A note on mergers and acquisitions

Purpose – Recently numerous mergers have been realized. The paper aims to discuss famous static models about the exchange ratio. The paper then seeks to propose a simple dynamical model to valuate both the immediate merger's effects and the delayed ones. Design/methodology/approach – The paper examines from an analytical viewpoint the inequalities of Larson and Gonedes and of Yagil about the exchange ratio. Then, it looks for a possible valuation of future dividends through a dynamical approach. Findings – The paper shows that the results of Larson and Gonedes and of Yagil are substantially the same and, in spite of appareances, do not propose real limitations, but only formal constraints, which need to be further treated before obtaining useful information. The paper then provides sufficient conditions to have dividends and/or prices greater than dividends and/or prices in absence of merger. Finally, an index to valuate synergy is proposed. Research limitations/implications – On the basis of real data, the model may be tested. Moreover, non-linear models and a stochastic framework could be considered. Practical implications – The paper provides a critical viewpoint to consider classical models. Furthermore, the valuation method for future dividends may be applied and the synergy index may be calculated. Originality/value – Both the results about the classical inequalities (to the authors' knowledge, there is no study in such a sense) and the dynamical model (the paper studies possible gains within a time horizon T and not only at time 0 and it does not obtain the fundamental value of stocks, as Yagil does, but their market price) are original.