The Gordon‐Shapiro Dividend Growth Formula and Inflation

Abstract

The share valuation model which discounts expected dividends is widely accepted in the finance literature. Beyond some point a constant growth rate in expected ividends is assumed. The accepted specification of this growth rate involves a constant retention rate for earnings, and is valid under no inflation. This paper derives the corresponding nominal formula under inflation using a retention rate defined in terms of inflation accounted earnings, and shows that its real counterpart is the accepted formula. It is also shown under inflation that the nominal formula using a retention rate defined in terms of historic cost earnings is considerably more complicated, and that a major error in share valuation results from mistakenly assuming the accepted formula to be valid in nominal terms with a retention rate defined in terms of inflation accounted earnings.

Inflation and the Constant Growth Model: Reconciling the Literature

“…When evaluating multi‐period investments by repeating a one‐period investment continuously the definition of capital maintenance is crucial to determining the invested capital for the next period. In the following we introduce additional notation to allow for the reconciliation of the works of Lally (), Bradley and Jarrell (), and Gordon and Shapiro (). It further allows the formulation of a generalized constant growth valuation model that is applicable to all constellations of capital maintenance, not only those introduced by the aforementioned literature.…”

“…Lally (, pp. 45–51) presents a model that is based on the model of Gordon and Shapiro (), where the preceding income is termed ‘inflation accounted earnings’ and their ‘dividend’ denotes the subsequent income.…”

“…44–45). Recently, a heated discussion concerning the relation of growth and the required retention has emerged (Lally, ; Bradley and Jarrell, , , ; Friedl and Schwetzler, ). For a discussion amongst German researchers refer to Friedl and Schwetzler () or Meitner ().…”

“…Bradley and Jarrell (, p. 66), for instance, correctly state that a ‘misspecification’ resulting from a ‘failure to account properly for the effects of inflation [leads to mispricing, which is] significant even at moderate levels of inflation’. Lally (, p. 48) states that ‘a major error in share valuation results … if the Gordon‐Shapiro formula is mistakenly assumed to be valid in nominal terms with a constant retention rate defined in terms of inflation accounted earnings’. Based on this discussion we present a generalized constant growth valuation model considering inflation in combination with a particular level of capital maintenance.…”

“…Based on this discussion we present a generalized constant growth valuation model considering inflation in combination with a particular level of capital maintenance. Our model is capable of deriving the various versions of the constant growth model according to Gordon and Shapiro (), Lally (), and Bradley and Jarrell (), which are based on different restrictive assumptions. Further the generalized constant growth valuation model allows for application to more realistic scenarios by avoiding these restrictive assumptions.…”