# The Gordon Growth Model

Let's return to the fundamental pricing model. The dividend discount model derived earlier is closely related to the Gordon Growth model. The latter also assumes that the market is infinitely lived and pays a periodic dividend (d), but which grows at a rate (g) over time. The current price of the index (p) is therefore the present value of the cash flow stream (we will derive our results without time subscripts): Solving this power series yields the following for which price is essentially the capitalized value of the expected dividend payout in the next period: If we assumed zero growth, then the Gordon Growth is identical to the dividend discount model derived at the beginning of this chapter. If dividends are expected to grow at a rate g, then for a given level, p, we can solve for the return on equity, r, as: For example, assume that the growth rate of nominal earnings is 5 percent and the dividend payout is .40. Also assume that the current price level on the S&P is 900 and that the current p/e multiple is 13.3. Then the p/d multiple is p/(.4e) = 13.3/.4 = 33.25 and the Gordon Growth model forecasts a return, r = 1.05/33.25 + .05 = .0816. or 8 percent. ...

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