Exchange Ratios in Merger with Stochastic Capital Reserves and Cross Shareholding: Fair Valuation and Embedded Options

Purpose – The purpose of this paper is to analyze how exchange ratios in mergers can be assessed when the companies economic capital valuation is carried out in a stochastic framework with financial assets and minimum guarantees. Design/methodology/approach – The paper is a theoretical one. Its main objective is to present a quantitative model for exchange ratios accounting, introducing a stochastic pricing model in the presence of stochastic cash-flows and representing contractual embedded real option such as minimum guarantees. Findings – The paper presents a financial model to evaluate the differences in exchange ratios induced by stochastic capital reserves in the merging companies. Research limitations/implications – Stochastic cash-flows in the economic capital of the merging companies set up a stochastic capital reserve which represents an additional value and could induce important differences in exchange ratios. Practical implications – The model is fully applicable, also in the presence of embedded real options such as minimum guarantees, but requires the volatility of the underlying. Originality/value – The paper should be useful under both a managerial and a theoretical use in order to evaluate stochastic exchange ratios.