The Implications of Capital Investments for Future Profitability and Stock Returns an Overinvestment Perspective

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1 The Implicaions of Capial Invesmens for Fuure Profiabiliy and Sock Reurns an Overinvesmen Perspecive Donglin Li* Haas School of Business, Universiy of California, Berkeley, CA9470 Phone: (510) January 004 Absrac This paper examines wheher overinvesmen can parially explain he negaive associaion beween capial invesmens (long erm asse accruals), fuure profiabiliy and sock reurns. Capial invesmen has a robus negaive implicaion for fuure profiabiliy. The negaive associaion is sronger when firms have greaer invesmen discreion, i.e., for hose firms wih higher free cash flow and lower leverage. Moreover, he negaive associaion beween invesmen, fuure profiabiliy and sock reurns is almos exclusively driven by posiive discreionary invesmen, i.e., where overinvesmen is more likely o occur, raher han by negaive discreionary invesmen, where overinvesmen is much less likely. Evidence in his sudy provides an underlying explanaion for Timan, Wei and Xie (003) s noion ha managers empire building behavior is responsible for he negaive associaion beween capial invesmen and fuure sock reurns. In addiion, o he exen ha long erm asse accruals capure invesmen inensiy, he resuls here may also provide an alernaive inerpreaion of he long erm asse accrual anomaly. Keywords: Overinvesmen, Free Cash Flow, Marke Efficiency, Financial Saemen Analysis. * I am mos indebed o Terry Marsh, for his invaluable guidance and advice. I would also like o hank Bok Baik, Sunil Dua, Qingao Fan, Taiana Fedyak, George Li, Maria Nondorf, Mark Seasholes, Wenbin Wei, Xiao-Jun Zhang and oher paricipans of Berkeley accouning workshop. All remaining errors are mine. Special hanks o Sco Richardson for he codes on Mishkin ess. 1

2 1. Inroducion Capial invesmens represen a fundamenal signal claimed by analyss o be useful in predicing fuure profiabiliy and sock reurns (Lev and Thiagrajan (1993)). I is also of cenral imporance in corporae finance research wheher firms make sub-opimal invesmens, and wheher marke paricipans fully undersand he implicaions of managers incenives o deviae from opimal invesmen levels when hey have he laiude o do so. This paper examines wheher he overinvesmen can parially explain he negaive associaions beween capial invesmens, fuure profiabiliy and sock reurns. Given he huge amoun of capial expendiure by Corporae America each year (e.g, in 001 he oal capial expendiure reaches 1.3 rillion dollars), i is surprising ha so few sudies have addressed he implicaions of capial invesmens for fuure profiabiliy. In he financial saemen analysis lieraure, Fairfield, Whisenan and Yohn (003a) documen a negaive associaion beween growh in ne long erm operaing asses and one year ahead fuure reurn on asses. Richardson, Sloan, Soliman and Tuna (003) find a similar associaion and aribue i o he lower reliabiliy of long erm asse accruals. I is reasonable, hough, o believe ha growh in long erm asse accruals also capure invesmen inensiy 1. Abarbanell and Bushee (1997) show ha capial expendiure conveys a negaive signal for fuure earnings. Thus, here seems o be a negaive relaion beween capial invesmen and fuure profiabiliy. However, here is lile evidence as o wha facors could explain his negaive associaion. I sudy his associaion from an overinvesmen perspecive, along wih he degree o which he negaive associaion beween invesmen and fuure profiabiliy is consisen wih he negaive associaion beween invesmen and fuure sock reurns. Timan, Wei and Xie (003a) repor ha he negaive associaion beween capial invesmens and fuure sock reurns is sronger in firms wih higher free cash flow and lower leverage. They inerpre heir evidence as invesor under-reacion o he overinvesmen behavior by managers wih empire building incenives. However, i is no clear wheher i is omied risk facors or value desroying discreionary invesmens ha drive heir resuls. To furher unravel he underlying causes, I invesigae how free cash flow and leverage can affec he associaion beween capial invesmen and fuure operaing performance. A significan finding would provide an underlying link o suppor Timan 1 In appendix B, I show hese variables are highly correlaed wih invesmen opporuniies and fuure realized firm growh. Richardson, Sloan, Soliman and Tuna (003) also call change in non-curren operaing asses as invesing accruals. Some researchers sugges ha invesmen growh may be a facor in asse pricing (Berk, Green and Naik (1999), and Li, Vassalou, and Xing (001)).

3 e al s resuls and srenghen he overinvesmen explanaion 3. There are a lo of anecdoes suggesing ha managers prefer o expand heir companies faser han hey should. For example, prior o is leveraged buyou (LBO) in 1988, RJR Nabisco s baking uni devised a plan o revamp and modernize is baking faciliy a a cos of $.8 billion. The annual savings from he modernizaion would have been only $148 million, providing a preax reurn of only 5 percen. Afer he LBO, he modernizaion plan was scaled back 4. More generally, he idea ha overinvesmen migh poenially explain he negaive associaion beween invesmens and fuure profiabiliy is no oally new, e.g., Abarbanell and Bushee (1997) conjecured ha capial expendiures could be a bad signal for fuure earnings if poor performing firms ake on excessive projecs, hough hey did no specifically invesigae his issue. If overinvesmen can parially explain he negaive associaion beween invesmen and fuure profiabiliy, we would also expec o observe a sronger resul in he sample where overinvesmen is more likely o occur. I argue ha overinvesmen is more likely o occur in he sample where firms make posiive invesmen han firms ha dives, where here may be even under invesmen. This assumes ha all firms have neural invesmen opporuniies. To beer conrol invesmen opporuniies, I also consrucs a parsimonious model of discreionary invesmen defined as invesmen no warraned by invesmen opporuniies and examines wheher he negaive associaions are sronger in he posiive discreionary invesmen sample han in he negaive discreionary invesmen sample. Since overinvesmen is more likely presen in he former group, I expec o see a sronger associaion in ha group. Noe ha oher explanaions such as a growh effec by Fairfield e al (003a) or accrual reliabiliy effec by Richardson e al (003) make no such predicions. Thus, resuls would provide furher evidence differeniaing he overinvesmen explanaion from ohers. Consisen wih my hypoheses, he negaive associaion beween invesmen and fuure profiabiliy is sronger in firms wih high free cash flow and lower leverages. Applying a parsimonious model o decompose invesmen ino a non-discreionary porion and a discreionary porion, I find ha he negaive associaion is mosly explained by he posiive (discreionary) invesmen sample. Nex, I examine wheher he marke can fully incorporae he implicaions of capial invesmens for fuure profiabiliy. There is a significan negaive associaion beween firm invesmen and fuure sock reurns and he associaion is mosly driven by he posiive discreionary invesmen sample. An 3 Sudying he implicaion of capial invesmen for fuure profiabiliy is also consisen wih he view expressed by Penman (199) ha predicing operaing performance, as opposed o explaining securiy reurns, should be he cenral ask of financial saemen analysis. 4 The Wall Sree Journal, Mar. 14,

4 invesmen sraegy which goes long in he lowes decile of invesmen and shor in he highes decile of invesmen appears o generae persisen hedge reurns. The abnormal reurn remains significan afer conrolling firm characerisics and risk facors commonly known o be associaed wih sock reurns. This sudy conribues o he exan lieraures of agency heory in corporae finance, financial saemen analysis, marke efficiency, and invesmen measuremen. Firs and foremos, i provides evidence abou how agency coss (proxied by free cash flow and leverage) affec he associaion beween invesmens and fuure operaing performance: he negaive implicaions of high capial invesmens are sronger for firms wih high free cash flow and lower leverages. This reinforces Jensen s and Timan e al s noion ha empire building incenives drive he negaive associaion beween capial invesmen and fuure sock reurns. My resuls are also consisen wih recen findings in Hennessy and Levy (00) ha empire building incenives appear o be he dominan agency issue disoring firm invesmen. Second, I empirically validae several commonly used measures of invesmen and find ha long erm asse accruals are good proxies of invesmen inensiy. To he exen ha long erm asse accruals capure capial invesmen inensiy, if agency coss can explain he negaive associaion beween invesmens and fuure profiabiliy, hey could poenially explain he negaive associaion beween long erm asse accruals and fuure profiabiliy. This paper hus provides a new perspecive on he long erm asse accruals anomaly ha is disinc and perhaps no muually exclusive from he reliabiliy conjecure by Richardson e al and growh explanaion by Fairfield e al. Third, I documen a srong sock marke reurn anomaly associaed wih firm invesmens. The finding cass doub on he efficien marke hypohesis. The negaive associaion beween invesmens and fuure reurns is robus o various risk facors and oher poenially associaed anomalies. The resuls may be of ineres o financial saemen users, such as managers, analyss and crediors who are ineresed in undersanding he implicaions of capial invesmen for firm performance. Las, I validae several commonly used measures of invesmen which should benefi fuure sudies. The remainder of he paper is organized as follows. In secion, I briefly describe prior research on invesmen and sock reurns and develop hypoheses. Secion 3 discusses he sample and variable measuremens while secion 4 presens empirical ess. Secion 5 provides concluding remarks. Appendix A describes variable definiions while Appendix B validaes invesmens proxies. 4

5 . Lieraure and Hypoheses Developmen.1 Lieraure The corporae finance lieraure is no seled as o wheher firms in general end o over inves or under inves 5. Empirically here is mixed evidence as o how he marke responds o capial invesmens 6. Beneish, Lee and Tarpley (001) find ha he magniude of capial expendiures is negaively relaed o fuure sock performance. Abarbanell and Bushee (1998) repor ha indusry-adjused capial expendiure growh is negaively associaed wih fuure reurns, a resul conradicory o heir hypohesis. Timan e al (003a) find a similar negaive relaion and provide evidence ha firm over-invesmen is responsible for his negaive associaion. Timan e al (003 b) compare Japanese keiresu firms and independen firms and find ha in he former groups here is a negaive associaion beween invesmen and fuure reurns while in he laer he associaion is posiive. The resul is consisen wih he idea ha keiresu firms, which have low-cos access o capial, end o over inves. Hennessy and Levy (00) find ha empire building is he dominan facor leading firms o over inves. None of hese sudies examines he implicaion of invesmens for fuure profiabiliy. The fundamenal analysis lieraure has documened ha various accouning iems are predicive of fuure earnings (e.g., Penman and Zhang (00)). Abarbanell and Bushee (1997) examine he implicaion of several fundamenal signals, including a measure of indusry-adjused growh in capial expendiures, for fuure profiabiliy. However, heir sample size is much smaller han mine (because of he requiremen of earnings forecas daa) and heir use of earnings per share as he dependan variable is subjec o criic issue ha scale effecs influence he resuls (Eason (1998)). I is imporan ha research conribues no only o idenifying variables ha can predic fuure profiabiliy, bu also o providing economic inerpreaion of he variables. Curren explanaions are mosly conjecures wih no supporing evidence. Fairfield, Whisenan and Yohn (003a) find ha wo componens of he annual changes in ne operaing asses--- accruals and long erm operaing accruals---are equally srong negaive predicors of one-year accouning reurn on oal asses and of 5 In fac, a finding ha invesmen is more sensiive o cash flows is subjec o differen inerpreaions: capial raioning and hence under invesmen (Fazzari e al 1988), over invesmen (Kaplan and Zingales (1997), Jensen (1986)). Wihou examining he implicaion of such invesmen for fuure profiabiliy, i is difficul o disinguish he wo conradicing heories. 6 In even sudies, McConnell and Muscarella (1985) indicae ha announcemens of increase in planned capial invesmens are generally associaed wih significanly posiive excess sock reurns. Blose and Shieh (1997) and Vogo (1997) find ha marke reacs o he level of capial invesmen announcemen. Anoher se of sudies examines he valuaion effecs of acual capial invesmen using annual reurns and he resuls are mixed. Even sudies may be subjec o wo problems, hough. Firs, firms may self selec o announce invesmen plans. Second, marke may misprice he invesmen in a shor window, which is a valid concern. In fac, in he longer window I sudies, marke seems canno fully undersand he implicaion of invesmen on fuure earnings. Lev and Thiagarajan (1993) find ou ha indusry adjused capial expendiure growh is posiively associaed wih conemporary reurns, while Abarbanell and Bushee (1997) find no such associaion. Park and Pincus (003) find incremenal informaion conen of capial expendiures beyond unexpeced earnings. 5

6 sock reurns. They conjecure ha he accrual anomaly documened by Sloan (1996) is acually a growh effec caused by diminished reurns from invesmen or conservaive accouning. However, Fairfield e al only examined he implicaion of growh in ne operaing asses for one-year-ahead profiabiliy. While discussing Fairfield, Whisenan and Yohn (003b), Dichev (003) argues ha he relaion beween growh and fuure profiabiliy has more of a ime-series flavor ha has no been documened: his sudy could be inerpreed as filling he impac of capial invesmen on one o weny years ahead performance. Richardson, Sloan, Soliman and Tuna (003) find ha invesors misinerpre he informaion conained in various operaing and financing accrual iems. They argue ha differen reliabiliies associaed wih various operaing accruals, eiher curren or non-curren, should resul in differen implicaions for fuure earnings and sock reurns. While highly convincing, heir sudy furnishes lile evidence on why some accruals are more or less reliable han ohers. Richardson and Sloan (003) consruc hree measures of ne exernal financing and find ha here is a sysemaic srong and negaive relaion beween exernal financing and fuure sock reurns. Based on he finding ha fuure sock reurns are negaively relaed o changes in operaing asses, hey sugges ha a poenial explanaion is firm over-invesmen in operaing asses. However, in he same paper, hey also ry o add an accrual manipulaion explanaion. There is much empirical evidence ha suggess ha free cash flow can exacerbae firm overinvesmen (e.g., Kaplan (1989), Blanchard e al (1994)) while deb can miigae overinvesmen (e.g., Harvey, Lins and Roper (001)). Resuls in his sudy are consisen wih above findings.. Hypoheses Developmen I firs confirm ha high invesmen inensiy leads o decreased fuure profiabiliy. Alhough his is no he focus of his paper, esablishing such a relaion is necessary for hypoheses o follow. Despie previous findings ha documen such an associaion, Dichev (003) argues ha capial invesmens could be posiively relaed o fuure profiabiliy, e.g., if capial follows profiabiliy. Given he resul ha invesmen and fuure profiabiliy are negaively relaed, i may be ha he relaion is explained by conservaive accouning. Penman (001, 561) argues ha conservaive accouning could make he profiabiliy of new invesmen appear relaively less profiable in earlier years and more profiable in laer years. If conservaive accouning is he only underlying force hen emporarily dampened reurn on asses will reverse someime in he fuure years. Penman and Zhang (00) argue ha he profiabiliy reversal should be more likely o be observed when firm invesmen growh slows down in he fuure. If his is rue hen capial invesmen may be a posiive poren for long erm fuure profiabiliy. This leads 6

7 o my firs hypohesis, saed as an alernaive o reverse: H1: The negaive associaion beween invesmen and fuure profiabiliy will no reverse in longer periods. If he resuls are consisen wih hypohesis H1, we can infer ha here is an economic explanaion for he invesmen-fuure profiabiliy associaion. While even opimal invesmen may lead o lower profiabiliy raios caused by diminished marginal rae of reurn, subopimal invesmen can furher impac profiabiliy. The separaion of managemen and ownership creaes he poenial for managemen o engage in subopimal aciviies including empire building behavior. Managers of firms wih high free cash flow can ac opporunisically and indulge in value desroying aciviies and o over inves and misuse he funds (Jensen (1986)). Excessive free cash flow enables managers o inves in negaive NPV projecs afer exhausing posiive NPV projecs (Blanchard e al (1994), Richardson (00)). On he oher hand, when firms have a cash shor fall, he possibiliy of over invesmen is miigaed because he firm is forced o raise funds hrough exernal markes, which provide a monioring role. If wanon overinvesmen resuls in lower fuure profiabiliy, ceeris paribus, we would expec o observe a more negaive relaion beween capial invesmen and fuure profiabiliy for high free cash flow firms. On he oher hand, capial raioning heory 7 (Myers and Majluf (1984), Fazzari e al (1988)) predic ha high free cash flow and high cash holdings can benefi a firm by reducing he cos of informaion asymmery ha places a wedge beween he coss of inernal and exernal capial. Thus high free cash flow enable firms o make opimal invesmen wih less cos and obain beer fuure operaing performance. I expec he overinvesmen effec dominae he cash raioning effec. Leverage could poenially miigae he overinvesmen problem. Leverage resrics he use of inernal funds generaed by he firm by forcing managers o use cash flow o mee conracual financial obligaions (Jensen (1986), Sulz (1990)). Managers empire building incenives may be consrained by crediors legal righs o reorganize or even liquidae he firm in case of defaul. The deb marke also provides managemen discipline (Rubin (1990)). Thus, he negaive associaion beween invesmen and fuure profiabiliy could reasonably be expeced o be weaker in firms wih high leverage. However, deb canno perfecly solve he problem (Grinbla and Timan (1998)). Lyandres and Zhdanov (003) also emphasized ha capial srucure canno by iself induce managers o inves opimally. High leverage also brings agency cos, e.g., bankrupcy cos. Thus, I expec he effec from 7 Recenly here is increasing evidence quesioning capial raioning heory (Kaplan and Zingales (1997), Cleary (1999) and Ali (003)). 7

8 leverage is of second order and weaker han ha from free cash flow. This leads o my main hypohesis, saed in alernaive form: Ha: The negaive associaion beween invesmen and fuure profiabiliy will be sronger in firms wih higher free cash flow, ceeris paribus. Hb: The negaive associaion beween invesmen and fuure profiabiliy will be weaker in firms wih higher leverage, ceeris paribus. If overinvesmen can parially explain he negaive associaion beween invesmen and fuure profiabiliy, we would also expec o observe a sronger resul in a sample where overinvesmen is more likely o occur. The negaive associaion probably would disappear in a sample of firm underinvesmen, where he associaion may be even posiive. I argue ha overinvesmen is more likely o occur in he sample where firms make posiive invesmen han firms ha dives 8. This holds if all firms have equally neural invesmen opporuniies. To beer conrol invesmen opporuniies, I also consruc a parsimonious model of discreionary invesmen (defined as invesmen no warraned by invesmen opporuniies, for esimaion see secion 3. and appendix B) and examine wheher he negaive associaions are sronger in he posiive discreionary invesmen sample han in he negaive discreionary invesmen sample. Since overinvesmen is more likely presen in he former group, where he derimen in firm value will manifes in lower fuure profiabiliy, I expec o see a sronger negaive associaion in ha group. If negaive discreionary invesmen correcly capures underinvesmen, here should be weaker or even posiive associaion in he negaive discreionary invesmen group. However, if firms generally over inves, as documened in Hennessy and Levy (00) and Richardson (00), hen my model ha ries o saisically parse ou discreionary and non-discreionary invesmen may resul in some esimaion error, i.e., posiive discreionary invesmen is more likely over invesmen, bu negaive discreionary invesmen could be eiher underinvesmen, over invesmen or simply esimaion error. Thus, here is no clear predicion on he sign of he associaion beween invesmen and fuure profiabiliy in he negaive discreionary invesmen group. Thus, I expec: H3: The negaive associaion beween invesmen and fuure profiabiliy is sronger in he sample of posiive (discreionary ) invesmen firms han in he sample of negaive(discreionary) invesmen firms. 8 Beyond free cash flow and leverages, here may be oher agency coss or asymmeric informaion ha affec firms o make subopimal invesmen (e.g., Myers and Majluf (1984), Dechow and Sloan (1991)). Alhough some researchers argue ha overinvesmen is he dominan effec (Hennessy and Levy (00) and Richardson (00)), ohers provide evidence of underinvesmen (Aggarwal e al (1999)). 8

9 Noe ha oher heories such as accrual manipulaion make no such predicion. Thus ess of H3 may o some exen disinguish he overinvesmen explanaion from he accrual reliabiliy explanaion which claims ha long erm operaing accruals are measured wih error, and he growh explanaion which recognizes ha when firms make invesmens, firms would grow in sizes. The nex hypohesis is based on he growing evidence ha he marke ofen does no fully undersand he implicaions of financial saemens iems (e.g., Sloan (1996), Holhausen and Larker (199)). If invesors do no undersand he negaive implicaions of invesmen for fuure earnings, hen a sraegy ha explois his informaion can earn abnormal reurns. Timan e al (003) argue ha empire building managers may have an incenive o pu he bes spin on heir invesmen opporuniies as well as on heir over all business when hey make high capial invesmens, perhaps o jusify heir acion. If invesors fail o recognize he over invesmen behavior or are fooled by he rosy picure of firm performance, hen he subsequen-period sock reurns of firms ha made excessive invesmen may deeriorae as overinvesmen resuls in lower han expeced performance. Moreover, he price correcion migh be expeced o concenrae around earnings announcemens. Based on hypoheses and 3, I also predic he following: H4a: The negaive associaion beween invesmens and fuure sock reurns will be sronger in firms wih higher free cash flow and lower leverage. H4b: The negaive associaion beween invesmens and fuure sock reurns will be sronger in firms of posiive (discreionary) invesmen han in firms of negaive (discreionary) invesmen. 3. Sample, Variable Measuremen and Descripive Saisics 3.1 Sample Firms financial saemen daa are obained from he Compusa annual acive and research daabases and sock reurns daa are from he CRSP daily reurns files. I use annual Compusa daa insead of quarerly daa because firms invesing aciviies are no uniform during a year (Callen e al (1996)). I sar my sample from 196 because from ha year he daa is available for a subsanial number of firms and also because Compusa daa prior o 196 suffers from serious survivorship bias (Sloan (1996)). Financial firms (SIC codes ) are excluded because heir invesing, operaing and financing aciviies may be no clearly demarcaed. The full sample consiss of 133, 77 firm-year observaions represening 14, 446 firms from 196 o 00 o be included in my leas resricive es. The number of observaions in any paricular es will vary depending on requiremens of he es. 9

10 3. Invesmen Measures and Model of Discreionary Invesmen In his secion I show ha long erm asse accruals (e.g., change in ne PPE or long erm asse) and capial expendiures are boh srong proxies of invesmen inensiy. My resuls in laer ess are robus wih respec o he use of each variable. In addiion, he quesion of wha is a good measure of invesmen inensiy is iself of grea pracical value and surprisingly, no previous sudies of he relaive properies of various measures seem o exis. I begin by choosing a benchmark ha relaes invesmen wih invesmen opporuniies 9. An invesmen proxy ha bes maches invesmen opporuniies may be considered more accurae. Hayashi (198) shows ha under some condiions, he following equaion hold 10 : I 1 = a + [ Q ] + λ (1) K α where I is firm invesmen, K is he beginning-of-period capial sock, α is a parameer linearly increasing in he cos of adjusmen funcion, Q is he presen value of profis from new capial invesmen, and λ is some echnology shock. Based on he Hayashi model, i seems ha a good measure of invesmen inensiy should be deflaed by eiher PPE (propery, plan and equipmen) or oal asses. In fac, mos researchers proxy invesmen wih capial expendiure scaled by PPE or oal asses (e.g., Kaplan and Zingales (1997), Hennessy and Levy (00), Minon and Chrand (1999)). I apply he following variables o proxy invesmen opporuniies: Tobin s Q, profiabiliy (ROA) (Blanchard, Rhee and Summers (1993)), pas sales growh (Shin and Sulz (1996)) and value of growh opporuniy (Vgo, Richardson (00)). Second, I choose a benchmark for ex pos realizaion of invesmen. Invesmen inensiy should be refleced in fuure growh in sales, earnings and book value. Following an approach similar o Kallpur and Trombley (1999) and Richardson(00), I focus on ex pos realized sales growh 11, and examine 9 Alhough I am only rying o evaluae wheher one measure is a good proxy for invesmen, no necessarily opimal invesmen, i can be shown ha under some condiions, a measure ha bes maches for invesmen opporuniies is more accurae. Assume here are wo measures of invesmen, boh measuring he underlying invesmen inensiy wih errors: I 1 and I, where * * I 1 = I + D + ε and 1 I = I + D + ε, where I* is opimal invesmen and D is he disored invesmen resuling from informaion cos or agency problem. Assuming ε 1 has a smaller variance han ha of ε and boh measuremen errors are independen of I, D and Q, hen i is obvious ha I 1 should be more closely correlaed wih eiher Q or (Q and profiabiliy) han I does. Furher I 1 should fi he model beer han I in muliple variables regression. 10 Specifically, adjusmen coss in invesmen are linearly homogeneous in invesmen and capial, so ha marginal and average q will equal. 11 I choose no o use growh in book value or earnings as he benchmark. Growh in book value firms may bias in favor of some measures I laer choose, e.g., growh in PPE. 10

11 how differen measures of invesmen are correlaed wih i. Specifically, I esimae he correlaion year by year and significance for he mean correlaion over he enire sample period is assessed by a Newey-Wes (1987) -saisics. Now I inroduce candidaes of invesmen measures. I selec several measures ha are represenaive of wha early sudies have applied: Capial expendiure/ppe (e.g., Hennessy and Levy (00)) (Capial expendiure-depreciaion)/oal asses (e.g., Shin and Sulz (1996)) Capial expendiure/toal asses (e.g., Gompers, Ishi and Merick (003)) Capial expendiure/sales (e.g., Anderson and Garcia-Feijoo (003), Timan e al (001)) Capial expendiure/value (e.g., Smih and Was (199)) R&D/oal asses (e.g. Gaver and Gaver (1993), Hall (199)) Growh in invenory (e.g., Kashyap, Lamon and Sein (1994)) Growh in capial expendiure (e.g., Lev and Thiagarajan (1993)) Growh in number of employees (Lang, Ofek, and Sulz (1996)) I also add several measures ha I conend make sense as well: Growh in PPE 1 Long erm asse accruals (Change in long erm asse deflaed by average oal asses) 13 Growh in long erm asse Finally, I adop a measure of a firm s invesmen applied by Baber, Janakiraman and Kang (1996), as he sum of capial expendiure on PPE, acquisiions, and research and developmen, hen deflaed by depreciaion expense. Anoher measure INV_CS is consruced o measure he cash flows in invesing aciviies: -(-increase in invesmen + sale of invesmen-capial expendiure + Sale of PPE-acquisiion), divided by average oal asses 14. Ex ane, we may predic he relaive performance among some of hese measures of invesmen 1 The growh measure also akes good care of possible fixed effec ha may be presen in oher measuremens. Thomas and Zhang (00) applied a similar measure o proxy for invesmen: change in ne PPE scaled by oal asses. 13 Harrison and Horngren (003) define invesing aciviies as Aciviies ha increase or decrease he long erm asses available o he business. (Invesmens) increase and decrease long-erm asses, such as compuers and sofware, land, buildings, equipmen, and invesmens in oher companies. The purchases and sales of hese asses are invesing aciviies. (003, P548 ). 14 The advanage of his measure is ha i is mos accurae in reflecing he cash spen in invesing aciviies. A weakness of his measure is ha i omis non-cash invesing aciviies. Companies make invesmens ha do no require cash. Non-cash invesing aciviies can be repored in a separae schedule ha accompanies he saemen of cash flows. Hence, I anicipae his measure is leas powerful compared o he growh in long erm asses or PPE. A possibly more accurae measure can be derived from saemen of cash flows (daa311) and reflec how much cash is spen in invesing. The disadvanage of his measure is ha his measure is only available afer

12 inensiy. For example, capial expendiure/sales( expendiure/ppe ( I K ) because I S I K S / K I ) probably would be a noisier measure han capial S = where he denominaor S is somehing like a PPE K urnover raio which varies across indusries and hus inroduces some noise ino he raio. Anoher issue concerns capial expendiure. Noe ha i is almos always posiive and omis reiremen of any PPE. Focusing on only capial expendiure ignores de-invesmen from sale of PPE and invesmen hrough acquisiion, e.g., where firms liquidae one invesmen iem o finance anoher invesmen projec. Such ransacions represen poenial omied variables and creae poenially an errors-in-variables problem in prior research. Also, using growh of capial expendiure may be problemaic if here is lile expendiure in a prior year. A beer measure migh be simply he change in PPE divided by lagged PPE. Afer all, his is wha he model is supposed o relae. To esimae discreionary and non-discreionary invesmen, I apply he following rank regression: INV = α + β1 Q 1 + β ROA + β 3Sales _ growh + indusrydummies + yeardummies + ε () These hree explanaory variables, Tobin s Q, profiabiliy and pas sales growh, have been shown o proxy for invesmen opporuniies. Q alone is widely known o be nooriously noisy. Ali (003) argues ha a subsanial par of Q represens he opion value of long erm growh poenial. Since he opion value is no very informaive abou near erm invesmen plans, Q does no proxy well for shor erm invesmen opporuniies. In addiion, if he marke is unaware of invesmen opporuniies wihin a firm, he Q measure canno sufficienly reflec invesmen opporuniies. Managers may also manipulae sock prices o jusify he expendiure. These issues sugges ha oher variables be considered as prxies for invesmen opporuniies. Based on he validaion resuls in appendix A, I choose growh in PPE (d_ppe) and long erm asse accruals (INV_bs) as my measures of invesmens 15 because of heir superior performance and because hey are also measures of accruals 16. The fied value is called o be he non-discreionary componen of invesmen while he residual is defined o be he discreionary invesmen. The explanaory power is comparable o various accrual models wih an R square of abou 4%. Replacing Q wih he value-of-growh-opion (vgo) measure inroduced by Richardson (00) yields almos idenical resuls. In robusness check, I also add pas sock reurns as an explanaory variable (Fama (1981)) in he model and obain very similar resuls. 15 These measures in spiri are similar o he new invesmen in Richardson (00) as hey are clean of depreciaion and amorizaion, he porion of invesmen seen as o mainain asses in place. 16 I choose no o combine hese measures wih R&D or invenory because he former has higher and he laer has lower adjusmen coss han invesmen in PPE, while according o (1) a measure of homogeneous adjusmen cos is preferred. In addiion, here is lile evidence ha managers over inves in R&D aciviies, perhaps because hese expendiures are expensed raher han capialized. Moon (001) find ha he subjec of overinvesmen may be capial expendiure and no R&D expendiure. 1

13 3.3 Reurn Variables This secion I inroduce measures of abnormal sock reurns, omiing he subscrip. Abr = Size adjused 1monh sock reurn, measured as he realized buy-and-hold sock reurns 17 from CRSP over he 1 monhs saring from he end of monh four afer he end of fiscal year, minus he buy-and-hold reurn on a value weighed porfolio of socks having similar marke capializaion. The size porfolios are formed by CRSP and are based on size deciles of NYSE and AMEX firms. The assignmen of each sock ino size porfolios is based on firm s marke capializaion a he beginning of he fiscal year in which he reurn cumulaing period sars. Characer = Twelve monh sock reurns adjused for firm characerisics. This is anoher approach I conrol for risk. I follow Daniel, Grinbla, Timan and Wermers (1997) o consruc excess reurns relaive o benchmarks ha are consruced based on firm characerisics (i.e., size, book o marke raio, and momenum). I form 15 benchmark porfolios based on firm characerisics of size, book o marke raio and momenum. The porfolios are formed in he following way: Saring wih May of fiscal year, socks are sored ino five porfolios based on each firm s size a he end of fiscal year -1. The breakpoins are obained by soring NYSE firms ino quiniles based on heir size measures. The size of socks in my sample is hen compared agains he breakpoins o assign each sock ino a size group. Firms in each size porfolio are furher sored ino quiniles based on he -1 fiscal year end book o marke raios. Las, firms in each size-bm porfolios are sored ino quiniles based on prior year s sock reurns ending March of fiscal year. I choose March in sead of April as he year-end o reduce he impac of bid-ask bounce and monhly reversals. In each of he 15 porfolios, value weighed reurns are calculaed monhly from May of fiscal year o April of fiscal year +1. Benchmark porfolios are rebalanced each year. Each sock s excess reurn, called he characer-adjused reurn, is hen calculaed by subracing he sock s corresponding porfolio s reurn from he sock s reurn. 3.4 Free cash flow (FCF) and Leverage (L) Jensen (1986) defines free cash flow as he porion of cash flow ha remains afer all posiive NPV projecs are aken. However, as Lang, Sulz and Walking (1991) and Gul and Tsui (1998) poined ou, he lieraure provides lile guidance on he measures of FCF as defined by Jensen (1986). Researchers ofen use earnings before ineres, axes and depreciaion (EBITDA) or operaing cash flow less ineres expense as proxies for free cash flow (e.g., Fenn and Liang 001).Several proxies are used in he finance 17 Delising reurn is applied where available. Where unavailable, I follow Shumway (1997) for NYSE/AMEX socks and Shumway and Warher (1999) for NASDAQ socks o correc for delising bias. I use 0.3 as he las reurn for NYSE/AMEX socks and 0.55 as he las reurn for NASDAQ socks delised for performance reasons. If he delising code is sill missing, I use 1. Afer he delising and before he end of he 1h monh, I assume he proceeds from delising are reinvesed in he value-weighed marke 13

14 lieraure and I follow hese sudies o define FCF as operaing income before depreciaion less ineres, axes and preferred and common dividends. Such definiions are normalized by eiher oal asses or oal book value of equiy in he previous year. I choose o scale by oal asses, consisen wih Lang e al (1991), and Gul and Tsui (1998). As robusness checks, I also apply growh in cash holdings (GrCash) as a second proxy (Harford (1999)) and Richardson (00) s surplus cash measure as a hird proxy. I measure leverage as oal liabiliy divided by he sum of oal liabiliy and equiy capializaion, similar o Timan e al. I also apply deb raio as a second proxy for leverage (Lang, Ofek, and Sulz (1996)). 3.5 Descripive Saisics Table 1 provides descripive saisics for he key variables. The median book o marke raio is over my sample period. The median sales growh is bu he mean is 3.040, hus some firms have undergone exreme growh. The median and mean accrual is negaive, consisen wih oher sudies and implying cash flow from operaions exceeds GAAP operaing income on average. From panel B, invesmen inensiy (d_ppe) is posiively correlaed wih size (log_cap) and profiabiliy (conemporaneous ROA); hus i seems ha firms wih low invesmen inensiy are generally less profiable and smaller in size, consisen wih he noion ha profiable firms end o inves more. The Spearman rank correlaions also show ha invesmen measures such as d_ppe, INV_bs and growh in number of employees (d_employee) are negaively relaed o one year ahead size adjused reurns (Abr). Accrual is also significanly relaed o fuure abnormal reurns, confirming ha he accrual anomaly is presen in my sample. Invesmen measures (d_ppe and INV_bs) are posiively correlaed wih invesmen opporuniies (lag_q). They are also posiively correlaed wih one year ahead ROA. However, his correlaion does no conrol for curren ROA. Also as expeced, hese measures of invesmen are posiively correlaed wih pas sock reurns (d), profiabiliy (ROA) and negaively correlaed wih book o marke raio, suggesing he need o conrol hese facors in reurn analysis. Excep for he correlaions beween profiabiliy measures in adjacen years, no correlaion exceeds 50%, suggesing ha mulicollinearliy is unlikely o be a serious issue in subsequen regression ess. 4. Empirical Analysis I presen he empirical ess in several seps. In secion 4.1 I confirm ha a robus negaive associaion beween invesmen and fuure profiabiliy, boh shor erm and long erm. The evidence index. Reurn resuls are no sensiive o he adjusmen of delising reurns. 14

15 suppors he noion ha he associaion is likely o have an economic explanaion. In 4., I examine how free cash flow and leverage affec he relaion beween capial invesmen and fuure profiabiliy. In 4.3 I break he sample ino posiive discreionary invesmen firms and negaive discreionary invesmen firms, and examine wheher he negaive associaion is mosly driven by he former sample where overinvesmen is more likely o occur. In 4.4 I examine wheher invesors fully undersand he above relaions by looking a sock reurns. I also examine wheher he mispricing is mosly driven by posiive discreionary invesmen firms. Since hypohesis 4a is mosly a corroboraion of Timan e al, I leave ha es in he end. 4.1 Time series relaion beween invesmen and profiabiliy. Tes of Hypohesis 1 When firms increase invesmen, conservaive accouning leads o repored earnings ha are lower han hey would have been under liberal accouning. To es wheher higher invesmen will depress shor erm profiabiliy bu improve long erm profiabiliy, I apply he following regressions 18 : ROA + n = + β ROA + γinv + ε + n α (3) where n runs from 1 o 10 years ahead, INV sands for capial invesmen, ROA is operaing income scaled by average of oal asses a he beginning and end of fiscal year 19. Invesmen will likely inflae fuure oal asses--he denominaor of ROA (Fairfield, Whisenan and Yohn (003b)). Thus he finding of such a negaive correlaion could be no more han a mechanical relaion raher han an economic one. However, his denominaor effec can no las long in disan years when capial invesmens are fully depreciaed. To furher miigae he possibiliy ha he negaive associaion is mechanical, I also examine earnings deflaed by sales (PM): PM + + n = α + β PM + β INV + ε (4) 1 n Panel A of able repor regression resuls applying d_ppe as he invesmen measure. The coefficien on curren ROA is significan ranging from for one year ahead ROA o for 10 year ahead. The magniudes of ROA persisence are similar o hose repored in previous sudies. The coefficien on invesmen is for one year ROA. This means ha 1% growh in PPE will decrease one year ROA by abou 1.8 basis poins. As n increases, he coefficiens on curren ROA and profi margin (PM) ge smaller, indicaing sronger mean reversion of profiabiliy over longer periods. In addiion, he negaive coefficiens on invesmen also ge weaker. This suggess ha he dampening 18 Indusry dummies (wo digi sic code) are also included in he regressions bu no repored for exposiion purpose. 15

16 effec from invesmen on fuure earnings becomes less severe in disan years. However, he coefficiens remain significanly negaive ou o 1 years ahead, hen become insignificanly negaive hereafer. This resul is inconsisen wih conservaive accouning which predics ha a some poin he coefficien should urn posiive. Thus, conservaive accouning is unlikely he only underlying cause for he negaive associaion 0. On he righ hand side of he panel, I examine fuure earnings deflaed by sales and obain similar resuls. In unrepored resuls, I replace all variables by heir percenile ranks and ge resuls ha are consisen wih panel A. In panel B of able, I use long erm asse accruals deflaed by oal asses (INV_bs) as a measure of invesmen and obain a similarly negaive coefficien on invesmen for he following 10 years performance (ROA). The negaive coefficiens are bigger in magniude han hose in panel A; his migh be caused by he fac ha d_ppe is posiively skewed while INV_bs is more symmerically disribued and hence less affeced by exreme values. The relaion documened above is no due o a few exreme years. For example, when regressing one-year-ahead ROA on d_ppe, he coefficiens are negaive in 39 of he 40 years. 1 I do no examine ess beyond 0 years because i is no clear wheher resuls will be reliable given he survival bias. To furher highligh he implicaions of capial invesmens for fuure profiabiliy, I presen graphical evidence. I use a wo-sage ranking procedure. Firs, I sor he sample ino en porfolios based on ranks of curren RNOA. Wihin each decile level of RNOA, I furher sor he observaions ino five porfolios based on invesmen inensiy (d_ppe). I hen pool all 10 sub-porfolios of each RNOA level ogeher ino one porfolio. Now I have five porfolios ha have subsanial variaion in invesmen inensiy bu nearly he same level of curren profiabiliy ( RNOA ).The wo way soring ensures ha he observed relaion beween changes in RNOA over ime and invesmen does no reflec he widely 19 Using operaing income before depreciaion does no change he resuls qualiaively. 0 To more direcly examine wheher here is profi reversal from he conservaive accouning effec, I also run he following regressions: ROA + 1 = α + β ROA + γinv n + ε +1 where n=, 5, 10 If here is subsanial reversal effec, we would expec o see a posiive coefficien on invesmen. Unrepored resuls show ha mos coefficiens are insignifican. However, I do no asser here is no effec from conservaive accouning. 1 Unrepored resuls show ha oher measures of invesmens, such as growh in number of employees, also implies decreased one year ahead ROA. Fairfield e al (003b) raise a concern ha invesmen is posiively correlaed wih fuure oal asses, he denominaor of ROA. Ineresingly I find ou ha one year ahead earnings by curren year s average oal asses is also negaively affeced by invesmens. Applying RNOA raher han ROA provides a robusness check. I repea he graphical procedure based on ROA and obain similar paerns. 16

17 known profiabiliy mean reversion. This conrol is imporan as high invesmen is correlaed wih higher curren RNOA. In figure 1, I plo he op and boom quiniles, applying median values of porfolio RNOA. Figure 1 shows ha, on average, RNOA is higher for high invesmen firms prior o year 0, consisen wih firm growh and high invesmen opporuniies. However, afer year 0, RNOA sars deerioraing. The low invesmen firms repor lower RNOA han he high invesmen firms, bu by year 0 hey repor similar levels of RNOA as he high invesmen group (by consrucion). Afer year 0, high invesmen firms repor persisenly lower profiabiliy. In fac low invesmen firms coninue o have higher ROA han do high invesmen firms for up o 15 subsequen years. We migh predic ha ROA would evenually cach up for high invesmen firms in laer years, e.g., if he low ROA occurred because no all he high invesmen expenses (benefis) are properly capialized (recognized). However, as shown in figure 1, he ROAs never exceed he ROAs for he low invesmen firms. This is inconsisen wih conservaive accouning explanaion which predics ha he wo lines should cross when he hidden reserve from pas invesmen brings higher fuure profiabiliy. Thus, i seems unlikely ha conservaive accouning can solely explain he resuls 3. The above ess resuls are consisen wih relaed research in Richardson e al (003c) ha asser ha Fairfield e al (003a) s resuls are no consisen wih conservaive accouning or diminished reurns o sale. In a relaed sudy, Abarbanell and Bushee (1997) also find evidence ha he associaion beween capial expendiure and fuure earnings does no evenually reverse. Thus, a plehora of evidence calls for an economic explanaion for he associaion. I invesigae wheher overinvesmen can provide a parial explanaion. 4. The Impac of Free cash flow and Leverage Tes of Hypohesis a In panel A of able 3, I examine how he negaive coefficiens on invesmen vary wih lagged free cash flow levels, using d_ppe as he measure for invesmen. I sor he whole sample ino five porfolios based on levels of free cash flow levels in he year prior o invesmen. Then wihin each porfolio, I repea regression (3) in model 1. In he lef half of panel A, I condiion he regression on FCF while on he righ side I condiion on growh in cash holdings (GrCash) prior o year of invesmen. To examine he effec of free cash flow beyond one year, I also conduc he following regression in 3 In fac, because of he dampening effec of increased invesmen, he rue economic profiabiliy of he high invesmen group as of year of invesmen may be higher han ha of he lower invesmen group. Tha would furher bias agains no finding he 17

18 model : FROA 5 = + β1roa + β INV + ε 5 α (5) where FROA is he average ROA from year + o year +5. Across boh he regressions for one-year-ahead ROA (model 1) and subsequen four year average ROA (model ), he coefficien on invesmen is significanly negaive, excep in he model 1 resul for he lowes FCF group, where i becomes marginally significan. More imporan, across boh models he coefficiens increase monoonically (becoming more negaive) as he levels of FCF rise. For example, in model 1, he coefficien increases from wih an insignifican saisic in he lowes FCF level group o wih a significan saisic in he highes FCF group. In addiion, he number of years when he coefficien is negaive ranges from 9 ou of 39 years in he lowes FCF group o 37 ou of 39 years in he highes FCF group. Resuls based on GrCash are similar. Unrepored rank regressions also repor similar paerns. Thus preliminary ess show ha free cash flow is associaed wih a sronger relaionship beween men and fuure profiabiliy. Panel B of able 3 is for long erm accruals (INV_bs) as a measure of invesmen. Again, as he free cash flow level increases, he negaive coefficien on invesmen increases in absolue magniude from (=-0.13) o (=-8.6) in model 1, and from (=-.60) o (=-6.47) in model. Tes of Hypohesis b Panel C of able 3 invesigaes he effec of leverage in he year prior o invesmen, using d_ppe as he measure of invesmen. On he lef side, I repor regression resuls for he five porfolios ranked by marke leverage while he resuls on he righ hand side are for rankings by deb raio. Clearly, leverage has an opposie effec o ha of free cash flow. In model 1, he negaive coefficien decreases from -0.01o as leverage increases. The model regression for fuure ROA beyond one-year-ahead exhibis a similar paern. Using deb raio as a robusness check yields similar conclusions. Panel D of able 3 uses INV_bs o proxy invesmen. On he lef side in he able, we can see ha he coefficien decreases wih leverage, alhough no monoonically; in he highes leverage porfolio, he coefficien even becomes insignifican. This is consisen wih he noion ha leverage can miigae he negaive associaion beween long erm asse accruals and fuure profiabiliy. Overall, resuls in able 3 are consisen wih Hb. However, one possible concern is ha he conservaive effec. 18

19 negaive associaion beween invesmen and fuure profiabiliy is nonlinear. Thus he above documened resuls are simply a reflecion of he posiive correlaion beween free cash flow and invesmen levels and negaive correlaion beween leverage and invesmen level. To address his concern, I firs sor he whole sample ino 0 porfolios based on invesmen inensiy. Then wih in each porfolio I furher sor by curren ROA ino 0 porfolios. Wihin each of he 400 porfolios I rank lag free cash flow (leverage) level ino quiniles. This procedure makes sure ha each free cash flow (leverage) quiniles has similar invesmen and curren ROA disribuions. I hen repea he above ess and obain similar findings. Figure plos regression slopes of nex year ROA on invesmen (d_ppe) in he lowes, median and highes quiniles of free cash flow porfolios, while figure 4 plos regressions slope in each quiniles sored by leverage. Higher free cash flow level leads o a seeper slope in figure, consisen wih Ha. In figure 3, i is ineresing o noe ha he miigaing effec from leverage comes mosly from highes leverage quiniles. This paern is also consisen wih resul in panel C and D of able 3. The above ess, how ever, do no provide saisical significance. Thus, I resor o he following regression o idenify he effecs from boh free cash flow and leverage. ROA FROA + 1 = α + β1roa + βinv + β3fcf + β4l + β5roa * FCF + β6roa * L + β7inv * FCF + β8inv * L + β9inv * FCF * L + ε = α + β1roa + βinv + β3fcf + β4l + β5roa * FCF + β6roa * L + β7inv * FCF + β8inv * L + β9inv * FCF * L + ε 5 (6) and (7). Wha we are ineresed in are coefficiens on he hree ineracive erms INV*FCF, INV*L and INV*FCF*L. The firs erm represen how free cash flow levels affec he negaive associaion beween invesmen and fuure profiabiliy. The second erm capures effec from leverage. The hird erm examines wheher leverage can miigae he overinvesmen issue rooed from free cash flow. Based on Ha and Hb, I expec he firs erm has a negaive coefficien while he oher wo bear posiive coefficiens. In he regression I also include conrol variables. I expec he coefficien on FCF o be posiive because free cash flow may iself presen a signal of profiabiliy. The implicaion of leverage is no clear so I do no make predicions. The effecs from ineracion erm of ROA*FCF and ROA*L are no clear, eiher. Table 4 repors resuls from regressions (6) and (7) where FCF and L are replaced by heir quinile indexes (e.g., lowes FCF akes value of 0 while highes level of FCF akes value of 4) 4. In panel A, invesmen is proxied by d_ppe. As expeced, coefficien of ROA is posiive while ha of invesmen 4 Using dummies or original values yield qualiaively similar resuls. 19

20 (INV) is negaive across boh models. Coefficiens on FCF are all significanly posiive; suggesing he need o conrol his variable as firms wih high FCF generally performs beer. Ineresingly, he coefficien on leverage (L) is significanly posiive in all models. ROA*FCF has posiive coefficien in model 1 bu negaive coefficien in model. In panel B his erm has negaive coefficien across boh models. One possible explanaion is ha firms ha perform exremely well in he pas (as refleced by his ineracion erm) canno keep he momenum and reverse o lower profiabiliy. The ineracion erm ROA*L has a significanly negaive coefficien (=-3.93) in model 1 and (=-7.8) in model. One possible explanaion is ha hese firms have excess cash boh from free cash flow and from exernal fund, hus providing more resource for managers o engage in negaive NPV projecs. Turning o variables of ineres, all coefficiens on INV*FCF are significanly negaive, consisen wih my predicion. Ineresingly, in model, he -saisic (=9.89) is even more significan han ha of INV (=-6.09). This suggess ha a significan par of he implicaion of invesmen for fuure profiabiliy can be explained by he free cash flow problem. The coefficien on INV*L is significanly posiive (=8.11 and =3.4) in model 1, (=8.06 and =.69 ) in model. The saisics are relaively smaller compared o INV*FCF. This is expeced because he miigaing effec from leverage is likely secondary. The las ineracion erm INV*FCF*L has a significanly posiive effec (=.8) in model 1 and model (=.58). This is evidence ha leverage can miigae he overinvesmen problem ha is caused by high free cash flow. Panel B repea he regression using long erm asse accrual as invesmen. Resuls are very similar o hose in panel A. Unrepored regressions ha apply growh in cash holdings (GrCash) and deb raios yields similar resuls. Thus, resuls are consisen wih Ha and Hb ha while free cash flow can exacerbae he negaive associaion beween invesmen and fuure profiabiliy, leverage can miigae his effec. 4.3 The Sronger Implicaions in he sample of Posiive (Discreionary) Invesmens versus in he sample of Negaive (Discreionary) Invesmens. Tes of Hypohesis 3 To es H3, I compare he regression (3) resuls in he posiive (discreionary) invesmen sample versus he negaive (discreionary) invesmen sample. H3 predics ha negaive associaion is presen in he former group bu no in he laer. Ideally I wish o ge a sample of overinvesmen; empirically his is no easy. One parsimonious approach is o classify posiive invesmen firms as overinvesmen sample and oher firms as underinvesmen. This approach implicily assumes ha all firms have zero 0