Felonius Inc. has just paid a dividend of $1.23 per share. The firm pays annual dividends, and analysts do not expect any changes in the payout ratio of the firm. It is expected by analysts that the earnings of Felonius will grow by 9% per year over the next five years. After that, the earnings will most likely grow at the current industry average of 4.5% per year. The cost of capital is 12.0%. What is Felonius’s share price?

To determine the share price of Felonius Inc. using the **Dividend Discount Model (DDM)**, we need to account for two stages of dividend growth: one for the next five years (with growth at 9%) and another after that (with growth at 4.5%).

### Step 1: Identify the given variables
- **Dividend just paid (D₀):** $1.23
- **Growth rate for the first 5 years (g₁):** 9% or 0.09
- **Growth rate after 5 years (g₂):** 4.5% or 0.045
- **Cost of capital (r):** 12% or 0.12

### Step 2: Calculate the dividends for the next 5 years
We use the formula to calculate the dividend for each year in the first stage:

\[
D_t = D₀ \times (1 + g₁)^t
\]

Where $ D_t $ is the dividend at year $ t $, and $ t $ is 1, 2, 3, 4, and 5.

### Step 3: Calculate the terminal value at the end of year 5
After year 5, the dividend grows at a constant rate of 4.5%. The terminal value (price of the stock at the end of year 5) is calculated using the Gordon Growth Model:

\[
\text{Terminal value} = \frac{D_6}{r - g_2}
\]

Where $ D_6 $ is the dividend in year 6 (the first dividend after the transition to the lower growth rate), calculated as:

\[
D_6 = D_5 \times (1 + g₂)
\]

### Step 4: Discount all future cash flows to the present value
We need to discount each dividend and the terminal value to present value using the formula:

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

### Step 5: Solve for the present value of the share price
Let's proceed with these calculations.# Given variables
D0 = 1.23  # dividend just paid
g1 = 0.09  # growth rate for the first 5 years
g2 = 0.045  # growth rate after 5 years
r = 0.12  # cost of capital
n = 5  # first stage period (5 years)

# Step 2: Calculate dividends for the next 5 years
dividends = [(D0 * (1 + g1)**t) for t in range(1, n + 1)]

# Step 3: Calculate terminal value at the end of year 5
D5 = dividends[-1]  # dividend in year 5
D6 = D5 * (1 + g2)  # dividend in year 6
terminal_value = D6 / (r - g2)  # terminal value at year 5

# Step 4: Discount all future cash flows (dividends and terminal value) to present value
# Discount dividends for the next 5 years
present_value_dividends = [dividends[t-1] / (1 + r)**t for t in range(1, n + 1)]

# Discount terminal value to present value
present_value_terminal_value = terminal_value / (1 + r)**n

# Step 5: Calculate the present value of the stock (sum of all PVs)
share_price = sum(present_value_dividends) + present_value_terminal_value
share_priceThe estimated share price of Felonius Inc. is approximately **$20.64**.

Would you like further clarification or additional details? Here are some related questions:

1. What factors influence the cost of capital in a dividend discount model?
2. How would a change in growth rates affect the share price?
3. What is the difference between the Gordon Growth Model and the two-stage DDM?
4. How does dividend payout stability impact stock valuation?
5. Can the Dividend Discount Model be applied to non-dividend-paying stocks?

**Tip:** In a two-stage dividend discount model, the stock price is more sensitive to changes in the long-term growth rate than the short-term rate.

Learn how to calculate Felonius Inc.'s share price using the Dividend Discount Model (DDM). Includes step-by-step calculations based on dividend growth rates, cost of capital, and terminal value. Estimated share price is $20.64.

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