Circularity and the Undervaluation of Privatised Companies

Transcription

1 CMPO Workig Paper Series No. 1/39 Circulariy ad he Udervaluaio of Privaised Compaies Paul Grou 1 ad a Zalewska 2 1 Leverhulme Cere for Marke ad Public Orgaisaio, Uiversiy of Brisol 2 Limburg Isiue of Fiacial Ecoomics, Uiversiy of Maasrich ugus 21 Revised December 21 bsrac Circulariy arises i regulaio if he value of a compay s asses used o se prices is iself deermied by fuure earig capaciy. The view ha i is o possible o deermie values ad prices i hese circumsaces has become well esablished i he lieraure. I his paper we formalise his precise circulariy resul. We he show ha if here is a possibiliy of fuure review ad he regulaor makes symmeric errors i esimaig he cos of capial kow o he compay he almos all valuaios ivolve udervaluaio of he asses of he privaised compay. JEL Classificaio: L33, L51 Keywords: Privaisaio, Regulaio, Udervaluaio. ckowledgemes We hak he Leverhulme Trus for fudig his research. ddress for Correspodece Deparme of Ecoomics Uiversiy of Brisol 8 Woodlad Road Brisol BS8 1TN Tel: p.a.grou@brisol.ac.uk CMPO is fuded by he Leverhulme Trus.

2 1. Iroducio The view ha i is o possible o deermie regulaory asse values ha are based o fuure earig capaciy has become a core oio i he lieraure o regulaio. I was firs ideified almos a hudred years ago i he US followig o from he Supreme Cour judgeme i Smyh v. mes I his case he Cour suggesed ha probable earig capaciy had o be cosidered whe valuig uiliies for regulaory purposes. Bu he a circulariy problem arises sice he value of asses i place is o be deermied by referece o fuure raes bu hese fuure raes are hemselves deermied by a fair reur o he value. There followed a leghy, holy dispued legal ad academic debae, which has coiued i various forms hroughou he weieh ceury, as o he appropriaed mechaism o value he asses of a uiliy. This lieraure is immese ad, while diverse o may issues, has bee uaimous o he problem of circulariy. The circulariy problem has re-appeared i he las decade as a resul of he wave of privaisaios of public uiliies ha have ake place aroud he world. Wih he geeral excepio of elecommuicaios, here has bee a srog edecy for he marke price of privaised uiliies o be below heir replaceme cos a privaisaio. Tha is, udervaluaio ad associaed uderpricig is commo place. large lieraure is developig o udervaluaio ad uderpricig alhough lile of his is cocered wih he coseque problem i creaes for regulaory policy. 1 The difficuly is o decide wha asse base should be used o se prices for hese regulaed uiliies. Texbooks have radiioally focused o replaceme cos or book value as 1 We use he sadard ermiology of udervaluaio o imply asses are purchased below heir replaceme cos ad uderpricig o imply hey are purchased below heir equilibrium value. 1

3 he appropriae valuaio for regulaory purposes. However, regulaory auhoriies ed o argue ha if hese are used as he asse base i privaisaios where shareholders have paid less ha his for he asses he here appears o be a ufair rasfer from cusomers o shareholders. Typically, he procedure used o avoid his rasfer has bee he implemeaio of a marke value deb plus equiy approach as he asse base. However, as is recogised i he lieraure, his brigs he circulariy problem back o he fore. This shor paper oulies he circulariy ad udervaluaio problem ad he makes wo mai coribuios. Oe, i formalises, we believe for he firs ime, he precise circulariy resul ad ivesigaes is robusess. We show ha he view ha i is ever possible o ie dow values ad prices is o paricularly robus bu ha here are more suble versios ha coradic some of he basic predicios whils reaiig a form of circulariy. Secod, we show ha here is a heoreical relaioship bewee he use of marke values wih is ihere circulariy ad udervaluaio of privaised asses. Secio 2 begis by providig a brief hisory of asse valuaio ad he circulariy problem i he US ad describes he udervaluaio problem ad how i has bee deal wih i he UK privaisaio programme. I he formalises he circulariy resul as i is commoly saed. I is show ha if exisig asses are valued accordig o heir earig power, i.e., prese value, he here is ideed o uique value o hese asses ad cosequely o uique regulaory prices. However, o obai his resul we assume ha he valuig exercise is coduced oce, i.e., here is o possibiliy of review. Secio 3 shows ha if here is a possibiliy of fuure reviews he siuaio 2

4 chages. We allow for reviews ha arrive by a Poisso process ad assume ha he regulaory agecy may make errors i heir esimaio of he cos of capial. I is show Proposiio 1 ha, while here is a ifiie se of valuaio pahs, o each pah almos every valuaio is close o replaceme cos. Tha is, oce he iiial valuaio is se he all fuure valuaios are fully deermied ad coverge o replaceme cos. I his sese he core circulariy problem, ha i is ever possible o ie dow he value of he uiliy ow or i he fuure, o loger holds. However, a far weaker ad subler form of circulariy exiss sice he iiial valuaio is sill ideermiae. lmos all valuaios have o be close o replaceme cos bu here is sill scope for ideermiacy a privaisaio. Circulariy ca oly be compleely avoided if we are willig o iroduce sroger assumpios o ake advaage of he saioariy of he problem. I paricular, if we are willig o impose he resricio ha wheever wo reviews are ideical i all respecs save for he ime label hey should have he same value, here is a uique valuaio. This is equal o he replaceme cos of he asses. Boh hese resuls i.e., he circulariy resul ad Proposiio 1 allow for he possibiliy ha he regulaory agecy makes a error i he esimae of he cos of capial we assume ha he error geeraig process has a bouded, symmeric desiy fucio wih zero mea. However, we assume ha, a he ime of valuaio, he precise error is ukow. I pracice, a regulaory agecy s choice of rae of reur is kow, a leas wihi a rage. Therefore, we also cosider wha happes if here is a possibiliy of fuure review ad a each review he regulaory agecy aouces he agecy s view of he appropriae cos of capial, before he valuaio process is coduced. Tha is, he marke kows he error whe prices are se. The valuaio is 3

5 uique bu, of course, is exac value depeds o he error draw from he error geeraig process. We ca, herefore, deermie a mea valuaio across all he possible errors. This provides a resul similar o Proposiio 1 save ha i his case o ay pah almos all hese mea valuaios will be sricly less ha replaceme cos Proposiio 2, i.e., we fid ha o average circulariy iduces udervaluaio of privaised asses. The paper is implicily cocered wih valuaios se i a sock marke bu, sice he model is drive by commo prese valuaio of cash flows, he geeral priciples should carry over o siuaios where he valuaio is deermied by aucio. Ideed, as log as poeial bidders have privaely kow sigals draw from a commo, sricly icreasig, aomless disribuio he he reveue equivalece heorem suggess ha his should be rue for all well kow ypes of aucios see, for example, Bulow ad Klemperer 1996 ad Riley ad Samuelso Circulariy 2.1 The circulariy problem ad associaed lieraure The problem of circulariy i regulaio goes back o he ieeeh ceury, arisig i he semial Supreme Cour case of Smyh v. mes The case cocered a dispue abou railroad raes i Nebraska. The sae of Nebraska s ewly creaed Board of Trasporaio se recommeded raes ha he railroads challeged o he basis ha hey were cofiscaory. The backgroud o he dispue was ha he 2 Of course, he commo disribuio is ceral for his e.g., Maski ad Riley

6 railroads had bee cosruced a he ime of he Civil War, whe prices were high, ad hey argued ha hey should receive a reur o his origial cos. I reachig a judgeme o he case, he Supreme Cour creaed he oio of fair value he Cour cocluded he compay was eiled o a fair reur o fair value. I argued ha value should be approached as follows: I order o ascerai ha value, he origial cos of cosrucio, he amou expeded i permae improvemes, he amou ad marke value of is bods ad sock, he prese as compared o he origial cos of cosrucio, he probable earig capaciy of he propery uder paricular raes prescribed by saue, ad he sum required o mee operaig expeses, are all maers for cosideraio, ad are o be give such weigh as may be jus ad righ i each case. We do o say ha here may o be oher maers o be regarded i esimaig he value of he propery. 3 The presece of i he marke value of is bods ad sock, ad ii he probable earig capaciy of he propery uder paricular raes prescribed by saue, as elemes ha had o be cosidered whe valuig uiliies raised he specrum of circulariy. The value of asses i place is o be deermied by referece o fuure raes bu hese fuure raes are hemselves deermied by a fair reur o he value. There followed a leghy, holy dispued legal ad academic debae, which has coiued i various forms hroughou he weieh ceury as o he appropriaed mechaism o value he asses of a uiliy. Uil he Secod World War, he Supreme Cour flucuaed i is views ad i was oly i 1944 ha he pracical issue was laid somewha o res as a resul of he Hope Naural Gas case. 4 I his case he Supreme Cour pu is emphasis o pragmaism ad a presumpio i favour of he 3 Smyh v. mes 169 U.S

7 Commissios - he who would upse he rae order uder he c carries he heavy burde of makig a covicig showig ha i is ivalid because i is ujus ad ureasoable i is cosequeces. 5 Bobrigh 1948 described he Hope case as: Oe of he mos impora ecoomic prooucemes i he hisory of merica Law. Uless he Cour reverses iself, o loger will i impose upo legislaures or commissios, sae or federal, he severe resricios upo heir powers o fix raes ha i previously imposed uder is docrie i Smyh vs. mes. The rule of reasoable reur o fair value may sill be reaied by saes ha choose o reai i. Bu i has ceased o be law of he lad. From his ime o regulaors exercised heir power ad, i he iflaioary era, eded o favour origial cos valuaios. 6 lhough he awkward oio of fair value remaied he law of he lad uil he Hope Naural Gas case, is problems ad, i paricular, he circulariy issue received heavy criicism by boh academics ad lawyers e.g., Bauer 1918, 1924, Bobrigh 1926, Souhworh 1922, ad he series of sessios i he papers ad proceedigs of merica Ecoomic Review i 1924, 1927 ad 1928 whe he debae was a is heigh. The iabiliy o value asses i he face of circulariy has become a idusry sadard e.g., see Kah s classic ex o regulaio Kah Ideed, eve by 1918 Bauer poied ou ha he circle of value ad raes has bee poied ou perhaps a housad imes. 4 Federal Power Commissio v. Hope Naural Gas Co. 32 U.S Federal Power Commissio v. Hope Naural Gas Co. 32 U.S , See Grou ad Jekis 21 for a assessme of he exe of opporuism displayed by regulaors as a resul of price chages. By 1991 a sudy of 53 regulaory commissios revealed ha 44 were usig 6

8 The circulariy problem appeared o have disappeared as a pracical issue i he pos war era ad was replaced for may years wih a focus o origial ad reproducio cos. However, as idicaed i he iroducio, he problem has reappeared o a major scale i he las decade wih he wave of privaisaios of public uiliies ha have ake place aroud he world. The backgroud o he ew circulariy problem i uiliy regulaio is ha, wih he geeral excepio of elecommuicaios, here is a edecy o sell asses below heir replaceme cos a privaisaio. The UK has bee a he forefro of privaisaio e.g., i he rece Deweer ad Malaesa 1997 ieraioal sudy of privaisaio, over 6% of he offers i heir mos complee regressio come from he UK so i is isrucive o look a he udervaluaio of privaised uiliies i he UK. This is summarised i Table 1 where he defiiio of marke value is deb plus equiy valued a he ed of firs day of radig. Table 1 Udervaluaio i UK Uiliy Privaisaios 7 Marke value divided Uiliy Compaies by CC book value Briish Telecom 97.3% Briish Gas 42.% Waer & Sewerage Compaies 3.6% Regioal Elecriciy Compaies 6.5% Naioal Grid Compay 4.4% Naioal Power 57.1% PowerGe 48.9% Railrack 68.8% There are likely o be may coribuory facors ha lead o udervaluaio. Here we provide a few examples. Firs, he oe ha we model i his paper, arises because he regulaory regime has o esimae he releva risk adjused cos of capial. This hisoric cos, while 7 sill adhered o fair value, ad wo commissios cosidered all he evidece, wihou a predeermied choice of rae base. 7 Source: Carey e al 1994 ad privaisaio prospecuses 7

9 affecs he valuaio sice i fixes fuure prices. Errors, or perhaps deliberae policies, by a regulaor ha lead o a iiial reur below he cos of capial will depress he price ha he marke is willig o pay for he asses. If his lower marke value is he he basis for asse valuaio used o deermie fuure price he he impac o he valuaio may be large. 8 secod example arises because he goverme has a precommime problem ha i may miigae by limiig he rasfer of owership. Peroi 1995 provides a formal model of his effec ad a heoreical argume for uderpricig of sock. 9 fial example arises if he pos privaisaio maageme may be able o provide performace ha is more efficie ha he performace of he radiioal public maageme ad superior o goverme suppored effors o reorgaise prior o privaisaio see for example, Lopez-de-Silaes 1997, ad Meggiso e al If such beefis ake ime o impleme he oe would expec asses o be udervalued a privaisaio. The udervaluaio of privaised uiliies causes a problem for regulaory policy. Wha asse base should be used for he review of prices? I he face of udervaluaio a shif o replaceme cos appears o provide a widfall gai o shareholders ad a price icrease for cosumers ha govermes are reluca o coemplae. While a soluio could be achieved by widfall axes ad lump sum rasfers here has bee lile aemp o follow his roue. The sadard procedure has 8 This may o be simply a direc impac o he cos of capial bu could be hrough suble mechaisms. Joes e al 1999, provide a deailed aalysis of he more explici ways ha way goverme s affec compaies aroud privaisaio. 9 Uderpricig of privaised sock is well documeed e.g., Jekiso ad Mayer 1988, Deweer ad Malaesa The evidece idicaes, for whaever reaso, ha he scale of uderpricig is greaer whe calculaed over a loger period ha if i is calculaed agais he ed of firs day radig. Therefore, eve if he regulaory asse value is se equal o he marke valuaio a he ed of firs day radig whe uderpricig should have uravelled, if prices coiue o rise for some ime he uderpricig will cause udervaluaio. 8

10 bee a isiuioalisaio of he marke value deb plus equiy approach as he regulaory soluio. The UK experiece is iformaive i his regard. The firs major uiliy privaisaio i he UK was Briish Telecom, which was iiially regulaed o a hisorical cos basis, ad he laer o a reproducio cos basis. s appears commo for elecommuicaios, he goverme was able o exrac he full replaceme value of he asses. The siuaio, however, was very differe for he oher privaisaios. I he case of Briish Gas, he allowed rae of reur was se a jus over 6 per ce of he rue risk adjused cos of capial. This mark-dow i he allowed reur was specifically o reflec he differece bewee he marke value of he asses ad replaceme cos. I he waer idusry he waer regulaor, Ofwa, explicily used a marke value of he compay as he asse base for regulaory purposes based o share prices averaged over he firs 2 days radig from he dae of privaisaio. I he elecriciy secor marke values a ed of firs day radig are also he sadard asse valuaio approach wih a mark-up o ed of firs day radig value ragig bewee 15% ad % depedig o he compay. Mos recely, Railrack s asse value is se a marke value based o he share price a he ed of he firs radig day wih o uplif. 1 Privaisaio ad he marke value approach o asse valuaio, which we migh hik of as he UK sadard, has brough he circulariy problem oce more o he fore. No surprisigly, he coveioal view, ha circulariy egaes he use of marke values, is also prese i he ew privaisaio ad regulaio debae. 11 For example, he 1 Railrack have ow ceased radig havig failed i he face of a uexpeced massive icrease i cos. 11 For example, he leadig ex o UK privaisaio ad regulaio saes: Usig marke values makes some sese because shareholders eed o be coviced ha hey will o be expropriaed a review 9

11 leadig ex o UK privaisaio ad regulaio saes Usig marke values makes some sese because shareholders eed o be coviced ha hey will o be expropriaed a review ime. Bu his rus he risk of circulariy, ad he use of marke values is o feasible for firms abou o be privaised or ha are subsidiaries ad o separaely quoed. rmsrog e al The basic model ad he circulariy resul I his secio we firs provide wha we believe o be he firs formalisaio of he circulariy resul. The problem arises, o from he valuaio of asses ha will be purchased i he fuure, bu from he valuaio of exisig asses. If here is a oe off valuaio of a busiess, ha will o be revised a some laer dae, he all asses ha will be purchased i he fuure have a value ha is se by heir marke price. 12 I paricular, if he marke for supply of physical capial is compeiive he fuure asses will be available a heir reproducio cos. The core problem is he asses ha are already i place a he ime of he review. I oe sese, of course, he marke also ses heir price bu his leads direcly o he problem of circulariy. Tha is, he marke price will be based o earig power bu, for a regulaed uiliy, he earig power depeds o he valuaio used o deermie fuure reurs. s Rose 1962 pois ou, The cos o he uiliy of faciliies previously employed is depede upo aicipaed earigs ad is iadmissible as he rae base. ime. Bu his rus he risk of circulariy, ad he use of marke values is o feasible for firms abou o be privaised or ha are subsidiaries ad o separaely quoed. rmsrog e al We assume hroughou ha he regulaor does o reage o policy; oherwise we ru io a ime cosisecy problem see, for example, Grou I Secio 3 we address he siuaio where he valuaio of asses is updaed i he fuure. 1

12 To aalyse he circulariy problem we assume ha he regulaory agecy values he asses i place a he curre ime a heir marke value i.e. heir earig power. We deoe his valuaio by. We assume ha hese asses will depreciae over ime a a rae >, so, if he value of he asses is se a he marke value, he a ay poi i he fuure he curre asses i place will have a value of e - sice 1-e - will have disappeared due o depreciaio. These will be replaced wih ew asses ha, i aggregae, cos. 13 Hece lookig forward o period he value of he compay s asses will be e - 1- e -. The compay will be allowed o ear a reur o hese asses which, if here are o errors, will be se a he releva risk adjused cos of capial. Tha is he compay is allowed o se prices o achieve he allowed cos of capial ad o cover depreciaio. The rue cos of capial is >. However, he regulaor has o esimae he risk adjused cos of capial ad may make a error,, i assessig he rue cos of capial. Therefore, he curre value of he sream of earigs ca be expressed as e 1 e e d. 13 There is o iflaio i he model so here is o disicio bewee origial cos ad replaceme cos; boh are equal o. 11

13 We assume ha he error geeraig process has a zero mea, symmeric desiy fucio φ : R R wih suppor -,, >. 14 We furher assume, for curre purposes, ha he realisaio of his error is ukow whe he valuaio of he compay s asses akes place. The expeced sream of earigs has a prese value of E e 1 e e d. The above formula represes he earig power of he compay save for he fac ha he compay has o fud he replaceme of asses. Regardless of he regulaory agecy s decisio ha he asses are oly worh ad oly allowed o ear heir marke value, he rue cos of replacig he asses is ad hece he compay has o pay his o mee depreciaio over he life of he asses. This is: e d. Therefore, he fuure earig power of he compay is E e 1 e e d e d. 1 The circulariy arises sice he expeced value of his fuure earig sream 1, based o, deermies he prese marke value, i.e., 14 The ierpreaio of is give i Secio 3. 12

14 e 1 e e d e E d. Solvig he equaio for marke value we obai E e 1 e e 1 e e e d d e d e d 1 1. Tha is, ay value of saisfies he equaio. Sice ca ake o ay value, he he prices ha he uiliy charges are hemselves ideermiae. This is he circulariy problem ideified i he lieraure which, o avoid cofusio wih laer proposiios, we call he circulariy resul. 3. Udervaluaio feaure of he circulariy model give i he previous secio is ha he marke value is deermied ad se oce ad for all. More geerally, i is reasoable o assume ha he valuaio is reviewed a cerai periods ad aoher ew asse base se, albei alog exacly he same lies as he previous oe. Tha is, a he h review he marke value,, ad earig power of he asses is reassessed ad his ew value is used for regulaory purposes. We hus eed o esablish a imig relaioship for 13

15 reviews o be coduced. We assume ha he life of he curre agreeme ad each fuure review is limied bu he exac imig of he ex review is ukow. We assume ha he imig of he reviews is described by a Poisso process, where N is he umber of reviews ha occur a or prior o ime, ad E N1. The marke value of he asse a each review depeds o he expeced value a he ex review. Le deoe a cosise ime pah of valuaios ad ϑ he se of all he cosise ime pahs of valauaios. I his secio, we cosider wo differe cases cocerig wha is kow a he iiial valuaio ad a he ime of he fuure reviews abou he regulaory error. he iiial valuaio ad each review we assume ha he regulaory agecy makes a fresh esimae of he cos of capial, i.e. a fresh draw from he same disribuio of. Case 1. We say ha is ukow a review if a he iiial valuaio ad each review he releva regulaory agecy s esimae of he cos of capial is revealed o he marke afer he valuaio has ake place. Case 2. We say ha is kow a review if a he iiial valuaio ad each review he regulaory agecy s esimae of he cos of capial for ha review is kow before he valuaio has ake place. Of course, a each curre review i case 2 he paricipas will o kow he ha is releva for he ex review, alhough i will become kow before he valuaio a he ex review. We would like o sress ha whe is kow a review he acual value will deped o he releva. I his case i is possible o calculae a expeced value before he releva is revealed ad he acual valuaio deermied. To avoid 14

16 cofusig ermiology we always refer o his expeced valuaio as he mea valuaio ad use his ermiology oly i his coex. The followig proposiio deals wih he case whe is ukow a review. This is also he assumpio i he previous secio so he model i Proposiio 1 is ideical o ha used o derive he circulariy resul save ha we ow allow he possibiliy of review. Proposiio 1. If is ukow a review ad is fiie, he almos all ϑ are arbirary close o replaceme cos. Proof. Firs, le us presume ha he firs review is kow o happe a ime T. The, he marke value of he busiess is T E e 1 e e d T e ~ d e T, where ~ is he expeced value of he compay s asses se as a resul of he review a ime T. T is a radom variable wih a expoeial disribuio ad he expeced value of regulaor s error is zero, hus he value of he compay a ime is 15

17 ~ ~ ~ dt e e e e e dt e e d e d e e e T T T T T T T T T Solvig his equaio for we obai:. 1 ~ 2 To disiguish he ime pah of he valuaios le us redefie 1 ad ~, where 1, 2, deoes he posiio i he sequece of reviews ad deoes he iiial valuaio. The he above equaio becomes 1 1, or 1. I oher words 1. 3

18 17 I immediaely follows ha because 1 <, he sequece { } has limi: lim. More echically, for ay ξ >, here exiss such ', ha for all > ', we have < ξ. Moreover, from equaio 3, i is easy o calculae ha ' is deermied due o he formula l l l l ' ξ. To complee he proof we eed o show ha whe he ime horizo is sufficiely large he probabiliy of havig almos all valuaios i he ξ- eighbourhood of is oe. More precisely, we eed o show ha whe goes o ifiiy he probabiliy measure of he raio of he se of valuaios ha lie wihi he ξ-precisio ierval o he se of all expeced valuaios ha would occur i he ime ierval [, ] is equal o oe. To demosrae his we prove ha, whe goes o ifiiy, for ay arbirary α > he probabiliy ha α < ' N is 1, i.e. 1 ' lim > α N P, The above is rue as! ' ' lim! lim ' ' α α α α α e e k N P k k, 4

19 where [x] deoes he larges ieger umber i ierval [,x]. Because he probabiliy of ay eve is always o-egaive, we coclude from 4 ha lim P N. α Proposiio 1 parially breaks he circulariy resuls. Oce ay oe valuaio is give he all fuure valuaios are fully deermied by he uique equilibrium pah. I his sese he core circulariy problem, ha i is impossible o ie dow he value of he uiliy ow or i he fuure, o loger holds. Of greaer sigificace, i mus be he case ha virually all of he valuaios of he uiliy will be approximaely equal o replaceme cos. However, he circulariy is o fully avoided i ha ay possible iiial valuaio is cosise wih some ime pah of equilibrium valuaios. Thus, havig iroduced he possibiliy of fuure reviews we have a weaker ad subler form of circulariy. Circulariy ca oly be compleely avoided if we are willig o iroduce sroger assumpios o ake advaage of he saioariy of he problem. Noe, a ay give review, he model a he ex review will be ideical o he curre review. Tha is he marke value a he ex review will deped o he earig power a he review, say a ime T i exacly same way ha depeds o he earig power a he curre review, say a ime T. If we are willig o impose he resricio ha if wo reviews are ideical i all respecs, save for he ime label, hey should have he same value, he he oly equilibrium is ha all valuaios mus be equal o replaceme cos. 18

20 The excepio o his occurs whe goes o ifiiy. For example, from equaio 2, ~ lim 1 lim ~. Of course, his esseially implies ha reviews ake place ifiiely ofe i ay small ierval of ime. We ow ur o he case whe is kow a review. Proposiio 2. If is fiie ad is kow a review, he here exiss a marke valuaio B such ha i B is sricly less ha replaceme cos ad ii almos all marke valuaios of he compay s asses ϑ are arbirary close o B. Proof. If he exac imig, T, of he firs review is ukow, he he prese value of he compay s asses i he ivesme period [,T] is deermied by he followig equaio T T ~ T T e 1 e e d e d e e dt, 19

21 2 or. ~ Because < here exiss a uique fiie soluio ~ 1. 5 Equaio 5 will be rue for ay followig ivesme period assumig ha he oher parameers of he model, i.e.,, are uchaged. Takig he mea value across all such ha < we obai φ φ φ, ~ ~ ~ d d d E E where φ is a desiy fucio of defied i Secio 2.2. s i he proof of Proposiio 1, le us redefie 1 ad ~, where 1, 2, deoes he posiio i he sequece of reviews ad deoes he iiial valuaio. The he above equaio becomes

22 21 φ d 1 1. Equivalely we ca wrie 1 1 Q Q Q Q Q where φ Q d. From he above represeaio i is obvious ha, because Jese s iequaliy guaraees Q > 1, he series { } ℵ has a fiie limi:. lim Q Deoig, Q B we coclude ha lim. B <

23 This is because < 1. Q To complee he proof ad show ha almos all valuaios,, of ay valuaio pah lie i ay arbirary small ξ-eighbourhood of valuaio B we eed o repea he reasoig we preseed i he proof o Proposiio 1, where ow ' l ξ l B. l l Q These calculaios are absoluely dual o hose preseed i he proof of Proposiio 2 ad are o preseed here. Proposiio 2 shows ha o average almos all valuaios exhibi udervaluaio. Ideed if we are willig o assume ha if wo reviews are ideical i all respecs, save for he ime label, hey should have he same value, he he iiial valuaio ad every review will o average exhibi udervaluaio. The iuiio for his udervaluaio arises from he expoeial srucure. For example, a prese value calculaio or a arrival rae of he Poisso process ake he form 1 / or 1 /. The regulaory error epsilo has he effec of reducig or, e.g., 1/. Therefore, he prese value a he curre review is a covex fucio of. I follows ha if he aicipaed value of he ex review is replaceme cos, he 22

24 he curre mea valuaio mus be greaer ha. Therefore cao be he seady sae soluio, which mus be less ha, hece udervaluaio. 4. Summary The paper has oulied he hisory of he circulariy problem ad he scale of udervaluaio of privaised asses. Despie he fac ha boh have araced large lieraures his is he firs paper o formalise ad ivesigae he received wisdom cocerig circulariy ad o provide a heoreical relaioship bewee he wo. We have show ha he view ha i is o possible o ie dow values ad prices whe fuure reurs form he valuaio base is o paricularly robus. If here is a possibiliy of fuure review he almos all valuaios are deermied. However, here is sill scope for ideermiacy a privaisaio. Tha is, here are more suble versios ha coradic some of he basic predicios whils reaiig a form of circulariy. We also cosider he siuaio where a each review he regulaory agecy aouces he agecy s view of he appropriae cos of capial before he valuaio process is coduced. Tha is, he marke kows he error whe prices are se. We show ha o ay valuaio pah almos all mea valuaios will be sricly less ha replaceme cos. Tha is, we fid ha o average circulariy iduces udervaluaio of privaised asses. This raises a core problem. The use of marke values isead of replaceme cos as he asse base is jusified solely o he basis of udervaluaio bu aoucig i advace ha his is he regulaory procedure iself icreases he likelyhood of udervaluaio. 23

25 Refereces: rmsrog M., S. Cowa, ad J. ickers, 1994 Regulaory Reform, MIT press. Bauer J., 1918 The Federal aluaio of Railroads, merica Ecoomic Review, 8. Bauer J., 1924 Fair alue for Effecive Rae Corol: Reply o Judge Rasom, merica Ecoomic Review. Bobrigh J.C., 1926 Progress ad Povery i Curre Lieraure o aluaio, Quarerly Joural of Ecoomics, 4. Bobrigh J.C., 1948 Uiliy Rae Corol Recosidered i he Ligh of he Hope Naural Gas Case, merica Ecoomic Review, Papers ad Proceedigs, 38. Burlow J. I., ad Klemperer P.D., 1999, ucios vs. Negoiaios, merica Ecoomic Review, 86, Carey., M. Cave, R. Duca, G. Houso ad K. Lagford, 1994 ccouig for Regulaio i UK Uiliies, Research Board of Isiue of Chared ccouas i Eglad ad Wales. Deweer, K.L. ad P.H Malaesa, 1997 Public Offerigs of Sae Owed ad Privaely Owed Eerprises; Ieraioal Compariso, Joural of Fiace, 52. Grou, P.., 1984, Ivesme ad Wages i he bsece of Bidig Coracs: Nash Bargaiig pproach, Ecoomerica, 52. Grou P.. ad. Jekis, 21, Regulaory Opporuism ad sse aluaio: Evidece from he US Supreme Cour ad UK Regulaio, Leverhulme Cere for Marke ad Public Ecoomics Workig Paper Series No1/38. Jekiso, T ad C Mayer, 1988 The Privaisaio Process i Frace ad he UK, Europea Ecoomic Review,

26 Joes, S,L, W.L. Meggiso, R.C. Nash, ad J.M. Neer, 1999 Share Issue Privaisaios as Fiacial Meas o Poliical ad Ecoomic Eds, Joural of Fiacial Ecoomics, 1999, 53. Kah.E.,1988 The Ecoomics of Regulaio: Ecoomic Priciples, repried by MIT press. Lopez-de-Silaes F., 1997 Deermias of Privaisaio Prices, Quarerly Joural of Ecoomics. Maski E. S, ad Riley J. G., 1985 ucio Theory wih Privae alues, merica Ecoomic Review, 75, Meggiso W.L., R.C. Nash, ad M. a Radeborgh, 1994 The fiacial ad operaig performace of ewly privaised firms: ieraioal empirical aalysis, Joural of Fiace, 49. Peroi, E.C., 1995 Credible Privaisaio, merica Ecoomic Review. Riley J. G, ad Samuelso W. F, 1981 Opimal ucios, merica Ecoomic Review, 71, Rose, J. R., 1962 Cofusio i aluaio for Public Uiliy Rae-makig, Miesoa Law Review, 47. Souhworh S.D., 1922 Some Rece Problems i Public Uiliy aluaio, merica Ecoomic Review,