Suppose we are interested in the price of a stock in five years, P5. We just paid a dividend of $2.20 and the growth rate is 4%. The required return is 12%. What is the price of the stock in five years?

Multiple Choice

$17.40

$24.00

$32.70

$34.80

$38.20

We can use the **Gordon Growth Model (Dividend Discount Model)** to determine the price of the stock in five years, $ P_5 $. This model assumes that dividends grow at a constant rate indefinitely and that the price of the stock is based on the present value of all future dividends.

The formula for the stock price based on the Gordon Growth Model is:

\[
P_t = \frac{D_{t+1}}{r - g}
\]

Where:
- $ P_t $ is the price of the stock at time $ t $,
- $ D_{t+1} $ is the dividend at time $ t+1 $,
- $ r $ is the required return,
- $ g $ is the growth rate of the dividends.

### Step-by-Step Solution:
1. **Current Dividend (D0)** = $2.20
2. **Growth Rate (g)** = 4% = 0.04
3. **Required Return (r)** = 12% = 0.12

The dividend in year 6 (because we are interested in $ P_5 $, which depends on the dividend in year 6) can be found by growing the current dividend:

\[
D_6 = D_0 \times (1 + g)^6 = 2.20 \times (1 + 0.04)^6 = 2.20 \times 1.265319 = 2.783702
\]

Now, applying the Gordon Growth Model formula to find $ P_5 $:

\[
P_5 = \frac{D_6}{r - g} = \frac{2.783702}{0.12 - 0.04} = \frac{2.783702}{0.08} = 34.80
\]

### Final Answer:
The price of the stock in five years is **$34.80**.

Would you like more details or have any other questions?

Here are 5 related questions for practice:
1. How would the price change if the growth rate were 5% instead of 4%?
2. What would the stock price be if the required return were 10%?
3. How would the price change if the dividend payout were $3.00 instead of $2.20?
4. What is the present value of the stock today using the same parameters?
5. How does a higher growth rate affect the stock price in the Gordon Growth Model?

**Tip**: When solving finance problems involving growth models, always double-check that you are calculating dividends at the correct future time!

Suppose we are interested in the price of a stock in five years, P5. We just paid a dividend of $2.20 and the growth rate is 4%. The required return is 12%. What is the price of the stock in five years?

Learn how to calculate the price of a stock in five years using the Gordon Growth Model. The stock just paid a dividend of $2.20 with a growth rate of 4% and a required return of 12%. This finance problem involves key formulas in stock valuation and dividend discount models.

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