To find the value of the stock, we will use the Dividend Discount Model (DDM), which involves estimating the future dividends and discounting them to their present value. We'll follow these steps:
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Calculate the Dividends for the First Three Years:
- The most recent dividend (D₀) is $2.59.
- The growth rate for the first three years (g₁) is 26.84%.
The dividends for the next three years (D₁, D₂, D₃) can be calculated as follows:
- \( D_1 = D_0 \times (1 + g_1) = 2.59 \times (1 + 0.2684) = 2.59 \times 1.2684 \approx 3.29 \)
- \( D_2 = D_1 \times (1 + g_1) = 3.29 \times (1 + 0.2684) \approx 3.29 \times 1.2684 \approx 4.17 \)
- \( D_3 = D_2 \times (1 + g_1) = 4.17 \times (1 + 0.2684) \approx 4.17 \times 1.2684 \approx 5.29 \)
Therefore, the estimated dividends are:
- \( D_1 \approx 3.29 \)
- \( D_2 \approx 4.17 \)
- \( D_3 \approx 5.29 \)
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Calculate the Dividend Beyond Year 3:
- The growth rate after the first three years (g₂) is 4.02%.
- The dividend in year 4 (D₄) will grow at this rate:
- \( D_4 = D_3 \times (1 + g_2) = 5.29 \times (1 + 0.0402) \approx 5.29 \times 1.0402 \approx 5.50 \)
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Calculate the Present Value of Dividends for the First Three Years:
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The required return (r) is 13.97%.
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The present values for the dividends are calculated using the formula \( PV = \frac{D}{(1 + r)^t} \):
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\( PV(D_1) = \frac{3.29}{(1 + 0.1397)^1} = \frac{3.29}{1.1397} \approx 2.89 \)
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\( PV(D_2) = \frac{4.17}{(1 + 0.1397)^2} = \frac{4.17}{1.3002} \approx 3.21 \)
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\( PV(D_3) = \frac{5.29}{(1 + 0.1397)^3} = \frac{5.29}{1.4770} \approx 3.58 \)
Sum of present values for the first three years: \[ PV_{1-3} = PV(D_1) + PV(D_2) + PV(D_3) \approx 2.89 + 3.21 + 3.58 = 9.68 \]
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Calculate the Present Value of All Future Dividends Beyond Year 3:
- Calculate the terminal value at the end of year 3 using the Gordon Growth Model: \[ TV = \frac{D_4}{r - g_2} = \frac{5.50}{0.1397 - 0.0402} = \frac{5.50}{0.0995} \approx 55.29 \]
- Now discount this terminal value back to the present value: \[ PV(TV) = \frac{55.29}{(1 + 0.1397)^3} \approx \frac{55.29}{1.4770} \approx 37.47 \]
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Calculate the Total Present Value of the Stock:
- Combine the present values of the dividends for the first three years and the present value of the terminal value: \[ PV_{total} = PV_{1-3} + PV(TV) \approx 9.68 + 37.47 = 47.15 \]
Therefore, the calculated value of the stock is approximately $47.15.