A THEORY OF NET DEBT AND TRANSFERABLE HUMAN CAPITAL

Transcription

1 A THEORY OF NET DEBT AND TRANSFERABLE HUMAN CAPITAL Bat M. Lambecht Lancaste Univesity Management School Gzegoz Pawlina Lancaste Univesity Management School Abstact Taditional theoies of capital stuctue do not explain the puzzling phenomena of zeo-leveage fims and negative net debt atios. We develop a theoy whee fims adopt a net debt taget that acts as a balancing vaiable between equityholdes and manages. Negative (positive) net debt occus in human (physical) capital intensive industies. The net debt atio falls in the [-1,1] inteval and contains moe infomation than taditional leveage measues because it is not left-censoed at zeo. Negative net debt aises because tadeable claims cannot be issued against tansfeable human capital. Heteogeneity in capital stuctue occus when fims have debt that is not fully collatealized. Physical capital intensive fims take on high leveage but may undeleve to avoid bankuptcy costs. This ceates excess ents fo manages (even if the supply of human capital is competitive) because wealth constaints pevent manages fom co-investing. Keywods: capital stuctue, net debt, human capital (JEL: G31, G32) The addess of both authos is: Depatment of Accounting and Finance, Lancaste Univesity Management School, Lancaste LA1 4YX, United Kingdom. coespondence can be sent to [email protected] o [email protected]. 0

2 1 Intoduction Although thee is an extensive liteatue in copoate finance on theoies of capital stuctue, these theoies typically emain silent about cash and its effect on leveage. Fo example, if a company boows moe money and keeps the poceeds as cash within the fim then this tansaction unambiguously aises the fim s debt and leveage. Howeve, the fim can subsequently evese the tansaction by using the cash to pay off the debt. As such the fim s net debt and net leveage have not changed, which may explain why standad valuation models subtact the amount of cash in the fim s balance sheet fom the value of outstanding debt in ode to detemine the fim s leveage. Rathe supisingly the tems net debt and net leveage baely featue in the finance liteatue and little o no significance has been attached to these measues. Thee ae theoies of debt, and theoies of cash (o liquidity) but to ou knowledge nobody has analyzed how both vay in aggegate. Why should we have a theoy of net debt? Fist, as mentioned befoe, a theoy of net debt fomally ecognizes that cash is (to a high degee at least) negative debt and may theefoe be a pat of the capital stuctue decision athe than an asset that is exogenously given. Second, by netting out liquid assets against debt liabilities the net debt atio (NDR) is no longe bounded by zeo but can vay fom -1 to +1. The NDR contains theefoe moe infomation than the taditional leveage atio, which is leftcensoed at zeo. A theoy of net debt may esolve the mystey of zeo-leveage fims, because all zeo leveage fims ae simply fims with a negative NDR. 1 Zeo-leveage is theefoe no longe an exteme pola case. 2 Thid, a theoy of net debt opens the 1 Stebulaev and Yang (2006)) povide empiical evidence of the widespead and pesistent phenomenon of zeo-leveage fims and ague that existing capital stuctue theoies stuggle to explain the puzzle. 2 Standad capital stuctue theoies do not model net debt o net leveage. This is immediately appaent fom the fact that fims without debt ae all categoized as zeo leveage fims, whethe they have cash o not. Of couse, the amount of cash (o liquid assets moe geneally) may influence the tax shield, expected bankuptcy o agency costs, the degee of infomation asymmety... but that is a diffeent matte because in those theoies cash entes as an exogenous vaiable, wheeas in ou model cash entes as an endogenous vaiable. 1

3 doo fo an integated theoy of debt and cash. While ou theoy of net debt leaves an element of indeteminacy (thee ae an infinite numbe of combinations of debt and cash that lead to the same amount of net debt), we show in elated wok that this indeteminacy can be esolved by intoducing additional fictions. 3 Fouth, a theoy of net debt may help explaining some puzzling tends. Bates, Kahle, and Stulz (2009) epot that the aveage (median) NDR fo US fims has fallen fom 16.5% (17.8%) in 1980 to -1.5% (-0.3%) in The negative tend is petty much monotonic ove time. The cuent widespead occuence of negative net debt implies that the majoity of fims would be capable of edeeming all debt with the cash they have available. This aises the obvious question as to why so many fims have negative debt and what thei common chaacteistics ae. As existing capital stuctue theoies cannot pedict negative leveage (the optimal leveage ange is the [0, 1] inteval), we need a new ingedient that can geneate negative net leveage tagets. This cucial ingedient is non-tadeable, tansfeable human capital. Its choice is not by accident but motivated by impotant economic consideations. Fist, the elative impotance of human capital in the economy has inceased ove time. The ise of the high-tech, bio-tech, health, media, sevices and knowledge based industies has shifted the emphasis towads human capital, away fom physical capital. Second, the amount of money and time that individuals invest in thei human capital in tems of education and taining has inceased a lot in ecent decades. Aggegating employees investment in tansfeable (i.e. non-fim specific) human capital within a fim can lead to non-tivial amounts, especially in sectos such as health cae, biotech and financial sevices. Thid, human capital has become much moe tansfeable and mobile. Human capital is much less tied to a paticula fim and has, in a 3 A simple, somewhat tivial example would be to assume that the inteest on cash is less than the inteest on debt. In that case the fim will not hold any cash (debt) if net debt is positive (negative). Theefoe, this simple fiction unambiguously pins down the amount of cash and debt once the net debt taget is known. Similaly, Achaya, Almeida, and Campello (2007) show that cash is not identical to negative debt if fims have pofitable futue investment oppotunities but face limited access to extenal funding. Anticipating these constaints fims pefe saving cash (educing debt) if the coelation between cash flows and investment oppotunities is low (high). In ou model cash is negative debt because fims do not have futue investment oppotunities. 2

4 globalized wold, also become moe mobile in a geogaphical sense. Many fims now conside human capital as thei most impotant asset. Yet, human capital is not ecoded as an asset on the fim s balance sheet. 4 Futhemoe, povides of human capital ae though thei pesonal investment in human capital (often paid fo by pesonal loans) indiectly financing fims. Knowledge wokes ae theefoe ightly consideed to be the new capitalists (The Economist (2001)). Howeve, while they clealy have a stake in the fim, they do not featue in the fim s liabilities, unlike bond- and equityholdes. 5 The cucial diffeence between human and physical capital is that the fome is not tadeable. Theefoe, unlike physical capital, no tadeable claims can be issued against tansfeable human capital. The mobility of human capital acoss fims and industies makes it difficult even to assign human capital to one specific fim. Human capital has in many way blued the boundaies of the fim. Zingales (2000) agues that the natue of the fim is changing, that human capital is emeging as the most cucial asset, and that existing copoate finance theoies seem to be quite ineffective in helping us cope with the new type of fim that is emeging. The case of the Bitish advetising agency Saatchi and Saatchi, descibed in Rajan and Zingales (2000) povides a stak illustation of the issues aised. 6 Given the special natue of human capital, in what way would one expect the capital stuctue and asset stuctue of human capital intensive fims to diffe fom fims that ae moe heavily based on physical capital? How does an industy s human capital intensity affect equilibium pofit ates, dividend payout and manageial compensation? What inefficiencies aise if owneship of human capital and physical capital ae sepaated? This pape pesents a theoy that addesses these questions. It is faily well undestood that scacity of, say, manageial talent ceates space fo manageial ents and esults in undeinvestment. We focus theefoe on the moe inteesting question whethe manages o equityholdes can captue excess ents when 4 One exception ae cetain types of spot clubs that buy and sell playes. 5 Even if the povides of human capital ae given shaes in the fim, thei claim emains clealy diffeent fom outside equity investos. 6 Afte thei geneous compensation package was voted down by shaeholdes, the chaiman and seveal senio executives of Saatchi and Saatchi left the fim and stated a ival fim that in a shot time captued a substantial pat of the business of the oiginal fim. 3

5 the supply of equity capital and human capital ae pefectly competitive. Ou model focuses on the effect of thee impotant fictions: 1) manageial wealth constaints, 2) non-tadeable human capital and 3) copoate bankuptcy costs. We abstact fom taxes and infomation asymmety. We conside fims that need both physical capital and human capital. The fome is financed by equityholdes and bondholdes, wheeas manages make the investment in human capital. Both types of capital have sepaate ownes because of manageial wealth constaints. Impotantly, human capital is tansfeable acoss fims within the industy. While the fim is opeational, equityholdes and manages bagain about fee cash flows (i.e. pofits afte inteest epayment). Some fims leave the industy in ecession because equityholdes and manages choose to execise thei outside option. Equityholdes liquidate the physical capital, wheeas manages take up thei esevation wage outside the industy. Manages have the option to subsequently etun when the industy ecoves. The value of manages outside option is theefoe detemined not only by the outside esevation wage, but also by the value of the embedded option to etun to the industy. With sepaation of equity and human capital, net debt acts as a balancing vaiable. Highe debt levels benefit equityholdes because fo evey dolla of debt aised, equityholdes need to contibute one dolla less of thei own money, while at the same time the constaining effect of inceased inteest epayments is shaed with manages. A highe debt level obviously hams manages as it educes the fee cash flows to be shaed. In an industy whee human and equity capital ae supplied competitively, the equilibium debt level ensues that the supply of human capital and equity capital match each othe. The esulting net debt level deceases (inceases) with the cost of investment in human (physical) capital and can become negative fo human capital intensive industies. Negative debt ceates the mio effect of standad debt: fo evey exta dolla of negative debt, equityholdes in effect put up a full dolla woth of high yield liquid assets, but they only captue a faction of the inteest that these assets subsequently geneate. Why can a negative net debt taget aise? Wheeas the fim owns physical capital, it has no popety ights ove human capital that can leave the fim at any time. 4

6 Theefoe the fim cannot issue tadeable claims like debt o equity diectly against tansfeable human capital. It is this asymmety between human capital and physical capital that can lead to a negative net debt taget. Manages only invest in human capital if they expect to get a fai etun ex post. In human capital intensive industies equityholdes theefoe contibute a net suplus of cash (i.e. negative net debt) that geneate ents to be shaed with manages. Competition ensues that the efficient industy output level is achieved fo as long as the optimal net debt level emains below the fim s liquidation value (i.e. the debt is fully secued). In this case both equityholdes and manages get the efficient compensation ate in booms and ecessions. Inefficiencies aise when the fim equies a lot of physical capital and elatively little human capital. In that case fims would like to put in place a high debt level that is not fully secued by the fim s assets in liquidation in ode to educe fee cash flows. Howeve, isky debt bings with it two souces of inefficiency: the standad Myes (1977) debt ovehang poblem and deadweight bankuptcy costs. These two costs deteioate the tems at which equityholdes can aise debt financing fo the fim. As a esult, fims may decide instead to cap the debt level to the value of the fim in liquidation, so as to keep the debt safe. The cost of unde-leveage is that manages can extact moe than thei fai shae of ents, which leads to undeinvestment in booms. If the investment in human capital is sufficiently lage then the cost of unde-leveage is smalle than the costs associated with isky debt. If, howeve, manages contibute vey little human capital then the cost of undeleveage is lage than the cost associated with isky debt, and fims theefoe adopt a debt level that exceeds the liquidation value of the fim. Even though all fims ae ex ante identical, unde-collatealized debt intoduces heteogeneity in fims capital stuctue. Some fims (i.e. the second moves into the industy) adopt a highe debt pincipal, have a highe maket leveage and default in ecession. Othe fims (i.e. the fist moves) adopt a lowe debt level, suvive in ecession and theefoe avoid bankuptcy costs. The tadeoff between bankuptcy costs and manageial ent captue induces heteogeneity in capital stuctue in a simila fashion as in Maksimovic and Zechne (1991), whee fims tade off the tax advantage of debt against the agency costs of debt. Manages of undeleveed fims captue excess ents in booms. These excess ents 5

7 can be patially clawed back in ecession when manages of undeleveed fims accept a salay ate that is below thei outside esevation wage. These manages ae willing to stick with the fim in ecession, because by doing so they enjoy again excess ents once the economy evets to a boom. What ae the fictions that allow manages to captue excess ents in a competitive labo maket? It is the combination of bankuptcy costs and manageial wealth constaints. Bankuptcy costs alone ae not sufficient because in a competitive labo maket unconstained manages would compete away all excess ents by co-investing in physical capital upon joining the fim. Since manages claim cannot be taded it is neithe possible fo an investo to co-invest on manages behalf. The esult has impotant implications. Fo example, excessive compensation in the banking secto is often attibuted to the scace supply of human talent. While scacity may be a contibuting facto, ou esult shows that the ownes of tansfeable human capital can captue excess ents in highly leveed industies even when labo makets ae competitive. We eview below a numbe of papes that have studied the link between capital stuctue and human capital. None of them has analyzed net leveage and, as such, these papes do not explain why some fims adopt a negative net debt taget. In fact, thee is no ole fo cash in these models. Anothe cucial diffeence is that we conside tansfeable human capital. Existing papes eithe explicitly assume human capital to be fim-specific (o elation-specific) o simply emain silent about outside oppotunities fo manageial human capital. Eithe way, human capital is tied to the fim making it optimal open fo the fim to issue some debt. We show that as a fim elies inceasingly on tansfeable human capital, its net debt position becomes negative and its equity claim is inceasingly backed by cash on the fim s balance sheet. In the limiting case whee only tansfeable human capital is equied (and no physical capital), we could end up with a cash-only fim that is all-equity financed esulting in an NDR of -1. On the othe hand, a fim whee manages contibute no human capital whatsoeve could be 100% debt financed with an NDR of 1. Unlike existing papes we also endogenize the value of equityholdes and manages outside options and explain how outside options affect payout, manageial compensation and capital stuctue. Hat and Mooe (1994) conside an entepeneu who needs to aise finance fom 6

8 an investo, but cannot commit not to withdaw his human capital fom the poject. They show that the theat of epudiation means that some pofitable pojects will not be financed. This type of undeinvestment does not occu in ou model because the availability of pofitable pojects would induce moe individuals to invest in human capital and offe thei sevices. The tansfeable natue of human capital in ou model is a double-edged swod fo manages: while it allows manages to withdaw and tansfe thei human capital elsewhee, it also means that othe people can be called in to fill thei seat. Competition between manages theefoe estoes efficiency in ou model, but insufficient enty in booms can esult fom anticipated bankuptcy costs and manageial wealth constaints. Jaggia and Thako (1994) study the link between capital stuctue and investment in fim-specific human capital (o elation-specific capital, moe geneally). High leveage inceases the likelihood of fims going bankupt and employees losing thei job. High leveage may theefoe undemine employees incentives and popensity to invest in fim-specific human capital, esulting in a loss of efficiency that can be taded off against a debt tax shield. Ou model does not equie taxes, and manages cannot be held up ex-post because human capital is tansfeable in ou model. 7 Cucially, since fim-specific capital is tied to the fim, it does by itself not lead to a negative net debt taget. In othe wods, thee is no explicit ole fo cash in Jaggia and Thako (1994). Fim-specific human capital is subject to a sevee holdup poblem, and enfoceable contacts may be equied to potect employees. Not supisingly, Jaggia and Thako (1994) adopt a contactual appoach. In contast, ou equilibium shaing ule between equityholdes and manages is suppoted by a self-enfocing implicit contact in which debt acts as a balancing vaiable. The idea that capital stuctue can affect implicit contacts was put fowad by Titman (1984) who showed that appopiate selection of capital stuctue assues that incentives between the fim and its stakeholdes (such as wokes, customes and supplies) ae aligned so that the fim implements the ex-ante value maximizing liquidation policy. Related papes show how debt povides a bagaining advantage to equityhold- 7 Muphy and Zabojnik (2007) pesent pesuasive empiical evidence that the incease in manageial compensation ove the peiod can be explained by an incease in the impotance of tansfeable skills (as opposed to fim-specific knowledge) in managing the moden copoation. 7

9 es when bagaining with wokes (eg. Baldwin (1983), Peotti and Spie (1993) and Dasgupta and Sengupta (1993)) o when negotiating with a supplie (eg. Hennessy and Livdan (2009)). Fo a detailed discussion of implicit contacts and the elated liteatue, we efe to Hennessy and Livdan (2009). Bek, Stanton, and Zechne (2010) develop a dynamic continuous-time model that exploes the link between human capital and capital stuctue within an economy with competitive capital and labo. They identify the negative effect of bankuptcy on the welfae of wokes as the key component of indiect bankuptcy costs. To compensate isk-avese wokes fo a highe isk of bankuptcy, highly leveed fims offe highe compensation. Unde the assumption that capital is less isky than labo, moe labointensive fims should have lowe leveage. Human capital is not tansfeable and net leveage is always positive in thei model. In ou model highe ents do not esult fom isk avesion but fom the combination of bankuptcy costs and manageial wealth constaints. Finally, some papes conside mechanisms othe than capital stuctue to induce elation-specific investment such as owneship (Hat and Mooe (1990)), egulation of access to citical esouces (Rajan and Zingales (1998)), dispesed owneship stuctue (Bukat, Gomb, and Panunzi (1997)) and (weak) govenance (Achaya, Gabao, and Volpin (2010)). The stuctue of the pape is as follows. In section 2 we pesent the model in its most basic, static fom. It shows that the pape s key esults equie only two key assumptions: tansfeable human capital and manageial wealth constaints. It allows the eade to appeciate how the esults ae affected by the subsequent intoduction of uncetainty, bankuptcy costs and outside options in sections 3 and 4. Section 3 deives the fist-best investment policy in a dynamic, competitive industy whee fims ae un by owne-manages. Section 4 analyzes the optimal investment policy with sepaation of equity capital and human capital. We deive closed fom solutions fo the optimal debt policy, payout policy and manageial compensation, and we discuss efficiency implications. Sections 5 and 6 pesent the pape s empiical implications and conclusions, espectively. 8

10 2 The static model Conside an industy populated with atomistic fims that each poduce a flow of one infinitesimal unit of output in continuous time. Let Q denote the total mass of industy output. 8 Each fim s pofit ate is given by π(q). In this section π(q) is static in pepetuity. All agents ae isk neutal. The isk-fee ate of inteest is denoted by. Fims need both physical capital and human capital to be opeational. Investment in physical capital costs a fixed, exogenous amount I (pe infinitesimal unit of output, and theefoe pe fim). I includes investment in tangible assets such as plant and equipment, as well as intangible investment expenditue such as maketing. Each fim has one manage who has to invest a fixed, exogenous amount H in human capital. 9 The cost H can be thought of as investment in time, education, taining, knowledge, netwoking and expeience necessay fo unning the fim. Impotantly, this investment, while sunk, only needs to be made once. In othe wods, should a manage leave the fim and join anothe fim within the industy, then thee is no need fo he to incu the investment in human capital again. Human capital is theefoe pefectly tansfeable in ou model. Manages who do not get hied can fall back on thei oppotunity wage ate w outside the industy. Assume fist a fictionless Modigliani and Mille (M&M) envionment. Consequently, the fim value V = π(q) is independent of the amount of outstanding debt D, making capital stuctue ielevant. Let us assume next that manages cannot povide the physical capital because of wealth constaints. The physical capital is financed by (pepetual) debt and equity. This foces the owneship of human capital and physical capital to be sepaated. Assume that equityholdes and manages claim ae, espectively, given by E = η(v D) and M = (1 η)(v D), whee the shaing ule η is detemined by the paties elative bagaining powe and whee D denotes the outstanding debt pincipal. Debt is a senio claim on the fim s assets. Investing in physical capital and in human capital is a positive investment fo 8 Fo a moe detailed desciption of how atomistic fims ae modeled in a dynamic, competitive industy, see Leahy (1993), among othes. 9 The manage is, in pactice, a metapho fo a team of manages. 9

11 equityholdes and manages, espectively, if and only if: E = η (V D) (I D) 0 and M = (1 η) (V D) H w 0 I ηv D and D V H+ w 1 η 1 η If the oveall NPV of the investment is positive (i.e. V I + H + w ) then a debt level that is acceptable to both paties always exists. A highe debt level unambiguously benefits equityholdes and huts manages. A sufficiently high level of human capital H foces the net debt level to become negative. Negative net debt means that equityholdes not only finance the physical assets, but on top contibute a (net) cash suplus equal to D. This cash is added to the fim s assets so that the fim s total net asset base to be shaed between both paties is now inceased to V D (> V ). Existing capital stuctue theoies take assets (and cash in paticula) as given and then detemine how optimally to finance these assets. Ou theoy says that copoate cashholdings can be endogenous to the capital stuctue decision. This esult follows diectly fom the non tadeable and fleeting natue of human capital. In the absence of popety ights on human capital, manages cannot be tied to a single fim. As a esult the fim cannot finance the investment in human capital by issuing tadeable claims against it. This explains why manages bea the cost of tansfeable human capital and why fims need cash to attact and etain human capital. So fa, ou theoy meely povides a ange of feasible debt levels. To pin down a unique debt level we need to intoduce additional assumptions. One could, fo example, assume that physical capital is vey limited in supply (e.g. a unique piece of land, a patent o a licence) but that human capital is abundant. In that case equityholdes would set D at the highest possible level that still satisfies manages paticipation constaint. Analogously, if human capital is scace elative to the supply of equity capital then competition between equity povides may esult in the lowest debt level at which equityholdes beak even, ceating space fo manageial ents. Limited supply of physical o human capital may also lead to insufficient enty ( undeinvestment ) into the industy. The effects of estictions on the supply side ae faily well undestood, and we theefoe adopt the following assumption: Assumption 1 The supply of equity capital and human capital is competitive. The assumption implies (in the absence of any othe fictions) that E = I D and 10

12 M = H + w. In othe wods, equityholdes and manages just beak even and eceive a competitive ate of etun on thei investment. Solving this system of beak-even conditions pins down the fim s opeating value (V ) and net debt value (D) in industy equilibium: V = I + H + w and D = I ( ) η ( H + w ) 1 η Assume that π (Q) < 0, π(0) = and π( ) 0. These conditions ensue that at all times thee is a unique, stictly positive level of industy output Q which is the solution to π(q) = V. The competitive manageial compensation ate is given by s = M = (1 η)(v D). Using the solutions fo V and D esults in the following poposition: (1) Poposition 1 In a static envionment the debt (D) taget, fim pofits (π) and manageial compensation ate (s) ae given by: D = I ( ) η ( H + w ) 1 η π(q) = (I + H) + w (3) (2) s = w + H (4) Manages and equityholdes eceive the competitive etun on thei investment. The efficient industy output level (fom a welfae viewpoint) is achieved. The poposition implies that the net debt taget is positively elated to the investment in physical capital (I) and negatively elated to the investment in human capital (H). While we assume thoughout the pape that all investment in physical and human capital happens upfont, this is not stictly necessay. Suppose, fo example, that an unanticipated positive industy development allows all fims to expand povided that they invest an exta I and H in physical and human capital, espectively. Unde pefect competition, we get that the change in the fim s opeating value and net debt ( ) level ae given, espectively, by V = I + H and D = I H. If only investment in physical capital is equied (i.e. H = 0) then the additional investment is fully debt financed, i.e. D = I. The financing policy of fims that 11 η 1 η

13 invest pimaily in physical capital theefoe esembles a stict pecking ode policy. If, howeve, only investment in human capital is equied (i.e. I = 0) then the fim ( ) issues equity to educe net debt, i.e. E = H = D. Fims that need to η 1 η attact tansfeable human capital theefoe issue equity. 10 Debt does not need to be fixed once and fo all. If cicumstances change in favo of manages (equityholdes) then the debt level would have to be educed (aised) in ode to keep both paties on boad. The esults in poposition 1 theefoe do not ely on any fom of pe-commitment. It is impotant to stess that the esults in poposition 1 (and all futue popositions) neithe depend on whethe equityholdes o manages set debt. Poposition 1 implies that the fim s total assets, equity value and manageial claim value incease with the absolute amount invested in human capital. This is not supising. A moe inteesting question is to see how these entities change with human capital and physical capital intensity, which we define espectively by h H+ w and V i I. Note that i + h = 1 by constuction. Let us next standadize the fim s claim V values by defining Ẽ E V, D D V, M M V and Ṽ V V = 1. This allows us to expess fims maket value balance sheet as a function of physical capital intensity i (0 i 1). Fims with positive net debt (D 0) Fims with negative net debt (D < 0) ( ) Ṽ = 1 D = i η η Ṽ = 1 Ẽ = (1 i) 1 η 1 η ( ) η Ẽ = (1 i) D = η i M = 1 i 1 η 1 η M = 1 i Ṽ D = 1 i 1 η Ẽ + M = 1 i 1 η Net debt is positive (negative) if i η (i η). In othe wods negative net debt aises if equityholdes contibution in tems of physical capital falls shot of thei elative bagaining powe. The net debt level addesses this imbalance by focing equityholdes to contibute cash in ode to incease the pie to be shaed between manages and equityholdes. 10 Note that an industy shock that does not involve additional investments (i.e. H = I = 0) does not esult in net debt changes (i.e. D = 0). Instead, a positive (negative) industy shock is absobed by industy enty (exit). We teat this case in detail in next sections. 12

14 The fim s equity maket capitalization deceases (inceases) with the degee of physical (human) capital intensity. Inteestingly, while the total (scaled) maket value of the assets is constant and given by Ṽ = 1 fo fims with positive net debt, the value of total assets Ṽ D = 1 i exceeds 1 and deceases (inceases) with physical (human) 1 η capital intensity when net debt is negative. This means that, all else equal, human capital intensive fims have lage balance sheets than physical capital intensive fims as a esult of accumulated cash. In the limiting case whee the fim is 100% human capital intensive (i.e. i = 0) we obtain Ẽ = D = η and M = Ṽ. The fim appeas like a cash-only fim whee 1 η the cash has been all-equity financed. The othe pola case whee the fim is 100% physical capital intensive (i.e. i = 1) esults in a fim that is 100% debt financed (i.e. Ṽ = D and Ẽ = M = 0). Since manages make zeo investment in human capital, only 100% debt financing pevents them fom getting a fee lunch. The maket value balance sheets lead to the following net debt atios: Ou NDR definition adjusts leveage fo the pesence of inside equity, and is simila to the one adopted by Lambecht and Myes (2008). The definition implies that debt is a pio claim to manages. A moe taditional leveage definition such as D D E+D (instead of ou D+E+M ) implicitly assumes that manages claim is senio to debt and teats payments to human capital as opeating costs. In othe wods, taditional capital stuctue models assume that opeating pofits π (and theefoe V ) ae measued net of wages, i.e. V = D + E (instead of V = D + E + M). 13

15 NDR = D V = D D+E+M = i η 1 η if D 0 (5) NDR = D V D = D E+M = i η 1 i if D 0 (6) The NDR unambiguously falls with equityholdes bagaining powe η. A highe η allows equityholdes to extact a highe faction of fee cash flows ex post, and theefoe equityholdes must contibute moe funds ex ante to compensate. Given that i [0, 1] it follows that NDR [ η, 1] with 0 η 1. In contast, taditional leveage measues based on debt (athe than net debt) fall within the [0, 1] inteval and lump all fims with negative net debt togethe in the zeo leveage categoy. This left-censoing leads to a substantial loss of infomation and may explain the widespead occuence of zeo-leveage fims. In summay, ou theoy of net debt is based on two key assumptions: 1) manages ae wealth constained, leading to a sepaation between ownes and manages and 2) human capital is tansfeable. The esults seem to suggest that the efficient outcome should pevail even with sepaation between equityholdes and manages. This outcome depends, howeve, on all othe M&M assumptions being satisfied. As such, ou baebone theoy of capital stuctue ignoes two fictions that have shown to be impotant deteminants of debt tagets, namely taxes and bankuptcy costs. We ignoe taxes in this pape because it tuns out that taxes do not add any new insights. Instead we focus on bankuptcy costs in conjunction with economic uncetainty. The potential closue of fims in a ecession aises inteesting new questions egading the ole of equityholdes and manages outside options when the fim is boken up and how these options affect industy output, copoate payout and manageial compensation ove the business cycle. In what follows sections 3 and 4 intoduce uncetainty and outside options into the model. Section 3 deives the optimal decision ules fo the owne-manage case wheeas section 4 consides the case whee equity capital and human capital ae sepaated. 14

16 3 The dynamic model with owne-manages At any moment in continuous time the industy can be in one of the following two states: boom o ecession. When the industy is in the boom (ecession), ecession (boom) aives accoding to a Poisson pocess with paamete λ (λ). Each fim s pofits in booms and ecessions ae given by π(q) and π(q), espectively, whee Q (Q) denotes the industy output in booms (ecessions). Fo a given industy output level Q, fims enjoy highe pofits in booms than in ecessions, i.e. π(q) > π(q). Futhemoe, fim pofits ae deceasing in the total industy output (π (Q) < 0 and π (Q) < 0). Fo analytical convenience, we assume that π(0) = π(0) =, π( ) 0, π( ) 0 and that Q : π (Q) < π (Q). These conditions ensue that at all times thee is a unique, stictly positive level of output. The stock of physical capital can at any time be liquidated fo a constant amount L, should the fim wish to leave the industy. In ode to ule out the existence of a money machine we assume that I L. I L epesents the intangible component of the investment (e.g. maketing expenses). The manage s oppotunity wage ate outside the industy is w and w duing booms and ecessions, espectively. 12 The basic model famewok is summaized in figue Some building blocks fo valuing claims Befoe we solve fo the owne-manages investment policy in industy equilibium, we intoduce the following poposition that povides the main building blocks fo ou futue valuation poblems (poofs ae given in the appendix). Poposition 2 (a) The value of a claim that pays 1 dolla the fist time when the economy switches fom a boom (ecession) to a ecession (boom) equals δ λ +λ ) λ (δ +λ 12 To avoid a pevese situation whee manages want to ente in ecession and leave in booms, we make the easonable assumption that manages esevation wage is highe in booms than in ecessions (i.e. w w). 15

17 (b) The value of a claim that pays a cash-flow ate π (π) fo as long as the cuent boom (ecession) lasts, and nothing theeafte, equals π ( π ) +λ +λ (c) The value of a pepetual claim that pays a cash flow π duing booms and π duing ecessions equals: V s (Q, Q) π(q) V s (Q, Q) π(q) (1 p) + π(q) p when cuently in a boom (1 p) + π(q) p when cuently in a ecession (7) whee p λ and p +λ+λ λ +λ+λ The valuation fomulas fo V s and V s have simple, intuitive intepetations. Fo example, V s is a weighted aveage of the pepetuities π and π, whee the fome (latte) pepetuity denotes the pesent value of eceiving the cash flow π (π) foeve. 13 The weights ae given by (1 p) and p, whee 0 p = λ +λ+λ 1. If the likelihood of a switch to a ecession is zeo (λ = 0 and hence p = 0) then V s simply equals π. As the hazad of switching fom a boom to a ecession becomes extemely lage compaed to the hazad of switching fom a ecession to a boom, the claim value V s conveges to π. 3.2 Fist-best investment policy We now study enty and exit decisions in a competitive industy whee each fim is un by an owne-manage who povides both the equied physical capital (I) and human capital (H). This benchmak case assumes that manages ae not wealth constained. Consequently, debt has no ole to play. The oppotunity cost to each investo of not investing in human capital is the oppotunity wage ate that could be eaned outside the industy. Should a potential owne-manage decide neve to invest then statement (c) in poposition 2 implies that the value of he claim in booms, W, and in ecessions, W, is given espectively by: W = w (1 p) + w p and W = w (1 p) + w p 13 We dop the agument of π (π) if doing so does not intoduce ambiguity. 16

18 Conside next an owne-manage who opeates in the industy duing booms, but leaves the industy duing ecessions. This type of owne-manage incus a one-off investment cost H in human capital. She pays I at the stat of each boom and eceives cash flows at a ate π duing each boom. She also eceives the liquidation value L at the stat of each ecession and he oppotunity wage ate w duing ecessions. Finally, an owne-manage who opeates in the industy duing booms and ecessions incus a one-off investment cost H and I at the stat of the fist boom, and eceives cash flows π (in booms) and π (in ecessions) theeafte. We focus in this pape on the case in which some fims leave in ecession. 14 We theefoe impose the following condition thoughout the pape (the deivation of this condition is given in the poof of poposition 3): Assumption 2 Demand shocks ae sufficiently high such that some fims leave in ecession, i.e.: π( Q) π( Q) > (I L) ( + λ + λ ) + w + H 1 p w (8) whee Q is the solution to V s ( Q, Q) = I + H + W. How big demand shocks have to be depends on the othe model paametes, such as the sunk cost of investment in human (H) and physical (I L) capital. Highe sunk costs discouage exit and theefoe need to be accompanied by elatively highe demand shocks fo exit to occu. One can show, fo example, that thee exists a citical theshold H such that exit occus fo H < H and no exit occus fo H H (holding all else constant). One can pove (see appendix) the following poposition: Poposition 3 The fist-best industy output in booms (Q) and ecessions (Q) ae the 14 The teatment of the case fo which no fims leave in ecession is available fom the authos upon equest. 17

19 solution to the following equations: π(q) = [ I + λ (I L) ] + [ w + H ] 1 p π o (L) (9) = chage fo physical capital + chage fo human capital π(q) = [ L λ (I L)] + w π o (L) (10) = chage fo physical capital + chage fo human capital The value of suvivos and leaves in espectively booms and ecessions ae: V s (Q, Q) = V l (Q, Q) = I + H + W and V s (Q, Q) = L + W + δ H (11) whee the subscipts l and s efe to fims that leave and suvive in ecession, espectively. The poposition gives simple, intuitive expessions fo the equilibium pofit ates in booms and ecessions. The equilibium pofits can be decomposed in a chage fo physical capital and a chage fo human capital. Duing booms the chage fo physical capital equals the oppotunity cost of the capital invested ( I) plus a isk pemium fo the hazad of ecession (λ (I L)). Convesely, duing ecessions the chage fo physical capital equals the oppotunity cost of liquidating the fim ( L) minus a discount fo the hazad of economic ecovey. Duing booms the chage fo human capital consists of the oppotunity wage w ( ) plus a chage equal to H = H 1 + λ fo the investment in human capital. In 1 p +λ the limiting case whee the industy stays in a boom foeve (λ = 0), the equied ate of etun on H is just the isk-fee ate. If the hazad ate of switching fom a boom to a ecession is stictly positive (λ > 0) then the equied ate of etun inceases by λ, which eflects the discounted value of fogoing H duing ecession +λ ( H ) times the hazad ate of a ecession aiving (λ) when the economy is in a boom. +λ Since manages that lose thei job in ecession meely ean the oppotunity wage w, the longe (shote) ecessions (booms) ae expected to last, the lage pofits have to be duing booms to ecove the investment in human capital. Conside the limiting case whee a ecession is expected to last foeve (λ = 0), once aived. In that case 18

20 human capital becomes useless fo those manages that leave the industy, and as a esult the equied ate of etun on human capital becomes H ( + λ ) : the inteest ate is simply augmented by λ, whee λ can now be intepeted as a isk of uin. Unlike physical capital, human capital cannot be taded. Consequently, it cannot be liquidated in ecession. Instead, it tempoaily leaves the industy and etuns in booms. This diffeence explains the asymmety in the expessions fo the chage fo human and physical capital. 4 The dynamic model with sepaation of equity and human capital We now intoduce sepaation between owneship of human capital and equity capital. As was shown in section 2 debt now acts as a balancing vaiable between equityholdes and manages. The following assumption fomalizes the concept of net debt and specifies the pioity stuctue at closue among the fim s stakeholdes: Assumption 3 The fim s net debt, D, is defined as the diffeence between the fim s debt liabilities and its liquid assets. The fim pays (eceives) a coupon flow D fo positive (negative) D until the fim is closed. 15 If net debt is negative (D < 0) then equityholdes eceive upon closue L plus the liquid assets D (i.e. L D). If net debt is positive then bondholdes have a fist claim (up to D) on the assets L in liquidation, with equityholdes having the entie esidual claim (L D) +. If the fim defaults on its debt obligations (D > L), then bankuptcy costs amount to φl. If D is positive then the fim s net debt position is equivalent to a standad pepetual debt contact with coupon D that is teminated when the fim defaults. We assume 15 We have consideed the case whee the fim invests in cash holdings that geneate a etun ρ less than. The analysis and esults ae available upon equest and have been omitted in the inteest of space. 19

21 that the debt is secued by the fim s physical assets, which means that at closue bondholdes eceive min{d, L (1 φξ)} (with ξ = 1 if D > L, and ξ = 0 othewise), wheeas equityholdes eceive (L D) +. This payoff follows fom the fact that upon default bondholdes liquidate the fim (like equityholdes, bondholdes ae unable to un the fim as a going concen). Equityholdes default on the debt contact if D > L. Bankuptcy costs associated with default ae a faction φ of the liquidation value L and educe bondholdes payoff. 16 The fim needs both physical capital (owned by shaeholdes) and human capital (owned by wealth constained manages) to be opeational. 17 No cash flows ae geneated while eithe paty abstains. It is this mutual cost of a stalemate that foces both paties to negotiate an ageement to shae the fee cash flows. When economic conditions deteioate and fee cash flows plummet, it may no longe be optimal fo equityholdes and manages to stay togethe within the fim. Each paty can pemanently abandon the fim: equityholdes can liquidate the physical assets, wheeas manages can esign to eceive thei outside esevation wage. While manages cannot liquidate thei human capital, they can e-ente the industy at some futue point without having to incu the investment in human capital again. Manages option to leave the industy in ecession theefoe embeds an option to etun in booms. We adopt the standad assumption that the cash flows geneated by the fim ae obsevable but nonveifiable. 18 In this pape we theefoe do not deive explicit contacts but self-enfocing ageements and emuneation that, at each moment in time, ae the outcome of bagaining between the equityholdes and the manages (also known 16 Since bankuptcy imposes deadweight costs on the lendes, this opens the doo fo stategic debt sevice o estuctuing post default. This issue has, howeve, been studied extensively in the liteatue (see e.g. Andeson and Sundaesan (1996) and Mella-Baal and Peaudin (1997), among othes). We theefoe do not include this possibility in the analysis. 17 This assumption does not exclude the possibility of manages being awaded shaes in the company. In that case manages would simply maximize a weighted aveage of thei manageial claim and equity stake. 18 See Hat and Mooe (1990, 1994), and the lage liteatue that elates to these papes. 20

22 as implicit contacts ). 19 We now need to decide on a bagaining model to detemine how fee cash flows ae shaed between equityholdes and manages. The main bagaining models used in the finance liteatue ae: the Nash (1950) bagaining model and the Rubinstein (1982) bagaining model (and thei vaiations). In the Rubinstein game the altenative oppotunity is modeled as an outside option whee a paty must quit the bagaining table pemanently in ode to take up the altenative oppotunity. Fo example, the manage must pemanently esign in ode to take up a post elsewhee. In the Nash-bagaining game the altenative oppotunity is modeled as a theat point. The undelying assumption is that a paty can collect its theat point payoffs fo as long as a bagaining ageement has not been eached. Fo example, the manage takes up a tempoay post elsewhee while bagaining takes place. 20 The diffeence between an outside option and a theat point esults in a diffeent bagaining solution. While in the Nash bagaining solution each paty s shae is stictly inceasing in the value of its theat point, in the Rubinstein bagaining solution each paty gets the best (i.e. the maximum) of his outside option and the bagaining shae that he would obtain in the absence of outside options. The outside option thus acts as a lowe bound o constaint on the equilibium shae. Since equityholdes decision to liquidate and manages decision to esign ae pemanent and ievesible we have a two playe game between equityholdes and manages whee each paty has an outside option. The value of this outside option in booms (ecessions) is denoted by o e and o m (o e and o m ) fo equityholdes and manages, espectively. We focus on the limiting case whee the bagaining inteval goes to zeo and bagaining can take place continuously. As such, ou game is a continuous-time vaiation of the Shaked and Sutton (1984) and Binmoe, Rubinstein, and Wolinsky (1986) models of bagaining with outside options and isk of beakdown duing nego- 19 Implicit contacts ae quite common. Gillian, Hatzell, and Paino (2009) find that less than half of the S&P 500 CEOs ae employed unde explicit ageements (ageements that specify the tems of the employment elationship) athe than implicit ageements. 20 Malcomson (1997) and Chiu and Yang (1999) discuss in detail the diffeences between the outside option pinciple and the theat point pinciple. 21

23 tiation. 21 Its solution is a faily standad esult in the bagaining liteatue and given below. 22 Result 1 Duing booms the compensation ate fo human capital (s) and the payout ate to equityholdes (d) both equal one half of the fee cash flows: s = d = π D 2. Duing ecessions the compensation and payout ate ae such that equityholdes and manages outside option exactly bind (i.e. E = o e and M = o m ). Duing booms, equityholdes and the povides of human capital each get half of the pofits afte inteest epayments if net debt is positive (D 0), o half of the combined value of opeating pofits and the inteest geneated by liquid assets if net debt is negative (D < 0). This popety is valid iespective of whethe any outside options bind in ecession, o whethe the debt is isky. This does, howeve, not mean that the payout to equityholdes and manages in booms is independent of what happens in ecession o of how much each paty invests. We show below that the equilibium pofits π and the optimal debt level D ae vey much influenced by the othe model paametes. In equilibium, fee cash flows ae equally shaed in booms (i.e. η = 0.5) because outside options do not bind in booms and both paties ae othewise symmetic (e.g. they have the same discount ate). standad featue of Rubinstein style bagaining models. 23 Equal shaing is unde those cicumstances a Impotantly, the esults that follow do not depend in any fundamental way on the shaes being exactly equal. 21 Ou setting also includes a isk of beakdown duing negotiations. If the economy switches egime duing the bagaining inteval then each paty eceives at the end of that inteval its claim associated with the new egime. If the fim suvives unde the new egime then bagaining (ove the new cashflow steam) can cay on, but if the fim cannot suvive unde the new egime then each paty eceives the value of its outside option unde the new egime. 22 A full deivation of the solution is available fom the authos upon equest. This deivation also shows how the bagaining paamete η can be endogenized in moe geneal tems. A continuous-time vaiation within a deteministic famewok can be found in Hat and Mooe (1994). 23 Moe geneally, η is a function of each paty s discount ate and the likelihood of negotiations beaking down due to the aival of a ecession. 22

24 As was shown in section 2 ou model and its esults can easily be genealized to the case whee s = η(π D) and d = (1 η)(π D) with 0 < η < 1. In ecession, each paty s claim value equals exactly its outside option value because when the economy switches fom a boom to a ecession fims keep leaving up to the point whee equityholdes and manages ae indiffeent between staying o leaving. 24 Poposition 2 and esult 1 togethe imply that the equityholdes and manages claim values ae given by: E = π D 2(+λ) and E = o e M = π D 2(+λ) and M = o m The above equations detemine the equityholdes and manages claim fo exogenously given pofit levels, debt pincipal and outside option values. We now endogenize the values of these entities. The following poposition states the value of a fim s outside options as a function of its debt pincipal. Poposition 4 In ecessions, the value of equityholdes outside option (o e ) and of manages outside option (o m ) ae given espectively by: o e = (L D) + o m = w (1 p) + [(+λ) I λl(1 φξ) D] It follows immediately fom equityholdes limited liability that thei payoff fom leaving the fim in ecession is given by o e p = (L D) +. The value of manages outside option in ecession, o m, equals the pesent value of the wage ate w that manages get when they leave the industy duing ecession, and the salay ate they eceive when etuning to the industy duing booms. Note that o m depends on the leaves debt level because manages option to leave the industy in ecession includes an option to etun in booms. Consequently, the debt level that new entants subsequently adopt in booms detemines manages futue salay. 24 Stictly speaking it is possible that in ecession only one paty s outside option binds. This scenaio aises when demand shocks ae so small that no fim leaves the maket in ecession. The countepaty that still enjoys a suplus then makes sufficient concessions so as to avoid the othe paty to jump ship. Assumption 2 ules out the possibility of no exit in ecession. 23

25 Amed with ou expessions fo o e and o m we can now solve fo the industy equilibium. We fist deive the claim value of those fims that, in equilibium, leave the maket. To do so we need to pin down the following 3 unknowns: π, s l, and D l (emembe that manages leave the industy duing ecession and theefoe s l = w). s l is detemined by the bagaining solution (i) s l = π D l. Equity capital is supplied competitively, causing equityholdes to beak even upon investment, i.e. (ii) E l = I B l 2, whee B geneally denotes the maket value of debt. This gives an equilibium condition fo π. Finally we need to detemine the debt pincipal D l of fims that leave the industy. Assuming without loss of geneality that equityholdes set debt policy then they choose the fim s debt pincipal D l (o coupon level D l ) so as to maximize thei payoff at investment, subject to the manages paticipation constaint. 25 O, equivalently, D l is the solution to the following constained maximization poblem: max D l { El ( I B l )} subject to M l W + H (12) A highe debt level unambiguously lowes manages claim because debt educes fee cash flows and theefoe manages salay ate s l = π D l (note that an atomistic 2 fim cannot influence π though its debt policy). On the othe hand a highe debt level inceases equityholdes payoff fom investment. Fo evey dolla of debt aised, equityholdes have to contibute one dolla less to the investment, but they shae the pain of the subsequent inteest epayment with manages (since d l = s l ). If equityholdes payoff wee eveywhee monotonically inceasing in the debt pincipal then equityholdes would aise debt up to the point whee manages paticipation constaint becomes binding and D l would simply be pinned down by condition (iii) M l = W + H. We show, howeve, in the appendix that equityholdes payoff E l (I B l ) is monotonically inceasing in D l, except at D l = L, whee thee can be a discete downwad jump if bankuptcy costs ae stictly positive. At D l = L, a maginal incease in the debt level leads to a discete fall in the maket value of the debt, B l, because of the deadweight cost of bankuptcy. Depending on the value of H, this leads to 3 possible egimes fo the optimal debt level: (1) Fo sufficiently high levels of H (i.e. H < H, whee H is defined below) D l is 25 As will become clea, the solution tuns out to be the same iespective whethe equityholdes o manages set the debt level. This point was peviously highlighted in the context of the static model. 24

26 the solution to (iii) M l level D l < L. = W + H and manages paticipation constaint binds at a (2) Fo sufficiently low levels of H (i.e. H < H, whee H is defined below) D l is again the solution to (iii) M l paticipation constaint binds exceeds L, i.e. D l > L. = W + H but the debt level D l fo which manages (3) Fo an intemediate egion (i.e. H H H ) a isky debt level (D > L) could be adopted while still ensuing manages paticipation. Howeve, the gain fom constaining manages is wiped out by the deadweight costs of bankuptcy, which educe the poceeds fom the debt issue in a discete fashion. The debt level is theefoe esticted to (iii) D l = L. By constaining debt to the fim s liquidation value, manages paticipation constaint is no longe binding (i.e. M l > W + H). Only when H is below H does it pay off to issue isky debt and to aise the pincipal by a discete amount ove and beyond L. Why can manages enjoy excess ents (M l > W + H) wheeas equityholdes cannot? Manages cannot commit to taking less than s l of the fee cash flows. Given that manages claim cannot be taded in financial makets (unlike equity) it is not possible fo investos to compete away excess value. Manages can neithe compete away among themselves the excess value because this would equie that they co-invest an amount equal to the pesent value of thei excess ents when joining the fim. Wealth constaints pevent manages fom doing this. We now sketch the deivation of the claim values of those fims that do not leave in ecession ( stayes ). To identify the claim values we need to solve fo 4 unknowns: π, s s, s s and D s. Competitive exit ensues that fims leave up to the point whee both paties outside options ae binding in ecession (i.e. manages and equityholdes ae indiffeent between staying o leaving in ecession): (i) E s = o e, and (ii) M s = o m. 26 The bagaining solution fo booms implies that (iii) π Ds 2. Finally, (iv) E s = I D s because outside equity is supplied on a competitive basis. 27 Conditions (i), (ii) (iii) 26 A situation whee one of the outside options is not binding cannot be optimal when thee is fim exit in ecession. E.g. if M s > o m then manages of fims that ae leaving would be bette off making concessions to equityholdes to stop them liquidating the fim. 27 Note that B s = D s because the debt of suviving fims is safe. 25

27 and (iv) detemine π, s s, s s and D s. 28 Ou analysis assumes that equityholdes set the debt level. Would the esults be diffeent if manages wee to set the debt level? The answe is no. In equilibium equityholdes paticipation constaint is always binding in a competitive equity maket. Equityholdes claim inceases in the debt level. As a esult it is not possible fo manages to educe the debt any futhe without violating equityholdes paticipation constaint. The same debt level is theefoe also constained optimal fom manages viewpoint. In what follows popositions 5, 6 and 7 state and discuss the industy equilibium fo diffeent levels H of investment in human capital. The solution natually splits up in 3 cases: high (H H), intemediate (H H < H ), and low (H < H ) levels of human capital. Poposition 5 If fims ae highly human capital intensive (i.e. if the investment H in human capital satisfies H H) then we obseve egime 1 in which all fims adopt the same isk-fee debt level and some fims leave in ecession. The debt, fim pofits and manageial compensation ae given by: D 1 (L) = D 1s (L) = D 1l (L) = I + λ (I L) w H 1 p = L (H H ) 1 p π 1 (L) = I + λ (I L) + w + H 1 p = πo (L) π 1 (L) = L λ (I L) + w = π o (L) s 1s = s 1l = w + H 1 p whee H is the solution to: and s 1s = s 1l = w w + H 1 p = (I L) ( + λ ) (13) Poposition 5 gives the optimal investment and debt policy when the investment in human capital H is elatively lage (i.e. H < H). We find that all fims adopt 28 We show in the appendix that manages paticipation constaint is always satisfied. 26

28 the same safe debt level (i.e. D s = D l D o < L). The optimal debt level has a vey simple intepetation. It is the debt level that sets equityholdes (leveage adjusted) payout ate in booms equal to manages salay ate, i.e.: d o (I D o ) + λ (I L) = w + H 1 p so (H). Manages (equityholdes) eceive the efficient salay (payout) ate at all times. The equilibium is identical to the fist-best solution in section 3 whee thee is no sepaation between equityholdes and manages. Full efficiency is achieved thanks to competition and an optimal debt policy that ensues that equityholdes and manages each get a fai etun on thei investment. If a fim equies moe investment in human capital then, all else equal, the level of debt in equilibium is lowe. Fo sufficiently high levels of investment in human capital, net debt gets negative. In paticula, negative debt occus if the sunk investment in human capital (H) and the oppotunity cost of human capital (w) ae sufficiently lage compaed to the sunk cost (I L) and the cost (I) of physical capital. The optimal debt level is deceasing in the fim s liquidation value. This last esult may come as a supise as it implies that leveage is negatively elated to tangibility, which is inconsistent, fo example, with the tadeoff theoy of capital stuctue. Since debt is ovecollatealized (D < L) bankuptcy costs ae, howeve, not an issue. Highe tangibility means simply that equityholdes get moe of thei capital investment back upon closue and, as a esult, ae willing to accept a lowe debt level. We show below that this negative elation between tangibility and leveage is evesed when fims constain thei debt level because of bankuptcy cost consideations. The following poposition descibes the solution fo egime 2, which pevails fo intemediate levels of human capital (i.e. H [H, H [). Poposition 6 Assume that bankuptcy costs ae not too high (i.e. φ < φ, whee φ is defined in poposition 7). If the investment H in human capital satisfies H H < H then we obseve egime 2 in which all fims adopt the same isk-fee debt level L and some fims leave in ecession. The debt, fim pofits and manageial compensation 27

29 ae given by: D 2 (L) = D 2s (L) = D 2l (L) = L π 2 (L) = I + ( + 2λ ) (I L) > π o (L) and π 2 (L) = L λ (I L) + w = π o (L) s 2s (L) = s 2l (L) = ( + λ ) (I L) and s 2s = s 2l = w whee H is the solution to: w + H 1 p = (I L) ( + λ ) λφl (14) Regime 2 only occus if bankuptcy costs ae stictly positive (i.e. H < H φ > 0). Regime 2 aises fo intemediate levels of human capital (i.e. if H H < H ). The optimal debt policy fo all fims is to adopt a debt level D s = D l = L. By constaining the debt level to L, manages investment in human capital has a stictly positive NPV (i.e. M s = M l > W + H). Bankuptcy costs make it, howeve, not optimal to aise debt levels. Equityholdes beak even in booms and ecessions. Since D = L, equity has a zeo (o abitaily small) value in ecessions. Manages salay ate exceeds the efficient compensation ate duing booms, and equals the outside wage ate duing ecessions. Equityholdes payout ate equals the efficient ate at all times. The total pofit ate in booms exceeds the fist-best pofit ate (π > π o ), which implies that thee is insufficient enty in booms. The industy output level is, howeve, efficient in ecessions. Poposition 7 pesents the solution fo low levels of human capital (i.e. H < H ). Poposition 7 Assume that bankuptcy costs ae not too high (i.e. φ φ ). If H < H then we obseve egime 3 in which some fims adopt a high debt level and some fims adopt a lowe debt level. The fome fims leave the industy in ecession. The debt value exceeds L fo all fims. The debt, pofits and manageial compensation 28

30 ae given by: D 3l (L) = I + λ (I L) + λ φ L w H 1 p = L + (H H) + 2 λ 1 p φl [ 1 D 3s (L) = ( + λ) I + λl(1 φ) w H ] = L + (H H) + 2λ 1 p ( + 2λ)(1 p) π 3 (L) = I + λ (I L) + λφl + w + H 1 p > πo (L) π 3 (L) = D 3s λ (I D 3s ) + s 3s = π o (L) + 2 (H H)( + λ + λ) ( + 2λ)(1 p)( + λ) s 3l = w + H and s 3l = w s 3s (L) = + λ + 2λ 1 p [ w + H 1 p ] + λ (I L(1 φ)) s 3s (L) = w λ + λ (s 3s s 3l ) = w λλ ( + λ) > s 3l [ ] (H H) ( + 2λ)(1 p) + φl λλφl + λ φ is the oot to π 1 [π 3 (I, L, H (φ ))] = π 1 [π 3 (I, L, H (φ ))], o equivalently to: π [ 1 I + (I L)( + 2λ) ] [ ] = π 1 π o λλφ L. Poposition 7 states that if the equied investment in human capital is low (i.e H < H ) then all fims adopt a debt level that exceeds L in ode to constain manages in booms. Futhemoe, fims that leave in ecession adopt a highe debt level than suvivos. High leveage pevents manages fom captuing excess ents in booms, but causes these fims to incu bankuptcy costs in ecession. Suvivos, on the othe hand, set thei debt level sufficiently low so that in ecession equityholdes and manages ae indiffeent between staying and leaving. By doing so these fims ae able to issue iskfee debt. Howeve, by constaining the debt level, manages of these fims get excess ents in booms (i.e. s 3s > s 3l ). 29 These excess ents ae patially clawed back in ecession when manages of the suviving fims get paid below thei esevation wage. +λ 29 The tadeoff between bankuptcy costs and manageial ent captue induces heteogeneity in capital stuctue in a simila fashion as in Maksimovic and Zechne (1991), whee fims tade off the tax advantage of debt against the agency costs of debt. In equilibium, some fims issue low amounts of debt, fogoing debt-elated tax shields but committing to the subsequent choice of the less isky poject with highe pe-tax cash flows, wheeas othe fims adopt moe debt, captuing lage benefits but ceating incentives to choose subsequently the iskie poject. 29

31 Manages ae willing to accept this cut because of the pospect of supeio ents in futue booms. 30 While manages of fims that leave in ecession beak even in booms and ecessions, manages of fims that stay have a positive NPV claim in booms (i.e. M 3s > W + H). This means that thee is a fist-move advantage fo manages that ente fist into the industy and it explains why these manages do not leave in ecession, despite being paid below the esevation wage. Fist moves have an inteest to adopt a low debt level because by doing so these fims captue upon investment a positive NPV equal to: E 3s + M 3s + D 3s I W H = M 3s W H > 0 Even though equityholdes of all fims only beak even, the maket capitalization of fist moves is lage (i.e. E 3s = I D 3s > E 3l = I B 3l since B 3l > D 3s ). Undecollatealized debt leads to inefficiencies because it bings with it bankuptcy costs and debt ovehang. The highly leveed fims anticipate futue bankuptcy costs and theefoe equie a highe equilibium pofit ate in booms to compensate. This ceates undeinvestment in booms. Fims that plan to stay in ecession constain thei debt level such that both manages and equityholdes outside option exactly binds in ecession. This lowe debt level gives manages excess ents in booms (s 3s > s 3l = w). These excess ents incease with bankuptcy costs and allow manages compensation λ to be cut in ecession below the esevation wage by an amount (s +λ 3s s 3l ). This povides space fo pofits to be educed in ecession by an equal amount. Bankuptcy costs theefoe ceate an oveinvestment effect in ecession. On the othe hand, the pofit ate π 3 inceases to the extent that D exceeds L. Since equityholdes have limited liability, undecollatealized debt leads to the well known Myes (1977) undeinvestment effect. To summaize, fo values of H just below H the bankuptcy cost effect dominates, esulting in oveinvestment (i.e. insufficient exit) duing ecession, wheeas fo lowe levels of H the debt level adopted is much highe and this causes the debt ovehang effect to dominate in ecession (i.e. too much exit). 30 Fo example, duing the ecent cisis GM s CEO at the time, Rick Wagone, and his countepat at Fod, Alan Mulally, offeed to accept salaies of $1 conditional on the implementation of the US fedeal govenment bailout plan, cf. High pice of a govenment lifeline to US camakes, Financial Times, 12 Dec

32 Regime 3 is deived unde the assumption that some fims leave in ecession. Howeve, as φ inceases the equilibium pofit ate in booms (ecessions) unambiguously ises (falls) (see poposition 7). Consequently, the industy output in booms (ecessions) monotonically falls (ises) as φ inceases. Thee exists theefoe a level φ fo which Q equals Q, and fims no longe leave the maket 31 : bankuptcy costs lowe the fim s liquidation value and, as such, lead to moe hysteesis. Fo sufficiently high levels of bankuptcy costs industy output theefoe emains constant. Typical values fo φ ae, howeve, unealistically high fom an economic viewpoint. 32 We theefoe do not discuss the case φ > φ. 33 Figue 2 illustates and summaizes the pape s main esults. 34 Panel A illustates the negative elation between the debt pincipal, D, and the (sunk) cost of human capital investment, H. The debt pincipal is not a stictly deceasing function of H. The flat segment is due to the pesence of bankuptcy costs. Fo H falling into the inteval [H, H [= [39.06, 53.12[ fims adopt in equilibium the second-best level of debt equal to L. Such a policy allows shaeholdes to avoid bankuptcy costs but is associated with excess ents fo manages. Fo H < H = the benefit of constaining manages dominates the expected bankuptcy costs: fims adopt isky debt that inceases expected bankuptcy costs but allows fo concessions fom manages. The figue confims that fo H < H fims that ae expected to leave the industy in ecession (i.e. the second moves) adopt a isky debt level (D > L) that is substantially 31 One can show that Q(H) Q(H) is minimized at H. Theefoe a sufficient and necessay condition fo no exit to occu fo some H (unde assumption 2) is that φ > φ, whee φ is the oot of Q(H (φ )) = Q(H (φ )), o equivalently the oot of π 1 [π 3 (I, L, H (φ ))] = π 1 [π 3 (I, L, H (φ ))]. A value fo φ always exists, but is not necessaily bounded by 1. Futhemoe, H can be negative. As a esult, a no-exit egion does not always exist fo the set of paamete values that ae economically elevant. 32 Remembe that I L captues the loss with espect to intangible assets. Theefoe 1 φ is the ecovey ate on the tangible assets, L. Fo the paamete values used in figue 2, φ equals 0.463, which is way above the degee of bankuptcy costs that would apply on tangible assets. 33 A full analysis of the case φ > φ is available fom the authos upon equest. 34 The figue is geneated using the following demand functions and paamete values. π(q) = p(q) = aq ɛ b and π(q) = p(q) = aq ɛ b, whee a = 200 and a = 25, b = b = 1 and ɛ = 1.1. Futhemoe, λ = λ = 0.075, = 0.05, I = 200, L = 150, w = 2, w = 1 and φ =

33 highe than thei suviving countepats (i.e. the fist moves). The NDR, is depicted in Panel B. 35 In booms, the NDR (as a function of the cost of human capital investment) follows closely the elation between the optimal debt pincipal and H. The (maket value) NDR diffes acoss fims in the egion in which isky debt is issued because the leaves adopt a highe debt level and incu bankuptcy costs upon exit. In ecessions, suvivos can have a zeo equity value, which means that equityholdes inject cash to keep the fim going. 36 The amount of cash equityholdes ae equied to inject is such that they ae exactly indiffeent between staying o leaving. Fo highly human capital intensive fims the NDR becomes negative. As mentioned befoe, negative NDRs ae a fequent occuence in pactice (see Bates, Kahle, and Stulz (2009)). Panel C plots the equilibium pofit ate. While the pofit ate is (weakly) inceasing with H in booms, this is not eveywhee the case in ecessions because the pofit ate π deceases with H in egime 3. The implications fo industy output ae illustated in Panel D. Fo H H = industy output is at the fist-best level. In the absence of fictions debt is set optimally to equalize the ents of shaeholdes and manages. Fo levels of human capital investment whee shaeholdes constain the debt to be isk fee (i.e. fo H [H, H [ = [39.06, 53.12[), thee is insufficient enty in booms but the efficient level of output in ecessions. The undeinvestment esults fom the fact that in booms manages extact a suplus due to the the level of debt being capped at L. Fo low levels of human capital investment (i.e fo H < H ) we obseve undeinvestment in booms because fims adopt a isky debt level that leads to debt ovehang and deadweight costs of bankuptcy. In ecessions we obseve ove o undeinvestment depending on whethe bankuptcy costs o debt ovehang costs dominate. 37 Notice the jump in Q at H whee the switch fom isky to safe debt occus. At this point oveinvestment in ecessions can be substantial even fo modest levels of bankuptcy costs. Panel E shows that the manageial compensation ate (weakly) inceases as a function of H and is equal to the fai ate of etun on human capital investment as long 35 The maket value NDR is defined as B/V fo D 0 and D/(V D) othewise (cf. section 2). 36 Note that NDR l = NDR = 1 if H = w = w = 0 (see also section 2). 37 Note that if bankuptcy costs ae zeo, undeinvestment in ecessions still occus. 32

34 as H H. Fo H [H, H [ manages eceive excess ents in booms. Fo H < H, manages ae paid below the esevation wage w in ecession. The model pedicts that fo industies with vey low human capital intensity (eg. steel industy) manageial compensation could become negative in ecession. This does not imply that the wealth constained manages ae actually injecting cash in the fim out of thei own pockets. Rathe it means that the povides of human capital make concessions on existing aangements egading job secuity, employe pension contibutions, holidays o social secuity. 38 Howeve, suviving manages ae on aveage still bette off because they enjoy lage excess ents in booms. Finally, panel F plots the payout ate in booms and ecessions. A high debt level (coesponding to low values of H) can lead to a negative payout. Equityholdes ae willing to inject cash into the fim because of the possibility of an economic ecovey. Duing booms the payout ate (weakly) inceases in H and is identical to manageial compensation (as ex-coupon cash flows ae equally split between shaeholdes and manages). In ecessions the payout ate is deceasing in the egion in which leaves adopt isky debt (i.e., fo H < H ) because of falling pofits. A highe investment in human capital equies (all else equal) highe equilibium pofits and a lowe debt level, both of which incease the fee cash flows available fo distibution duing booms. 5 Empiical implications The pape (and popositions 5-7 in paticula) povide a numbe of testable empiical hypotheses. H1: Fims within a given industy have a net debt taget D that is a linea function of 4 vaiables: physical capital (I), investment in human capital (H), the oppotunity cost of human capital (w) and the value of the fim s physical capital upon closue (L): D = (β 1 + γ 1 S) I + (β 2 + γ 2 S) H + (β 3 + γ 3 S) w + (β 4 + γ 4 S) L (15) 38 A notable example in the cuent ecession is the pactice of feezing defined benefit pension schemes to existing membes. Negative ents can also be intepeted as manages contibuting sweat equity (see Lambecht and Myes (2008) fo futhe discussion). 33

35 whee S = 1 fo old fims (fist moves o suvivos ) S = 0 fo young fims (second moves o leaves ) Ou model pedicts a net debt taget. This is a new hypothesis that has not yet been tested in the liteatue. The egession coefficients ae non-linea functions of the maco-economic factos: the isk-fee ate of inteest, and the hazad of booms and ecessions (see popositions 5, 6 and 7). The coefficients can vay accoding to whethe the fim is old (S = 1) o young (S = 0). The fome coesponds to fist moves that suvive ecessions, wheeas the latte elates to second moves that ae expected to leave in ecession. 39 Ou pedictions egading the heteogeneity of capital stuctue ae consistent with MacKay and Philips (2005) who find that entants have a highe financial leveage atio compaed to incumbents, and that leaves exit thei industy much moe leveaged than suviving incumbents. The theoetical esult that ex-ante identical fims can adopt diffeent capital stuctues may help explain the pesistent heteogeneity in fims capital stuctues documented in Lemmon, Robets, and Zende (2008). By scaling all vaiables in (15) by total assets we obtain a egession model with the net leveage as dependent vaiable. 40 The coesponding independent vaiables ae now physical capital intensity, two complementay measues of human capital intensity, and tangibility. 41 Since liquid assets ae netted out against debt liabilities, net leveage is no longe bounded by zeo, but can actually get negative. Net leveage contains moe infomation than the taditional leveage atio that is left-censoed at zeo. 39 To contol fo industy effects one can un the model on fims within a given industy. Fo example, popositions 5 to 7 show that the egessions coefficients vay accoding to the level of human capital intensity (coesponding to egimes 1, 2 o 3). While fims within a given industy ae likely to fall within the same egime because they have simila levels of human capital intensity, this is less likely to be the case fo fims that come fom diffeent industies (say a biotech fim vesus a steel manufactue). 40 Ideally, we want to scale by the maket value of total assets, but this vaiable is not obsevable. One possible poxy is to use the sum of the fim s stock maket capitalization, its debt and the value of all outstanding claims by manages (such as stock options, pension ights etc). 41 The vaiable L is a poxy fo the fim s tangible assets, and is heeafte loosely efeed to as the tangibility vaiable. 34

36 H2: Net leveage is positively elated to physical capital intensity but net leveage of industy suvivos is less sensitive to physical capital intensity than net leveage of industy leaves (β 1 + γ 1 > 0 but γ 1 0). Net leveage is negatively elated to human capital intensity vaiables but net leveage of industy suvivos is less sensitive to human capital intensity vaiables than net leveage of industy leaves (β 2 + γ 2 < 0 and β 3 + γ 3 < 0 but γ 2, γ 3 0). Ou model pedicts that net leveage inceases with physical capital intensity and deceases with human capital intensity. These pedictions ae boadly suppoted by the existing empiical liteatue. Contolling fo a faily compehensive list of taditional capital stuctue deteminants, Qian (2003) finds a negative elation between financial leveage and human capital. She shows that human capital intensity has explanatoy powe in addition to the collateal value of fim assets and the fim s gowth oppotunities. H3: The elation between net leveage and tangibility is negative (positive) if a dolla of exta debt leads to a low o zeo (high) maginal incease in expected bankuptcy costs. In paticula, the elation is negative, i.e. β 4 < 0 (positive, i.e. β 4 > 0) fo high (intemediate) levels of human capital intensity, with γ 4 = 0. Fo low levels of human capital intensity, the elation is positive, i.e. β 4 + γ 4 > 0 (negative, i.e. β 4 < 0) fo suvivos (leaves), and theefoe γ 4 > 0. The hypothesis with espect to tangibility is new and might help explain some conflicting esults in the liteatue egading the effect of tangibility. We know that debt is ovecollateized fo fims that ae elatively moe human capital intensive. Default is theefoe not an issue, and highe tangibility means that equityholdes get moe of thei capital investment back upon closue and, as a esult, ae willing to accept a lowe debt level. Tangibility and leveage ae theefoe negatively elated when debt is ovecollatealized. When fims ae elatively moe physical capital intensive then they wish to adopt undecollatealized debt. Bankuptcy costs may, howeve, discouage fims fom adopting a debt level as high as they would wish, causing tangibility to be positively elated to leveage: highe tangibility means moe collateal and allows fims to issue moe debt without inceasing expected bankuptcy costs. A positive coefficient fo tangibility is theefoe indiect evidence that the fim is constaining debt because 35

37 of bankuptcy cost consideations. Note that tangibility and leveage ae negatively elated fo highly physical capital intensive fims that ae sue to go bankupt in ecession, because an exta dolla of debt does not alte the default pobability and expected bankuptcy costs. H4: A sufficiently high level of human capital intensity leads to negative net debt. Bates, Kahle, and Stulz (2009) epot that the aveage (median) NDR fo US fims has fallen fom 16.5% (17.8%) in 1980 to -1.5% (-0.3%) in The negative tend is petty much monotonic ove time. The pape finds a substantial ise in cash holdings that is linked to an inceasing tend in R&D and a decline in fims net woking capital (paticulaly inventoies) and capital expenditues. The authos conclude that thei findings ae consistent with an explanation fo the change in cash holdings that elies on the pecautionay motive and on changes in fim chaacteistics which affect the demand fo cash by fims. Ou model suggests anothe possible hypothesis that could be exploed, namely that ove the past decades fims have become moe eliant on tansfeable human capital and less on physical capital. This fundamental change in the natue of the fim has been eflected in fims capital stuctue. H5: Net leveage is countecyclical and, theefoe, negatively elated to the fims pofitability. Since fim value is positively elated to pofits, it follows that moe pofitable fims have lowe leveage. Net leveage is countecyclical: it falls in booms and ises in ecessions. These simple pedictions ae in line with the consensus that leveage deceases with pofitability (see Hais and Raviv (1991) and Rajan and Zingales (1995)). H6: Highe sunk costs of physical and human capital (I L and H) educe output volatility but incease pofit volatility. Ou model pedicts that highe sunk costs ae associated with lowe inetia, which tanslates into fewe fims leaving the industy in ecessions. As a consequence, the industy output fluctuates less in the pesence of highe sunk costs (ecall that each fim s output is constant) and economic shocks ae pimaily absobed by the output pice leading to highe pofit volatility (cf. Novy-Max (2011)). 36

38 The effect of sunk costs on pofit volatility feeds though into the volatility of dividend payout and manageial compensation, as highlighted in the following two hypotheses. H7: Manageial compensation and dividend payout ae pocyclical. The volatility of manageial compensation is positively elated with human capital intensity. The volatility of payout deceases with asset tangibility. Manages get paid moe in booms than in ecession. The vaiation in pay acoss the business cycle is of the ode H, which is a isk pemium to compensate manages fo 1 p thei sunk investment in human capital. 42 The volatility in manageial pay is theefoe highe in human capital intensive industies. Futhemoe, the shote booms and the longe ecessions ae expected to last, the lage this isk pemium to compensate manages fo the fact that they may be laid off duing ecession. Ou esults imply that manageial compensation should incease when investment in geneal, tansfeable skills become moe impotant, which is suppoted by the empiical findings of Fydman and Saks (2010) and Muphy and Zabojnik (2007). Abdel-Khalik (2003) finds that human capital factos ae a significant deteminant of the atio of pefomance-based compensation to base salay. This atio anges fom 2.85 fo public utilities to fo compute and infomation technology. Financial institutions and health cae ae next in ank to compute and IT. Ou model implies that dividend payout is pocyclical. The vaiation in payout acoss the business cycle is of the ode ( + λ + λ ) (I L). As a esult, fims with moe tangible assets have a moe stable payout. Shote business cycles (high λ and λ) futhe incease payout vaiation. 42 Poposition 7 demonstates that bankuptcy costs can intoduce additional volatility in pay fo fims with low human capital intensity. Compaed to the tem H 1 p deteminant of manageial compensation as was illustated in figue 2. this is, howeve, a second ode 37

39 6 Conclusions This pape pesents a theoy of net debt that is based on impotant diffeences between physical capital and tansfeable human capital. While the fim owns the physical capital, it has no popety ights ove human capital. Tansfeable human capital can at any time leave to join anothe fim, making it impossible fo fims to issue tadeable claims diectly against tansfeable human capital. Consequently, it is manages who have to bea the cost of investing in tansfeable human capital. It is this asymmety between physical capital and tansfeable human capital that can cause net debt to be negative in ou model. Manages only invest in human capital if they expect to be compensated ex post. In human capital intensive industies equityholdes theefoe contibute a net suplus of liquid assets that thow off ents to be shaed with the manages. If manages finance thei investment in human capital (e.g. education) by pesonal debt (instead of savings) then these ents seve to pay off the manages debt. Negative net copoate debt theefoe indiectly ceates space fo pesonal debt taken on by the fim s manages o employees. While the fim cannot boow against human capital, its manages o employees can take out pesonal debt against the futue ents poduced by its human capital. Tansfeable human capital is financed by the manage and not by the fim in ode to ovecome a hold-up poblem: if a manage withdaws he human capital fom the fim, then any financial liabilities associated with this key asset also leave the fim. The pape povides a seies of novel empiical hypotheses that ae listed in the pevious section. Ou poposed linea egession model fo the fim s net debt taget could fom the basis of an empiical study. While the empiical model itself is simple, the main challenge fo empiicists will be to constuct suitable poxies fo the human capital elated vaiables. We efe to Qian (2003) fo examples of possible poxies. Thee ae also theoetical extensions that emain to be exploed. While financing policy is allowed to vay acoss fims, we hold investment and poduction policy constant, ignoing the effect of gowth options o heteogeneity of poductivity. The pape also assumes that investment in human capital can be financed efficiently. Cedit ationing o fictions in the maket fo pesonal debt could lead to undeinvestment in human capital and have effects on the industy equilibium. Finally, the pape does not 38

40 conside manages incentives to exet effot. These incentives ae paticulaly elevant fo manages that leave the industy in ecession. 7 Appendix Poof of Poposition 2 Unde isk neutality the claim value δ must satisfy the following elationship: δ = λ [ 1 δ ]. Solving gives the expession fo δ. The value Π of a claim that pays π fo as long as the cuent boom lasts must satisfy the following equation: Π = π + λ [ 0 Π ]. Solving gives: Π = π +λ. In booms (ecession) the value V (V ) of a pepetual claim that pays π duing booms and π duing ecessions satisfies: V = π + λ [ V V ] and V = π + λ [ V V ]. Solving this system of 2 equations gives the expessions fo V and V. Poof of Poposition 3 The pesent value of all cash flows geneated (in pepetuity) by an owne-manage who opeates in the industy duing booms but leaves duing ecessions equals: P V = Σ j=0 = [ ( π(q) + λ I + δ ( π(q) I + δ L + + λ 1 δδ w +λ L + ) w )] (δ ) j δ H + λ whee Q denotes the industy output duing booms and whee δ = H (16) λ +λ and δ = λ +λ ae discount factos peviously defined in poposition 2. The above expession sums up the cash flows ove all futue business cycles. The facto δδ is the discount facto that applies to one business cycle (i.e. it is the value of a claim that pays 1 dolla as soon as the economy has switched state twice). Enty is pefeable to no enty if P V W. In a maket with competitive enty, fims beak even in equilibium, that is, P V W = 0. Solving the beak-even condition fo π 39

41 yields the equilibium pofits in booms: π(q) = I + λ (I L) + w + H 1 p (17) We know that in competitive equilibium the value V l of a fim that leaves in ecession is given by V l = π +λ + δv l = I + W + H. Solving fo V l gives: V l = L + W + δ H (18) The equilibium pofits in ecession ae detemined by the industy output duing ecessions (Q). If some exit is optimal when the industy switches fom a boom to a ecession (Q > Q), then fims keep leaving the maket till, in equilibium, thei ownes ae indiffeent between staying in the maket and leaving. On the othe hand, it could be that no fims leave the maket (Q = Q). This would happen if at the existing output level Q all fims wee stictly bette off staying than leaving. Conside the elevant case whee some fims leave the maket (Q > Q). Assuming we ae in a ecession, then the pesent value, V s, of all pofits geneated by staying foeve in a competitive maket is given by: V s (Q, Q) = π(q) (1 p) + π(q) p (19) When the economy switches fom a boom to a ecession, fims keep leaving the industy up to the point whee they become indiffeent between staying o leaving, i.e.: V s (Q, Q) = V l (Q, Q) = L + W + δ H (20) Combining the above two equations allows to solve fo π(q): π(q) = L λ (I L) + w (21) Fo given pofit functions π(q) and π(q), the above equilibium conditions yield Q and Q. One can veify that V s = I + W + H. Now, conside what would happen if it was optimal fo no fim to leave duing ecessions. Competitive enty implies that the value V s obtained fom enty equals the sum of all 40

42 investment costs (I, H) and oppotunity costs (W ): V s ( Q, Q) = π( Q) (1 p) + π( Q) p = I + H + W (22) This condition pins down Q, the industy output that pevails conditional on the industy output to emain constant acoss booms and ecessions (i.e. unde no exit). We now want to detemine a necessay and sufficient condition fo exit to occu, i.e. Q > Q. Since the pofit functions ae continuous and monotonically deceasing in output, thee exists a tansition bounday whee we shift fom a egime with some exit (Q > Q) to a egime with no exit (Q = Q). At that bounday thee is oom fo one atomistic fim to be indiffeent between staying o leaving the industy. Fo this atomistic fim the value (in ecession) of staying in the industy foeve is given by: V s ( Q, Q) = π( Q) (1 p) + π( Q) p (23) On the othe hand, if this atomistic fim leaves the industy then its value was shown to be given by: V l (Q, Q) = L + W + δh (24) Since it concens one infinitesimally small atomistic fim this implies that Q Q Q. Using a continuity agument it follows that at the tansition bounday it must be the case that: V s ( Q, Q) = π( Q) (1 p) + π( Q) p = L + W + δh = V l (Q, Q) (25) Consequently, V s ( Q, Q) V s ( Q, Q) = ( π( Q) π( Q) ) ( 1 p p ) = I L + ( W + H W δh ) (26) Afte eaanging and simplifying, we obtain: π( Q) π( Q) = (I L) ( + λ + λ ) + w + H 1 p w (I, L, H) (27) Given that π(q) and π(q) ae continuous and monotonically deceasing in Q, it follows that a necessay and sufficient condition fo exit to occu is given by π( Q) π( Q) > (I, L, H) whee Q is the solution to V s ( Q, Q) = I + W + H. 41

43 Poof of Poposition 4 It follows immediately fom equityholdes limited liability that thei payoff fom leaving the fim in ecession is given by o e = (L D) +. The value of manages outside option in ecession equals the maximum value of two possible stategies. A fist stategy is that manages leave the industy in ecessions but etun in booms. A second stategy is fo manages to stay out of the industy in both booms and ecessions. This latte stategy esults in a lowe bound fo the value of the manages outside option given by o m = W = w (1 p) + w p. Unde the fome stategy, the value of the outside option equals: o m = w (1 p) + s l p, whee s l is manages salay ate in booms, conditional on manages leaving in ecessions. We know fom esult 1 that s l = π D l 2. The pofit level π is detemined by the bounday condition E l = I B l, which eflects the fact that the maket fo outside equity is competitive. Poposition 2 and esult 1 togethe imply that: E l = π 2( + λ) + δ(l D l)(1 ξ) (28) B l = D l + λ + δ [ξl(1 φ) + (1 ξ)d l] (29) whee ξ = 1 if D l > L and ξ = 0 othewise. Theefoe: E l + B l = π + D l + 2λL(1 φξ) 2( + λ) (30) Equityholdes payoff E l ( I B l ) = El + B l I is monotonically inceasing in D l, except at D l = L whee thee is a discete downwad jump because of the deadweight bankuptcy costs φl. Solving (i) s l = π D l 2 and (ii) E l = I B l fo s l and π gives: s l (D l ) = ( + λ ) I λ(1 φξ) L D l and π = 2 ( + λ ) I 2λ(1 φξ) L D l Substituting the expession fo s l into o m gives the expession fo o m. To see that it is neve optimal fo a manage not to etun to a fim in a boom (and to eceive outside wage w only), one needs to veify that in equilibium s l (D l ) > w. The equilibium value fo D l is given in popositions 5-7 accoding to the 3 egimes that can aise. 42

44 Conside egime 1 fist (see poposition 5). Substituting the value fo D 1l into s l (D l ) gives: s l (D 1l ) = ( + λ)i λl ( + λ)i + λl + w + H 1 p (31) = w + H 1 p = s 1l > w (32) Similaly, one can veify that s l (D 2l ) = s 2l > w and s l (D 3l ) = s 3l > w. Poof of Popositions 5, 6 and 7 We assume that it is optimal fo some fims to leave in ecession (i.e. Q > Q) and subsequently deive the condition unde which this assumption is indeed valid. We deive fist the policies and claim values fo fims that exit in ecessions, and subsequently deive the solution fo fims that emain in the industy at all times. We deive the poof assuming that equityholdes set the debt policy, but show that equityholdes paticipation constaint is always binding in a competitive equity maket and that manages (equityholdes ) claim deceases (inceases) in the debt level. As a esult it is not possible fo manages to aise the debt level any futhe without violating equityholdes paticipation constaint. The same debt level is theefoe also constained optimal fom manages viewpoint. I. Policies and claim values fo fims that exit in ecession Upon enty equityholdes of fims that leave in ecessions solve the following optimization poblem: max Dl [ El ( I B l )] s.t. M l W + H. We know fom equation (30) that: E l + B l = π + D + 2λL(1 φξ) 2( + λ) whee ξ = 1 if D > L and zeo othewise Equityholdes payoff E l + B l I is monotonically inceasing in D, except at D = L whee thee is a discete downwad jump because of the deadweight bankuptcy costs φl. It follows that it can only be optimal to adopt isky debt (D > L) athe than constain the debt to the maximum safe debt level (D = L) if and only if: π + D + 2λL(1 φ) 2( + λ) > π + L + 2λL 2( + λ) D > L + 2λLφ (33) Manages paticipation constaint equies that: M l = (π D l) (1 p) + w [ 2 p W + H D π 2 w + H ] 1 p (34) 43

45 To identify the maximum debt pincipal that can be issued, we fist need to solve fo π. With competitive enty π is the solution to E l = I B l, and is given by: π = 2 [ I + λ (I L) + φλlξ ] D (35) Substituting (35) into (34), we find that the maximum debt level that satisfies manages paticipation constaint equals: D l = I + λ (I L) + λφlξ w H 1 p (36) Using (33) and (36) it follows that equityholdes choose isky debt if and only if: D l = I + λ (I L) + λφl w H 1 p > L + 2λφL (37) ( + λ ) (I L) λφl > w + H 1 p H < H (38) whee H is defined as: ( + λ ) (I L) λφl = w + H 1 p. It follows immediately that: B l > L D l + λ + λl(1 φ) + λ > L (I L)( + λ) > w + H 1 p (39) which is satisfied since by assumption H < H. Conside next the case whee the optimal debt level is safe (D l < L). Fom (36) (with ξ = 0) it follows that: D l = I + λ (I L) w H 1 p < L ( + λ)(i L) < w + H 1 p H > H (40) whee H is defined as:( + λ)(i L) = w + H 1 p. Theefoe, D l < L is optimal fo H < H. The equilibium pofit ate fo H > H can be found by substituting back the optimal debt level into (35). The manageial compensation ate in booms is given by solving s l = π D l 2. We know that D l > L fo H < H and that D l < L fo H > H. What is the optimal debt level fo the intemediate inteval [H, H ]? Since H > H, it follows that D l L (cf. (40)). Theefoe L is the highest debt level that equityholdes wish to adopt. Manages 44

46 paticipation constaint equies that M l [ ] L π 2 w + H 1 p W + H o, equivalently (cf. (34) fo D = L): = 2 [ I + λ(i L) ] [ ] L 2 w + H 1 p (41) w + H 1 p ( + λ)(i L) H H (42) which is satisfied since H [H, H ]. Consequently, fo H [H, H [ the manages paticipation constaint does not bind, i.e. M l > W + H (as (42) is a stict inequality in this case). Regime 2 aises if the inteval [H, H [ is not empty, i.e. H < H. Since (H H ) 1 p = λφl, it follows that egime 2 only occus if φ > 0. II. Policies and claim values fo fims that do not exit in ecession Since the debt of stayes is isk-fee, it follows that B s = B s = D s. The claim values fo fims that do not exit ae given by: E s = π ss E s = π s s (1 p) + π s s p D s M s = ss (1 p) + s s p (1 p) + π ss p D s M s = s s (1 p) + ss p In a competitive equilibium with exit, the outside options of both equityholdes and manages bind in ecession, and theefoe E s = o e and M s = o m. We fist deive explicit expessions fo o m. Substituting the solution fo D l into the expession fo o m (see poposition 4) and using the fact that ξ = 0 fo egimes 1 and 2 (H H) and ξ = 1 fo egime 3 (H < H ) gives (ecall that the manage that decides to leave duing a ecession would etun to a leave duing a boom): ( ) o m = w (1 p) + w + H 1 p p = W + δ H = M l fo H H o m = w ((+λ)(i L)) (1 p) + p = M l > W + δ H fo H H < H ( ) o m = w (1 p) + w + H 1 p p = W + δ H = M l fo H < H Note that M s = M l and, in equilibium, fims ae theefoe indiffeent between leaving o staying. Equityholdes solve the following constained optimization poblem: max E s ( ) I B s s.t. M s = o m and M s W + H D s 45

47 Conside fist the effect of an incease in D s on manages paticipation constaint. We know that M s = M l and consequently: s s = [ M l πp 2 + D ] s p p (43) Substituting (43) into the expession fo M s gives: M s = π Ds 2(+λ) + δm l. Note that M l is detemined by s l and w, which ae unaffected by the behavio of fims that do not exit (since s l = π D l 2 is detemined by the maginal entant that leaves the maket duing ecessions). Consequently, equityholdes of fims that do not exit affect M s only though D s, and M s D s < 0. Inceasing D s unambiguously lowes manages claim, and the paticipation constaint theefoe puts a cap on D s. Conside next the effect of an incease in D s on the equityholdes payoff. Using the bagaining solution fo s s we get: Using (43) we find that s s D s = p 2(1 p). Substituting into the equityholdes payoff function it follows that: E s + D s = π (1 p) (π D s) 2 [Es + Ds I] D s (1 p) + (π s s) p (44) > 0. It follows that aising D s unambiguously inceases equityholdes payoff. Equityholdes theefoe want to adopt the highest debt level that satisfies manages paticipation constaint. The equilibium condition equies that M s = M l, which ensues that manages do not have an incentive to leave in ecession. It emains to be shown that also M s W + H. As M s = ss +λ + δm s and M s = M l W + δh, a sufficient condition fo the paticipation constaint to be satisfied is that: s s ( + λ ) [ W + H δw δδh ] s s w + H 1 p (45) We can subsequently veify that the equilibium solution indeed satisfies this condition. The equilibium solution fo π, s s, s s and D s can now be deived as the solution to the system of equations: (i) E s = o e (ii) M s = o m (iii) s s = π Ds 2 and (iv) E s = I D s. Condition (iv) eflects the fact that outside equity is supplied on a competitive basis. Substituting the peviously deived expessions fo π and o m into the system of equations, and solving, gives the expessions fo π, s s, s s and D s as in popositions 5, 6 and 7. One 46

48 can immediately veify that M s M l W + H, and theefoe manages paticipation constaint is satisfied. We now need to veify whethe Q > Q as oiginally assumed. In egime 1, the solution fo π and π coincides with the fist-best outcome given in poposition 3. Fom assumption 2 it follows then immediately that Q > Q. In egime 2, π and π ae independent of H, and hence Q and Q ae constant, and theefoe so is Q Q. In egime 3, π H means that [Q Q] H π > 0 and H < 0, which < 0. Futhemoe, one can show that π (and theefoe Q) is continuous at H, wheeas π (Q) displays a discete downwad (upwad) jump at H if φ > 0. It follows that if some fims leave in ecession fo H = H (i.e. if Q(H ) > Q(H )) then exit occus fo all values of H that satisfy assumption 2, and a sufficient and necessay condition fo exit to occu is theefoe that Q(H ) > Q(H ). Substituting the expession fo H into π and π gives: The condition fo exit theefoe becomes: π(h ) = I + ( + 2λ ) (I L) (46) π(h ) = L λ (I L) + w λλφl + λ π 1 [ I + ( + 2λ ) (I L) ] [ > π 1 L λ (I L) + w λλφl ] + λ This condition is satisfied fo φ = 0 since in that case H (47) = H and we peviously showed that exit occus at H. Howeve, since Q(H ) φ > 0, it follows that fo φ sufficiently lage thee will be a cossing point whee Q = Q. Define φ as the oot of the equation Q(H (φ )) = Q(H (φ )). If φ < φ then the exit condition is eveywhee satisfied. If φ φ then the exit condition is violated at H. Theefoe, if φ > φ then thee exists a egion fo which no fims leave the maket. 47

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53 Industy I Outside industy BOOM π(q) Competition Competition V V V w λ λ V Competition V w π(q) RECESSION L Figue 1: Industy dynamics. V and V denote the fim value in booms and ecessions, espectively, I is the physical investment cost, L is the liquidation value, w and w (π(q) and π(q)) epesent outside wages (pofits) in booms and ecessions, espectively, and λ (λ) denotes the hazad ate associated with the aival of a ecession (boom). 52

54 Net Debt Pincipal, D H H Panel A: Debt Pincipal Investment in Human Capital, H D l D s L Net Debt Ratio, NDR,NDR H H Panel B: Net Debt Ratio Investment in Human Capital, H NDR l NDR s NDR Fim Pofit, Π,Π H H Π Π Π 0 Π 0 Panel C: Total Pofit Investment in Human Capital, H Industy Output, Q,Q H H Panel D: Industy Output Investment in Human Capital, H Q Q 0 Q 0 Manageial Compensation Rate, s,s Panel E: Manageial Compensation H H s l s s s s Investment in Human Capital, H Payout Rate, d,d H H d l d s d s Panel F: Payout Investment in Human Capital, H Figue 2: Compaative statics esults fo debt pincipal, net debt atio, total pofit, industy output, manageial compensation and payout to shaeholdes geneated fo the following paamete values: π(q) = aq ɛ b and π(q) = aq ɛ b, whee a = 200 and a = 25, b = b = 1 and ɛ = 1.1. Futhemoe, λ = λ = 0.075, = 0.05, I = 200, L = 150, w = 2, w = 1, and φ =