Final answer:
The present value of dividends expected from the stock that grows at different rates is calculated using a dividend discount model (DDM). The price is derived by summing the present values of the dividends during the high growth phase and the terminal value calculated by the Gordon Growth Model for the constant growth phase.
Step-by-step explanation:
The problem at hand involves calculating the present value of a series of dividends that are expected to grow at varying rates over time, in order to determine the fair price of a stock today given a certain required rate of return. To solve this, we use a dividend discount model (DDM) with a multistage growth approach.
First, we calculate the present value of dividends during the high growth phase (first three years). Then, we calculate the terminal value or the present value of all dividends expected after the high growth phase, using the constant growth model since dividends are expected to grow at 4% thereafter. Finally, we sum these present values to find the fair price of the stock.
Here's a breakdown of that calculation:
- Dividend in one year (D1): $6.4
- Dividend in two years (D2) = D1 × (1 + first growth rate) = $6.4 × 1.18
- Dividend in three years (D3) = D2 × (1 + first growth rate) = D1 × 1.18^2
- Terminal Value at the end of year 3, which is the present value of all subsequent dividends growing at a constant 4%, is calculated using the Gordon Growth Model.
Then, each future amount is discounted to present value using the given discount rate of 14.9%, and we sum these present values to get the fair stock price.