Synergy Modelling and Financial Valuation: the contribution of Fuzzy Integrals

Résumé En Fr

Financial valuation are characterised by: the importance of the role assigned to human judgement in decision making, the use of qualitative information and the dominant role of subjective evaluation. The aim of the article is to examine the specific problems posed by modelling of the synergy between the assets of a firm. As a process which aggregates information and subjective opinions, the financial evaluation of the company raises very many problems relating to ideas of measurement, imprecision and uncertainty. The methods used in the process of financial evaluation are based on classic operators of aggregation possessing properties of additivity. Through their construction, these methods abandon the idea of expressing the phenomena of synergy (or redundancy) linked to over-additivity (or under-additivity) that may be observed between the elements of an organised set such as a firm's assets. This synergy effect (or conversely, redundancy) may lead to the value of the set of assets being superior (inferior) to the sum of the values of each asset. This is particularly the case in the presence of intangible assets as goodwill. We will explore the possibilities offered by non-additive aggregation operators (Choquet, 1953; Grabisch et al., 1995; Sugeno, 1977) with the aim of modelling this effect with the help of fuzzy integrals (Casta and Bry, 1998; Casta and Lesage, 2001). More specifically, considering mainly subjective evaluation problems, we propose a formal model of financial valuation including the synergy.cf. working paper : BRY X. et J. F. CASTA : Synergy Modelling and Financial Valuation : Contribution of Fuzzy Integrals, Cahier de Recherche CEREG, n° 2003-4, Université Paris Dauphine, 2003.http://www.dauphine.fr/cereg/cahiers.php?date=2003

Les méthodes d'évaluation financière utilisent des opérateurs d'agrégation reposant sur les propriétés d'additivité. De ce fait, elles occultent les phénomènes de renforcement et de synergie qui peuvent exister entre les éléments d'un ensemble organisé comme un patrimoine, c'est-à-dire entre les actifs et passifs idientifiables. Le présent article se propose d'explorer les possibilités offertes par des opérateurs d'agrégation tels que les intégrales floues (Sugeno, Grabisch, Choquet) dans le but de modéliser l'effet de synergie : cet effet, souvent relevé dans les évaluations financières lors des regroupements d'entreprises, se traduit par la reconnaissance d'un goodwill — c'est-à-dire par la valorisation d'un actif incorporel non identifiable.