Assessment of the synergistic effect from solvency changes in M&A transactions based on a dynamic model

The main goal of most merger and acquisition (M&A) transactions is to achieve a synergistic effect. This study proposes a method and a model for predicting the consequences of merger and acquisition transactions from the perspective of achieving synergy. The authors consider the possibility of obtaining a synergistic effect in mergers/acquisitions, which originates from a negative correlation between the liquidity flows passing through companies participating in an M&A transaction. This effect can be determined and assessed using a model that describes a company's cash flows as a Wiener process coming out of a point with a certain liquidity cushion L0. Increments in the company's liquidity cushion at each subsequent stage are viewed as independent random values (positive or negative) governed by the normal law of distribution. Each subsequent liquidity cushion value meets the conditions of the Markov process. Solvency is assessed using a dynamic index TX -- the time during which the probability of losing the liquidity cushion for the company will not exceed X%. For each individual company, the TX value depends on the parameters of the liquidity flow -- L0, mean value μ, and standard deviation σ. Upon conclusion of M&A transactions, the flows are combined. Calculations performed using simulation modeling based on the proposed model show that the TX indicator of the combined company is determined not only by the values of L0, μ,and σ of the M&A participants, but also by the pair correlation coefficient of cash flows ρ. It is found that with the reduction of the correlation coefficient ρ the solvency of the combined company within the framework of the proposed approach increases, reaching its maximum with the correlation coefficient ρ = -1. In addition, by reducing correlation between the flows it is possible to achieve a significant saving of the amount of liquid funds through the reduction of its initial value L0. Another important aspect is the possibility of preliminary quantitative assessment of the synergistic effect. The findings of the study are confirmed only by calculations based on hypothetical models, although they use liquidity flow parameters of actual Russian companies.