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Chapter 26
Mergers and Acquisitions: Strategic and Informational
Issues
David Hirshleifer
School of Business Administration, University of Michigan, 701 Tappan, Ann Arbor, MI 48109-1234, U.S.A.
1. Introduction
A merger is a transaction that combines two firms, leaving one surviving entity. An acquisition is the purchase of one firm by another individual or firm. Both transactions fall under the more general heading of takeovers. Takeovers can play a constructive economic role, for example by removing inefficient management or by achieving economies of scale and complementarity. On the other hand, they can have the possibly less desirable effect of redistributing wealth, as in takeovers that exploit tax benefits or expropriate bondholders or stakeholders. Finally, takeovers may reduce efficiency if they reflect agency problems on the part of bidding managers, or result simply from misjudgments. There are many important conflicts of interest and informational differences among parties to takeovers: bidding shareholders who only want an acquisition if the price of the target is not too high compared to underlying value, bidding man- agement who may seek self-aggrandization through takeover, target shareholders who wish to obtain a price that fully reflects any possible takeover improvements, target management who wish to retain private benefits of control, and potential competing bidders deciding whether to make their own offers. This essay describes the relationships between different models of the takeover process, and where possible provides analytical syntheses to integrate major trends in the literature. I focus mainly on three types of models: (1) models of tender offers, which examine the decisions of individual shareholders whether to tender (sell) their shares to a bidder, (2) models of competition among multiple bidders, and (3) models that examine the voting power of target managers who own shares, l Beginning with (1), tender offers to purchase shares directly from shareholders are a crucial mechanism for overcoming management opposition to takeover,
1 These categories are neither mutually exclusive nor exhaustive. In practice, however, most theoretical papers on takeovers have fallen into one of these categories. Many of the insights from these papers would also apply to other cases, such as the analysis of merger bid when there is little competitive threat, or the analysis of tender offers when there is competitive threat.
839
840 D. Hirshleifer
as contrasted with merger bids which require management approval. Models of the tender offer process may be classified according to whether (i) all parties are identically informed, or alternatively the bidder has superior information about the posbtakeover value of the target; and whether (ii) individual target shareholders take the probability of offer success as given, or else recognize the influence of their individual tendering decisions upon offer success or failure. Issues (i) and (ii) are important for understanding target managers' defensive measures and bidders' incentives to undertake mergers and acquisitions, and so for the design of regulatory policy. With regard to (i), superior bidder information presents target shareholders with an inference problem. One would expect that this informational disadvantage could lead target shareholders to be skeptical about the adequacy of the offer, and thus reluctant to tender their shares. I therefore examine the effect of bidder information on its probability of success and expected profits, and how defensive measures affect the informational advantage. With regard to (ii), if target shareholders take probability of success as given, then their tendering decisions will be nonstrategic - - being based on a simple comparison of gains from tendering or not. If a shareholder's decision influences the probability of success, however, she has a stronger incentive to tender in order to bring about success. This essay will therefore examine the determinants of how likely it is that individual shareholders will be pivotal in determining offer success, and the effect of this probability on the expected profitability of takeovers for bidders. Turning to point (2), models of competition, any attempt to understand compet- itive takeover auctions must address the anomaly that bidding in takeover contests generally occurs in a few large jumps, rather than many small increments as predicted by the conventional analysis of bidding in costless English auctions. This essay therefore examines models of costly investigation and costly bid revision, wherein successive bids may increase by large increments when bidders try to intimidate their competitors into quitting. Since the intimidated bidder may be able to increase value more than the intimidator, this may not be a good thing. This leads to consideration of the effects of regulations that influence the cost of investigation and the ease of preemption. I will also consider how the choice of means of payment (cash, equity, or other securities) can signal information, and thus can be used as a tool for preempting competitors. Finally, with regard to point (3) above, the share ownership and voting power of target m a n a g e m e n t that values control can be important for the outcome of a tender bid and for the bidder's decision whether to undertake a tender offer or a proxy fight. It is therefore important to understand how a manager may be able to alter his effective control of voting rights either directly through share purchases or indirectly through changes in capital structure. This essay mainly covers topics that have been the focus of several related models that yield divergent results. It is for these topics that integrated discussion and analysis seems most valuable and feasible. The cost of this approach is that many other important topics are not addressed here or are only briefly touched upon. Such topics include the analysis of why takeover occur, bidder/target
842 D. Hirshleifer.
Tender offer success versus failure is often highly uncertain, as evidenced by
the negative reaction of the target stock price to offer failure [see Bradley,
Desai & Kim, 1983; Samuelson & Rosenthal, 1986; Ruback, 1988] and by the
positive bidder stock price reaction to success and negative reaction to failure [see
Bradley, 1980]. Offer success is positively related to the bid premium and to the
initial shareholding of the bidder in the target [Walkling, 1985].
Target management defensive measures on average reduce the probability of a
takeover occurring [Walkling, 1985; Pound, 1988]. The target stock price reaction
to greenmail is on average negative [Bradley & Wakeman, 1983; and Dann &
DeAngelo, 1983], as is the average reaction to antitakeover amendments, poison
pills, defensive restructurings, and several other defensive measures [see, e.g.,
Bhagat & Jefferis, 1991; Malatesta & Walkling, 1988; Ryngaert, 1988; and Dann &
DeAngelo, 1988].
There is evidence that target managers can position their firms in ways that alter
bidder behavior. Stulz, Walkling & Song [1990] provide evidence that the bid level
is on average higher when target management owns a greater share of the target.
Palepu [1986] finds that the probability of a hostile takeover attempt is decreasing
with the target's debt-equity ratio.
Certain items of evidence have provided sharp empirical challenges to theories
of the takeover transaction process. The traditional solution to the English
auctions model with multiple buyers involves many small bid increments. This has
faced a glaring challenge from the evidence that takeover bidding occurs by small
numbers of enormous jumps, a challenge taken up in Section 4. In Jennings &
Mazzeo [1993] the majority of initial bid premia were over 20% of the market
value of the target 10 days prior to the offer. Since price runup may occur earlier,
this is likely to be an underestimate of premia relative to non-takeover value.
A second challenge is provided by the often puzzlingly low ownership in target
firms accumulated by bidders prior to making a takeover bid. Given the very
high premia paid in tender offers, we would expect bidders to buy up shares at
the open market price prior to the bid up to the limits of market liquidity. In
fact, the majority of tender offer bidders own no target shares [Bradley, Desai &
Kim, 1988], 3 and even among those that do, the potential profit on these holdings
appears to be modest compared to bidding costs [Bhagat & Hirshleifer, 1995].
This challenge is taken up by theories discussed in Section 3.1.5.
A third empirical challenge is the mixed evidence regarding the effect of means
of payment (stock versus fixed payments) on bidder and target stock abnormal
stock returns. There is evidence, consistent with the Myers & Majluf [1984]
adverse selection problem with equity issuance, that bidder and target returns for
stock offers are on average lower than for cash offers (see, e.g., Huang & Walkling
[1987] on target returns). However, the U.S. result that average abnormal bidder
returns are negative in stock offers does not apply in France, the UK or Canada
3 In a sample of successful post-1968 offers, Stulz, Walkling & Song [1990] find a positive median
bidder share ownership of 2.35% among successful offers, and a 4.75% ownership in successful
single bidder contests.
Ch. 26. Mergers and Acquisitions: Strategic and ln¢brrnational Issues 843
(Eckbo, Giammarino & Heinkel [1990] and citations therein). Furthermore, Lang, Stulz & Walkling [1991] report that the effect of means of payment in the U.S. is subsumed by a cash flow variable. The associated theoretical issues are discussed in Section 5.
3. Tender offers and share tendering decisions
A tender offer can be either conditional or unconditional. A conditional offer is not binding on the bidder unless a given number of shares are tendered. An offer may require acceptance of all tendered shares (an unrestricted offer), or alterna- tively the bidder may not be obliged to purchase more than a prespecified number of shares (a restricted offer). An offer that is unconditional and unrestricted is often called an 'any-or-all' offer. Consider a bidder who can increase the value of the target only if he obtains control. Except where otherwise specified, in this essay the non-takeover value of the target firm is normalized to zero. Also, I assume that the bidder obtains no control unless he succeeds in buying a given fraction of target shares, in which event he obtains complete control. Let v be the post-takeover value of a firm's shares. Ignoring taxes, a risk-neutral target shareholder i should tender if the price offered for the firm's shares, b, exceeds the expected value of her share if she retains it: Tender if b > Pr (Success [i Retain)v. (1) A target shareholder will be more willing to tender if she believes that post- takeover value v is low, and if she believes that her individual decision not to tender will reduce the takeover's probability of succeeding. Section 3.1 presents a model (due to Grossman & Hart [1980], Shleifer & Vishny [1986a], and Hirshleifer & Titman [1990]) in which each shareholder believes he will not be pivotal. This model allows for possible informational superiority of the bidder. Section 3.2 discusses models (by Bagnoli & Lipman [1988] and Holmstrom & Nalebuff [1992]) which allow for the fact that individual shareholders are sometimes pivotal, but assume symmetric information.
3.1. A nonpivotal shareholder model
3.1.1. The model under complete information
Consider a bidder who can increase the value of the target to $100 per share if he obtains control, which requires >50% of the target's shares. Assume the offer is conditional upon obtaining control. Under some circumstances, he will be unable to profit on the shares that he purchases owing to a free-rider problem among target shareholders [Grossman & Hart, 1980; Bradley, 1980]. Suppose he makes a rather generous offer of $80 per share. Each shareholder reasons that if the offer fails, the value of her retained shares remains the same regardless of whether she tenders; while if the offer succeeds, she is better off receiving the
Ch. 26. Mergers and Acquisitions: Strategic and Informational Issues 845
The first term is the improvement'in value of the bidder's initial shareholding. The second term is the profit on the shares purchased in the tender offer. If follows trivially (letting o~ and 3 approach zero) that:
Proposition 2. Under complete information, if a bidder's initial shareholding (o
in the target and dilution opportunities (3) are sufficiently small, then a conditional
unrestricted tender offer is unprofitable.
Four further points are worth noting. First, diluting target value may be costly, in the sense that the bidder's gain is less than target shareholder's loss. If so, then it is a dominant strategy for the bidder to make an unrestricted offer as assumed above. 7 Second, the second term in Proposition 1 shows that having an initial shareholding reduces the value of the dilution threat, because to some extent the bidder would be diluting his own holdings. Third, the profit deriving from initial shareholdings tends to be fairly small because of low shareholdings (see empirical synopsis). Fourth, if a shareholder may be pivotal, or if the offer is unconditional,
then a threat by the bidder to reduce the target's non-takeover value would also
encourage shareholders to tender. 8
3.1.2. Share tendering decisions under asymmetric information
A bidder usually knows what he plans to do with the target better than target shareholders. Superficially, it might appear that a bidder could on average profit even without dilution or an initial shareholding, based on superior information about the post-takeover value of the target (v). However, rational expectations (or in game-theoretic terminology, perfect Bayesian equilibrium) implies that if the bidders were on average offering less than post-takeover value in tender offers, shareholders would be aware of this and would refuse to tender. Thus, the free-rider problem remains when asymmetric information is introduced. In such a generalized model, two equilibria are of interest. In one, the price offered is uninformative, and offers always succeed [Shleifer & Vishny, 1986@ In the other, the level of the offer reveals the bidder's valuation, and the probability of offer success increases with the amount offered [Hirshleifer & Titman, 1990]. 9
3.1.2.1. Uninformative offer levels'. If a bidder's information about post-takeover
value or about potential dilution is superior to that of target shareholders, then shareholders must draw some inference about the bidder's valuation from the level of the offer. Shleifer & Vishny [1986a] provide a model in which the level of
7 If there is no wastage, then whether the offer is restricted is a matter of indifference. Even if wastage is arbitrarily close to 1/00%, as Proposition 1 shows, the bidder benefits substantially from the threat of dilution since it allows him to buy shares cheaply. 8 Gilbert & Newbery [1988] examine a model in which a bidder acquires cheaply because he can threaten to enter an industry and reduce the profits of a member of an oligopoly. 9 In what follows, it is assumed that the only information asymmetry is about post-takeover value v; information is symmetric about the initial shareholding ce. Regulations require the bidder to file information about share ownership with the S.E.C. at the time of the bid.
846 D. Hirshleifer
the offer is u n i n f o r m a t i v e in equilibrium, b e c a u s e shareholders foresee perfectly the price t h a t will be offered if a bid occurs. Since it is a s s u m e d that at any offer level t h e b i d d e r knows with certainty w h e t h e r shareholders will tender, the e q u i l i b r i u m price offered is set to be just high e n o u g h to induce s h a r e h o l d e r s to a c c e p t the offer. W h e n indifferent, it is a s s u m e d that target s h a r e h o l d e r s tender. F o r simplicity, assume that there is no dilution (6 --- 0), that bidding is costless (c B ~ 0), a n d that (possibly owing to financing costs) the offer is restricted to the m i n i m u m a d d i t i o n a l fraction of the firms shares n e e d e d for control, co. T h e n to p e r s u a d e target s h a r e h o l d e r s to t e n d e r , a b i d d e r must offer target s h a r e h o l d e r s at least
b* = E[v [Offer], (4)
w h e r e the R H S is the expected v a l u a t i o n of the b i d d e r given that he m a k e s an offer. In the p r o p o s e d equilibrium, a b i d d e r with low valuation cannot r e d u c e the a m o u n t offered, b e c a u s e if he bid any less, b < b*, shareholders would infer that his v a l u a t i o n was higher than the a m o u n t offered, v > b, and so would retain their
shares. Thus, the probability of success P(b) is a step function of the level of the
offer, i.e., P(b) = 0 if b < Ely], and P(b) = 1 if b > E[v] (as illustrated by the
d a r k line segments in F i g u r e 1).
P r o p o s i t i o n 3. Under asymmetric information, there is an equilibrium in which
a bidder who makes an offer pays a price equal to the expected post-takeover
valuation of the shares he purchases. His gain on the shares he buys is positive if the
improvement v is high, and is' negative if v is low. He derives an expected profit from
the increase in value of his initial shareholding in the target.
O n average a b i d d e r does not profit on the s h a r e s p u r c h a s e d in a t e n d e r offer. (If he did, s h a r e h o l d e r s w o u l d not w a n t to tender!) A b i d d e r with v a l u a t i o n v close to zero will not m a k e an offer, b e c a u s e he takes a loss on the shares p u r c h a s e d in the offer of v - b, and his initial holding profit o~v is low. For larger v, the b i d d e r ' s profits b o t h on shares p u r c h a s e d and on the initial holding increase. T h e r e is a critical value v such that profits are zero. T h e b i d d e r makes an offer if and only if
v > v. Thus, the bid in (4) is b = E[v I v > i)*]. 1°
3.1.2.2. Revealing offer levels. T h e b i d d e r ' s gain from succeeding is increasing
with its v a l u a t i o n of the target. Since a low offer reduces the probability of offer success [Walkling, 1985], a low-valuation b i d d e r has a stronger incentive to save m o n e y by defecting to a low offer than a high-valuation bidder. 11 T h e probability
1{}If bidding is costly, the critical value increases. An empirical implication is that if the cost of bidding decreases, the critical level for bidding decreases, so premia on average decrease. 11 A low-valuation bidder who makes a lower bid will profit under a wider set of shareholder responses than a high-valuation bidder. This suggests that investors should believe his valuation is low, and should accept his offer. Thus, the pooling equilibrium of the preceding section is removed by the strong refinement criterion of Banks & Sobel [1987]. However, the pooling equilibrium survives several other criteria, such as those of Grossman & Perry [1986] and Cho & Kreps [1987].
848 D. Hirshleifer
optimal level of the bid exists" for each bidder valuation, then the level of" the bid is
increasing in the bidder's valuation of the target (db / dv > 0). Therefore, the bidder's
information is fully revealed by his bid.
This proposition takes shareholder behavior as exogenous, so we cannot yet con- clude that there is a revealing equilibrium. O n e is displayed later. Proposition 4, however, shows that almost any reasonable model of tender offers will lead to separation for at least a range of bidder types. For example, in a model in which target m a n a g e m e n t can take defensive action but cannot with perfect effectiveness 'just say no', we expect the intensity of opposition to the takeover to decrease with the a m o u n t bid, so the probability of offer success should increase smoothly. Such a model leads to full revelation. A steadily increasing probability of success as a function of the bid can also be derived f r o m a model where shareholders have different capital gains bases [Stulz, 1988; Bagwell, 1991]. 12 In the pooling equilibrium of the previous section, there is no revelation because it violates the assumption of a continuous probability of success. In the model developed here, there is a unique equilibrium in which the level of the bid is a fully revealing signal of the bidder's valuation. In this equilibrium, the bidder offers his valuation, the minimum a m o u n t e d needed to have a chance of succeeding, b = v [compare with equation (4)]. Instead of assuming that indifferent shareholders always tender, let us now (consistent with evidence cited earlier) allow for the possibility that the outcome of the offer is uncertain from the viewpoint of the bidder. This uncertainty is modelled as arising from randomization by shareholders as to whether to tender in a mixed strategy equilibrium. 13 In the mixed strategy equilibrium, the bidder's uncertainty about his probability of success at different bid levels is such that he optimally makes a bid that leaves shareholders indifferent as to whether to tender. Imposing the indifference condition (b = v) in (6) leads to a differential equation that determines the probability of success,
e'(b) w
- - ( 7 )
P(b) oeb
The relevant boundary condition is that the highest possible bid (made by the highest valuation bidder) always succeeds, P (~5) = 1. The solution,
P ( b ; ~ ) = , (8)
is illustrated by the dark curves in Figure 1. T h e probability of an offer's success increases with the bid premium and with the initial holding oe (consistent with
12Pooling among the highest valuation types, however, remains a possibility because if a very
high offer is sure to succeed, above this bid level P(b) is no longer increasing.
13A mixed strategy equilibrium is a way of modeling the fact that, owing to small amounts of uncertainty about payoffs, the behavior of some players (target shareholders) seems uncertain from the point of view of another player (the bidder) [see Harsanyi, 1973]. For example, the Bidder may not know the liquidity or capital gains tax considerations that affect shareholders' tender decisions.
Ch. 26. Mergers"and Acquisitions: Strategic and Infolrnational Issues 849
evidence cited earlier) of Walkling [1985], and decreases with the number of addi- tional shares needed for control o0.14 Offer failure is caused by the informational superiority of the bidder. Shareholders recognize the bidder's temptation to offer less than the post-takeover value of their shares, and are therefore reluctant to tender at low prices (i.e., they tender with lower probability). The model therefore predicts that actions that improve the information of target shareholders will (by shifting the upper bound 7? in (8) downward toward the true value v < ~) increase the probability of offer success. 15 Like an initial shareholding, proportional dilution increases the benefit to achiev- ing success. It therefore increases the incentive to bid high. This reduces sharehold- ers' skepticism of the offer, and increases the probability of offer success. 16 This model assumes that if the offer fails, the bidder does not acquire the target and hence loses a valuable profit opportunity. In reality, if an offer fails, the bidder can revise his offer upward. This opportunity can potentially eliminate the separating equilibrium. In order for a separating equilibrium to survive, it is crucial that failure impose an opportunity cost on the bidder that is increasing in the size of the potential value improvement. This can occur for several reasons: (1) initial failure gives entrenched managers more time to mobilize blocking defensive strategies, (2) failure may give target management time to announce changes that preempt the potential takeover improvement, (3) loss of time can involve the loss of a window of opportunity to exploit a synergy between the firms, and (4) rejection may give a competing bidder time to enter. The arrival of a competitor is costly to a bidder who hopes to profit by diluting minority shareholders [see Hirshleifer & Titman, 1990, section I.D]. In evaluating defensive measures in the next section, it should be kept in mind that the efficiency consequences of failure of an initial offer depend on which of the costs of failure listed above are relevant.
3.1.3. Management defensive strategies
We focus in this section on the revealing equilibrium, since it permits analysis of how defensive strategies affect the information revealed by the bid and the probability of offer success.
14 Thus, a supermajority antitakeover a m e n d m e n t reduces the probability of offer success. An untested implication of the model is that the ratio of the target stock price increase at the a n n o u n c e m e n t of the bid to the bid premium is increasing in both the bid level and o~, and decreasing in co. T h e model also implies that average premia are lower when the initial shareholding o~ is higher (consistent with evidence of Walkling & Edmister [1985]), and when the required n u m b e r of shares ~o is lower. 15 This is consistent with Walkling's [1985] evidence that share solicitation activity increases the probability of success. ~6 Asquith [1991] extends this model by allowing for a probability that the bidding manager is afflicted with 'hubris' [see Roll, 1986] in the sense that he incorrectly believes he can increase target value (i.e., he believes that v > 0 when actually v = 0). Asquith shows that the presence of hubristic bidders allows nonhubristic bidders to profit, even without dilution and without initial shareholdings. Target shareholders become willing to tender even if rational bidders offer below post-takeover value owing to the chance that the offer is from a hubristic bidder. Thus hubris can improve efficiency despite the obvious cost of inefficient takeovers.
Ch. 26. Mergers and Acquisitions: Strategic and Informational Issues 851
staggered board terms that delays transfer of control to the bidder in the event of offer success will reduce bid levels, and so the probability of success. Evidence cited earlier indicating that defensive measures tend to prevent takeover from occurring [Walkling, 1985; Pound, 1988] suggests that target managers may often be acting against shareholder interest by adopting those strategies that prevent takeovers.
3.1.3.2. Effects on asymmetry of information. A subtler effect of defensive strate-
gies is to change the informational advantage of the bidder over target share- holders. Consider a value-reduction strategy, defined as a defensive activity that reduces the post-takeover value of the target. A n example would be the sale of an asset that, as part of the target, could be improved by the bidder ('sale of the crown jewels', also known as the 'scorched earth defense'.). A value-reducing defensive measure can reduce or increase informational asymmetry. Suppose that the bidder can increase the value of the target by v = x ÷ y, where x is an improvement that is known to shareholders perfectly while y is known to the bidder but not the target. If a value-reduction strategy eliminates the possibility of the u n k n o w n improvement y, then the informational asymmetry is removed, and the bidder can ensure success by offering just above x. Thus, a value-reduction strategy can reduce informational asymmetry and promote success. Conversely, if a value-reduction strategy eliminates the known improvement x, then the probability of success is
P(b; o~) =. (9)
The probability of success at any level of the bid b is higher than in (8).17 However, the probability of success is reduced for a given bidder because he bids less when his valuation is reduced, is
P r o p o s i t i o n 6. A value-reduction defensive strategy, by decreasing (increasing) the
importance of publicly known improvements relative to improvements" known pri-
vately by the bidder, can decrease (increase) the probability of tender offer success.
3.1.4. Target private information
T h e target as well as the bidder may have private information. If the target is undervalued by the market, then by signalling high value, managers can make shareholders less willing to tender. Increasing leverage and repurchasing shares, actions which can signal high value, are often used defensively. Ofer & Thakor [1987] analyze signalling through repurchase; Bagnoli, Gordon, & Lipman [1989] analyze repurchase signalling as a defensive strategy.
17This is not surprising, since a given level of the bid becomes more attractive when compared to a smaller post-takeover value. la Without the value-reduction measure, the probability of a bidder with valuation v succeeding
is (v/v) ~°/~. With the defensive measure, the probability is [(v - x)/(O - x)] ~°/~.
852 D. Hirshleifer
3.1.5. Pre-tender offer share acquisition
Prior to announcing his offer, a takeover bidder has private information about an event that will increase the market price of the target's stock. This leads to an incentive to acquire shares of the target quietly at a lower price. Pre-takeover share acquisition is limited by disclosure requirements and by the depth of the market, because in a thin market a large purchase of shares will more quickly reveal the information of an informed trader. Kyle & Vila [1991] point out that if the possibility of a takeover is foreseen, then a potential bidder can profit by either buying shares secretly before making a takeover bid or selling shares short and not making a bid. In any case, the evidence mentioned in the empirical synopsis that the majority
of actual tender offer bidders do not accumulate any target shares is puzzling.
One explanation has to do with the desire to signal low-valuation to target shareholders. Since a high valuation bidder has an incentive to bid higher (see Section 3.1.2.2), he has a stronger incentive to accumulate shares prior to the offer. But this means that the disclosure of the initial shareholding required at the time of an offer for a U.S. firm reveals the bidder's valuation. It follows that there is an incentive to accumulate fewer shares in order to persuade target shareholders to tender their shares at a lower price [Chowdhry & Jegadeesh, 1994]. 19
3.1.6. The general free-rider problem
The free-rider problem has been discussed in the context of conditional tender offers. However, the conclusion that in the absence of dilution and initial holdings the bidder cannot profit holds very generally, so long as target shareholders do not perceive themselves to be pivotal.
Let us define a tender offer as an offer to buy shares in which the same
prespecified price is offered for all purchased shares, no share is purchased unless it is tendered by the shareholder, and if it is tendered, whether it is purchased is a function of the tendering decisions of all shareholders. 2° Suppose that there are two control states, bidder control and target control, leading to target firm values of v or 0 respectively. The state is determined by whether the critical fraction of shares is tendered. If a shareholder is virtually never pivotal, then she perceives herself as being in a virtually constant-sum game with the bidder. Shareholders as a whole are in a nonconstant sum game with the bidder, but any individual shareholder partakes of only a vanishingly small fraction of the joint benefit derived from her decision to tender. Thus, any offer that gives the individual shareholder an expected profit will give the bidder an expected loss on purchases from that shareholder.
19 Another possible explanation for low initial holdings is that the bidder wishes to keep the preoffer share price low, if the legally permissible amount of dilution in a freeze-out merger is constrained by this price [Ravid & Spiegel, 1991]. 20 These conditions hold for both conditional and unconditional offers, for either restricted or unrestricted offers, and for offers in which oversubscription leads to pro-rationing, first-come- first-serve, or to discrimination by the bidder amongst different shareholders in acceptance of shares.
854 D. Hirshleifer
large blockholders even in many large firms, this is an important escape from the free-rider problem. 21 H o l m s t r o m & Nalebuff [1992] point out that the increased probability of offer success resulting from the tender of one share by a blockholder increases the expected value of retaining her other shares. A large blockholder therefore has a greater incentive to tender some of her shares than a small one, leading to an equilibrium that gets close to equalizing the number of nontendered shares by l a r g e r stockholders. By tendering only a fraction of her shares, a blockholder partly internalizes the benefit accruing to nontendering shareholders.
3.2. 2. Pure strategy equilibria with pivotal shareholders
U n d e r complete information, in either a conditional or an unconditional tender offer, there are many equilibria in which just enough shares are tendered to cause a transfer of control. Consider a conditional tender offer for 20,000 shares in a takeover that will increase value. Consider a set of shareholders whose shares total to exactly 20,000. A n equilibrium is for these shareholders to tender all their shares, and for the others to retain their shares. In the equilibrium, If any shareholder were to tender one less share, the offer would fail, reducing the value of her n o n t e n d e r e d shares. Thus, a bidder can succeed with a very small p r e m i u m [Bagnoli & Lipman, 1988], apparently solving the flee-rider problem.
Proposition 8. Under complete information, and in the absence of management
defensive measures, in both an unconditional tender offer and a conditional offer
for the minimum number of shares required to shift control, there exist strong Nash
equilibria in which the bidder offers just above zero and receives exactly enough
shares to transfer control. Therefore the bidder can effect any desirable change in the
target even if he owns no shares in the target and cannot dilute.
3.2.3. Mixed strategy equilibria with pivotal shareholders'
There are also many mixed strategy equilibria in which shareholders are sometimes pivotal. Continuing the assumption of complete information, let us focus on any-or-all offers. Intuitively, if other shareholders tender with high probability, then the offer is likely to succeed, in which case a given shareholder would do better to retain her shares; while if other shareholders tender with low probability, then the offer is likely to fail, in which case a given shareholder does better by tendering. Thus, there is a stable outcome in which shareholders tender with intermediate probability (see Bagnoli & Lipman, 1988; H o l m s t r o m & Nalebuff, 1992]. 22
2t This is related to the general principle, important in the theory of political pressure groups, that the small free-ride on the large [see Olson, 1965]. 22 Intuitively, if an individual shareholder does not know the precise liquidity or capital gains situation of other shareholders, from her point of view their behavior is random. The logic described in the text causes shareholders to be near indifference, so that small uncertainties about payoffs lead to substantial uncertainty about behavior.
Ch. 26. Mergers'and Acquisitions: Strategic and Informational Issues 855
To develop this point, I follow the presentation of Hohnstrom & Nalebuff [1992]. Consider a firm with N risk neutral shareholders each of whom owns a single share. Suppose that the bidder needs exactly K shares to obtain control. It is informative to focus on the symmetric equilibrium in which shareholders randomize with identical probabilities. Let the improved value of the target be v = 1. Shareholder i's tendering decision will be based on a comparison of
the certainty of receiving the per-share offer price b / N versus a probability
P(b [ i does not tender) of the per-share improved value of the firm 1/N. She
will be indifferent if
b = P(b I i does not tender). , (10)
Let p(b) be the probability that a single shareholder tenders, and let P(b) be the
probability that the offer succeeds given equilibrium behavior by all shareholders. Then the bidder's expected surplus is the difference between the total expected
surplus, P(b), and the expected surplus going to shareholders, b. Thus, the
bidder's expected surplus is
P(b) - b =- P(b) - P(b l i does not tender). (11)
On the RHS, P(b) is the probability that at least K shareholders tender, and
P (b ] i does not tender) is the probability that at least K shareholders other than i tender. The difference is therefore the probability that the other shareholders tender exactly K - 1 shares, and shareholder i also tenders, i.e.,
N--ICK-1 p(b)X[1 -- p(b)] N-K, (12)
where U 1CK-I is the number of combinations by which K - 1 tendering share- holders other than shareholder i can be selected from the N - 1 possible shareholders. Maximizing this quantity over p (which the bidder controls through b) gives the following proposition.
Proposition 9. In the symmetric equilibrium of the any-or-all tender offer game
of this section, the tendering probability is p* = K / N , and the bidder's expected
profit is positive. This profit approaches zero, ceteris paribus, as the number of"
shareholders N becomes large.
By making the expected number of shares tendered equal to the number of shares needed for success, the bidder maximizes the probability that a given shareholder will be pivotal. The proposition's last statement is shown in Bagnoli & Lipman [1988]. Holmstrom and Nalebuff examine a more general setting in which shareholders hold any number of shares. They find an equilibrium in which all sufficiently large shareholders tender down to a common range of either m or rn + 1 shares. Large shareholders randomize between these two possibilities, the offer sometimes succeeds and sometimes fails, and the bidder makes a positive gross profit. Those with less than m shares do not tender. Since each large shareholder randomizes
Ch. 26. Mergers and Acquisitions: Strategic and Informational Issues 857
holders, it seems unlikely that shareholders perceive themselves to have a signifi-
cant chance of being pivotal. Why don't the models match the a priori intuition?
In general, in games with many players, a plausible equilibrium (I contend) should be robust with respect to 'misbehavior' by a small (though not necessarily infinitesimal) fraction of individuals. Consider a widely held firm of N sharehold- ers, and suppose that h of the shareholders will not tender their shares in the relevant range of offer prices, where h is a discrete r a n d o m variable, 0 < h < H,
and H / N is 'small', but not infinitesimal (say 1/50). 25
! make the quantitative conjecture that under mild conditions on the distribu- tion of h, there will be no equilibrium in which shareholders have a significant chance of being pivotal. T h e reason is that, not knowing h, strategic shareholders have no way of knowing how many shares they must jointly tender in order to make the offer succeed. Suppose shareholdings are identical, for example, with H = 100, and N = 5,000. Substantial exogenous uncertainty about the character- istics of even 100 shareholders would seem to make it exceedingly unlikely that the decision of a single shareholder will determine success or failure. In experiments in which shareholders can tender all or none of their shares, Kale & N o e [1991] provide evidence that is only partly consistent with the argument pro- vided here. They found that the probability of success in conditional tender offers to 41 shareholders was at some prices substantially below that predicted by a mixed strategy equilibrium with pivotal shareholders. However, the probability of success in any-or-all offers to 32 shareholders was greater than the equilibrium prediction.
4. Competitive bidding
Most models of the free-rider problem assume only one bidder for a given tar- get. The models of competing bids discussed here generally makes the assumption that the target will always accept the highest offer made by any bidder, so long as it is above some minimum reservation price. The analysis in this section should thus be viewed as referring to merger bids, or else to tender offers in which the threat of dilution limits free-riding. We focus on models of competitive bidding in which bidders have differing private valuations of a target, and examine the effects of investigation costs and bidding costs on auction outcomes. Perhaps the simplest model of takeover bidding is the standard analysis of
English auctions. In this model, bidders costlessly make offers and counteroffers,
each bid incrementaliy higher than the previous one, until the bidder with highest valuation wins at a price equal to the valuation of the second highest bidder. I will
call this outcome the ratchet solution.
25 This 'misbehavior' could be rational, if their are costs of tendering such as locked in capital gains of size known only to the individual. The upper bound H could be quite low, e.g., 1/50 of outstanding shares, but the argument may fail if probability bunches too close to zero. Thus, the plausibility concept suggested here ditters in this respect from Selten's trembling hand equilibrium.
858 D. Hirshleifer
In the conventional English auction analysis, rather than paying a substantial initial premium, an initial bidder should bid the minimum reservation price, and increase the offer only if a competitor actually arrives. Suppose that the first
bidder (FB) has a known valuation of vl = $80, and a potential competing bidder
(SB) has a valuation of v2 = $0, $30 or $100 with equal probability. Normalize
the reservation price of the target to zero. Then FB will begin with a bid of
zero. If v2 = 0, FB buys the target at this price. If v2 = $30, FB still wins, but
the price is driven up to $30. If v2 = $100, then SB buys the target at a price
of $80. Competition in the bidding process not only helps target shareholders, it increases total surplus, because of the possible realization of a larger improvement ($100). The ratchet solution illustrates the potential gain to the target and society of competition. It is, however, not descriptive of actual takeover contests, in which initial bids are typically made at a substantial premium to the market price (see the empirical synopsis), and each successive bid typically involves a significant i n c r e a s e over the previous outstanding bid.
4.1. Costly investigation and preemptive takeover bidding
A possible explanation for a high initial bid in a takeover contest derives from the .fact that takeover benefits are partly specific to the acquirer (e.g., complemen- tarities), but partly common (e.g., gains derived from replacing inefficient target management). Owing to correlated valuations, an initial bid will alert potential c o m p e t i t o r s to the potential desirability of the target. 26 This suggests that in planning its initial offer, an initial bidder will consider the incentives created for potential competitors. Specifically, such a bidder may wish to offer a substantial premium on his initial bid in order to deter potential competitors [Fishman, 1988; Png, 1985]. In Fishman's model, an initial bid alerts a second potential bidder to a state of the world in which the target is potentially profitable. However, the model assumes that conditional upon this state of the world, the valuations of the first and second
bidder are independent. FB and SB can acquire information about the target at a
cost of ck By investigating, a bidder learns his private valuation of the target. 27 If both bidders enter, it is assumed that a costless English auction ensues, so that the target is sold to the highest valuation bidder at a price equal to the valuation of
the second highest bidder, min(vl, v2) (i.e., the ratchet solution).
In the unique equilibrium in this game (applying the equilibrium concept of Grossman & Perry [1986]), the bidder offers the minimum reservation price for
the target if his valuation is below a critical threshold level v*. In this event SB
investigates, and the target is sold in a costless English auction. If v > v*, FB
makes a high bid b D that deters SB from investigating. The initial bid is therefore
a coarse signal of the first bidder's valuation.
ze,See, e.g., Grossman & Hart [1981]. 27 Low valuations are assumed to be so likely that it does not pay to bid without investigating.
