Investment Reversibility and Agency Cost of Debt

Transcription

1 Invesmen Reversibiliy and Agency Cos of Deb Gusavo Manso Ocober 24, 2007 Absrac Previous research has argued ha deb financing affecs equiyholders invesmen decisions, producing subsanial inefficiency. This paper shows ha he size of his inefficiency depends on he degree of invesmen reversibiliy. In a dynamic model of financing and invesmen, he paper provides an upper bound for he inefficiency produced by deb financing. The upper bound is decreasing in he degree of invesmen reversibiliy and is zero when invesmen is perfecly reversible. Keywords: Agency problems, real opions, deb financing, asse subsiuion, deb overhang, underinvesmen. MIT Sloan School of Managemen, 50 Memorial Drive E52-446, Cambridge, MA ( manso@mi.edu). I hank Ana Admai, Malcolm Baker, Peer DeMarzo, Darrell Duffie, John Robers, Ilya Srebulaev, a co-edior, and hree anonymous referees for helpful commens.

2 1 Inroducion The relaion beween financing and invesmen decisions of he firm has occupied he finance lieraure for he las fify years. In heir seminal work, Modigliani and Miller (1958) prove ha if capial markes are perfec and invesmen decisions are fixed, hen he value of he firm does no depend on is financing decisions. Subsequen work, however, has dispued he assumpion ha invesmen decisions can be aken independen of financing decisions. Jensen and Meckling (1976) argue ha since equiyholders do no bear he full cos of low reurns, hey have incenives o ake riskier projecs, poenially exracing value from he debholders. This conflic of ineres beween he equiyholders and he debholders is referred o as he asse subsiuion problem. Myers (1977) argues ha equiyholders of a leveraged firm will underinves because a fracion of he resuls of heir invesmen will accrue o debholders. This conflic of ineres beween he equiyholders and debholders is referred o as he deb overhang or underinvesmen problem. The broad consensus a presen is ha he use of deb financing affecs equiyholders invesmen decisions, producing subsanial inefficiency, which is commonly referred o as agency cos of deb. The conribuion of his paper is o show ha he agency cos of deb depends on he degree of invesmen reversibiliy. The analysis is based on he srucural models of credi risk of Black and Cox (1976) and Leland (1994). However, insead of a fixed cash-flow process, i incorporaes dynamic invesmen decisions as in Duffie (2001, pp ). In he model, he firm may swich over ime among alernaive echnologies. Each echnology has an associaed cash-flow process ha evolves exogenously according o a general 2

3 diffusion process. When he firm swiches from one echnology o anoher i incurs a lump-sum swiching cos. The resul of he paper is ha he agency cos of deb is lower han he presen value of he maximum of he swiching coss paid upon defaul. Therefore, if invesmen is perfecly reversible, in he sense ha here are no swiching coss beween echnologies, hen deb financing does no lead o inefficien invesmen decisions. The paper is relaed o he lieraure on real opions, which sudies dynamic invesmen decisions of he firm. Dixi and Pindyck (1994) provide a survey of he real opions lieraure. A sandard work in his lieraure ha fis lierally ino he model of invesmen sudied here is ha of Dixi (1989), which analyzes enry and exi decisions of a firm whose oupu price follows a geomeric Brownian moion. The opimal invesmen policy of an unlevered firm is characerized under he assumpion ha he firm pays a lump-sum cos every ime i swiches from acive o inacive and vice-versa. Benolila and Berola (1990) and Abel and Eberly (1996) are oher examples of real opions models ha sudy cosly reversible invesmen. In conras o he real opions lieraure, I invesigae invesmen disorions caused by deb financing. More closely relaed o his paper is he lieraure on dynamic invesmen and financing decisions of he firm. 1 For example, Mauer and Trianis (1994) sudy a firm ha can cosly shu-down and resume operaions. Childs, 1 This lieraure includes Mello and Parsons (1992), Mauer and Trianis (1994), Leland (1998), Mauer and O (2000), Décamps and Faure-Grimaud (2002), Hennessy (2004), Timan, Tompaidis, and Tsyplakov (2004), Childs, Mauer, and O (2005), Ju and Ou- Yang (2006), Moyen (2007), Sundaresan and Wang (2006), and Lobanov and Srebulaev (2007). 3

4 Mauer, and O (2005) sudy a firm ha can cosly exercise and reverse he exercise of a growh opion. Oher aricles in his lieraure have assumpions ha depar from he cosly reversible invesmen framework and make he upper bound obained here inapplicable. For example, Mauer and O (2000) sudy opions o expand ha canno be reversed a any cos. Sundaresan and Wang (2006) sudy invesmen projecs ha mus be aken in a given order. Lobanov and Srebulaev (2007) sudy growh opions ha are los if no exercised a a paricular ime. Leland (1998) sudies invesmen projecs ha, if aken, affec he fuure cash flows of he oher available projecs. In addiion o deparures from he cosly reversible invesmen framework, some aricles in his lieraure consider alernaive deb srucures (finie-mauriy deb and deb refinancing) and oher marke imperfecions (bankrupcy coss and ax benefis of deb). The resul obained here can be exended o incorporae hese alernaive assumpions abou deb srucure and marke imperfecions, bu for ease of exposiion I resric he analysis o financing hrough a consol bond wih neiher bankrupcy coss nor ax benefis of deb. 2 The Model The model is based on Duffie (2001, pp ). The firm may swich over ime among m alernaive echnologies. The cash-flow rae processes δ R m of he m available echnologies follow a diffusion governed by he equaion dδ() = µ(δ(), )d + σ(δ(), )db(). (1) 4

5 where µ R m and σ R m R m saisfy he classic assumpions for he exisence of a unique srong soluion o (1) and B R m is a sandard Brownian moion. If echnology i is employed a ime, i produces cash flows a he rae δ i (). When he firm swiches from echnology i o echnology j, i incurs a lump-sum cos ϕ(i, j), wih ϕ(i, i) = 0. A echnology-choice process is a righ-coninuous adaped process ζ aking value in {1,..., m}. A any ime in which ζ() ζ( ) lim s ζ(s), he firm swiches from echnology ζ( ) o ζ(). The iniial echnology ζ 0 is given. Given a echnology-choice process ζ, he firm s oal cumulaive cash flow by ime is given by D ζ, where D ζ 0 = 0 and dd ζ = δ ζ() ()d ϕ(ζ( ), ζ()). All agens are risk-neural and discoun fuure cash flows a he rae r. The marke value of he firm s oal fuure cash flows a ime is given by [ A ζ = E e r(s ) dds ζ The marke value of an all-equiy firm a ime is A fb = sup A ζ. (2) ζ The firm s capial srucure consiss of deb and equiy. For simpliciy, deb is in he form of a consol bond ha promises o pay coupons a a oal rae c, coninually in ime, unil defaul. Equiyholders receive he residual cash flow in he form of dividends a he rae D ζ c a ime, unil defaul. A defaul, he firm s fuure cash flows are assigned o debholders. Wih deb a a coupon rae c, he valuaion of equiy a any ime before 5

6 defaul is [ T T S = sup E e r(s ) dds ζ e r(s ) cds. (3) ζ,t Given he echnology-choice process ζ and he defaul sopping ime T of equiyholders, he valuaion of deb a any ime before defaul is Y = E e r(s ) cds + e r(t ) A ζ T. (4) Because of he conflic of ineres beween equiyholders and debholders, one expecs inefficiencies due o invesmen disorions o arise. Equiyholders may engage in asse subsiuion, choosing risky and inefficien echnologies, or underinvesmen, saying longer wih inefficien echnologies o avoid paying he swiching coss. The agency cos of deb is defined as α = A fb (S + Y ). I is equal o he difference beween he oal value of he all-equiy and levered firms. Since here are no oher marke imperfecions in he model, he agency cos of deb capures he loss in value of he firm due o he invesmen disorions produced by he presence of deb. Proposiion 1 provides an upper bound for he agency cos of deb. Proposiion 1 The agency coss α of deb are bounded above by E [e r(t ) max ϕ(i, j). (5) i,j 6

7 Proof Adding equaions (3) and (4), we have S + Y = E e r(s ) dd ζ s T + E e r(s ) c [ e r(s ) c + E e r(t ) A ζ T. (6) where ζ and T are he soluions o (3). The value of he unlevered firm can be wrien as A fb = E e r(s ) dd ζfb s T + E e r(s ) c [ e r(s ) c + E e r(t ) A ζfb T. (7) where he firs-bes policy ζ fb is he soluion o he invesmen problem (2) of an all-equiy firm. Because equiyholders maximize he presen value of cash flows minus coupon paymens before defaul, E e r(s ) dd ζ s T e r(s ) c E e r(s ) dd ζfb s T e r(s ) c Afer defaul, he debholders ake conrol of he firm and can swich o any echnology by paying a swiching cos. Therefore, [ [ E e r(t ) A ζfb T E e r(t ) A ζ T E [e r(t ) max ϕ(i, j) i,j The upper bound on α follows from (6), (7), (8), and (9). (8). (9) The upper bound (5) is he presen value of he maximum of he swiching coss paid upon defaul. The inuiion for he resul is as follows. Equiyholders maximize he presen value of cash flows minus coupon paymens before 7

8 defaul. Therefore, he presen value of cash flows before defaul mus be greaer han or equal o wha i would have been under he firs-bes policy. I is hus only afer defaul ha invesmen disorions due o he presence of deb can negaively impac he firm s cash flows. Afer defaul, debholders ake conrol of he firm and maximize he presen value of cash flows of he firm. However, by paying a swiching cos, debholders can obain from ha poin on exacly he same cash flows as if he firs-bes invesmen policy had been used all he way unil defaul. Therefore, he agency cos of deb mus be lower han he presen value of he maximum of he swiching coss paid upon defaul. References Abel, A., and J. Eberly, 1996, Opimal Invesmen wih Cosly Reversibiliy, Review of Economic Sudies 63, Benolila, S., and G. Berola, 1990, Firing Coss and Labour Demand: How Bad is Eurosclerosis, Review of Economic Sudies 57, Black, F., and J. Cox, 1976, Valuing Corporae Securiies: Some Effecs of Bond Idenures Provisions, Journal of Finance 31, Childs, P., D. Mauer, and S. O, 2005, Ineracions of Corporae Financing and Invesmen Decisions: The Effecs of Agency Conflics, Journal of Financial Economics 76, Décamps, J., and A. Faure-Grimaud, 2002, Excessive Coninuaion and Dynamic Agency Cos of Deb, European Economic Review 46,

9 Dixi, A., 1989, Enry and Exi Decisions Under Uncerainy, Journal of Poliical Economy 97, Dixi, A., and R. Pindyck, 1994, Invesmen Under Uncerainy. (Princeon Universiy Press Princeon). Duffie, D., 2001, Dynamic Asse Pricing Theory. (Princeon Universiy Press New Jersey) hird edn. Hennessy, C., 2004, Tobin s Q, Deb Overhang, and Invesmen, Journal of Finance 59, Jensen, M., and W. Meckling, 1976, Theory of he Firm: Managerial Behavior, Agency Coss, and Ownership Srucure, Journal of Financial Economics 3, Ju, N., and H. Ou-Yang, 2006, Asse Subsiuion and Underinvesmen: A Dynamic View, Working paper, Duke Universiy. Leland, H., 1994, Corporae Deb Value, Bond Covenans, and Opimal Capial Srucure, Journal of Finance 49, Leland, H., 1998, Agency Coss, Risk Managemen, and Capial Srucure, Journal of Finance 53, Lobanov, S., and I. Srebulaev, 2007, A Theory of Dynamic Financing and Invesmen, Working paper, Sanford GSB. Mauer, D., and S. O, 2000, Agency Coss, Underinvesmen, and Opimal Capial Srucure: The Effec of Growh Opions o Expand, in M. Bren- 9

10 nan, and L. Trigeorgis, eds.: Projec Flexibiliy, Agency, and Compeiion (Oxford Universiy Press, Oxford ). Mauer, D., and A. Trianis, 1994, Ineracions fo Corporae Financing and Invesmen Decisions: A Dynamic Framework, Journal of Finance 49, Mello, A., and J. Parsons, 1992, Measuring he Agency Cos of Deb, Journal of Finance 47, Modigliani, F., and M. Miller, 1958, The Cos of Capial, Corporaion Finance and he Theory of Invesmen, American Economic Review 48, Moyen, N., 2007, How Big is he Deb Overhang Problem?, Journal of Economic Dynamics and Conrol 31, Myers, S., 1977, Deerminans of Corporae Borrowings, Journal of Financial Economics 5, Sundaresan, S., and N. Wang, 2006, Dynamic Invesmen, Capial Srucure, and Deb Overhang, Working paper, Columbia Universiy. Timan, S., S. Tompaidis, and S. Tsyplakov, 2004, Marke Imperfecions, Invesmen Flexibiliy, and Defaul Spreads, Journal of Finance 59,