Chapter 2, Problem 28QP

a)

Summary Introduction

To critically think about: The reason why the tax rate rises to 39 percent from 34 percent when the taxable income is $100,001 and falls to 34 percent when the income is 335,001.

Introduction:

Income tax refers to the charge levied by the government on the income of the company. The company has a legal obligation to pay taxes. The tax rate differs based on the income of the company. The tax rate is as follows:

Taxable income	Tax rate
$0 to $50,000	15%
$50,001 to $75,000	25%
$75,001 to $100,000	34%
$100,001 to $335,000	39%
$335,001 to $10,000,000	34%
$10,000,001 to $15,000,000	35%
$15,000,001 to $18,333,333	38%
$18,333,334 and above	35%

Explanation of Solution

The originators of the present tax structure state that there are only four tax rates namely, 15 percent, 25 percent, 34 percent, and 35 percent. However, the marginal taxes move up and down. The marginal taxes rise to 39 percent from 34 percent, then fall back to 34 percent, again rise to 38 percent, and finally end with 35 percent.

However, under this tax structure, the average tax always rises, even though the marginal tax rate falls. The jump and fall in the marginal tax rates help the average tax rate to match the marginal tax rate. Thus, the tax bubbles like 38 percent and 39 percent prevent the companies with higher income from taking advantage of the lower marginal tax rates.

Although there is a difference in the marginal tax rates, the average tax rate always increases to reach 34 percent for income up to $10,000,000 and 35 percent for income more than $18,333,334.

b)

Summary Introduction

To compute: The average tax rate when the taxable income is $335,001 and $18,333,334 and to confirm the answer in Part (a).

Introduction:

Income tax refers to the charge levied by the government on the income of the company. The company has a legal obligation to pay taxes. The tax rate differs based on the income of the company. The tax rate is as follows:

Taxable income	Tax rate
$0 to $50,000	15%
$50,001 to $75,000	25%
$75,001 to $100,000	34%
$100,001 to $335,000	39%
$335,001 to $10,000,000	34%
$10,000,001 to $15,000,000	35%
$15,000,001 to $18,333,333	38%
$18,333,334 and above	35%

The average tax rate refers to the total tax bill divided by the total taxable income.

Answer to Problem 28QP

The average tax rate is 34% for taxable income of $335,001, and the average tax rate is 35% for the taxable income of $18,333,334.

Explanation of Solution

The formula to calculate average tax rate:

$\text{Average tax rate}=\frac{\text{Total taxes}}{\text{Total taxable income}}\times 100$

Compute the income tax for $335,001:

The taxable income of $335,001 falls under five tax brackets. They are 15 percent, 25 percent, 34 percent, 39 percent, and 34 percent.

Taxable income	Tax calculation	Income tax
$50,000	$50,000×15%	$7,500.00
$25,000 ($75,000−$50,000)	$25,000×25%	$6,250.00
$25,000 ($100,000−$75,000)	$25,000×34%	$8,500.00
$235,000 ($335,000−$100,000)	$235,000×39%	$91,650.00
$1 ($335,001−$335,000)	$1×34%	$0.34
Total income tax		$113,900.34

Hence, the income tax is $113,900.34.

Compute the average tax rate for $335,001:

$\begin{array}{c}\text{Average tax rate}=\frac{\text{Total taxes}}{\text{Total taxable income}}\times 100\\ =\frac{\$113,900.34}{\$335,001}\times 100\\ =0.34\times 100\\ =34\%\end{array}$

Hence, the average tax rate for $335,001 is 34%.

Compute the income tax for $18,333,334:

The taxable income of $18,333,334 falls under eight tax brackets. They are 15 percent, 25 percent, 34 percent, 39 percent, 34 percent, 35 percent, 38 percent, and 35 percent.

Taxable income	Tax calculation	Income tax
$50,000	$50,000×15%	$7,500.00
$25,000 ($75,000−$50,000)	$25,000×25%	$6,250.00
$25,000 ($100,000−$75,000)	$25,000×34%	$8,500.00
$235,000 ($335,000−$100,000)	$235,000×39%	$91,650.00
$9,665,000 ($10,000,000−$335,000)	$9,665,000×34%	$3,286,100.00
$5,000,000 ($15,000,000−$10,000,000)	$5,000,000×35%	$1,750,000.00
$3,333,333 ($18,333,333−$15,000,000)	$3,333,333×38%	$1,266,666.54
$1 ($18,333,334−$18,333,333)	$1×35%	0.35
Total income tax		$6,416,666.89

Hence, the rounded off income tax is $6,416,666.90.

Compute the average tax rate:

$\begin{array}{c}\text{Average tax rate}=\frac{\text{Total taxes}}{\text{Total taxable income}}\times 100\\ =\frac{\$6,416,666.90}{\$18,333,334}\times 100\\ =0.35\times 100\\ =35\%\end{array}$

Hence, the average tax rate for $18,333,334 is 35%.

Determine whether the above calculations on “average tax rate” confirm the answer in Part (a):

The calculation on average tax rate confirm that there are only four tax rates namely 15 percent, 25 percent, 34 percent, and 35 percent. Although the marginal tax rate rises from 34 percent to 39 percent for the income of $100,001 to $335,000, the marginal tax rate falls back to 34 percent for the income above $335,001. However, the average tax rate for the income above $335,000 up to $10,000,000 will be only 34 percent.

Similarly, the average tax rate will be 35 percent for the income above $18,333,334 even if the taxable income moves through different tax rates. Hence, it is clear that the tax rates such as 38 percent and 39 percent help in matching the average tax rate with the marginal tax rate.

c)

Summary Introduction

To determine: The new tax bubble, if the threshold of 39 percent tax bracket is reduced from $335,000 to $200,000.

Introduction:

Income tax refers to the charge levied by the government on the income of the company. The company has a legal obligation to pay taxes. The tax rate differs based on the income of the company. The tax rate is as follows:

Taxable income	Tax rate
$0 to $50,000	15%
$50,001 to $75,000	25%
$75,001 to $100,000	34%
$100,001 to $335,000	39%
$335,001 to $10,000,000	34%
$10,000,001 to $15,000,000	35%
$15,000,001 to $18,333,333	38%
$18,333,334 and above	35%

Tax bubble refers to the rise in the marginal tax rate in order to match the average tax rate. The 38 percent tax bracket and the 39 percent tax bracket are tax bubbles because they help to maintain the average tax rate of 34 percent and 35 percent respectively.

Answer to Problem 28QP

The new tax bubble is 45.75%.

Explanation of Solution

The income up to $10,000,000 has an average tax rate of 34 percent, even though the marginal tax rate differs. As the tax bubble aims to match the average tax rate with the marginal tax rate, the average tax rate is always equal to the marginal tax rate.

The formula to calculate average tax rate:

$\text{Average taxes}=\text{Taxable income}\times \text{Average tax rate}$

$\text{Average tax rate}=\text{Marginal tax rate}$

Compute the average taxes for the income up to $200,000:

$\begin{array}{c}\text{Average taxes}=\text{Taxable income}\times \text{Average tax rate}\\ =\$200,000\times 0.34\\ =\$68,000\end{array}$

Hence, the average taxes for the income of $200,000 are $68,000.

Compute the tax bubble for the income between $100,001 and $200,000:

$\begin{array}{c}\text{Average tax rate}=\text{Marginal tax rate}\\ \text{Average taxes}=\text{Marginal taxes}\\ \$68,000=\left[\begin{array}{l}\left(\$50,000\times 0.15\right)+\left(\$75,000-\$50,000\right)\times 0.25+\\ \left(\$100,000-\$75,000\right)\times .34+\left(\$200,000-\$100,000\right)\times x\end{array}\right]\\ \$68,000=\left(\$15,000\times 0.15\right)+\left(\$25,000\times 0.25\right)+\left(\$25,000\times 0.34\right)+\$100,000\times x\end{array}$

$\begin{array}{c}\$68,000=\$7,500+\$6,250+\$8,500+\$100,000\times x\\ \$68,000=\$22,250+\$100,000\times x\\ \$100,000\times x=\$68,000-\$22,250\\ \$100,000\times x=\$45,750\end{array}$

$\begin{array}{c}x=\frac{\$45,750}{\$100,000}\\ x=0.4575\text{ or }45.75\%\end{array}$

Hence, the tax bubble for the income between $100,001 and $200,000 is 45.75%.