Corporate Governance, Agency Cost and Takeover Decision
Tao-Hsien Dolly King, Weidong Tian and Cinder Xinde Zhang
1
University of North Carolina at Charlotte Department of Finance 9201 University City Blvd. Charlotte, NC 28223 July 6, 2009
1 King,
Tian and Zhang are from University of North Carolina at Charlotte and can be reached at
[email protected],
[email protected] and
[email protected], respectively. We thank Lixin Huang for his helpful comments.
Abstract
We study how internal and external corporate governance mechanisms jointly affect the large shareholder’s takeover decision. The large shareholder monitors the management and has option to take over the firm, while manager steals from the firm resulting in agency costs. Small shareholders are free riders in monitoring benefits (in the non-takeover case) and in takeover gains (in the takeover case). External corporate governance controls impose stealing costs to the manager, whereas internal controls are closely related to the monitoring costs for large shareholders. In equilibrium, large shareholder’s takeover decision, takeover premium, manager’s stealing strategy and firm value are determined endogenously. We find that both internal and external controls have significant effects on agency costs and takeover decision. Our results are robust in the presence of managerial defenses and when the model is dynamic.
1
Introduction
In a world of agency problems and imperfect corporate controls, manager may choose investments that do not maximize firm value. Various corporate governance mechanisms are structured for investor protection and better corporate control. Internal control mechanisms include board independence, corporate charters related to the market for corporate control, management compensation, and debt structure. External control mechanisms, on the other hand, are related to imperfect investor protection at the country level. These external pressures are from regulatory and enforcement mechanisms aimed for protecting the minority shareholders. The literature on corporate governance and agency conflicts has been extensive both theoretically and empirically. Recent studies focus on how imperfect corporate control affects firm value and investor wealth. For example, Dow, Gorton and Krishnamurthy (2005) integrate one of the agency theories, namely Jensen’s (1986) free cash flow theory, into an equilibrium asset pricing model to show how imperfect corporate control influences security prices and investment. In particular, due to the agency problem measured by free cash flow, Dow, Gorton and Krishnamurthy (2005) assume that investors have access to a costly auditing technology, which represents a broad array of internal control mechanisms. They suggest that corporate investment and therefore asset prices are affected by free cash flow and the auditing/monitoring technology helps reduce the agency cost associated with free cash flow. In addition, Albuquerque and Wang (2008) examine asset pricing in the framework of imperfect investor protection at the country level, i.e., the external corporate control mechanisms. In the model, investment decisions are made by large shareholders who extract private benefits (steal) from small shareholders. External control mechanisms determine the cost of stealing. Their model predicts that in countries with weak investor protection
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(the cost of stealing is minimal), firms are more likely to overinvest and have greater return volatility. They argue that firm value increases with investor protection. Closely related to corporate governance, the market for corporate control receives support for its impacts on firm value through either the market pressure of takeover or the actual takeover events. For example, Shleifer and Vishny (1986) present a model in which a large shareholder plays an important role in takeovers and serves as a monitor of the manager. They present various ways in which large shareholders can create value for the firm via monitoring or takeover. Manne (2008) suggests that the market for corporate control is the only needed mechanism1 . Empirical evidence found by Gompers, Ishii and Metrick (2003), Cremers and Nair (2005), and Cremers, Nair and John (2009) suggest that good corporate governance and the threat of takeovers improve firm value. In addition, Jensen and Ruback (1983), among others, find that hostile takeovers improve firm value. In this study, we integrate internal and external corporate governance mechanisms into an equilibrium framework to examine the takeover decision made by large shareholders. While the previous literature addresses the internal or external corporate governance mechanism individually, we model the internal and external governance controls simultaneously in a framework of agency conflicts. In particular, we model the takeover decision in a framework in which agency problem, corporate governance structure, and free rider problem are explicitly addressed. In the model, we consider three players, large shareholder (also the raider), small shareholder, and manager. All players make interrelated decisions simultaneously. Similar to Shleifer and Vishny (1986), we assume that the large shareholder has an exclusive ability to improve the firm’s performance and makes the decision to take over or remain as an active monitor. The large shareholder has two main reasons for taking over the firm: she can gain through better asset allocation or better use of the asset (improvement 1 See also Manne (1965), (2003), (2008), and Jensen (1993), (2000). This group of literature claim that the market of corporate control can be an effective force to improve efficiency
2
hypothesis) and/or reduction in agency cost (inefficient management hypothesis). As one of the key elements in the model, we model agency cost by allowing for manager stealing. Following Albuquerque and Wang (2008), we assume that manager bears the risk of stealing, and the stealing cost is the loss in efficiency that does not accrue to any other players in the model. Manager act in his own interests by stealing from the firm. His decision on the amount of stealing depends on the strength of the governance controls. Minority shareholders are free riders in both takeover and monitoring events. In the takeover event, large shareholder must pay a premium so that small shareholders are willing to tender their shares. We explicitly model the strength of internal governance structure, the pressure from external governance forces, and agency costs due to management stealing. In equilibrium, the optimal holding of the large shareholder, tender premium, manager’s stealing, and firm value are determined simultaneously. The main results of this paper can be summarized as follows. First, between the large and small shareholders, we show that the tender premium is determined by several parameters and state variables. When the maximum takeover gain is greater (less) than the cost of takeover, tender premium paid by the large shareholder is increasing (decreasing) in the number of shares acquired. On a per share basis, tender premium is always greater than the expected takeover gain. Second, when the large shareholder and manager are considered, we present the optimal management stealing as a function of the external governance control, large shareholder’s final holding, and management compensation. Third, we present how internal and external corporate controls interact and affect the takeover decision. In the base case where no external controls exist, it is always optimal for the large shareholder to take over. Given external controls, when the internal controls are very weak, the large shareholder takes over the firm. On the other hand, when the internal controls are very
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strong, the large shareholder prefers to remain as a monitor rather than taking over the firm. When the internal controls are of moderate strength, the takeover decision for the large shareholder is ambiguous. Fourth, given the simultaneous decisions by the three players (large and small shareholders, and manager) and the inclusion of all factors (internal and external governance controls, large shareholder monitoring cost, management stealing cost, and benefits of improvement to large shareholder), the model predicts the following. The large shareholder will take over the firm when external controls are extremely weak. On the other hand, the large shareholder will take over only when the initial holding exceeds one-sixth, given sufficient improvement potential and a bounded takeover transaction cost. Lastly, the large shareholder will never take over when the takeover transaction cost is extremely large and the initial holding is less than one-fourth. Finally, we perform two model extensions: dynamic model and managerial defenses. We expand the static oneperiod model to a dynamic setting. We also incorporate various managerial defenses into the model. In the presence of these defensive tactics, our main results are unchanged. The model presents several implications. We show how internal and external corporate controls, transaction costs, initial holding of the large shareholder affect the takeover decision in a static and dynamic setting. When monitoring costs, which are closely related to the internal governance structure, are high for the large shareholder, takeover is more likely to occur. In addition, when the external governance factors are strong so as to make management stealing difficult, the firm is less likely to be taken over. Furthermore, transaction costs associated with takeover have a negative impact on the probability of takeovers. We also find that the large shareholder is more likely to take over for the purpose of improving performance through greater profitability or better asset allocation when the gain from the initial holding is large. On the other hand, when the gain from the initial holding is low, large shareholder tends to takes over for efficiency (i.e., reducing agency cost).
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In addition, we show that the optimal holding of the large shareholder can deviate from the fixed and legally binding threshold required to control the firm. In other words, in the event of a takeover, the optimal holding can be between 50% and 100%, rather than at 50% (or other fixed thresholds required for control). Furthermore, while previous literature establishes a link between governance structures and firm value2 , we link corporate governance controls to the utilities of the agents and show that, given governance structures, firm value can be created by takeover events. The endogeneity of the takeover/monitoring decision by the large shareholder enables us to examine the effects of the internal and external corporate governance mechanisms simultaneously. Lastly, we show that the initial holding of the large shareholder and the expected improvement in firm value due to the takeover have significant impacts on the utility of the large shareholder and thus the takeover decision (i.e., the optimal holding of the large shareholder). It is the combined effects of the initial holding and improvement, rather than the effects of either one element, that is important to the large shareholder’s decision. Our study provides significant contributions to the literature by examining, in a simultaneous framework, the effects of internal and external governance mechanisms on takeover decisions and firm value. In particular, previous studies on the relation between governance and firm value suggest that the existence of various internal and external governance controls has a positive impact on firm value. The implicit assumption is that the pressure from the 2 Gompers, Ishii and Metrick (2003) find that firms adopting less anti-takeover provisions are associated with higher excess return, higher profits, higher growth, higher firm value, less corporate acquisitions and less capital expenditures. Cremers and Nair (2005) document that a portfolio consisting of buying the highest level of takeover vulnerable firms and shorting the lowest level of takeover vulnerable firms yields an annualized return of 10 to 15 percent, if the public pension fund ownership is high. Ferreira and Laux (2007) use idiosyncratic risk as an instrument and find that firms with fewer anti-takeover provisions are more efficient in term of marginal q. They suggest that the quality of corporate governance is associated with the efficiency of corporate investment. John, Litor and Yeung (2008) find that the quality of investor protection is positively related to corporate risk-taking and firm growth rate worldwide. Masulis, Wang and Xie (2007) study the effects of the anti-takeover provisions in mergers and acquisitions. See also DeMarzo and Urosevic (2006).
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buyout market (or the market for corporate control) leads to a credible threat for the manager to perform better. We extend this literature by presenting a framework that explicitly models the complex relations among the internal and external governance structures, buyout decision, and firm value. In addition, our model is closely related to the literature on the probability and benefits of takeover. Our model is closely related to Shleifer and Vishny (1986). We extend the model in the following aspects. First, we introduce agency costs and the role of manager by modeling the manager’s decision to steal from the firm. Large shareholder considers the tradeoff between the cost of monitoring and the gain from takeover. Following La Porta, Lopez-de-Silanes, Shleifer and Vishny (2002) and Albuquerque and Wang (2008), we assume that manager can steal from the firm if he is in control. Second, we assume that the information and resource of the raider (large shareholder) are exclusive. We shall not consider the probability of takeover success as in Hirshleifer and Titman (1990).3 All tender offers made based on the equilibrium solution will always be succeed. As in Shleifer and Vishny (1986) and Hirshleifer and Titman (1990), we treat the large shareholder and raider as the same agent. We find that anti-takeover actions can be beneficial to minority shareholders only if these actions do not block out the raider. One important issue in the market for corporate control is the free rider problem. In the context of corporate governance, there are two free rider problems. We address both problems in the model. The first free raider problem lies in the monitoring event. Minority shareholders have little incentive to monitor the management since the benefit relative to cost is minimal. Therefore, minority shareholders are likely to free ride on the benefits of monitoring performed by large shareholders. The second free raider problem is related to 3
Hirshleifer and Titman (1990) consider unsuccessful takeover and draw implications on different defensive strategies. They find that even though most anti-takeover actions reduce the probability of takeovers, certain manager’s defensive actions increase the probability of a takeover success because these actions can either increase the tender premium or reduce information asymmetry.
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tender offers or buyouts. Minority shareholders may choose not to tender their shares since they wish to free ride on the gain that will be realized by the raider if the offer is accepted. The consequence is a failed tender offer or a higher tender premium. Gross and Hart (1980) suggest that, given the free rider problem, all tender offers fail unless we give raider the right to dilute the payout to the free riders. Shleifer and Vishny (1986) show that large shareholders can overcome the free rider problem since they offer a part of their gain from the successful tender offer to small shareholders in the form of a tender premium. We address the monitoring problem by assuming that small shareholders do not monitor the manager. Following Shleifer and Vishny (1986), we consider the second free rider problem by offering the small shareholders a tender premium. Our paper is also closely related to Dow, Gorton and Krishnamurthy (2005) and Albuquerque and Wang (2008). In Dow, Gorton and Krishnamurthy (2005), large shareholders monitor the management to reduce agency cost via an auditing/monitoring technology. We use a similar approach by introducing the cost of monitoring. Albuquerque and Wang (2008) explicitly model manager’s stealing cost under imperfect investor protection at the country level. In this paper, we analyze the tradeoff between monitoring and controlling in the presence of management stealing cost (external control). The remaining of the paper is structured as follows. In Section 2, we present the model and equilibrium solutions. In Section 3, we discuss sensitivity analysis and model implications. In Section 4, we present two model extensions by extending to a dynamic setting and by incorporating managerial defenses, respectively. Section 5 concludes. Appendix contains the technical derivations and proofs.
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2
Model
We consider a one-period economy with two securities: one is a locally riskfree asset with risk free rate, r = 0; the other is the equity of a firm with a certain production technology. The firm is owned by two types of shareholders: one large shareholder (L, hereafter) and a group of atomistic shareholders (S, hereafter). Initially, no one holds more than 50% of the shares. The initial firm value is V0 . It grows at a production rate q before agency costs. All agents are assumed to be risk neutral. At the beginning of the period, a manager (M, hereafter) is hired by the shareholders. The manager receives a compensation package as follows:4 manager receives a constant proportion of the realized firm value, θ ∈ (0, 1), if manager remains employed. He receives nothing if he is replaced. The obligation of the compensation package is never violated. For simplicity, we assume that the manager’s initial wealth is zero. At the end of the time period, the production technology is realized and the payouts to all the agents are realized at the same time. L initially owns α0 < 50% of the firm. We assume that α0 is large enough to motivate L to seek improvements in the firm. L has an exclusive access to the technology for identifying and implementing valuable improvements using the firm’s current assets and her own resources (see Shleifer and Vishny (1986)). We assume that L has better management quality and are more willing to exert effort into the firm than M. These advantages give L the capability to improve firm value to (Z + q)V0 , where Z is a nonnegative random variable. We also assume that L and M do not collaborate to exploit S. 4
According to Dittmann and Maug (2007), restricted stock is more beneficial to the firm owners than the employee stock option. The model can be easily extended to the case that some cash amounts are included in the compensation package. In the compensation package we consider, the manager is fully entrenched since he receives nothing if he is replaced.
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L realizes the existence of agency problems and the improvement opportunity. She makes the decision to take over the firm or to stay as a monitor. L’s decision is materialized by her new level of holding α. If α ≥ 50%, L takes over the firm. However, in order to obtain control, L must acquire enough shares from S. We assume that L makes a tender offer to buy shares from S. S will tender only if L gives them enough incentive, i.e. a premium on their shares. We use π(α) > 0 to denote the takeover premium. L also bears the cost of transferring ownership, preparing legal documentation, reorganization and other necessary efforts to realize the improvement. The takeover transaction cost is denoted as cV0 where c is non-stochastic. If α < 50%, L stays as a monitor of M. S does not have any incentive to monitor M and free-rides. So, L is the only insider who monitors M. We denote the monitoring cost as I(α). The more shares L holds, the more motivated is L to monitor. On the other hand, the more shares L holds, the more power she has to force M to disclose information. Thus, we assume I 0 (α) > 0 and I 00 (α) < 0. To facilitate future analysis, we assume 1 I(α) = γα2 V0 . 2
(1)
where γ represents the easiness of monitoring i.e. the level of internal control. As an internal control parameter, γ can be viewed as the proxy of the internal corporate governance structure and firm characteristics such as board composition, firm charter, bylaws, industry sector, and R&D level. S free rides in both takeover and monitoring events. When α < 50%, M imposes agency costs to the firm. We use a stealing technology to demonstrate this cost. Assume M steals β fraction of the firm. As in Albuquerque and Wang (2008), Johnson, La Porta, Lopez-de-Silanes and Shleifer (2000), and La Porta, Lopez-deSilanes, Shleifer and Vishny (2002), the external controls impose a stealing cost
5
on the
manager’s wealth. This cost is efficiency lost which no one benefits from. Three factors 5
It is also termed as the cost-of-theft function in La Porta, Lopez-de-Silanes, Shleifer and Vishny (2002).
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influence the stealing costs. First, the more M steals, the higher the cost but the marginal cost is less. Second, as a monitor, L puts pressure on M’s stealing. When L holds more shares, the incentive for L to reduce such stealing is greater. Third, as shown in Albuquerque and Wang (2008), shareholder protection level in this economy (denoted as η) limits M’s stealing. Therefore, we have ∂Φ ∂Φ ∂ 2Φ ∂Φ > 0, 2 > 0, > 0, > 0, ∂β ∂α ∂η ∂β
(2)
where η is the external control parameter which can be viewed as a proxy for legal system, regulations and social norms. For simplicity, we assume
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1 Φ(α, β, η, V1 ) = αβ 2 ηV1 . 2
(3)
As we will show below, L’s decision is affected by the internal control (γ) and the external control (η) jointly. For now, we assume that there is no management defensive action when L decides to take over the firm. We consider M’s defenses in Section 4.2. Firm value at time t = 1, L’s takeover decision, M’s stealing strategy, and the takeover premium are determined simultaneously in the equilibrium. Table 1 displays how firm value and the final wealth of L and M are affected by L’s holding decision and M’s stealing decision. If L takes over the firm (α ≥ 50%), she needs to pay a premium of (α − α0 )π(α) to S and bears the takeover transaction cost c. Therefore, the final wealth W l is αV1 minus (α − α0 )(V0 + π(α)V0 ), which reflects the amount payout to S and the transaction cost cV0 . If L doesn’t take over the firm, M has the opportunity to 6
The convexity assumption of the stealing cost with respect to β is standard. Our choice of the stealing cost is the same as in Albuquerque and Wang (2008) except for in our case α is involved. We argue that our choice is reasonable in a framework with both internal and external controls. Albuquerque and Wang (2008) do not consider the monitoring case.
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Table 1: Affects of External and Internal Control on M’s and L’s Wealth This table shows firm value, large shareholder’s wealth and the manager’s wealth, at time t = 1. α and β are two decision variables of L and M, respectively. Firm Value V1
L’s final wealth W l
M’s final wealth W m
Takeover
V0 (q + Z)
αV1 − (α − α0 )(V0 + π(α)V0 ) − cV0
0
Monitor
V0 q
α(1 − θ)(1 − β)V1 − I(α) − (α − α0 )V0
θ(1 − β)V1 + βV1 − Φ(α, β, η, V1 )
steal β fraction of the firm, and the firm’s value is reduced to (1 − β)V1 . After the manager’s compensation, θ(1 − β)V1 , the firm has (1 − θ)(1 − β)V1 to distribute to its shareholders. Consequently, the final wealth W l is α(1 − β)(1 − β)V1 minus (α − α0 )V1 and then minus the monitoring cost I(α). The final wealth of the manager can be derived using the same logic.
2.1
Takeover Premium
We determine the takeover premium π(α) in this section. When L makes a tender offer, S assumes that L has the ability to make improvement and therefore demands a premium. We follow Shleifer and Vishny (1986) that the takeover premium π(α) is determined at the point where S is indifferent to tender or not tender. Thus, S’s expectation of the improvement given that L makes a tender offer is:
π(α) = E[Z|αZ − (α − α0 )π(α) − c ≥ 0].
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(4)
We assume that Z is uniformly distributed on [0, Zmax ].7 Then, by equation (4), we obtain
π(α) =
Zmax α + c α + α0
(5)
and ∂π(α) Zmax α0 − c = ∂α (α + α0 )2
(6)
We now have the following result.
Proposition 1
1. If the expected takeover gain from the L’ s initial holding, α0 Zmax , is greater than half of the takeover transaction cost, then the tender premium is increasing with respect to the number of shares she purchases. 2. The takeover premium,π is positively correlated with the takeover transaction cost, c,. 3. The takeover premium is always greater than the expected takeover gain.
This proposition presents the general behavior of the takeover premium. L takes over the firm only if the takeover is more attractive than staying as monitor of M. She evaluates the amount that she can gain from the takeover, especially the gain from her initial holding before the tender offer. Meanwhile, L must pay the transaction cost c. Hence the takeover gain from L’s initial holding and transaction cost determine the shape of takeover premium. If the expected gain from L’s initial holding can cover most of the transaction cost, the number 7
The uniform distribution assumption is only used in this paper for illustrative purpose. Other distributions of Z can be imposed and the main findings of this paper are still the same as long as S observes some information of the distribution of Z. For instance, if S observes Z + where is a noise independent of Z, the equation (4) still holds.
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of shares L acquires reflects her confidence in the benefits from the potential improvement. This indicates to S as a signal of high potential profit. So, the takeover premium increases with the number of shares of L’s tender offer. By the same token, when the expected gain cannot cover most of the transaction cost, S asks for smaller premium. In Section 2.4, we show that takeover is still possible when external and internal controls are weak, and L holds either 50% or 100% of the firm’s shares. Whenever L makes a tender offer, S expects nonnegative improvement. Thus S tenders his shares only if L offers no less than the expected takeover gain. Finally, holding all else constant, given that L makes a tender offer, a larger transaction cost indicates better future prospects. As a result, S asks for a larger premium to tender his shares. The analysis on the takeover premium forms the basis for our subsequent derivation of the Nash equilibrium. We first examine the manager’s stealing decision and then L’s decision to take over or monitor the firm.
2.2
Manager’s Stealing Decision
Suppose that M observes L’s holding decision α, and chooses his optimal stealing amount β, the manager’s expected utility is
r
E[W ] =
1 2 θ(1 − β) + β − αηβ E[V1 ]. 2
(7)
By solving the first order condition (FOC), M’s optimal stealing fraction β is
β ∗ = argmaxβ E[W r ] =
13
1−θ . αη
(8)
β is inversely related to the numbers of holding, α, and the external control parameter η. High η represents a strong external control environment which leads to less manager’s stealing. Equation (8) shows how the external (η) and internal controls affect the manager’s stealing decision and reduce the agency cost. The internal control factor is nested in L’s holding decision.
2.3
Equilibrium of Large Takeover Gain from L’s Initial Holding
In this section we characterize the equilibrium when α0 E[Z] > 2c . A large takeover gain from L’s initial holding, α0 E[Z], gives L a strong incentive to take over the firm. However, as shown in Proposition 1, takeover premium is increased with respect to the number of shares purchased, reducing the takeover profit. Hence L needs to compare her welfare of taking over the firm (i.e., α ≥ 50%) and that of not taking over the firm. L’s optimal decision is the one giving her higher payout. We first consider a benchmark model where no external control exists, i.e., η = 0.
Proposition 2 If there is no external control, L always takes over the firm.
Proof: See Appendix A.
This proposition asserts that in a world without external control L always takes over the firm. The result is intuitively appealing. In a world without investor protection, M does not need to disgorge any cash back to the shareholders. L thus takes over the firm to protect her investment. However, minority shareholders may stay on since L, as an entrepreneur,
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returns cash back to investors due to future financing concern8 . In the presence of external control, L may remain as a monitor of M as shown below. To see this, we examine L’s expected utility closely. First, in the “takeover” region where α ≥ 50%, the optimal holding α∗ depends on how large the expected improvement E[Z] can be achieved. Precisely, if the expected improvement is greater than E[q] − 1, α∗ = min{max{50%, α∗1 }, 100%},
(9)
where α∗1
r :=
s − α0 , u
s := 2α0 (α0 Zmax − c), u := E[Z] − (E[q] − 1) On the other hand, if the expected improvement is less than E[q] − 1, then it is optimal to purchase 100% of the firm. In equation (9), α∗1 is crucial. The equation states that the optimal holding is α∗1 if α∗1 is bounded by 50% and 100%. Note that takeover transaction cost can be large in reality. If α0 E[Z] > 2c , it is more likely that E[Z] > E[q] − 1. Since the improvement opportunity is significant, L is likely to take over the firm. Given the attractive improvement opportunity, should L always hold 100% of the firm? As shown in Proposition 1, while more holding give L greater wealth, she also needs to pay more to purchase additional shares. Based on this tradeoff, 100% may not be optimal. Similarly, 50% may not be the optimal either in this case where L cannot reap the full benefits of improvement. Equation (9) follows from the tradeoff between the costs and benefits. Second, according to Table 1, L’s expected utility 8
See Shleifer and Vishny (1997) for further discussion. On the other hand, internal control cannot force M to disgorge cash back to shareholders because contract violation is not charged.
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in the monitoring region that α < 50% is concave. Its maximum expected utility is achieved at α∗2 =
(1 − θ)E[q] − 1 , γ
whenever α∗2 < 50%. L’s optimal decision is determined by comparing L’s expected utilities in the takeover and monitoring regions. The next proposition asserts that, under certain circumstance of the corporate controls, L does not take over the firm.
Proposition 3 Given an external control environment with shareholder protection η > 0, when the internal control is weak, L takes over the firm; when the internal control is strong, L does not take over the firm; when the internal control is moderate, L’s decision depends on internal and external controls in a way shown in Proposition A.1 of Appendix.
Proof: A general version of this result, Proposition A.1, is given and proved in Appendix. The intuition is that a weak internal control (high γ) is closely related to a significant monitoring cost. While the external control environment provides investor protection from a systematic perspective, L’s decision also depends on how monitoring is. When the monitoring cost is high, L is more likely to take over the firm. On the other hand, if the internal control is strong, is more likely to remain as a monitor and she can acquire shares to enhance her monitoring position.9 By increasing her holding on the firm, the agency cost is deduced by equation (8). Figure 1 shows how the takeover decision is affected jointly by the external and internal corporate controls. In Figure 1, both the monitoring and takeover regions are presented. The parameters in this figure are Zmax = 8, E[q] = 4, α0 = 1%, θ = 1%, V0 = 1 and c = 0.05. 9
We will extend the model to a dynamic setting later in which this result will be used.
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Takeover region vs η and η 30
25
γ
20
Takeover region
15
10 Monitor region 5
0
0
1
2
3
4 η
5
6
7
8
Figure 1: This figure shows the takeover region and the monitoring region in term of the external and internal controls. The parameters of this figure are Zmax = 8, E[q] = 4, α0 = 1%, θ = 1%, V0 = 1 and c = 0.05. There are two different situations: η ≤ 3.32 and η > 3.32. L takes over the firm if η ≤ 3.32.
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The takeover gain from L’s initial holding is α0 E[Z] = 21 α0 Zmax = 0.04 > 2c . According to Proposition A.1 in Appendix, the critical monitor parameter γ ∗ = 2{(1 − θ)E[q] − 1} = 5.92, and the critical external parameter η ∗ = 3.32. When η ≤ 3.32, L takes over the firm. When η > 3.32, L’s decision depends on the internal and external controls. As presented by Proposition A.1, L takes over the firm if
γ≥
1 ((1 − θ)E[Z] − 1)2 2 , (1−θ)2 E[Z] A − α + 0 η V0
where A is L’s maximum expected utility in the takeover region. Otherwise, L remains as a monitor. L does not to take over the firm in the latter case because L is willing to monitor the firm when the internal control is efficient and the external control is strong. We now show how the external control parameter η affects the takeover decision.
Proposition 4
1. L takes over the firm in a weak external control environment. 2. When E[Z] is large and the takeover transaction cost c is bounded, then L never takes over the firm if her initial holding α0 ≤ 16 . 3. L takes over the firm if her initial holding α0 > 16 . 4. L never takes over the firm when the takeover transaction cost c is large and α0 ≤ 14 .
Proof: See Appendix.
When η is small, the market is close to the benchmark model. Similar to the benchmark model, since external control cannot protect investors effectively, L takes over the firm. If 18
L’s initial holding is large, she takes over the firm to enjoy the improvement. On the other hand, when the expected improvement is large but the initial holding is very small, L prefers not to take over the firm. Moreover, when c is large whereas L’s initial holding is small, the large transaction cost discourages L from the takeover. L remains as a monitor of the manager through internal control mechanisms.
2.4
Equilibrium of Small Takeover Gain from L’s Initial Holding
We have characterized the equilibrium in which the takeover gain from the initial holding is large. In this section, we derive the equilibrium where the takeover gain from L’s initial holding is small. That is α0 E[Z] < 2c . We use the same logic as in the previous section to investigate the optimal holding in the takeover and monitoring regions, respectively. There is one noteworthy difference in the optimal holding of L when the takeover gain from the initial holding is either small or large. When the takeover gain from L’s initial holding is small, L’s optimal holding is either 50% or 100% while the optimal holding can be anywhere between 50% and 100% if the gain is large. Moreover, L takes over the firm by purchasing just 50% of the firm’s shares for a reasonable level of the takeover transaction cost c.10 The difference is explained by L’s expected utility. When the initial takeover gain is large, L’s expected utility is a concave function with respect to her holding α, similar to a standard expected utility in economics. Therefore, the global maximum point is not necessarily 50% nor 100%. On the other hand, L’s expected utility becomes convex when the takeover gain from L’s initial holding is small. This convexity follows from the trade-off between the benefits of acquiring more shares and the costs of takeover (takeover premium and takeover 10
See Proposition A.2 , Appendix for its proof.
19
transaction cost). Since L’s utility function is convex, the maximum of this function is always at the binding point, α = 50% or the fully control point, α = 100%. These patterns are shown in Figure 2. Figure 2: L’s optimal holding in the takeover region This figure shows L’s expected utility in the takeover region with respect to her holding α. In the upper panel, c = 0.15, E[Z] = 0.75, q = 1.12, and α0 = 0.4. α0 E[Z] > 2c . The expected utility is concave and the optimal holding α∗ = 35.6%. In the lower panel, α0 = 0.05, E[Z] = 0.005 while other parameters are the same as in Panel A. In this case, the expected utility behaves as a convex function. The optimal holding α∗ = 50%. Panel A L's Takeover Utility--Large Initial Gain U
Α
Panel B L's Takeover Utility--Small Initial Gain U
Α
After determining the optimal holding α∗ in the takeover region, we can solve the Nash Equilibrium. The next proposition interprets the role of the internal control parameter,γ, in a given external control environment when α0 is small.
20
Proposition 5 Assume L’s initial holding α0 is small. In a given external control environment, L takes over the firm if the internal control is weak. That is ( 1 γ > M ax (1 − θ)E[q] − 1, 2
((1 − θ)E[q] − 1)2 E[q−Z−1] 2
+ η1 (1 − θ)2 E[q] − c
) .
Proof: See Appendix.
This proposition affirms that L takes over the firm when the internal control is weak. The intuition is similar to Proposition 3. Regardless of the size of takeover gain from the initial holding, better external corporate governance (high η) and internal corporate governance (low γ), reduce the possibility of a change of control. In addition, the higher the θ, the higher the possibility of a change of control if E[q] >
1 . 1−θ
Takeover transition cost, on the
other hand, reduces the monitoring value of market of corporate control. When c is large, L does not have much incentive to seek information to improve firm performance.
Figure 3 shows the monitoring and takeover regions in the presence of the external control. In this figure, Zmax = 8, E[q] = 4, α0 = 0.5%, θ = 1%, V0 = 1 and c = 0.05. The takeover gain from L’s initial holding is α0 E[Z] = 21 α0 Zmax = 0.02 < 2c . Similar to Figure 1, the critical monitor parameter γ ∗ = 2{(1 − θ)E[q] − 1} = 5.92 and the critical external parameter η ∗ = 3.16. When η ≤ 3.16, L takes over the firm. When η > 3.16, L’s decision depends on how the internal control works jointly with the external control. Precisely, when
γ>
2 ((1 − θ)E[q] − 1)2 E[q−Z−1] 2
+ η1 (1 − θ)2 E[q] − c
,
L takes over the firm since the monitoring cost is too high. Otherwise, it is optimal for L to monitor the manager when both internal and external controls are effective.
21
Takeover region vs η and η 60
50
Takeover region
γ
40
30 Monitor region 20
10
0
0
1
2
3
η
4
5
6
7
Figure 3: This figure shows the takeover and the monitoring region in the presence of external control. The parameters of this figure are Zmax = 8, E[q] = 4, α0 = 0.5%, θ = 1%, V0 = 1 and c = 0.05. There are two different situations: η ≤ 3.16 and η > 3.16. L takes over the firm if η ≤ 3.16.
22
So far we have discussed the effects of internal control given the external control. Below we investigate the effects of other market parameters including the transaction cost, expected improvement and external control.
Proposition 6 Assume α0 E[Z] < 2c . L does not take over the firm if one of the following conditions holds:
1. The cost c is very large and the expected improvement E[Z] is moderate. 2. The expected improvement E[Z] is significant but α0 ≤ 25%.
However, L takes over the firm if the external control is weak.
Proof: See Appendix.
This proposition states that a large transaction cost c is able to block out takeovers. L faces a difficult situation given the small gain from her initial holding. No matter how large the potential takeover improvement is, L cannot profit from the acquired shares if she takes over the firm. However, when η is extremely small, L must protect herself by taking over the firm as argued in Proposition 4. The proposition is intuitive. If η is very small, the market is close to the benchmark model discussed in Proposition 2. Due to weak investor protection, L protects herself by controlling the firm. If the cost structure c is very high, then L prefers not to take over the firm. Actually, by making the tender offer when c is high, L sends out the signal that the expected improvement is high. Small shareholders read the information and require a greater premium. Given that the E[Z] can only be in a reasonable range and the initial holding is also bounded, the high transaction cost c takes away all possible takeover profits.
23
External&Internal Control and L's Optimal Utility
U
Η
Γ
Figure 4: This figure shows how the internal (γ) and external (η) controls affect L’s optimal utility. In general, L’s utility is negatively correlated with γ and positively correlated with η. Parameters of this figure are α0 = 0.4, q = 1.12, c = 0.15, E[Z] = 0.25 and θ = 0.003.
24
To illustrate the joint effects of the external and internal corporate controls simultaneously, we plot L’s expected utility with respect to γ and η in Figure 4. As displayed, L’s expected utility increases when the external control is stronger(large η), or when the internal control is efficient(small γ). The effects of these controls are initially significant when the parameters are small. Given external control η, γ is only effective before the critical point in Proposition 3, and Proposition 5 where takeover occurs. When η is less than the critical point, L takes over the firm. L’s utility then does not depend on these two parameters. We have shown the effects of internal and external governance mechanisms on the takeover decision and firm value. We now turn to model implications.
3
Model Implications
We show that in equation (9), the optimal shares α∗ of L is not necessarily the binding point 50% when the initial holding is large. Below we present a complete characterization of the circumstance under which α∗ 6= 50%.
Corollary 3.1 Assume that α0 E[Z] >
c 2
and E[Z] > E[q] − 1. The optimal holding α∗ is
not equal to binding level 50% as long as the initial holding α0 satisfies p u + 2c + 2 u(c + E[Z]) + c2 α0 > , 2(4E[Z] − u) where u := E[Z] − (E[q] − 1). Moreover, the optimal holding α∗ ∈ (50%, 100%) if and only if p p u + 2c + 2 u(c + E[Z]) + c2 u + c + 2 2u(c + E[Z]) + c2 < α0 < . 2(4E[Z] − u) 4E[Z] − u
25
(10)
Proof: See Appendix.
This result states that α∗ > 50% when the initial holding α0 is large, or E[Z] − (E[q] − 1) is relatively small. The intuition is as follows. When the expected improvement is close to the expected return without taking over, firm return remains constant before and after the takeover. L’s decision is similar to a standard portfolio choice decision. Therefore, the optimal number of shares is not necessarily 50%. On the other hand, if the expected improvement is relatively large, or α0 is relatively small, then L’s optimal holding is 50%, as predicted in previous literature (e.g. Shleifer and Vishny (1986) and Goldman and Qian (2005)). In Shleifer and Vishny (1986), a competitive takeover market exists and all the potential raiders are required to give S the best tender price. Therefore, all raiders have to offer the same price and acquire the least number of shares to take control, which is 50% of the firm’s outstanding shares. We relax the competitive market constraint, so L can make a more flexible decision. Our result asserts that even without the competitive takeover market, raider will acquires 50% of the shares when the initial holding is relatively small, or the expected improvement is large. Indeed, one can easily argue that the initial holding α0 is often small, or the expected improvement should be high. Therefore the optimal shares must be 50% as claimed in previous literature. However, this is not necessarily true in a dynamic model, which we will discuss later.11 Figure 5 shows the region of α0 when the optimal holding α∗ is 50%, 100% or some interior points in [50%, 100%]. There are three boundaries; the lower boundary is given by the lower bound in formula (10) while the upper boundary is given by the upper bound in 11 The models in Shleifer and Vishny (1986) and Goldman and Qian (2005) among others are static in sprit. The remarkable difference between the static and the dynamic model is that the initial holding changes in each time period, hence it might be large. The consideration of the dynamic extension motivates us to examine both the large and small initial takeover gain in our paper.
26
the formula (10). We see that, if α0 is small, α∗ = 50%. However, when α0 is in a reasonable range, it is possible for L to take an interior solution due to the concavity of the utility function.
L's Holding Region Α0 0.6
Upper Bound *
Α =100%
0.5
Lower Bound
Α* ÎH50%,100%L
0.4
c
0.3
Α0 E@ZD=
2
0.2 E@ZD 0.45 0.50 0.55 0.60 0.65 0.70
Figure 5: This Figure shows L’s optimal holding if she takes over the firm and α0 E[Z] > c/2. In this figure, the brown dish line is the line of α0 E[Z] = 2c , the blue upper bound line is the upper boundary of inequality (10) and the green lower bound line is the lower boundary of inequality (10). In the area above the brown dish line α0 E[Z] = 2c , L’s optimal holding is between 50% and 100% in the area between the blue upper bound and the green lower bound lines. Parameters of this figure are q = 1.25, c = 0.07 and θ = 0.003. Since the optimal holding is not always fixed at 50%, the next result presents the property of α∗1 with respect to α0 .
12
Corollary 3.2 If L’s optimal holding α∗ depends on α0 , then it is a concave function of α0 . 12
Its proof is straightforward and omitted.
27
The concavity suggests that there is an optimal level of initial holding for L if she takes over the firm. In Goldman and Qian (2005), they find the same effect of the initial holding in the content of toehold. In their model L attempts to acquire only the binding percentage 50% and raider faces possible losses if the tender offer fails. In our model, L decides the optimal ex post holding, α and the tender offer never fails. We next examine how the initial holding α0 and the expected improvement affect the tender premium.
Corollary 3.3 The tender premium is always negatively correlated to α0 . If the takeover gain from L’s initial holding is small, the tender premium is positively correlated to E[Z]. If the takeover gain from L’s initial holding is large, the correlation between the tender premium and E[Z] can be either positive or negative.
Proof: See Appendix.
This result is well known when the optimal holding for L is always 50%. Corollary 3.3 says that the relationship between the takeover premium and the initial holding is robust in our model. The effect of the expected improvement, however, is complicated. This is shown in Figure 6.
Corollary 3.4 L’s optimal holding does not depend on the level of external control, η. The manager’s stealing, β ∗ , is negatively correlated to η.
We show L’s takeover decision depends on both external and internal controls. However, L’s holding does not rely on the level of the external control. Since the manager considers legal and social costs, stealing is negatively related to the effectiveness of the external control. The monitoring cost reduces L’s wealth, hence the external control doesn’t affect L’s optimal 28
Expected Improvement and Takeover Premium Π
E@ZD
Figure 6: This figure shows the relationship between expected takeover improvement and the takeover premium. It shows that these two parameters can be either positive or negatively correlated. Parameters of this figure are α0 = 0.4, q = 1.25, c = 0.07, γ = 1, η = 1 and θ = 0.003. holding but L’s decision to take over. Only when the social environment does not provide adequate shareholder protection, L decides to take over. Our result is supported by the fact that countries with weak shareholder protection are often associated with a high concentration of ownership, as documented by Albuquerque and Wang (2008). In these countries, top manages or their family members are often the large shareholders. In the countries with effective shareholder protection, i.e. η is large , takeover action is often favored by large shareholders. It is consistent with the fact that there are many firms with large shareholders in the US but takeover is still an extreme phenomenon (Shleifer and Vishny (1986)).
Corollary 3.5 L’s optimal holding depends negatively on γ in the monitoring region.
29
This result asserts that shareholders choose to reduce their holding when monitoring manager is difficult. We see support from empirical evidence that large firms with a powerful management team often have a dispersed ownership structure.
4
Extensions
We have presented a one period model in which the manager has no takeover defenses. A more realistic situation would be that the large shareholder acquires shares gradually, and the manager are able to fight off the tender offer. In this section, we extend the static model to a dynamic model and incorporate the managerial defense.
4.1
Dynamic Extension
We have shown how the external and internal controls jointly affect the takeover decision, management stealing and firm value in a single-period model. We now extend the static model to a dynamic setting. Without a loss of generality, we assume that E[Z] > c ≥ E[q]−1. We assume that production rates qt are i.i.d and improvement Z in each time period are i.i.d. We also assume that the compensation package is renewed in each time period. The next result establishes that, if
(1−θ)E[q]−1 γ
≥ 50%, L takes over the firm in the dynamic
framework. Proposition 7 If
(1−θ)E[q]−1 γ
≥ 50%, then L takes over the firm in the first time period or
in the second time period. Moreover, if L takes over the firm in the second time period, L holds 50% shares of the firm. Proof: See Appendix.
30
This result is interesting in several aspects. First, the takeover occurs eventually when the internal control is not efficient, i.e., γ ≤ 2{(1 − θ)E[q] − 1}. Second, this result is true regardless of the level of the external shareholder protection. Third, L’s optimal holding is at the binding point 50%. In the static model, it is possible that the new holding α∗ is less than 50%. If so, α∗ either equals to
(1−θ)E[q]−1 , γ
or is close to 50%. Hence the initial holding in the subsequent
time period could be large. Because of the lower level of γ, more close to 50% is α∗ in the first time period. L then takes over the firm in the second period. We now move to the case where
(1−θ)E[q]−1 γ
< 50%. In this case, as shown in the next
result, the takeover decision is affected by both the external and internal controls as in the static model.
Proposition 8 Assume production rate q is i.i.d, improvement Z is i.i.d. and
(1−θ)E[q]−1 γ
2{(1 − θ)E[q] − 1}. In this case L takes over the firm when the external control is weak. These results are consistent with to the real world situation in which the internal control is more efficient than the external control. Our results, however, do not undermine the importance of the external control. Rather, these results present the tradeoff between the external and internal controls. The dynamic model also demonstrates that even in the case without a large shareholder initially, the market of corporate control can be enforced by fostering a large shareholder. Raider can accumulate shares up to the point where takeover is favorable to her. Therefore, a large shareholder emerges endogenously in the market.
4.2
Managerial Defense
In the real world, management has the options to defend the target with various anti-takeover actions. In this section, we show that in the presence of managerial defenses, our main results of the previous sections hold. Following Hirshleifer and Titman (1990), we consider three categories of defensive measures. These defensive measures are given exogenously. L anticipates such anti-takeover actions, so she takes these actions into consideration when making the takeover decision.
32
4.2.1
Contingent Defense
In the first case, M uses some form of poison pills which impose costs on the bidder, and thus redistribute wealth from L to S. For this reason, let the excess return to S be
Z + a,
where 0 ≤ a ≤ 1 represents the extra amount shifted to S in the successful takeover event. By using the same procedure as in Proposition 1, we obtain
π a (α) =
c + αZmax + a(1 + α) , α + α0
(11)
and α0 Zmax − c − a(1 − α0 ) ∂π a (α) = . ∂α (α + α0 )2
(12)
By comparing the takeover premium with equation (5), this type of contingent defense is in essence to impose a higher takeover transaction cost, from c to c + a(1 − α0 ). Therefore, previous results can be applied in this case. Since the takeover transaction cost is increased, this strategy essentially introduces higher barriers of takeover. If raider anticipates such action ex ante, but still decides to go ahead with the tender offer, then minority shareholders benefit from such action. However, if the raider decides not to acquire the firm, the manager can steal a proportion of the firm and remains in control. While both a and α0 as exogenously given, all the results from the previous sections follow in a static model. In a dynamic setting, α0 changes over time. If L accumulates shares over time, the manager’s defense will delay the takeover action. Small shareholders
33
benefit from such anti-takeover defense strategy if the takeover still occurs. The case a < 0 corresponds to strategy that L has the dilution right as described in Grossman and Hart (1980). In this case, L is more likely to acquire less to obtain control to maximize her return.
4.2.2
Reduction in Firm Improvement
Another possible managerial defense strategy is to sell the units from which the most post takeover improvement can be made. This strategy can be represented by examining the effect ˜ Due to this defense strategy, of the possible improvements, namely, reduced from Z to Z. Z˜ is still distributed uniformly. The only difference is Z˜max = Zmax − δ, where δ > 0. Our main results in the previous sections apply for given δ. If the strategy reduces the improvement significantly from the large gain region to the small gain region, some L’s flexibilities are limited. Consequently, tender premium is reduced. Therefore, this strategy also hurts minority shareholders. It is worth noting that this strategy does not necessarily lead to a reduction in L’s utility. In addition to paying less tender premium, L can adjust her holding decision to reflect the reduction of improvement. Manager is a potential winner under this strategy even though the management compensation is affected negatively. The reason is that L is less likely to take over the firm. The manager is more likely to keep his job.
4.2.3
Impose Cost to Raider Ex Ante
Imposing cost to the raider before the tender offer is another managerial defense strategy. Let’s recall that in the model, whenever a tender offer is made, it is always successful. In other words, L predicts manager’s stealing and has considered other costs in her decision. If she finds takeover to be suboptimal, L simply does not tender and remains as a monitor 34
of the manager. Therefore such a strategy essentially leads to an increase of the takeover transaction cost c. So previous results apply.
5
Conclusion
In this study, we integrate internal and external governance controls into an equilibrium framework to examine the takeover decision made by large shareholders. We provide the first attempt to explicitly model both internal and external controls in a framework of agency conflicts and to directly examine the utilities of various agents in the monitoring/takeover game. In particular, we model the takeover decision in a framework in which agency problem, corporate governance structure, and free rider problem are explicitly addressed. By incorporating the takeover market, monitoring and external controls, we are able to demonstrate the inter play of all relevant factors. We show that takeover probability is determined by not just the pre-takeover firm performance, but a matrix of many factors. We show how internal and external corporate controls, transaction costs, initial holding of the large shareholder affect the takeover decision in a static and dynamic setting. In addition, we show that the optimal holding of the large shareholder can deviate from the fixed and legally binding threshold required to control the firm. Furthermore, we link corporate governance controls to the utilities of the agents and show that, given the governance structures, firm value can be created by takeover events. Finally, we show that the combined effects of the initial holding of the large shareholder and the expected improvement in firm value are significant determinants of the utility and optimal holding of the large shareholder. Our model assumes information symmetry such that the each of the three players (large and small shareholders and the manager) predicts and takes into account the actions by the other players. In real life, there is likely to be asymmetric information about the takeover, 35
management stealing, and potential firm improvement, as in Hirshleifer and Titman (1990) and Goldman and Qian (2005). Moreover, this model assumes there is only one large shareholder who also serves as a possible raider. In the real world, there exists a competitive market consisting of various types of raiders and not all raiders serve as the same role as the large shareholders defined in our model. In future research, it will be interesting to extend the model to consider information asymmetry and a competitive raider’s market.
36
References Albuquerque, R. and Wang, N., Agency Conflicts, Investment and Asset Pricing, Journal of Finance, 53, pp. 1-40, 2008. Agrawal, A. and Jaffe, J. F., Do Takeover targes underperform? Evidence from Operating and Stock Returns, Jounal of Financial and Quantitative Analysis, 38, pp. 721-746, 2003. Asquith, P., Bruner, R. F. and Mullins, D. W., The Gains to Bidding Firms from Mergers, Journal of Financial Economics, 11, pp. 121-139, 1983. Cremers, M. and Nair, V., Governance Mechanisms and Equity Prices, Journal of Finance, 50, pp. 2859-2894, 2005. Cremers, M. and Nair, V. and John, K., Takeovers and the Cross-Section of Returns, Review of Financial Studies, Volume 22, Number 4, April 2009 DeMarzo, P. M. and B. Urosevic., Owership Dynamics and Asset Pricing with a Large Shareholder, Journal of Political Economy, 114, pp. 774-815, 2006. Dittmann, I. and Maug, E., Lower Salaries and no Options? the Optimal Structure of Executive Pay, Journal of Finance, 62, pp. 303-343, 2007. Dow, J., Gorton, G. B. and Krishnamurthy, A., Equilibrium investment and asset prices under imperfect corporate control, American Economic Review, 95, pp. 659-681, 2005. Ferreira, M. and Laux, P., Corporate Governance, Idiosyncratic Risk and Information Flow, Journal of Finance, 42, Vol. 52, pp. 951-989, 2007. Goldman, E. and Qian, J., Optimal Toeholds in Takeover contests, Journal of Financial Economics, 77, pp. 321-346, 2005.
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Gomper, Ishii and Metrick, Corporate Governance and Asset Price, Quarterly Journal of Economics, Vol. 118, No. 1, pp. 107-155, February 2003. Grossman S. and Hart, O., Takeover Bids, the Free-Rider Problem and the Theory of the Corporation, Bell Journal of Economics, vol. 11(1), pp. 42-64, Spring, 1980. Hirshleifer, D. and Titman, S., Share Tendering Strategies and the Success of Hostile Takeover Bids, Jornal of Political Economy, 98, pp. 295-324, 1990. Jarrell, G. A., Brickley, J. A., Netter, J. M., The Market for Corporate Control: The Empirical Evidence Since 1980, Journal of Economic Perspectives, Vol. 2, No. 1, pp. 49-68, 1988. Jensen, M. 1986, Agency Cost of Free Cashflow Corporate Finance and Takeovers, American Economic Review 25, pp. 393-408, 1986. Jensen, M. C., The Modern Industrial Revolution, Exit and the Failure of Internal Control Systems, Journal of Finance, Vol. 48, No. 3, January 5-7, pp. 831-880, 1993. Jensen, M. C., Theory of the Firm: Governance, Residual Claims and Organizational Forms, Harvard University Press, 2000. Jensen M. and Meckling, W., Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure. Journal of Financial Economics, 3, pp. 305-360, 1976. Jensen, M. and Ruback, R., The Market for Corporate Control: The Scientific Evidence. Journal of Financial Economics, 11, pp. 5-50, 1983. John, K., Litor, L. and Yeung, B., Corporate Governance and Managerial Risk Taking: Theory and Evidence, Journal of Finance, Vol. 63, pp. 1729-1775, 2008.
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Johson, S., La Porta, R., Lopez-de-Silanes, F. and Shleifer, A., Tunneling, American Economic Review Papers and Proceedings, 90, pp. 22-27, 2000b. La Porta, R., Lopez-de-Silanes, F., Shleifer, A. and Vishny, R., Investor Protection and Corporate Valuation, Journal of Finance, Vol. 52, pp. 1147-1170, 2002. Lang, L. H. P., Stulz, R. M. and Walkling, R. A., Managerial Performance, Tobin’s q and the Gains from Successful Tender Offers, Journal of Financial Economics, 24, pp. 137-154, 1989. Manne, H. G., Mergers and the Market for Corporate Control, Journal of Political Economy, Vol. 73, No. 2. (Apr., 1965), pp. 110-120, 1965. Manne, H. G., A Free Market Model of a Large Corporationg System, Emory Law Journal, Vol. 52, pp. 1381-1400, 2003. Manne, H. G., Corporate Governance – Getting Back to Market Basics, SEMINARIO CONSOB 10 NOVEMBRE 2008. Masulis, R. W., Wang, C., Xie, F., Corporate Governance and Acquirer Returns, The Journal of Finance, Volume 62 Issue 4, pp. 1851 - 1889, 2007. Matos, P., Gaspara, J. and Massa, M., Shareholder Investment Horizons and the Market for Corporate Control, Journal of Financial Economics, Vol. 76, No. 1, pp. 135-165, 2005. Shleifer, A. and Vishny, R. W., Large Shareholders and Corporate Control, Journal of Political Economy, vol. 94(3), pp. 461-488, 1986. Shleifer, A. and Vishny, R. W., Management Entrenchment : The Case of Manager-Specific Investments, Journal of Financial Economics, Vol. 25(1), pp. 123-139, 1989.
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Shleifer, A. and Vishny, R., A Survey of Corporate Governance, Journal of Finance, 42, pp. 737–783, 1997.
40
A
Appendix
The optimal holding in the takeover region: In the takeover region, L’s expected utility is
αE[V1 ] − (α − α0 )(V0 + V0 π(α)) − cV0
f (α) :=
= α0 V0 + α(E[V1 ] − V0 ) − (α − α0 )π(α)V0 − cV0 .
By straightforward calculation, yield 1 Zmax α2 + 2α0 Zmax α + 2α0 c − α20 Zmax f (α) = V0 E[q] + Zmax − 1 − V1 2 (α + α0 )2 V0 2 = (α + α ) (E[q] − E[Z] − 1) + 2α (α Z − c) , 0 0 0 max (α + α0 )2 0
and f 00 (α) = −
4α0 (Zmax α0 − c) V0 . (α + α0 )3
(A-1)
By assumption, Zmax α0 > c, the function f (α) is concave with respect to the percentage α. Case (1). Assume that E[q] < E[Z] + 1.Then by the first order condition, the maximum point of the function f (α) is
α∗1
r =
s − α0 . E[Z] + 1 − E[q]
(A-2)
Since α∗ ∈ [50%, 100%], then
α∗ = min{max{50%, α∗1 }, 100%}.
41
(A-3)
Case (2). Assume that E[q] ≥ E[Z]+1. Then f 0 (α) > 0. Hence the optimal α∗ = 100%. The next proposition characterizes L’s decision completely when the initial takeover gain is large. Proposition A.1 Assume (1 − θ)E[q] < 12 γ + 1. Then 1. If A ≥ V0
n
1 [(1 2γ
o − θ)E[q] − 1]2 − η1 (1 − θ)2 E[q] + α0 , then L takes over with the op-
timal number of shares α∗ . 2. If A < V0
n
1 [(1 2γ
o − θ)E[q] − 1]2 − η1 (1 − θ)2 E[q] + α0 , then L decides to acquire shares
up to α∗2 without paying a tender premium to take over the company. Assume (1 − θ)E[q] ≥ 21 γ + 1. Then n 1. If A ≥ V0 − 18 γ − η1 (1 − θ)2 E[q] −
(1−θ)E[q] 2
o − ( 12 − α0 ) , then L takes over the firm
with the optimal number of shares α∗ . n 2. If A < V0 − 81 γ − η1 (1 − θ)2 E[q] −
(1−θ)E[q] 2
o − ( 12 − α0 ) , then L decides against the
takeover. However, L purchases shares as close to 50% as possible.
Proof: Recall α∗2 ≡
(1 − θ)E[q] − 1 . γ
For simplicity of notation let B ≡ g(α∗2 ) and C ≡ limα↑50% g(α). If (1 − θ)E[q] < 12 γ + 1, then α∗2 is strictly smaller than 50%, by the above expression of g(α), L’s optimal holding in the monitoring region is α∗2 . Hence, L’s maximum expected utility in the monitoring region is B = g(α∗2 ). By simple calculation, we see B = V0
1 1 2 2 [(1 − θ)E[q] − 1] − (1 − θ) E[q] + α0 . 2γ η 42
If (1 − θ)E[q] ≥
1 γ 2
+ 1, the expected utility g(α) is increasing with respect to α in the
monitoring region {α < 50%}. Consequently, there exists no interior maximum point in the monitoring region and the expected utility is less than but can be close enough to C. By simple calculation we get C = V0
1 (1 − θ)E[q] 1 1 2 − ( − α0 ) . − γ − (1 − θ) E[q] − 8 η 2 2
The rest of proof of this proposition follows easily from the above discussion. Proof of Proposition 2. When η → 0, we see that B = C → −∞ < A. So L takes over the firm always. Proof of Corollary 3.1. By equation (9), α∗ > 50% if and only if α∗1 > 50%, and equivalently, 1 u( + α0 )2 < 2α0 (α0 Zmax − c). 2 It is equivalent to 1 α20 (4E[Z] − u) − α0 (u + 2c) − u > 0. 4 Since E[Z] > E[q] − 1 ≥ 0 by assumption, then there exists one positive and one negative root of the quadratic equation (4E[Z] − u)x2 − (u + 2c)x − 14 u = 0. Therefore, the last inequality holds if and only if the initial α0 satisfies p u + 2c + 2 u(c + E[Z]) + c2 α0 > . 2(4E[Z] − u)
43
(A-4)
Note that, the right side of the above inequality is an increasing function of the variable u and takes limit
c Zmax
when u ↓ 0. Therefore, when u is closes to zero, or when α0 is large,
the above inequality holds. Hence α∗1 > 50%. On the other hand, if u is relatively large, or α0 is small, we see α∗1 ≤ 50%. By the same argument, we can show that α∗1 < 1 if and only if u+c+2
p 2u(c + E[Z]) + c2 < α0 . 4E[Z] − u
Proof of Proposition 4. In the monitoring region, it is straightforward to see that B = V1
1 1 2 2 [(1 − θ)E[q] − 1] − (1 − θ) E[q] + α0 , 2γ η
and 1 (1 − θ)θE[q] 1 1 2 C = V1 − γ − (1 − θ) E[q] − − ( − α0 ) . 8 η 2 2 Since lim B = lim C = −∞,
η→0
η→0
then A > max{B, C} when η is very small. Hence L will take over the firm. On the other hand, since p u + 2c + 2 u(c + E[Z]) + c2 = 50%, lim u→∞ 2(4E[Z] − u)
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(A-5)
then by the proof in Corollary 3.1, L’s optimal holding in the takeover region is α∗ = 50%. In this case, it is easy to see that −∞, if α0 < 1 ; 6 lim A = u→∞ ∞, if α0 > 1 6
(A-6)
Assume α0 < 16 . Hence A < B and A < C if the expected increment is very large. Then L doesn’t take over the firm. By the same derivation, L takes over the firm by the same reason when α0 > 61 . When the cost structure c is very large, by assumption α0 E[Z] > 2c , the expected increment E[Z] must be large too. Hence
lim
c→∞,α0 E[Z]> 2c
p u + 2c + 2 u(c + E[Z]) + c2 ≥ 50%, 2(4E[Z] − u)
(A-7)
then by the proof in Corollary 3.1 again, the optimal holding in the takeover region is α∗ = 50%. Therefore, the maximum expected in the takeover region is E[q] − 1 1 − 2α0 1 − 6α0 A = α0 + − c+ E[Z] 2 1 + 2α0 2(1 − 2α0 ) E[q] − 1 c [−8α20 − 2α0 + 1] ≤ α0 + − 2 4α0 (1 + 2α0 )
Hence for any α0 < 14 , since 8α20 + 2α0 − 1 < 0, we have lim A = −∞.
c→∞
Hence L doesn’t take over the firm.
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The characterization of L’s takeover decision when the initial takeover gain is small is presented by the next result.
Proposition A.2 For a reasonable cost structure c, L takes over the firm by purchasing 50% of the firm’s shares. For any cost structure c, L either chooses α∗ = 0.5 or α∗ = 1. Moreover, α∗ = 1 if and only if, the expected improvement is smaller than the expected return before taking over, α∗1 > 0.5, and c is small enough such that
c
E[Z]. Then α∗ = 50% if either α∗1 ≤ 50%, or α1 > 50%, f (50%) ≥ f (100%). On one hand, by the proof of Corollary 3.1, α∗1 ≤ 50% if and only if c ≥ α0
E[Z] (2α0 + 1)2 − u. 2 8α0
On the other hand, f (50%) ≥ f (100%) if and only if the following inequality holds: 2(1 − α0 )(Zmax + c) (1 − 2α0 )(Zmax + 2c) − ≥ E[q + Z] − 1, 1 + α0 1 + 2α0
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or equivalently, c < 2α0 E[Z] −
(1 + α0 )(1 + 2α0 ) u. 4α0
(A-8)
Hence, for a reasonable cost structure c, the optimal holding in the takeover region is always 50%. Proof of Proposition 5. The proof is similar to the proof of Proposition A.1 and omitted.
Proof of Proposition 6. The proof is similar to the proof of Proposition A.1 when the η is very small. By Proposition A.2, A = f (50%). It is easy to see that limc→∞ A = −∞ while E[Z] is bounded. On the other hand, since α0 E[Z] ≤ 2c , we have E[q] − 1 1 − 2α0 1 − 6α0 A = α0 + − E[Z] c+ 2 1 + 2α0 2(1 − 2α0 ) E[q] − 1 1 − 2α0 ≤ α0 + + (8α20 + 2α0 − 1)E[Z]. 2 2(1 + 2α0 ) Hence limE[Z]→∞,α0 E[Z]≤ 2c A = −∞ when α0 < 25%. The proof of this proposition is finished.
Proof of Corollary 3.3 For α∗ = k, where k = 0.5 or 1 : αZmax + c α + α0 kZmax + c = k + α0
π =
So, π is increasing with Zmax = 2E[Z] but decreasing with α0 .
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In large takeover gain region from L’s initial holding region, if α∗ = αZmax + c α + α0 q
π =
2α0 (α0 Zmax −c) E[Z]+1−E[q]
=
q
q
2α0 (α0 Zmax −c) E[Z]+1−E[q]
− α0 :
− α0 Zmax + c
2α0 (α0 Zmax −c) E[Z]+1−E[q]
α0 Zmax − c = Zmax − q
2α0 (α0 Zmax −c) 0.5Zmax +1−q
s = Zmax −
(α0 Zmax − c)(0.5Zmax + 1 − q) 2α0
∂π = ∂α0
∂ Zmax −
q
(α0 Zmax −c)(0.5Zmax +1−q) 2α0
∂α0 √ − 2c (0.5Zamx − q + 1)
= 2α20
q
1 α0
(α0 Zamx − c) (0.5Zamx − q + 1)
So, π is decreasing with α0 . Proof of Proposition 7. By proposition A.1, after the first time period, there are five possible scenarios of the optimal holding, that is the optimal holding α∗ = 50%, 100%, α∗1 , α∗2 , or a number approaching to 50% from left. Under assumption, in all cases except for the last one, L will takeover the firm. Hence it suffices to assume that L takes a number of shares which is close to 50% and what happens in the next time period. We follow the same derivation in Proposition A.1 in the next time period with a new initial holding α0 → 50% and we will prove that L would take at least 50% in this case.
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In fact, since c ≥ E[q] − 1, we have s lim α∗1 =
α0 →50%
0.5Zmax − c − 0.5 ≤ 50%. E[Z] + 1 − E[q]
Then by Corollary 3.1, L takes exactly 50% of the firm in the takeover region and A = f (50%). By using the assumption that α∗2 ≥
1 , 2
it suffices to compare A and C when
α0 → 50%. It is straightforward to check that 1 lim A = E[q + Z]V0 . α0 →50% 2 and lim C = V0
α0 →50%
1 1−θ 1 2 − γ+ E[q] − (1 − θ) E[q] . 8 2 η
Hence limα0 →50% A > limα0 →50% C. Therefore, by Proposition A.1, L takes over the firm. The proof of this proposition is finished. Proof of Proposition 8. It suffices to assume that α0 =
(1−θ)E[q]−1 γ
in the subsequent time period. We use f (α, α0 ),
g(α, α0 ) denote the utility f (α) and g(α), respectively, to highlight the initial input α0 . A = maxα≥50% f (α, α0 ) is determined by equation (9) and V = g(α0 , α0 ). Since
(1−θ)E[q]−1 γ
< 0.5
by assumption, it suffices to compare A and B. First note that A doesn’t depend on η and in this case (with the choice of α0 ) (by ignoring firm value)
B=
[(1 − θ)E[q] − 1]2 (1 − θ)E[q] − 1 1 + − (1 − θ)2 E[q]. 2γ γ η
Moreover, lim B =
η→∞
[(1 − θ)E[q] − 1]2 (1 − θ)E[q] − 1 + . 2γ γ
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If γ is very large in the sense that A ≥ limη→∞ B, then L takes over the firm. If A < limη→∞ B, since limη→0 B = −∞, when η is very small in the sense that
η≤
(1 − θ)2 E[q] limη→∞ B − A
(A-9)
then B < A. Therefore L takes over the firm. Otherwise, A is less than B and L doesn’t take over the firm and will keep the same number shares α0 . Hence the proposition has been proved.
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