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 V_t of book value b_t, earnings x_t, and dividends d_t. The aggregation conditions imply that V_t must be of the form V_t = (1 ? k)bt + k [f xt ? dt]. f is the permanent earnings capitalization factor and undetermined weight k may be any function of Δ_t ≡[φx_t ? d_t] ? b_t. 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 Δ_t, V_t is nonlinear in earnings. Hence, this result specifies how V_t 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 Δ_t, and not from the clean surplus relation and abnormal earnings as many now believe.