### What Is the Marginal Tax Rate on Pass-through Business Income?

I am a sole proprietor and a C-corp owner, so the 2017 tax legislation (unofficially, the Tax Cuts and Jobs Act) affects me in multiple ways.

I had a simple question: What is the marginal tax rate on sole proprietor income, taking account of the new deduction for "qualified business income"?

A quick online search did not provide a clear answer, so I pulled out a blank sheet of paper.

The new IRC Section 199A creates a deduction that starts at 20% and declines to 0% as income grows. For single filers, the phaseout range is \$157,500 to \$207,500; for married/joint filers, the range is \$315,000 to \$415,000.

Mercifully, the phaseout is linear, so the deduction can be described by the equation for a line.

Let

`Income` = income (as used in determining the deduction)
`Tax` = income tax
`DeductionRate` = deduction percentage (from 20% to 0%)
`LowerBound` = lower end of phaseout range
`UpperBound` = upper end of phaseout range
`TaxBracket` = tax bracket (i.e., the marginal rate shown in tax tables)
`Constant` = difference between the actual tax and what it would be if the tax bracket applied to all income
(`Constant` doesn’t matter for marginal tax calculations; it is here for completeness.)
`MarginalTaxRate` = marginal tax rate, taking account of the deduction for qualified business income

The equation for the deduction percentage is in three pieces:

1. If `Income` is less than `LowerBound`, then `DeductionRate = 20%`;
2. If `Income` is greater than `UpperBound`, then `DeductionRate = 0%`; and
3. If `Income` is between `LowerBound` and `UpperBound`, then the slope of the line is `-0.20/(UpperBound – LowerBound)`, and the y-intercept of the line is `0.20 + 0.20(LowerBound)/(UpperBound – LowerBound)`.

For single filers, the slope is -0.20/50000 and the y-intercept is 0.83, so the equation for this piece of the line is

`DeductionRate = 0.83 – (0.20/50000)(Income)`

Also, `Tax = Constant + (TaxBracket)(Income)(1 – DeductionRate)`, so

`Tax = Constant + (TaxBracket)(Income)[1 – 0.83 + (0.20/50000)(Income)]`, so

`Tax = Constant + (TaxBracket)[(0.20/50000)(Income)2 + (0.17)(Income)]`.

By definition, the marginal tax rate is the change in tax divided by the change in income. Using calculus, we want to know the first derivative of `Tax` with respect to `Income`.

`MarginalTaxRate` = `dTax/dIncome = (TaxBracket)[(0.40/50000)(Income) + 0.17]`

So this tells us that the marginal tax rate is equal to the tax bracket times a multiplier, and the multiplier is a function of income.

This table shows the relationship between the tax bracket and the marginal tax rate at selected income levels. Within the phaseout range, the marginal tax rate is much higher than the tax bracket.

Single Filers
Income Tax
Bracket
Multiplier Marginal
Tax Rate
\$150,000 24% 0.80 19.20%
\$160,000 32% 1.45 46.40%
\$170,000 32% 1.53 48.96%
\$180,000 32% 1.61 51.52%
\$190,000 32% 1.69 54.08%
\$200,001 35% 1.77 61.95%
\$210,000 35% 1.00 35.00%

How fast does the marginal tax rate increase as income grows? For that, we need to know the second derivative of `Tax` with respect to `Income`.

`d2Tax/dIncome2 = (TaxBracket)(0.40/50000)`

Within each tax bracket, the marginal tax rate changes at a constant rate. For example, for each \$10,000 additional income in the 32% tax bracket, the marginal tax rate increases by (0.32)(0.40/50000)(10000) = 0.0256, as shown in the table.

For married/joint filers, the middle section of the `DeductionRate` line has a slope of -0.20/100000 and a y-intercept of 0.83.

`Tax = Constant + (TaxBracket)(Income)[1 – 0.83 + (0.20/100000)(Income)]`, so

`Tax = Constant + (TaxBracket)[(0.20/100000)(Income)2 + (0.17)(Income)]`, so

`MarginalTaxRate` = `dTax/dIncome = (TaxBracket)[(0.40/100000)(Income) + 0.17]`

With doubled income, the results for married/joint filers are similar to those for single filers.

Married/Joint Filers
Income Tax
Bracket
Multiplier Marginal
Tax Rate
\$300,000 24% 0.80 19.20%
\$320,000 32% 1.45 46.40%
\$340,000 32% 1.53 48.96%
\$360,000 32% 1.61 51.52%
\$380,000 32% 1.69 54.08%
\$400,001 35% 1.77 61.95%
\$420,000 35% 1.00 35.00%

The lower end of the phaseout range and the tax brackets will be adjusted for inflation, so these numbers will change until this whole mess disappears in 2026.

#### Really?

In my blog post "Life Settlements Get a Boost From Tax Reform", I criticized the process that produced the Tax Cuts and Jobs Act. Optimal tax theory has many analytical models leading to many results. You can even find support for decreasing marginal tax rates, 0% tax on corporate income and 0% tax on capital gains. I doubt that there is any serious work that provides support for the rate structure that we are now burdened with.

Note: I have probably overlooked relevant details of the tax law that will affect these calculations. Consult your tax adviser.