To find the value of the stock, we'll use the Dividend Discount Model (DDM), which accounts for the changing growth rates of dividends. We will determine the present value of the dividends over the first three years, and then calculate the present value of the terminal value, which is the value of all future dividends after the growth rate stabilizes to a perpetual growth rate.
Step 1: Calculate the expected dividends for the first three years.
Given:
- \( D_0 = 1.63 \) (the dividend just paid)
- Dividend growth rate for the first three years = 21.81%
We can calculate the dividends for years 1, 2, and 3.
- \( D_1 = D_0 \times (1 + g_1) = 1.63 \times (1 + 0.2181) = 1.63 \times 1.2181 \approx 1.9892 \)
- \( D_2 = D_1 \times (1 + g_1) = 1.9892 \times (1 + 0.2181) \approx 1.9892 \times 1.2181 \approx 2.4197 \)
- \( D_3 = D_2 \times (1 + g_1) = 2.4197 \times (1 + 0.2181) \approx 2.4197 \times 1.2181 \approx 2.9489 \)
Step 2: Calculate the terminal value at the end of Year 3.
After Year 3, the dividend grows at a perpetual growth rate of 4.39%. We can find the terminal value \( TV \) at the end of Year 3 using the Gordon Growth Model:
\[ TV_3 = \frac{D_4}{r - g_2} \]
Where:
- \( D_4 = D_3 \times (1 + g_2) = D_3 \times (1 + 0.0439) \approx 2.9489 \times 1.0439 \approx 3.0804 \)
- \( r \) is the required return calculated using CAPM: \[ r = r_f + \beta \times (r_m - r_f) = 3.26% + 1.50 \times 6.42% = 3.26% + 9.63% \approx 12.89% \] or as a decimal, \( r = 0.1289 \).
- \( g_2 = 0.0439 \) (perpetual growth rate).
Now calculate the terminal value: \[ TV_3 = \frac{3.0804}{0.1289 - 0.0439} = \frac{3.0804}{0.0850} \approx 36.235 \]
Step 3: Calculate the present value of the dividends and terminal value.
Now, we need to calculate the present value of the dividends and terminal value:
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Present Value of \( D_1 \): \[ PV(D_1) = \frac{D_1}{(1 + r)^1} = \frac{1.9892}{(1 + 0.1289)^1} \approx \frac{1.9892}{1.1289} \approx 1.7623 \]
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Present Value of \( D_2 \): \[ PV(D_2) = \frac{D_2}{(1 + r)^2} = \frac{2.4197}{(1.1289)^2} \approx \frac{2.4197}{1.2725} \approx 1.9016 \]
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Present Value of \( D_3 \): \[ PV(D_3) = \frac{D_3}{(1 + r)^3} = \frac{2.9489}{(1.1289)^3} \approx \frac{2.9489}{1.4367} \approx 2.0569 \]
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Present Value of Terminal Value \( TV_3 \): \[ PV(TV_3) = \frac{TV_3}{(1 + r)^3} = \frac{36.235}{(1.1289)^3} \approx \frac{36.235}{1.4367} \approx 25.1999 \]
Step 4: Calculate the total present value (stock value).
Now we add up the present values: \[ PV_{\text{total}} = PV(D_1) + PV(D_2) + PV(D_3) + PV(TV_3) \] \[ PV_{\text{total}} \approx 1.7623 + 1.9016 + 2.0569 + 25.1999 \approx 30.9207 \]
Final Answer
The estimated value of the stock is approximately $30.92.