Brickhouse is expected to pay a dividend of $3.10 and $2.44 over the next two years, respectively. After that, the company is expected to increase its annual dividend at 3.8 percent. What is the stock price today if the required return is 11.2 percent?

To determine the stock price today given the expected dividends over the next two years and the perpetual growth of dividends after that, we can use a multi-stage Dividend Discount Model. Here's how we can solve it:

### Step 1: Present Value of Dividends for the First Two Years

We need to calculate the present value of the dividends for the first two years.

Given:
- $ D_1 = 3.10 $ (Dividend in Year 1)
- $ D_2 = 2.44 $ (Dividend in Year 2)
- $ r = 11.2\% = 0.112 $ (Required return)

The present value of the dividends is calculated using the formula:

\[
PV = \frac{D_1}{(1 + r)} + \frac{D_2}{(1 + r)^2}
\]

\[
PV = \frac{3.10}{(1 + 0.112)} + \frac{2.44}{(1 + 0.112)^2}
\]

\[
PV = \frac{3.10}{1.112} + \frac{2.44}{1.237344}
\]

\[
PV = 2.7887 + 1.9723 = 4.761
\]

### Step 2: Calculate the Price at the End of Year 2

After the first two years, the dividend is expected to grow at a constant rate of 3.8%. We can use the Gordon Growth Model to find the price at the end of Year 2 (which we'll call $ P_2 $):

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

Where:
- $ D_3 = D_2 \times (1 + g) $
- $ g = 3.8\% = 0.038 $

\[
D_3 = 2.44 \times (1 + 0.038) = 2.44 \times 1.038 = 2.53272
\]

\[
P_2 = \frac{2.53272}{0.112 - 0.038} = \frac{2.53272}{0.074} = 34.2286
\]

### Step 3: Present Value of $ P_2 $

Now, we need to discount $ P_2 $ back to the present value (at time $ t = 0 $):

\[
PV(P_2) = \frac{34.2286}{(1 + 0.112)^2} = \frac{34.2286}{1.237344} = 27.661
\]

### Step 4: Calculate the Total Stock Price Today

Finally, we sum the present value of the dividends for the first two years and the present value of $ P_2 $ to get the current stock price:

\[
P_0 = PV(Dividends) + PV(P_2)
\]

\[
P_0 = 4.761 + 27.661 = 32.422
\]

### Conclusion:
The stock price today would be approximately **$32.42**.

Would you like more details, or do you have any questions?

---

Here are 5 related questions to explore further:

1. How would the stock price change if the dividend growth rate after Year 2 was higher?
2. What impact does increasing the required return have on the current stock price?
3. How would you calculate the stock price if dividends were expected to decline instead of grow after Year 2?
4. Can the Dividend Discount Model be used for companies that don't pay dividends? Why or why not?
5. What are some limitations of the Dividend Discount Model in valuing stocks?

**Tip:** Multi-stage dividend discount models are useful when a company's dividend growth is expected to change significantly in the future.

Learn how to calculate the stock price today using dividend growth projections. This detailed guide includes step-by-step calculations for present value of dividends, Gordon Growth Model application, and required return considerations. Suitable for finance professionals and advanced learners.

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