# Dividend Discount Model (DDM)
The DDM values a share as the present value of all expected future dividend payments, discounted at an appropriate risk-adjusted rate. The price it produces is the intrinsic value of the stock.
$$\text{Intrinsic value} = \text{PV of all future dividends} + \text{PV of stock sale price}$$
$$\text{Stock Intrinsic Value} = \frac{D_1}{(1+K_e)^1} + \frac{D_2}{(1+K_e)^2} + \dots + \frac{D_n}{(1+K_e)^n} + \frac{RV_n}{(1+K_e)^n}$$
where $RV_n$ is the realizable/terminal value at year $n$.
There are three variants depending on the assumed growth pattern of dividends.
## A. Zero Growth Model
Dividend stays constant forever (a perpetuity):
$$P_0 = \frac{D}{K_e}$$
| Symbol | Meaning |
|---|---|
| $D$ | Constant annual dividend |
| $K_e$ | Cost of capital |
| $P_0$ | Current market price |
## B. Constant Growth Model
Dividends grow at a single constant rate $g$ forever. This is exactly the same as Gordon's Model:
$$P_0 = \frac{D_1}{K_e - g}$$
## C. Variable (Multi-stage) Growth Model
Used when more than one growth rate applies — e.g. high growth for a few years, then a constant long-run rate. Discount each explicit-period dividend individually, then apply Gordon's formula to the terminal value and discount it back.
Assuming growth becomes constant after year 4:
$$P_0 = \frac{D_1}{(1+K_e)^1} + \frac{D_2}{(1+K_e)^2} + \frac{D_3}{(1+K_e)^3} + \frac{D_4}{(1+K_e)^4} + \left[\frac{D_5}{K_e - g} \times \frac{1}{(1+K_e)^4}\right]$$
The last bracket computes the share value at the end of year 4 using the constant-growth formula (with the first post-stable dividend $D_5$) and then discounts that lump sum back to today.