User:Fyre4ce/Marginal tax rate

 is a tax rate applicable to a "small" amount of additional income. It is calculated by dividing the change in tax by the applicable change in income.

The marginal tax rate is often the same as the individual's tax bracket, but not always.

In particular, a marginal tax rate is not the average (a.k.a. "effective") tax rate paid on one's entire income.

Calculation
The marginal tax rate defined as the ratio of the additional tax owed to the additional income, for a "small" amount of additional income. To calculate a marginal income tax rate, calculate how much tax you would owe if you made a "small" amount of additional income, subtract from the current tax, and divide by the additional income. In theory, the smaller the amount the more precise the result, but in practice some factors can complicate this. Most tax software rounds numbers to the nearest dollar, so using $1 of additional income probably won't be accurate. Additionally, if your tax is computed using the IRS tax tables then taxable income is rounded to the nearest $50, so an amount of at least a few $100 would be required. Additionally, if your tax is computed using the IRS tax tables then taxable income is rounded to the nearest $50, so an amount of at least a few $100 would be required. If the amount is not arbitrary, but instead is a specific amount for which you are making some choice, use that amount.

Often your marginal tax rate will be equal to your tax bracket, calculated using your taxable income (Adjusted Gross Income minus deductions). However, the actual marginal rate can be complicated if your taxes include credits, deductions, and exemptions which are phased out with income; if you are nominally in the 25% bracket but you lose $5 in tax credits for every additional $100 you earn, your marginal rate is actually 30%. For example, the phase-out of the child tax credit causes the following behavior for an MFJ (Married Filing Jointly) return with one eligible child:

Note: This example uses tax law prior to the 2018 Tax Cuts and Jobs Act.

State Taxes
Your state income tax rate adds to your federal income tax rate. For example, if your federal tax bracket is 24%, your state tax bracket is 8%, you aren't affected by credits, phase-outs, etc., and can't deduct the additional state tax, an extra $1 of income would cause you to pay 8 cents in state tax and 24 cents in federal tax, so your marginal rate is 32%. If you can deduct the additional state tax, the 8 cents in state taxes mean that you pay federal tax on only 92 additional cents, which is 22.08 cents of federal tax (22.08% = 92 cents * 24%) and a marginal rate of 30.08% = (22.08% + 8%).

Social Security Benefits
Taxation of Social Security benefits causes many moderate-income retirees to be subject to a much higher marginal tax rate than their tax bracket. If you are in the range in which Social Security becomes taxable, each additional $1 of income causes an extra 50 or 85 cents of Social Security to be taxable at the same tax rate, until 85% of the whole benefit is taxable. If you are in the 12% bracket and each $1 causes an extra 85 cents to be taxable, that extra $1 of income increases your taxable income by $1.85, with 22.2 cents due in tax giving you a marginal tax rate of 22.2%. If you are in the 22% bracket and each $1 causes 85 cents to be taxable, your marginal tax rate is 40.7%. This phase-in of taxation can cause a "bump" in marginal rate over a narrow income range, above which the marginal rate drops back down once the maximum 85% of Social Security benefits are taxable. Retirees near this spike may choose to alter their tax strategy, to try to either fall just before the spike, or far above it.

Section 199A Deductions
The 2018 Tax Cuts and Jobs Act allows certain types of businesses to deduct 20% of certain types of income, called Qualified Business Income (QBI). Every $1 of QBI causes only 80 cents of additional taxable income. So, if you are in the 24% tax bracket, it results in 19.2 cents of additional tax, and your marginal federal tax rate is 19.2%. For Specified Service Professions subject to the phase-outs of the Section 199A deduction ($157,500-$207,500 single and $315,000-$415,000 married filing jointly), the marginal tax rate gets more complicated and varies over the phase-out range.

Child Tax Credit Phase-Out
The 2018 Tax Cuts and Jobs Act offers a tax credit of $2,000 per qualifying child, with phase-out of $50 credit reduction for every $1,000 above the limits of $200,000 Modified Adjusted Gross Income for single filers and $400,000 MAGI for married filers. Each additional dollar of income over these limits reduces the credit by 5 cents ($50/$1,000), raising the marginal tax rate by 5% until the credit is phased out completely, over a range of $20,000 per child.

Student Loan Interest Deduction Phase-Out
Qualifying student loan interest is capped at $2,500 per return for either single or married joint filers (married separate filers can't deduct student loan interest). The phase-out for this deduction is between $65,000-$80,000 Adjusted Gross Income for single filers and $135,000-$165,000 for married joint filers. Both of these phase-outs are in the 22% bracket. For single filers, each additional dollar of income causes ~16.67 cents ($2,500/$15,000) of interest to become non-deductible, generating ~3.67 cents (~16.67 * 22%) of addition tax, so the marginal tax rate is increased by ~3.67%. For married joint filers, each additional dollar of income causes ~8.33 cents ($2,500/$30,000) of interest to become non-deductible, generating ~1.83 cents (~8.33 * 22%) of addition tax, so the marginal rate is increased by ~1.83%. If the taxpayer paid less than $2,500 in qualifying student loan interest, the marginal rate increase would be proportionally less.

Long-Term Capital Gains and Qualified Dividends
Long-term capital gains and qualified dividends are taxed at a reduced rate by the IRS:

Additionally, the IRS assesses the Net Investment Income Tax (NIIT) on the lesser of investment income and MAGI over $200,000 for single filers or $250,000 for married joint filers. For high earners this can result in a federal marginal rate on long-term capital gains and qualified dividends of up to 23.8%.

Payroll Taxes
The IRS assesses Payroll Taxes (also called FICA Taxes) on earned income. For employees, their employers generally pay half of the payroll tax directly to the IRS, and the employee sees the employee half deducted from their paychecks. The tax rates are as follows:

Self-employed individuals (either Sole Proprietors or incorporated) are required to pay both halves of payroll taxes, so payroll taxes could increase ones marginal tax rate by up to 16.2% on top of income taxes.

Most sources do not include payroll taxes when discussing marginal tax rates. The reason is that the most common use of marginal tax rates is making investment decisions, either calculating after-tax rates of return or deciding between Traditional and Roth contributions. For both of these purposes, payroll taxes do not come into play. However, for other purposes (see below, Marginal Utility of Additional Income), payroll taxes would need to be included.

Marginal rate of zero
A tax with a marginal rate of zero is a fixed-amount tax, such as a tax of $100 on every house rather than a percentage of the value of the house.

Flat rate tax
A flat rate tax has a constant marginal tax rate. Sales taxes and property taxes are normally flat, a fixed percentage of the value. Income taxes in some states are almost flat; typically, there is a fixed amount (such as a standard deduction) which is exempt from tax, and everyone making more than that fixed amount pays the same marginal tax rate, so the average tax rate varies.

Multiple Rates and Combined Rates
Note that you may have a different marginal tax rate on different types of income and savings. Consider the State Tax example above, with a marginal rate on ordinary income of 32%. The marginal tax rate on Treasury bonds (which are fully taxed by federal, not taxed by the state) is only 24%. The marginal tax rate on capital gains is 15% federal but probably fully taxed by the state at 8%. If additional state tax is deductible, then the marginal rate on capital gains will be 21.08% (15% + 8% - (24% x 8%) for deduction of the state tax), otherwise 23%. For either single or married joint filers, Section 199A Qualified Business Income (QBI) will have a different marginal rate than non-QBI, and if the Section 199A deduction is being phased out, the rates will be variable. An investor with a small business and a reasonably simple portfolio could have at least eight separate marginal rates for different types of income and savings:


 * Earned income, subject to income tax, phase-outs, and payroll tax (including the Additional Medicare Tax)
 * Investment income, subject to income tax, phase-outs, and Net Investment Income Tax
 * Long-term capital gains and qualified dividends, subject to reduced income tax rates, phase-outs, and Net Investment Income Tax
 * Section 199A Qualified Business Income (QBI), subject to income tax and phase-outs but offering the QBI deduction
 * Social Security income, taxed as income at a rate determined by the Social Security Benefits Worksheet in IRS Form 1040 Instructions
 * Treasury bond income, subject to federal income tax and phase-outs, but exempt from state income tax
 * Municipal bond income, tax-free, except for the phase-in of Social Security benefits
 * Marginal savings rate for tax-deferred contributions may be different from the marginal tax rate on income due to the Saver's Credit

Unusually high marginal rates can result from the 0% tax rate on qualified dividends and capital gains at low incomes. There is a taxable-income level X which is the top of the 12% bracket. Ordinary taxable income up to X is taxed at a marginal rate of 12%, and ordinary income above X is taxed at a marginal rate of 22%. Qualified dividends and capital gains are then added to your ordinary taxable income; the amount which is still below X is taxed at 0%, and the amount above X is taxed at 15%. Thus, if your ordinary-taxable income is less than X but your total taxable income is more than X, your marginal tax rate is 27%. Every additional $1 of ordinary income is below X and thus taxed at 12%, but it also moves $1 of qualified dividends from below X to above X, and that $1 is now taxed at 15% rather than 0%.

Combining this effect with Social Security benefits can produce even higher rates. For a single person age 65, with $12,000 in qualified dividends, $27,000 from social security, and $24,000 in traditional IRA distributions, the marginal rate for more Not all high marginal rates are unfavorable. E.g., due to the saver's and earned income credits, marginal savings rates can be much higher than the tax bracket would suggest.
 * traditional IRA distributions is 49.95%
 * qualified dividends is 37.95%
 * social security income is 11.475%

Using the Marginal Rate
Understanding how marginal rates affect the consequences of your financial choices can help you make better choices. Some examples are given below.

Marginal Return of Additional Income
The marginal tax rate tells the taxpayer how much of each additional dollar they earn they get to keep. For this reason, those who can control how much income they earn might choose to work just up to the point that their marginal tax rate jumps up.

After-Tax Value of Investments
The marginal tax rate determines the relative after-tax value of different investments. The after-tax rates of return using the formula:


 * [After-tax return] = [Pre-tax return] * (1 - [marginal tax rate])

Consider the individual from the State Taxes section above, considering three bond investments: a corporate bond, a Treasury bond, and a municipal bond from the individual's state. The corporate bond is fully taxable at both federal and state levels, and state income tax is federally deductible. The Treasury bond is deductible at the federal level, but not state. The municipal bond is tax-free at both federal and state levels. Assume each bond is purchased at par value. The after-tax returns of each investment are as follows:

Assuming no other factors (eg. risk) are being considered, the municipal bond has the highest after-tax return and would therefore be the best investment.

Traditional vs. Roth
Deciding between Traditional and Roth contributions is another use for marginal rates. In general, Traditional contributions are better as long as your predicted marginal tax rate in the future is lower than your marginal tax rate now. Roth contributions are better when your predicted marginal tax rate in the future is higher than your marginal tax rate now. See that article for more details.

One should also recognize that, over the range of allowable retirement contributions, the marginal tax rate may vary considerably, at breakpoints in the tax bracket structure and when phase-outs come into play. In those cases, splitting contributions between Traditional and Roth may be the best strategy.

E.g., take a couple making $54K/yr with two young children. In 2016, that puts them in the "15% bracket." Yet, due to various combinations of the saver's and earned income credits, as they increase 401k contributions from $0 to $18,000 their marginal savings rates (calculated a dollar at a time) go through regions of 25%, 46%, 36%, 31%, and 21% - plus some spikes due to tiers in the saver's credit. Their maximum marginal savings rate of 33.4% comes when "some amount" of 401k contribution is $14,000. In graphical form:

Compare the above couple's situation to a single person making $54K/yr. That person is in the "25% bracket" with a marginal savings that is also 25% - until $6,000 has been contributed to a 401k, at which point both the tax bracket and marginal savings rate drop to 15%.

Note: These examples use tax law prior to the 2018 Tax Cuts and Jobs Act.

Tax Bracket
Q. Last year I paid 7% of my income in income taxes. Is this my marginal tax rate? Does this mean I'm in the 10% tax bracket? Or am I in the 28% tax bracket because I made $100,000 and my filing status is single and the 28% tax bracket is between $87,850 to $183,250 in the year 2013?

A. If your gross income was $100,000 and you paid $7,000 in taxes, then you did pay 7% of your income in taxes. While that figure might be interesting to know, it doesn't necessarily help you make borderline decisions in the way that knowing your marginal tax rate can.

A tax bracket is the range of taxable income to which a tax rate applies. To know which tax bracket you're in, look at your taxable income (not your salary) on line 43 of your 1040 tax return, and then cross reference that against IRS tax tables and your filing status.

Appendix: Marginal rates explained
The tax code, particularly when taxable income is under $100,000 and Tax Tables are used, produces a very non-smooth function of tax vs. income. With the Tax Tables, for most changes in income the tax does not change at all, but every $50 there is a step change.

Comparison of difference vs. derivative
Your income increases from $20,000 to $20,100; which provides you with $100 of extra income. This additional $100 of income results in $15 of additional tax. The marginal rate is therefore 15% = $15 / $100.

$$ \begin{align} {marginal\ tax\ rate\ at\ income\ of\ $20,000} & = \frac{tax(20,000 + 100) - tax(20,000)}{(20,000 + 100) - (20,000)} \\ \\ {marginal\ tax\ rate(I)}&= \frac{tax(I + \Delta) - tax(I)}{\Delta}\\ \end{align} $$ The last equation above is the general form for calculating the tax rate for the given change of income. The step below will be familiar to those who remember differential calculus, but is not recommended for use with tax calculations when the tax function is non-smooth, due to the lack of useful information it provides. $$ \begin{align} \frac{df(x)}{dx}&=\lim_{\delta\rightarrow 0} \frac{(f(x+\delta)-f(x))}{\delta} \end{align} $$

As a partial derivative
A partial derivative indicates that the tax is not a function of one income, e.g. total income, but several different types of income. For example, wages and capital gains. So we have not a function of one variable tax(income) but a function of two variables tax(wages,gains).

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 marginal tax rates are usually calculated. Refer to the previous example. At an income of $20,000, the marginal tax rate on wages is 15% because an extra $100 of wages increase taxes by $15. However, the marginal tax rate on capital gains is 0% because an extra $100 of capital gains results in $0 extra tax.

The same concept applies to the difference form of the calculation: one independent variable changes while the others are held constant.

As a full derivative
Now, let's convert some of the wages into capital gains (through various investments). Both wages and capital gains are a function of a third variable, the proportion chosen to allocate to gains, x, which results in a form of tax(wage(x),gain(x)). Looking how this tax changes as the allocation changes results in a full derivative in the case of tax with respect to x (formally as  d(tax(x))/dx).

Forum discussions

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