Predicting firm value: the superiority of q-theory over residual income

Abstract

One of the contributions of residual income theory is that it establishes an equivalence between valuation of a firm based upon a discounted stream of future dividends and valuation based on accounting data in which book value and a discounted stream of future residual incomes take centre stage. However, this equivalence result is non-unique: residual income is only one of many income measures for which equivalence can be shown to hold. Given this non-uniqueness, the traditional residual income equivalence result provides at best a weak defence for the necessity of accounting via residual income. The principal objective of the current paper is to address this central limitation of existing research. We consider how to move on from dependence on equivalence as a weak defence for accounting-based valuation, to a framework in which strict preference between alternative valuation methods is possible. The principal reason why previous research has not considered such issues is because it has lacked an underlying microeconomic theory of managerial choice providing a framework within which to rank alternative valuation rules. From first principles we develop a dynamic optimisation model of managerial choice that provides the benchmark by which we can objectively appraise valuation based upon residual and other income measures. We show that hysteresis (non-uniqueness of valuation) can typically arise for residual income, whereas in contrast for the q-theory based income measure which we derive, valuation is, as expected intuitively, increasing in income (under some mild regularity conditions). Furthermore, we show how our proposed g-theory income measure could be estimated empirically and that our model provides an explanation for some of the apparent anomalies in the Burgstahler-Dichev empirical findings.