Paper_A theory of LBO activity based on repeated debt-equity conflicts

A theory of LBO activity based on repeated

debt-equity con�icts�

Andrey Malenko

MIT Sloan School of Management

Nadya Malenko

Carroll School of Management, Boston College

December 2012

Abstract

We develop a theory of LBO activity based on repeated interactions betweenprivate equity (PE) �rms and creditors. PE �rms repeatedly compete for targets inan auction, and the winning bidder partly �nances the deal with debt. Debt createsan agency problem between the PE �rm and creditors, but this problem can bealleviated by the need of the PE �rm to raise �nancing for deals in the future. Cyclesof LBO activity can arise even if there is no mispricing between debt and equitymarkets and the potential for value creation is similar every period. Di¤erences inthe quality of PE �rms are ampli�ed through their access to debt markets. Theanalysis provides implications for the relation between aggregate LBO activity, dealcharacteristics (takeover premiums, composition of acquirers, and buyout leverage)and economy-wide conditions.

�We thank Nittai Bergman, Edith Hotchkiss, Francisco Perez-Gonzalez, and Antoinette Schoarfor helpful comments and discussions. Andrey Malenko: [email protected]. Nadya Malenko:[email protected].

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1 Introduction

Leveraged buyouts (LBOs) have experienced boom-and-bust periods over the last decades.

For example, the wave of buyouts of the 1980s, with a peak volume of more than $60 billion

in 1988, was followed by weak activity in the early 1990s, with only $4 billion in 1990

(Kaplan and Stein, 1993). The buyout market took o¤ again in the late 1990s, declined

in the early 2000s, increased signi�cantly from 2004 to June 2007, and then dropped with

the onset of the �nancial crisis (Kaplan and Stromberg, 2009). The LBO activity is shown

to be related to economy-wide credit spreads, discount rates, buyout leverage ratios and

transaction prices.1

In this paper, we present a theory of LBO activity that studies the joint dynamics

of buyout activity, aggregate economic conditions, takeover premiums and leverage ratios.

The theory is based on two key ingredients - con�icts between private equity (PE) �rms

and debtholders, and repeated interactions of PE �rms with the debt market. First, a

typical leveraged buyout transaction, involving a leverage ratio of 60% - 90%, creates a

con�ict of interest between ex-post incentives of the private equity �rm on one side and

debtholders of the portfolio company on the other side. One prominent example of such

con�icts of interest are dividend recapitalizations. It has become increasingly common

for private equity �rms to load their portfolio companies with additional debt in order to

pay themselves a dividend. At Simmons Bedding, for example, Thomas H. Lee Partners

conducted at least two dividend recapitalizations and paid itself $375 million in dividends

before the company �led for bankruptcy in 2009.2 In 2012 alone, companies have borrowed

a record $54 billion in order to pay dividends to their PE owners.3

The second key element of the theory is that PE �rms access the debt market repeatedly

1See, e.g., Kaplan and Stein (1993), Demiroglu and James (2010), Shivdasani and Wang (2011), Haddad,Loualiche, and Plosser (2011), and Axelson et al. (2012).

2See �Pro�ts for Buyout Firms as Company Debt Soared,�The New York Times, October 4, 2009. In amore recent example, the creditors of bankrupt Mervyn�s sued Mervyn�s private equity owners for strippingMervyn�s of valuable real estate assets, while paying themselves hundreds million dollars in managementfees and dividends. See �Buyout �rms pay $166 mln to end suit over Mervyn�s sale,�Reuters, October 2,2012.

3See �Debt Fuels a Dividend Boom,� the Wall Street Journal, October 18, 2012.

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and thus may refrain from expropriating debtholders in order to preserve their reputation

and obtain cheap �nancing in future deals. The notion that PE �rms�reputation is an

important factor that a¤ects both their actions and the terms on which they obtain debt

�nancing has been emphasized by Demiroglu and James (2010), Ivashina and Kovner (2011),

Hotchkiss, Smith, and Strömberg (2011), and Huang, Ritter, and Zhang (2012), among

others. Moody�s, for example, has started incorporating PE �rms� prior propensity to

increase leverage and make large dividend payments in their credit ratings on LBO deals.4

We consider a simple dynamic model of LBO transactions that captures these and

other important features of the industry. In every period, with some probability, there is

a target that can increase in value from the change of ownership. This potential for value

creation can be due to poor quality of the incumbent management team, bad incentives,

or suboptimal investment and �nancing decisions.5 There are two potential acquirers, PE

�rms, who compete for the target in an English auction. The PE �rms di¤er in their intrinsic

quality. A higher quality �rm is more likely to generate a higher value from the deal than a

lower quality �rm, both in the current and future periods, although each speci�c realization

of value can be lower.

To realize the value from the deal, each acquirer needs to lever up the target. Even if

the value from the deal is positive, it does not guarantee that the deal takes place since the

acquirer�s ability to raise debt might be limited by the potential future agency con�ict with

debtholders. Speci�cally, if ex post the deal turns out to be unsuccessful, the PE �rm may

choose to expropriate debtholders, for example, by engaging in a dividend recapitalization.

In a one-shot interaction, the PE �rm will always expropriate debtholders ex post, even

though ex ante it would like to commit not to do it since it bears the cost of expropriation

by paying high interest rates on debt. However, when the PE �rm�s interactions with the

debt market occur repeatedly, it may refrain from expropriating debtholders in order to get

4For certain PE �rms that have been particularly aggressive in extracting dividends, the rating assignedby Moody�s to the initial transaction sometimes re�ects the potential for increased leverage in the future.See �Private Equity: Tracking the Largest Sponsors,�Moody�s Investors Service, January 2008.

5This potential value need not correspond to social value. Instead, it can re�ect a wealth transferto equityholders from existing stakeholders, such as debtholders (e.g., Asquith and Wizman, 1990) oremployees (e.g., Shleifer and Summers, 1988).

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cheaper �nancing for future LBO deals. More speci�cally, the PE �rm trades o¤the bene�ts

of expropriation today against the costs of hurting its reputation in the debt market and

thereby reducing its value from future deals. This trade-o¤ determines the �rm�s ability to

commit not to expropriate debtholders.

The model leads to a number of implications, many of which are consistent with the

existing empirical evidence and many have not been tested yet.6 First, the model predicts

that LBO activity can exhibit boom-and-bust patterns even if the availability of potential

targets and the value-added from the buyouts do not change. Intuitively, deal activity

depends, among other things, on the ability of private equity �rms to obtain cheap debt

�nancing, which, in turn, depends on their ability to commit not to expropriate debtholders.

Factors like aggregate discount rates and expectations of future deals a¤ect the trade-o¤

between the costs and bene�ts of expropriation and thus have a direct e¤ect on buyout

activity.

Formally, there are two types of equilibria, those with high buyout activity and those

with low buyout activity. In the former, at least one PE �rm commits to no expropriation

and hence all positive-value deals take place. In the latter, both �rms expropriate debthold-

ers, so �nancing is expensive and hence only deals with value exceeding some threshold take

place. Aggregate economic factors a¤ect the sustainability of the equilibrium with high deal

activity. For example, more optimistic expectations about future availability of buyout tar-

gets increase the value of reputation in the debt market and make it costlier for a PE �rm

to expropriate debtholders, sustaining the equilibrium with high activity. Thus, a change

in expectations about future deal activity feeds back to current deal activity, even if the

potential for current deal activity (the number of targets and/or the opportunities for value

improvement) is una¤ected. A decrease in the risk-free rate plays a similar role: it increases

the present value from future deals, making expropriation more expensive. Perhaps sur-

prisingly, a decrease in the risk premium need not have the same e¤ect on deal activity as

a decrease in the risk-free rate. Intuitively, a decrease in the risk premium has two e¤ects.

6These implications are discussed in more detail in Section 5.

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The �rst e¤ect is similar: the present value of future deals increases. However, because

low states become relatively less important and because expropriation is concentrated in

low states, a decrease in the risk premium reduces the present value of the expropriation

costs. Empirically, LBO activity appears to be negatively related to the market-wide risk

premium (Haddad, Loualiche, and Plosser, 2011), suggesting that the �rst e¤ect is more

important in the data.

The model also has implications for how takeover premiums and the composition of

the winning acquirers change with the cycle. To illustrate these results, consider a gradual

change in the expectations about future deal activity, from very low to very high.7 Note that

other things equal, a higher quality PE �rm �nds it easier to commit not to expropriate

debtholders because its expected value from future deals is higher and hence its cost of

hurting its reputation and putting future deals at risk is also higher. When expectations of

future activity are very low, no PE �rm can credibly commit not to expropriate debtholders,

and when these expectations are very high, both PE �rms can credibly commit not to

expropriate debtholders. Hence, in both cases, the two bidders share the same cost of debt

�nancing, which implies that the target is always acquired by the bidder with the highest

potential for value creation, irrespective of its quality.

In contrast, if expectations of future activity are in the middle range, then the higher

quality PE �rm can commit not to expropriate debtholders but the lower quality �rm

cannot. As a result, the higher quality �rm pays a lower cost of debt and can thus outbid

the lower quality �rm even if its potential for value creation is lower. In this middle range,

the di¤erence in the quality of the two �rms is ampli�ed: not only the higher quality �rm

is more likely to generate a higher value by acquiring the target, but it also raises �nancing

on more favorable terms. Hence, the probability of the higher quality bidder winning the

auction is disproportionately high. This argument implies that as LBO activity increases,

the fraction of targets acquired by higher quality PE �rms follows an inverted U-shaped

pattern.

7The same logic applies to changes in the risk-free rate, from very high to very low.

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The above logic also suggests that takeover premiums may not increase monotonically

as buyout activity increases. This is because competition among PE �rms is most severe

at the peak of the expansion, when both �rms can commit not to expropriate debtholders

and thus obtain �nancing on favorable terms. In contrast, competition is very weak in the

middle of the expansion, when the higher quality PE �rms get an additional advantage over

lower quality �rms through cheap debt �nancing. It is the competition among acquirers

that leads to higher takeover premiums and lowers returns to the acquirers. Consistent

with this logic, we show that while takeover premiums in the middle of the expansion are

always lower than at the peak of the expansion, they can be both higher and lower than at

the beginning of the expansion, depending on parameters.

We next explore the implications of the model for the dynamics of buyout leverage

ratios by endogenizing the debt that PE �rms take. We show that leverage ratios do not

monotonically change with buyout activity. Intuitively, when choosing the optimal amount

of debt, the PE �rm faces a trade-o¤. On the one hand, lower leverage may come at a

cost of underutilizing the tax and incentive bene�ts of debt �nancing, but on the other

hand, lower leverage serves as a commitment device for the PE �rm not to expropriate

debtholders, thereby preserving its reputation. As the expected value from future deals

decreases (e.g., due to higher discount rates or lower expectations about future activity),

maintaining commitment to no expropriation requires increasingly lower leverage. At some

point, the cost of suboptimal leverage becomes too high and PE �rms choose to lever

up their portfolio companies to the optimal level, even though debtholders expect to be

expropriated and charge high interest rates. Thus, while deal activity is low in this case,

deals involve high leverage ratios.

The paper is related to several strands of literature. First, it builds on previous research

that examines repeated interactions between borrowers and lenders. The idea that repeated

interactions help overcome borrower-lender agency problems goes back at least to Jensen

and Meckling (1976).8 Diamond (1989) is the most closely related paper in this literature.

8On page 351, Jensen and Meckling (1976) write: �It seems clear, for instance, that the expectation offuture sales of outside equity and debt will change the costs and bene�ts facing the manager in making

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It examines how the incentive e¤ect of reputation evolves as the borrower acquires more

reputation over time. Diamond (1991) extends Diamond (1989) by allowing lenders to

monitor borrowers, which is interpreted as bank �nancing as opposed to issuing bonds or

commercial paper. Our paper is di¤erent from these papers in two important ways, both of

which re�ect the speci�cs of the private equity market as opposed to corporate borrowing.

First, as noted above, LBO activity has historically followed a boom-and-bust pattern,

related to economy-wide factors such as credit spreads and discount rates. For this reason,

we abstract from the dynamics of reputation over the life-cycle of the �rm, which is the focus

of Diamond (1989, 1991), and instead focus on how the incentive e¤ect of future borrowing

changes with aggregate economic conditions. Because of our focus on aggregate as opposed

to within-�rm dynamics, we model reputation as sticking to a �good�equilibrium in the

repeated game instead of introducing uncertainty about the intrinsic type of a borrower,

as in Diamond (1989, 1991).9 Our paper is also di¤erent from Diamond (1989, 1991) in

its focus on competition between private equity �rms, which is an important feature of the

LBO market (e.g., Fidrmuc et al., 2012, and Gorbenko and Malenko, 2012). We emphasize

that due to competition, reputational e¤ects have externalities: the ability of one PE �rm to

commit not to expropriate debtholders makes it a stronger competitor, thereby negatively

a¤ecting other PE �rms and their ability to commit to no expropriation. Our analysis leads

to novel predictions about how the identity of acquirers and the size of takeover premiums

change with aggregate economic conditions.

The paper also contributes to the literature on private equity. Several other explanations

have been proposed for the boom-and-bust pattern of LBO activity. Kaplan and Stein

(1993) hypothesize that the evolution of buyouts in the 1980s was due to �overheating:�

the success of �rst deals attracted new funds that were invested in poor deals. The �market

timing� hypothesis (e.g., Baker and Wurgler (2002)), discussed in Axelson et al. (2012),

decisions which bene�t himself at the (short-run) expense of the current bondholders and stockholders. Ifhe develops a reputation for such dealings, he can expect this to unfavorably in�uence the terms at whichhe can obtain future capital from outside sources.�

9Chapter 15 in Mailath and Samuelson (2006) discusses these two approaches to modeling reputation.The second approach, pioneered by Kreps and Wilson (1982) and Milgrom and Roberts (1982), typicallyinvolves �commitment�(or �crazy�) types who always take the good action.

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suggests that PE �rms play the role of arbitrageurs between debt and equity markets. If

relative valuation of debt and equity markets changes over time, LBO activity will change

too. Both �overheating�and �market timing�theories require some irrationality on the side

of investors, while our theory is based on perfectly rational behavior. Axelson, Stromberg,

and Weisbach (2009) argue that the organizational structure of a fund creates an agency

con�ict between the general partner (the PE �rm) and limited partners of a fund, which

can make buyout valuations and leverage depend on credit market conditions. We abstract

from the con�ict between general and limited partners and instead focus on the con�ict

between the PE �rm and debtholders of the portfolio company. Haddad, Loualiche, and

Plosser (2011) provide another rational theory of buyout waves. In their model, taking

the company private trades o¤ the bene�t of higher cash �ow growth against the cost

of underdiversi�cation of LBO investors, and the present values of the two change with

aggregate discount rates. Our theory, in contrast, is based on the changing ability of

PE �rms to promise their creditors not to expropriate them in the future. One way to

distinguish between the two theories would be to look at whether PE �rms are more likely

to expropriate debtholders in lean times and whether such expropriation a¤ects future costs

of debt for these PE �rms. While the exact test is yet to be performed, empirical evidence

in Demiroglu and James (2010), Ivashina and Kovner (2011), and Hotchkiss, Smith, and

Strömberg (2011) suggests that there is indeed a large heterogeneity in the costs of debt

�nancing and post-buyout behavior among di¤erent PE sponsors.

The remainder of the paper is organized as follows. Section 2 describes the model setup

and considers the benchmark case of full commitment. Section 3 solves the basic model.

Section 4 presents an extension of the basic model to the case of endogenous debt. Section

5 relates the predictions of previous sections to the existing empirical evidence and provides

new empirical predictions. Finally, Section 6 concludes.

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2 Model

The model is discrete-time, in�nite-horizon, and time is indexed by t = 0; 1; 2; :::. There

are three types of agents: two private equity (PE) �rms, targets, and lenders. Figure 1

presents the timeline of the game.

(1)With prob. a targetis available and each

PE firm learns itssurplus .

(2)PE firms obtain

financing and bidfor the target. The

winning bidderacquires the target.

(3)State is realized.

(4)The PE firm decides

how much cashflows to divert.

(5)All agents receive

cash flows.

Period Period

Figure 1: Timeline

In every period t, there is a probability that a target is available. If the target

is available, PE �rm i privately learns surplus zi � 0 that can potentially be generated

from the deal, i = 1; 2. We assume that zi is an i.i.d. draw from the distribution with

a distribution function F (�j�i) on Z. Parameter �i 2 (�; ��), which is common knowledge,

stands for the quality of PE �rm i. In particular, we assume that F (�j�2) �rst order

stochastically dominates F (�j�1) for any �2 > �1.

We assume that to generate surplus zi from the deal, the PE �rm needs to raise debt with

face valueD. The rest is �nanced from the acquirer�s own capital. In other words, we assume

that debt is necessary for shareholder value creation from a private equity transaction. This

can be due to di¤erent reasons. First, this can be due to the tax bene�ts of debt that are

underused by the current management team of the target. Alternatively, it can be due to

the incentive role of debt, as argued by Jensen (1989). For now, we assume that the level of

debt D is exogenous. Later we discuss what happens if this assumption is relaxed. Let D0i

denote how much the creditors are willing to lend in return for a promise of face value D at

the end of the period. D0 is endogenous, and the implied interest rate on debt is DD0i� 1.

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Depending on the interest rates charged by the creditors, each PE �rm may decide

whether or not to undertake the deal. If no �rm decides to undertake the deal, the target

remains independent. If only one �rm decides to undertake the deal, it makes a take-it-

or-leave-it o¤er to existing shareholders of the target. If both �rms decide to undertake

the deal, the two �rms bid for the target. We assume that bidding takes place through

an English �button�auction, where the price is gradually increased until only one bidder

remains (see, e.g., Milgrom and Weber (1982)). Let V1 and V2 be the valuation (i.e., the

maximum willingness to pay for the target) of the �rst and the second bidder respectively.

In the English auction, the bidder with the highest valuation wins the auction and pays

the valuation of the other bidder. Hence, the ultimate price paid by the winning bidder is

minfV1; V2g.

Finally, a publicly observable state s 2 fH;Lg is realized. With probability p, s = H,

in which case the value of the target is XH + zi if it was acquired by the PE �rm i, and XH

if it remained independent. With probability 1 � p, s = L, in which case the value of the

target is XL regardless of whether it was acquired or not.10 After the state is realized but

before investors get the cash �ows, the PE �rm can divert any amount between zero and

the realized value of cash �ows. Diverting x of the cash �ows generates only �x in value

to the PE �rm, where � < 1. Thus, diversion is ine¢ cient. Suppose that if the PE �rm

is indi¤erent between diverting cash �ows and not, it does not divert. At the end of the

period, all agents receive their respective payo¤s.

We make the following assumption on D:

Assumption 1: (1� �) (XH + z) � D > XL, where z is the lowest element of Z.

The assumption D > XL ensures that debt is risky even if the PE �rm does not expro-

priate debtholders.

10The assumption that the value of the �rm in the low state does not depend on zi is made for simplicity.If the value of the �rm in the low state depended on zi, the decision whether to expropriate or not in thelow state would also depend on zi; which would complicate the analysis with generating little additionalinsight.

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The assumption (1� �) (XH + z) � D guarantees, as shown below, that for any realiz-

ation of surplus zi, the PE �rm does not expropriate debtholders in the high state.

We assume that there exists a risk-neutral probability q. Then, if the risk-free rate is

rf , the stand-alone value of the target is given by

V0 =qXH + (1� q)XL

1 + rf:

Since V0 2 [ XL1+rf; pXH+(1�p)XL

1+rf], then q 2 [0; p]. Let � be the risk premium de�ned by the

equation

V0 =pXH + (1� p)XL

1 + rf + �:

Then � = p�qqXH+(1�q)XL (XH �XL) (1 + rf ) and hence � is decreasing in q.

2.1 Benchmark case: Full commitment

We start by analyzing the benchmark case, where each PE �rm can commit to never

expropriate debtholders. For example, if expropriation is veri�able, the PE �rm can sign

a contract with the debtholders that imposes a large enough penalty for expropriation. In

this case, the equilibrium is a repetition of the equilibrium in the single period game with

commitment. In particular, in each period, debtholders get face value D in the high state

and XL in the low state. Hence, the debtholders are willing to invest

Dc0 =

qD + (1� q)XL

1 + rf;

where the superscript stands for �commitment.�The implied promised interest rate on debt

is

rcD =D

Dc0

� 1 = rf +(1� q) (1 + rf )q + XL

D�XL

:

It is higher than the risk-free rate rf because with a positive probability the low state is

realized and debtholders get XL < D: Thus, if the PE �rm pays price P for the target, it

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must invest P �Dc0. The net surplus for the PE �rm of undertaking the deal is therefore

q (XH + zi �D)1 + rf

� (P �Dc0) = V0 +

qzi1 + rf

� P:

Hence, the PE �rm�s maximum willingness to pay for the target equals

V ci = V0 +qzi1 + rf

: (1)

It follows that whenever the target is available, the deal takes place. The bidder with

the highest surplus zi wins the auction and pays a premium 1V0

qzj1+rf

. The following lemma

follows.

Lemma 1 Suppose that both PE �rms can commit never to expropriate debtholders. Then

all available targets get acquired irrespective of rf , �, and . The bidder with the highest

surplus zi wins the auction and pays a premiumqzj

qXH+(1�q)XL .

3 Analysis of the basic model

In this section, we analyze the basic model, where the PE �rm cannot commit not to

expropriate debtholders by signing a contract. In this case, the ability of the PE �rm

to commit not to expropriate is endogenously determined by the �rm�s characteristics,

expectations of future potential deals, and discount rates.

3.1 Single deal setting

We start the analysis by considering a one-shot interaction, i.e., when the game ends after

t = 0. First, consider the low state. If the PE �rm expropriates, it gets �XL. If it does

not expropriate, it gets zero since D > XL. Hence, if s = L, the PE �rm expropriates,

debtholders get nothing, and the PE �rm gets �XL.

Next, consider the high state. If the PE �rm expropriates, it gets �(XH + zi). If it does

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not expropriate, it gets XH + zi �D. Hence, the PE �rm will not expropriate in the high

state if and only if

(1� �) (XH + zi)�D � 0:

By Assumption 1, the PE �rm does not expropriate debtholders in the high state for any

realization of zi.

Realizing that the PE �rm will divert cash �ows in the low state, the debtholders are

willing to invest

Dnc0 =

qD

1 + rf;

where the superscript stands for �no commitment.�The implied interest rate is:

rncD =D

Dnc0

� 1 = rf +(1� q) (1 + rf )

q:

This implies the credit spread of (1� q) (1 + rf ) =q. The promised interest rate and credit

spread exceed the interest rate and credit spread in the commitment case because debthold-

ers get zero, rather than XL, in the low state. If the PE �rm pays price P for the target,

it must �nance the rest, P �Dnc0 . The net surplus for the PE �rm of undertaking the deal

is therefore

q (XH + zi �D) + (1� q)�XL

1 + rf� (P �Dnc

0 ) = V0 +q (zi � z)1 + rf

� P;

where

z =1� qq

(1� �)XL:

Hence, the PE �rm�s maximum willingness to pay for the target equals

V nci = V0 +q (zi � z)1 + rf

: (2)

Since the target will not accept any o¤er below V0, a PE �rm with zi < z can never buy

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the target and hence will not bid for the target. Intuitively, since expropriation creates a

dead-weight loss, only PE �rms that can generate a su¢ ciently high surplus, zi � z; choose

to undertake the deal.

3.2 Equilibria with repeated deals

We next analyze the basic, in�nite-horizon, setting, where PE �rms repeatedly �nd potential

targets. As in other repeated games, the game we consider has many Nash equilibria. We

focus on three types of equilibria. In the �no commitment�equilibrium, both bidders always

divert cash �ows in the low state and are charged rate rncD on debt. In the �full commitment�

equilibrium, neither of the bidders diverts cash �ows in the low state and lenders charge

interest rate rcD. In the �bidder i commitment�equilibrium, bidder i does not divert cash

�ows and pays interest rate rcD, and bidder j always diverts cash �ows in the low state and

pays rncD . In each of these equilibria, the bidders never divert cash �ows in the high state.

In the �commitment�and �bidder i commitment�equilibria, creditors play a grim trig-

ger strategy. If in the �full commitment�equilibrium, PE �rm i deviates and expropriates

debtholders in one of the periods, creditors start charging this �rm rate rncD in all periods

after that, and hence e¤ectively, the game switches to the �bidder j commitment� equi-

librium. Similarly, if in the �bidder i commitment� equilibrium, PE �rm i deviates and

expropriates debtholders in one of the periods, creditors start charging this �rm rate rncD

in all periods after that, and hence e¤ectively, the game switches to the �no commitment�

equilibrium.

Bidder i�s maximum willingness to pay for the target is given by (1) if it can commit

not to expropriate and by (2) otherwise. This allows us to analyze the price paid for the

target and the per-period surplus of both bidders in each of the three types of equilibria.

(A) �Full commitment�equilibrium

The deal always takes place, the premium paid for the target is q

V0(1+rf)minfz1; z2g and

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the per-period surplus of bidder i is

q

1 + rf(zi � zj)+: (3)

(B) �Bidder 2 commitment�equilibrium

Depending on the values z1; z2, the following cases are possible.

1. If z1 < z, bidder 1 does not bid for the target. Hence, bidder 2 acquires the target and

pays the value under its current management, V0. The surplus of bidder 2 isq

1+rfz2.

2. If z < z1 < z2 + z, both bidders participate in the auction, bidder 2 wins, pays

V0 +q

1+rf(z1 � z) and gets surplus q

1+rf(z2 � z1 + z).

3. If z1 > z2 + z; bidder 1 wins, pays V0 +q

1+rfz2 and gets surplus

q1+rf

(z1 � z � z2).

To summarize these cases, the deal always takes place, the premium paid by the winning

bidder isq

V0 (1 + rf )minfz2; (z1 � z)+g;

the per-period surplus of bidder 2 is

q

1 + rf

�z2 � (z1 � z)+

�+; (4)

and the per-period surplus of bidder 1 is

q

1 + rf[z1 � z � z2]+ : (5)

The analysis of the �bidder 1 commitment�equilibrium is similar.

(C) �No commitment�equilibrium

The deal only takes place if z < maxfz1; z2g. If minfz1; z2g < z < maxfz1; z2g, the

bidder with the lowest zi does not participate in the auction, so the takeover premium is zero

15

and the surplus of the winning bidder (say, bidder i) is q1+rf

(zi�z)+. Ifminfz1; z2g > z; both

bidders participate in the auction, so the price paid for the target is V0+q

1+rf(minfz1; z2g�z)

and the surplus of bidder i is q1+rf

(zi � zj)+.

To summarize these cases, the per-period surplus of bidder i is

q

1 + rf

�(zi � z)+ � (zj � z)+

�+=

q

1 + rf[zi �maxfzj; zg]+: (6)

We now derive the conditions for each of these equilibria to exist. Without loss of

generality, suppose �2 � �1.

Assumption 1 guarantees that regardless of the equilibrium, the PE �rm will not divert

cash �ows if the high state is realized. Indeed, under Assumption 1, diversion is not optimal

in the high state even in a one-shot interaction. For bidder i, in the �no commitment�or

�bidder j commitment�equilibrium, each period is a repetition of a one-shot interaction

and hence diversion in the high state is not optimal either. In the �commitment�or �bidder

i commitment�equilibrium, diversion is even more unpro�table because debtholders start

charging higher interest rates once diversion takes place.

First, consider the �full commitment�equilibrium. Bidder 1 compares the bene�t from

diversion, �XL, to the bene�t of sustaining the �full commitment�equilibrium as opposed

to switching to the �bidder 2 commitment� equilibrium.11 Using the one-shot deviation

principle, equations (3) and (5), and the fact that each period the potential target is avail-

able with probability , the bidder does not have incentive to divert cash �ows if and only

if

�XL �

rf

q

(1 + rf )E�(z1 � z2)+ � (z1 � z � z2)+

�(7)

=q

rf (1 + rf )E [z1 � z2]z0 ;

11Note that if bidder 2 does not have incentive to divert cash �ows in the �commitment� equilibrium,he does not have incentive to divert cash �ows in the �bidder 2 commitment� equilibrium either. Thisis because bidder 1 is weaker relative to the �commitment� equilibrium, which allows bidder 2 to gain ahigher surplus.

16

where [y]ba denotes y, truncated at a below and at b above. Similarly, bidder 2 does not

have incentive to divert cash �ows in the low state if and only if

�XL �q

rf (1 + rf )E [z2 � z1]z0 :

Since F (�j�2) �rst order stochastically dominates F (�j�1) for �2 � �1, then E [z2 � z1]z0 >

E [z1 � z2]z0 ;12 and hence (7) is the necessary and su¢ cient condition for the �full commit-

ment�equilibrium to be sustainable.

Using similar arguments and equations (4) and (6), the �bidder 1 commitment�equi-

librium is sustainable if and only if

�XL �q

rf (1 + rf )Eh�z1 � (z2 � z)+

�+ � (z1 �max fz2; zg)+i (8)

=q

rf (1 + rf )E [z1 +min f0; z � z2g]z0 ;

and the �bidder 2 commitment�equilibrium is sustainable if and only if

�XL �q

rf (1 + rf )E [z2 +min f0; z � z1g]z0 : (9)

Lemma A.1 in the appendix shows that if the �bidder 1 commitment�equilibrium exists,

then the �bidder 2 commitment�equilibrium exists as well. Intuitively, the higher quality

bidder �nds it easier to commit not to expropriate debtholders than the low quality bidder

because his expected surplus from future deals is higher.

Using (7), (8) and (9), we derive the following proposition, which characterizes equilibria

of the model as a function of the discount rate r, risk premium �, and expectations of future

deal activity .

Proposition 1 For any �1 and �2; �1 � �2; there always exists a �no commitment�

equilibrium. In addition, there exist rf1 � rf2 � rf3 ( 1 � 2 � 3) such that:12See Appendix, Lemma A.1, for the proof of this statement.

17

1. the �full commitment�equilibrium exists if and only if rf � rf1 ( � 1);

2. the �bidder 1 commitment�equilibrium exists if and only if rf � rf2 ( � 2);

3. the �bidder 2 commitment�equilibrium exists if and only if rf � rf3 ( � 3).

Intuitively, when the risk-free rate is lower (expected availability of targets in future

periods is higher), the present value of the bene�ts from high reputation and cheap future

�nancing is higher. This allows private equity �rms to credibly commit not to expropriate

debtholders, sustaining the equilibrium with commitment.

Interestingly, the e¤ect of the risk premium on sustainability of equilibrium with com-

mitment is di¤erent from the e¤ect of the risk-free rate. There are two opposite e¤ects: on

the one hand, similar to an increase in the risk-free rate, an increase in the risk premium

decreases the present value of future deals and thus makes expropriation in the current

period more attractive. On the other hand, a higher risk premium corresponds to a higher

probability of the low state. Since expropriation only occurs in the low state, debtholders

charge higher risk-free rates whenever the private equity �rm cannot commit to not expro-

priating. This e¤ect widens the gap between the private equity �rm�s expected per-period

surplus with and without expropriation, and thus makes it easier to sustain the equilibrium

with commitment.

We next examine the properties of the three types of equilibria. We start by noting that

the level of buyout activity is the same in the �full commitment�and �bidder i commitment�

equilibrium: whenever a target is available, the deal takes place. In contrast, in the �no

commitment�equilibrium, buyout activity is low: only deals with high enough value (zi > z)

go through because the private equity �rm needs to be compensated for the high cost of

debt �nancing.

Although the �full commitment�and �bidder i commitment�equilibria share the same

level of buyout activity, they are characterized by a di¤erent composition of the winning

acquirers and by di¤erent takeover premiums. First, note that in both the �full commit-

18

ment�and �no commitment�equilibria, the two private equity �rms obtain debt �nancing

on similar terms and hence the bidder with the highest value zi always wins the auction.

In contrast, in the �bidder 2 commitment�equilibrium, the higher quality bidder obtains

�nancing at lower interest rates than the lower quality bidder. This gives an additional

advantage to the higher quality private equity �rm when competing with the lower quality

�rm: even with equal or lower value it can create by buying the target, the higher quality

�rm is able to outbid the lower quality �rm. As a result, higher quality private equity �rms

acquire a disproportional fraction of targets. The following lemma formalizes this intuition.

Lemma 2 The fraction of targets acquired by the higher quality private equity �rm in the

�bidder 2 commitment�equilibrium is higher than both in the �no commitment�and in the

�full commitment�equilibrium.

The �bidder i commitment�and the�full commitment�equilibria are also characterized

by di¤erent takeover premiums. In the former, the lower quality bidder obtains debt �n-

ancing at unfavorable terms and hence is not willing to pay a positive premium for the

target unless the value it can create is su¢ ciently high. Hence, the higher quality bidder

faces little competition, which leads to low takeover premiums. In contrast, in the �full

commitment�equilibrium, both types of bidders participate in the auction, leading to high

takeover premiums. Formally, q

V0(1+rf)Eminfz1; z2g, which is the expected premium in the

�full commitment� equilibrium, is strictly higher than q

V0(1+rf)Eminf(z1 � z)+ ; z2g, the

expected premium in the �bidder 2 commitment�equilibrium.

Interestingly, takeover premiums may not monotonically change with buyout activity. In

particular, the expected premium in the �no commitment�equilibrium, where the takeover

activity is low, may be strictly higher than the expected premium in the �bidder 2 commit-

ment�equilibrium. The intuition is the following. In the �no commitment�equilibrium,

deals where both bidders�valuations are su¢ ciently low (minfz 1; z2g < z) do not take place.

In contrast, in the �bidder 2 commitment�equilibrium, such deals take place because the

19

higher quality bidder obtains �nancing at favorable rates. Hence, as buyout activity in-

creases, the marginal deals that take place feature low valuations and hence low takeover

premiums, leading to a decrease in the average takeover premiums. Note, however, that

there is another e¤ect, which acts in the opposite direction. Since bidder 2�s willingness to

pay for the target is higher in the �bidder 2 commitment�equilibrium, the premium that

bidder 1 pays conditional on winning is higher in this equilibrium. The following example

shows that both e¤ects can potentially dominate.

Example Suppose z1 = 0:1 with prob. � and z1 = 0:9 with prob. 1 � �. Similarly,

z2 = 0:1 with prob. � and z2 = 1 with prob. 1� �, and is independent of z1. Suppose also

that z = 0:4. Then the expected premium in the �bidder 2 commitment�equilibrium is, up

to a constant q

V0(1+rf), equal to Eminf(z1 � z)+ ; z2g = (1� �)� (0:1)+(1� �)2 (0:5). The

expected premium in the �no commitment�equilibrium is, up to the same constant, equal

to E�(minfz1; z2g � z)+ j maxfz1; z2g > z

�= (1��)2(0:5)

1��2 . It is straightforward to show that

the expected premium in the �no commitment�equilibrium is higher if and only if � > 0:25.

The above properties of the three equilibria are demonstrated in Figure 2, which con-

siders the following parameters: XL = 0:06, XH = 0:12, q = 0:5, � = 0:5, zi � F (�; �i)

on [0; 1], where F (x; �) = x�, �1 = 0:24, �2 = 0:25. The �rst graph presents deal activity,

de�ned as the percentage of positive-value deals that take place. The second graph presents

the fraction of targets acquired by the higher quality PE �rm, and the third graph presents

the average takeover premium. As Figure 2 demonstrates, the composition of acquirers does

not monotonically change with buyout activity: the fraction of deals done by the higher

quality PE �rm is the highest in the �bidder 2 commitment�equilibrium. Takeover premi-

ums are the lowest in the �bidder 2 commitment� equilibrium, where the higher quality

�rm faces little competition.

20

0%

25%

50%

75%

100%

No commitment Bidder 2 commitment Full commitment

Buyout activity

0%

15%

30%

45%

60%

No commitment Bidder 2 commitment Full commitment

Fraction of targets acquired by high quality firms

0%5%

10%15%20%25%30%

No commitment Bidder 2 commitment Full commitment

Average takeover premium

Figure 2: Deal activity, composition of winners, and premiums

4 Extension: Endogenous debt

The base model assumes that the face value of debt that a portfolio company takes, D, is

exogenous. Thus, the capital structure decision by the private equity sponsor is binary: it

either takes debt D or does not undertake the deal at all. While this assumption simpli�es

21

the analysis considerably, it is at odds with existing empirical evidence. Indeed, Axelson et

al. (2012) �nd that the leverage in buyouts varies substantially, and its main determinants

are not target characteristics but rather economy-wide credit conditions. In this section, we

extend the base model by allowing PE �rms to decide on the amount of debt. This extension

captures many of the empirical facts of Axelson et al. (2012) and provides additional

implications, discussed in the following section.

To model endogenous debt in a realistic and tractable way, we assume that if PE �rm

i raises debt of face value D � 0 to buyout the portfolio company, then the additional

value that the portfolio company generates in the high state is g (D) + zi. Function g (D)

is assumed to satisfy the following conditions:

Assumption g (0) = 0 , g00 (D) < 0 , limD!0 g0 (D) =1, and g0 (D�) = 0 for some �nite

D�, such that (1� �) (XH + z) � D� > XL.

This assumption ensures two properties. First, the PE �rm will almost surely raise a

positive amount of debt to �nance its transaction. This is because the marginal value of

adding an in�nitesimal amount of debt is in�nite. Second, there is an optimal amount

of debt, D�, that maximizes the surplus from the transaction. Thus, D� represents the

optimal capital structure of a portfolio company if there were no equityholder-debtholder

frictions. The assumption on the boundaries for D� mimics that in the base model.

We proceed in two steps. First, we solve for the optimal leverage and expropriation

strategy of a single PE �rm, taking the strategy of the other PE �rm as given. Then, we

consider equilibria of the whole game.

4.1 Optimal leverage and expropriation by a single PE �rm

Consider the leverage and expropriation decisions of a PE �rm, ignoring their e¤ects on

choices of the other PE �rm. By the assumption above, expropriation can never happen in

22

equilibrium in state H.13 Because g (D) is strictly increasing in the range D � D�, without

loss of generality, we can restrict attention to two levels of debt: D� and the highest level

of debt that supports the absence of expropriation. Suppose that expropriation leads to a

decrease in future surplus by �S. In the next subsection, we endogenize �S , but for now

we assume that it is given. Let us �nd the highest level of debt that supports the absence

of expropriation. Expropriation is suboptimal if and only if

max fXL �D; 0g � �XL ��S;

which can be rearranged as

D � (1� �)XL +�S:

If �S is high enough so that (1� �)XL + �S � D�, then the equilibrium with always

choosing D� exists.

Consider the case of (1� �)XL +�S < D�. Then, the highest face value of debt that

makes the promise of the PE �rm not to expropriate credible is (1� �)XL+�S. Consider

the discounted payo¤ of the PE �rm from its �nancing portfolio �rms with this amount of

debt and not expropriating debtholders in perpetuity. For a single deal, debtholders supply

q ((1� �)XL +�S) + (1� q)XL

1 + rf

of capital. The expected surplus of the PE �rm is then

q (XH + g ((1� �)XL +�S) + zi) + (1� q)XL

1 + rf� P; (10)

where P is the acquisition price. Alternatively, the PE �rm can raise the unconstrained

optimal amount of debt D� but at a higher interest rate, as debtholders will expect com-

pensation for getting expropriated in the low state. In this case, debtholders will supply

13To see this, note that in equilibrium D � D�, and because D� � (1� �) (XH + z), the payo¤ of thePE �rm from no expropriation is always weakly higher than its payo¤ from expropriation.

23

qD�= (1 + rf ), and the expected surplus to the PE �rm from a single buyout will be

q (XH + g (D�) + zi) + (1� q)�XL

1 + rf� P: (11)

The di¤erence between (10) and (11) is independent of zi and given by

(1� q) (1� �)XL + q (g ((1� �)XL +�S)� g (D�))

1 + rf: (12)

If (12) is positive, then the optimal strategy of the PE �rm is to �nance deals with

(1� �)XL + �S face value of debt and to never expropriate debtholders. Otherwise, if

(12) is negative, then the optimal strategy of the PE �rm is to �nance deals with D� face

value of debt and to expropriate debtholders. Because (12) is strictly increasing in �S in

the range (1� �)XL +�S < D�, the optimal strategy of the PE �rm as a function of �S

can be summarized in the following proposition:

Proposition 2. Let �S be de�ned as the point at which (12) equals zero if such point

exists, and as �S = 0 if (12) is positive for any �S � 0. Let ��S � D��(1� �)XL. Then,

the optimal policy of the PE �rm satis�es:

1. If �S < �S, then the PE �rm �nances deals by issuing debt with the face value of

D� and always expropriates debtholders if state L is realized.

2. If �S < �S < ��S, then the PE �rm �nances deals by issuing debt with the face value

of (1� �)XL +�S and never expropriates debtholders.

3. If �S > ��S, then the PE �rm �nances deals by issuing debt with the face value of

D� and never expropriates debtholders.

Figure 3 illustrates the non-monotonicity of debt implied by Proposition 2. If the e¤ect

of expropriation on future surplus �S is high enough (�S > ��S), it prevents the PE �rm

24

from expropriating debtholders in the low state, even if the face value of debt D is at the

optimal level D�. As a consequence, the buyout debt is D�, and expropriation does not

occur. If the e¤ect of expropriation on future surplus �S is not so high, then the PE �rm

cannot raise the optimal level of debt D� and at the same time credibly commit not to

expropriate debtholders. In this case, it has to either raise a lower than optimal debt or

raise the optimal level of debt at a high interest rate that takes into account expropriation

in the low state. If �S is above a certain level �S, then even though the PE �rm cannot

credibly commit not to expropriate while raising D�, it can commit not to expropriate while

raising a high enough debt. In other words, the loss due to expropriation is higher than

the loss from lower-than-optimal leverage of a portfolio company, so the PE �rm prefers

to under-lever portfolio companies but not to expropriate debtholders. However, if �S is

too low (�S < �S), then the PE �rm is unable to raise even moderate debt while credibly

promising to not expropriate debtholders. Hence, the cost of lower-than-optimal leverage of

a portfolio company exceeds the loss due to expropriation, so the PE �rm prefers to lever

portfolio companies optimally, even though it (and debtholders) know that expropriation

will occur should the low state arise.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Loss of future surplus from expropriation, ∆S

Deb

t, D

Optimal debt;Expropriation

Suboptimal debt;No expropriation

Optimal debt;No expropriation

Figure 3: Optimal debt

25

4.2 Equilibria with two PE �rms

A complete analysis of equilibria of competition among two PE �rms with endogenous

debt is di¢ cult for a number of reasons. First, as showed in the base model, there exist

asymmetric equilibria even if debt is exogenous. In fact, sometimes, these are the only

equilibria. With endogenous debt, it is likely that there exists a continuum of asymmetric

equilibria. Second, because the two PE �rms impose externalities on each other, a deviation

of one PE �rm from its strategy may potentially a¤ect the strategy that the other PE �rm

uses in its subgame. Because of these reasons, rather than characterizing the full set of

equilibria, in the next proposition, we establish how the existence of each equilibrium is

a¤ected by aggregate parameters:

Proposition 3. Assume that g (D) is such that

(1� q) (1� �)XL + q (g ((1� �)XL)� g (D�)) < 0:

If there exists an equilibrium in which the two PE �rms follow strategies (Di; Ei), where

Di 2 [(1� �)XL; D�] and Ei 2 fexpropriate, no expropriateg, i 2 f1; 2g, in perpetuity,

then the same equilibrium also exists if, all else equal, the risk-free rate is lower or is

higher.

This proposition implies that a lower risk-free rate or a higher expectation about fu-

ture deal activity expands the set of equilibria by allowing for �better� equilibria. As a

consequence, if one implements a similar choice among equilibria as in the base model,

equilibrium leverage ratios will follow the same pattern with changes in rf and as shown

in Figure 3. Intuitively, a lower risk-free rate or a higher reduces the present value of

future deal activity, and hence, �S, holding all else equal. Therefore, leverage ratios do not

26

monotonically change with buyout activity.

5 Related empirical literature and testable predictions

In this section, we discuss the implications of the model. First, we discuss existing empirical

evidence and relate it to the model�s predictions. Then, we provide a number of additional

testable hypotheses that, to our knowledge, have not been examined yet.

5.1 Relation to existing empirical evidence

Aggregate LBO activity and economic conditions. Aggregate LBO activity �uctu-

ates considerably over time (e.g., Kaplan and Stein, 1993; Kaplan and Strömberg, 2009).

High activity in the 1980s was followed by few LBO deals during the 1990s, which were

followed by another wave of deals between 2004 and the �nancial crisis. It slowed down

substantially during the �nancial crisis and is now increasing. Such boom-and-bust pat-

terns are consistent with our theory. As the model shows, expectations of high (low) deal

activity in the future feed back into high (low) deal activity today. As a result, deal activity

becomes self-ful�lling, leading to persistent periods of high (low) deal activity observed in

the data. In the model, a switch to a di¤erent deal activity equilibrium can be triggered by

either a change in expectations about future deal activity or by a change in discount rates.

One plausible shock to investors�expectations about future activity is sudden availability

of �easy�debt �nancing, such as rapid development of the junk bond market in the 1980s

(Kaplan and Stein, 1993) and growth in securitization in 2004-2007 (Shivdasani and Wang,

2011). In particular, the e¤ect of the availability of debt �nancing on activity today is likely

to be signi�cantly ampli�ed by its indirect e¤ect on the expectations of future deal activity.

The importance of discount rates is emphasized by Haddad, Loualiche, and Plosser

(2011), who �nd that buyout activity is related to aggregate discount rates, most notably

aggregate risk premium. In our model, a decrease in risk premium has two e¤ects on buyout

activity. On the one hand, it increases the importance of future deals relative to current

27

deals, which improves the ability of PE �rms to commit not to expropriate debtholders. On

the other hand, a lower risk premium reduces the cost of expropriating debtholders since

expropriation is concentrated in low states. The �rst e¤ect increases LBO activity, while

the second e¤ect decreases it. Evidence in Haddad, Loualiche, and Plosser (2011) suggests

that the �rst e¤ect dominates in the data.

Leverage decisions and economic conditions. Axelson et al. (2012) �nd that variation

in buyout leverage is mainly explained by variation in economy-wide credit conditions, as

opposed to cross-sectional factors, suggested by traditional capital structure theories. In

particular, Axelson et al. (2012) �nd that higher deal leverage is associated with lower

economy-wide credit spreads. As shown in Section 4, economy-wide conditions can have a

signi�cant e¤ect on buyout leverage when PE �rms and creditors interact repeatedly. As

economy-wide conditions (as measured by rf , , and q) �uctuate, buyout leverage will �uc-

tuate too, and these �uctuations could potentially outweigh heterogeneity among portfolio

companies in their optimal leverage (D�). Speci�cally, as committing not to expropriate

debtholders becomes more di¢ cult, PE �rms react by underlevering their portfolio com-

panies, as is evident from the middle interval of Figure 2.

Di¤erential cost of debt �nancing and leverage ratios for di¤erent PE �rms.

The model suggests that the identity of the private equity sponsor should be an important

determinant of both the cost of debt and the leverage of the portfolio company. Demiroglu

and James (2010) and Ivashina and Kovner (2011) provide evidence consistent with this

prediction. Demiroglu and James (2010) �nd that portfolio companies of more reputable

private equity sponsors (as measured by their market share, age, and the number of com-

pleted deals) raise debt at a lower cost and use more leverage. Ivashina and Kovner (2011)

show that prior bank relationships of a private equity sponsor are an important determinant

of the cost of debt of its portfolio companies. It should be noted that while the evidence in

Demiroglu and James (2010) and Ivashina and Kovner (2011) is consistent with our model,

28

these papers do not provide a direct test of the channel examined in our paper. A more

direct test would measure PE �rms� reputation by looking at PE �rms� track record of

expropriating debtholders, such as the past use of dividend recapitalizations and creditor

litigations against the PE sponsors.

5.2 Additional testable predictions

1. Takeover premiums in LBO transactions. Conditional on a similar deal, takeover

premiums are higher in periods of higher aggregate buyout activity. Unconditionally,

takeover premiums either strictly increase or have a U-shaped form in measures of

aggregate buyout activity.

Axelson et al. (2012) �nd that transaction multiples, as measured by EV/EBITDA,

are higher in more active periods. Although not a direct test of this prediction since

EV/EBITDA is di¤erent from a takeover premium, this �nding is consistent with our

prediction.

2. Composition of acquirers. The fraction of deals done by higher-quality private

equity �rms has an inverted U-shaped form in drivers of deal activity, such as expect-

ations of future deal activity and discount rates.

The intuition is the following. At the bottom of the LBO cycle, neither high-quality

nor low-quality PE �rms can credibly commit not to expropriate debtholders. Hence,

all PE �rms raise debt at high credit spreads, so the identity of the winning bidder

is determined solely by who has a higher potential for value creation. However, in

the middle of the LBO cycle, high-quality PE �rms can commit not to expropriate

debtholders, while low-quality PE �rms cannot. Hence, high-quality PE �rms enjoy

an advantage by being able to raise debt at a lower cost. This advantage no longer

exists at the peak of the cycle, where low-quality PE �rms are also able to raise debt

at low costs and hence the identity of the winning bidder is again determined by who

has a higher potential for value creation.

29

Demiroglu and James (2010) study how the annual average of PE �rms�reputation,

as measured by their age, number of deals and market share over the prior three years,

changes over time between 1997 and 2007, but a direct test of this prediction is yet

to be performed.

3. Expropriation decisions in LBO transactions. A private equity sponsor is more

likely to expropriate creditors of its portfolio company if (1) it is of lower quality, (2) it

has a track record of expropriating creditors in the past, (3) the private equity market

is less active, (4) the economy-wide discount rates are higher.

While the quality of a private equity sponsor is not observed directly, it can be ap-

proximated, for example, by returns on past deals. The most closely related paper is

Hotchkiss, Smith, and Strömberg (2011), who study the resolution of �nancial distress

among �rms backed by di¤erent PE sponsors. They �nd evidence that �rms backed

by PE sponsors with more �nancial and reputational capital (as measured by their

age) are associated with a higher likelihood of survival and more e¢ cient resolution

of �nancial distress. A more direct test of our theory would be to look at how the

probability of a PE �rm engaging in expropriation (for example, evidenced by a di-

vidend recapitalization followed by a default) is related to the identity of the PE �rm,

its past track record, and current economy-wide conditions.

4. Di¤erential cost of debt. (1) Higher-quality PE �rms and PE �rms with a track

record of not expropriating debtholders of their portfolio companies raise debt at lower

costs; (2) This premium for quality and track record decreases when the LBO cycle

reaches its peak.

As noted above, the �rst part of this prediction is consistent with the evidence in

Demiroglu and James (2010) and Ivashina and Kovner (2011), but a more re�ned

test is needed to test it directly.

30

6 Concluding remarks

This paper analyzes LBO activity through the channel of repeated interactions between

private equity �rms and creditors. It is based on two key ingredients. First, high lever-

age employed in LBO transactions creates a con�ict of interest between PE sponsors and

debtholders of their portfolio companies. Second, this con�ict can be partly alleviated by

PE �rms�reputational concerns due to their need to raise �nancing for future deals, but the

disciplining e¤ect of reputation depends on economy-wide conditions and expectations of

future deal activity. In the model, PE �rms compete for targets with each other, and this

competition drives takeover premiums and the composition of acquirers over the buyout

cycle. We show two sets of results. First, cycles of LBO activity can naturally arise even

if there is no mispricing between debt and equity markets and the potential value created

in buyout deals is similar every period. These cycles are related to aggregate economic

conditions. Second, characteristics of LBO activity, such as average takeover premiums,

the composition of acquirers, and buyout leverage ratios, change with the stage of the

LBO cycle. Many of these implications are consistent with existing empirical evidence, but

several have not been tested yet.

While the focus of the paper is on the ex-post agency con�ict between the PE �rm and

debtholders in a leveraged buyout, the model is also applicable to con�icts between the PE

�rm and other stakeholders of their portfolio �rms, such as employees (e.g., Shleifer and

Summers, 1988). For example, frequent buyouts can make PE �rms�promises to employees

more credible and thereby make it easier to get concessions from organized labor ex ante.

Our conjecture is that a model focused on other con�icts may lead to similar implications

for cycles of LBO activity, but will not generate implications for leverage and the cost of

debt.

31

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32

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33

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34

Appendix

Proof of Proposition 1

Since z1� z2 � min fz1; z1 + z � z2g, then [z1 � z2]z0 � [z1 +min f0; z � z2g]z0 and hence

the bound for the �full commitment�equilibrium, Bfullcomm =q

rf(1+rf)E [z1 � z2]z0, is smaller

than the bound for the �bidder 1 commitment�equilibrium, B1comm =q

rf(1+rf)E [z1 +min f0; z � z2g]z0.

Since z2 FOSD dominates z1, then, as Lemma A.1 shows,

B1comm � B2comm =q

rf (1 + rf )E [z2 +min f0; z � z1g]z0 :

De�ne rf1, rf2, and rf3 ( 1, 2 and 3) as the levels of the risk-free rate (the probability

of an available target) that make (9), (8), and (7) to be satis�ed as equalities. Note that

each of the three bounds decreases in rf and increases in , and hence these values are

uniquely de�ned.

Note also that Bfullcomm is not monotonically increasing in q. There are two opposite

e¤ects. On the one hand, higher q (and hence lower �) means that the PE �rm discounts

the value from potential future deals less. This makes it easier for the �rm to commit not

to expropriate, increasing Bfullcomm. On the other hand, the di¤erence in expected surplus

between the equilibrium with and without commitment conditional on the high state of

the world, E [(z1 � z2)+ � (z1 � z � z2)+], is lower when q is higher. Intuitively, when the

probability of a good state is higher, expropriation happens less frequently and hence the

di¤erence in interest rates charged by the debtholders, rncD � rcD, is also lower. This e¤ect

makes it harder for the PE �rm to commit not to expropriate, decreasing Bfullcomm.

Proof of Lemma 2

The fraction of deals won by the higher quality acquirer in the �bidder 2 commitment�

equilibrium is Pr (z2 > z1 � z), which is strictly higher than Pr (z2 > z1), the corresponding

fraction in the �full commitment�equilibrium.

Let S1 = f(z1; z2): minfz1; z2g > z; z1 > z2g, S2 = f(z1; z2): minfz1; z2g > z; z2 > z1g

35

and S3 = f(z1; z2): minfz1; z2g < zg. Then the fraction of deals won by the higher quality

acquirer in the �no commitment�equilibrium is Pr(S2)Pr(S1)+Pr(S2)

. Note also that if (z1; z2) 2 S3or S2, then z2 > z1� z and hence Pr (z2 > z1 � z) > S2+S3 and Pr (z2 < z1 � z) < Pr (S1).

Hence, Pr(S2)Pr(S1)+Pr(S2)

< Pr(z2>z1�z)Pr(S1)+Pr(z2>z1�z) < Pr (z2 > z1 � z), which completes the proof.

Proof of Proposition 3

[To be completed]

Lemma A.1 If the distribution of z2 �rst order stochastically dominates the distri-

bution of z1; then for any z, E [z2 � z1]z0 � E [z1 � z2]z0 and E [z2 +min f0; z � z1g]z0 �

E [z1 +min f0; z � z2g]z0.

Proof of Lemma A.1

Let F1; F2 be the corresponding distribution functions. For any t;

Pr(z2 � z1 < t) =ZF2(x+ t)dF1(x) �

ZF1(x+ t)dF1(x)

since by FOSD, F2(x) � F1(x) 8x: Since F1(x + t) is non-decreasing in x, then according

to the property of �rst order stochastic dominance,

ZF1(x+ t)dF1(x) �

ZF1(x+ t)dF2(x) = Pr(z1 � z2 < t):

Hence, for any t; Pr(z2 � z1 < t) < Pr(z1 � z2 < t), which by de�nition implies that the

distribution of z2 � z1 �rst order stochastically dominates the distribution of z1 � z2: Since

the function u(x) = xjz0 is non-decreasing, the �rst statement of the lemma follows from the

property of �rst order stochastic dominance.

By the same argument, the distribution of z2+min f0; z � z1g �rst order stochastically

36

dominates the distribution of z1 +min f0; z � z2g. Indeed, for any t,

Pr (min fz2; z2 + z � z1g < t) = Pr (z2 < t or z2 + z � z1 < t) = Pr (z2 < maxft; t+ z1 � zg)

=

ZF2 (maxft; t+ x� zg) dF1 (x)

�ZF1 (maxft; t+ x� zg) dF1 (x)

Since F1 (maxft; t+ x� zg) is non-decreasing in x, then according to the property of �rst

order stochastic dominance,

ZF1 (maxft; t+ x� zg) dF1 (x) �

ZF1 (maxft; t+ x� zg) dF2 (x)

= Pr (min fz1; z1 + z � z2g < t) ;

which completes the proof of the second statement of the lemma.

37