Refinancing under Yardstick Regulation with Investment Cycles The Case of Long-Lived Electricity Network Assets

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1 Dscusson Paper No Refnancng under Yardstck Regulaton wth Investment Cycles The Case of Long-Lved Electrcty Network Assets Domnk Schober and Chrstoph Weber

2 Dscusson Paper No Refnancng under Yardstck Regulaton wth Investment Cycles The Case of Long-Lved Electrcty Network Assets Domnk Schober and Chrstoph Weber Download ths ZEW Dscusson Paper from our ftp server: De Dscusson Papers denen ener möglchst schnellen Verbretung von neueren Forschungsarbeten des ZEW. De Beträge legen n allenger Verantwortung der Autoren und stellen ncht notwendgerwese de Menung des ZEW dar. Dscusson Papers are ntended to make results of ZEW research promptly avalable to other economsts n order to encourage dscusson and suggestons for revsons. The authors are solely responsble for the contents whch do not necessarly represent the opnon of the ZEW.

3 Refnancng under Yardstck Regulaton wth Investment Cycles The Case of Long-Lved Electrcty Network Assets by Domnk Schober*, and Chrstoph Weber ** Abstract In the context of yardstck regulaton wth long-lved assets, the nfluence of heterogeneous nvestment cycles on the ablty to recover captal s found to be mportant. The applcaton of effcent frm standards based on hstorc (straght-lne) deprecaton gven heterogeneous nvestment and cost cycles wll cause nstantaneous yardstck levels below the long-run refnancng level. The effcent frm standard wll prevent captal recovery n later perods. An llustratng example from electrcty dstrbuton llustrates the relevance of the problem. Fnally, two alternatves, branch average cost yardstck determnaton and correcton factors based on the share of captal under deprecaton, are dscussed. Keywords yardstck regulaton, nfrastructure nvestment, captal-recovery, sustanable refnancng, electrcty dstrbuton JEL Classfcaton L51, L52 * ZEW Centre for European Economc Research and MaCCI, L7,1, Mannhem, Germany ** Char of Management Scence and Energy Economcs, Unversty of Dusburg Essen, Unverstätsstr. 12, Essen, Germany Correspondng author; Emal: schober@zew.de 1

4 Refnancng under Yardstck Regulaton wth Investment Cycles The Case of Long-Lved Electrcty Network Assets Abstract In the context of yardstck regulaton wth long-lved assets, the nfluence of heterogeneous nvestment cycles on the ablty to recover captal s found to be mportant. The applcaton of effcent frm standards based on hstorc (straght-lne) deprecaton gven heterogeneous nvestment and cost cycles wll cause nstantaneous yardstck levels below the long-run refnancng level. The effcent frm standard wll prevent captal recovery n later perods. An llustratng example from electrcty dstrbuton llustrates the relevance of the problem. Fnally, two alternatves, branch average cost yardstck determnaton and correcton factors based on the share of captal under deprecaton, are dscussed. Keywords yardstck regulaton, nfrastructure nvestment, captal-recovery, sustanable refnancng, electrcty dstrbuton JEL Classfcaton L51, L52 2

5 1. Introducton The development of actve and drect competton n network ndustres, especally electrcty dstrbuton, s often hndered by the monopolstc bottleneck character of the nfrastructure (see Sharkey, 1982). Consequently, a regulatory authorty has to create mechansms, whch nduce the necessary pressure on costs and prces ndrectly. Extensve theoretcal lterature shows that ths goal can hardly be acheved by cost plus regulaton. 1 Alternatvely, there exst numerous forms of ncentve based regulaton schemes. 2 The RPI-X-regulaton (see Lttlechld, 1983) s the domnant ncentve scheme among the ncentve based regulaton methods, lnkng frms prces to a general prce ndex (RPI) and deductng for the expected productvty or effcency gan (X). 3 Decouplng prces and revenues from frms costs, strong ncentves for cost reductons arse as the frm s the resdual clamant of cost savngs. 4 A specal form of the RPI-X-regulaton usng cost observaton and comparson of the regulated frms to reduce ther prvate nformaton s yardstck regulaton. 5 Ideally a sngle frm wll not nfluence the benchmark and wll therefore have no ncentve to explot regulatory revews for revenue augmentaton as the ratchet effect would predct. At the begnnng t was ntended to employ some sort of mean of the total costs of all regulated frms to determne the yardstck (see Shlefer, 1985). In theory, frms would then reveal ther prvate nformaton and drect competton could be mmcked perfectly. However, 1 See Müller and Vogelsang (1979) and Fnsnger and Kraft (1984). For dscussons of rate of return regulaton, whch has analogous ncentve effects see Averch and Johnson (1962), Westfeld (1965), Takayama (1969), Baumol and Klevorck (1970), Baley (1973), El-Hodr and Takayama (1970), Peles and Sten (1976), Das (1980), El-Hodr and Takayama (1981), Tran (1991), Sherman (1992) and Bös (1994). 2 For an overvew see Joskow and Schmalensee (1986). 3 For a theoretcal treatment of how to set the X-factor see Bernsten and Sappngton (1999). Berg et al. (2006) gve a good overvew of dfferent benchmarkng methods n ther study for the World Bank. 4 Some other early works on ncentve regulaton are Baley (1974), Laffont and Trole (1986), Sappngton (1986), Bradley and Prce (1988), Acton and Vogelsang (1989), Cabral and Rordan (1989), Tran (1991). Overvews of the development of ncentve regulaton can be found n Crew and Klendorfer (2002), Vogelsang (2002) and Joskow (2005). In an emprcal work A and Sappngton (2002) show the ambguous possble mpacts of ncentve regulaton on revenue, proft, aggregate nvestment or prces relatve to rate of return regulaton. 5 For further fundamental work on yardstck regulaton see Lazear and Rosen (1981), Nalebuff and Stgltz (1983a,b), Demsk and Sappngton (1984), Mookherjee (1984), Demsk et al. (1988), Aurol and Laffont (1992), Meyer and Vckers (1997). 3

6 contrary to ths proposton regulators recently tend to employ an effcent frm standard to determne cost targets and prces for frms, as s currently the case for electrcty dstrbuton n Germany. 6 Ths may lead to serous under-recovery of nvested captal when operatng n an envronment of heterogeneous nvestment cycles. We therefore study the condtons under whch yardstck regulaton wll lead to refnancng problems under the effcent frm standard. In electrcty hstorc cost measures are stll the most wde-spread n regulatory use. Furthermore, determnng hstorc cost measures frst and, on ths bass, frm s revenues, seems approprate to solve the endogenety problem, whch s nherent n the smultaneous determnaton of deprecaton and revenues n yardstck regulaton under forward-lookng revenue settng. Otherwse, typcally used economc deprecaton would lead to a crcularty problem, because future revenue-changes nduce value- and thus revenue-changes today. Yardstck regulaton n such an envronment s only magnable under very restrctng condtons, e.g. when the entre nvestment cycle enters the benchmarkng ex ante (equvalent to franchse bddng). Ths wll be explaned n more detal later. We therefore stck to classcal straght-lne deprecaton. The most mportant element of our model s the consderaton of varable lfetmes of assets whch nduce cost varatons n a certan year. Unplanned asset falures and fully deprecated assets may cause devatons of a sngle perod s current deprecaton (and captal cost) from a statonary long-run deprecaton level. Another way to ntutvely con ths central effect s to depart from the nvestment cycle tself. The exstng captal has to be allocated by some rule to derve meanngful cost nformaton. Ths cost conssts of deprecaton and captal cost on remanng book value. Typcally, the deprecaton perod s less than the maxmum possble lfetme of assets. Ths s an mportant aspect, because costs then 6 Cf. ARegV (2012). Gven the number of electrcty dstrbuton companes n many countres the ntroducton of ndrect competton appears promsng and s already partally n use, e.g. n Great Brtan, Norway or the Netherlands. A sample of the number of electrcty dstrbuton companes n Europe: Span (320), France ( ), Norway (174), Sweden (170), Denmark (130), Fnland (90), Austra (160), Germany (900), Belgum (30), UK (14), or the Netherlands (10). 4

7 may vary over tme dependng on how much of the total captal stock s currently under deprecaton. At ths pont, t s mportant to note that frms usually operate n dfferent geographc areas wth dfferent nvestment hstores due to e.g. demographc development. Ths may cause substantally dfferent shares of captal stock under deprecaton. In addton, premature falure may ncrease cost heterogeneously. The typcal snap-shot comparson n yardstck regulaton then may lead to revenues for the whole branch, whch are below the necessary level for long-run refnancng. Ths temporary under-recovery (or over-recovery) s not a severe problem as long as exact captal recovery over the whole lfetme of the asset s stll possble. Ths would presume alternatng phases wth supra- and subcompettve profts, whch, under an effcent frm standard, wll only exst under very restrctve and unrealstc assumptons. Of course, ths recovery problem wll not arse n a perfectly symmetrc case of homogeneous captal structures. Droppng ths assumpton mght stll not be crtcal. In a sudden death scenaro, yardstck regulaton wll mpose no problems on refnancng captal. 7 Ths s ntutvely smple: The share of assets under deprecaton s always complete and no correctve replacement s necessary, because assets are assumed to have a certan maxmum lfetme T and not to suffer deteroraton n the meantme. Consequently, deprecaton wll guarantee captal recovery over the entre asset s lfetme and all that s necessary s to adapt the captal costs accordng to the current average age of all assets n order to consder already deprecated nvested captal. However, the sudden-death assumpton s not very realstc n envronments lke electrcty dstrbuton, where long-lved assets reach lfetmes of 40 to 80 years for transformers and cables respectvely. Dependng on the actual realzaton of ther lfetme, asset ages can devate 7 Ths s also known as one-hoss shay pattern. The asset does not age untl t suddenly fals at a fxed and known date. Cf. e.g. Salnger (1998) or Mandy and Sharkey (2003). 5

8 sgnfcantly from ther expected retrement age. Ths nduces the yardstck dstortons descrbed above. To derve the man conclusons of ths artcle, we use a hstorc cost straght-lne deprecaton framework. The net present value formula taken from Schmalensee (1989) can help to descrbe the dlemma a regulated frm wll be exposed to. Wth ntal cost I, deprecaton D, allowed rate of return r, cost of captal ρ and regulatory error ε T t ρ t 1 ε t NPV = I + D + +, where Rt = = 1 t= 1 Rt R t= 1 Rt τ = 1 ( 1 + ρ ) andε = r ρ. τ t t t As long as the regulator sets the allowed rate of return at the cost of captal, the last term vanshes and the frm receves ts cost of captal and ndependent of the deprecaton schedule earns ts ntal nvestment spendng. The problem occurrng under yardstck regulaton wth heterogeneous captal structures s a possble shortfall n the perods rate bases D t. Ths further splls over to cumulated payments for allowed cost of captal, because temporarly lower rate bases nduce lower cost of captal payments. Whereas the optmal prcng lterature mostly renounces to consder explct competton, ths artcle explctly analyzes how the dependence of allowed deprecaton (and prces) on other frms deprecaton (and prce) allowances wll nfluence the own rate bases, D t, and the ablty to recover nvestors captal outlays. We fnd that frms wll usually fal to recover ther captal when varable lfetmes of assets lead to temporarly devatng deprecaton for a subset of frms. In general, rate-settng under yardstck competton 8 s qute an under-researched topc n regulaton. Ths seems surprsng for a long-lved nvestment good and gven that yardstck 8 Yardstck competton and yardstck regulaton are used nterchangeably throughout the text. 6

9 regulaton has become popular among regulators. Even f they do not use t explctly, most regulators conduct less complex cost comparsons ndependent of the use of rate of return or prce-cap regulaton. To our knowledge research has solely focused on optmal prcng and deprecaton of long-lved nvestment goods wthout consderng explctly effects of (n-)drect competton so far. 9 One of the most dffcult problems to solve s the endogenety of rate and deprecaton settng. As Mandy and Sharkey (2003) explaned, the regulator has the choce between settng prces, settng deprecaton or settng both. 10 Settng prces s standard n forward-lookng schemes, whereas settng deprecaton s typcal for hstorc, cost-based approaches. Subsequently, ether deprecaton s calculated accordng to prces, e.g. wth economc deprecaton, or prces are set accordng to hstorc deprecaton, e.g. straght lne deprecaton. In the context of ths endogenety, settng prces and usng economc deprecaton nvolves some dffculty. One of the man models nvestgatng the welfare effects of nter-temporal cost allocaton for a sngle frm s due to Baumol (1971). He lends from peak-load prcng to fnd cost shares and accordngly deprecaton. An nterestng aspect n ths artcle s an effect dervng from the deprecaton schedule he uses, economc deprecaton, whch dates back to Hotellng (1925). He defnes economc deprecaton as the value dfference of an asset over a certan perod. Thereby, The value of a machne and that of a unt of ts output are nterrelated, each affectng the other. (Hotellng (1925), p.353) Prces depend on the value of the machne and the value of the machne tself depends on market condtons. Both are nterrelated by tme, rate of nterest, operatng cost, useful lfe and scrap value. Deprecaton then s calculated respectng these characterstcs and 9 Crew and Klendorfer (1992) and Salnger (1998) e.g. nvestgate the effect of competton on optmal deprecaton schedules and prcng assumng a rather mplct and exogenous varaton of compettve ntensty. 10 Latter ends wth the result of potentally devatng rate of returns relatve to the target rate, one of the research objectves of ths artcle. 7

10 smultaneously optmzng asset usage. Based upon ths nterrelaton, Baumol fnds that a decrease n market prces would then lead to an ncrease n deprecaton and consequently rase prces today to guarantee captal-recovery. At ths pont, the endogenety problem of yardstck regulaton wth economc deprecaton becomes evdent. Independent of how low or hgh prces are set n the future, an accordng hgh or low deprecaton today would compensate frms today. Prce settng becomes to a certan pont arbtrary, where no meanngful cost comparson s possble n the short run. A theoretcal resoluton to ths problem would obvously be the determnaton of the yardstck over the whole antcpated nvestment cycle of all frms usng nformaton on customer needs. In practce, ths s barely possble. Regulators therefore typcally resort to the second opton gven by Mandy and Sharkey (2003) and set prces based on some (arbtrary) deprecaton schedules. Followng Schmalensee (1989), arbtrary deprecaton schedules can be nterpreted as economc deprecaton n the sense that n a regulated envronment, the regulator sets a deprecaton schedule and then adapts prces accordngly (ths s hs nvarance proposton ). 11 Ths exactly may lead to the descrbed volaton of cost-recovery, when yardstck regulaton s n use. Apart from ths, there has been a great deal of research focussng on nvestment ncentves under dfferent cost measures and dfferent deprecaton schedules. Burness and Patrck (1992) dscuss back- and front-loadng ncentves under rate of return constrant. For rates greater than cost of captal, they dscover a back-loadng ncentve. For return rates set exactly equal to the cost of captal, they replcate Schmalensee s nvarance proposton and the tmng of cost coverage (the deprecaton schedule) becomes rrelevant. Rogerson (1992) shows that regulatory lag may also make a very decelerated schedule optmal, whch s named the real constant schedule and whch 11 Ths of course s dependent on three assumptons. The allowed rate of return s set at the cost of captal, the frm earns ts cost of captal and competton s excluded. Then, perfect regulaton adjusts cash flows so that all deprecaton schedules are Hotellng (p.295). Cf. Hotellng (1925) for the orgns of value-based deprecaton. 8

11 exhbts constant real payments over tme. Nomnal and real straght lne deprecaton (and all other more accelerated schedules than the real constant) n comparson wll lead to undercaptalzaton and suboptmal captal-labour-ratos. Crew and Klendorfer (1992) analyze the mpact of technologcal progress and expected arrvng competton. They use a straght lne deprecaton schedule under rate of return regulaton. Ther assumpton s that arrvng competton wll make recovery mpossble due to technologcal change. As long as there s a lttle leeway n the technologcal progress at the begnnng, a swtch of the deprecaton scheme and front-loadng (equvalent to relaxng the regulatory constrant) s stll possble. They further dentfy a wndow of opportunty and a correspondng pont, from where on captal recovery over the entre lfetme s not possble anymore. If the regulator wll not accelerate deprecaton or ncrease the allowed rate of return, ths under-recovery wll result n dsnvestment n the ndustry, whch s the compettve captal market s response to the sgnal of under-recovery. (Crew and Klendorfer (1992), p.56) Another author examnng the effects of competton s Salnger (1998). In a framework buldng on forward-lookng cost and economc deprecaton, he derves that...the possblty of competton ncreases forward-lookng costs whenever a frm must undertake sunk nvestments.... Ths s because the nvestor poses the queston what prce s needed today to provde the ncentve to nvest? (both Salnger (1998), p.157) Therefore costs are not necessarly decreased, but may ncrease to recover ntal costs when threats lke technology ntroducton, asset cost, competton, demand changes wll or mght occur. Smlar to the demand effect n Hotellng (1925), whch would decrease prces and consequently ncrease Hotellng deprecaton because of loss of value, Salnger goes one step further and makes revenues dependent on market shares. As these are assumed to decrease at the advent of competton, decreasng revenues wll devaluate the asset and n consequence ncrease current 9

12 deprecaton and prce. Ignorng these nfluences would be equvalent to understate forwardlookng costs. (Salnger (1998), p.159) Bglaser and Rordan (2000) nvestgate optmal dynamc prcng under economc deprecaton. They fnd that, theoretcally, optmal prcng s also possble under rate of return regulaton. Three precondtons have to be met: the allowed s equal to the compettve rate of return, the allowed s equal to economc deprecaton (consderng nfluences lke real deprecaton of assets, nput prce and operatng cost changes), and capacty s replaced effcently. 12 Ths s further nvestgated by Rogerson (2011) who examnes the condtons allowng effcent cost based prces. He shows that the relatve replacement cost rule (RRC) can be used to calculate user-cost and effcent prces, whch () allow the frm to break even and () are equal to the hypothetcal perfectly compettve cost of rentng suffcent captal to produce one unt of output. They can be used to calculate the long-run margnal cost of producton therefore allowng effcent prcng based on hstorcal cost. Rogerson does not consder dfferent deprecaton patterns explctly, but takes a more general formulaton and nvestgates how technologcal progress should alter a gven pattern to match the (hypothetcal perfectly compettve) user cost of captal. Mandy and Sharkey (2003) assume a one-hoss shay falure pattern and nvestgate the error a regulator ncurs n choosng a straght-lne deprecaton n combnaton wth forward-lookng prcng. They also analyze statc and dynamc problems of captal under-recovery wth forward-lookng prcng under hgher regulatory revew frequency. Adaptaton factors for prcng paths are calculated for dfferent prce settng frequences and dynamcally for dfferent technologes. Evans et al. (2006) 12 Nevertheless, Bglaser and Rordan (2000) show that decreasng prce under rate of return regulaton s optmal and that ntally too hgh but overall defcent nvestment may occur under rate of return regulaton. Ths holds when some arbtrary constant deprecaton rate s chosen and t should be optmal to keep old captal n ts rate base ndefntely because t s nfntely lved. These assumptons are questonable, because they do not relate deprecaton to maxmum asset lve. In ther equaton (13) prce evoluton s dependent on deprecaton contaned n movement equatons (13) and (14), whch s zero f deprecaton s removed and consequently prce would reman constant. The decreasng prce effect they derve s best magnable as a temporary effect, whch vanshes wth consderaton of renvestment at the pont where maxmum age s acheved and new deprecaton occurs. 10

13 compare nvestment ncentves n a real opton framework under hstorc and forward-lookng prce settng regmes. They fnd superor nvestment ncentves for hstorc cost measures. What these artcles have n common s that even though some consder competton mplctly, they do not ncorporate drect comparson of companes costs explctly. In the context of a longlved nvestment good ths research focuses on, t seems of consderable mportance how structural dfferences n nvestment cycles wll mpact the determnaton of deprecaton and prces. 13 Ths s the am of ths artcle. We show how a pont-wse mnmum operator wll necessarly lead to refnancng problems of frms n the long run f nvestment cycles do occur. 14 It stll remans an nterestng and yet unresolved queston how prces and deprecaton under yardstck regulaton can be set to follow customer valuaton and equal user cost of captal, also n lght of the results of ths artcle. The remander s organzed as follows. It s shown how the vntage structure of the captal stock under a yardstck regme nfluences deprecaton, cost of captal employed, benchmarks and the capablty of refnancng. In the next chapter, chapter 2, we frst set up a smple model wthout any explct age structure as a reference case. Refnancng of the captal stock s possble n ths context f the amortzaton perods are dentcal and approprate. 15 In a frst extenson n chapter 3, we analyse the consequences of a heterogeneous captal structure by addng captal vntages to the model, stll assumng a constant lfetme of captal goods ( sudden death or one-hoss shay).we also show that yardstck regulaton s feasble wthout dscrmnaton or dffcultes concernng long-term sustanablty of network nvestment. Further we consder a heterogeneous captal stock wth non-constant lfetme. Non-constant lfetme may ether result from stochastc decay (falures) or from 13 Ths s surprsng gven that regulators recently have a tendency, ndependent whether they use rate of return or ncentve-based regulaton, to devote to some form of X-factor descrbng a productvty measure ncludng some form of effcency comparson. 14 For more general research on the mpact of yardstck regulaton on nvestment see Lyon (1991), Laffont and Trole (1993, Ch.1), Dalen (1998), Sobel (1999) and Dalen (2000). They nvestgate potental undernvestment (n nnovaton and cost reducton) caused by commtment problems of the regulator. 15 In our analyss we focus on physcal assets. We do not treat problems of the fnancng structure of a frm (see De Fraja and Stones (2004)). 11

14 endogenous replacement decsons or the combnaton of both. Whatever may be the cause, we show that under these condtons pure yardstck regulaton among frms wll result n a benchmark, whch wll not allow for captal-recovery. In a second extenson n chapter 4, we consder cost of captal employed beng an addtonal part of captal expendture next to bare deprecaton. The effect of advanced deprecaton of older assets wll lead to comparablty problems of the cost bases and hence to unrealstc benchmarks and lackng nvestment even n the case of constant lfetme of assets. We further show that ths problem s allevated easly by usng average asset age adaptatons to the rate base. In the subsequent chapter, chapter 5, we wll further llustrate the practcal relevance of the problem by an emprcal example of some German network operators. Ther hstorcal nvestment behavour s used to derve yardstcks under an effcent frm standard over the last 30 years. In addton, advantages and dsadvantages of measures lke a correcton based upon the share of captal stock under deprecaton or the use of average nstead of effcent cost standard are dscussed. A fnal chapter concludes. 2. Smple Model: Homogeneous captal stock Startng pont of our consderatons s a set S of frms, whch undergo an ncentve regulaton regardng ther network charges. The permtted revenue s determned through regulatory benchmarkng, whch further mples a pure yardstck regulaton. We take the followng assumptons as startng pont to keep the argumentaton as smple as possble: The frms do not dffer regardng ther network structure. Therefore benchmarkng can be conducted by a smple cost comparson. More complcated approaches lke DEA or SFA wll not be necessary to determne the effcent cost base for the respectve network operator. 12

15 Each frm only offers a unque network servce. Its quantty remans constant over tme. Therefore prce- and revenue-cap regulatons are dentcal. The provson of the network servce requres only captal goods of the same type. As a consequence, dfferent lfetmes and amortzaton perods for varous assets do not have to be taken nto account. The model s based on a straght-lne deprecaton scheme. Ths s the mandatory method for cost-accountng deprecaton n Germany and most other countres worldwde. Also, lke the BNetzA n Germany, regulators n general use cost bases derved from straght-lne deprecaton based schemes for benchmarkng. 16 There s no technologcal progress over tme. Thus the captal stock K, whch s necessary for the effcent provson of the servce, does not vary over tme. K K = 0 t t t 1 ( 1 ) Operatng expenses are neglgble. Ths means that there are solely captal expenses whch have to be taken nto account for servce provson. Inflaton rate s zero. A calculaton wth constant nstead of nomnal values could be conducted as well. For reasons of clarty we renounce modelng nflaton n the followng dscusson. 17 The relevant dscount rate s zero. Ths surely s a qute unconventonal assumpton. Yet t smplfes the followng dscusson substantally because the present value of cash flow seres 16 See Stromnetzentgeltverordnung (2005), 6 (2) and (4). Here we abstan from assumng economc deprecaton because of ts lackng practcal relevance n regulated ndustres. It s left for further research to nvestgate the potental of permttng network operators to employ economc deprecaton methods n the context of benchmarkng. In ths context t has to be mentoned that some authors derved crcumstances under whch economc deprecaton and straght-lne deprecaton lead to equvalent decson bases (net present value). See e.g. Green et al. (2002). 17 In conjuncton wth the assumpton of the absence of technologcal progress t follows that there s no dfference between the cost accountng prncples of Realkaptalerhaltung (real captal sustanment) and Nettosubstanzerhaltung (tangble asset sustanment) dstngushed n the German regulatory debate. See Seben and Maltry (2002). 13

16 can be wrtten as a smple sum wthout havng to employ dscountng. Furthermore the CAPEX relevant for the benchmarkng reduces to the plan deprecaton cost, whereas usually nterest payments have to be consdered as well. However, ths assumpton s abandoned n secton 4, when the model s extended to nclude costs of captal employed. All network operators work effcently. I.e. that a state beng acheved after several regulatory perods s observed, when regulaton wll have already been successful. Consequently there wll also occur no entry e.g. by rvals overtakng assets of frms havng left the market. 18 Also, full usage of capacty n every year s assumed. The demand sde effects and gans n consumers surplus due to snkng prces do not matter. The problem we focus on s manly a problem of falng cost coverage; consumers do not matter. Possble short term gans n consumers surplus resultng from a transfer due to network operators losses n revenue caused by a benchmark set below the network operators own costs thus are rrelevant. In the long run frms would not be able to cover ther costs and thus leave the market. Ths s assumed to set off any possble gans n short term consumers surplus. All assumptons are chosen to smplfy the analytcal treatment of the problem under study. However, the basc queston to be answered remans the same: Is the advsed regulatory regme sustanable,.e. does t allow the frms to recover ther costs from ther permtted revenues permanently? The answer to ths basc queston s probably not substantally modfed, f we replaced the restrctve assumptons by more general ones. 18 For ratonales of a hgher rsk premum and cost base for an ncentve regulated frm to trgger effcent nvestment when the technology exhbts ncreasng economes of scale, costs are sunk and a more effcent replacement frm can enter the market see Evans and Guthre (2006). For a stranded-cost context see Kolbe and Boruck (1998). 14

17 In a frst smple model n addton to the prevous hypothess we further assume that the captal stock s not only a homogeneous asset but that t s also not dfferentable wth respect to ts age structure. Wth an average lfetme of the asset of N years we obtan annual nvestment needs I t I = δ ( 2 ) t K t usng the defnton of an annual falure rate δ: 1 δ = ( 3 ) N The relevant cost base for regulatonc results from: t C t = ak t ( 4 ) We assume a lnear deprecaton wth the deprecaton rate a as the recprocal value of the amortzaton perod A: 1 a = ( 5 ) A Both K t and C t are dentcal for all frms because frms are homogeneous regardng ther network structure and effcency. Ths s why ndexng of these values over the frms s suppressed n the equatons above. The benchmark B t for regulaton s derved as: B t mn Ct, S = ( 6 ) In vew of the precedng we get: B t = C, S ( 7 ) t A necessary condton for sustanable network operaton s however: B t = I t ( 8 ).e. under statonarty, the annually necessary nvestments have to be covered exactly by the revenues determned by the benchmark B t. 15

18 Ths s the case when the deprecaton perod s set equal to the average lfetme A = N ( 9 ) or equvalently: a = δ ( 10 ) Ths result s smple and corresponds to the practcal regulatory rule that the deprecaton perod should correspond to the techncal lfetme. Each frm s able to cover ts nvestment needs of each perod by ts revenue derved from benchmarkng. Next we wll show that ths rule wll lead to sustanablty problems when the heterogeneous age structure of the captal stock s consdered. Ths precsely occurs when frms are heterogeneous wth respect to ther age structure and asset lfetmes are varable. 3. Model extenson I: heterogeneous captal stock In realty the captal stock of frms s not homogeneous. Instead, t conssts of dfferent assets wth dfferent acquston or commssonng dates, correspondng to dfferent vntages. The total captal stock K G,t, of a frm at tme t s therefore the sum of the respectve captal fractons K t,,τ wth ther respectve age τ and correspondng commssonng date t - τ N = max, t, τ = 1 K G K t,, τ ( 11 ) Thereby the vntages wthn the amortzaton perod underle deprecaton. Under lnear deprecaton a deprecaton rate of a = 1 has to be taken nto account. Consequently the A correspondng cost base of perod t s: A C t = ak, τ = 1 t,, τ ( 12 ) The replacement need and thus the nvestment n ths settng are: 16

19 , N = max I t δ K ( 13 ) τ = 1 τ, t τ + 1,,1 Wth δ τ descrbng the replacement rate for the assets of age τ,.e. the fracton of the ntal captal stock K t-τ+1,,1, that has to be replaced after τ years. The followng dynamc equatons hold for the evoluton of captal vntages over tme: K K t,,1 t,, τ = I = K = K t 1, t 1,, τ 1 t τ + 1,,1 δ K 1 τ, τ τ ' = 1 t τ + 1,,1 δ τ ', τ > 1 ( 14 ) Investments undertaken n year t-1 wll hence only be added to the captal stock n the followng year t. Reference for the replacement rate δ τ, of age τ s always the respectve ntal captal stock K t-τ+1,,1 wth age 1 (whch corresponds the nvestment I t-τ of year t-τ). For δ τ,, the followng dentty then has to be satsfed: N max τ = 1 δ τ, = 1 ( 15 ) Moreover, all δ τ, have to be nonnegatve of course. Whether the δ τ, result from an exogenous agng or falure process or from an optmzng calculus of the asset owners, s not of prmary mportance for the subsequent consderatons. Possble dstrbutons for δ τ, are llustrated n fgure 1. Obvously n all cases but the most smple one the mean lfetme dffers from the maxmum lfetme. The only excepton s the case of a constant and determnstc lfetme (depcted upper left). Below we wll start dscussng ths smple case and subsequently the varable lfetme models. 17

20 δ τ determnstc lfetme, sudden death δ τ constant falure rate related to remanng populaton, exponental decay N =N max τ N τ N max δ τ δ τ constant falure rate techncal decay 1/N max N =N max /2 N max τ N N max τ Fgure 1: Dfferent falure patterns 1. Fxed lfetme of captal vntages To refnance the ntal nvestments over the lfetme of a vntage, the sum of the allowed revenues has to be equal to the ntal nvestment volume keepng n mnd the assumptons of zero nflaton and dscount rate. The permtted revenue n a year of observaton t under effcent frm benchmarkng results from the constrant B t mn Ct, = ( 16 ) If the amortzaton perod A s set equal to the lfetme N max assumed as fxed lke n the smple model, equaton (12) wll result n: Nmax C t, = a Kt,, = akg, t, τ = 1 τ ( 17 ) 18

21 Gven that network operators are structurally dentcal and there are no dfferences regardng ther effcency, and gven that the necessary captal stock does not change wthout technologcal progress, physcal captal stocks are dentcal between network operators and over tme: KG, t, = KG t, ( 18 ) For the benchmark and thus for the permtted revenues, one obtans from the above equatons: B t = ak = C, t ( 19 ) G t K t,τ captal structure network operator 1 captal structure network operator 2 captal structure network operator 3 N max τ Fgure 2: Companes wth dfferent captal structures The assumpton that captal goods have a fxed lfetme leads to the followng dstrbuton for δ τ : 0 f τ < N max δ τ = ( 20 ) 1 f τ = N max 19

22 From equaton (13) nvestment needs can be derved as: I t, = K = I t Nmax + 1,,1 t Nmax, ( 21 ).e. as a result fxed nvestment cycles of length N max are obtaned. If the ntal captal stocks for the dfferent frms vary (see Fgure 2), the annual nvestments wll as well. But ths wll not have any effect on the benchmark because the benchmark s based on deprecatons whch comprse the entre captal stock as long as lfetme and amortzaton perod are dentcal. For a sngle year t and a partcular frm t can thus occur that: I B t, t ( 22 ) Especally n the case of a frm dsposng of assets whch have an age above the average, for some early years t wll be the case that I > B t, t. Hence nvestments cannot be covered by permtted revenues n that partcular year. But the key queston for the sustanablty of regulaton s whether or not frms ncur systematc defcts under the regulatory regme. To determne profts or losses a look at the frm s balance sheet s helpful, from whch ncurred losses or profts can be derved. For the modelled network operator the followng transactons are relevant for the frm s balance sheet: Addton of tangble assets correspondng to the amount of nvestments I t,. Reducton of fnancal assets Z t, and/or ncrease of labltes V t, for fnancng nvestments Cash nflow,.e. addton of lqud assets from transmsson and dstrbuton charges. Those are determned by the benchmark and thus are equal to B t. 20

23 Dmnuton of the asset base correspondng to the amount of deprecaton. Gven the above assumptons these are equal to costs C t,. Wth excepton of the fnancng of nvestments by credts all of the above actvtes concern the asset sde of the balance sheet. As the form of fnancng has no systematc mpact on effcency (n ths smple model), for the sake of smplcty the fnancng of nvestments s assumed to be undertaken from lqud assets. For ths reason only changes on the asset sde have be consdered. The frm wll realse profts G t, f addtons on the asset sde wll exceed asset reductons. In contrast the frm wll realse losses f reductons on the asset sde wll exceed addtons, formally: G t, It, Zt, + Bt Ct, = ( 23 ) If barganng of extra dscounts or n-house producton of assets are excluded the amount of fnancal assets Z t, necessary for the fnancng of nvestments wll be equal to the amount of nvestments I t,. Accordngly the proft balance reduces to: = B C ( 24 ) G t, t t, Benchmarkng wll lead to sustanable network operaton f benchmarkng revenues do not fall short of expenses systematcally. In our case expenses are solely based on deprecaton. Gven equaton (19) one obtans for all frms and all years: G t, = 0 t, ( 25 ) Ths result s derved under the assumpton that the amortzaton perod s equal to the lfetme. In the subsequent secton we wll show that the generalsaton of ths approach for the case of varable lfetmes s problematc. 21

24 2. Varable lfetme of captal vntages In practce t s unlkely that all producton facltes of the same type also have the same lfetme. On the one hand premature falure can be observed. Such falures are rather stochastc, partly dependng on varatons n the asset producton process (e.g. materal nhomogenetes), partly dependng on stochastc dfferences n the materal wear and tear durng operaton (e.g. varyng weather mpact on lnes). Alongsde these stochastc premature falures an optmsed replacement strategy can lead to the choce of varyng lfetmes for dfferent producton facltes of the same type as a consequence of unequal stress. Qualtatvely, n most cases a progresson as depcted n fgure 1 on the bottom rght wll result. It shows the case of low replacement rates durng the frst years and hgher ones later around the customary lfetme. Independently of the precse dstrbuton of falures and correspondng replacement rates t has to be noted that n all cases lfetme s a varable parameter and that the mean lfetme N s exceeded or undercut for partcular producton facltes. In realty t wll often be dffcult to determne the exact upper lmt N max for the lfetme, especally for newly developed producton facltes. Ths occurs notably n the case of a constant falure rate for the remanng populaton as exemplfed on the upper rght hand sde of fgure 1. In ths context the benchmark and consequently the capablty of refnancng nvestments s agan hghly nfluenced by the deprecaton perod A. Three alternatves are prncpally possble: A = N : the deprecaton perod s set equal to the average lfetme. Gven the optmalty condtons derved n the above sectons ths seems a natural choce. A < N : the deprecaton perod falls short of the average lfetme. Ths allows avodng the stuaton of havng to replace producton facltes before the end of the deprecaton 22

25 perod. Such premature replacements always have to be accompaned by an extra deprecaton on the replaced asset n the balance sheet. Otherwse no longer usable assets would stll be valued n the balance sheet. A > N : the deprecaton perod exceeds the average lfetme, at the extreme case t s A = N max. Ths avods the use of already amortzed producton facltes, whch would otherwse dstort the benchmark (see below). The general equatons (23) and (24) stll hold for the frms proft n all cases. Equaton (12), nevertheless, has to be extended for the frm s amortzaton and expenses: C A ( ak + ( a) K t + ) t,, τ τ, τ τ 1,,1 t, = 1 τ = 1 Here the second term τ, ( 1 ) K t τ 1,, 1 1 a K t + value ( ) τ 1,, 1 δ ( 26 ) δ τ reflects the extra deprecaton on assets wth resdual a + τ havng to be replaced durng the deprecaton perod. 19 Defnng the ~ replacement rate δ wth respect to the resdual captal stock τ, ~ δτ, δτ, = ( 27 ) τ 1 1 δτ ', τ ' = 1 ~ (wth by defnton δ 1 throughout), equaton (26) can be wrtten: C = Or equvalently: τ A ~ ( a + τ, ( τa ) t, 1 τ = 1 δ K ( 28 ) t,, τ 19 For the weghtng factors of the above equaton t can be proven that: a 1 A τ 1 δ ', +, ( 1 ) τ δτ τa = 1 τ = 1 τ ' = 1.e. that each vntage s deprecated exactly once altogether under the consderaton of regular and extra deprecaton. 23

26 C t, N max = a = ak τ = 1 G K t,, τ a N a max τ = A+ 1 N max τ = A+ 1 K t,, τ K + t,, τ A τ = 1 + ~ δ A τ = 1 τ, ~ δ τ, ( 1 τa) ( 1 τa) K t,, τ K t,, τ ( 29 ).e. total costs consst of regular deprecaton on the total captal stock dmnshed by deprecaton on captal fractons wth age greater than the deprecaton perod plus extra deprecaton accountng for premature falure. Whereas the frst term s ndependent of the captal structure ths does not hold for summands two and three. The second (negatve) term takes hgh values partcularly for frms wth relatvely old assets. In contrast, the thrd term wll only show hgh values f producton facltes are replaced before the regular endng of the deprecaton perod. Whatever the choce of the deprecaton perod, be t longer, shorter or equal compared to the average lfetme, one of the latter two terms wll always be dfferent from zero. If the amortzaton perod s chosen to be relatvely short (.e. A < N ) premature deprecaton can be avoded almost completely and the latter term can be elmnated. Yet conversely the fracton of captal beng captured by the second term wll grow because the dstance between deprecaton perod A and maxmum lfetme N max s relatvely large. If the opposte extreme of an amortzaton perod equal to the maxmum lfetme s chosen (A=N max ) the second term wll dsappear. But n ths case a lot of premature deprecaton wll occur and thus the thrd term wll be of consderable relevance. Hence the ndvdual captal structure always has an nfluence on effectve costs even under the assumpton of structurally comparable frms whch are n addton of dentcal effcency. Obvously, ths result holds also for any value A lyng between the extreme ponts consdered. The basc benchmarkng relatonshp (16) then stll holds, but from B t C t, ( 30 ) 24

27 follows that the set S of all frms (wth dfferent vntage structures) can be separated nto two dsjont, non-empty sets: S S B, t NB, t = = { S Bt = Ct, } { S B < C } t t, ( 31 ) The frms belongng to S NB,t show a defct for year t accordng to equaton (24). Ths defct cannot be refnanced by profts n the precedng or followng years, because from the benchmarkng relaton (30) follows that a frm could, at best, acheve a zero defct. Thus, benchmarkng cannot lead to sustanable network operaton f the age structure of assets for frms s dfferent n the frst place. 4. Model extenson II: cost of captal employed So far, the analyss has gnored the fact that frms also have to pay nterest on ther productve captal. Ths cost of captal employed has to be consdered as well as deprecaton, because t wll nfluence the cash flows and the balance sheet of the network operator 20. Includng cost of captal employed wll change the results obtaned from the analyss conducted solely ncludng deprecaton as follows. As before (see equaton (16)) the benchmark s set by the cost of the network operator wth the lowest cost level: B t = mn Ct, 20 Inflaton thought of as general prce ncreases or specfc prce ncreases of assets analogously affects the cost base but wth alterng sgns. No addtonal nsght s generated by explctly modellng nflaton and t s therefore suffcent to model the cost of captal employed. 25

28 Consderng cost of captal employed, the nterest payments have to be added to the cost base (17) leadng for the case of sudden-death to 21 : C A t, = akg, t, + (1 aτ ) τ = 1 κ K ( 32 ) t τ + 1, The second term descrbes the costs of the captal employed n perod t wth nterest rate κ. No dfferentaton s made between debt and equty, n lne wth the Modlgan-Mller theorem (Modlgan and Mller 1958). Interest payments are only due on the captal n use, as s common busness practce, whch s also reflected by regulatory defntons of the allowable cost base. Deprecated captal s assumed to be recompensed suffcently and thus can be neglected. Consequently, employed captal n perod t conssts solely of the remanng balance sheet captal stock ( 1 a ) K t τ + 1, τ of each vntage τ. The nterest rate to be pad on the captal employed s gven by κ and assumed to be postve and constant. If regulaton s to be sustanable, exogenous and non-nfluenceable factors must not lead to dfferent costs for frms of equal effcency. Otherwse, the benchmarkng wll lead for some frms to revenues whch undercut the ncurred costs, makng refnancng based on these benchmarks mpossble and thus the system nsustanable (see above). Yet, transformng (32) makng use of (11), (18) and of A = N max, shows that costs n the present case depend on the average asset age: C A = ( a + κ K aκ τ K ( 33 ) t, ) Ths may be wrtten as: t G G τ = 1 G t τ + 1, C, = ( a +κ) K aκ τ K ( 34 ) wth the average asset age 21 We assume the cost of captal employed to be calculated on a balance sheet bass. 26

29 A 1 τ = τ K ( 35 ) KG τ = 1 t τ + 1, The older the average asset age, the more of the nvestments have taken place n perods wth hgher τ and the more of these early nvestments are wrtten off already. Consequently, compared to the reference case of an entrely new captal stock the postve term the costs gradually dmnsh as the network operator s assets grow older and the deprecated part of the captal stock the negatve term gans more weght. As a consequence of equaton (34), the frm wth the oldest asset base wll set the benchmark: B t = ( a + κ) K aκ K maxτ ( 36 ) G G Obvously, for all frms j wth a lower average asset age τ j, one has: C > B j τ < τ t, j t j ( 37 ) and consequently those wll earn less than ther cost. As n the prevous case, ths lack of revenue may not be compensated n other perods, because the own costs always form an upper bound to the revenues. Thus the smple benchmarkng rule wll lead to unsustanable results, as soon as frms dffer n ther average asset age. To be more precse: nvestment cycles are not by themselves an obstacle to the correct functonng of the benchmarkng procedure. But as soon as nvestment cycles are not dentcal for all frms, the benchmarks obtaned wll not lead to cost recovery. Ths result obvously may be generalzed to the case of varable lfetmes dscussed n the prevous secton. 27

30 5. Illustraton of refnancng gaps and allevatng cost standardzatons In ths secton we llustrate the mpact heterogeneous nvestment cycles can exhbt on captal recovery under yardstck regulaton. Cyclcal dfferences are estmated by the means of nvestment data for seven German network operators. In addton, the annual mean of nvestments of the whole branch s gven. As the data s confdental frm names are as well. Followng fgure shows the evoluton of nvestment over the last 70 years. The graphs depct nvestment of each frm n percent of the frm s total captal stock % 100.0% Cumulatve Investment 80.0% 60.0% 40.0% 20.0% Frm 1 Frm 2 Frm 3 Frm 4 Frm 5 Frm 6 Frm 7 Branch AVG Statonary 0.0% Fgure 3: Dstrbuton of cumulatve nvestment 22 The nvestment tme seres contan nformaton on the medum voltage cables, because of the most relable data avalablty. Investments n other asset classes lke transformers s to our knowledge analogous, because of budgets beng dstrbuted n more or less fxed proportons. Further, much of the nstallatons s connecton of new areas, where assets of all classes are necessary. 28

31 It s obvous from the pcture that the seven companes n the sample nvested much less than the branch average untl the md-sxtes and then nvested more durng the subsequent decade. Afterwards, the seven frm average parallels more or less the branch average. These nvestment tme seres allow a rough approxmaton of current yardstck revenues. The man cost drver s the current captal stock under deprecaton, whch shall serve as a proxy for current cost. We assume the deprecaton horzon to be 40 years for all companes and replacement age to be set at 69 years. 23 Ths allows us to consder the last 30 years for a yardstck assessment. The captal stock under deprecaton then covers the last 40 of 69 years. In a statonary envronment, a frm would thus have 77% of the total captal stock under deprecaton, ncludng premature falure. 24 The remanng 23% would then be deprecated already. Ths statonary replacement s depcted n Fgure 4 as the horzontal sold black lne. Fner lnes are assocated to the frms cost evoluton. The dashed sold black lne shows the current yardstck assumng the effcent frm standard whereas the sold brght lne shows the branch average. Heterogeneous nvestment cycles lead to substantal devatons from the statonary renvestment. 23 We use Webull dstrbuton assumptons to characterze the falure behavour. Cf. Appendx for detaled falure assumptons. Cf. Obergünner (2005) for cost data wth an assumed 10 penalty per kwh lost. Replacement age then smply results n an expected cost mnmzaton wth expected cost from premature falure beng about 20% of replacement nvestment cost. 24 Under the gven assumptons the statonary age as a non-lnear progressvely decreasng functon of tme can be derved. Ths dstrbuton s used to calculate the share of captal stock under deprecaton, whch results n about 77%. 29

32 Asset share under deprecaton 100% 80% 60% 40% 20% 0% -20% -40% -60% Frm 1 Frm 2 Frm 3 Frm 4 Frm 5 Frm 6 Frm 7 Branch AVG Statonary (Webull) Yardstck Frm Yardstck - Statonary Renvest' Branch AVG - Statonary Renvest' Fgure 4: Cost evoluton over the last 30 years The lower two dashed lnes show the dfference of the yardstck frm s cost and the statonary renvestment cost (dark gray) as well as the dfference between the branches average cost and the statonary renvestment cost (lght gray). In the former case, at the extreme the revenue n a sngle year falls short of more than 40%. At the end of the observaton perod ths dfference amounts agan to smlar values of about 30%. On average the dfference between the statonary and the yardstck asset share under deprecaton s about 18%. Ths s mpressve and demonstrates that serous captal-recovery problems may occur n the future, f the German regulator stays wth the effcent frm standard. In the latter case, the branch average of companes n Germany s taken and compared to the statonary renvestment case, whch reduces the dfference sgnfcantly to less than 2%. 30