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.