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?


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:

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

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

### 2. Capital Gains Yield
The capital gains yield is calculated by determining the price appreciation:

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

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

### 3. Dollar Return
The dollar return includes both the dividends received and the capital gains:

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

Calculating this step by step:

- **Capital Gains:** $ (113.65 - 104.32) \times 250 = 9.33 \times 250 = 2332.50 $
- **Dividends:** $ 2.34 \times 250 = 585 $

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

### 4. Rate of Return
The rate of return is the total return (dollar return) relative to the initial investment:

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

\[
\text{Initial Investment} = 250 \times 104.32 = 26080
\]

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

### 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.

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?

Discover how to calculate dividend yield, capital gains yield, dollar return, and rate of return for stock investments with our detailed example involving 250 shares purchased at $104.32. This guide is perfect for high school students and those interested in finance.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation