RFS Advance Access published March 29, 2010
Acquisition Values and Optimal Financial (In)Flexibility Ulrich Hege HEC School of Management, Paris
This article analyzes optimal financial contracts for an incumbent and potential entrant accounting for prospective asset mergers. Exercising a first-mover advantage, the incumbent increases his share of surplus by issuing public debt that appreciates in the event of merger. Incumbent debt reduces the equilibrium value of entrant assets and thus reduces the return to (likelihood of) entry through two channels: venture capitalists recover less in default and ownership rights provide weaker managerial incentives. High incumbent leverage has a countervailing cost, since the resulting debt overhang prevents ex post efficient mergers if merger surplus is low. Event risk covenants limiting counterparty debt are optimal for the incumbent, further limiting the entrant’s share of merger surplus. A poison-put covenant is also optimal for the incumbent, allowing him to extract the same surplus with lower debt face value. (JEL G32, G34)
According to conventional wisdom, the deep pockets of an incumbent serve to deter entry. In large part, the theoretical basis for this view rests upon the model of Bolton and Scharfstein (1990), who show that an unconstrained cashrich incumbent can fund predation in order to increase the likelihood of venture capitalists terminating projects. While there is certainly validity to the conventional view, our article builds upon the insights of Shleifer and Vishny (1992) to show that there is a dark side to an incumbent maintaining financial flexibility: a deep-pocketed incumbent represents an attractive merger partner and may inadvertently encourage entry for buyout. The argument starts from a simple premise: the willingness of financiers to fund projects is determined by the equilibrium value of entrant assets. Further, the highest value use of entrant assets often entails merging them with We would like to dedicate this article to the memory of Antoine Faure-Grimaud, whose comments on an earlier version helped us enormously and whose untimely death is a tremendous loss for the field. We are grateful to Aydogan Alti, Patrick Bolton, David Scharfstein, and an anonymous referee for detailed feedback and to Paolo Fulghieri, the editor, for valuable guidance. We thank seminar participants at the University of Colorado, London School of Economics, Michigan State, American University, UC Berkeley, Zurich, University of Paris-Dauphine, Wharton, the EFA Athens meetings, and the AFFI and DGF conferences. We also thank Tahereh Khorram for excellent research assistance. Hege is also affiliated to ECGI, Europlace Institute of Finance and GREGHEC. Hennessy is also affiliated to CEPR and ECGI. Hege acknowledges finacial support from Federation Bancaire Francaise 997 Chair in Corporate Finance. Send correspondence to Ulrich Hege, Department of Finance, HEC Paris, 1 Rue de la Liberation, 78351 Jouy-en-Josas, France; telephone: +33 1-3967-7299; fax: +33 1-3967-7085. E-mail:
[email protected]. c The Author 2010. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail:
[email protected]. doi:10.1093/rfs/hhq017
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Christopher Hennessy London Business School
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those of the incumbent (e.g., via trade sale). Consequently, expected merger payoffs should play an important part in determining the ability of entrants to obtain funding from venture capitalists. From this premise, our argument is straightforward. The sale of debt prior to merger increases a debt issuer’s share of merger surplus. Thus, the anticipation of a potential merger creates an incentive for targets and acquirers to issue debt. However, a mature incumbent enjoys a natural first-mover advantage in public debt markets. This first-mover advantage should be exercised, since preemptive debt issuance by an incumbent achieves three objectives: crowding out entrant debt, increasing the incumbent’s share of merger surplus, and reducing the likelihood of entry. Our model highlights the following trade-off faced by the incumbent in choosing its debt level. With high debt, the incumbent extracts a larger share of total surplus if a merger is consummated. In addition to the obvious direct benefit conferred ex post, such surplus extraction also lowers the return to and likelihood of entry. However, by taking on high debt ex ante, the incumbent risks preventing a merger in some states of nature. A failure to merge results in intense second-stage product market competition, a prospect that is particularly troubling for growth firms. The model thus predicts that value firms will resolve the implied trade-off by taking on high debt in order to increase the probability of deterring entry. In contrast, growth firms will choose lower debt in order to facilitate mergers should entry occur. Our analysis reveals that there is a complex strategic interaction between incumbent debt and entrant debt. For very low levels of incumbent debt, debts are strategic complements in that incumbent debt actually crowds in entrant debt. For sufficiently high levels of incumbent debt, debts become perfect strategic substitutes, with each dollar of incumbent debt crowding out a dollar of entrant debt. In equilibrium, the incumbent always chooses sufficiently high debt such that the debts are strategic substitutes, since very low levels of debt only serve to encourage entry. Thus, consistent with empirical evidence, the model predicts that mature firm debt crowds out that of young firms. Our model is also unique in illustrating how bond covenants, as distinct from debt levels, influence product market competition. The baseline model considers a Stackelberg game in public debt levels. In that game, the entrant (follower) has an incentive to issue its own public debt prior to merger negotiations in order to capture any residual merger surplus. Although being a second mover is a disadvantage, it does carry one benefit: superior information regarding merger surplus. We show that the entrant will use this informational advantage by “filling the debt void” left by the incumbent. This makes the incumbent worse off, since it increases the entrant’s share of merger surplus and increases the expected return to entry. Thus, a strategic role for bond covenants emerges: the incumbent can prevent filling of the debt void by including in its own earlier debt flotation a covenant prohibiting the assumption of counterparty debt in the event of merger. Thus, the model illustrates that the optimality of incumbent financial rigidity extends beyond debt levels and carries over to bond covenants.
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The model also rationalizes an incumbent attaching a poison-put covenant specifying that its bondholders are entitled to a large immediate payment in the event of merger. As we show, the objective of the incumbent in floating debt is to sell a claim that appreciates by an optimal amount in the event of merger. That is, there is an optimal externality its lenders should capture in the event of merger. One way to increase this externality is to increase the face value of debt. Alternatively, the incumbent can achieve the same externality, with lower debt face value, by including in the bond a poison-put provision. The main contribution of our article is to illustrate how an incumbent can use its financial contracts to influence merger markets, with the aim of deterring entry. Since the focal point of our analysis is entry deterrence, it is worth discussing the causal mechanism in greater detail. We begin by noting that our model deliberately rules out standard risk-shifting arguments, which posit that debt encourages aggressive quantity or price setting. In our model, entry deterrence is achieved by depressing the value of entrant assets in the event of merger. This reduction in entrant asset value serves to tighten its financing constraint through two distinct channels. The first channel is the recovery channel: if the venture capital contract calls for the manager to forfeit ownership, financiers obtain a lower merger payoff if the incumbent has high debt and tight covenants. The second channel, labeled the incentive channel, is more subtle. The financial inflexibility of the incumbent also reduces the value the entrant’s manager attaches to retaining control of the firm, since she anticipates low merger payoffs. This reduces the power of managerial incentives that can be provided by control rights. Both channels serve to lower the financier’s return on investment, reducing the likelihood of project funding. In addition to influencing the entrant’s level of public debt, incumbent debt is shown to have a profound influence on optimal venture capital contracts. If the incumbent has high debt, the entrant manager places lower value on retaining control of her firm. Therefore, in order to induce the manager to pay out first-stage project returns, the venture capitalist must grant strong control rights to the manager. In this way, the model predicts that entrant managers should have stronger control rights and high-powered contracts when facing incumbents with high debt and/or tight covenants. By shaping optimal venture capital contracts, incumbent financial structure is also predicted to influence the identity of the acquirer in a merger. As argued above, entrant managers are more likely to maintain ownership of their firm’s assets when the incumbent has high debt. Since these managers are likely to have high private control benefits and/or managerial competence, they are more likely than their financiers to act as the acquirer in a merger. Consistent with empirical evidence, the model thus predicts that more indebted incumbents are less likely to be the acquirer. To the extent possible, we adopt the assumptions of Bolton and Scharfstein (1990) to facilitate comparison. The model opens with an unconstrained incumbent pondering a leveraged recapitalization. The incumbent is uncon-
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strained in that it operates a well-known time-tested production technology, preventing its manager from misrepresenting costs and allowing the firm to issue debt backed by its real assets. The owner–manager of the entrant has no wealth and is initially unable to access public securities markets, since she cannot yet distinguish her viable technology from pretenders. This forces the manager to turn to a venture capitalist, who is the only investor capable of determining the viability of the new technology. The venture capitalist is reluctant to fund the project because the novelty of the entrant’s production technology allows its manager to overstate costs and divert cash flows. In terms of realism, this setup captures the fact that mature firms enjoy superior access to public securities markets, while young firms are typically forced to rely upon venture capitalists for seed capital. The difference between our conclusions and those of Bolton and Scharfstein (1990) is due to two differences in assumptions. First, Bolton and Scharfstein consider a setting where the only punishment available to the venture capitalist is to liquidate the entrant project at an exogenous payoff of zero. Their second assumption, related to the first, is that the incumbent cannot acquire the entrant’s asset or vice versa. Thus, the asset merger channel central to our model is necessarily absent from their model. The assumptions of Bolton and Scharfstein are appropriate in settings where regulators prohibit asset consolidation. However, empirical evidence suggests that asset mergers are common. Gompers (1995) documents that many (38%) venture-backed projects end in trade sales. Further, Brau and Fawcett (2006) document that many firms go public to facilitate acquisitions. Finally, regulators have shown an increasing willingness to consider “failing firm defenses” under which otherwise questionable mergers are permitted for distressed firms. Faure-Grimaud (2000) and Povel and Raith (2004) extend the model of Bolton and Scharfstein to a continuous profit space. In their models, the liquidation payoff is positive but exogenous. In our model, the venture capitalist contract calls for rewards and punishments using ownership rights rather than liquidation threats. Regardless of who has ownership rights, venture capitalist or manager, they maximize the value they get from the assets. In particular, they maximize asset value by relevering their firm in an optimal manner prior to merger negotiations and by engaging in merger only if there is positive bilateral merger surplus. Khanna and Schroder (2008) analyze a variant in which the liquidation of the levered rival in the first period may lead to the entry of a stronger rival in the second period. To reduce this negative externality, the competitor’s behavior will be less aggressive, which in turn allows the levered rival to adopt an optimal contract with less liquidation threats. They do not consider that the number of competitors may be endogenous, either through liquidation (Bolton and Scharfstein) or through merger (our article). Our article is also closely related to that of Israel (1991), who shows that debt issuance by an acquisition target increases the target’s share of the merger
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surplus. The first important difference between the models is that Israel assumes that the acquisition target is already in the industry, so his model is silent on the entry deterrence channel central to our model. Second, there is no agency conflict in Israel’s model, ruling out the analysis of feedbacks from incumbent debt to entrant contracts. In our model, incumbent debt influences the venture capital contract and with it, the identity of the acquirer. Third, Israel only analyzes the financial structure of the target. In contrast, we analyze strategic interactions between the debts of a mature incumbent and a young upstart who are free to issue public debt sequentially. This allows us to show that debt levels can be complements as well as substitutes, and that they are substitutes in equilibrium. The differences in models lead to sharply different empirical predictions. For example, Israel’s model predicts that young target firms should have high leverage. In contrast, our model predicts that mature incumbents should have high debt, crowding out entrant debt. Finally, Israel does not analyze bond covenants, whereas we show that event-risk covenants can be understood as optimal responses to the surplus extraction motive of entrants. Dasgupta and Sengupta (1993), Perotti and Spier (1993), and Hennessy and Livdan (2009) present models featuring a bargaining benefit of debt in settings where only one party, an employer, has the power to issue debt. Mueller and Panunzi (2004) show that the use of debt finance in a bootstrap acquisition can be used by a raider to overcome the free-rider problem in takeovers. There are important differences between models. Mueller and Panunzi do not analyze strategic interactions between debt levels and debt contracts, the entrydeterrence value provided by debt, bond covenants, and the prevention of ex post efficient mergers as a key cost of high debt. Our model shares with Shleifer and Vishny (1992) a focus on the relationship between financial structure and equilibrium asset prices. However, the entry deterrence channel is necessarily absent from their model, since they examine financial interplay between two firms already in an industry. Further, the cost of maintaining deep pockets in their model is that managers waste free cash flow. In contrast, the cost of deep pockets in our model is that it reduces the incumbent’s share of merger surplus and promotes entry. The model is linked to that of Myers (1977), since all effects of leverage stem from externalities accruing to public debtholders. An important contribution of Myers’ model is that it explains why growth firms avoid debt. However, it fails to explain why mature value firms generally have high debt. In contrast, our model shows that the high debt of value firms can be understood as serving a strategic purpose. As discussed above, the causal mechanisms in our model are logically distinct from existing papers arguing that debt serves as an entry deterrent, in particular McAndrews and Nakamura (1992) and Fulghieri and Nagarajan (1996). Our model differs in three key respects. First, these papers are based on the premise that debt causes an incumbent to be more aggressive in quantity and/or price setting. Our model deliberately abstracts from such potential effects by
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t −1
t0
I chooses debt B
e’s entry contract (r, β ) chosen
t1
t +1
t2
t2
merger 1st stage entrant owner: 2nd stage negotiation production production vc or m ? t 2 -profits Π1 , π 1 owner observes π2 , chooses b realized realized
t +2
debts B, b due final payments
Figure 1 Time line.
1. The Economic Setting 1.1 Timing and payoffs Figure 1 presents the time line. The discount rate is zero, and all agents are risk neutral. Capital letters denote the incumbent, and lowercase letters denote the entrant. Tildes denote random variables, while upper bars denote unconditional expected values. At the outset, the incumbent firm I has already made the sunk investment needed to be in the industry and has zero debt. The incumbent is owned and operated by manager M. In order to abstract from free-rider problems and manager–shareholder agency conflicts, there are no outside shareholders. We follow Bolton and Scharfstein (1990) in assuming that the incumbent enjoys frictionless financing. In particular, M has unlimited outside wealth that can be injected into the firm with zero deadweight loss. Further, cash flows generated by the incumbent firm’s asset, denoted asset I , are publicly observed. Intuitively, investors generally have a better understanding of mature businesses. This assumption implies that the mature incumbent has high debt capacity, consistent with empirical observation. There are two periods of potential product market competition taking place at dates t1 and t2 . Prior to product market competition, at time t−1 , the incum-
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assuming that leverage has no direct effect on price and/or quantity setting. This is important given that empirical evidence suggests that debt typically makes firms more likely to lose market share or to exit and less likely to lower prices (e.g., Phillips 1994; Chevalier 1995; Zingales 1998; Khanna and Tice 2005). Second, entry deterrence is only one of two benefits coming from debt in our model, with debt also allowing the incumbent to extract more merger surplus should entry occur. Finally, the existing literature on entry deterrence is necessarily silent on the subject of merger-related bond covenants. Section 1 discusses the economic setting. Section 2 discusses optimal debt levels in the absence of merger-related covenants. Section 3 discusses bond covenants and optimal contracts. Section 4 discusses existing empirical evidence and new testable implications. Section 5 concludes.
Acquisition Values and Optimal Financial (In)Flexibility
d γ, A1 : m 2 = 2 +
where γ is drawn from [0, ∞), with density g and cumulative distribution function G. There are an infinite number of entrepreneurs who can claim to have a viable competitor technology. However, only one entrant is truly viable. Nonviable firms would generate negative cash flows in both periods. Firm e is the only viable entrant, with initial manager–owner m. Each entrepreneur knows whether her firm is viable.
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bent can undertake a publicly observed leveraged recapitalization. In the recapitalization, all proceeds raised from the flotation of a long-term zero-coupon bond will be distributed as a dividend. The bond is floated on a perfectly competitive public debt market. The face value of incumbent debt B is due at time t2+ after second-period production. This maturity assumption is adopted without loss of generality, since any short-term debt obligation of firm I would have no effect on the incumbent’s payoff. The creditors have a senior claim to the second-period cash flow generated by asset I . Following Hart (1991) and Shleifer and Vishny (1992), we assume that public debt contracts are not renegotiable. It will be in the interest of the incumbent to write a contract that is not amenable to renegotiation ex post, since this creates commitment value. Public debt is a security particularly well suited to this objective. As argued by Smith and Warner (1979), the strictures of the Trust Indenture Act (TIA) make it difficult to renegotiate public debt. In particular, TIA requires bondholder unanimity to change any core term of an indenture. Aside from coordination issues, the unanimity requirement in TIA encourages lenders to free ride, making renegotiation more difficult. Consistent with this model assumption, Gilson, John, and Lang (1990) and Asquith, Gertner, and Scharfstein (1994) find that public debt is the single best predictor of failed private workouts. In the baseline model (Section 2), we assume that the only covenant in the incumbent bond is a prohibition against firm I issuing any additional debt. Smith and Warner (1979) document that such covenants are common devices used to prevent dilution of the claim held by senior lenders. The bond contains no covenant restricting dividend payments out of asset I ’s cash flow in period t1 . Such a covenant would only serve to destroy value by undoing M’s initial debt choice. If there is a competitor in the market in period t1 , asset I generates a duopoly cash flow d1 . If there is no competitor in the market in t1 , asset I generates d a monopoly cash flow m 1 > 1 . In period t2 , asset I generates a duopoly d cash flow 2 if there is a competitor. If there is no competitor, the monopoly cash flow of the incumbent in the second period m 2 is characterized by the stochastic monopoly gain γ , with
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Neither manager M nor the general public of investors can initially distinguish firm e from the pretenders. However, there is a single investor (vc) who is able to identify the viable entrant. This has three implications. First, the incumbent cannot acquire firm e until after the first period of product market competition, at which point e’s viability will be demonstrated. Second, the entrant cannot float public debt at the time of entry, since investors do not yet know it is viable. Rather, the entrant must demonstrate viability in period t1 before gaining access to the public debt markets. Third, the inability of manager m to distinguish her firm at the time of entry leaves her in a weak bargaining position relative to the venture capitalist. k. The enEntry can only occur at time t0 and requires capital investment try cost k is drawn from [0, ∞) with density z(·) and cumulative distribution function Z (·). The distribution of k has no atoms and satisfies z(k) > 0 for all k ∈ [0, ∞). When M makes his leverage decision at date t−1 , he only knows the distribution of k. Manager m has zero wealth. Consequently, she cannot enter without the funds provided by vc, who holds an information monopoly regarding her viability. For this reason, we assume that vc holds all bargaining power in his negotiations with m. Venture capitalists frequently enjoy high bargaining power, since their skills and capital are scarce, and our information assumption captures this situation. This assumption is also convenient, since we are interested in identifying conditions under which entry is feasible, conditions that we can characterize most simply by computing the gross return to the financier assuming he holds all bargaining power. The bargaining power assumption could be switched, in which case one obtains a slightly different venture capital contract. For example, Faure-Grimaud (2000) and Povel and Raith (2004) derive the optimal venture capital contract under the assumption that the manager holds all bargaining power. Following Bolton and Scharfstein (1990), the entrant’s asset, denoted asset e, generates cash flows that are privately observed by its manager. Intuitively, investors have a relatively poor understanding of young businesses, giving managers the ability to overstate costs and understate cash flows. This limits the ability of immature firms to raise external finance. When operated as a competitor to asset I , asset e generates a random π1 with support 0, π1max and a strictly duopoly cash flow in period t1 equal to positive atomless density f and cumulative distribution function F. If asset e continues to be operated as a competitor to asset I during the second period, it will generate a stochastic duopoly cash flow with value π2 ∈ 0, π2max . With probability θ, this random variable will have mean π 2h , and with probability (1 − θ ), its mean value will be π l2 ∈ 0, π 2h . The incumbent enjoys a monopoly in both periods if e does not enter at time t0 . If e does enter, the incumbent necessarily faces product market competition in period t1 , since buyout prior to entry is impossible. However, there need
Acquisition Values and Optimal Financial (In)Flexibility
1 For production, a manager must own either asset e or asset I . That is, assets are essential, not managers. 2 This seniority assumption is redundant once we allow firms to write covenants restricting mergers; see
Section 3.
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not be product market competition in period t2 . This is because just prior to period t2 , at time t2− , the owners of asset I and asset e have the option to merge.1 If there is a merger, the dominant asset, asset I , will be operated, and all outstanding debts will be placed on equal priority.2 The financial contract between vc and m is written at time t0 when the entry cost k is observed. As in Bolton and Scharfstein (1990), the manager cannot be forced to disgorge cash flow but must be induced to make payments by the venture capitalist’s threat to seize asset e. The space of legally enforceable contracts consists of a reimbursement schedule r that m pays to vc from the t1 cash flow and a reward probability β, with both based upon the cash flow reported by m. The reward β is the probability of m retaining ownership of asset e at time t1+ . The set of contracts is not limited to deterministic schemes: the fact that the reward is stochastic reflects the fact that, at a theoretical level, deterministic schemes are dominated. Further, randomization has an interesting economic interpretation in that it approximates the type of deviations from absolute priority that are routinely observed in bankruptcies. As shown in fig. 1, the party ownership of asset e privately observes winning its expected cash flow π 2 ∈ π l2 , π 2h at the end of period t1+ , after π1 has been realized and ownership allocated but prior to any merger negotiation. The entrant owner then either operates asset e independently or engages in a merger negotiation at time t2− . Only at time t2− does the entrant’s stand-alone expected cash flow (π 2 ) become observable to the incumbent as the two parties to the merger perform detailed due diligence. Intuitively, this timing assumption captures the idea that the entrant better understands the stand-alone value of her own firm for some time period. This informational assumption can also be understood as capturing one particular form of second-mover advantage enjoyed by the entrant. In particular, the entrant will be able to condition her own public debt issuance upon information (π 2 ) that was not available to the incumbent at the time of his own earlier debt issuance. The entrant manager m derives a known nontransferable nonpecuniary control benefit y > 0 from being a CEO, as in Bolton and Scharfstein (1990). No other agent derives such a benefit. The existence of this control benefit has two important implications. First, it is ex post inefficient to allocate ownership of asset e to the venture capitalist, implying a trade-off between incentives and ex post efficiency. Second, if the entrant manager m were to negotiate a merger with the incumbent manager M, the two parties would make m the CEO in order to maximize bilateral merger surplus. That is, m would be the acquirer. Conversely, the venture capitalist and M would be indifferent regarding who became CEO of a combined entity. Consequently, we shall assume without loss
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A2 : γ > π 2h . Despite the fact that merger is ex post efficient, debt can drive a wedge between the goals of firm value maximization and shareholder value maximization. Efficient mergers do not necessarily occur, since shareholders ignore the benefits that mergers provide to lenders. This is a variant of the debt overhang problem first analyzed by Myers (1977). In contrast to earlier work on optimal entrant contracts, we shall derive endogenously the values that vc and m attach to ownership. Further, we allow both vc and m to relever their firm in anticipation of subsequent merger negotiations. Specifically, the entrant gains access to the public debt market at time t1+ , just prior to the merger negotiation at time t2− . The face value of firm e’s debt b is due at time t2+ . Endowing the entrant with the ability to issue public debt against secondperiod cash flow is important, since it increases the share of merger surplus that it can extract ex post. This relaxes the entrant’s financing constraint through two channels. First, by floating his own public debt prior to merger negotiations, vc is able to obtain a higher payoff if he wins ownership of asset e. Second, the ability to float public debt prior to merger negotiations causes manager m to place a higher value on winning asset ownership, increasing her willingness to deliver first-stage cash flows to the venture capitalist. 2. Analysis of Financial Structure The model is solved via backward induction. We first analyze how debt levels influence merger bargaining. We then determine how the entrant will choose its own level of public debt in light of prospective merger bargaining. Next, we determine the optimal venture capital contract at the time of entry. Finally, we analyze optimal incumbent debt in anticipation of potential entry.
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of generality that M will be the acquirer should he find himself negotiating a deal with the venture capitalist. The control benefit introduces uncertainty regarding the identity of the target and acquirer in the simplest possible way. Critically, this modeling setup allows us to show that none of the results hinge upon endowing one firm or the other with the status of “acquirer.” To make the analysis independent of any specific assumption on the distribution of the merger surplus between acquirer and target, we assume that the two firms equally share bilateral merger surplus ex post. Using appropriate stock conversion ratios, the bilateral surplus from any merger will be divided evenly between M and the entrant owner (vc or m). This division of surplus can be understood as arising from an alternating offers (Rubinstein–Stahl) bargaining game or from Nash’s axiomatic formulation. We next adopt a technical assumption ensuring that it is always ex post efficient to merge:
Acquisition Values and Optimal Financial (In)Flexibility
2.1 Debt overhang and merger viability At date t2− , the owner–managers of the entrant and incumbent decide whether to merge. They will do so if and only if there is positive bilateral surplus from merger. In order to compute bilateral merger surplus, it is necessary to compute debt values with and without merger. Suppose first that merger does not occur. The incumbent then operates as a duopolist and generates cash flow d2 . The resulting market value of the incumbent’s debt would then be equal to L d (B) = min{B, d2 }.
(1)
L m (B + b) = B + b.
(2)
Otherwise, the debt of the post-merger monopoly is risky and has a market value at t2− of
B+b−d2
L m (B + b) = 0
(d2 + γ )g(γ )dγ + (B + b) 1 − G(B + b − d2 ) .
(3) The total externality accruing to public debt lenders from an asset merger is equal to the change in total debt value: (B, b) ≡ L m (B + b) − L d (B).
(4)
For brevity, the variable will be referred to as debt overhang. Bilateral merger surplus (S) is equal to merged firm equity value less the value of the equity of each stand-alone firm (the control benefit y nets out if manager m assumes control):
m S(B, b, π 2 ) ≡ 2 − L m (B + b) − d2 − L d (B) − π 2 .
(5)
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In the absence of a merger, any debt obligation of firm e would be worthless, since the manager–owner would always report that the second-stage cash flow generated by asset e was zero. A similar prediction arises in the model of Bolton and Scharfstein (1990). In both models, a stand-alone entrant has low debt capacity in the final period. However, in our model, the entrant derives nontrivial debt capacity in the second stage based upon the possibility of a merger. Effectively, the incumbent asset serves as the true underlying collateral for the public debt of the entrant. Suppose next that merger occurs. The merged entity operates asset I as a monopoly and assumes the debt obligations of both firms. If B + b ≤ d2 , the monopolist’s debt is safe. The market value of the debt at the time of the merger negotiation (t2− ) is then equal to
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Rearranging terms, the bilateral merger surplus can be expressed as S(B, b, π 2 ) = [γ − π 2 ] − (B, b) .
(6)
Solving the equation above, we find: l S(B H , 0, π l2 ) = 0 ⇔ B H = L −1 m (2 − π 2 ). m
(8)
Note that if the incumbent were to choose the high debt level B H while the entrant chose b = 0, merger would only occur with probability 1 − θ . Next define a (relatively) low level of incumbent debt such that exactly zero bilateral merger surplus is available if b = 0 and π 2h is realized: h S(B L , 0, π 2h ) = 0 ⇔ B L = L −1 m (2 − π 2 ). m
(9)
Note that if the incumbent were to choose B L while the entrant chose b = 0, merger would occur with probability one. The advantage of low debt from the perspective of the incumbent is that there is never a competition in the second period, since merger is always profitable to shareholders. However, by taking on low debt, the incumbent leaves on the table “residual surplus” whenever π l2 is realized, since S(B L , 0, π l2 ) = π 2h − π l2 > 0.
(10)
2.2 Public debt of the entrant as a best response We continue the backward induction by analyzing the choice of public debt by the entrant at the end of period t1+ . For this purpose, let (B, b, π 2 ) denote
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The first bracketed term in Equation (6) measures the expected increase in total cash flow resulting from merger. Note that merger surplus decreases in the stand-alone value of the entrant (π 2 ). The second term in S captures the fact that debt overhang creates a disincentive for the manager–shareholders to merge. If both firms are unlevered, A2 implies that merger always occurs. In fact, there are two sources of debt overhang. First, if b = 0, there is a debt overhang arising from the fact that the value of incumbent debt is higher under monopoly for all B > d2 . Second, the owners of entrant debt necessarily benefit from merger, since their claim is worth (b/(b + B))L m (b + B) if there is a merger and worth zero otherwise. It is convenient to define a sufficiently high level of incumbent debt such that exactly zero bilateral merger surplus is available when b = 0 and π l2 is realized. To this end, let B H denote the unique solution of
m S(B H , 0, π l2 ) = 2 − L m (B H ) − d2 − L d (B H ) − π l2 = 0. (7)
Acquisition Values and Optimal Financial (In)Flexibility
the value of the claim held by the entrant owner at time t1+ , excluding nonpecuniary control benefits. Further, let b∗ (B, π 2 ) denote optimal entrant debt conditional upon incumbent debt and the stand-alone value of the entrant. To determine b∗ (B, π 2 ), consider first an arbitrary pair (B, π 2 ) such that S(B, 0, π 2 ) ≤ 0. Here, any debt issued by the entrant would be worthless. To see this, note that a strictly positive value of b would result in no merger. If there is no merger, the entrant debt is worth zero, since the lenders would have no way to compel delivery of the unobservable second-stage cash flow generated by asset e. It follows that (11)
Consider next all pairs (B, π 2 ) such that S(B, 0, π 2 ) > 0. For any b sufficiently small such that bilateral merger surplus remains positive, the total value received by the entrant owner (excluding the nonpecuniary benefit y) is equal to the sum of the value of her debt flotation plus her reservation value plus one-half the bilateral surplus from merger: (B, b, π 2 ) = π 2 +
b 1 L m (b + B) + S(B, b, π 2 ). b+B 2
(12)
This objective function is strictly increasing in b on the interval under consideration, with 1 2 1 − G(b + B − d2 ) ⇒ 2 (B, b, π 2 ) = 2 B+b−d
2 B d + + γ g(γ )dγ . 2 (b + B)2 0
B + b < d2 ⇒ 2 (B, b, π 2 ) = B + b > d2
(13)
It follows that the best response for the entrant satisfies the following condition: S(B, 0, π 2 ) > 0 ⇒ S B, b∗ (B, π 2 ), π 2 = 0.
(14)
That is, the best response for the entrant is to “fill any void” in the merger surplus by issuing sufficient debt such that there is exactly zero bilateral merger surplus left. Although the issuance of debt by the entrant reduces the bilateral surplus S, the fact that she only gets one-half of the surplus and all of the value of her own debt flotation implies that she prefers to deplete the pool of bilateral merger surplus. This brings up an obvious question: Why does the incumbent not fill the void himself? The answer is that the incumbent, in contrast to the entrant, does not know the realized value of π 2 when choosing his own debt
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S(B, 0, π 2 ) ≤ 0 ⇒ b∗ (B, π 2 ) = 0.
The Review of Financial Studies / v 00 n 0 2010
level B. Consequently, the incumbent risks jeopardizing mergers whenever he chooses B > B L . This highlights the informational second-mover advantage enjoyed by the entrant. Inverting Equation (14) yields an analytical solution for the best response function for the entrant that we summarize in Lemma 1. The proof of the lemma is sketched below. Lemma 1. The entrant does not float any public debt if S(B, 0, π 2 ) ≤ 0. If B ≤ d2 , then (15)
and entrant debt and incumbent debt are strategic complements. If B > d2 , then b∗ (B, π l2 ) = B H − B b∗ (B, π 2h ) = B L − B
,
(16)
and entrant debt and incumbent debt are perfect strategic substitutes. At time t1+ , the entrant owner chooses b∗ (B, π 2 ) according to the realization of π 2 so that the remaining surplus in Equation (5) is zero, implying L m (B + b∗ ) − L d (B) = 2 − d2 − π 2 , m
(17)
where the right-hand side is exogenously given and deterministic for him, since he knows the true value of π 2 . Debt L m (B + b∗ ) is then necessarily risky. Applying the implicit function theorem to expression (17), the entrant’s best response b∗ (B, π 2 ) satisfies: L (B) ∂ ∗ b (B, π 2 ) = d − 1. ∂B L m (B + b∗ )
(18)
For B ≤ d2 , we find the following relationship between incumbent debt and entrant best response (since L d (B) = B): 1 ∂ ∗ b (B, π 2 ) =
−1≥0 ∂B L m (B + b∗ )
∀
B < d2 .
(19)
As expression (19) shows, at low levels of B, marginal increases in incumbent debt actually crowd in entrant debt. The intuition is as follows. The entrant optimally responds to any void by issuing enough of her own debt to drive bilateral merger surplus down to zero. An increase in incumbent debt at low levels will increase the value of duopoly debt L d (B) by more than the relatively riskier monopoly debt L m (B + b∗ ). Hence the size of the void left by the incumbent is actually increasing in B for B < d2 .
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b∗ (B, π 2 ) = L −1 m (γ − π 2 + B) − B,
Acquisition Values and Optimal Financial (In)Flexibility
Consider next B > d2 . Here, from (1), it follows that L d (B) = 0, so that the entrant’s reaction (18) simplifies to ∂ ∗ b (B, π 2 ) = −1 ∂B
∀
B > d2 .
(20)
B ≤ d2 ⇒ B, b∗ (B, π 2 ), π 2
B = π 2 + 1 − −1 [γ − π 2 + B] . L m (γ − π 2 + B)
(21)
For higher incumbent debt levels, we obtain π 2 = π l2 ⇒ B, b∗ (B, π l2 ), π l2
BH − B m l 2 − π l2 ∀ B ∈ d2 , B H = π2 + BH h π 2 = π 2 ⇒ B, b∗ (B, π 2h ), π 2h
BL − B m 2 − π 2h ∀ B ≤ d2 , B L . = π 2h + BL
(22)
Finally, it is useful to assess how marginal increases in B affect the entrant’s ex post payoff, . We know that if S(B, 0, π 2 ) ≤ 0, then = π 2 and marginal changes in B have no effect on . Next, considering the cases where S(B, 0, π 2 ) > 0, total differentiation of yields d B, b∗ (B, π 2 ), π 2 dB
⎧ L m (B+b) ⎪ b 1 − + ⎨ B+b B+b = ⎪ ⎩ −L m (B+b) <0 B+b
B L m (B+b) (B+b)2
1
L m (B+b)
−1 >0
∀ B < d2 ∀ B > d2 (23)
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In other words, for sufficiently high levels of B, the public debt commitments of the two firms are perfect strategic substitutes: marginal increases in incumbent debt perfectly crowd out entrant debt. We obtain analogous insights when we analyze the value of the entrant owner’s claim under her best response (exclusive of the manager’s benefit y). The value depends on B and π 2 . First, if the incumbent issues sufficiently high debt such that S(B, 0, π 2 ) ≤ 0, then no merger occurs and = π 2 . If incumbent debt is very low, we know
The Review of Financial Studies / v 00 n 0 2010
2.3 Optimal venture capital contract Continuing the backward induction, we next analyze the optimal venture capital contract, which is written at time t0 . Since the cash flows from asset e are not observable, the contract must be based upon a verifiable cash flow report made by m. The venture capital contract consists of a pair of functions (r, β) mapping the manager’s first-stage cash flow report ( π1 ) to reimbursements to vc and ownership probabilities for m, respectively. In order to derive the optimal contract, it is necessary to compute the expected value the venture capitalist attaches to winning ownership of asset e, with the expectation taken at the time of contracting, date t0 . The ex ante valuation that the venture capitalist attaches to winning ownership of the entrant asset is denoted p. It depends on the incumbent’s leverage and can be expressed as
(24) p(B) ≡ (1 − θ ) B, b∗ (B, π l2 ), π l2 + θ B, b∗ (B, π 2h ), π 2h . The analysis of p (B) leads to an important result, stated as Lemma 2. The lemma itself follows from Equations (21), (22), and (23).
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Equation (23) establishes the important result that the ex post payoff to the entrant is initially increasing in B and then decreasing in B. This is consistent with the discussion above regarding whether the debt levels are strategic complements or substitutes. For B < d2 , marginal increases in B induce an increase in the pool of surplus S available to the entrant. This leads to a crowding-in of entrant debt and an increase in the entrant’s ex post payoff. Conversely, once incumbent debt becomes risky, with B > d2 , there is a crowding-out effect, and the ex post payoff to the entrant decreases in B. Thus, we observe an interesting nonmonotonicity in the strategic interaction of the two firms’ debt levels, with debts being strategic complements for low levels of incumbent debt, switching to perfect strategic substitutes for higher levels of incumbent debt. We observe a similar change in sign in the marginal effect of incumbent debt on the ex post payoff to the entrant (). We will show that in our model, the incumbent will only choose B > d2 in equilibrium. So, debt levels will be perfect strategic substitutes for all debt levels chosen in equilibrium. Figure 2 plots the entrant’s best response functions: b∗ (·, π l2 ) and b∗ (·, π 2h ). From Lemma 1, we know that the best response functions start at values b∗ (0, π 2 ) = L −1 m (γ − π 2 ). They then increase in a weakly monotone fashion to b∗ (d2 , π l2 ) = B H − d2 and b∗ (d2 , π 2h ) = B L − d2 , respectively. From the point B = d2 onward, marginal increases in incumbent debt crowd out entrant debt one for one.
Acquisition Values and Optimal Financial (In)Flexibility
b*(B,π2) 2.50
2.00
1.50
1.00
0.00 0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 BH BL Π2d
B
Figure 2 Entrant debt b∗ B, π¯ 2 as a function of incumbent debt B This figure shows the entrant’s debt b∗ B, π¯ 2 as a function of incumbent debt B and the entrant stand-alone profit π¯ 2 that is privately observed by the entrant owner in t1+ . The continuous line (on top) depicts b∗ B, π¯ 2l , and the dashed line (below) depicts b∗ B, π¯ 2h . Both lines reach their maximum at d2 and reach zero at B L d m d and B H , respectively. We assume the following parameter values: m 1 = 2.5, 1 = 1, 2 = 2.5, 2 = 1, y = 1, θ = 0.5. The payoff variables that are random are assumed to be uniformly distributed, with γ ∼ U [0, 3], π2l ∼ U [0, 0.25], π2h ∼ U [0, 1]; and entry costs k˜ are exponentially distributed, Z (k) = 1 − exp(−λk), where we assume λ = 0.5.
Lemma 2. The ex ante value the venture capitalist attaches to winning ownership of the entrant asset depends upon incumbent debt in the following nonmonotonic way:
p (B)
⎧ ⎨ > 0 ∀ B ∈ (0, d2 ) < 0 ∀ B ∈ (d2 , B H ) . ⎩ = 0 ∀ B > BH .
(25)
The entrant manager m attaches a higher value to winning control of the asset than does vc, since she also captures the benefit y. Her ex ante valuation of asset ownership is thus x(B) ≡ y + p(B).
(26)
Having determined the ex ante value of ownership rights, we now derive the optimal venture capital contract for arbitrary pairs ( p, x), such that p < x. Before doing so, we adopt a final technical assumption ensuring that first-stage
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0.50
The Review of Financial Studies / v 00 n 0 2010
cash flows are not too large. The assumption is not essential and only serves to simplify the algebra.3 A4 : (1 − θ )π l2 + θπ 2h + y > π1max .
xβ(π ) − r (π ) ≥ xβ( π ) − r ( π ) ∀ (π, π ) ∈ [0, π1max ] × [0, π1max ] . (27) This condition is satisfied with equality at all points on the state space when r = xβ . The IC condition is informative about the trade-offs facing the venture capitalist in choosing β. By increasing β marginally, the value of his ownership rights fall by pβ . However, there is a larger compensating gain, since m is willing to increase the reimbursement by xβ . The optimal contract solves π max 1 v≡ [r (π ) + (1 − β (π )) p] f (π ) dπ (28) max r,β
0
subject to LL : r (π ) ≤ π IC : r (π ) = xβ (π ) β(π ) ∈ [0, 1] . Lemma 3 characterizes the optimal contract. Lemma 3. The optimal venture capital contract is β( π1 ) =
π1 x
r ( π1 ) = π1 . The gross return to the venture capitalist under the optimal contract is
π1 v(B) ≡ π 1 + 1 − p(B). x(B)
(29)
(30)
The function v is increasing on the interval (0, d2 ), decreasing on (d2 , B H ), and constant for B ≥ B H . 3 This assumption simplifies determining the probability of managerial ownership.
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The optimal contract maximizes the gross return to vc, which consists of firststage cash reimbursements r plus the value of his ownership rights. Limited liability (LL) demands r (π1 ) ≤ π1 at each point on the state space [0, π1max ]. From the revelation principle, it follows that attention can be confined to contracts eliciting truthful reporting of first-stage cash flow. The global incentive compatibility (IC) condition is
Acquisition Values and Optimal Financial (In)Flexibility
Proof: See Appendix A.
Thus, the gross return to the venture capitalist is decreasing if and only if p is decreasing, consistent with Lemma 3. The slope of p is described above in Lemma 2. The first part of Equation (31) illustrates how incumbent debt influences the return to entry through two channels: the recovery rate effect and the incentive effect. The term involving p captures the fact that incumbent debt influences the return to entry by altering the amount the venture capitalist expects to recover in the event that he seizes assets after the first stage. The term involving x captures the role played by incentives. In particular, the incumbent debt influences the return to entry through its effect on the value that the entrant manager attaches to retaining ownership. High levels of incumbent debt reduce the value the entrant manager attaches to retaining ownership, diminishing her incentive to return cash to her investors.
2.4 Incumbent debt level Having determined the optimal response of the entrant to the leverage chosen by the incumbent, the last step in the backward induction is to determine the optimal public debt for the incumbent, denoted as B ∗ . Let V denote the cumdividend value of the claim held by the incumbent at time t−1 as a function of his choice of B. Consider first B ∈ [0, B L ). For such debt levels, merger always occurs, regardless of the realized value of π 2 . In the event of no entry, the incumbent gets monopoly profits in both periods. If entry does occur, the incumbent earns a duopoly profit in the first period. In the following period, he earns the monopoly profit less the value obtained by the entrant. Thus, for all B ≤ BL : m
d V (B) = [1 − Z (v(B))][m 1 + 2 ] + Z (v(B)) 1
+Z (v(B)) [2 − (1 − θ )(B, b∗ (B, π l2 ), π l2 ) m
−θ (B, b∗ (B, π 2h ), π 2h )].
(32)
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Lemma 3 indicates that the optimal venture capital contract calls for vc to receive all first-stage cash flows, with m being encouraged to deliver higher cash flows via the promise of increased ownership rights. The gross return to vc is then simply the expected first-stage cash flow plus the expected value of his ownership claim. It is also worth noting that π1 p(B)π 1 p (B) + x (B) v (B) = 1 − x(B) (x(B))2 π1 p(B) (31) 1− p (B). = 1− x(B) x(B)
The Review of Financial Studies / v 00 n 0 2010
Differentiating this expression yields d ∗ l l V (B) = −z (v(B)) v (B)[m 1 − 1 + (1 − θ )(B, b (B, π 2 ), π 2 )
+θ (B, b∗ (B, π 2h ), π 2h )] d −Z (v(B)) (1 − θ ) (B, b∗ (B, π l2 ), π l2 ) dB
d (B, b∗ (B, π 2h ), π 2h ) . +θ dB
(33)
V (B) < 0 ⇒
V (0) > V (B)
V (B) > 0 ⇒
V (B L ) > V (B) ∀ B ∈ [d2 , B L ) .
∀ B ∈ (0, d2 ]
(34) (35)
Consider next B ∈ (B L , B H ). Such high levels of debt have the advantage of reducing the ex post payoff to any entrant and depressing v, as shown in Lemma 3. However, if π 2h is realized, no merger takes place, and the incumbent faces intense produce market competition in the second period. The resulting firm value expression is m
V (B) = [1 − Z (v(B))][m 1 + 2 ]
m +Z (v(B)) d1 + (1 − θ ) 2 − (B, b∗ (B, π l2 ), π l2 ) + θ d2 m
m d = [m 1 + 2 ] − Z (v(B)) [1 − 1
+(1 − θ )(B, b∗ (B, π l2 ), π l2 ) + θ γ ].
(36)
Differentiating this expression, one obtains d ∗ l l V (B) = −z (v(B)) v (B)[m 1 − 1 + (1 − θ )(B, b (B, π 2 ), π 2 ) + θ γ ] d −Z (v(B)) (1 − θ ) (B, b∗ (B, π l2 ), π l2 ). (37) dB
Above, we again see the two key benefits coming from marginal increases in incumbent debt: reduction in the probability of entry and reduction in the surplus that the entrant can capture. From Equation (23) and Lemma 3, it follows that V (B) > 0 ⇒
20
V (B H ) > V (B) ∀ B ∈ (B L , B H ).
(38)
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The first line in Equation (33) captures the effect that marginal changes in B have on the probability of entry, while the second line captures the effect on the ex post payoff to the entrant conditional upon entry having taken place. From Equation (23) and Lemma 3, it follows that
Acquisition Values and Optimal Financial (In)Flexibility
From the results stated in (34), (35), and (38), it follows that the optimal incumbent debt is B ∗ ∈ {0, B L , B H }. Further, we know m
m d V (B H ) = m 1 + 2 − Z (v(B H )) [1 − 1
+(1 − θ )(B H , b∗ (B, π l2 ), π l2 ) + θ γ ] m
m d l = m 1 + 2 − Z (v(B H )) [1 − 1 + (1 − θ )π 2 + θ γ ], (39)
and m
m d V (0) = m 1 + 2 − Z (v(0)) [1 − 1 m
m d = m 1 + 2 − Z (v(0)) [1 − 1 + γ ].
(40)
It is readily verified that p(0) = γ > p(B H ) = (1 − θ )π l2 + θ π 2h ⇒ v(0) > v(B H ) ⇒ V (B H ) > V (0).
(41)
In other words, it is always better for the incumbent to issue high debt rather than having no debt at all and letting the entrant capture all merger surplus. It follows that the optimal incumbent debt is B ∗ ∈ {B L , B H }. The choice between B L and B H can now be immediately characterized. We know that m
m d V (B L ) = m 1 + 2 − Z [v(B L )][1 − 1
+(1 − θ )(B L , b∗ (B L , π l2 ), π l2 ) + θ π 2h ].
(42)
Comparison of Equations (39) and (42) yields the following proposition. Proposition 1. The optimal m l B H = L −1 m (2 − π 2 ) if
public
debt
for
the
incumbent
is
d l l h ∗ (m Z (v(B H )) 1 − 1 ) + (1 − θ )(B L , b (B L , π 2 ), π 2 ) + θ π 2 ≤ , (43) d l Z (v(B L )) (m 1 − 1 ) + (1 − θ )π 2 + θ γ m
h and B L = L −1 m (2 − π 2 ) if not.
Proposition 1 indicates that the choice between high and low debt involves the following trade-off. High debt discourages entry but risks jeopardizing merger and facing second-stage competition should entry deterrence fail. To see this formally, recall Lemma 3, which established that Z (v(B H )) < Z (v(B L )), as the high level of incumbent debt reduces the ex post payoff to entry by crowding out entrant debt. Thus, Proposition 1 states that high debt is optimal when the entry-deterrence effect, captured by the left-hand side of Equation (43), is sufficiently strong relative to the loss from foregone merger if π 2h is realized.
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+(1 − θ )(0, b∗ (0, π l2 ), π l2 ) + θ (0, b∗ (, π 2h ), π 2h )]
The Review of Financial Studies / v 00 n 0 2010
Corollary 1. The attractiveness of high debt increases in short-term monopoly rents and decreases in long-term monopoly rents. Corollary 1 is consistent with the stylized fact that value firms choose higher debt levels than growth firms, which is typically interpreted as supporting the theory of Myers (1977), who argues that growth firms want to avoid debt in order to protect growth options. Our model generates a similar prediction. However, Myers’ theory fails to explain why value firms take on debt. In his framework, the optimal debt for all firms is zero. By way of contrast, our model provides a rationale for voluntary leveraged recapitalizations by value firms. Figure 3 plots the value of the equity claim of the incumbent V at time t−1 as a function of B for the numerical example specified in the caption. We dis-
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The first bracketed terms in the numerator and denominator of the right-hand side of Equation (43) capture the likelihood that entry will be deterred and that the monopoly profit will be captured in the first period. Since Z (v(B H )) < Z (v(B L )), the stated ratio condition is more easily satisfied the higher the first-stage monopoly rent. Intuitively, the only way the incumbent can capture the first-stage monopoly rent is by deterring entry. High debt has a stronger entry-deterrence effect. Thus, a testable implication of the model is that value firms should have higher leverage. The second terms in the numerator and denominator of Equation (43) capture an ex post benefit to high debt: reduction in the portion of surplus captured by an entrant should π l2 be realized. When the incumbent chooses high debt, he maximizes his share of surplus should π l2 be drawn, since the entrant is then pinned to her reservation value of π l2 . By way of contrast, when B L is chosen by the incumbent, the entrant can capture a much greater share of surplus via her own strategic issuance of debt. The final terms in both the numerator and denominator capture the cost of high debt; the loss of second-stage monopoly rents if high debt overhang prevents a merger from taking place when π 2h is realized. Clearly, when the second-stage monopoly rent (γ ) is high, the ratio condition is less likely to be satisfied. Thus, another testable implication of the model is that growth firms should issue relatively less public debt than value firms. It is worth noting that high debt can be optimal for the incumbent if there is zero entry deterrence effect. This is because high debt has two benefits: entry deterrence and surplus extraction ex post. In some cases, the latter effect may be sufficient to make B H optimal. For example, it can be seen that the righthand side of Equation (43) exceeds unity for θ sufficiently close to zero, in which case high debt is necessarily optimal, even if there is no entry deterrence effect. We summarize this analysis, focusing on empirical implications in Corollary 1.
Acquisition Values and Optimal Financial (In)Flexibility
3. Optimal Contracts and Bond Covenants In this section, we first analyze the role of covenants limiting counterparty debt in a merger and show that such covenants are always optimal for the incumbent. We then show that standard public debt is, in fact, an optimal contract for
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cuss first the top line in fig. 3, which depicts results under the model’s working assumptions that entry has not yet occurred (Z < 1), with the entrant choosing its best response b∗ . For B ∈ [0, d2 ), the payoff to the incumbent is decreasing in B, since here marginal increases in debt serve to increase the bilateral merger surplus and crowd-in entrant debt. For B > d2 , the payoff to the incumbent increases in B, since here incumbent debt crowds out entrant debt, reducing the entrant’s ability to capture surplus and deterring entry. The figure also depicts a jump down in incumbent firm value if the incumbent increases debt infinitesimally beyond B L . Intuitively, at this point, a marginal increase in debt only prevents a merger from happening if π 2h is realized. For B > B L , we see firm value increasing in B as marginal increases in debt reduce the entrant’s share of merger surplus in the event that π 2h is realized. In turn, this reduces the probability of entry. The figure also depicts another jump down in firm value if the incumbent increases debt infinitesimally at B H , where increases in debt only prevent mergers from happening if π l2 is realized. The optimality of B H in the numerical example of fig. 3 is best understood by decomposing the factors at work. To this end, the middle line in fig. 3 depicts incumbent value under two assumptions unfavorable to high incumbent debt: Entry has already occurred (Z = 1), and the entrant cannot issue public debt (b = 0). Effectively, this pair of assumptions deliberately shuts off two of the advantages we posit for incumbent debt: entry deterrence ex ante and the crowding out of entrant debt ex post. Although he uses a different setup, these assumptions are comparable to those implicit in Israel (1991), since in his model, both firms are already in the market, and one firm cannot issue debt. Under this pair of assumptions, it is optimal for the incumbent to choose relatively low debt equal to B L . Further, there is a relatively large gap between the value achieved at B L versus that achieved at B H . Finally, the bottom line in fig. 3 continues to shut off the entry deterrence channel by assuming that entry has already occurred (Z = 1) while returning to our working assumption that the entrant is free to implement a best response b∗ to the first-moving incumbent’s debt. Here, it is also optimal for the incumbent to choose relatively low debt equal to B L . However, comparing this case to the middle line, which sets b = 0, we see that the case for high incumbent debt of B H becomes stronger. Intuitively, even if there is no entry-deterrence effect, high incumbent debt has strategic value by crowding out entrant debt. Thus, the optimality of high incumbent debt in the baseline model (top line in fig. 3) is properly understood as being motivated by the desire to achieve entry deterrence and to crowd out entrant debt, with the latter effect helping the incumbent to extract a higher share of surplus ex post.
The Review of Financial Studies / v 00 n 0 2010
V(B) 4.5 4 3.5 3 2.5 2
1 0.5 0 0.00
0.50
1.00 Π 2d
1.50
2.00
2.50 BL
3.00
B BH
Figure 3 Ex ante incumbent value V(B) as a function of incumbent debt B This figure shows the incumbent’s ex ante value V(B) as a function of incumbent debt B . The dashed line (top) ˜ depicts V(B) if entry is stochastic according to k and has not yet occurred, and the entrant issues optimal debt b∗ B, π¯ 2 . The continuous line (middle) depicts V(B) if entry has already occurred ( Z = 1), and the entrant cannot issue debt because of a covenant of the incumbent restricting counterparty debt in mergers, b∗ B, π¯ 2 . The dotted line (bottom) depicts V(B) if entry has already occurred ( Z = 1), and the entrant issues optimal d m d debt b∗ B, π¯ 2 . We assume the following parameter values: m 1 = 2.5, 1 = 1, 2 = 2.5, 2 = 1, y = 1, θ = 0.5. The payoff variables that are random are assumed to be uniformly distributed, with γ ∼ U [0, 3], π2l ∼ U [0, 0.25], π2h ∼ U [0, 1]; and entry costs k˜ are exponentially distributed, Z (k) = 1 − exp(−λk), where we assume λ = 0.5.
the incumbent provided that it includes such a covenant. Finally, we argue that standard debt is not uniquely optimal, since appropriately designed poison-put covenants lead to the same incumbent payoffs. All covenants are assumed to be non-renegotiable, since they are part of public debt issues.
3.1 Covenants restricting counterparty debt Bond covenants routinely place restrictions on firms’ ability to engage in mergers and acquisitions. Typically, such covenants are justified as devices for mitigating agency problems (e.g., potential risk shifting associated with a risky acquisition). Here, we show that such covenants can play an important role in determining the division of surplus in asset mergers. We consider the following simple covenant. At the time of issuance, incumbent bondholders can include a covenant prohibiting a merger if the counterparty debt exceeds bmax . Similarly, the entrant can include in her debt a covenant prohibiting a merger if incumbent debt exceeds Bmax . What is the equilibrium of the resulting Stackelberg game in bond covenants? Using backward induction, we first analyze the optimal entrant
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1.5
Acquisition Values and Optimal Financial (In)Flexibility
m
m d l Vc (B H ) = m 1 + 2 − Z (v(B H )) [1 − 1 + (1 − θ )π 2 + θγ ].
(44)
The addition of a bond covenant, restricting counterparty debt, does increase the relative attractiveness of B L , with the firm value expression increasing to
m d Vc (B L ) = m + − Z )) m (v(B L 2 1 1 − 1 + (1 − θ )(B L , 0, π l2 ) + θ π 2h . (45) The covenant increases firm value when B L is chosen, since in the absence of a covenant prohibiting counterparty debt, the entrant would issue debt b∗ (B L , π l2 ) > 0 at the expense of the incumbent. Such debt issuance increases the payoff to the entrant ex post and encourages entry ex ante. The following proposition summarizes these results. Proposition 2. Any public debt obligation of the entrant would not restrict B. Public debt of the incumbent optimally contains a covenant stipulating bmax = 0, and the entrant does not float public debt. The optimal public debt for the m l incumbent is B H = L −1 m (2 − π 2 ) if m − d1 + (1 − θ )(B L , 0, π l2 ) + θ π 2h Z (v(B H )) ≤ 1 , d l Z (v(B L )) (m 1 − 1 ) + (1 − θ )π 2 + θ γ
(46)
m
h and B L = L −1 m (2 − π 2 ) if not.
The ratio test for the optimality of high incumbent debt stipulated in (46) is more stringent than that specified in (43), since the covenant prohibiting the assumption of entrant debt serves to mitigate surplus extraction by the entrant when B L is chosen.
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covenant. Since mergers are voluntary, the entrant is always weakly better off if merger occurs. Therefore, as the follower, the entrant finds it optimal to accommodate whatever debt level is chosen by the incumbent. That is, the entrant should not write any covenant restricting counterparty debt. From Lemma 1, we know that the entrant can increase its share of surplus at the expense of the incumbent by issuing its own debt. Therefore, the incumbent will find it optimal to attach to its bond flotation a covenant stipulating bmax = 0. With such a covenant, the incumbent firm value changes. We denote the incumbent’s ex ante value if such a covenant is in place by Vc (B). Using arguments directly analogous to those applied in Section 2, Appendix B shows that with the bond covenant, the optimal level of incumbent debt remains B ∗ ∈ {B L , B H }. Further, we recall that when the incumbent chooses B H , the entrant never issues any public debt even in the absence of a covenant, so the firm value expression in this case remains the same as that derived in the previous section, with
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Proposition 2 provides a number of strong testable implications. First, it confirms that incumbent firms should have high debt, while entrants should have low debt. Second, incumbent firms should write tight debt covenants, while entrants should write loose covenants, at least with respect to limitations on mergers. Third, if such covenants are used, then both incumbent firms and entrant firms will on average deploy lower levels of debt than in the absence of such covenants.
s(C, c, π 2 ) ≡ γ − π 2 − δ (C, c) .
(47)
Since the game is zero-sum post-entry, the incumbent will optimally write a covenant prohibiting merger with the entrant if it has issued third-party claims. The entrant will accommodate this covenant, so we may restrict attention to the case where there is no third-party contract outstanding on the entrant side, c = 0. In this case, bilateral surplus is s(C, 0, π 2 ) ≡ γ − π 2 − δ (C, 0) .
(48)
There are three possible merger scenarios ex post: always merge, merge only if π l2 is realized, or never merge. Consider first all securities such that merger always occurs, implying s(C, 0, π 2h ) ≥ 0. Within the set of securities satisfying this inequality, any optimal security for the incumbent satisfies s(C, 0, π 2h ) = 0. Such a security minimizes the share of surplus received by the entrant for each realized value of π 2 subject to the stipulated constraint. By construction, public debt with face value B L attains the optimum within this set. Consider next all securities such that merger only occurs if π l2 is realized, implying that s(C, 0, π 2h ) < 0 ≤ s(C, 0, π l2 ).
(49)
Within the set of securities satisfying the constraints above, any ex ante optimal security for the incumbent satisfies s(C, 0, π l2 ) = 0. Such a security minimizes
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3.2 The optimality of public debt for the incumbent Thus far, we have confined attention to the issuance of public debt by the incumbent. We turn now to the question of optimal security design for the incumbent. Suppose that the incumbent can write any contract that conditions payments upon the cash flow generated by asset I . We now show that no security can improve upon the ex ante payoffs attained by the incumbent using public debt combined with a covenant stipulating bmax = 0. Let δ (C, c) denote the change in the total value of arbitrary third-party claims issued by the incumbent and entrant in the event of merger, which is the analog of the function defined in Equation (4) for the specific case of public debt. The arguments in the function δ represent parameters of the incumbent and entrant’s third-party claims, respectively. An argument of zero is used to denote no contract. The bilateral merger surplus is
Acquisition Values and Optimal Financial (In)Flexibility
the share of surplus received by the entrant when π l2 is realized. By construction, public debt with face value B H attains the optimum within this set. Finally, consider any security such that merger never occurs. Such a security is dominated by public debt with face value B H . Both securities generate the same payoff to entry, but B H ensures that a merger occurs with positive probability. It follows that the incumbent can attain his maximal ex ante payoff using long-term public debt with B ∈ {B L , B H }. The following proposition summarizes.
3.3 The role of poison-put covenants The discussion in the previous subsection reveals that the optimality or suboptimality of a security for the incumbent hinges upon the change in its value in the event of merger, denoted as δ. It follows that securities other than the standard debt described in Proposition 3 can also be optimal provided that they achieve the optimal value of δ. For example, suppose that the incumbent would like to achieve the same ex ante payoff as that attained under standard public debt with face value B L > d2 but wants to avoid triggering default in the event that merger does not take place, as would necessarily be the case under the standard debt contract with face B L . In this case, the incumbent could issue a bond with face value B0 < d2 and achieve the desired level of debt overhang by including in the bond a poison put stipulating that lenders are entitled to immediate payment of B P P in the event of merger. In order to achieve the same δ as that achieved under standard debt with face B L , it must be the case that B P P − B0 = (B L , 0) = γ − π 2h ⇒ B P P = B0 + γ − π 2h .
(50)
So, the term γ − π 2h determines the premium above face value that must be paid in the event of merger. Similarly, the incumbent can achieve a degree of debt overhang equivalent to that under B H and avoid default if merger fails to occur by choosing B0 < d2 and specifying a higher merger premium equal to γ − π l2 . More generally, these examples illustrate that poison puts offer a convenient substitute for high leverage, especially given that high debt face values may generate other costs outside the scope of the model. Another testable implication of the model is that value firms should employ tough poison-put provisions relative to growth firms. As shown in Section 2, value firms are more likely to choose high debt levels (B H ) since they are most concerned with entry deterrence. Further, they can achieve the same degree of debt overhang by putting in poison-put covenants with high merger premi-
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Proposition 3. Long-term public debt with face value B ∈ {B L , B H } and a covenant stipulating bmax = 0 is an optimal security for the incumbent.
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ums. Conversely, growth firms should stipulate relatively low merger premiums above face value. 4. Empirical Implications
4.2 Acquisition premiums and distressed asset values Our model predicts that shallow-pocket acquirers will pay less for acquisitions. Consistent with this prediction, Uysal (2006) finds that bidders with low leverage experience lower announcement returns. Bidder returns have also been shown to be negatively related to bidder cash flow (Lang, Stulz, and 4 In
contrast, earlier models with related predictions apply only to (Maksimovic and Zechner 1991; Williams 1995; Fries, Miller, and Perraudin 1997).
competitive
industries
5 Poison-put covenants were included in a large majority of bond issues in the 2000s (Chava, Kumar, and Warga
2010). Already in the 1980s, 40% of investment-grade bonds contained event-risk covenants (Crabbe 1991).
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4.1 Industry financial structure Our model predicts high leverage for incumbents and low debt for entrants. This prediction is consistent with the findings of Rajan and Zingales (1995) and Faulkender and Petersen (2006), who document that leverage increases with firm age. Our model also predicts an inverse relation between incumbent and entrant debt. Further, the model implies that this effect should be most important in concentrated industries.4 Consistent with this prediction, MacKay and Phillips (2005) find that firms adjust their leverage inversely to the mean adjustment in their industry and that “the sensitivity of capital structure decisions to industry-peer decisions is much stronger in concentrated industries.” Our model also predicts that value firms should choose high debt relative to growth firms, with the effect being strongest in concentrated industries. This prediction matches the stylized fact that value firms have more debt (e.g., Rajan and Zingales 1995). In particular, it is consistent with the finding of MacKay and Phillips (2005) that leverage ratios are higher in concentrated industries and that profitability and high incumbent leverage are both strongly persistent. A novel set of predictions in our model is related to event-risk covenants. The model predicts that incumbent firms will write event-risk covenants limiting the assumption of counterparty debt in mergers. Further, the model predicts that value firms should write tighter covenants than growth firms. In fact, the use of ERCs is pervasive.5 Consistent with the model’s predictions, Nash, Netter, and Poulsen (2003) find that value firms use event-risk covenants more than twice as often as growth firms. Another novel set of predictions of our model concerns the effect of incumbent debt on venture capital contracts. The model predicts that venture capitalists must respond to high incumbent debt by offering managers stronger control rights and high-powered incentives. To the best of our knowledge, there is no empirical research on this issue.
Acquisition Values and Optimal Financial (In)Flexibility
4.3 Merger activity Our model predicts a negative relationship between incumbent leverage and acquisition activity due to debt overhang. An extensive empirical literature documents that mergers are more prevalent when industry capital liquidity is high and financial constraints are less important (e.g., Schlingemann, Stulz, and Walkling 2002; Harford 2005). More specifically, Harford (1999) shows that firms with large financial slack are more likely to make acquisitions. Almazan et al. (2007) show that the acquisition frequency of firms is inversely related to their leverage and that the effect is stronger if the firm is located in an industry cluster with heightened merger activity. The model predicts that the entrant is more likely to be the acquirer when the incumbent has high debt. This is because an optimal venture capital contract grants the entrant manager stronger control rights in response to high incumbent debt. In turn, the higher likelihood of entrant manager control increases the likelihood of the entrant being the acquirer. These predictions are consistent with the empirical literature showing that acquirers have lower leverage than targets and more unused debt capacity (e.g., Ghosh and Jain 2000; Andrade and Stafford 2004). A related and subtle prediction implied by our model is that the probability of the entrant being the acquirer, rather than the target, increases with lagged entrant performance. To see this, recall that high first-stage cash flow increases the probability of the original owner–manager retaining ownership and that she is more likely than the venture capitalist to acquire other firms because she has nonpecuniary control benefits. This prediction is consistent with the empirical literature showing that the identity of the acquirer depends on past performance (e.g., Rhodes-Kropf, Robinson, and Viswanathan 2005; Dong et al. 2006).
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Walkling 1991; Schlingemann 2004). Dong et al. (2006) find that acquirer leverage reduces bid premiums and target announcement returns. Relatedly, the model predicts that liquidation values in bankruptcy auctions are low when incumbents have high debt, in particular in concentrated industries. Indeed, Acharya, Bharath, and Srinivasan (2007) find that recovery ratios on defaulted debt are lower in heavily levered industries and that this effect is more pronounced for concentrated industries. Also, industry-wide financial distress appears to simultaneously reduce liquidation prices and increase the odds of piecemeal liquidation or sales to buyers outside the industry (e.g., Pulvino 1998; Eckbo and Thorburn 2008). Our model predicts higher merger returns for firms that include ERCs in their bond issues. Maquieira, Megginson, and Nail (1998) find that bondholder merger returns increase when the bond contains ERCs; Billett, Jiang, and Lie (2008) find a negative abnormal return for bondholders without covenant protection and a positive abnormal return for those with protection. A more precise test of our model would have to study the combined merger return for bondholders and shareholders, but this question is empirically unexplored.
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Our model predicts that waves of entry should be followed by merger waves. The conventional wisdom in this area is that entry induces acquisitions. Our theory shows that the causation also works in the other direction: the prospect of future consolidation encourages entry. Indeed, waves of entry are followed by merger waves (Mitchell and Mulherin 1996; Andrade, Mitchell, and Stafford 2001), and IPO waves precede merger waves (Rau and Stouraitis 2008). 5. Conclusion
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There is no denying the value conferred upon an incumbent with deep pockets. In this article, we show that maintaining deep pockets has a countervailing strategic cost. By maintaining low debt, an incumbent allows future merger counterparties to capture a larger share of merger surplus. In addition to the obvious direct cost involved, this effect may be sufficient to tilt the balance in favor of entry. The existence of such an effect is illustrated using a simple contracting model with endogenous price determination in asset merger markets. In this model, zero debt is never optimal for the incumbent. Rather, he should at least create a minimal level of debt overhang so that all bilateral merger surplus is exhausted when total surplus is low. By taking on even higher levels of debt, the incumbent increases his ability to extract additional surplus when the latter is high. However, this comes at the cost of an increased probability of failed merger if total surplus is low. In general, the incumbent’s optimal level of debt overhang features a tradeoff between merger probability, share of merger surplus, and entry deterrence. Finally, in terms of incumbent financial structure, it is shown that event-risk covenants, such as poison puts, can be value increasing for incumbent shareholders, since they limit entrants’ ability to access merger surplus. We also show that the financial posture adopted by an incumbent will have a significant effect on entrant financial structure. In equilibrium, the public debt of the incumbent crowds out the public debt of the entrant dollar for dollar. Further, the shape of venture capital contracts is also influenced by incumbent debt. In particular, the debt and/or covenants of an incumbent limit the funding capacity of entrants. This effect operates through two distinct channels. First, high incumbent debt reduces the value financiers receive in the event of asset sales. Second, high incumbent debt reduces the value the entrant manager places on retaining ownership. This weakens the power of feasible incentives and necessitates granting stronger control rights to the entrant manager. The more general message delivered by the model is that the overhang problem, first discussed by Myers (1977), is not isolated to the particular firm operating under a high debt burden. Rather, the high debt of an incumbent will tend to discourage both entry and merger activity in its sector and hence entrepreneurial activity. This is because the sell price of capital, typically treated as an exogenous parameter in investment models, is an endogenous variable
Acquisition Values and Optimal Financial (In)Flexibility
that is decreasing in the leverage of existing firms. Our model shows that such overhang may confer a benefit to incumbents, allowing them to capture economic rents. However, such strategic behavior is clearly detrimental to product market competition, economic efficiency, and innovation. Appendix A. Venture Capital Contract Proof of Lemma 3. There are two state variables for the control problem, r and β. The control is ξ ≡ β . The Lagrangian for the control problem is (A1)
+λ(π )[π − r (π)] + m(π)[1 − β(π )] + m(π)β(π).
(A2)
The optimality condition is ∂ = μβ (π) + xμr (π) = 0 ∂ξ ⇒ μ β (π) = −xμr (π)
∀
π
∀ π.
(A3)
The multiplier conditions are ∂ = p f (π) + m(π) − m(π) ∂β ∂ μr (π) = − = λ(π ) − f (π) ∀ π. ∂r
μ β (π) = −
∀
π. (A4)
Substituting the multiplier conditions into the differential equation implied by the optimality condition, one obtains (A5) xλ(π ) + m(π) − m(π) = (x − p) f (π) ∀ π. The transversality condition for this problem is β(0) = 0. Next note since x > p, it follows that β(π ) < 1 ⇒ r (π) = π under the optimal program.
Appendix B. Incumbent Firm Value with Covenant Let VC (·) denote incumbent firm value at time t−1 when debt flotations contain a covenant stipulating bmax = 0. The venture capitalist return function v derived in Lemma 3 is still applicable. However, the functions p and x change given bmax = 0. It is readily verified that B H dominates all B > B H , since the latter prevents merger in all states. Let pc (B) = p(B|b = 0). Confining attention to the relevant interval where B ≤ B H , we know that 1 1 B ≤ B L ⇒ p(B|b = 0) = (1 − θ ) π l2 + S(B, 0, π l2 ) + θ π 2h + S(B, 0, π 2h ) (B1) 2 2 1 (B2) B ∈ (B L , B H ] ⇒ p(B|b = 0)) = (1 − θ ) π l2 + S(B, 0, π l2 ) + θ π 2h . 2 With this in mind, consider first B ∈ (0, B L ). For B ∈ (0, B L ): m
m
d Vc (B) = [1 − Z (v(B))][m 1 + 2 ] + Z [v(B)][1 + 2 − p(B|b = 0)] m
m d ⇒ Vc (B) = m 1 + 2 − Z [v(B)][1 − 1 + p(B|b = 0)].
(B3)
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≡ f (π)[r (π) + p(1 − β(π ))] + μβ (π)ξ(π) + μr (π)xξ(π )
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Hence:
d ∂ d Vc (B) = −z[v(B)]v (B)[m 1 − 1 + p(B|b = 0)] − Z [v(B)] ∂ B p(B|b = 0) > 0 dB (B4) ⇒ Vc (B L ) > Vc (B) ∀ B ∈ [0, B L ).
And for B ∈ (B L , B H ):
m
+ Z [v(B)]θ d2
m m − d + (1 − θ ) π l + 1 S(B, 0, π l ) + θ γ . ⇒ Vc (B) = m + − Z [v(B)] 2 1 1 1 2 2 2 (B5)
Hence:
d 1 − d1 + (1 − θ ) π l2 + S(B, 0, π l2 ) + θ γ Vc (B) = −z[v(B)]v (B) m 1 dB 2 1 − Z [v(B)](1 − θ )S B (B, 0, π l2 ) 2 > 0. ⇒ Vc (B H ) > Vc (B)
∀
B ∈ (B L , B H ).
(B6)
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