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Michael's Incorporated, just paid $2.55 to its shareholders as the annual dividend. Simultaneously, the company announced that future dividends will be increasing by 5.5 percent. If you require a rate of return of 9.7 percent, how much are you willing to pay today to purchase one share of the company's stock?

To find out how much you would be willing to pay today to purchase one share of Michael's Incorporated stock, we can use the **Dividend Discount Model (DDM)** for a growing dividend, also known as the **Gordon Growth Model**. The formula is:

\[
P_0 = \frac{D_1}{r - g}
\]

Where:
- $ P_0 $ = Current price of the stock
- $ D_1 $ = Dividend expected next year
- $ r $ = Required rate of return
- $ g $ = Growth rate of the dividend

### Step 1: Calculate $ D_1 $
The dividend expected next year ($ D_1 $) is the current dividend ($ D_0 $) multiplied by $ (1 + g) $.

\[
D_1 = D_0 \times (1 + g)
\]

Given:
- $ D_0 = 2.55 $ (current dividend)
- $ g = 5.5\% = 0.055 $

\[
D_1 = 2.55 \times (1 + 0.055) = 2.55 \times 1.055 = 2.68875
\]

### Step 2: Calculate $ P_0 $
Now, use the Gordon Growth Model formula to calculate $ P_0 $:

\[
P_0 = \frac{2.68875}{0.097 - 0.055} = \frac{2.68875}{0.042} \approx 64.02
\]

### Conclusion:
You should be willing to pay approximately **$64.02** today to purchase one share of Michael's Incorporated stock.

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

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Here are 5 related questions to further your understanding:

1. How does the required rate of return affect the price you are willing to pay for a stock?
2. What would happen to the stock price if the dividend growth rate increased?
3. How would the stock price change if the required rate of return decreased?
4. What assumptions does the Gordon Growth Model make about dividend growth and its sustainability?
5. Can the Gordon Growth Model be used for stocks with highly volatile dividends? Why or why not?

**Tip:** The Gordon Growth Model works best for companies with stable and predictable dividend growth rates.

Learn how to calculate the current price of Michael's Incorporated stock using the Dividend Discount Model (DDM). This problem involves determining the stock price based on a growing dividend rate, with specific data such as annual dividend, growth rate, and required rate of return. Suitable for advanced learners and investors.

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