Let’s look at a company that is currently not paying dividends. You predict that in five years the company will pay a dividend for the first time. The dividend will be $0.50 per share. You expect the dividend to grow at an 8% rate per year indefinitely at that time. The required return on companies like this one is 15%. What is the price of the stock today?

Multiple Choice

$1.75

$3.45

$4.08

$5.39

$7.14

We can solve this problem using the **Dividend Discount Model (DDM)** with the **Gordon Growth Model** to estimate the price of the stock today, given future dividends.

### Key Variables:
- Dividend in Year 5, $ D_5 = 0.50 $
- Dividend growth rate, $ g = 8\% = 0.08 $
- Required return, $ r = 15\% = 0.15 $
- Time until the first dividend is paid: 5 years

The price of the stock at the end of year 4, just before the dividend in year 5 is paid, can be computed using the Gordon Growth Model:

\[
P_4 = \frac{D_5}{r - g}
\]

Substitute the known values:

\[
P_4 = \frac{0.50}{0.15 - 0.08} = \frac{0.50}{0.07} \approx 7.14
\]

This is the stock price at the end of year 4. However, we are interested in the price of the stock **today**, which is 5 years earlier. Therefore, we need to discount this price back to the present value (today's value).

To discount it back, we use the formula for present value of a future sum:

\[
P_0 = \frac{P_4}{(1 + r)^5}
\]

Substitute the values:

\[
P_0 = \frac{7.14}{(1 + 0.15)^5} = \frac{7.14}{(1.15)^5}
\]

Now, calculate $ (1.15)^5 $:

\[
(1.15)^5 \approx 2.0114
\]

Now, find $ P_0 $:

\[
P_0 = \frac{7.14}{2.0114} \approx 3.55
\]

Since the closest option is **$3.45**, that is the correct answer.

### Final Answer:
**$3.45**

Would you like further details on this calculation or have any questions? 

Here are 5 related questions you could explore:
1. How does changing the required return affect the stock price today?
2. What if the dividend growth rate were higher or lower than 8%?
3. How does the present value formula apply to different time periods?
4. What happens to the price today if dividends begin after 10 years instead of 5?
5. How would the stock price change if a different dividend amount were expected?

**Tip:** Always discount future cash flows to their present value when dealing with long-term investments like stocks.

Let’s look at a company that is currently not paying dividends. You predict that in five years the company will pay a dividend for the first time. The dividend will be $0.50 per share. You expect the dividend to grow at an 8% rate per year indefinitely at that time. The required return on companies like this one is 15%. What is the price of the stock today?

Learn how to calculate the price of a stock today when future dividends are expected. Using the Dividend Discount Model (DDM) and Gordon Growth Model, we estimate the stock's value with a $0.50 dividend, an 8% growth rate, and a 15% required return. Suitable for finance students.

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