Final answer:
The value of a stock with an initial dividend of $1.81 growing at a rate of 26.61% for two years and then at 3.27% thereafter, with a required return of 12.33%, is calculated using a dividend discount model and is determined to be $31.69.
Step-by-step explanation:
The value of a stock taking into account expected dividend growth and the required return can be calculated using a dividend discount model (DDM). In this scenario, a stock has just paid a dividend of $1.81, which is expected to grow at 26.61% for two years before settling at a long-term growth rate of 3.27%. Considering the required return on the stock is 12.33%, we can calculate the stock's value.
First, we forecast the dividends for the first two years with the higher growth rate. For year 1, the dividend would be $1.81 * (1 + 0.2661) = $2.29. For year 2, it's $2.29 * (1 + 0.2661) = $2.90. Next, we calculate the present value of these dividends:
- Year 1 PV = $2.29 / (1 + 0.1233) = $2.04
- Year 2 PV = $2.90 / (1 + 0.1233)^2 = $2.30
After year 2, the dividend grows at a constant rate of 3.27%. So, the present value of all future dividends starting from year 3, known as the terminal value, is calculated using the Gordon Growth Model:
Terminal Value at Year 2 = $2.90 * (1 + 0.0327) / (0.1233 - 0.0327) = $34.56
The present value of the terminal value at Year 2 is:
Terminal Value PV = $34.56 / (1 + 0.1233)^2 = $27.35
Finally, the value of the stock is the sum of the present values:
Stock Value = Year 1 PV + Year 2 PV + Terminal Value PV
Stock Value = $2.04 + $2.30 + $27.35 = $31.69
Therefore, the value of the stock, given the expected dividend growth rates and the required return, is $31.69.