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In finance and
investing Investment is the dedication of money to purchase of an asset to attain an increase in value over a period of time. Investment requires a sacrifice of some present asset, such as time, money, or effort. In finance, the purpose of investing i ...
, 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 The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees. The University of Roc ...
, 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: P is the current stock price. g is the constant growth rate in perpetuity expected for the dividends. r is the constant
cost of equity In finance, the cost of equity is the return (often expressed as a rate of return) a firm theoretically pays to its equity investors, i.e., shareholders, to compensate for the risk they undertake by investing their capital. Firms need to acquire cap ...
capital for that company. D_1 is the value of dividends at the end of the first period. :P = \frac


Derivation of equation

The model uses the fact that the current value of the dividend payment D_0 (1+g)^t at (discrete) time t is \frac, and so the current value of all the future dividend payments, which is the current price P, is the sum of the
infinite series In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mat ...
: P_0= \sum_^ \frac This summation can be rewritten as :P_0= r' (1+r'+^2+^3+....) where :r'=\frac. The series in parenthesis is the geometric series with common ratio r' so it sums to \frac if \mid r'\mid<1. Thus, : P_0 = \frac Substituting the value for r' leads to : P_0 = \frac, which is simplified by multiplying by \frac , so that :P_0 = \frac = \frac


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. :\frac = P_0 is rearranged to give \frac + g = r So the dividend Yield (D_1/P_0) plus the Growth (g) equals Cost of Equity (r). 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.Spreadsheet for variable inputs to Gordon Model
/ref> :\text + \text = \text


Growth cannot exceed cost of equity

From the first equation, one might notice that r-g 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: :P = \sum_^N \frac + \frac Therefore, :P = \frac \left 1- \frac \right+ \frac, where g denotes the short-run expected growth rate, g_\infty denotes the long-run growth rate, and N 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. :P_0 = \frac. b) This equation is also used to estimate the
cost of capital In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate ne ...
by solving for r. :r = \frac + g. c) which is equivalent to the formula of the Gordon Growth Model ''(or Yield-plus-growth Model)'': :P_0 = \frac where “P_0” stands for the present stock value, “D_1” 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 . #The presumption of a steady and perpetual growth rate less than the
cost of capital In economics and accounting, the cost of capital is the cost of a company's funds (both debt and equity), or from an investor's point of view is "the required rate of return on a portfolio company's existing securities". It is used to evaluate ne ...
may not be reasonable. #If the stock does not currently pay a dividend, like many
growth stock In finance, a growth stock is a stock of a company that generates substantial and sustainable positive cash flow and whose revenues and earnings are expected to increase at a faster rate than the average company within the same industry. A growth c ...
s, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Modigliani-Miller hypothesis of dividend irrelevance is true, and therefore replace the stock's dividend ''D'' with ''E''
earnings per share Earnings per share (EPS) is the monetary value of earnings per outstanding share of common stock for a company. It is a key measure of corporate profitability and is commonly used to price stocks. In the United States, the Financial Accounting ...
. However, this requires the use of earnings growth rather than dividend growth, which might be different. This approach is especially useful for computing the residual value of future periods. #The stock price resulting from the Gordon model is sensitive to the growth rate g chosen; see


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.


References


Further reading

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External links


Alternative derivations of the Gordon Model and its place in the context of other DCF-based shortcuts
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