional plot, you are wanting to introduce, x1 .. xn where all these different "x"s impact y, thereby converting our nice 2D figure into a multidimensional jigsaw.

- Porcupine
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Fri Mar 15, 2013 11:03 am

porcupine wrote:Let me see if I understand it right. The basic interpretation is that the effective tax rate is the extra tax that one would pay if one made a buck more (in the income bucket).

What you are adding to that interpretation is that that extra tax rate would vary depending on what it is that resulted in the extra buck being added to income, right? In other words, from a basic rise (in taxes, on the y-axis) over run (in income, on the x-axis) in a two-dimensional plot, you are wanting to introduce, x1 .. xn where all these different "x"s impact y, thereby converting our nice 2D figure into a multidimensional jigsaw.

- Porcupine


That's all true and was the point grabiner made in his recent addition to the wiki.

The point I was trying to make in that post is that economists are doing math but pretending otherwise. :twisted: So I guess I wasn't clear. :oops:
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Re: Effective Tax Rate [How to Calculate?]

Postby retiredjg » Sat Mar 16, 2013 10:20 am

Epsilon Delta wrote:
porcupine wrote:Let me see if I understand it right. The basic interpretation is that the effective tax rate is the extra tax that one would pay if one made a buck more (in the income bucket).

That's all true....

Well, then maybe I'm very confused. I believe that would be the marginal rate, not the effective rate.
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Re: Effective Tax Rate [How to Calculate?]

Postby LadyGeek » Sat Mar 16, 2013 4:12 pm

^^^ I agree that it's the marginal rate. See the updated wiki article (below). If the math is too hard, just read the example.

Epsilon Delta wrote:
LadyGeek wrote:
Epsilon Delta wrote:It probably would not be helpful to point out the "marginal tax rate" is really a partial derivative. :D

I'm also partial to derivatives, care to expand? :D

I'll try to explain, but it can be tricky because I'm not sure what you already understand. I'm going to assume you already know some calculus and have read some economics but never put them together.
...
I will now wish a good day to my one remaining reader.

Exactly. I have seen the equations before, but the point was never brought home. Your post was clear and insightful. To help others, I took it a step further. Take a look in the wiki: Marginal Tax Rate, your post is under Marginal rates explained (with a few modifications). :)

Comments / questions / concerns are welcome.
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Sun Mar 17, 2013 1:18 am

retiredjg wrote:
Epsilon Delta wrote:
porcupine wrote:Let me see if I understand it right. The basic interpretation is that the effective tax rate is the extra tax that one would pay if one made a buck more (in the income bucket).

That's all true....

Well, then maybe I'm very confused. I believe that would be the marginal rate, not the effective rate.

:oops: Your right it should be the marginal rate.
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Re: Effective Tax Rate [How to Calculate?]

Postby Epsilon Delta » Sun Mar 17, 2013 1:48 am

LadyGeek wrote:Exactly. I have seen the equations before, but the point was never brought home. Your post was clear and insightful.

Comments / questions / concerns are welcome.


Thank you for your kind words.

I have read the wiki and have no objection to you using my text. To me it does not seem as coherent as the rest of the article, I'm not sure if could be tweaked or if it belongs elsewhere. If anything else comes to me I'll post again.

I do have two specific suggestions.
1) An introductory sentence might add context. Something similar to "Marginal tax rates are examples of partial derivative." The next two sections then explain why it's a derivative and why it's partial.

2) The last paragraph ("Putting these concepts together ..." ) is the most jarring. But if you leave it in please change the
two script '∂'s in the last line to roman 'd's. The script ∂ is used for partial derivatives and the point is that this is a full derivative so it should be "d(tax(x))/dx".
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Re: Effective Tax Rate [How to Calculate?]

Postby assumer » Sun Mar 17, 2013 5:55 am

Should we distinguish on the wiki about marginal effective rate? Because the marginal rate is based on your tax bracket, but what is described is,

consider how much additional tax you would owe if you added $1 to your income.


However, to me, using that definition verbatim would really be a "marginal effective rate" because it considers deductions, and everything else taken into account when thinking about the "tax you would owe"?
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Re: Effective Tax Rate [How to Calculate?]

Postby JW Nearly Retired » Sun Mar 17, 2013 9:03 am

This is interesting but, IMO, a more personally useful marginal rate is the EMTP. That's the amount that the taxing authorities are sent for each additional dollar you make and then spend at Home Depot. For a single person making $100k wages in a high tax state like mine, that comes around $0.63 ..... (2x7.65% +28% +10% +10% = 63.3%).
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Re: Effective Tax Rate [How to Calculate?]

Postby LadyGeek » Sun Mar 17, 2013 10:30 am

Epsilon Delta wrote:...I have read the wiki and have no objection to you using my text. To me it does not seem as coherent as the rest of the article, I'm not sure if could be tweaked or if it belongs elsewhere. If anything else comes to me I'll post again.

I do have two specific suggestions....

Based on your introduction, I realized that I made a mistake on the meaning of the full derivative (not just due to the symbol "∂"). I revised the introductory wording and put each paragraph into a separate sub-section.

Here's the next version: Marginal Tax Rate
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