Centre for Discrete and Applicable Mathematics 

CDAM Research Report, LSECDAM200508May 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 κ_{max} of the following `bordered diagonal matrix'
lies between the first largest and second largest among λ_{1},...,λ_{n}.
An affirmative answer necessarily restricts the
dividend policy vector (ω_{1},..., ω_{n+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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Last modified: 9th May 2005