Mariota Corporation just paid a dividend of $4.30 per share on its stock. The dividend growth rate is expected to be 3.2 forever and investors require a return of 13.6 percent on this stock. What will the stock price be in 14 years?

Multiple Choice

$64.26

$66.32

$11.13

$58.38

$50.71

To find the price of the stock in 14 years, we can use the **Dividend Discount Model (DDM)**, specifically the **Gordon Growth Model**. This model is used when dividends are expected to grow at a constant rate.

The formula 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 in year $ t+1 $,
- $ r $ is the required rate of return (investor's required return),
- $ g $ is the growth rate of the dividends.

### Step 1: Find the dividend in 14 years
The dividend just paid is $ D_0 = 4.30 $, and the dividend grows at a constant rate of $ g = 3.2\% $.

The dividend in 14 years, $ D_{14} $, can be calculated using the formula:

\[
D_{14} = D_0 \times (1 + g)^{14}
\]

Substituting the values:

\[
D_{14} = 4.30 \times (1 + 0.032)^{14} = 4.30 \times (1.032)^{14}
\]

\[
D_{14} \approx 4.30 \times 1.5633 = 6.721
\]

### Step 2: Calculate the stock price in 14 years
Now, we can use the Gordon Growth Model to find the stock price in 14 years:

\[
P_{14} = \frac{D_{15}}{r - g}
\]

Where $ D_{15} = D_{14} \times (1 + g) $:

\[
D_{15} = 6.721 \times 1.032 \approx 6.935
\]

Now, substitute $ D_{15} = 6.935 $, $ r = 13.6\% = 0.136 $, and $ g = 3.2\% = 0.032 $ into the Gordon Growth Model:

\[
P_{14} = \frac{6.935}{0.136 - 0.032} = \frac{6.935}{0.104}
\]

\[
P_{14} \approx 66.68
\]

### Conclusion:
The closest value among the options provided is **$66.32**.

So, the correct answer is **$66.32**.

Would you like further details on any steps or have any questions?

Here are 5 related questions for practice:
1. How would the stock price change if the dividend growth rate increased to 4%?
2. What would happen to the stock price if the required return dropped to 12%?
3. How would the stock price in year 14 change if the initial dividend was $5.00 instead of $4.30?
4. What would the stock price be today using the same data?
5. If dividends were expected to grow at a decreasing rate over time, how would that affect the stock price?

**Tip**: In the Gordon Growth Model, a small change in the growth rate or required return can lead to significant changes in the stock price, so these inputs must be estimated carefully.

Mariota Corporation just paid a dividend of $4.30 per share on its stock. The dividend growth rate is expected to be 3.2 forever and investors require a return of 13.6 percent on this stock. What will the stock price be in 14 years?

Calculate the stock price of Mariota Corporation 14 years from now using the Gordon Growth Model. This problem involves the dividend discount model, exponential growth, and financial calculations. The dividend is $4.30, with a 3.2% growth rate, and a required return of 13.6%.

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