Aggregation, Dividend Irrelevancy, and Earnings†Value Relations

In this paper I show that the aggregation of operating and financial income imposes three conditions on earnings†based value functions. These three conditions provide a shortcut way to identify dividend irrelevant value functions. For example, consider any value function Vt of book value bt, earnings xt, and dividends dt. The aggregation conditions imply that Vt must be of the form Vt = (1 − k)bt + k [f xt − dt]. f is the permanent earnings capitalization factor and undetermined weight k may be any function of Δt ≡[φxt − dt] − bt. The Ohlson 1995 model is the special case when k is constant. But generally k does not have to be constant to maintain dividend irrelevancy. Whenk varies with Δt, Vt is nonlinear in earnings. Hence, this result specifies how Vt may be nonlinear in earnings in settings with limited liability or production or abandonment options and still be dividend†irrelevant. An even more remarkable feature of this result is that it holds whether accounting is clean surplus or not. One must conclude that accounting†based valuation properly builds from accounting aggregation and Δt, and not from the clean surplus relation and abnormal earnings as many now believe.