Math Problem Statement

Consider three unmarried investors who need to partially liquidate investments to raise cash. In this​ case, all investments have been held for 3 or more years. Investor A waited for a ​$2 comma 000 qualified dividend distribution from her mutual​ fund, and Investor B received ​$2 comma 000 in interest income from a certificate of deposit.​ However, because Investor C could not wait for a​ distribution, he decided to sell appreciated stock shares with a​ long-term capital gain of ​$2 comma 000. Assuming no​ commissions, no sales​ charges, no state income​ tax, and other taxable income of​ $100,000, which investment will provide the greatest​ after-tax amount?

Solution

To determine which investment provides the greatest after-tax amount for each investor, we need to look at the tax treatment for each type of income and calculate the after-tax amount based on their respective tax rates.

Given Assumptions:

  • All investors have other taxable income of $100,000.
  • We assume the investments have been held for 3 or more years, meaning qualified dividends and long-term capital gains tax rates apply.
  • There are no state taxes, commissions, or sales charges involved.

Types of Income:

  1. Investor A: $2,000 in qualified dividend income.
  2. Investor B: $2,000 in interest income from a certificate of deposit (CD).
  3. Investor C: $2,000 in long-term capital gains from the sale of appreciated stock.

Federal Tax Rates for the Given Income Level:

  • Qualified Dividends: Qualified dividends are taxed at the same rate as long-term capital gains. Based on the taxable income of $100,000, the long-term capital gains tax rate will likely be 15% for Investor A.
  • Interest Income: Interest income is taxed at ordinary income tax rates, which would be the marginal tax rate for someone with $100,000 in taxable income. Based on the 2023 tax brackets, this would likely fall in the 24% tax bracket for Investor B.
  • Long-Term Capital Gains: Long-term capital gains are taxed at a special rate, likely 15% for Investor C, similar to qualified dividends.

After-Tax Calculations:

1. Investor A (Qualified Dividends):

  • Qualified dividends are taxed at 15%.
  • Tax on $2,000 = $2,000 × 0.15 = $300.
  • After-tax amount = $2,000 - $300 = $1,700.

2. Investor B (Interest Income):

  • Interest income is taxed at the marginal income tax rate (24%).
  • Tax on $2,000 = $2,000 × 0.24 = $480.
  • After-tax amount = $2,000 - $480 = $1,520.

3. Investor C (Long-Term Capital Gains):

  • Long-term capital gains are taxed at 15%.
  • Tax on $2,000 = $2,000 × 0.15 = $300.
  • After-tax amount = $2,000 - $300 = $1,700.

Comparison of After-Tax Amounts:

  • Investor A (Qualified Dividends): $1,700
  • Investor B (Interest Income): $1,520
  • Investor C (Long-Term Capital Gains): $1,700

Conclusion:

Both Investor A (qualified dividends) and Investor C (long-term capital gains) will receive the highest after-tax amount of $1,700. Investor B, who received interest income, has the lowest after-tax amount of $1,520 because interest is taxed at the higher ordinary income tax rate.


Do you have any questions or need more details on any part of this explanation?

Here are 5 related questions you might want to consider:

  1. How would the results change if the investors had lower taxable income, say $50,000?
  2. What are the tax implications if the interest income was earned from a municipal bond?
  3. How does the holding period affect the tax treatment of dividends or capital gains?
  4. What if Investor C had a short-term capital gain instead of a long-term one?
  5. How would state income taxes impact the after-tax results?

Tip: Holding investments for over a year qualifies gains as long-term, which often leads to lower tax rates than short-term gains taxed as ordinary income.

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Math Problem Analysis

Mathematical Concepts

Taxation
Percentage Calculation

Formulas

After-tax amount = Income - (Income × Tax rate)
Qualified Dividends Tax Rate = 15%
Interest Income Tax Rate = 24%
Long-Term Capital Gains Tax Rate = 15%

Theorems

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Suitable Grade Level

College-level finance or taxation