To find the value of the stock based on its dividends, we can use the Dividend Discount Model (DDM), which accounts for the expected dividends and their growth.
Step 1: Calculate the Expected Dividends
- D0: The most recent dividend paid is $2.10.
- Growth Rate for Years 1 and 2: 24.62%
The expected dividends for the next two years (D1 and D2) are calculated as follows:
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D1 (dividend for Year 1): \[ D1 = D0 \times (1 + \text{growth rate for Year 1}) = 2.10 \times (1 + 0.2462) \approx 2.10 \times 1.2462 \approx 2.6150 \]
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D2 (dividend for Year 2): \[ D2 = D1 \times (1 + \text{growth rate for Year 2}) = D1 \times (1 + 0.2462) = 2.6150 \times 1.2462 \approx 3.2597 \]
- Growth Rate for Year 3 and beyond: 3.31%
Now we calculate D3:
- D3 (dividend for Year 3): \[ D3 = D2 \times (1 + \text{growth rate for Year 3}) = 3.2597 \times (1 + 0.0331) = 3.2597 \times 1.0331 \approx 3.3645 \]
Step 2: Discount the Expected Dividends to Present Value
The required return on the stock is 11.86%, or 0.1186.
Using this rate, we can discount the expected dividends back to present value:
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PV of D1: \[ PV(D1) = \frac{D1}{(1 + r)^1} = \frac{2.6150}{(1 + 0.1186)^1} \approx \frac{2.6150}{1.1186} \approx 2.3398 \]
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PV of D2: \[ PV(D2) = \frac{D2}{(1 + r)^2} = \frac{3.2597}{(1 + 0.1186)^2} \approx \frac{3.2597}{1.2519} \approx 2.6013 \]
Step 3: Calculate the Present Value of D3 and Future Dividends Using Gordon Growth Model
For the dividends from Year 3 onwards (starting with D3), we use the Gordon Growth Model (GGM):
\[ P2 = \frac{D3}{r - g} = \frac{3.3645}{0.1186 - 0.0331} = \frac{3.3645}{0.0855} \approx 39.3142 \]
Now, we need to discount \( P2 \) back to present value:
- PV of P2: \[ PV(P2) = \frac{P2}{(1 + r)^2} = \frac{39.3142}{1.2519} \approx 31.4071 \]
Step 4: Total Present Value
Now we sum up all the present values:
\[ \text{Total Present Value} = PV(D1) + PV(D2) + PV(P2) = 2.3398 + 2.6013 + 31.4071 \approx 36.3482 \]
Final Stock Value
Thus, the estimated total value of the stock is approximately:
\[ \text{Value of the Stock} \approx 36.35 \]
The value of the stock is approximately $36.35.