Final answer:
To find the current stock price, we calculate the present value of the projected dividends for the first three years and add it to the present value of the perpetual dividends that grow at a constant rate from year four onwards, using the Gordon Growth Model.
Step-by-step explanation:
The current stock price can be calculated using the discounted cash flow model for dividend payments. Given the dividends of $2.8, $3.9, and $4.8 in the first three years and a constant growth of 6% per year thereafter, we will first calculate the present value of these dividends at the discount rate of 10%. Then, since the dividends grow at a constant rate after the third year, we will use the Gordon Growth Model to determine the present value of all future dividend payments from year four onwards.
- Year 1: PV = D1 / (1 + r) ^1 = $2.8 / (1 + 0.10) ^1
- Year 2: PV = D2 / (1 + r) ^2 = $3.9 / (1 + 0.10) ^2
- Year 3: PV = D3 / (1 + r) ^3 = $4.8 / (1 + 0.10) ^3
For the dividends from year four onwards, we use the formula PV = D4 / (r - g), where D4 is the dividend in year 4, r is the discount rate, and g is the perpetual growth rate. So here, D4 is $4.8 * 1.06 (because of the 6% growth from year 3 to year 4).
The sum of the present values of the dividends gives the current stock price. Remember, when calculating the present value of the perpetual growth dividends, it's important to first find the value of the dividends one year after the last projected dividend (which in this case, is the dividend for year 4).