The Bell Weather Company is a new firm in a rapidly growing industry. The company is planning on increasing its annual dividend by 15 percent a year for the next 4 years and then decreasing the growth rate to 4 percent per year. The company just paid its annual dividend in the amount of $1.50 per share. What is the current value of one share of this stock if the required rate of return is 7.00 percent?

Multiple Choice

$69.38

$78.09

$76.59

$90.95

$92.45

To determine the current value of one share of Bell Weather Company stock, we can apply the **dividend discount model (DDM)**, especially given the change in growth rate over time. This involves discounting each expected dividend to its present value, and then calculating the stock’s terminal value from year 4 onwards with the perpetual growth formula.

### Given:
- Initial dividend, $ D_0 = 1.50 $
- Initial high growth rate, $ g_1 = 15\% $ for the first 4 years
- Long-term growth rate, $ g_2 = 4\% $ from year 5 onwards
- Required rate of return, $ r = 7\% $

### Solution Steps:
1. **Calculate Dividends for the First 4 Years (15% growth rate):**
   - Year 1 dividend: $ D_1 = D_0 \times (1 + g_1) = 1.50 \times 1.15 = 1.725 $
   - Year 2 dividend: $ D_2 = D_1 \times (1 + g_1) = 1.725 \times 1.15 = 1.98375 $
   - Year 3 dividend: $ D_3 = D_2 \times (1 + g_1) = 1.98375 \times 1.15 = 2.2813125 $
   - Year 4 dividend: $ D_4 = D_3 \times (1 + g_1) = 2.2813125 \times 1.15 = 2.623509375 $

2. **Calculate the Terminal Value at the End of Year 4 (Using the 4% Long-term Growth Rate):**
   The terminal value, $ TV_4 $, is the present value of all dividends from year 5 onward:
   \[
   TV_4 = \frac{D_5}{r - g_2} = \frac{D_4 \times (1 + g_2)}{r - g_2}
   \]
   - $ D_5 = D_4 \times (1 + g_2) = 2.623509375 \times 1.04 = 2.72844975 $
   - Substitute values to find $ TV_4 $:
     \[
     TV_4 = \frac{2.72844975}{0.07 - 0.04} = \frac{2.72844975}{0.03} = 90.948325
     \]

3. **Calculate the Present Value of Each Dividend and Terminal Value:**
   Using the required rate of return (7%), discount each dividend back to the present value:
   \[
   PV(D_1) = \frac{1.725}{(1.07)^1} = 1.61215
   \]
   \[
   PV(D_2) = \frac{1.98375}{(1.07)^2} = 1.73244
   \]
   \[
   PV(D_3) = \frac{2.2813125}{(1.07)^3} = 1.86506
   \]
   \[
   PV(D_4) = \frac{2.623509375}{(1.07)^4} = 1.99996
   \]
   \[
   PV(TV_4) = \frac{90.948325}{(1.07)^4} = 69.3845
   \]

4. **Sum the Present Values:**
   \[
   \text{Current Value of Stock} = PV(D_1) + PV(D_2) + PV(D_3) + PV(D_4) + PV(TV_4)
   \]
   \[
   = 1.61215 + 1.73244 + 1.86506 + 1.99996 + 69.3845 = 76.5941
   \]

### Answer:
The current value of one share of Bell Weather Company stock is approximately **$76.59**.

### Correct Choice:
**$76.59**

---

Would you like further details on any part of this calculation or have questions about different dividend growth models?

Here are some questions that might further your understanding:
1. What are other types of dividend discount models used for valuing stocks?
2. How would the stock value change if the required rate of return increased?
3. How sensitive is the stock value to changes in the growth rates?
4. Can this model be applied to companies that do not pay dividends?
5. What alternative valuation models are available for high-growth companies?

**Tip:** When dealing with changing growth rates, always calculate dividends for each phase separately before moving to a perpetuity assumption.

Explore how to calculate the current value of Bell Weather Company's stock using a multi-phase Dividend Discount Model. This problem includes initial 15% dividend growth followed by a long-term 4% growth rate, with a required 7% rate of return. This example demonstrates advanced financial valuation techniques suitable for Grades 11-12 and college students.

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