Valuation and Growth

Abstract

This paper concerns the terminal value calculation, represented by {numerator/(r-g)} where r and g define, respectively, the discount factor and the growth rate. Expressions of this kind derive from discounting a geometric series of payoffs, the Gordon-Williams model providing the prototype. Textbooks and research, implicitly if not explicitly, suggest g>0 to allow for (positive) growth. The analysis in this paper shows that under mild conditions g can be substantially less than zero, yet the setting permits positive growth in dividends, earnings and book values. To obtain a g<0 and positive growth, the modelling depends on two critical ingredients. First, it requires an unbiased valuation anchor which in the long run coincides with the asymptotic solution. Second, short term and long term growth rates differ. Now g relates directly to the speed at which short term growth rate converges to long term rate. But even when the two growth rates are the same, the forward E/P differs from {r minus long term growth}. None of these conclusions negate the importance of growth: the forward E/P ratio decreases if either long term or short term earnings growth increases, holding other factors constant.

Keywords: Valuation, Growth

JEL Classification: M41, G12