زمان بندی بهینه و استراتژیک ترکیب و ادغام با انگیزه هم افزایی و تنوع ریسک

This paper analyses a real options model of mergers and takeovers between two firms experiencing different, but correlated, uncertainty. It is assumed that mergers do not just lead to efficiency gains, but are also an act of diversification. Due to the latter assumption the region where a merger is optimal is a bounded interval and not a half-space as in most real options models. It is shown that if the roles of the bidder and the target are determined endogenously the option value of the mergers vanishes completely, implying that, in equilibrium, the mergers occur sooner than when these roles are exogenously given. It is also shown that mergers can be optimal even if synergies are negative.

In recent years, several papers have used the real options approach to analyse various aspects of merger and acquisition (M&A) activity. This approach views the possibility of M&A as an option comparable to a perpetual American call option. In the generic real option model, a firm's uncertain profit stream takes the place of the underlying asset in the standard no-arbitrage theory of (financial) options. In this paper, a two-factor model with two firms is considered. Both firms maximise expected profits and face different, but correlated, risk. Profits for both firms as well as the merged entity consist of a deterministic part and a diffusion. There are positive synergies to the merger if the resulting deterministic profit is larger than the sum of the deterministic profits of the constituent firms. The possibility of negative synergies, however, is not ruled out a priori. In addition to the synergy effect, the diffusion shock of the merged firm is taken to be an iso-elastic transformation of the diffusions of the constituent firms. This reflects the possibility that the merger makes the firms less vulnerable to random shocks, because they are more flexible to react to different market conditions. As an example, consider the recent merger between Air France and KLM Royal Dutch Airlines. Because both airlines can now pool resources in, say, buying aircraft and oil derivatives they become less exposed to the risks posed in their respective markets. This is called the diversification effect. Furthermore, the chosen functional form enables us to view the resulting optimal stopping problem as essentially one-dimensional, thereby simplifying the analysis. Two M&A scenarios are studied. In the first scenario, one exogenously determined firm (the ‘bidder’) has the option to take over the other firm (the ‘target’). In the second scenario, the roles of bidder and target are determined endogenously. Throughout it is assumed that the bidder offers the shareholders of the target a share in the new company, which makes them indifferent between accepting and rejecting the bid. This is a different assumption than the one made in several recent papers on M&A activity, like, for example, Lambrecht (2004), Morellec and Zhdanov (2005), and Lambrecht and Myers (2007). In those papers the terms of the merger are determined by both the bidder and the target simultaneously in a Pareto optimal way. When the firm roles are exogenously given, the option to acquire the target is simply an exchange option to the bidder, as was already pointed out by Margrabe (1978). Indeed, the option is to exchange the stand-alone profit stream for a share of the profit stream of the merged firm. It is shown that the optimal time to make a bid for the target is when the ratio of the two underlying diffusions hits a certain bounded interval for the first time. This implies that mergers can take place both during economic upturns as well as downturns. A similar result has been obtained by Alvarez and Keppo (2002) and Alvarez and Stenbacka (2004) in settings different from M&A activity. In the case of endogenous roles, both firms can make a bid for the other firm at any time. It is assumed that if both make a bid simultaneously, they agree to a merger. In that case they use the Nash bargaining solution to determine how the merger surplus is divided. So, in this paper, there is a fundamental difference between takeovers and mergers. It is shown that there exists a subgame perfect equilibrium where (hostile) takeovers never occur. Interestingly, this region is independent of the bargaining power of each firm. The empirical implications of the model are in line with many facts on M&A activity as recorded by, for example, Andrade et al. (2001). Firstly, our model predicts that mergers occur in waves. It is well known that mergers often result from shocks that can be both positive (the arrival of new technologies, for example) and negative (for example, increases in prices of raw materials). In the model this is captured by the fact that the optimal merger regions can be reached either from below or from above. Also, in our model, the optimal merger regions increase in the correlation between the two underlying diffusions, which mimics the stylised fact that mergers are clustered in industries. Finally, the equilibrium region for mergers is a bounded interval which contains the interval from the exogenous firm roles scenario. This indicates that more M&A activity will take place with endogenous firm roles, which is consistent with the stylised fact that deregulation leads to higher M&A activity. The paper is related to several recent papers that analyse various aspects of M&A in the framework of real options theory. The first real options analysis of mergers was by Lambrecht (2004) who analysed a framework where two firms determine the jointly optimal time and terms of a merger. The underlying uncertainty, however, is assumed to be the same for both firms. Furthermore, the two firms determine the terms of the merger as if they operate as a single coalition, thereby leading to a Pareto optimal merger decision. The resulting optimal stopping region takes, contrary to our results, the standard form of a half open interval. Lambrecht and Myers (2007) extend this basic framework to analyse mergers and disinvestment in declining industries. They focus specifically on agency problems between managers and dispersed outside investors, thereby linking to the study by Schleifer and Vishny (2003). Lambrecht and Myers (2007) show that, absent takeovers, closures take place too late. They then argue that the possibility of takeovers enforces optimal disinvestment, although hostile takeovers can happen too early. Another paper that uses the Nash bargaining framework to determine the terms of a merger is Alvarez and Stenbacka (2006). They characterise the optimal distribution of the merger surplus and find a link between the incentives to merge and the bargaining power of the firms. Like Lambrecht (2004) and Lambrecht and Myers (2007) they assume a single underlying diffusion and characterise when the optimal merger policy is to do so as soon as the underlying diffusion exceeds a certain threshold. An important difference with the present analysis is that, in this paper, the actual bargaining power of the firms turns out to be irrelevant in equilibrium. The paper is closely related to Morellec and Zhdanov (2005), who study mergers where the profit flows of both the firms are influenced by different, but correlated, diffusions. The terms of the merger are determined as in Lambrecht (2004) and they derive a unique threshold for the ratio of both the profit streams above which a merger or acquisition is optimal. These results are then used to explain excess returns on shares prior to M&A announcements. Morellec and Zhdanov (2005) assume that the diffusion underlying the profits of the merged firm is an arithmetic transformation of the two diffusions, whereas we study an iso-elastic transformation. Furthermore, they assume that shareholders have imperfect information, whereas we analyse a complete information situation. The main difference of the current paper with the contributions mentioned above lies in the diffusion underlying the merged firm's profits. By taking an iso-elastic transformation, we introduce a diversification effect in the analysis of mergers as real options. As a result, the optimal takeover or merger policy is no longer characterised by a unique threshold. Instead, we find two thresholds and the optimal policy is to engage in M&A activity if the smaller (larger) threshold is reached from below (above). Furthermore, we make an explicit distinction between takeovers and mergers. In the former case, the shares of the merged firm are split as to be just incentive compatible for the target's shareholders. In the latter case, on the other hand, the terms of the merger are determined as the result of a bargaining process. In the resulting equilibrium it turns out that the bargaining power of the firms is irrelevant. This is basically due to the threat of each firm to the other that if a merger cannot be agreed upon, either firm makes a (hostile) takeover bid, which the target's shareholders will accept. It turns out that cooperation is a (weakly) dominant strategy for either firm. The paper is organised as follows. In Section 2 the case of the roles of the bidder and the target are given exogenously. In Section 3 these roles are assumed to be determined endogenously. Finally, Section 4 discusses the results and concludes.