# 2013 Income Tax Calculation Details

When I presented The Simple Income Tax, I made the claim that currently the working classes pay a marginal tax rate close to 30%, and that we could simplify things enormously by combining the two payroll taxes (FICA and Medicare) with The Income Tax Proper and just give every adult citizen a prebate/dividend. In this article, I’ll detail how I came up with the first charts modeling the current tax system.

For my original presentation of The Simple Income Tax I compared it to the 2013 tax year. I did this because I had the 2013 tax guides available, the 2013 tax year had a system familiar to everyone, and figuring out the ObamaCare subsidies was a painful challenge best deferred.

## Total vs. Nominal Income

The first two columns in the first table might seem a bit strange. I have Nominal Income and Total Income. What gives?

Suppose you are an employee earning $10/hour. You get a paycheck
for this amount times the number of hours worked less an assortment
of deductions that your employer takes out on your behalf –
estimated Income Tax, FICA, Medicare, etc. However, this is
*not* what your employer is actually paying for your services.
Social Security and Medicare tax both employees *and*
employers. This was apparently more politically palatable back in
the day, and there is a certain economic logic to the arrangement:
income and payroll taxes are a tax on the labor *transaction*.
Both employee and employer share in the tax hit. Exactly who is
paying the most depends on the elasticity of the job market. By
dividing payroll taxes as we do, we limit the error in showing who
is taking the hit.

However, this division has zero impact on who actually takes the tax hit save for the small impact on the minimum wage. And while it provides a bit of transparency in who pays the taxes, it also makes computing payroll significantly more complicated. So for the Simple Income Tax, I opt for a one-sided calculation and leave it for the economically sophisticated to understand that the tax burden is in fact shared.

So, to compare The Simple Income Tax with the current arrangement, I convert from Nominal Income to Total Income – the total amount that comes out of the employer’s bank account. A quick check with Wikipedia shows that the FICA tax (Federal Insurance Contributions Act) is 6.2% each for employers and employees. Medicare taxes are 1.45% each. So we have:

Total Income = (1.0 + .062 + .0145) * Nominal Income

For high income employees, the FICA portion stops above $113,700. This gives for higher income earners:

Total Income = (1.0 + .0145) * Nominal Income + $113,700 * .062

For my married couple tables, I assume that both spouses earn the same amount. For them, FICA caps out at twice $113,700. If their earnings are not symmetric, the total payroll taxes could be lower. (Maybe in the future I will update the charts to show a range for payroll taxes and Total Income, but this might confuse more than it enlightens.)

## Payroll Tax

Payroll tax is just FICA and Medicare combined – employee and employer portions. That is:

Payroll Tax = 2 * (.062 + .0145) * Nominal Income

At least, that’s the case for moderate income workers. For a single wage earner making above the FICA maximum, we have:

Payroll Tax = 2 * .0145 * Nominal Income + 2 * .062 * $113,700

And for a high income couple where both spouses make above the FICA max:

Payroll Tax = 2 * .0145 * Nominal Income + 2 * .062 * 2 * $113,700

## Income Tax

To model the Income Tax proper, I start with the 2013 marginal income tax rates:

Based on this table it appears that Congress wants professional couples making around $200K each to get a divorce. Admittedly, the marriage penalty isn’t that high, however.

The tricky part is getting from Nominal Income to Taxable Income. This depends not only on income levels but also on financial arrangements. This is why I have a range for Income Tax. Let’s go into the details of how I get this range.

### Health Insurance

If you buy your health insurance through your employer, you get to deduct health insurance costs from Nominal Income. This is a “top line” deduction affecting Adjusted Gross Income. For my model, I assume a cost of $300/month per adult family member and $150/month/child for low taxpayers and no health coverage for high taxpayers. Obviously, this is a bit crude, but given the variance of insurance costs by age, location and type of plan, there is no perfect solution here. Anyway, my formula is:

Adjusted Gross Income = Nominal Income – 12 * $250 * (nAdults + nChildren)

For 2014 and beyond this formula is way too simplistic. ObamaCare creates a new negative income tax in the form of the new health insurance subsidy. While I find the principle laudable, the implementation is ridiculously complicated and reportedly results in very high effective marginal tax rates at certain income levels.

I’ll cover my model for ObamaCare subsidies in a future article.

### Retirement Plan Deductions

IRAs, 401(k)s, and other retirement plans also go
off the top line. However, I did *not* include them in my
model because I do think The Simple Income Tax should allow for a
savings deduction as well. It will be simpler than the current
nightmarish web of possibilities, of course. But it will be
generous. The middle class needs to save more – a lot more if
we want to narrow the wealth gap, reduce dependence on big
government and/or reduce moral hazards.

### Charitable Deductions

If you are giving it away, it isn’t really your income. So I don’t include it in my model. The Simple Income Tax continues charitable deductions; however, I would get rid of some of the tricks that the wealthy use to abuse this deduction. Stay tuned.

### State Income Tax Deduction

For both passive and aggressive filers, I assume a state income tax deduction with a flat tax rate of 5%. Obviously, this is not universally true. Most state income taxes are progressive. And some states have no income tax at all. Consider this a rough approximation.

Do note that this deduction is moot for passive filers in the lower income brackets since they take the Standard Deduction instead.

### Home Ownership Deductions

For the home mortgage and property tax deductions, I assume that aggressive filers have mortgage payments equal to 30% of Nominal Income. I use a fairly crude model to figure out how much of this is tax deductible.

For the mortgage, I assume that the aggressive filer did put 20% down (which isn’t super aggressive!), and that mortgage payments are 1.2 times the interest. I use an interest rate of 4%. That is:

Bank Payment = 1.2 * .04 * Debt

For property tax, I use a rate of 1.5%. If debt is 80% of home value we have:

Property Tax = .015 * (Debt / 0.8)

Put the two together we have:

Mortgage Payment = (1.2 * .04 + .015/0.8) * Debt = .3 * Nominal Income

From there you can solve for Debt in terms of Nominal Income and then get:

Deduction = (.04 + .015/.08) * Debt

The IRS caps the amount of deductible debt at $500,000 per
adult, save for old mortgages grandfathered in. (See page A-7 of
the *2013 1040 Instructions*.) I ignored the grandfathering
and capped the deductible interest for all high income filers. For
a high income single taxpayer, we have:

Deduction = .04 * $500,000 + (.015/.08) * Debt

For a married couple at the high end:

Deduction = .04 * $1,000,000 + (.015/.08) * Debt

For passive filers (the high end of Income Tax) I assume that the taxpayer rents, thus getting no interest or property tax deductions.

### Standard Deduction

For either high or low taxpayers, if deductions end up less than the Standard Deduction, the Standard Deduction is used. The high end is for taxpayers who don’t live their lives according to the tax code; it is not meant to indicate inability to properly file.

### Alternative Minimum Tax

I did not take into account the Alternative Minimum Tax for any income level.

### Personal Exemption

Not only does the federal government want high income couples to divorce, the government also wants to keep them from breeding. The personal exemption phases out for single taxpayers making over $250,000 and couples making over $300,000. This petty tax provision proves that Congress isn’t merely dishonest; it is outright malevolent. We have higher tax brackets for the well to do. The personal exemption is less significant at higher income levels anyway. Adding this phase-out simply pollutes the tax code and adds yet more pages to the tax manual.

Anyway, with a great deal of brain sweat, I was able to reverse engineer the worksheet on page 40 of the 1040 and convert the algorithm from IRS formeze into math and computer code.

For families under the phase-out gross income, the personal exemption is $3,900 times the number of family members. For those above, you lose 2% for every $2500 over the phase-out income. That is we apply a factor of:

1 – ((Adjusted Gross Income – Phaseout Income)/$2500) * .02

If this factor goes negative, then there is no personal exemption.

### Child Tax Credit

The deductions above determine taxable income. Then I apply the tax brackets. Finally, I subtract out a couple of tax credits, starting with the Child Tax Credit.

Once again, the federal government does not want high income
taxpayers to breed. It seems our leaders saw the movie *Idiocracy*
and thought it portrayed a utopia.

Anyway, for single parents making less than $75,000 or couples making less than $110,000, the tax credit is $1000 per child. However, this particular credit cannot produce a negative tax – unlike the Earned Income Credit, which we will get to next. If the credit exceeds Income Tax owed, then Income Tax owed is set to zero at this stage.

For those above the phase-out income values, reduce the credit by 5% of the amount over the phase-out value – yet another petty way to hide a higher marginal tax rate for the professional class. (In all fairness Congress was also sadistically petty towards the unemployed poor as we’ll cover in a bit.) So, for a professional class couple the Child Tax Credit is:

Child Credit = nChildren * $1000 - .05 * (Adjusted Gross Income - $110,000)

If this value is negative, then set it to zero. Replace $110,000 with $75,000 for single parents.

### Earned Income Credit

The Earned Income Credit could not have been devised by a human Congress. Either sadistic space aliens hacked the government printing office as the code was drafted, or Skynet is already self aware, but decided to toy with us via the tax code before launching the nukes.

The 2013 1040 Instructions have *eight* pages of flowcharts
and worksheets for determining eligibility for and amount of the
Earned Income Credit. That’s not counting the tables.

Since I didn’t want to type the tables into my C# program, I had to search around the Internet to find how they are generated. The Tax Policy Center provides a handy chart of credit rates, phase-out incomes and phase-out rates. I just applied these to the Adjusted Gross Income, both for aggressive and passive tax filers. Unlike the Child Credit, the EIC can result in negative Income Tax values. Here is the relevant part of the chart (I used 2013 values):

For families of more than three children, my program just uses the three-child parameters. I do not compute the Additional Child Tax Credit.

Anyway, to use this chart, I multiply the Nominal Income (not Adjusted Gross Income) by the Credit Rate Percent converted to a decimal. For example, for one child, multiply by 0.34. If this value is more than the Maximum Credit, I set to the Maximum Credit. If Nominal Income is greater than the beginning income for the phase-out, then:

EIC = Maximum EIC – (Nominal Income – Beginning Income) * Phaseout Rate

If negative, I set to zero.

This is subtracted from the Income Tax already compute by this point. If the result is negative, then the Income Tax is negative.

### Additional Child Tax Credit

Earlier, I said that the Child Tax Credit cannot make your income tax go negative. This is not strictly true. You might get to use that leftover credit as a negative income tax if you qualify for the Additional Child Tax Credit. This is another ridiculous petty tax provision aimed at the unemployed poor.

It appears that the intent of the sadistic mutant space aliens that occupy the Capital was to allow the rest of the Child Tax Credit to be used against payroll taxes vs. The Income Tax Proper. How it works (I think!) is that you can compare the unused Child Tax Credit ($1000 *nChildren – income tax), and compare it with this value:

Line6= (nominalIncome - $3000) * 0.15

If this value is greater than the leftover tax credit, you can take is as the Additional Child Tax Credit. If this value is less but still greater than 0, you can take the Line6 value as the Additional Child Tax Credit.

However, if Line6 is less than the leftover credit, and you have more than three children, you can try for Line11:

Line11 = Employee FICA + Employee Medicare – Earned Income Credit

If Line11 is greater than Line6, you can use it instead – up to the value of the leftover child tax credit.

Why deprive the nonworking poor of this fairly small tax credit? If they cannot qualify for the credit, then they can qualify for either unemployment insurance, or several welfare programs, so what’s the point? Why? Why? WHY???

## Total Tax and Tax Rates

The Total Tax column is simply the Payroll Tax plus the Income Tax. This is a range since we have a range of possible Income Tax owed.

The Average Rate column is the Total Tax divided by the
*Total* Income expressed as a percentage.

To get the Marginal Tax column, I did a simple numerical differentiation. I added $500 to the Nominal Income to compute Total Income(2) and Total Tax(2). The Marginal Rate is then:

Marginal Rate = ((Total Tax(2) – Total Tax)/(Total Income(2) – Total Income)) * 100%

## Simple Income Tax Calculations

The Simple Income Tax tables were rather easier to compute. I started with the Total Income already computed for today’s tax rate tables. These are not very round numbers, but I didn’t feel like figuring out how to get from Total Income back to today’s Nominal Income.

For the single-tier Simple Income Tax we have:

Simple Income Tax = Total Income * rate – AdultPrebate * nAdults – ChildPrebate * nChildren

For my first table, the rate is 30% and the Adult Prebate is $3000. The average percent is simply Simple Income Tax divided by Total Income expressed as a percentage. For the last column I have:

Simple Income Tax – Total Tax High
*to* Simple Income Tax – Total Tax Low

where Total Tax High and Total Tax Low are the high and low tax values under the current system.

For the Two Tier charts, the Simple Income Tax is slightly more complicated. For low to mid income taxpayers it is the same as before. For high income taxpayers it is:

Simple Income Tax = Threshold * nAdults * rate1 + (Total Income – Threshold*nAdults) * rate2 – AdultPrebate * nAdults – ChildPrebate * nChildren

This second equation only applies when Total Income is greater than Threshold * nAdults.

That’s it! Two equations. No additional worksheets to handle petty takeaways from the well off. No sadistically complex worksheets to handle takeways from the unemployed poor.

You can comment on this article here.