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 assertion that intrinsic value is determined by the sum of future cash flows from dividend payments to shareholders, discounted back to their present value. 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.
13-423: When dividends are assumed to grow at a constant rate, the variables are: P {\displaystyle P} is the current stock price. g {\displaystyle g} is the constant growth rate in perpetuity expected for the dividends. r {\displaystyle r} is the constant cost of equity capital for that company. D 1 {\displaystyle D_{1}}
26-516: A firm's cost of debt and cost of equity and attributed to these two kinds of capital sources. A firm's overall cost of capital, which consists of the two types of capital costs, is then determined as the weighted average cost of capital . Knowing a firm's cost of capital is needed in order to make better decisions. Managers make capital budgeting decisions while capital providers make decisions about lending and investment . Such decisions can be made after quantitative analysis that typically uses
39-566: A firm's cost of capital as a model input. While a firm's present cost of debt is relatively easy to determine from observation of interest rates in the capital markets, its current cost of equity is unobservable and must be estimated. At the least, though, as a firm's risk increases/decreases, its cost of capital increases/decreases: capital providers expect reward for offering their funds to others. Such providers are usually rational and prudent preferring safety over risk. They naturally require an extra reward as an incentive to place their capital in
52-412: Is expected to exceed the cost of equity in the short run, then usually a two-stage DDM is used: Therefore, where g {\displaystyle g} denotes the short-run expected growth rate, g ∞ {\displaystyle g_{\infty }} denotes the long-run growth rate, and N {\displaystyle N} is the period (number of years), over which
65-505: Is the value of dividends at the end of the first period. The model uses the fact that the current value of the dividend payment D 0 ( 1 + g ) t {\displaystyle D_{0}(1+g)^{t}} at (discrete) time t {\displaystyle t} is D 0 ( 1 + g ) t ( 1 + r ) t {\displaystyle {\frac {D_{0}(1+g)^{t}}{{(1+r)}^{t}}}} , and so
78-519: 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 capital from others to operate and grow. Individuals and organizations who are willing to provide their funds to others naturally desire to be rewarded. Just as landlords seek rents on their property, capital providers seek returns on their funds, which must be commensurate with
91-608: The current value of all the future dividend payments, which is the current price P {\displaystyle P} , 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 r ′ {\displaystyle r'} so it sums to 1 1 − r ′ {\displaystyle {\frac {1}{1-r'}}} if ∣ r ′ ∣ < 1 {\displaystyle \mid r'\mid <1} . Thus, Substituting
104-580: The growth ( g ) {\displaystyle (g)} equals cost of equity ( r ) {\displaystyle (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. From the first equation, one might notice that r − g {\displaystyle r-g} cannot be negative. When growth
117-444: The present stock value, “ D 1 {\displaystyle 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. The following shortcomings have been noted; See also Discounted cash flow § Shortcomings . The dividend discount model does not include projected cash flow from
130-447: The risk undertaken. Firms obtain capital from two kinds of sources: lenders and equity investors. From the perspective of capital providers, lenders seek to be rewarded with interest and equity investors seek dividends and/or appreciation in the value of their investment ( capital gain ). From a firm's perspective, they must pay for the capital it obtains from others, which is called its cost of capital . Such costs are separated into
143-432: The sale of the stock at the end of the investment time horizon. A related approach, known as a discounted cash flow analysis , can be used to calculate the intrinsic value of a stock including both expected future dividends and the expected sale price at the end of the holding period. If the intrinsic value exceeds the stock’s current market price, the stock is an attractive investment. Cost of equity In finance ,
SECTION 10
#1732881057185156-578: The short-run growth rate is applied. Even when g is very close to r , P approaches infinity, so the model becomes meaningless. 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 r {\displaystyle r} . c) which is equivalent to the formula of the Gordon Growth Model (or Yield-plus-growth Model) : where “ P 0 {\displaystyle P_{0}} ” stands for
169-510: The value for r ′ {\displaystyle r'} leads to which is simplified by multiplying by 1 + r 1 + r {\displaystyle {\frac {1+r}{1+r}}} , so that 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 ( D 1 / P 0 ) {\displaystyle (D_{1}/P_{0})} plus
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