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
A dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a portion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-i ...
payments, discounted back to their present value. In other words, DDM is used to value stocks based on the
net present value
The net present value (NPV) or net present worth (NPW) applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the discount ...
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 Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
, the
University of Rochester
The University of Rochester (U of R, UR, or U of Rochester) is a private university, private research university in Rochester, New York. The university grants Undergraduate education, undergraduate and graduate degrees, including Doctorate, do ...
, and the
University of Toronto
The University of Toronto (UToronto or U of T) is a public university, public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park (Toronto), Queen's Park. It was founded by royal charter in 1827 ...
, 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
John Burr Williams (November 27, 1900 – September 15, 1989) was an American economist, recognized as an important figure in the field of fundamental analysis, and for his analysis of stock prices as reflecting their " intrinsic value".
He is ...
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:
is the current stock price.
is the constant growth rate in perpetuity expected for the dividends.
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.
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
at (discrete) time
is
, and so the current value of all the future dividend payments, which is the current price
, 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, math ...
:
This summation can be rewritten as
:
where
:
The series in parenthesis is the geometric series with common ratio
so it sums to
if
. Thus,
:
Substituting the value for
leads to
:
,
which is simplified by multiplying by
, 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.
:
is rearranged to give
So the dividend Yield
plus the Growth
equals Cost of Equity
.
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>
:
Growth cannot exceed cost of equity
From the first equation, one might notice that 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 denotes the short-run expected growth rate, denotes the long-run growth rate, and 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.
:.
b)
This equation is also used to estimate the cost of capital by solving for .
:
c)
which is equivalent to the formula of the Gordon Growth Model ''(or Yield-plus-growth Model)'':
: =
where “” stands for the present stock value, “” 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 may not be reasonable.
#If the stock does not currently pay a dividend, like many growth stocks, 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. 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 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
*
*
External links
Alternative derivations of the Gordon Model and its place in the context of other DCF-based shortcuts
{{stock market
Stock market
Financial models
Valuation (finance)