Dividend discount model
In finance and investing, the dividend discount model (DDM) is a method of valuing the price of a company's stock based on the fact that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In other words, DDM is used to value stocks based on the net present value of the future dividends. The constant-growth form of the DDM is sometimes referred to as the Gordon growth model (GGM), after Myron J. Gordon of the Massachusetts Institute of Technology, the University of Rochester, and the  University of Toronto, who published it along with Eli Shapiro in 1956 and made reference to it in 1959. Their work borrowed heavily from the theoretical and mathematical ideas found in John Burr Williams 1938 book "The Theory of Investment Value," which put forth the dividend discount model 18 years before Gordon and Shapiro. When dividends are assumed to grow at a constant rate, the variables are: formula_1 is the current stock price. formula_2 is the constant growth rate in perpetuity expected for the dividends. formula_3 is the constant cost of equity capital for that company. formula_4 is the value  of dividends at the end of the first period. Derivation of equation. The model uses the fact that the current value of the dividend payment formula_6 at (discrete) time formula_7 is formula_8 This summation can be rewritten as where The series in parenthesis is the geometric series with common ratio formula_11 so it sums to formula_12 if formula_13. Thus, Substituting the value for formula_11 leads to which is simplified by multiplying by formula_17, so that Income plus capital gains equals total return. The DDM equation can also be understood to state simply that a stock's total return equals the  sum of its income and capital gains. So the dividend Yield formula_21 plus the Growth formula_22 equals Cost of Equity formula_23. Consider the dividend growth rate in the DDM model as a proxy for the growth of earnings and by extension the stock price and capital gains. Consider the DDM's cost of equity capital as a proxy for the investor's required total return. Growth cannot exceed cost of equity. From the first equation, one might notice that formula_25 cannot be negative. When growth is expected to exceed the cost of equity in the short run, then  usually a two-stage DDM is used: Therefore, where formula_2 denotes the short-run expected growth rate, formula_29 denotes the long-run growth rate, and formula_30 is the period (number of years), over which the short-run growth rate is applied. Even when "g" is very close to "r", P approaches infinity, so the model becomes meaningless. Some properties of the model. a) When the growth "g" is zero, the dividend is capitalized. This equation is also used to estimate the cost of capital by solving for formula_3. which is equivalent to the formula of the Gordon Growth Model: where  “formula_34” stands for the present stock value, “formula_4” stands for expected dividend per share one year from the present time, “g” stands for rate of growth of dividends, and “k” represents the required return rate for the equity investor. Problems with the constant-growth form of the model. The following shortcomings have been noted; see also . Related methods. The dividend discount model is closely related to both discounted earnings and discounted cashflow models. In either of the latter two, the value of a company is based on how much money is made by the company. For example, if a company  consistently paid out 50% of earnings as dividends, then the discounted dividends would be worth 50% of the discounted earnings. Also, in the dividend discount model, a company that is not expected to pay dividends ever in the future is worth nothing, as the owners of the asset ultimately never receive any cash.