Exchange ratios in a merger with stochastic capital reserves: 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.