Math Problem Statement

Suppose a stock had an initial price of $87 per share, paid a dividend of $1.80 per share during the year, and had an ending share price of $73.00.

Compute the percentage total return.

Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

What was the dividend yield?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

What was the capital gains yield?

Note: A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.

Solution

Let's compute each component step-by-step.

1. Percentage Total Return

The formula for total return is: Total Return=Ending PriceInitial Price+DividendInitial Price×100\text{Total Return} = \frac{\text{Ending Price} - \text{Initial Price} + \text{Dividend}}{\text{Initial Price}} \times 100

Substitute the values: Total Return=7387+1.8087×100\text{Total Return} = \frac{73 - 87 + 1.80}{87} \times 100 =14+1.8087×100= \frac{-14 + 1.80}{87} \times 100 =12.2087×100= \frac{-12.20}{87} \times 100 =14.02%= -14.02\%

2. Dividend Yield

The formula for dividend yield is: Dividend Yield=DividendInitial Price×100\text{Dividend Yield} = \frac{\text{Dividend}}{\text{Initial Price}} \times 100

Substitute the values: Dividend Yield=1.8087×100\text{Dividend Yield} = \frac{1.80}{87} \times 100 =2.07%= 2.07\%

3. Capital Gains Yield

The formula for capital gains yield is: Capital Gains Yield=Ending PriceInitial PriceInitial Price×100\text{Capital Gains Yield} = \frac{\text{Ending Price} - \text{Initial Price}}{\text{Initial Price}} \times 100

Substitute the values: Capital Gains Yield=738787×100\text{Capital Gains Yield} = \frac{73 - 87}{87} \times 100 =1487×100= \frac{-14}{87} \times 100 =16.09%= -16.09\%

Summary of Answers

  • Percentage Total Return: 14.02%-14.02\%
  • Dividend Yield: 2.07%2.07\%
  • Capital Gains Yield: 16.09%-16.09\%

Would you like further details or have any questions?

Here are some related questions for exploration:

  1. How would these calculations change with a higher dividend?
  2. What would be the impact if the ending share price was higher than the initial price?
  3. Can you calculate the total return if dividends were not included?
  4. What are the implications of a negative capital gains yield in investment analysis?
  5. How is the total return metric useful for comparing different stocks?

Tip: When analyzing stocks, always separate capital gains yield from dividend yield for a clearer understanding of your returns.

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Math Problem Analysis

Mathematical Concepts

Percentage Total Return
Dividend Yield
Capital Gains Yield

Formulas

Total Return = ((Ending Price - Initial Price + Dividend) / Initial Price) * 100
Dividend Yield = (Dividend / Initial Price) * 100
Capital Gains Yield = ((Ending Price - Initial Price) / Initial Price) * 100

Theorems

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Suitable Grade Level

Grades 11-12