Final answer:
To value a stock with complex dividend growth, we would use the Gordon Growth Model to calculate the present value of dividends for a two-phase growth period and sum these values to find the total stock value.
Step-by-step explanation:
Calculating the Value of a Stock
To find the value of a stock given the described conditions, we can use the Gordon Growth Model (a version of the Dividend Discount Model) for the two-stage growth period described. First, we need to calculate the present value of dividends during the high-growth phase (first five years) and then calculate the present value of the terminal value (representing the perpetuity growth after year five).
The risk-free rate is 3.82% and the market risk premium is 9.97%. With a beta (β) of 0.98, we can determine the expected return of the stock (also known as the discount rate) using the Capital Asset Pricing Model (CAPM): Expected Return = Risk-Free Rate + β*(Market Risk Premium).
To calculate the present value of the dividends during the first five years, we discount each expected dividend by the calculated expected return. After the fifth year, the dividends grow at a constant rate of 4.98% forever. The present value of the terminal value (beginning at year 5) is calculated using the formula for a perpetuity: Terminal Value = Dividend at year 6 / (Expected Return - Constant Growth Rate).
The intrinsic value of the stock is the sum of the present values of all expected dividends during the fast-growth period and the present value of the terminal value.