To determine the value of the stock using the Dividend Discount Model (DDM) with variable growth rates, we need to follow these steps:
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Calculate the required rate of return (K) using CAPM: \[ K = \text{Risk-free rate} + \beta \times \text{Market risk premium} \] \[ K = 1.82% + 1.49 \times 8.38% \] \[ K = 1.82% + 12.48% \] \[ K = 14.30% \]
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Calculate the expected dividends for the next 5 years (D1 to D5): The first dividend just paid is \(D_0 = 1.49\). The expected growth rate for the next five years is 22.33%.
\[ D_1 = D_0 \times (1 + g_1) = 1.49 \times (1 + 0.2233) = 1.49 \times 1.2233 = 1.820
D_2 = D_1 \times (1 + g_1) = 1.820 \times 1.2233 = 2.223
D_3 = D_2 \times (1 + g_1) = 2.223 \times 1.2233 = 2.724
D_4 = D_3 \times (1 + g_1) = 2.724 \times 1.2233 = 3.329
D_5 = D_4 \times (1 + g_1) = 3.329 \times 1.2233 = 4.075 \]
So, we have: \[ D_1 \approx 1.82, \quad D_2 \approx 2.22, \quad D_3 \approx 2.72, \quad D_4 \approx 3.33, \quad D_5 \approx 4.08 \]
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Discount the expected dividends for the first 5 years back to present value: \[ PV(D_1) = \frac{D_1}{(1 + K)^1} = \frac{1.82}{(1 + 0.1430)^1} \approx \frac{1.82}{1.1430} \approx 1.59 \] \[ PV(D_2) = \frac{D_2}{(1 + K)^2} = \frac{2.22}{(1.1430)^2} \approx \frac{2.22}{1.3064} \approx 1.70 \] \[ PV(D_3) = \frac{D_3}{(1 + K)^3} = \frac{2.72}{(1.1430)^3} \approx \frac{2.72}{1.4947} \approx 1.82 \] \[ PV(D_4) = \frac{D_4}{(1 + K)^4} = \frac{3.33}{(1.1430)^4} \approx \frac{3.33}{1.7078} \approx 1.95 \] \[ PV(D_5) = \frac{D_5}{(1 + K)^5} = \frac{4.08}{(1.1430)^5} \approx \frac{4.08}{1.9476} \approx 2.10 \]
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Sum the present values of the dividends: \[ PV_{\text{dividends}} = PV(D_1) + PV(D_2) + PV(D_3) + PV(D_4) + PV(D_5) \] \[ PV_{\text{dividends}} \approx 1.59 + 1.70 + 1.82 + 1.95 + 2.10 \approx 9.16 \]
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Calculate the terminal value at the end of year 5 using the constant growth formula (Gordon Growth Model): The dividend growth rate after year 5 is 3.01%.
\[ D_6 = D_5 \times (1 + g_2) = 4.08 \times (1 + 0.0301) \approx 4.08 \times 1.0301 \approx 4.21 \]
The terminal value (TV) at the end of year 5 is: \[ TV = \frac{D_6}{K - g_2} = \frac{4.21}{0.1430 - 0.0301} = \frac{4.21}{0.1129} \approx 37.29 \]
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Discount the terminal value back to present value: \[ PV(TV) = \frac{TV}{(1 + K)^5} = \frac{37.29}{1.9476} \approx 19.17 \]
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Sum the present value of the dividends and the present value of the terminal value: \[ \text{Stock Value} = PV_{\text{dividends}} + PV(TV) \approx 9.16 + 19.17 \approx 28.33 \]
Thus, the estimated value of the stock is approximately $28.33.