To find the value of the stock, we can use the Dividend Discount Model (DDM), which calculates the present value of future dividends. Given the information provided, we need to take into account the different growth rates for the dividends for the specified time frames.
Step 1: Calculate the required rate of return using CAPM
Using the Capital Asset Pricing Model (CAPM):
\[ \text{Required Return} = \text{Risk-free rate} + \beta \times \text{Market risk premium} \]
Given:
- Risk-free rate = 1.80% = 0.018
- Market risk premium = 9.11% = 0.0911
- \(\beta = 1.71\)
Calculating the required return: \[ \text{Required Return} = 0.018 + 1.71 \times 0.0911 \]
\[ \text{Required Return} = 0.018 + 0.1552801 = 0.1732801 \approx 17.33% \]
Step 2: Forecast dividends for the first three years
The last dividend (D0) is $1.14. The growth rate for the next three years is 22.29% (0.2229).
Calculating the dividends for the next three years:
-
Year 1 (D1): \[ D_1 = D_0 \times (1 + g_1) = 1.14 \times (1 + 0.2229) = 1.14 \times 1.2229 \approx 1.39 \]
-
Year 2 (D2): \[ D_2 = D_1 \times (1 + g_1) = 1.39 \times 1.2229 \approx 1.70 \]
-
Year 3 (D3): \[ D_3 = D_2 \times (1 + g_1) = 1.70 \times 1.2229 \approx 2.08 \]
Step 3: Forecast dividends starting from Year 4
After Year 3, the dividend grows at a constant rate of 3.36% (0.0336).
Calculating D4: \[ D_4 = D_3 \times (1 + g_2) = 2.08 \times (1 + 0.0336) \approx 2.08 \times 1.0336 \approx 2.15 \]
Step 4: Calculate the present value of the dividends for the first three years
Now we will discount the dividends back to present value using the required return (17.33% = 0.1733).
\[ PV(D_1) = \frac{D_1}{(1 + r)^1} = \frac{1.39}{(1 + 0.1733)^1} \approx \frac{1.39}{1.1733} \approx 1.18 \] \[ PV(D_2) = \frac{D_2}{(1 + r)^2} = \frac{1.70}{(1 + 0.1733)^2} \approx \frac{1.70}{1.3764} \approx 1.24 \] \[ PV(D_3) = \frac{D_3}{(1 + r)^3} = \frac{2.08}{(1 + 0.1733)^3} \approx \frac{2.08}{1.6131} \approx 1.29 \]
Step 5: Calculate the present value of dividends starting from Year 4
From Year 4 onward, dividends will grow at a constant rate (3.36%). The value of all future dividends starting from Year 4 can be calculated using the Gordon Growth Model (or Perpetuity formula):
\[ PV(D_4) = \frac{D_4}{r - g_2} = \frac{2.15}{0.1733 - 0.0336} = \frac{2.15}{0.1397} \approx 15.39 \] This value is at the end of Year 3, so we need to discount it back to present value: \[ PV = \frac{15.39}{(1 + r)^3} = \frac{15.39}{1.6131} \approx 9.54 \]
Step 6: Add the present values together
\[ \text{Total PV} = PV(D_1) + PV(D_2) + PV(D_3) + PV(D_4) \] \[ \text{Total PV} = 1.18 + 1.24 + 1.29 + 9.54 \approx 13.25 \]
Conclusion
The value of the stock is approximately $13.25.
0 answers