Final answer:
The current stock price is calculated using the dividend discount model, which involves finding the present values of projected dividends and the perpetuity value after the specified growth period. Based on the given dividends, growth rate, and discount rate, the calculation leads to a current stock price of approximately $79.92.
Step-by-step explanation:
The current stock price for a company with known future dividends can be calculated using the dividend discount model (DDM). The DDM requires estimating the present value of future dividends, taking into account a constant rate of growth after a certain period, and the discount rate. We have the future dividends for the next three years as well as a perpetual growth rate thereafter.
First, calculate the present value of the dividends for the first three years using the formula Present Value (PV) = Dividend / (1 + discount rate)^n, where n is the number of years until the dividend is received. After that, use the Gordon Growth Model to calculate the present value of the perpetuity. The Gordon Growth Model formula is PV of perpetuity = Dividend year 4 / (discount rate - growth rate).
For the dividends given and perpetual growth after year 3, the calculation is as follows:
- PV of $2.2 dividend in year 1 = $2.2 / (1 + 0.09)^1 = $2.02
- PV of $3.9 dividend in year 2 = $3.9 / (1 + 0.09)^2 = $3.28
- PV of $4.8 dividend in year 3 = $4.8 / (1 + 0.09)^3 = $3.68
- Dividend in year 4, assuming 2% growth from year 3, is $4.8 * (1 + 0.02) = $4.896
- PV of perpetual dividends starting in year 4 = $4.896 / (0.09 - 0.02) = $69.94
To get the current stock price, we add up the present values calculated:
$2.02 + $3.28 + $3.68 + $69.94 = $79.92
The current stock price, therefore, is approximately $79.92.