Method of valuing a stock
In financial economics, the
dividend discount model
(
DDM
) is a method of valuing the price of a company's
capital stock
or business value based on the fact that their corresponding value is worth the sum of all of its future
dividend
payments, discounted back to their present value.
[1]
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.
[2]
[3]
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:
is the current stock price.
is the constant growth rate in perpetuity expected for the dividends.
is the constant
cost of equity
capital for that company.
is the value of
dividends
at the end of the first period.
Derivation of equation
[
edit
]
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
This summation can be rewritten as
where
The series in parentheses 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
[
edit
]
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.
[4]
Growth cannot exceed cost of equity
[
edit
]
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
[
edit
]
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
[
edit
]
The following shortcomings have been noted;
[
citation needed
]
See also
Discounted cash flow § Shortcomings
.
- 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
Sustainable growth rate § From a financial perspective
Related methods
[
edit
]
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
[
edit
]
Further reading
[
edit
]
External links
[
edit
]