Math Problem Statement

You purchased 250 shares of a stock at the beginning of the year at a price of $104.32. The stock paid a dividend of $2.34 per share and the stock price at the end of the year was $113.65. What is the dividend yield? What is the capital gains yield? What was your dollar return on this investment? What was your rate of return?

Solution

To analyze your stock investment, let's calculate the dividend yield, capital gains yield, dollar return, and rate of return step-by-step.

1. Dividend Yield

The dividend yield is calculated as follows:

Dividend Yield=Annual Dividend per SharePurchase Price per Share\text{Dividend Yield} = \frac{\text{Annual Dividend per Share}}{\text{Purchase Price per Share}}

Dividend Yield=2.34104.320.0224 or 2.24%\text{Dividend Yield} = \frac{2.34}{104.32} \approx 0.0224 \text{ or } 2.24\%

2. Capital Gains Yield

The capital gains yield is calculated by determining the price appreciation:

Capital Gains Yield=Ending PriceBeginning PriceBeginning Price\text{Capital Gains Yield} = \frac{\text{Ending Price} - \text{Beginning Price}}{\text{Beginning Price}}

Capital Gains Yield=113.65104.32104.320.0895 or 8.95%\text{Capital Gains Yield} = \frac{113.65 - 104.32}{104.32} \approx 0.0895 \text{ or } 8.95\%

3. Dollar Return

The dollar return includes both the dividends received and the capital gains:

Dollar Return=(Ending PriceBeginning Price)×Number of Shares+(Annual Dividend per Share×Number of Shares)\text{Dollar Return} = (\text{Ending Price} - \text{Beginning Price}) \times \text{Number of Shares} + (\text{Annual Dividend per Share} \times \text{Number of Shares})

Calculating this step by step:

  • Capital Gains: (113.65104.32)×250=9.33×250=2332.50(113.65 - 104.32) \times 250 = 9.33 \times 250 = 2332.50
  • Dividends: 2.34×250=5852.34 \times 250 = 585

Dollar Return=2332.50+585=2917.50\text{Dollar Return} = 2332.50 + 585 = 2917.50

4. Rate of Return

The rate of return is the total return (dollar return) relative to the initial investment:

Rate of Return=Dollar ReturnInitial Investment\text{Rate of Return} = \frac{\text{Dollar Return}}{\text{Initial Investment}}

Initial Investment=250×104.32=26080\text{Initial Investment} = 250 \times 104.32 = 26080

Rate of Return=2917.50260800.1118 or 11.18%\text{Rate of Return} = \frac{2917.50}{26080} \approx 0.1118 \text{ or } 11.18\%

Summary of Results

  • Dividend Yield: 2.24%
  • Capital Gains Yield: 8.95%
  • Dollar Return: $2,917.50
  • Rate of Return: 11.18%

If you have any questions or need further details, feel free to ask! Here are some related questions you might consider:

  1. How would changes in stock price affect your capital gains yield?
  2. What factors influence dividend payments from a company?
  3. How do you calculate the total return on a portfolio of stocks?
  4. What risks are associated with investing in stocks?
  5. How does inflation impact the real rate of return?

Tip: Always consider both dividends and capital gains when evaluating stock performance to get a complete picture of your investment return.

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Math Problem Analysis

Mathematical Concepts

Finance
Investment Analysis

Formulas

Dividend Yield = Annual Dividend per Share / Purchase Price per Share
Capital Gains Yield = (Ending Price - Beginning Price) / Beginning Price
Dollar Return = (Ending Price - Beginning Price) * Number of Shares + (Annual Dividend per Share * Number of Shares)
Rate of Return = Dollar Return / Initial Investment

Theorems

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Suitable Grade Level

Grades 10-12