Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2005-08

May 2005

Dividend Policy Irrelevance and Eigenvalue Location

Adam Ostaszewski

This note gives a qualified affirmative answer to a natural question, asked by Ohlson and motivated by some earlier work, concerning the irrelevance of dividend policy to the calculation of equity in the context of an Ohlson style general linear accounting dynamic. Does Dividend Irrelevance occur when discounting at a rate of interest R if and only if R is set equal uniquely to the dominant eigenvalue of the principal submatrix? The latter submatrix relates the accounting variables to each other in the absence of any dividend payout. The question reduces to the assertion that the maximum eigenvalue  κmax of the following `bordered diagonal matrix'

 lies between the first largest and second largest among |λ1|,...,|λn|. 
An affirmative answer necessarily restricts the dividend policy vector (ω1,..., ωn+1). The results show that an algebraic condition equivalent to dividend irrelevance derived previously is not vacuous.

Key words: Dividend irrelevance, dominant eigenvalue, bordered diagonal matrix.

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