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:
- Investor A: $2,000 in qualified dividend income.
- Investor B: $2,000 in interest income from a certificate of deposit (CD).
- 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:
- How would the results change if the investors had lower taxable income, say $50,000?
- What are the tax implications if the interest income was earned from a municipal bond?
- How does the holding period affect the tax treatment of dividends or capital gains?
- What if Investor C had a short-term capital gain instead of a long-term one?
- 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
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