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 b.lambecht@lancaste.ac.uk o g.pawlina@lancaste.ac.uk. 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