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Friday, September 26, 2008

Gordon model

Gordon growth model is a variant of the Discounted cash flow model, a method for valuing a stock or business. Often used to provide difficult-to-resolve valuation issues for litigation, tax planning, and business transactions that are currently off market. It is named after Myron Gordon, who was a professor at the University of Toronto.

It assumes that the company issues a dividend that has a current value of D that grows at a constant rate g. It also assumes that the required rate of return for the stock remains constant at k which is equal to the cost of equity for that company. It involves summing the infinite series which gives the value of price current P.

 P= \sum_{t=1}^{\infty}  D\times\frac{(1+g)^t}{(1+k)^t}.
Summing the infinite series we get,

P = D\times\frac{1+g}{k-g}, In practice this P is then adjusted by various factors e.g. the size of the company.
k=\frac{D\times\left(1+g\right)}{P}+g, k denotes expected return = yield + expected growth.

It is common to use the next value of D given by D1 = D0(1 + g), thus the Gordon's model can be stated as [1]

P_0 = \frac{D_1}{k-g}.

Note that the model assumes that the earnings growth is constant for perpetuity. In practice a very high growth rate cannot be sustained for a long time. Often it is assumed that the high growth rate can be sustained for only a limited number of years. After that only a sustainable growth rate will be experienced. This corresponds to the terminal case of the Discounted cash flow model. Gordon's model is thus applicable to the terminal case.


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