Stapled Finance Stapledfin 1

Stapled Finance Journal of Finance, forthcoming Abstract Stapled Finance is a loan commitment arranged by a seller in an M&A setting. Whoever wins the bidding contest has the option (not the obligation) to accept this loan commitment. We show that stapled finance increases bidding competition, by subsidizing weak bidders, who raise their bids and thereby the price that strong bidders (who are more likely to win) must pay. The lender expects not to break even and must be compensated for offering the loan. This reduces but does not eliminate the seller’s benefit. It also implies that stapled finance loans will show poorer performance than other buyout loans. ∗ Stapled Finance is a loan commitment that is “stapled” onto an offering memorandum, by the investment bank advising the seller in an M&A transaction. It is available at pre-specified terms to whoever wins the bidding contest for the asset or firm that is being put up for sale; but the winner is under no obligation to accept the loan offer. It has become quite common, both in the US and in Europe (see the next section for institutional details). Practitioners and observers regard stapled finance as a tool that reduces transaction frictions: it makes financing available to all parties, if needed, thereby reducing risk and delays to the sale process and potentially increasing the pool of bidders. In this paper we show that arranging stapled finance also affects the bidding itself, by making it more competitive. We show that an appropriately designed stapled finance package increases the expected price that will be paid to the seller. Three characteristics are crucial for this to be beneficial for the seller. First, the stapled finance offer is optional: the winning bidder has the right, but not the obligation, to accept a loan whose terms have been fixed before the takeover contest started. Second, the stapled finance is a non-recourse claim, i.e., the debt is supported only by the target’s assets and cash flow, not by the other assets and operations that the winning bidder owns. Third, there are bidders who plan to hold the target as a portfolio company, i.e., who do not plan to integrate it into their other operations if they win. (Private equity funds often structure their holdings this way.) Our arguments do not rely on financial constraints of any sort; stapled finance is accepted by bidders for strategic reasons, even if they have sufficient internal or outside funds to pay for an acquisition. We show that if the stapled finance package is designed optimally, then the investment bank providing it expects not to break even. The reason is that stapled finance is optional, so it is accepted only if the terms are attractive to the bidder — and therefore unattractive to the lender. This suggests that stapled finance that benefits the seller can be arranged only if it is possible to compensate the investment bank for its expected loss, for example with an up-front fee, or by retaining it for other fee-based services. It also suggests that stapled finance loans that investment banks and other financial institutions retained on their balance sheets should perform worse than buyout loans that were negotiated independently. We analyze a simple auction model in which two financial buyers compete for the target firm. Financial buyers plan to hold the target firm as a portfolio firm, separate from their other operations and assets. The availability of stapled finance makes the bidders compete more aggressively, leading to a higher expected price (which benefits the seller). However, this distorts the allocation of the target firm, since the highest-valuation bidder does not necessarily win. Less value is created in the auction, which harms the seller since her aim is to extract as much value as possible from the bidders. Also, the winner will sometimes accept the stapled finance, and the seller must compensate the lender for the expected loss. Nevertheless, the seller benefits from any stapled finance package 1 that has a positive probability of being accepted by the winner. That is, the increased competition between the bidders more than compensates for the drawbacks of arranging stapled finance. The availability of stapled finance invites bidders to act opportunistically (if they win with a low signal, they accept the stapled finance), but the seller is able to turn this opportunism against the bidders themselves, creating a bidding environment that resembles a prisoners’ dilemma. A simple intuition for the benefits that accrue to the seller is to regard the option to accept the stapled finance as a subsidy, whose value to a bidder depends on her signal. More precisely, its value is decreasing in the realized signal. The subsidy therefore makes weaker bidders (bidders with lower signals and valuations) more competitive (they increase their bids by their valuation of the subsidy), but being weak bidders, they are less likely to win than strong bidders. So the seller benefits from the more intense competition, and the risk of actually having to provide the stapled finance (which would cause a loss) is limited. As we discuss in the next section, the institutional details about stapled finance are consistent with our results. Furthermore, in Section V we discuss (informal) explanations for the popularity of stapled finance that practitioners provide, and how our results differ from predictions that follow from those explanations. In short, our model generates cross-sectional predictions that are novel and unique. Some of these predictions are consistent with stylized facts and the others will need to be tested by empirical researchers in the future. Being a fairly recent creation, stapled finance has not entered the academic mainstream, yet. An exception is Boone and Mulherin (2008), who find that M&A contests with stapled finance availability are more competitive. The role of debt in takeover settings has been analyzed before, see, e.g., Jensen (1986); Harris and Raviv (1988); Stulz (1988); Israel (1991, 1992); Clayton and Ravid (2002); Müller and Panunzi (2004). These papers do not analyze debt that is arranged by the seller, but instead debt that is either on the target’s or a bidder’s balance sheet before the bidding starts, or that is taken on after the bidding contest is over. Similarly, auction models have been used before to analyze takeover contests. Our model is most closely related to Povel and Singh (2004, 2006, 2007), who analyze the role of informational asymmetries between bidders on optimal auction design, and the role of sale-backs in bankruptcy.1 Closer in spirit to ours are papers on “bidding with securities.”2 These papers analyze auctions in which the seller requires bids in the form of a specific security (royalties in the case of oil lease auctions, for example, or debt in the case of spectrum auctions). DeMarzo et al. (2005) provide the most detailed analysis of such auctions. They show that the expected price is higher if the seller can commit to decline all cash bids and to accept security bids (like debt, equity, call options, etc.) from a specific set, only. The seller benefits because the winner’s price is a state-contingent security, i.e., the ultimate value of the winner’s payment depends on the value that she realizes from the target. Stapled finance, as modeled in our paper, benefits the seller because the value of the debt payment to the lender depends on the value realized by the winning bidder, and since this debt payment is part of the winner’s overall price, stapled finance links the value of the winner’s price to the target value that she eventually realizes. We do not, however, require the bidders to accept the stapled finance. In fact, high-value bidders in our model optimally choose to decline the offer. This distinction is important given that DeMarzo et al. (2005) show that bidders, if given a choice, prefer “flatter” securities. Thus, when the bidders can choose whether to bid cash or shares (a common choice in takeover contests), they prefer cash bids. Our paper shows that even with cash bids, it is possible to extract a higher price from the bidders by making stapled finance available, which (again) is accepted by the winning bidder voluntarily, if at all. The rest of the paper proceeds as follows. We discuss institutional details and how they relate to our results in Section I. In Section II, we present the model. In Section III, we derive the equilibrium bidding strategies, given the details of the stapled finance offer. In Section IV, we show that the seller benefits from arranging any stapled finance package when facing two financial buyers. In Section V, we discuss other benefits the seller enjoys when arranging stapled finance. In Section VI, we show that the results are robust, and what model extensions we analyzed. Section VII concludes. Some proofs are in the appendix; additional proofs and robustness checks are in the Internet Appendix. I. Stapled Finance: Institutional Details Stapled finance refers to a type of financing that is made available through the seller’s efforts in an M&A transaction. Stapled finance can consist of one loan, or a package of term loans, bond placements, bridge loans, and other securities. The details being offered are negotiated between the seller and the investment bank, before potential buyers are contacted. The term3 itself derives from the idea that the loan commitment is “stapled” onto an offering memorandum, by the investment bank advising the seller in an M&A transaction. Information about stapled finance can be drawn mainly from practitioner publications, newspapers, and SEC filings by firms that needed shareholder approval for M&A transactions.4 Useful practitioner-oriented overviews include Kevin Miller, “In Defense of Stapled Finance,” Boardroom Briefing, Vol. 3(3), Fall 2006, pp. 44–49 (published by Directors & Boards magazine) and The Vernimmen.com Newsletter, No. 20, November 2006. See also the discussion of stapled finance in a recent textbook, Rosenbaum and Pearl (2009). There is no systematic evidence on the supply of and demand for stapled finance in M&A transactions. Investment banks started including the possibility of offering stapled finance in their sales pitches to potential sellers in 2001 (see “Bally calls in Deutsche for staple,” TheDeal.com, May 4, 2006). Since then, stapled finance seems to have become quite common. In 2004, 39% of the US deals that involved private equity firms saw the seller arranging stapled finance; in the first half of 2008, that decreased to 14% (see Julie MacIntosh, “Crunch boosts staple financing,” Financial Times, July 29, 2008). Stapled finance seems to have been more common in Europe. “Staple financing was offered by banks this year in about 90 percent of the auctions in Europe where buyout firms sold businesses to other buyout firms. . . . Staple financing is rapidly becoming standard practice due to the increasing importance of private equity as buyers of businesses.” (“‘Stapled’ loans create potential conflicts for merger advisers,” Bloomberg, October 24, 2005.) A survey of participants in the European private equity industry found that nearly one in two private equity funds had recently arranged stapled finance when putting up assets for sale. (“Private equity in 2006: The year of living dangerously,” Financial News, February 2006.) For more articles discussing the popularity of stapled finance, see “Staple financing gains following in M&A deals,” Corporate Financing Week (Institutional Investor), June 27, 2004; and “Popular LBO staple financing raises eyebrows,” Dow Jones News Service, January 10, 2005. Large deals with seller-arranged financing include (besides the examples from SEC filings listed above) Reed Business Information (“Staple finance shortfall for Reed Business,” Financial Times, September 26, 2008.); Diageo’s sale of Burger King in 2002 and Daimler’s sale of Chrysler in 2007 (see “Private equity widens search,” Financial Times, October 31, 2007); Michaels Stores (see “JPMorgan helps Michaels Stores to fast and favourable results,” Financial Times, January 25, 2007), Bally Total Fitness Holding (see “Bally calls in Deutsche for staple,” TheDeal.com, May 4, 2006), and Dunkin Brands (see “Bidders show strong appetite for a taste of Dunkin Brands,” Financial Times, October 10, 2005). The non-recourse debt financing offered by the US Treasury (and loan guarantees from the FDIC) as part of the “Public-Private Investment Program” (PPIP) also represents a form of stapled finance.5 The main institutional features of stapled finance are that (i ) it is a loan commitment arranged by the seller in an M&A transaction; (ii ) it is optional; (iii ) it is (with some exceptions) available to whoever wins the takeover contest; (iv ) its terms are often regarded as being aggressive; (v ) it is often declined by the winning bidder, but sometimes accepted, primarily by private equity funds. These features are consistent with the results of our model. Stapled finance should be (i ) arranged by the seller, because it benefits the seller. It should be (ii ) optional, because it is the optionality that induces certain bidders to self-select and submit higher bids. It should be (iii ) available to whoever wins the takeover contest, including in particular buyout funds, for it to be effective. In practice, the target’s competitors have sometimes been excluded from the offer, because sellers did not want to give them access to financial data about the firm; that is of no consequence to the seller in our model, since (as we show in Section ?? of the Internet Appendix) trade buyers do not change their bidding strategy if stapled finance is available, so there is no loss from not making it available to them in the first place. Next, (iv ) the terms of stapled finance packages should be aggressive, since unattractive loan terms would not affect bidders’ strategies. It is not necessary for our results that all details of the loan commitment are fully specified. All we require is that some terms are specified that the lender may regret after the auction has ended. In other words, as long as there is some option value in the loan commitment, our results will hold. For example, stapled finance packages often include loan sizes that are above the bidders’ (and observers’) expectations. “Most buyout executives contacted for this article agree that the staple financing typically represents the most generous deal available.” (“Popular LBO staple financing raises eyebrows,” Dow Jones News Service, January 10, 2005.) “According to a general partner of a private equity fund, ‘Banks are being pressured to come up with aggressive staple financing and sometimes it means they are not comfortable with the amount of debt they are putting forward. In one case recently, the bank actually told us it didn’t want to lend the amount included in the staple package. Inevitably, that made us nervous.’ . . . Others agreed banks were sometimes being too aggressive in offering staple financing. David Silver at Robert W Baird said: ‘With the advent of staple financing and leverage multiples where they’ve been, we have seen some transactions where banks are willing to lend and private equity firms are put off because the staple finance package implies a valuation they’re not comfortable with.’” (“Private equity in 2006: The year of living dangerously,” Financial News, February 2006.) See also “Bidders show strong appetite for a taste of Dunkin Brands,” Financial Times, October 10, 2005. And finally, stapled finance (v ) should often be declined by the winning bidder. It is attractive to low-valuation financial buyers, who are willing to use high financial leverage and potentially let the target firm default. But low-valuation bidders are less likely to win, so the realized acceptances are less frequent than the planned acceptances. The more likely winners, high-valuation buyers, plan to decline the stapled finance offer. The main benefits of stapled finance are described by practitioners as follows. First, it guarantees financing to firms that have difficulties arranging financing themselves, or obtaining information 5 about the terms of possible loan commitments. This reduces the risk that a deal falls through because the winning bidder could not line up sufficient funds, or because those funds ended up being too expensive. Second, the sale process takes less time, because the due diligence for early-round “indicative” bids is simplified. Third, this also makes it cheaper for bidders to prepare indicative bids, which potentially increases the pool of bidders. Fourth, for the same reason, the seller can restrict access to financial information early in the process (information that would be needed to negotiate financing), so confidentiality is preserved early in the process. We are not claiming that these explanations are invalid. In fact, many of the benefits are complementary to the ones we analyze. The aim of this paper is to analyze bidding effects that have been overlooked so far. This allows us to describe a novel mechanism that makes stapled finance attractive to a seller when certain bidders are present (financial buyers); to explain why some bidders dislike stapled finance; and to explain why M&A financing that was part of a stapled finance package should be expected to perform poorly, compared with other M&A financing packages. These predictions are inconsistent with existing explanations but easily understood, based on our model. We discuss below (in Section V) how the predictions from our model differ from predictions that the existing explanations would generate, if formalized. Specifically, we discuss how bid premia, bidder share price run-ups, post-takeover operating performance, and the performance of the loans themselves can be used to test our model’s predictions; and how certain features of the bidding environment (number of bidders, technological or other execution risk) affect the likelihood of stapled finance being arranged. Some practitioners have also identified possible drawbacks of arranging stapled finance. The fees that investment banks earn for arranging high-yield loans are much higher than the fees earned for advisory work, which may cause a conflict of interest if investment banks play both roles: that of advising the seller on which bid is the best; and that of arranging loans (the investment bank may even coerce bidders into promising to accept the stapled finance). We abstract from this issue in our paper. The conflict of interest is quite obvious, and in practice, sellers have started to split the lending and advisory functions between two independent investment banks. Furthermore, in practice the stapled finance is often declined or shopped around, which suggests that such abuse of power is not widespread. II. The Model A target firm is for sale, and two bidders, 𝑖, 𝑗 ∈ {1, 2}, are interested in buying it. These bidders have independent and uncertain value estimates of the target. We assume that the bidders’ full information values of the target firm are 𝑡1 and 𝑡2 , independently and identically distributed on the 6 [ ] support 𝑡, 𝑡 , with density 𝑓 and c.d.f. 𝐹 . Denote the expected value of 𝑡𝑖 by 𝐸[𝑡𝑖 ]. We assume ( ) [ ] that 𝑓 is continuous and differentiable on 𝑡, 𝑡 , and strictly positive on 𝑡, 𝑡 . The bidders cannot observe the realizations of 𝑡𝑖 . Instead, they (privately) observe signals 𝑠𝑖 such that { 𝑠𝑖 = 𝑡𝑖 with prob 𝜑 𝜏𝑖 with prob 1 − 𝜑, (1) where 𝜏1 and 𝜏2 are i.i.d. random variables that have the same distributions as 𝑡1 and 𝑡2 . Thus, with probability 𝜑 the signal 𝑠𝑖 is informative, and with probability 1 − 𝜑 it is pure noise. Since the signal is completely uninformative if 𝜑 = 0, we will assume in the following that 0 < 𝜑 ≤ 1.6 Given the signal 𝑠𝑖 , the expected value of the target to bidder 𝑖 is 𝑣(𝑠𝑖 ) = 𝜑𝑠𝑖 + (1 − 𝜑)𝐸[𝑡𝑖 ]. (2) This is a private values auction model, in which the bidders’ signals are noisy estimates of their valuations. We have analyzed an alternative model of private values, in which the realized value is a continuous function of a bidder’s signal and an unobserved random variable; the results are unchanged (see Section VI below and Section ?? of the Internet Appendix for details). We have also analyzed a model with common values, in which the realized value is a weighted average of the two (independent) signals; again, the results are unchanged (again, see Section VI below and Section ?? of the Internet Appendix for details). The seller cannot observe the bidders’ signals, and she plans to hold an ascending auction:7 the bids are continuously raised, and the auction ends when only one bidder is left in the auction; the price at which the second-last bidder withdrew is the price that the winner, the last remaining bidder, has to pay. The ascending auction is a realistic model for takeover contests: these usually require that winning bids are exposed to overbids from third parties, so, strategically speaking, the bidders face the same incentives as in a standard ascending auction. The ascending auction has the additional benefit that it is easy to analyze (the bidders have dominant strategies). We also discuss alternative auction models (e.g., the first-price auction) and show that they lead to the same results (see Section VI below and Section ?? of the Internet Appendix for details). The timing is as follows: First, the seller asks an investment bank to prepare a loan commitment, available to the winner of the bidding contest, irrespective of their identity. Second, the bidders compete for the target in an ascending auction, in which the bids are raised continuously until one of the bidders decides to drop out. The remaining bidder is declared the winner and pays the price 6 Setting 𝜑 = 1 would simplify the algebra slightly, but the results would be less realistic: if a buyer accepted the stapled finance, she would default on it with certainty. 7 Also known as an “open outcry” or “English” auction, in our setting equivalent to a second-price sealed-bid auction. 7 at which the other bidder dropped out.8 We assume that if both bidders drop out simultaneously, a coin flip determines the winner. Third, the winning bidder decides whether to accept the stapled finance offer. If the winning bidder declines the stapled finance offer, then she pays the winning price out of her own funds, or she raises financing from a third-party lender at competitive terms.9 Finally, the winner realizes cash flows from the target (the random variable 𝑡𝑖 ) and makes payments to the investment bank if the stapled finance package was accepted. Our aim is to analyze how stapled finance affects the outcome of a takeover contest, if the bidders may accept the stapled finance for strategic reasons, and not because of financial constraints. We isolate the strategic effects by assuming that the bidders have access to large internal or external funds to finance an acquisition. As we show, even deep-pocket bidders may accept the stapled finance if the terms are sufficiently attractive. This happens only if a bidder is a financial buyer, i.e., a bidder (for example, a private equity fund specializing on buyouts) who plans to hold the target as a portfolio firm, separate from other holdings. Some bidders (“trade” or “strategic” buyers) plan to integrate the target into their operations if they win. As we discuss below, in Section VI, such trade buyers do not benefit from the availability of stapled finance, so their bids are unaffected; yet, as long as there are financial buyers in the pool of bidders, the seller benefits from arranging stapled finance (see Section ?? of the Internet Appendix for details). The stapled finance is a simple loan in our model: the winning bidder can borrow an amount 𝐿 if she promises to repay an amount 𝐷 at a later stage. We assume that this is a non-recourse loan, i.e., the lender’s claim is supported by the target firm’s cash flow and assets, only. The winner is protected by limited liability: if the realized value is below 𝐷, she can just default on the loan. This limited liability makes the debt risky, and we allow for the possibility that the lender may not break even when offering stapled finance. We assume that since this can be anticipated in equilibrium, the seller has to compensate the investment bank ex ante for providing the loan. The investment bank thus expects to break even in expected terms, and strategically, the investment bank makes the decisions that the seller wants her to make. (The investment bank is passive in this model; the seller could actually provide the loan commitment herself, but that rarely happens in practice.) As a benchmark, consider the ascending auction equilibrium if stapled finance is unavailable. It is a dominant strategy for the bidders to bid their own valuations, i.e., to plan to drop out of the bidding once the bid reaches their valuation: 𝑏𝑛𝑜𝐷 (𝑠𝑖 ) = 𝑣(𝑠𝑖 ) = 𝜑𝑠𝑖 + (1 − 𝜑)𝐸[𝑡𝑖 ]. 8 (3) A “bidding strategy” refers to the bid at which a bidder plans to drop out. That is, lenders only ask to break even in expected terms (to simplify this, assume that bidders can credibly reveal their signal realization; if only bids are observable, signal jamming complicates the analysis, see Liu (2008)). 9 8 The seller’s expected price is then Π𝑛𝑜𝐷 = 𝜑𝐸 [min {𝑠𝑖 , 𝑠𝑗 }] + (1 − 𝜑)𝐸[𝑡𝑖 ] (4) (since the bidder with the higher signal submits the higher bid and wins, and her price is the bid submitted by the other, losing bidder). If stapled finance is available, the bidding behavior changes, because stapled finance is accepted only if it is beneficial, so its availability increases the bidders’ valuations and therefore their bids. We analyze these effects in what follows. III. Equilibrium Bidding Strategies Suppose the bidding is over, and the winner has to pay the loser’s bid. With limited liability, her expected payoff increase from accepting the stapled finance is 𝑥(𝑠𝑖 ) = 𝐿 − 𝜑 min {𝑠𝑖 , 𝐷} − (1 − 𝜑)𝐸 [min {𝑡𝑖 , 𝐷}] . (5) (We omit the arguments 𝐿 and 𝐷 from 𝑥, for simplicity.) The function 𝑥(𝑠𝑖 ) is positive if 𝐿 is high enough, and if 𝐷 and 𝑠𝑖 are low enough. Recall that 𝐿 is the loan size, received upon accepting the loan; the remaining two terms are the expected repayment, which may be less than 𝐷 (the promised repayment) because of limited liability. In our auction setup, it is a dominant strategy to bid one’s valuation of the target. This valuation includes the value of the option to accept stapled finance (the bidders know whether they will accept the stapled finance if they win), so the optimal bid is 𝑏𝐷 (𝑠𝑖 ) = 𝑣(𝑠𝑖 ) + max {𝑥(𝑠𝑖 ), 0} . (6) Proposition 1 If the seller arranges stapled finance such that its terms seem attractive to some bidders, then the expected price is higher than if no stapled finance was arranged. Proof. From (3) and (6), we have 𝑏𝐷 (𝑠𝑖 ) ≥ 𝑏𝑛𝑜𝐷 (𝑠𝑖 ) ∀𝑠𝑖 , with a strict inequality if 𝑥(𝑠𝑖 ) > 0. If such a bidder (with 𝑠𝑖 such that 𝑥(𝑠𝑖 ) > 0) is defeated, then the winner’s price is higher (the winner’s price is the losing bid, which is higher). If she defeats a rival only because of the bid increase, the price paid by the winner is higher, too. The more generous the stapled finance offer, the larger the increase in the seller’s expected price will be. This increased competition is what makes arranging stapled finance attractive for a seller. However, it comes at a cost. 9 Proposition 2 The expected net payoff for the lender (who provides the stapled finance commitment) is negative. Without compensation from the seller, stapled finance will not be offered by any lender. Proof. The stapled finance offer is accepted if and only if 𝑥(𝑠𝑖 ) ≥ 0, i.e., if the expected net payoff from lending is negative. This result follows from the option feature of the stapled finance offer: the winning bidder has the right, but not the obligation, to accept the loan. The lender (the investment bank providing the loan commitment) is the writer of this option and therefore expects to make a loss whenever the stapled finance offer is accepted. She must be compensated by the seller for offering to lend, which offsets the seller’s benefit from offering stapled finance. In the next section, we show that the seller’s net benefit, incorporating the compensation for the lender, remains positive. 𝑥(𝑠𝑖 ) 6 0 𝑡 𝐷 𝑠ˆ - 𝑡 𝑠𝑖 𝑥(𝑠𝑖 ) Figure 1: A financial buyer’s expected net benefit from accepting stapled finance. In the following, it will be convenient to work with the cut-off signal 𝑠ˆ that determines whether a bidder plans to accept or decline the stapled finance offer. For any values of 𝐿 and 𝐷, the function 𝑥 is well-defined. Notice that 𝑥(𝑠𝑖 ) is weakly decreasing in 𝑠𝑖 : it is strictly decreasing if 𝑠𝑖 < 𝐷, and flat if 𝑠𝑖 > 𝐷 (cf. (5) and Figure 1). So if 𝐿 and 𝐷 are such that 𝑥(𝑡) < 0, then 𝑥(𝑠𝑖 ) < 0 for all 𝑠𝑖 ∈ [𝑡, 𝑡]. Similarly, if 𝑥(𝑡) > 0, then 𝑥(𝑠𝑖 ) > 0 for all 𝑠𝑖 ∈ [𝑡, 𝑡]. Both cases can be ignored without loss of generality: (1) If 𝑥(𝑠𝑖 ) < 0 for all 𝑠𝑖 ∈ [𝑡, 𝑡], then the bidders always plan to decline the stapled finance offer, and offering it has no effect on the outcome of the auction; this is equivalent to offering stapled finance such that 𝑥(𝑡) = 0 (this is achieved by increasing 𝐿 to 𝐿′ = 𝐿 − 𝑥(𝑡)). (2) If 𝑥(𝑠𝑖 ) > 0 for all 𝑠𝑖 ∈ [𝑡, 𝑡], then the bidders always plan to accept the loan offer and, absent discounting, the seller is indifferent between offering stapled finance at these terms, and offering stapled finance such that 𝑥(𝑡) = 0 (this is achieved by reducing 𝐿 to 𝐿′ = 𝐿 − 𝑥(𝑡)). The allocation will not be changed by this, and the net effect on the seller’s net payoff is zero: the prices will be reduced by 𝐿 − 𝑥(𝑡) for any signal realization, but the loss to the lender will also be reduced by that amount. So without loss of generality, we can focus on stapled finance packages that set 𝑥(𝑡) ≤ 0 ≤ 𝑥(𝑡). 10 We can thus define a cut-off signal 𝑠ˆ, such that a bidder plans to accept the stapled finance offer if and only if 𝑠𝑖 < 𝑠ˆ: 𝑠ˆ = min { 𝑠 ∣ 𝑥(𝑠) = 0 } . (7) 𝑠∈[𝑡,𝑡] Notice that the slope of 𝑥 (downward sloping if 𝑠𝑖 < 𝐷, flat if 𝑠𝑖 > 𝐷) and the restriction that 𝑥(𝑡) ≤ 0 ≤ 𝑥(𝑡) together imply that 𝑠ˆ ≤ 𝐷. In other words, the cut-off signal lies in the interval of signals for which 𝑥 has a negative slope (as shown in Figure 1). When designing the stapled finance package, the seller must decide what values of 𝐿 and 𝐷 to offer. We now show that this problem is equivalent to choosing a cut-off signal 𝑠ˆ ∈ [𝑡, 𝑡]. Lemma 1 The problem of choosing the optimal values of 𝐿 and 𝐷 is equivalent to the problem of choosing the optimal value of 𝑠ˆ. Proof. 𝐿 and 𝐷 affect the outcome only if at least one of the bidders plans to accept the stapled finance, i.e., if max {𝑥(𝑠𝑖 ), 𝑥(𝑠𝑗 )} > 0. It is sufficient to show that the function 𝑥 can be written as a function of 𝑠ˆ and 𝑠𝑖 , only (and not of 𝐿 and/or 𝐷), on the interval [𝑡, 𝑠ˆ]. Using 𝑠ˆ ≤ 𝐷, we can write 𝑥(𝑠𝑖 ∣𝑠𝑖 < 𝑠ˆ) = 𝐿 − 𝜑𝑠𝑖 − (1 − 𝜑)𝐸 [min {𝑡𝑖 , 𝐷}] . (8) Solving (5), evaluated at 𝑠𝑖 = 𝑠ˆ, for 𝐿, yields (since 𝑥(ˆ 𝑠) = 0) 𝐿 = 𝜑ˆ 𝑠 + (1 − 𝜑)𝐸 [min {𝑡𝑖 , 𝐷}] . (9) Substitute into (8), to obtain 𝑥(𝑠𝑖 ∣𝑠𝑖 < 𝑠ˆ) =𝜑ˆ 𝑠 + (1 − 𝜑)𝐸 [min {𝑡𝑖 , 𝐷}] − 𝜑𝑠𝑖 − (1 − 𝜑)𝐸 [min {𝑡𝑖 , 𝐷}] =𝜑(ˆ 𝑠 − 𝑠𝑖 ). (10) That is, the function 𝑥 can be written as a function of 𝑠ˆ and 𝑠𝑖 , only. Given the optimal choice of 𝑠ˆ, there is one degree of freedom in choosing the corresponding values of 𝐿 and 𝐷: given 𝑠ˆ, the seller can choose any 𝐷 ∈ [ˆ 𝑠, 𝑡]; and 𝐿 is then determined using (9). We can now describe the equilibrium bids if the seller arranged stapled finance with a cut-off signal 𝑠ˆ. If 𝑠𝑖 > 𝑠ˆ, their bids are not affected, since they plan to decline the stapled finance offer (they regard it as overpriced, given their valuation of the target firm). If 𝑠𝑖 < 𝑠ˆ, the terms are attractive, so the bid is increased by 𝑥(𝑠𝑖 ), the value of the option to accept the stapled finance. 11 The bid is increased to what a bidder would bid if her signal was exactly 𝑠ˆ: 𝑏𝐷 (𝑠𝑖 ∣𝑠𝑖 < 𝑠ˆ) =𝑣(𝑠𝑖 ) + 𝑥(𝑠𝑖 ) =𝑣(𝑠𝑖 ) + 𝑥(𝑠𝑖 ) − 𝑥(ˆ 𝑠) =𝜑𝑠𝑖 + (1 − 𝜑)𝐸[𝑡𝑖 ] − 𝜑𝑠𝑖 + 𝜑ˆ 𝑠 =𝑣(ˆ 𝑠). (11) Thus, with stapled finance, the equilibrium bids are 𝑏𝐷 (𝑠𝑖 ) = max{𝑣(𝑠𝑖 ), 𝑣(ˆ 𝑠)}. IV. (12) The Optimality of Arranging Stapled Finance If the seller arranged stapled finance, then bidders with signal realizations 𝑠𝑖 < 𝑠ˆ increase their bids to 𝑣(ˆ 𝑠), to incorporate their valuation of the option to accept the stapled finance; bidders with signal realizations 𝑠𝑖 > 𝑠ˆ do not change their bids, because they plan to decline the offer if they win (see (12)). To analyze the seller’s optimization problem (when evaluating the benefits and costs of arranging stapled finance), it is helpful to distinguish four types of signal realizations. See Figure 2. 𝑠2 6 𝑡 Region D2: Bidder 2 wins; declines stapled finance Region B: Bidder 2 wins; declines stapled finance; price higher Region D1: Bidder 1 wins; declines stapled finance 𝑠ˆ Region A: Either bidder may win; winner accepts stapled finance; price higher Region C: Bidder 1 wins; declines stapled finance; price higher 𝑡 𝑡 - 𝑠ˆ 𝑡 𝑠1 Figure 2: Auction outcomes with two financial buyers. The availability of stapled finance does not affect the outcome in Region D Figure 2, where both signal realizations are above 𝑠ˆ. Both bidders plan to decline the offer, so their bids are unchanged, 12 and the seller’s expected net payoff is unchanged. The seller’s expected net payoff is increased in Regions B and C of Figure 2. Here, one bidder realized a signal above 𝑠ˆ, while the other bidder realized a signal below 𝑠ˆ. Both with and without stapled finance, the winner is the same bidder, the bidder who realized the signal above 𝑠ˆ (see (12)). However, if stapled finance is arranged, the losing bidder’s bid is 𝑣(ˆ 𝑠) instead of 𝑣(𝑠𝑖 ) < 𝑣(ˆ 𝑠). Thus, the price the winner has to pay increases from 𝑣(𝑠𝑖 ) to 𝑣(ˆ 𝑠). This price increase is the only effect on the outcome, since the winner plans to decline the stapled finance offer. So the seller clearly benefits from arranging stapled finance if the signal realizations are in Regions B or C. The analysis is more involved in Region A of Figure 2, where both signal realizations are below 𝑠ˆ. Arranging stapled finance has several effects. First, both bidders plan to accept the stapled finance if they win, so it is accepted with certainty. The lender thus expects a loss with all realizations in Region A, and the seller must compensate this expected loss when arranging the stapled finance. Second, both bids equal 𝑣(ˆ 𝑠), and a coin toss must determine the winner. So the allocation is distorted, since the winner is not necessarily the bidder with the higher valuation. Less value is created (in expected terms), which is bad for the seller, since it is her goal to extract as much value as possible from the bidders, and extracting value becomes harder if less value is being created to begin with. Third, and offsetting the two earlier effects, the bidders both bid 𝑣(ˆ 𝑠), that is, more than their valuation of the target firm alone. In fact, they compete away their entire rent. Since both bidders bid their entire valuation of winning, including the expected value of the stapled finance, and since both bidders bid the same amount, the winner’s price equals her valuation. The bidders’ rents are thus zero for signal realizations in Region A of Figure 2. The price paid is always 𝑣(ˆ 𝑠) in Region A, but net of the compensation due to the lender, the seller’s expected net payoff is equal to the winning bidder’s valuation of the target firm alone (because for 𝑠𝑖 < 𝑠ˆ, we have 𝑣(𝑠𝑖 ) = 𝑣(ˆ 𝑠) − 𝑥(𝑠𝑖 ), cf. (11)). The seller’s expected net payoff is therefore equal to the value created. If stapled finance is not arranged, the seller’s expected net payoff is equal to the expected price, which equals the expected losing bid. Arranging stapled finance thus increases the seller’s expected net payoff (for signal realizations in Region A) by 𝐸[𝑣(𝑠𝑖 )∣𝑠𝑖 < 𝑠ˆ] − 𝐸[min{𝑣(𝑠1 ), 𝑣(𝑠2 )∣𝑠1 , 𝑠2 < 𝑠ˆ] =𝜑𝐸[𝑠𝑖 ∣𝑠𝑖 < 𝑠ˆ] − 𝜑𝐸[min{𝑠1 , 𝑠2 ∣𝑠1 , 𝑠2 < 𝑠ˆ], (13) which is strictly positive if 𝑠ˆ > 𝑡. To sum up, the seller’s expected net payoff increase is strictly positive in Regions A, B and C of Figure 2, and zero in Region D. We conclude: Proposition 3 The seller always strictly benefits from arranging stapled finance that is at least 13 sometimes accepted (i.e., if 𝐿 and 𝐷 are chosen such that 𝑠ˆ > 𝑡). The arguments used to prove Proposition 3 rely on explicitly comparing net payoffs and allocations for all signal realizations. DeMarzo et al. (2005) use the “linkage principle” to show that security-bid auctions are beneficial for sellers. We cannot use the same approach here, since, given a signal realization in Region A of Figure 2, the allocation with and without stapled finance is not the same with probability one. (With stapled finance, the bidder with the higher signal wins with probability one half, only.) Standard proofs using the linkage principle (see also Krishna (2002)) compare auctions that lead to identical allocations and therefore cannot be directly used to prove that arranging stapled finance is beneficial. Stapled finance is beneficial for the seller because it allows her to play off the bidders against each other, increasing competition between them. The bidders are strictly worse off: Corollary 1 The availability of stapled finance reduces the bidders’ expected net payoffs. Proof. The two financial buyers expect the same payoff before observing their signals. The sum of their payoffs and that of the seller equals the total value that is created. The total value creation is reduced (in Region A) by introducing stapled finance, and the seller’s expected net payoff is increased. Consequently, the bidders’ expected payoff must be lower. The financial buyers find themselves in a situation that resembles a prisoner’s dilemma: they would prefer stapled finance not to be available, but once it is available, it is a dominant strategy (with signal realizations 𝑠𝑖 < 𝑠ˆ) to accept it. Notice that the winner of the bidding contest is not forced to accept the offer, since (by assumption) the bidders are not liquidity constrained. Instead, the bidders merely have the option to take advantage of the lender’s offer, but the stapled finance package allows the seller to turn the financial buyers’ opportunism against themselves. It is instructive to compare stapled finance, a tool for increasing the seller’s expected price, with an alternative tool, setting a reserve price. Offering stapled finance achieves a similar goal: high-signal bidders must pay a high price even if their rival has a very low signal realization. Unlike the case of a reserve price, however, the target firm is not permanently withdrawn from sale if the reserve price is not met (a commitment that is necessary for reserve prices to be effective). Instead, the target firm is sold, and the two bidders compete away their rents (including the benefit they expect from the option to accept the stapled finance), so the seller’s expected net payoff is positive instead of zero. An important characteristic of stapled finance is that the value of the promised repayment to the lender depends on the winning bidder’s private information. The benefits of state-contingency in extracting value from buyers has been analyzed before, in different settings. Hansen (1985); Samuelson (1987); Crémer (1987); Riley (1988); Zheng (2001); Rhodes-Kropf and Viswanathan (2000, 2005); DeMarzo et al. (2005); and Board (2007) assume that sellers can require bids in the 14