A firm does not pay a dividend. It is expected to pay its first dividend of $0.36 per share in three years. This dividend will grow at 8 percent indefinitely. Use a 9 percent discount rate.

Compute the value of this stock.

To compute the value of the stock today, we will use the **Dividend Discount Model (DDM)** for a stock that will begin paying dividends in the future and grow indefinitely at a constant rate. The steps for this problem are as follows:

### Step 1: Calculate the value of the stock at the time the first dividend is paid.
The dividend growth formula, known as the **Gordon Growth Model**, is used to find the stock value at the time the dividends start. This model is given by:

\[
P_2 = \frac{D_3}{r - g}
\]

Where:
- $P_2$ = Stock price at time $t=2$ (right before the first dividend is paid in year 3),
- $D_3 = 0.36$ = The first dividend to be paid at year 3,
- $r = 9\%$ or 0.09 = Discount rate (required rate of return),
- $g = 8\%$ or 0.08 = Growth rate of the dividends.

So, we compute $P_2$ as:

\[
P_2 = \frac{0.36}{0.09 - 0.08} = \frac{0.36}{0.01} = 36
\]

Thus, the stock price at the end of year 2 is $36.

### Step 2: Discount this stock price to the present value (time $t = 0$).
Since the stock price calculated above is the price at the end of year 2, we need to discount it back to today (present value at $t = 0$). The formula for discounting a future value is:

\[
PV = \frac{FV}{(1 + r)^t}
\]

Where:
- $FV = 36$ (the stock price at the end of year 2),
- $r = 9\%$ or 0.09 (the discount rate),
- $t = 2$ (since the stock price is at year 2).

Now, we discount $P_2$ to the present value:

\[
PV = \frac{36}{(1 + 0.09)^2} = \frac{36}{1.09^2} = \frac{36}{1.1881} \approx 30.30
\]

### Conclusion:
The present value of the stock today is approximately **$30.30**.

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:
1. What if the growth rate changes after 10 years?
2. How would the stock value change with a higher discount rate?
3. What if the firm delays the first dividend to year 5?
4. How do we calculate stock price if dividends grow at a variable rate?
5. What happens to stock valuation when there is no expected growth?

**Tip:** Always ensure the growth rate is lower than the discount rate in the Gordon Growth Model for the formula to work properly.

A firm does not pay a dividend. It is expected to pay its first dividend of $0.36 per share in three years. This dividend will grow at 8 percent indefinitely. Use a 9 percent discount rate. Compute the value of this stock.

Compute the value of a stock expected to pay its first dividend of $0.36 in three years, growing indefinitely at 8%, with a 9% discount rate. This detailed solution walks through the Dividend Discount Model (DDM) and Present Value calculations, ideal for finance students.

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