Math Problem Statement

After reading this​ chapter, it​ isn't surprising that​ you're becoming an investment wizard. With your newfound​ expertise, you purchase 100 shares of KSU Corporation for ​$32.71 per share. Assume the price goes up to $ 41.24 per share over the next 12 months and you receive a qualified dividend of ​$0.59 per share. What would be your total return on your KSU Corporation​ investment? Assuming you continue to hold the​ stock, calculate your​ after-tax return. How is your realized​ after-tax return different if you sell the​ stock? In both cases assume you are in the 25 percent federal marginal tax bracket and 15 percent​ long-term capital gains and qualified dividends tax bracket and there is no state income tax on investment income. Question content area bottom Part 1 Your total rate of return on your KSU Corporation investment is

27.88​%. ​ (Round to two decimal​ places.) Part 2 Assuming you continue to hold the​ stock, your​ after-tax rate of return is

27.61​%. ​ (Round to two decimal​ places.) Part 3 Your realized​ after-tax rate of return if you sell the stock is

enter your response here​%. ​ (Round to two decimal​ places.)

Solution

To calculate your total return on your KSU Corporation investment and the after-tax returns in both scenarios, let’s break it down step by step.

Part 1: Total Return Calculation

  1. Initial Investment: Initial Investment=100 shares×32.71 USD/share=3,271 USD\text{Initial Investment} = 100 \text{ shares} \times 32.71 \text{ USD/share} = 3,271 \text{ USD}

  2. Final Value of Investment: Final Value=100 shares×41.24 USD/share=4,124 USD\text{Final Value} = 100 \text{ shares} \times 41.24 \text{ USD/share} = 4,124 \text{ USD}

  3. Dividends Received: Dividends=100 shares×0.59 USD/share=59 USD\text{Dividends} = 100 \text{ shares} \times 0.59 \text{ USD/share} = 59 \text{ USD}

  4. Total Return: Total Return=(Final Value+Dividends)−Initial Investment\text{Total Return} = (\text{Final Value} + \text{Dividends}) - \text{Initial Investment} Total Return=(4,124+59)−3,271=912 USD\text{Total Return} = (4,124 + 59) - 3,271 = 912 \text{ USD}

  5. Total Rate of Return: Total Rate of Return=Total ReturnInitial Investment×100=9123,271×100≈27.88%\text{Total Rate of Return} = \frac{\text{Total Return}}{\text{Initial Investment}} \times 100 = \frac{912}{3,271} \times 100 \approx 27.88\%

Part 2: After-Tax Rate of Return (Holding the Stock)

  1. Tax on Dividends: Tax on Dividends=59 USD×0.15=8.85 USD\text{Tax on Dividends} = 59 \text{ USD} \times 0.15 = 8.85 \text{ USD} After-Tax Dividends=59−8.85=50.15 USD\text{After-Tax Dividends} = 59 - 8.85 = 50.15 \text{ USD}

  2. After-Tax Total Return: After-Tax Total Return=912 USD−8.85 USD=903.15 USD\text{After-Tax Total Return} = 912 \text{ USD} - 8.85 \text{ USD} = 903.15 \text{ USD}

  3. After-Tax Rate of Return: After-Tax Rate of Return=903.153,271×100≈27.61%\text{After-Tax Rate of Return} = \frac{903.15}{3,271} \times 100 \approx 27.61\%

Part 3: Realized After-Tax Rate of Return (If Sold)

  1. Tax on Capital Gains:

    • Capital Gain: Capital Gain=Final Value−Initial Investment=4,124−3,271=853 USD\text{Capital Gain} = \text{Final Value} - \text{Initial Investment} = 4,124 - 3,271 = 853 \text{ USD}
    • Tax on Capital Gain: Tax on Capital Gains=853×0.15=127.95 USD\text{Tax on Capital Gains} = 853 \times 0.15 = 127.95 \text{ USD}
    • After-Tax Capital Gain: After-Tax Capital Gain=853−127.95=725.05 USD\text{After-Tax Capital Gain} = 853 - 127.95 = 725.05 \text{ USD}

  2. Total After-Tax Return if Sold: Total After-Tax Return=After-Tax Capital Gain+After-Tax Dividends=725.05+50.15=775.20 USD\text{Total After-Tax Return} = \text{After-Tax Capital Gain} + \text{After-Tax Dividends} = 725.05 + 50.15 = 775.20 \text{ USD}

  3. Realized After-Tax Rate of Return: Realized After-Tax Rate of Return=775.203,271×100≈23.69%\text{Realized After-Tax Rate of Return} = \frac{775.20}{3,271} \times 100 \approx 23.69\%

Final Results

  1. Total Rate of Return: 27.88%
  2. After-Tax Rate of Return (Holding): 27.61%
  3. Realized After-Tax Rate of Return (If Sold): 23.69%

If you have any questions or need further details, let me know! Here are some related questions to consider:

  1. How would a change in the tax bracket affect the after-tax returns?
  2. What impact does holding the stock longer have on total returns?
  3. How do dividends influence the total return on an investment?
  4. What factors should you consider when deciding to sell or hold a stock?
  5. How would your investment strategy change if you anticipated a market downturn?

Tip: Keep track of both capital gains and dividend income for accurate tax reporting and to optimize your investment returns.

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Math Problem Analysis

Mathematical Concepts

Finance
Investment Return Calculations
Tax Calculations

Formulas

Total Return = (Final Value + Dividends) - Initial Investment
Total Rate of Return = (Total Return / Initial Investment) * 100
After-Tax Return = Total Return - Tax on Dividends
Tax on Dividends = Dividends * Dividend Tax Rate
Realized After-Tax Return = After-Tax Capital Gain + After-Tax Dividends

Theorems

Basic principles of investment returns and taxation

Suitable Grade Level

Grades 10-12

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