Profitability, Earnings and Book Value in Equity Valuation : A Geometric View and Empirical Evidence

This paper develops the geometric representation of an equity valuation model to illustrate how equity value relates simultaneously to profitability, earnings, and equity book value, and empirically tests those relations. We depict Zhang's (2000) model as a quot;surfacequot; in the three-dimensional space, defined by profitability (ROE), book value, and equity value, to provide a quot;full viewquot; of the valuation mapping. The geometry offers a convenient way to show visually how balance sheet and income statement measures are integrated and how equity value behaves in relation to different accounting measures. We predict that equity value is an increasing and convex function of profitability (and earnings) given book value, a linear function of book value given profitability, and a non-monotonic and convex function of book value given earnings. We further show that these predicted effects are more pronounced for firms with greater growth opportunities. Empirical results are consistent with our predictions. The study provides a framework to unify empirical findings (including those from prior studies). It presents a more complete and integrated picture of how accounting data are mapped into value