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.

To calculate the dividend yield and capital gains yield, we must first understand the formulas:

1. **Dividend Yield** is the ratio of the dividend received to the stock price:
   \[
   \text{Dividend Yield} = \frac{D_0}{P_0}
   \]
   where $D_0$ is the dividend just received, and $P_0$ is the current stock price.

2. **Capital Gains Yield** is the expected percentage increase in the stock price, often represented by the dividend growth rate for the stock:
   \[
   \text{Capital Gains Yield} = g
   \]
   where $g$ 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, $D_0 = 370$
  - Dividend growth for the first 4 years = 11%
  - Dividend growth rate after 4 years = 4.2%
  - Expected return on stock, $r = 5.6\%$

### Finding the Stock Price ($P_0$):

The current stock price ($P_0$) 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:
\[
P_0 = \sum_{t=1}^{4} \frac{D_t}{(1 + r)^t} + \frac{P_4}{(1 + r)^4}
\]
where $P_4$ is the stock price at the end of the fourth year and can be calculated using:
\[
P_4 = \frac{D_5}{r - g_2}
\]
where $D_5 = D_4 \times (1 + g_2)$ is the dividend in the fifth year and $g_2 = 4.2\%$ is the long-term growth rate.

Let's calculate the stock price first, and then we will calculate the yields.### Results:

1. **Current Stock Price ($P_0$)**: \$35,297.58
2. **Dividend Yield**: 1.05% (or 0.0105)
3. **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:
1. How does the dividend growth rate impact the stock price?
2. What factors can influence the dividend growth rate in a company?
3. How would an increase in the required rate of return affect the dividend yield?
4. What is the relationship between dividend yield and overall stock returns?
5. 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.

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.

Learn how to calculate the dividend yield and capital gains yield for a stock with dividends growing at 11% annually for four years, then at 4.2% thereafter. This problem covers key finance concepts, including the Dividend Discount Model and stock valuation with growth rates. Suitable for undergraduate finance students.

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