To determine the price of RLX Co.’s stock at different future years given the provided information, we will utilize the Gordon Growth Model (also known as the Dividend Discount Model for a constantly growing dividend). This model is designed to calculate the present value of an infinite series of future dividends that grow at a constant rate.
### Key Information:
- Dividend just paid ([tex]\(D_0\)[/tex]): \[tex]$3.20
- Dividend growth rate (\(g\)): 4% or 0.04 annually
- Required return (\(r\)): 10.5% or 0.105 annually
- Years to find the stock prices for: 2 years, 3 years, and 15 years
### Steps to Determine the Stock Price:
1. Calculate the Dividend for the Given Year \(t\):
The dividend in year \(t\) (\(D_t\)) can be calculated using the formula:
\[ D_t = D_0 \times (1 + g)^t \]
2. Calculate the Stock Price for the Year \(t\):
Using Gordon Growth Model, the price of the stock in year \(t\) (\(P_t\)) can be calculated as:
\[ P_t = \frac{D_t}{r - g} \]
where:
- \(D_t\) = Dividend in year \(t\)
- \(r\) = Required return (0.105)
- \(g\) = Growth rate (0.04)
### Calculate the Stock Price in 2 Years:
1. Calculate \(D_2\):
\[ D_2 = 3.20 \times (1 + 0.04)^2 = 3.20 \times 1.0816 = 3.4592 \]
2. Calculate \(P_2\):
\[ P_2 = \frac{3.4592}{0.105 - 0.04} = \frac{3.4592}{0.065} = 53.248 \]
### Calculate the Stock Price in 3 Years:
1. Calculate \(D_3\):
\[ D_3 = 3.20 \times (1 + 0.04)^3 = 3.20 \times 1.124864 = 3.5995648 \]
2. Calculate \(P_3\):
\[ P_3 = \frac{3.5995648}{0.105 - 0.04} = \frac{3.5995648}{0.065} = 55.37792 \]
### Calculate the Stock Price in 15 Years:
1. Calculate \(D_{15}\):
\[ D_{15} = 3.20 \times (1 + 0.04)^{15} = 3.20 \times 1.802832743 = 5.7690641536 \]
2. Calculate \(P_{15}\):
\[ P_{15} = \frac{5.7690641536}{0.105 - 0.04} = \frac{5.7690641536}{0.065} = 88.6618341172636 \]
### Summary of Stock Prices:
- Price in 2 years: \$[/tex]53.248
- Price in 3 years: \[tex]$55.37792
- Price in 15 years: \$[/tex]88.6618341172636
