To calculate the value of the stock using the two-stage dividend discount model, we need to use the formula:
\[ \text{Stock Value} = \frac{D_0 \times (1 + g_1)}{r - g_1} + \frac{D_0 \times (1 + g_1) \times (1 + g_2)}{(1 + r)^2 \times (r - g_2)} \]
Where:
- \( D_0 \) = current dividend per share = $1.30
- \( g_1 \) = first-stage growth rate = 18% or 0.18
- \( g_2 \) = second-stage growth rate = 9% or 0.09
- \( r \) = discount rate = 11% or 0.11
Let's plug in the values:
\[ \text{Stock Value} = \frac{1.30 \times (1 + 0.18)}{0.11 - 0.18} + \frac{1.30 \times (1 + 0.18) \times (1 + 0.09)}{(1 + 0.11)^2 \times (0.11 - 0.09)} \]
\[ \text{Stock Value} = \frac{1.30 \times 1.18}{-0.07} + \frac{1.30 \times 1.18 \times 1.09}{(1.11)^2 \times 0.02} \]
\[ \text{Stock Value} = \frac{1.534}{-0.07} + \frac{1.6617}{0.0242} \]
\[ \text{Stock Value} = -21.914 + 68.666 \]
\[ \text{Stock Value} = $46.752 \]
So, the value of the stock is approximately $46.75.
