Computech Corporation is expanding rapidly and currently needs to retain all of its earnings; hence, it does not pay dividends. However, investors expect Computech to begin paying dividends, beginning with a dividend of $1.00 coming 3 years from today. The dividend should grow rapidly—at a rate of 31% per year—during Years 4 and 5, but after Year 5, growth should be a constant 8% per year. If the required return on Computech is 18%, what is the value of the stock today? Do not round intermediate calculations. Round your answer to the nearest cent.

To find the value of Computech Corporation's stock today, we can use the Dividend Discount Model (DDM) for stocks with varying dividend growth rates. Specifically, we'll apply a two-stage dividend growth model, where:

1. The first stage involves rapid growth of dividends (for years 3 through 5).
2. The second stage involves constant growth after year 5.

Here's how we can break down the calculation:

### Step 1: Determine the dividends for the first five years
- Dividend at the end of Year 3: $ D_3 = 1.00 $ (given)
- Dividend at the end of Year 4: $ D_4 = D_3 \times (1 + 0.31) = 1.00 \times 1.31 = 1.31 $
- Dividend at the end of Year 5: $ D_5 = D_4 \times (1 + 0.31) = 1.31 \times 1.31 = 1.7141 $

### Step 2: Calculate the dividend at the end of Year 6, where growth becomes constant
- Dividend at the end of Year 6: $ D_6 = D_5 \times (1 + 0.08) = 1.7141 \times 1.08 = 1.85123 $

### Step 3: Calculate the stock price at the end of Year 5 (start of constant growth phase)
We can calculate the price of the stock at the end of Year 5, using the constant growth model, since dividends will grow at a constant rate of 8% after Year 5.

The formula for the price at Year 5 is:

\[
P_5 = \frac{D_6}{r - g}
\]

Where:
- $ D_6 = 1.85123 $
- $ r = 0.18 $ (required return)
- $ g = 0.08 $ (constant growth rate)

\[
P_5 = \frac{1.85123}{0.18 - 0.08} = \frac{1.85123}{0.10} = 18.5123
\]

### Step 4: Calculate the present value of dividends and stock price
Now, we'll calculate the present value of each dividend (from Years 3 to 5) and the stock price at the end of Year 5, discounting them back to today using the required return of 18%.

The present value formula for each cash flow is:

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

Where $ D_t $ is the dividend in year $ t $, and $ r = 0.18 $.

- Present value of $ D_3 = \frac{1.00}{(1.18)^3} = \frac{1.00}{1.597} = 0.62622 $
- Present value of $ D_4 = \frac{1.31}{(1.18)^4} = \frac{1.31}{1.8852} = 0.69484 $
- Present value of $ D_5 = \frac{1.7141}{(1.18)^5} = \frac{1.7141}{2.2257} = 0.77036 $
- Present value of $ P_5 = \frac{18.5123}{(1.18)^5} = \frac{18.5123}{2.2257} = 8.32002 $

### Step 5: Calculate the total present value (stock price today)

The total value of the stock today is the sum of the present values of the dividends and the present value of the stock price at the end of Year 5:

\[
\text{Stock Price Today} = 0.62622 + 0.69484 + 0.77036 + 8.32002 = 10.41144
\]

So, the value of the stock today is **$10.41**.

---

Would you like more details or have any questions?

Here are some related questions:

1. How would the stock price change if the required return increased to 20%?
2. What happens to the stock price if dividend growth is constant from Year 3 instead of Year 6?
3. How does a change in the initial dividend ($1.00) affect the stock valuation?
4. What is the impact of a different constant growth rate after Year 5 on the stock price?
5. How does the rapid growth in dividends during Years 4 and 5 affect the stock price compared to a steady growth?

**Tip:** When valuing stocks with multiple growth phases, it's essential to discount each cash flow back to the present based on its timing.

Calculate the present value of Computech Corporation's stock based on dividend growth of 31% for Years 4 and 5, and a constant 8% growth thereafter. This step-by-step solution uses the Dividend Discount Model and shows how to discount dividends and stock price to find the stock's value today with an 18% required return.

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