THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 175

CHAPTER Stocks, Rational Expectations, and the Efficient Market Hypothesis 143 The generalized dividend valuation model requires that we compute the present value of an infinite stream of dividends, a process that could be difficult, to say the least Therefore, simplified models have been developed to make the calculations easier One such model is the Gordon growth model, which assumes constant dividend growth The Gordon Growth Model Many firms strive to increase their dividends at a constant rate each year Equation rewrites Equation to reflect this constant growth in dividends: P0 where D0 g )1 (1 g )2 (1 D0 (1 ke ) D0 (1 (1 g) (1 ke ) ke ) D0 g ke the most recent dividend paid the expected constant growth rate in dividends the required return on an investment in equity (4) Equation has been simplified using algebra to obtain Equation 5.1 (1 D0 P0 (ke g) D1 (ke g) g) (5) This model is useful for finding the value of stock, given a few assumptions: Dividends are assumed to continue growing at a constant rate forever Actually, as long as they are expected to grow at a constant rate for an extended period of time, the model should yield reasonable results This is because errors about distant cash flows become small when discounted to the present The growth rate is assumed to be less than the required return on equity, ke Myron Gordon, in his development of the model, demonstrated that this is a reasonable assumption In theory, if the growth rate were faster than the rate demanded by holders of the firm s equity, in the long run the firm would grow impossibly large To generate Equation from Equation 4, first multiply both sides of Equation by (1 and subtract Equation from the result This yields: (1 P0 (1 ke ) P0 g) (1 D0 D0 (1 ke ) /(1 g) g) ke ) Assuming that ke is greater than g, the term on the far right will approach zero and can be dropped Thus, after factoring P0 out of the left-hand side: c P0 1 1d ke g D0 Next, simplify by combining terms to: P0 P0 (1 ke ) (1 (1 D0 (ke g) g g) g) D0 D1 (ke g)