To calculate the value of the stock, we will follow the steps below:
- Calculate the dividends for the first three years when the dividend grows at 27.28%.
- Calculate the stock price at the end of Year 3 based on the constant growth of 4.92%.
- Discount all future cash flows (dividends and terminal value) back to the present value to find the stock's value today.
Step 1: Calculate Dividends for the First Three Years
The dividend just paid is \( D_0 = 2.51 \).
Year 1:
\[ D_1 = D_0 \times (1 + g_1) = 2.51 \times (1 + 0.2728) = 2.51 \times 1.2728 \approx 3.197 \]
Year 2:
\[ D_2 = D_1 \times (1 + g_1) = 3.197 \times (1 + 0.2728) = 3.197 \times 1.2728 \approx 4.067 \]
Year 3:
\[ D_3 = D_2 \times (1 + g_1) = 4.067 \times (1 + 0.2728) = 4.067 \times 1.2728 \approx 5.177 \]
Step 2: Calculate the Terminal Value at Year 3
Starting from Year 4, the dividend will grow at a constant rate of 4.92%. We need to calculate the dividend for Year 4:
\[ D_4 = D_3 \times (1 + g_2) = 5.177 \times (1 + 0.0492) = 5.177 \times 1.0492 \approx 5.437 \]
Next, we calculate the terminal value at the end of Year 3, which is the present value of all dividends from Year 4 onward:
\[ TV_3 = \frac{D_4}{r - g_2} = \frac{5.437}{0.1124 - 0.0492} = \frac{5.437}{0.0632} \approx 86.051 \]
Step 3: Discount Future Cash Flows Back to Present Value
Now, we will discount the dividends and the terminal value back to the present value using the required return of 11.24% (r = 0.1124).
Present Value of Dividends
\[ PV(D_1) = \frac{D_1}{(1 + r)^1} = \frac{3.197}{(1 + 0.1124)^1} \approx \frac{3.197}{1.1124} \approx 2.872 \]
\[ PV(D_2) = \frac{D_2}{(1 + r)^2} = \frac{4.067}{(1 + 0.1124)^2} \approx \frac{4.067}{1.2437} \approx 3.269 \]
\[ PV(D_3) = \frac{D_3}{(1 + r)^3} = \frac{5.177}{(1 + 0.1124)^3} \approx \frac{5.177}{1.3845} \approx 3.740 \]
Present Value of Terminal Value
\[ PV(TV_3) = \frac{TV_3}{(1 + r)^3} = \frac{86.051}{(1 + 0.1124)^3} \approx \frac{86.051}{1.3845} \approx 62.141 \]
Total Present Value
Now, we sum all the present values:
\[ PV_{Total} = PV(D_1) + PV(D_2) + PV(D_3) + PV(TV_3) \approx 2.872 + 3.269 + 3.740 + 62.141 \approx 72.022 \]
Thus, the estimated value of the stock is approximately $72.02.