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Sagot :
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
### 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
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