Assume Gillette Corporation will pay an annual dividend of $ 0.64 one year from now. Analysts expect this dividend to grow at 12.9 % per year thereafter until the 2th year.​ Thereafter, growth will level off at 2.4 % per year. According to the​ dividend-discount model, what is the value of a share of Gillette stock if the​ firm's equity cost of capital is 7.8 %​?


To value the share of Gillette Corporation stock using the **dividend-discount model (DDM)**, we use the **two-stage growth model** due to the changing growth rates at different periods.

### Given:
- **Dividend at Year 1** ($D_1$) = $0.64
- **First growth rate** ($g_1$) = 12.9% per year until the 2nd year (two years of higher growth).
- **Second growth rate** ($g_2$) = 2.4% per year (constant growth from Year 3 onward).
- **Equity cost of capital** ($r$) = 7.8%.

### Step 1: Calculate Dividends for Years 1, 2, and beyond

The dividend grows at 12.9% for the first two years:

- **Dividend in Year 2** ($D_2$) = $ D_1 \times (1 + g_1) = 0.64 \times (1 + 0.129) $
- **Dividend in Year 3** ($D_3$) = $ D_2 \times (1 + g_1) = D_2 \times 1.129 $

Then, from Year 3 onward, the dividend grows at a constant 2.4%. 

- **Dividend in Year 4** ($D_4$) = $ D_3 \times (1 + g_2) = D_3 \times (1.024) $

### Step 2: Calculate the Present Value of Dividends for Years 1 and 2

For the dividends in the first two years, we discount them back to the present using the equity cost of capital:

- Present value of $D_1$ = $ \frac{D_1}{(1 + r)} $
- Present value of $D_2$ = $ \frac{D_2}{(1 + r)^2} $

### Step 3: Calculate the Terminal Value at Year 2

Starting in Year 3, the dividend grows at a constant rate of 2.4%. We can calculate the **present value of all dividends from Year 3 onward** using the constant-growth formula (Gordon Growth Model) at Year 2:

\[
\text{Terminal Value at Year 2} = \frac{D_3}{r - g_2}
\]

This gives the value of all dividends starting from Year 3, discounted to Year 2. We then discount this terminal value back to the present.

### Step 4: Sum of Present Values

Finally, we sum the present values of the dividends from Year 1, Year 2, and the terminal value.

Let's now calculate these steps numerically.The value of a share of Gillette Corporation stock, according to the dividend-discount model, is approximately **$14.22**.

Would you like further clarification or details on any step? Here are some related questions to deepen your understanding:

1. How does the dividend-discount model account for fluctuating growth rates?
2. What assumptions underlie the use of the Gordon Growth Model for constant dividend growth?
3. How sensitive is the stock price to changes in the equity cost of capital?
4. What impact does a higher long-term growth rate have on the stock's value?
5. How do inflation and real interest rates affect the required return on equity?

**Tip:** Always ensure that growth rates in the dividend-discount model are less than the cost of capital for the formula to make sense mathematically.

Assume Gillette Corporation will pay an annual dividend of $ 0.64 one year from now. Analysts expect this dividend to grow at 12.9 % per year thereafter until the 2nd year.​ Thereafter, growth will level off at 2.4 % per year. According to the​ dividend-discount model, what is the value of a share of Gillette stock if the​ firm's equity cost of capital is 7.8 %​?

Learn how to value Gillette stock using the dividend-discount model. This detailed solution explores the two-stage growth model, calculating the value with dividends growing at 12.9% for the first two years and leveling at 2.4% after. The solution incorporates key financial concepts like present value of dividends and the Gordon Growth Model.

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