The value of a firm with periodically changing profitability

The Williams-Gordon-Shapiro valuation model is extended so as to allow for fluctuations in both total dividends and the fundamental value of a firm. To this end, the profitability of a firm is supposed to be periodically varying. As a consequence, reference is made to a discrete time, linear and periodic system, which is taken into a pair of linear and time invariant systems through a suitable sampling procedure. The extended valuation model, obtained by computing the eigenvectors of those systems, is capable of three dynamic behaviors: (1) dividents and the fundamental value grow steadily; (2) dividents fluctuate around a rising trend, with the fundamental value increasing steadily; (3) both variables, oscillate, each around its rising trend.