Notes on Two-Stage DDM and Related Models

The Two-Stage Dividend Growth Model (DDM) is utilized to value a stock by discounting its expected future dividends, assuming a two-stage growth process: an initial high-growth stage followed by a perpetual stable-growth stage. The model involves several key notations: the current dividend just received, the growth rate for the first set of years (Stage 1), the perpetual growth rate that initiates after the first stage (Stage 2), and the discount rate or required rate of return.

During Stage 1, dividends are calculated for each year based on the current dividend and the first growth rate. These dividends during the first stage collectively form a growing annuity.

Following Stage 1, Stage 2 commences with perpetual growth at a different rate, starting from the year after the first stage ends. The dividend for the initial year of Stage 2 is determined by taking the last dividend from Stage 1 and applying the perpetual growth rate. The terminal value, calculated at the end of Stage 1, represents the estimated stock price if it were to be sold at that point, using a valuation method for perpetual growth.

To ascertain the price of the stock today, the present values from both stages are summed. This involves individually discounting each dividend projected during Stage 1 back to the present. Concurrently, the calculated terminal value, which accounts for all future dividends in Stage 2, is also discounted back to today. The total price today is the sum of these two components.

The entire two-stage DDM can also be articulated through a closed-form expression. This single formula combines the present value of the dividends from the high-growth stage and the present value of the terminal value (representing the stable-growth stage) to directly calculate the stock price today.