# Difference between revisions of "User:Fyre4ce/Marginal tax rate"

Fyre4ce/Marginal tax rate is the tax rate on a change in income (i.e. change in tax/change in income). The marginal rate is often described as the tax rate on the "next dollar" or "last dollar" of income.[1] [2] [3] [4] [5] [6] However, due to rounding errors, actual tax rates on a single dollar change can be misleading. For accurate numbers, the marginal tax rate is often either calculated on a larger change in income, or by using theoretical values from the tax code.

The marginal tax rate is often the same as the individual's tax bracket, but not always.[note 1][note 2]

A marginal tax rate is not the average (a.k.a. "effective") tax rate paid on one's entire income.[7] Marginal tax rates are useful in many contexts for making decisions, because they describe the effect of a particular change. While the average tax rate is interesting to know, it doesn't help in making decisions the same way the marginal tax rate can.

## Calculation

The marginal tax rate is the ratio of the additional (or decreased) tax owed to the additional (or decreased) income. To calculate a marginal income tax rate, calculate how much tax you would owe with the income change, subtract from the current tax, and divide by the income change. Most commonly, the term "marginal" denotes a "small" change. In the context of tax rates, "small" means a change in income small enough to capture only the local tax effects. Assuming that your marginal tax rate is equal to your federal tax bracket is sometimes correct. However, due to the complexity of the tax code, the actual marginal rate can be much different. Income can also phase out benefits and phase in additional taxes. For a single filer with $10K long term capital gains (LTCG), if nominally in the 12% bracket but an additional dollar of ordinary income pushes a dollar of LTCG from its 0% bracket to its 15% bracket, the marginal rate on that ordinary income is 27% as shown below. The 27% is the sum of 12% on the ordinary income dollar, plus the 15% on the LTCG dollar. Charts such as the one above may be generated for individual households using the personal finance toolbox Excel spreadsheet.[8], which handles most common tax situations. In certain situations, it may be meaningful to calculate a marginal tax rate for a larger change in income, usually when that change cannot be meaningfully divided into smaller changes for a particular reason. One can find occasional reference to a marginal tax rate calculated using larger, specific chunk of income about which one is making a decision.[9] It is calculated by dividing the change in tax by the applicable change in income. #### Example A single taxpayer earns$75,000 gross income. After taking the federal standard deduction of $12,200 and deducting another$10,000 contribution to a 401(k), their taxable income is $52,800, putting them in the 22% federal tax bracket. Assuming no phase-outs, their marginal tax rate is 22%, meaning each additional dollar earned results in an additional 22 cents of federal income tax. The total federal income tax due for this individual is$7,474.50 ($970 in the 10% bracket,$3,573 in the 12% bracket, and $2,931.50 in the 22% bracket; see: Tax bracket), for an "average" tax rate of only 9.966% relative to gross income. #### Estimation A taxpayer's marginal tax rate can either be calculated based on the various components coming directly from the tax code, or estimated by preparing an alternative tax return with additional income added. As discussed in this article's appendix, the "next dollar" or "last dollar" definition of marginal tax rate comes from the calculus concept of a derivative, and is often useful in microeconomic theory. However, in the United States, income and taxes are rounded to the nearest dollar, so a change of at least$100[10] [11] is usually required for sufficient resolution (1% or less) on one's marginal tax rate. When tax is determined by the IRS tax tables, income is rounded to the nearest $50, so taxable income can change by up to$49 with no change in tax. Therefore, when calculating a marginal tax rate when the IRS tax tables are used, using a multiple of $50 will help avoid rounding errors, which could otherwise be large. ## Components ### Federal income taxes Except for certain tax exemptions, income in the United States is generally subject to income tax from the federal government. Federal income tax is typically the largest, and in some cases the only, component of a taxpayer's marginal tax rate. Tax is applied according to a progressive tax bracket system, meaning that income within a given year is taxed at a progressively higher rate, depending on how much income falls within that bracket. Note that the bracket rate applies only to income within that bracket, not all income. For 2019, federal income tax rates are as follows: Rate Single Married Filing Jointly Head of Household 10%$0 to $9,700$0 to $19,400$0 to $13,850 12%$9,700 to $39,475$19,400 to $78,950$13,850 to $52,850 22%$39,475 to $84,200$78,950 to $168,400$52,850 to $84,200 24%$84,200 to $160,725$168,400 to $321,450$84,200 to $160,700 32%$160,725 to $204,100$321,450 to $408,200$160,700 to $204,100 35%$204,100 to $510,300$408,200 to $612,350$204,100 to $510,300 37% Over$510,300 Over $612,350 Over$510,300

Federal income tax payers are allowed to deduct the greater of the appropriate federal standard deduction, or itemized deductions on Form 1040 Schedule A, effectively adding an additional 0% bracket to the bottom of the bracket structure. For 2019, the federal standard deductions are:

Filing Status Standard Deduction
Single $12,200 Married Filing Jointly$24,400

### 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$40,000 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

Main article: Qualified dividend

Long-term capital gains and qualified dividends are taxed at a reduced rate by the IRS: either 0%, 15%, or 20% depending on income. 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

Main article: Payroll tax

The IRS assesses Payroll Taxes (also called FICA Taxes) on earned income (wages). The tax has three components:

### 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.

### Marginal rate greater than 100%

A marginal tax rate of greater than 100% means that a taxpayer's total tax liability increases faster than their income, meaning they take home less money the more they earn. Generally, tax codes are written to try to avoid situations where marginal tax rates are greater than 100%, due to the obvious disincentive for work and economic productivity it would create. Nonetheless, tax analysts sometimes find cases under current or proposed tax laws where a combination of additional tax, loss of subsides, and other factors combine to create effective marginal tax rates greater than 100%.[12] When they do occur, most often such rates are for rare situations and over only a small range of income.

Abrupt changes in tax liability with income can produce "spikes" in marginal tax rates far greater than 100%, see below.

When a tax kicks in or a benefit is lost abruptly, as opposed to being phased in or out gradually, the calculated marginal tax rate on the income that causes the change can be very large. For example, in a case analyzed in the Traditional versus Roth article, an additional $200 Saver's credit is earned for a$12,500 retirement savings contribution. The last dollar that gains the additional credit has a calculated marginal savings rate of 20,000% ($200/$1), and if calculated using the last cent the marginal savings rate is 2,000,000% ($200/$0.01). These numbers are correct, but are not as useful for making decisions because they only apply to a tiny amount of savings or income. In this case, it would be more useful to calculate the rate over the entire contribution necessary to gain the credit; that rate is 1.6% ($200/$12,500) in addition to other components of the overall rate. This figure is a better reflection of the value in making that contribution. For those very close to a spike in a marginal rate, even the rate over the entire change may be high; if only $500 savings were necessary to earn a$200 credit, the savings rate would be the rate on the $500 plus 40% ($200/$500). ## 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 (NIIT) • Long-term capital gains and qualified dividends, subject to reduced income tax rates, phase-outs, and NIIT • 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 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[8]

• traditional IRA distributions is 49.95%
• qualified dividends is 37.95%
• social security income is 11.475%

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.

## 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:

{\displaystyle {\begin{aligned}{\text{[after-tax return]}}&={\text{[before-tax return]}}\cdot \left(1-{\text{[marginal tax rate]}}\right)\end{aligned}}}

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 taxable 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:

Investment Yield Marginal Tax Rate After-Tax Return
Corporate Bond 4.00% 30.08% 2.797%
Treasury Bond 3.50% 24% 2.660%
Municipal Bond 3.00% 0% 3.000%

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.

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. Predicting future tax rates can be difficult; it depends on future tax laws, long-term investment performance, and your ability to continue to make contributions over many years. See that article for more details and strategy.

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.

## 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.

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. {\displaystyle {\begin{aligned}{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{aligned}}} 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. {\displaystyle {\begin{aligned}{\frac {df(x)}{dx}}&=\lim _{\delta \rightarrow 0}{\frac {(f(x+\delta )-f(x))}{\delta }}\end{aligned}}} ### 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 of20,000, 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.

## Notes

1. Since the income tax structure includes various types of income, deductions, exclusions, credits, and taxes that are not subject to the same treatment under tax laws, the marginal tax rate is not always apparent. See: Individual Income Tax Rates and Shares, 2010, Statistics of Income Bulletin, Winter 2013, page 23 (printed), from the IRS.
2. A "tax-bracket" is not formally defined, but inspection of US law shows the intended usage. Note that the term "rate bracket" is also used. From 26 U.S. Code § 1 - Tax imposed:
• (f) Phaseout of marriage penalty in 15-percent bracket;
• ...maximum dollar amounts for each rate bracket...
• (7) Special rule for certain brackets