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Pricing mergers & acquisitions using agent-based modeling.


Pricing of Mergers & Acquisitions (M&A) transactions is usually quite hard due to behavioral factors that impact such a valuation. Behavioral finance has had significant impact on pricing of mergers and acquisitions. While, Baker, Pan and Wurgler (2009) have shown how investors will accept an offer near the 52 week high stock price as significant enough in a merger or acquisition scenario. However, there are numerous psychological factors that impact pricing of M&A transactions, including optimistic behavior of sellers, risk-averse behavior of buyers, fear, greed and similar behavioral biases. Kahneman and Tversky (1979) have shown how these behavioral biases have significant downward tilt, where positive factors have less value than negative factors. According to Baker, Pan and Wurgler (2009), it seems that prices offered by buyers for a potential merger or acquisition would stay the same, being the 52 week high stock price. However, behavioral finance would say otherwise, as these theories show that investors react differently in falling markets compared to rising markets. Kahneman and Tversky (1979) have themselves shown that behavioral factors are biased to the downside. Humans give more weight to negative factors compared to positive factor, as reflected by the prospect theory loss aversion ratio. Another question to add to this problem will be to see if the business cycle phase has any impact on the behavioral biases and the pricing of M&A transaction. As a result, this paper intends to understand if the price premium paid by buyers is different based on the buyer and seller's behavior and if this premium differs based on the state of the business cycle when these offers are made. So, how do you price M&A transactions considering the behavior of the acquirer and target firms, while considering the changes in the business cycle?

While, business cycles and behavioral biases potentially could have an impact on the pricing of M&A transactions, there can also be a severe impact due to the extreme behavior of the seller. For example, if the seller plans to undertake a hostile takeover of the target firm. In the previous case, we review the change in M&A pricing due to changes in the business cycle. Though, here we consider a different situation, where the acquirer undertakes a hostile takeover. A hostile takeover is when the acquirer tries to convince the shareholders of the organization and bypasses the target firm's board of directors and senior management. It is an attempt to forcefully takeover the firm by obtaining shareholder approval. When pricing a merger in such a situation, the behavioral factors associated in pricing such a transaction are important. So, would it be sufficient for a hostile takeover to be possible in the same manner as any other type of merger transaction? This paper discusses how behavior of the acquirer and target firms impact the pricing of a hostile takeover transaction. We use agent-based modeling to analyze this problem and graphically show the differences based on behavioral changes. The next section provides a brief literature review and the remaining sections develop the methodology and results of this paper.

Before we look at the literature review, we need to ask why this research problem is important. It is important as M&A transactions play a significant role in business and the pricing of these transactions has an impact on the value of the firm and shareholder capital. While, research reviewing the impact of behavioral factors on M&A transaction pricing has been limited, it is of great value to companies and shareholders, who would like to obtain the highest price for their investment.

Mergers & Acquisitions and Agent-based Models

Mukherjee, Kiymaz and Baker (2004) under took a survey of CFOs and found that mergers occur in order to increase synergies, while divestures occur to concentrate on core business, while spinning off or selling non-core assets. Rhodes-Kropf, Robinson and Viswanathan (2005) have shown that merger occur in waves, and state that this occurs due to misvaluations, where high book to market value firms buy low book to market value firms. Shleifer and Vishny (2003) also provide support for misvaluation, medium of payment that defines these mergers and reasons for merger waves to occur. While, Krummer and Steger (2008) state that these merger waves re-occur over time. Shelton (1986) found that buyer that merged or acquired seller in new but related markets obtained the most value from the merger. Bouwman (2009) finds that many mergers take place at the peak of the business cycle, while these enjoy significantly higher announcement returns (increase in stock price when the merger is announced). But, they face lower long-run returns and sub-optimal operating performance compared to mergers and acquisitions that occur in business cycle troughs. Bouwman (2009) that this excess number of mergers occur due to managerial herding behavior, where excess valuations may allow managers to consider taking over other low book to market value companies. Eccels, Kersten and Wilson (1999) provide practical techniques to value merger and acquisition deals and state that managers should walk away from overvalued deals.

Agarwal and Zeephongsekul (2011; 2012; 2013) also provide a model of pricing M&A transactions using a game theoretic model and real options pricing. Baker, Pan and Wurgler (2012) provide a further extension of the psychological pricing of M&A transactions explaining the reference point theory, while, Alexandridis et al. (2010) talk about gains from M&A transactions. Erel et al. (2012) have discussed M&A valuation in relation to crossborder M&A transactions, Cummins et al. (2015) and Andreou et al. (2012) review the transaction pricing in view of the global insurance and logistic industries respectively. While, Fu et al. (2013) identify how M&A activity is driven by stock overvaluation. While, mergers and acquisitions occur at different phases of the business cycle and the behaviors of the buyer and the seller are intertwined in such decisions. As a result, it is important to analyze such situations using agent-based modeling, which allows us to simulate such a scenario and understand how these behaviors impact merger and acquisition valuation. Also, how does it interact with the different business cycle phases and which part of the business cycle provides lower or higher prices and price premiums for the buyer and seller. Gilbert and Terna (2000), Duffy (2006) and Windrum, Fagiolo and Moneta (2007) explain how to build complex system models for social science experiments. While, Farmer and Foley (2009) show how agent-based models can be developed to analyze economic problems. Chan, LeBaron, Lo, Poggio, Yy, and Zz (1999) and Cont (2007) explain agent-based models of financial markets using experiments.

A merger or acquisition occurs between an acquirer and target firm, which act as two players in a non-cooperative game, which is built in MATLAB 2008b as an agent-based model. This model is developed to understand the interaction between the changes in price premium based on the change in the risk-averse--risk-taking characteristic of the acquirer and optimistic--pessimistic characteristic of the target firm. We see the change in the acquirer's characteristic on the y-axis and the target's characteristic on the x-axis, compared to the change in price premium (utility) on the z-axis of the graphs provided below. The definition of utility is the same as is generally used in the field of economics and is an alternative measure to the price premium provided by the acquirer to purchase the target firm. Further, this game is played with a pool of thousand players, where two players are picked up at random and they play a merger game where they are assigned different levels of risk-averse--risk-taking and optimistic--pessimistic characteristics. These players play a thousand rounds before the price premium is calculated and averaged across these rounds. Then, a hundred games are played by different acquirers and target firms, which are also picked at random from the pool of thousand players. At the end of the hundred games, the price is averaged for each 0.1 increment on the risk-averse--risk-taking and optimistic--pessimistic continuums.

Results of the Merger & Acquisition Game

As the merger game progresses, we notice that the price increases as the risk taking behavior of the buyer increases. This potentially occurs as buyer (acquiring firm) is willing to offer a higher price for taking over the seller (target firm). We also notice that the seller's optimistic behavior has little impact on price. However, if the seller is optimistic, then it is likely that they will decline lower offers and as a result will only accept higher offers. So, a combination of a risk-taking buyer and optimistic seller will result in the highest price being offered for the merger or acquisition deal. If the buyer wants to pay a lower price, then they should be more risk-averse and provide lower offers. While, the seller will want to be more optimistic, in order to obtain higher offers from buyers and to reject lower offers. It is obviously that many deals will not go through where the combination of the buyer's and seller's behaviors does not align. The graph below only provides the potential price levels for deals that are successful, which is reflected in figure 1 provided below. There can be many other factors except price that may impact on the merger or acquisition deal being unsuccessful, for example, organizational culture.

However, this dynamic can change during business cycles, as there are fewer buyers during business cycle troughs (when the economy is weak). In such a situation, sellers do not decline offers as they may be in a difficult financial situation. Buyers also know that sellers are in a difficult situation and as a result, they do not offer a higher offer to merge or acquire the seller. Figure 2 below reflects this price dynamics in a merger game during a business cycle trough.

In a business cycle trough, buyers are usually opportunistic and often unwilling to pay a higher price to merge or acquire a seller. This is not the same, when the business cycle turns and the economy starts improving. In an improving economy, buyers know that the price of the seller's business is increasing and a greater number of sellers will negotiate to obtain a higher price.

Acquisition Game in a Business Cycle Trough

Figure 3 below reflects this price dynamics in a merger game during an improving business cycle. It is important to notice how steeply the price increases with the improvement in the risk-taking and optimistic behavior of buyers and sellers respectively. In this scenario, the highest price obtained due to behavioral biases (when a buyer is risk-taking and seller is optimistic) is higher than the other two scenarios, when the economy is at the trough or peak. This may be the case, as the value of the seller may be low in a trough and the seller may not have many options.

On the other hand, buyers fear of paying too high a price at a market peak and will often not pay too high a price when they are risk-taking. So, the best time to be optimistic for a seller is during an improving market. In such an instance, if the buyer is not risk-taking then the value of the seller will increase as the market improves. As a result, the buyer will be willing to pay a higher premium to undertake the merger or acquisition.

When the business cycle peaks, the potential value of company is at the highest level for that business cycle. So, it would not be wise for buyers to pay a high premium to merger or acquire the seller. As a result, the premium paid for the seller is not as high as that paid when the business cycle has bottomed and is improving from a trough. Regardless, the premium paid is highest in any condition when the buyer is risk-taking and the seller is optimistic.

In a hostile takeover, the merger game is often one-sided with the acquirer trying to be aggressive that results in a quite a different situation when the merger is mutually agreeable between the acquirer and target firm. This dynamics further empowers the risk-taking characteristics of the acquirer, as higher the acquirer's risk-taking ability, the more it will be willing to hold out to purchase the target firm. Figure 5 below provides the scenario where the acquirer shows low hostile takeover characteristics; in effect this is a more scenario where the merger would occur on a mutually agreeable basis. The figure shows that the target firm's optimistic--pessimistic behavior is of less use, when the acquirer is not risk taking in which case the deal may potentially fall through.

However, if the target firm is more pessimistic, it will potentially receive a lower price premium when the acquirer is risk-averse. When, the acquirer increases their risk-taking behavior it will favor the target firm to be more optimistic and to hold out for a better deal. Regardless, the price premium will not increase after an initial increase and will be expected to stay reasonably stable. A quick equilibrium to such a game is likely as the price premium is mutually agreed and the risk-aversion behavior of the acquirer and optimism behavior of the target firm seem to mainly impact pricing of the merger, when both acquirer and target firm show low levels of these behaviors.

When, we increase the hostile takeover characteristic of the acquirer we notice that the risk-taking behavior of the acquirer becomes more important (see figure 6 above). In this circumstance, both the risk-taking behavior of the acquirer and optimistic behavior of the target firm are important. When, the acquirer is more risk-averse it will reduce the price premium provided to the target and often these deals will fall through. When, the target firm becomes more optimistic and holds out the price premium provided by the acquirer potentially can increase. However, the best outcome occurs when the acquirer is more risk-taking and the target firm is more optimistic. In such a case, the acquirer is willing to pay more to acquire the target firm, while the target firm demands a higher offer price to be provided to undertake the merger.

This situation can be accentuated when the acquirer shows extremely hostile takeover characteristics, in which case, the acquirer is determined to purchase the target firm (see figure 7 below). In this situation, the acquirer will not provide a sufficient enough price premium when the acquirer is risk-averse and target firm is pessimistic. The price increase is significantly correlated with increasing risk-taking behavior of the acquirer and optimistic behavior of the target firm. If the target firm requires a better price, it will have to hold out further to be able to obtain a better offer. If the acquirer is risk-taking and highly hostile, it will more likely increase its offer to purchase the target firm.


Analyzing the merger or acquisition price depends on the behavior of the buyer and seller. In this paper, we only look at the risk-taking--risk-averse behavior of buyers and optimistic-pessimistic behavior of sellers. Results show that optimistic sellers always receive a higher price, especially when they deal with risk-taking buyer, who is willing to take higher risk by paying a greater price for the merger or acquisition. This increases when the business cycle is improving after it has bottomed. Premiums are lowest at the trough and peak of a business cycle. This aligns with the idea that most buyers would prefer to undertake mergers or acquisitions at the business cycle trough. Otherwise, as the business cycle improves the price and the premium (markup) paid to merge or acquire the seller will increase. The price will be the highest at the business cycle peak, but the premium paid by the buyer will be low (similar to what would be paid at the business cycle trough), as buyers are scared of paying higher prices as the value of the seller has peaked for that business cycle. While, the buyer pays a low premium to merger or acquire the seller in the business cycle trough and peak, nonetheless, the reasons for this low premium are different.

Further, the pricing of mergers and acquisitions transactions are quite complex, especially when you include behavioral characteristics and a hostile takeover scenario. This paper has analyzed three situations, where the acquirer is less hostile, moderately hostile and extremely hostile. Results showed that the acquirers and target firms' behavioral characteristics of risk-averse risk-taking and optimistic--pessimistic respectively have greater impact when the acquirer is more hostile. If a target firm is more optimistic and holds out for a better deal, then they will receive a higher price premium with a more hostile acquirer, while, the price premium will not increase significantly with a less hostile acquirer. However, in all situations, low risk-taking behavior of the acquirer and low optimism behavior of the target firm will often result in a sub-optimal price premium for the merger or the deal may often fall through.


Received 28 February 2016 * Received in revised form 18 March 2016 Accepted 19 March 2016 * Available online 1 April 2016


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University of New England (corresponding author)


University of New England

Caption: Figure 1 Price Dynamics in a 2-player Merger and Acquisition Game

Caption: Figure 2 Price Dynamics in a 2-player Merger and

Caption: Figure 3 Price Dynamics in a 2-player Merger and Acquisition Game in an improving Business Cycle

Caption: Figure 4 Price Dynamics in a 2-player Merger and Acquisition Game in a Business Cycle Peak

Caption: Figure 5 Price Dynamics in a 2-player M&A Game with Low Hostile Takeover Characteristics

Caption: Figure 6 Price Dynamics in a 2-player M&A Game with Medium Hostile Takeover Characteristics

Caption: Figure 7 Price Dynamics in a 2-player M&A Game with High Hostile Takeover Characteristics
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Author:Agarwal, Nipun; Kwan, Paul
Publication:Economics, Management, and Financial Markets
Article Type:Report
Date:Mar 1, 2017
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