Math Problem Statement
A firm recently paid an annual dividend of $6.90 per share. This divided increases at 4.1% per year. The stock currently sells for $36.09 per share. What is the rate of return?
Solution
To calculate the rate of return (also called the dividend yield or required rate of return) on the stock, we can use the Dividend Discount Model (DDM) or the Gordon Growth Model since the dividend is growing at a constant rate.
The formula for the rate of return is:
Where:
- is the expected dividend next year.
- is the current stock price.
- is the growth rate of the dividend.
Step 1: Calculate the expected dividend next year .
Since the most recent dividend was $6.90 and the dividend grows at 4.1%, the expected dividend next year is:
Step 2: Plug values into the formula.
Now, we can calculate the rate of return:
Conclusion:
The rate of return for the stock is approximately 24.0%.
Would you like further details or have any questions? Here are some related topics you could explore:
- How does the Gordon Growth Model differ from other dividend valuation models?
- What factors affect the stock price in the long term?
- How can a firm adjust its dividend policy to increase its stock price?
- How does the rate of return impact investment decisions?
- What are the risks associated with relying on dividend growth models for stock valuation?
Tip: The rate of return is sensitive to the growth rate and the stock price. Even small changes in the growth rate can have a big impact on your expected return!
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Math Problem Analysis
Mathematical Concepts
Finance
Dividend Discount Model
Growth Rate
Rate of Return
Formulas
r = D1 / P0 + g
Theorems
Dividend Discount Model (Gordon Growth Model)
Suitable Grade Level
Grades 11-12
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