To find the value of the stock, we will use the Dividend Discount Model (DDM) to calculate the present value of future dividends. The dividends will grow at two different rates: 21.50% for the first three years and then 4.84% thereafter.
Step 1: Calculate the expected dividends for the first three years.
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Year 1 Dividend (D1): \[ D1 = D0 \times (1 + g_1) = 2.03 \times (1 + 0.215) = 2.03 \times 1.215 = 2.47 \]
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Year 2 Dividend (D2): \[ D2 = D1 \times (1 + g_1) = 2.47 \times (1 + 0.215) = 2.47 \times 1.215 = 3.00 \]
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Year 3 Dividend (D3): \[ D3 = D2 \times (1 + g_1) = 3.00 \times (1 + 0.215) = 3.00 \times 1.215 = 3.65 \]
Step 2: Calculate the expected dividend at the end of Year 3, when the dividend will start to grow at the lower rate of 4.84%.
- Year 4 Dividend (D4): \[ D4 = D3 \times (1 + g_2) = 3.65 \times (1 + 0.0484) = 3.65 \times 1.0484 = 3.83 \]
Step 3: Calculate the present value of the dividends for the first three years (D1, D2, D3).
The present value of each dividend is calculated using the formula: \[ PV = \frac{D_t}{(1 + r)^t} \] where \( D_t \) is the dividend at time \( t \), \( r \) is the required return (13.06% or 0.1306), and \( t \) is the year.
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PV of D1: \[ PV(D1) = \frac{2.47}{(1 + 0.1306)^1} = \frac{2.47}{1.1306} \approx 2.18 \]
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PV of D2: \[ PV(D2) = \frac{3.00}{(1 + 0.1306)^2} = \frac{3.00}{1.2764} \approx 2.35 \]
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PV of D3: \[ PV(D3) = \frac{3.65}{(1 + 0.1306)^3} = \frac{3.65}{1.4436} \approx 2.53 \]
Now, add the present values of the first three dividends: \[ PV(First 3 Years) = PV(D1) + PV(D2) + PV(D3) \approx 2.18 + 2.35 + 2.53 \approx 7.06 \]
Step 4: Calculate the present value of all dividends from year 4 onward.
Starting from year 4, we will treat D4 as a perpetuity that grows at 4.84%. The formula for the present value of a perpetuity is: \[ PV = \frac{D}{r - g} \]
Where:
- \( D \) is the dividend in Year 4 (\( D4 = 3.83 \)),
- \( r \) is the required return (0.1306),
- \( g \) is the growth rate (0.0484).
Calculating the present value from Year 4 onward:
\[ PV = \frac{3.83}{0.1306 - 0.0484} = \frac{3.83}{0.0822} \approx 46.56 \]
To find the present value of this amount, we must discount it back to the present (Year 0):
\[ PV(Terminal Value) = \frac{46.56}{(1 + 0.1306)^3} = \frac{46.56}{1.4436} \approx 32.29 \]
Step 5: Add the present values together.
Finally, the total present value of the stock is: \[ Value_{Stock} = PV(First 3 Years) + PV(Terminal Value) \approx 7.06 + 32.29 \approx 39.35 \]
**Value of the stock is approximately **$39.35.
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