Math Problem Statement
You have just received a $370 dividend from your common stock. The dividends are expected to grow at a rate of 11% annually for the next four years, and at 4.2% thereafter. You anticipate earning a 5.6% return on this stock. Calculate dividend yield and capital gains yield.
Solution
To calculate the dividend yield and capital gains yield, we must first understand the formulas:
-
Dividend Yield is the ratio of the dividend received to the stock price: where is the dividend just received, and is the current stock price.
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Capital Gains Yield is the expected percentage increase in the stock price, often represented by the dividend growth rate for the stock: where is the dividend growth rate after the period of higher growth (after year 4 in this case).
Step-by-Step Breakdown:
- We know:
- Initial dividend,
- Dividend growth for the first 4 years = 11%
- Dividend growth rate after 4 years = 4.2%
- Expected return on stock,
Finding the Stock Price ():
The current stock price () is determined by the Dividend Discount Model (DDM), which factors in both the high-growth period and the stable growth period.
The price is given by the present value of future dividends: where is the stock price at the end of the fourth year and can be calculated using: where is the dividend in the fifth year and is the long-term growth rate.
Let's calculate the stock price first, and then we will calculate the yields.### Results:
- Current Stock Price (): $35,297.58
- Dividend Yield: 1.05% (or 0.0105)
- Capital Gains Yield: 4.2% (or 0.042)
The dividend yield is based on the initial dividend relative to the current stock price, while the capital gains yield corresponds to the long-term growth rate of 4.2%.
Would you like further details on the calculation or any additional questions?
Here are 5 related questions to expand the topic:
- How does the dividend growth rate impact the stock price?
- What factors can influence the dividend growth rate in a company?
- How would an increase in the required rate of return affect the dividend yield?
- What is the relationship between dividend yield and overall stock returns?
- How do different stock valuation models compare, such as the Gordon Growth Model vs. the Dividend Discount Model?
Tip: When estimating stock returns, it's essential to distinguish between dividend income and potential capital appreciation to get a holistic view of expected returns.
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Math Problem Analysis
Mathematical Concepts
Finance
Stock Valuation
Dividend Growth
Capital Gains
Formulas
Dividend Yield = D_0 / P_0
Capital Gains Yield = g
P_0 = Σ(D_t / (1 + r)^t) + (P_4 / (1 + r)^4)
P_4 = D_5 / (r - g_2)
Theorems
Dividend Discount Model (DDM)
Gordon Growth Model
Suitable Grade Level
Undergraduate (Finance, Economics, or Business Studies)
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