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Part 1

Summit Systems will pay a dividend of

$ 1.62$1.62

this year. If you expect​ Summit's dividend to grow by

6.2 %6.2%

per​ year, what is its price per share if the​ firm's equity cost of capital is

10.9 %10.9%​?

To calculate the price per share of Summit Systems, we use the **Dividend Discount Model** (DDM) for a company with constant dividend growth, also known as the **Gordon Growth Model**:

\[
P_0 = \frac{D_1}{r - g}
\]

where:
- $ P_0 $ is the price of the stock today.
- $ D_1 $ is the dividend expected in the coming year.
- $ r $ is the equity cost of capital (discount rate).
- $ g $ is the growth rate of dividends.

### Given Data:
- $ D_1 = 1.62 $
- $ r = 10.9\% = 0.109 $
- $ g = 6.2\% = 0.062 $

### Step-by-Step Solution
1. Substitute the values into the formula:

   \[
   P_0 = \frac{1.62}{0.109 - 0.062}
   \]

2. Calculate the denominator:

   \[
   0.109 - 0.062 = 0.047
   \]

3. Now, divide the dividend by the result:

   \[
   P_0 = \frac{1.62}{0.047} \approx 34.47
   \]

### Answer
The price per share of Summit Systems is approximately **$34.47**.

Would you like further clarification on this calculation or details on related concepts?

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Here are five additional questions that could deepen understanding:
1. How would a change in the growth rate affect the stock price?
2. What happens to the stock price if the equity cost of capital increases?
3. How does the Dividend Discount Model differ from other stock valuation methods?
4. What is the impact of dividends growing faster than the discount rate?
5. How can we calculate a company's growth rate if the price and dividend are known?

**Tip:** In the DDM, a higher dividend growth rate leads to a higher estimated stock price, as future dividends are valued more optimistically.

Summit Systems will pay a dividend of $1.62 this year. If you expect Summit's dividend to grow by 6.2% per year, what is its price per share if the firm's equity cost of capital is 10.9%?

Find the price per share of Summit Systems using the Dividend Discount Model (DDM). With a dividend of $1.62, a growth rate of 6.2%, and an equity cost of capital of 10.9%, learn step-by-step how to calculate the stock price. This guide covers key finance concepts and is suitable for college-level finance students.

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