An Internally Consistent Approach To Common Stock Valuation

Abstract

A modern corporate finance curriculum typically extends the one-stage Gordon (1962) dividend discount model into a multi-stage environment. In such instances, each regime of constant dividend growth defines a distinct stage. The rate of sustainable dividend growth in each stage is typically determined by specifying the firms return on asset (ROA) and plowback (PB) ratios in each stage, and then computing the implied dividend growth rate as g = ROAPB.

In a two-stage problem, current convention typically advocates that the first dividend in the second stage should equal the last dividend in the first stage, multiplied by 1 + g₂, where g₂ is the growth rate of dividends in the second stage. We show that the dividend stream generated with this methodology is inconsistent with the ROA and plowback assumptions used previously to compute g₂. The implication is that the conventional pricing methodology results in stock valuations that are inconsistent with ROA and PB assumptions. For a common textbook problem, we demonstrate pricing errors on the order of 30%. In order to address the issue, we provide an alternative pricing methodology that results in valuations that are consistent with underlying assumptions.

Pedagogically, when the proposed approach is contrasted with the traditional approach, the student is forced to develop a deeper fundamental understanding of how stock valuation relates to (i) operational efficiency, (ii) dividend policy, and (iii) the economic environment in which the firm competes.