Merger waves and timing of acquisitions: real options approach

Abstract

The existence of merger waves has been well documented over the past decades. Many propositions on why mergers tend to follow a cyclic path have been made based on both theoretical models and empirical studies. However, a clear consensus on the matter is still missing.

In this paper, we study the optimal timing of acquisitions through stochastic real option models, where we model the uncertainty using geometric Brownian motion. We consider firms’ decision to engage in acquisitions as an optimal stopping problem, where firms have an option at every instant to either continue at their current state or to stop the process, pay for the acquisition and receive the benefits of it. However, we consider that the benefits are not certain, creating an optimization problem in the midst of uncertainty.

We begin by building the simplest form of acquisition model where we simply exclude the impact of uncertainty. We show that even in such scenario, there might be value in postponing the acquisition. Then, we build a stochastic model where we allow for uncertainty. With the stochastic model we show how an increase in cash flow uncertainty can increase the value of waiting. Finally, we build a more sophisticated model, where we show that it is not only the cash flow uncertainty, but also the divestment and implementation uncertainties that can increase the incentives to defer acquisitions.

Then, we build two models through which we explain how asymmetric information can impact the timing of acquisitions. We begin by building a simple deterministic model through which we show how undervaluation of the target company can promote merger incentives in cash transactions and how overvaluation of the acquiring firm can promote merger incentives in share transactions. Then, we build a stochastic model where we explain how an increase in the information gap between the well-informed managers and the less-informed general public can promote merger incentives.

Finally, we build two models considering positive and negative industry shocks. We show how positive industry shocks can drive up the return to scale parameters in the company’s production function and decrease the merger threshold. In addition, we show how negative demand shocks can cause a number of companies to prefer to cease operations. We argue that under certain conditions, this could promote merger activity, especially if the demand shock is temporary.