Chapter 3, Problem 18P

a.

Summary Introduction

To determine: The federal tax liability.

Personal Taxes:

The personal taxes refer to those taxes which an individual has to pay on his income. This tax is an important source of revenue and the amount of tax is used for the welfare activities of the society.

Capital Gain or Loss:

Whenever a security is bought or sold, there is the difference between the buy price and the selling price. If the selling price is greater than the price at which it was bought, there is a capital gain and if the buying price is more than the selling price, there is a capital loss. The capital gains are subject to tax.

Explanation of Solution

Calculation of the federal tax liability:

$\text{Federal}\text{tax}\text{liability}=\left(\begin{array}{l}\text{Tax}\text{on}\text{dividend}\text{income}\\ +\text{Tax}\text{on}\text{long-term}\text{capital}\text{gain}\\ +\text{Tax}\text{on}\text{other}\text{income}\end{array}\right)$

Substitute $1,800 for the tax on dividend income, $1,950 for tax on long-term capital gain and $12,793.75 for the tax on other income (working note) in the above formula.

$\begin{array}{c}\text{Federal}\text{tax}\text{liability}=\left(\$1,800+\$1,950+\$12,793.75\right)\\ =\$16,543.50\end{array}$

The federal tax liability is $16,543.50.

Working note:

The calculation of taxable income:

1. 1. Income from salary is $82,000.

Income from investment includes:

1. 2. Dividend received is $12,000.
2. 3. Stock purchased is $9,000. So, the capital gain is $13,000 $\left(\$22,000-\$9,000\right)$. As the stock is held more than one year, as it is a long-term capital gain.
3. 4. Another stock has been purchased six months back at $7,500 and it is sold at $10,000. The capital gain is $2,500 $\left(\$10,000-\$7,500\right)$
4. 5. The total income of the person subject to tax is $114,500 $\left(\$82,000+\$12,000+\$5,000+\$13,000+\$2,500\right)$
5. 6. As per federal guideline, $4,000 exemption is available for taxpayer and also for the dependents. Also, the itemized deduction will be $7,500.

Calculation of the taxable income:

$\begin{array}{c}\text{Taxable}\text{income}=\left(\begin{array}{l}\text{Gross}\text{income}-\text{Total}\text{exemption}\text{of}\$4,000\text{each}\\ -\text{Itemized}\text{deduction}\end{array}\right)\\ =\left(\$114,500-\$4,000-\$7,500\right)\\ =\$103,000\end{array}$

The taxable income should be $103,000.

1. 7. Out of $103,000 taxable income, 15% will be paid on long-term capital gain and dividend.
2. 8. The tax amount is,

   $\begin{array}{c}\text{Taxable}\text{income}=\text{Long-term}\text{capital}\text{gain}+\text{Dividend}\\ \text{=\$13,000}+\text{\$12,000}\\ \text{=\$25,000}\end{array}$

3. 9. The income tax at the ordinary rate is $78,000 $\left(\$103,000-\$25,000\right)$

Calculation of the tax on dividend income:

$\begin{array}{c}\text{Tax}\text{on}\text{dividend}\text{income}=\$12,000\times 15\%\\ =\$1,800\end{array}$

The tax on dividend income is $1,800.

Calculation of the tax on long-term capital gain:

$\begin{array}{c}\text{Tax}\text{on}\text{long-term}\text{capital}\text{gain}=\$13,000\times 15\%\\ =\$1,950\end{array}$

The tax on the long-term capital gain is $1,950.

Calculation of tax on other income:

$\begin{array}{c}\text{Tax}\text{on}\text{other}\text{income}=\left[\begin{array}{l}\left(\$9,225\times 10\%\right)+\left(\$28,225\times 15\%\right)\\ +\left(\$30,550\times 25\%\right)\end{array}\right]\\ =\$922.50+\$4,233.75+\$7,637.50\\ =\$12,793.75\end{array}$

The tax on other income is $12,793.75.

Conclusion

Thus, the federal tax liability is $16,543.75.

b.

Summary Introduction

To determine: The marginal tax rate.

Personal Taxes:

The personal taxes refer to those taxes which an individual has to pay on his income. This tax is an important source of revenue and the amount of tax is used for the welfare activities of the society.

Capital Gain or Loss:

Whenever a security is bought or sold, there is the difference between the buy price and the selling price. If the selling price is greater than the price at which it was bought, there is a capital gain and if the buying price is more than the selling price, there is a capital loss. The capital gains are subject to tax.

Explanation of Solution

The marginal tax rate is the tax rate applicable to the last dollar taxable income. So, the highest tax rate applied is 25%.

Conclusion

Thus, the marginal tax rate is 25%.

c.

Summary Introduction

To determine: The average tax rate.

Personal Taxes:

The personal taxes refer to those taxes which an individual has to pay on his income. This tax is an important source of revenue and the amount of tax is used for the welfare activities of the society.

Capital Gain or Loss:

Whenever a security is bought or sold, there is the difference between the buy price and the selling price. If the selling price is greater than the price at which it was bought, there is a capital gain and if the buying price is more than the selling price, there is a capital loss. The capital gains are subject to tax.

Explanation of Solution

Explnation:

Calculated,

The total tax paid is $16,543.75. (refer part a.).

The taxable income is $103,000 (refer part a.)

Calculation of the average tax rate:

The formula to calculate the average tax rate is,

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

Substitute $16,543.75 for the total tax paid and $103,000 for the total taxable income in the above formula.

$\begin{array}{c}\text{Average}\text{tax}\text{rate}=\frac{\$16,543.75}{\$103,000}\times 100\\ =16.06\%\end{array}$

Conclusion

Thus, the average tax rate is 17.79%.