Math Problem Statement
A stock's current price is $25.70 and its next dividend of $3.79 will be paid exactly one year from now. You expect future dividends will grow at a constant rate of 2.2% per year thereafter. What is the stock's required rate of return? Enter your answer as a decimal and show four decimal places. For example, if your answer is 5.25%, enter .0525
Solution
To find the stock's required rate of return, we can use the Gordon Growth Model (Dividend Discount Model), which is given by:
where:
- is the expected dividend one year from now,
- is the current stock price,
- is the growth rate of dividends.
Given values:
Calculation:
-
Calculate the dividend yield (the ratio of to ):
-
Add the growth rate to the dividend yield to find :
Answer:
The stock's required rate of return is 0.1695 (or 16.95%).
Would you like more details, or do you have any questions?
Here are five additional questions related to this topic:
- How does the dividend growth rate affect the stock’s required rate of return?
- What would the required rate of return be if the dividend growth rate was 3% instead of 2.2%?
- How does a decrease in the current stock price affect the required rate of return?
- What assumptions does the Gordon Growth Model rely on?
- How would a change in the next dividend amount impact the required rate of return?
Tip: When using the Gordon Growth Model, ensure that the growth rate is less than the required rate of return; otherwise, the model becomes invalid.
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Math Problem Analysis
Mathematical Concepts
Financial Mathematics
Dividend Discount Model
Stock Valuation
Formulas
r = (D1 / P0) + g
Theorems
Gordon Growth Model
Suitable Grade Level
Grades 10-12
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