If you haven't heard, the U.S. Congress is likely to pass a new income tax bill this week. CNN.com has a graphic with the existing and new income brackets and associated tax rates. This seems like a good time to talk a little about the difference between the marginal tax rates, total tax bills, and the average tax rate paid, as I have found that principles students (and other adults) often find this confusing.

First a few definitions:

The marginal tax rate is the tax rate that you pay on the last dollar you earn. For example, if your taxable income is such that you fall into the 33% tax bracket, that means you will pay 33% of the last dollar you earn to the federal government. An important note is that this does NOT mean that you pay 33% of all of your income to the federal government. Just 33% of the last dollar you earn.

Your total tax bill is calculated by adding up the marginal tax you pay on each dollar of taxable income you earn, up to the last dollar you earn.

Your average tax rate is found by dividing your total tax bill by your taxable income.

I know I just made things more confusing. So let's look at a simple example, and then we will look at the actual tax rates that exist currently and the proposed new tax rates to illustrate the concepts.

A simple example: Let's suppose there are only two defined income brackets. The lowest income bracket goes from $0 to $50,000 of taxable income. This income bracket is taxed at a marginal rate of 10%. The second income bracket is anything greater than $50,001 of taxable income. This income bracket is taxed at marginal rate of 25%.

The correct way to to interpret these brackets is as follows: No matter how much taxable income you earn, each dollar of taxable income you make, up to $50,000, is taxed at a rate of 10%. So if you make $25,000 a year in taxable income, each of your dollars is taxed at a marginal tax rate of 10%, meaning your total tax bill will be $25,000 * 0.10 = $2,500.

If you earn $35,000 of taxable income, then you still fall in the 10% marginal tax bracket, and your total tax bill will $35,000 * 0.10 = $3,500.

If you earn $50,000 of taxable income, then you still fall in the 10% marginal tax bracket, and your total tax bill will $50,000 * 0.10 = $5,000.

But hear's where things get interesting (and probably more confusing). Suppose you earn $50,001 of taxable income. You now fall in the 25% marginal tax bracket. Many people interpret this to mean that your tax bill will now be $50,001 * 0.25 = $12,500.25. But this would be WRONG.

The correct way to calculate your new tax bill is to recognize that you pay a rate of 10% for each dollar you earn up to $50,000 of taxable income, and then you pay 25% for each dollar you earn above $50,000 of taxable income. So if your income is $50,001 of taxable income, then you will pay 10% in taxes for each dollar up to $50,000 ($50,000 * 0.10 = $5,000) plus 25% for the $1 you earned over $50,000 ($1 * 0.25 = $0.25). So your total tax bill is now $5,000 + $0.25 = $5,000.25.

To calculate your average tax rate, you now divide your total tax bill ($5,000.25) by your taxable income ($50,001) and convert to a percentage (100 * $5,000.25/$50,001) to get an average tax rate of 10.0003%. Notice that the average tax rate is below the marginal tax rate (25%). This will always be the case.

Let's extend the example. Suppose your salary is $125,000 of taxable income per year. Everyone pays 10% on the first $50,000 of taxable income earned, so you pay $5,000 on the first 50,000 of taxable income. On the remaining $75,000 of taxable income (the $75,000 above $50,000), you will pay a marginal tax rate of 25% ($75,000 * 0.25 = $18,750), so your total tax bill is $5,000 + $18,750 = $23,750, and your average tax rate is 100 * $23,750/$125,000 = 19% (notice it is still below the marginal rate of 25%.

So that's the end of the simple example (SIMPLE?!, IKR). So what does the new tax bill do to income brackets and marginal tax rates?

Here are the current and new income bracket and marginal tax rates under the proposed bill for unmarried individual filers (that's right, to make things even more complicated, tax rates change depending on your filing status--individual, married, or married filing individually, but that's for a later post):

Let's take a look at someone making $50,000 of taxable income per year. Under the current tax plan, this person will pay:

- 10% of the first $9,525 of taxable income earned: $952.50
- 15% of each $1 earned between $9,525 and $38,700 of taxable income (($38,700-$9,525)*0.15) = $4,376.25
- 25% of each $1 earned between $38,700 and $50,000 of taxable income (($50,000-$38,700)*0.25) = $2,825

Adding these together, the current total tax bill for someone making $50,000 of taxable income per year is $8,153.75, and the average tax rate is (100 * $8,153.75/$50,000) = 16.31%

The new tax bill drops the marginal tax rates in the second and third income brackets to 12% and 22% respectively, so the total tax bill for someone making $50,000 of taxable income per year falls to $6,939.50 and the average tax rate falls to 13.88%.

It looks like the new tax plan offers a tax cut to someone making $50,000 of taxable income per year.

And that's true...IF WE ONLY BASED TAXES ON INCOME AND DIDN'T FILL THE REST OF THE TAX BILL WITH DEDUCTIONS, LOOPHOLES, GIFTS, POLITICAL PAYOFFS AND RIDICULOUS CRAP THAT KEEPS ACCOUNTANTS EMPLOYED* AND POLITICIANS HAPPY.

I'VE BEEN CAREFUL THROUGHOUT THIS POST TO MAKE SURE I QUALIFY INCOME AS TAXABLE INCOME. WHAT THIS POST FAILS TO EXPLAIN, BECAUSE NO ONE CAN REALLY EXPLAIN IT BECAUSE NO ONE HAS ACTUALLY READ THE TAX BILL, IS THAT TAXABLE INCOME WILL CHANGE DUE TO CHANGES IN DEDUCTIONS, LOOPHOLES, GIFTS, POLITICAL PAYOFFS AND RIDICULOUS CRAP THAT KEEPS ACCOUNTANTS EMPLOYED* AND POLITICIANS HAPPY.

OK, that's out of my system. As you can see from the tax table above, comparisons between current and new tax bills get more complicated as incomes increase, because not only do marginal tax rates change, but the income brackets change too. For example, someone who makes $175,000 per year currently falls in the fourth income bracket, but under the new bill falls in the fifth bracket. I won't bore you with all of the calculations, but,

- Under the current system, someone making $175,000 in taxable income pays a marginal tax rate of 28%, has a tax bill of $41,842.75 and an average tax rate of $23.91%
- Under the new system, someone making $175,000 in taxable income pays a marginal tax rate of 32%, has a tax bill of $37,689.50 and an average tax rate of $21.54%

*In full disclosure, my spouse is gainfully employed by a tax accountant and makes her living by helping people take advantage of DEDUCTIONS, LOOPHOLES, GIFTS, POLITICAL PAYOFFS AND RIDICULOUS CRAP THAT KEEPS ACCOUNTANTS EMPLOYED AND POLITICIANS HAPPY.

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