Levelised cost, a general formula for calculations of unit cost in integrated resource planning

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1 Levelised cos, a general formula for calculaions of uni cos in inegraed resource planning Simon Fane and Suar Whie Insiue for Susainable Fuures, Universiy of Technology Sydney, PO Box 123, Broadway, NSW 2007, Ausralia. Simon.Fane@us.edu.au Key words: Inegraed resource planning, Leas cos planning, demand managemen, waer conservaion, uni cos, levelised cos. Absrac Levelised cos describes he uni cos of conserved waer or energy. Disagreemen, however exiss as o he appropriae mehod for calculaing his imporan meric. This paper argues ha levelised cos mus be applicable o boh supply and conservaion opions and provide a fair comparison of relaive cos across scales. To achieve his, levelised cos ough o be calculaed by aking he presen value of all coss for an opion divided by he presen value of he sream annual waer or energy ha would be saved or supplied. Unlike oher formulae, levelised cos as described, is an appropriae measure for idenifying leas cos opions in IRP as i does no sysemaically under represen he cos of large scale projecs and is direcly comparable o he marginal cos of supply. Opposiion o he levelised cos as described however exiss. This opposiion focuses on he concepually problemaic idea of discouning a sream of fuure waer or energy. Opponens mainain ha his is nonsensical. This paper dispels hese concerns by correcly idenifying he variable of he conservaion/supply sream in he levelised cos equaion as being demand saisfied. A quaniy ha should be discouned o accoun for a consumer s ime preference for consumpion. 1. Inroducion Inegraed resource planning is an open, paricipaory, sraegic planning process, emphasising he leascos analysis of all opions for meeing uiliy supply service needs (Vickers, 2001). Inegraed resource planning was developed for he elecriciy indusry in he Unied Saes in he 1980 s (Beecher, 1995), he aim being o compare energy demand managemen programs wih increased generaion as sources of supply. In he 1990's he conceps and mehods of IRP were applied o oher uiliy supplies, such as waer (Menke and Woodwell, 1990; Beecher, 1995) and gas (Greenberg and Harshbarger, 1993). Of cenral concern for supply uiliy's engaged in IRP is he poenial of demand managemen and oher conservaion measures o delay or avoid he need for expensive augmenaions o bulk supply. Demand managemen measures are designed o promoe conservaion hrough eiher changes in consumer behaviour or changes o he sock of resource using equipmen (Greenberg and Harshbarger, 1993). Operaional conservaion measures which decrease leakage or loss from disribuion neworks are anoher area of conservaion commonly argeed by supply uiliies (Whie, 1998). In urban waer, bulk supplies will also be conserved hrough providing or encouraging secondary sources of supply which can off se paricular end-uses. Examples being greywaer collecion sysem for oile flushing and rainwaer collecion o supply ho waer and garden waering (Whie and Fane, 2002). Beecher (1996) describes he concep of disribued resources o cover boh small-scale local sources and demand managemen. Disribued resources are smaller unis of supply locaed wihin he exising disribuion nework. By using disribued resources, i is easier o mainain supply and demand in close proximiy as hey can be implemened incremenally. This means ha he adverse environmenal and cos impacs ha accompany large-scale projecs will be avoided (Beecher 1996). The key principle of IRP is ha conservaion measures should be reaed as equivalen o supply by he uiliy supplier (Beecher, 1995). Furher, IRP should accoun for he advanages of disribued resources (Beecher 1996). Despie his, inconsancies are eviden in he manor in which mehods used for leas-cos analysis in IRP rea conservaion and supply opions and how sources of differing scales are handled. Afer a review of he exising mehods, his paper oulines a mehodology which is applicable o any supply or conservaion opion and can provide a fair comparison of relaive cos across scales.

2 2. Mehods used for evaluaing conservaion measures In he waer IRP lieraure, he evaluaion of conservaion measures is framed in various ways. Some auhors (Skeel e al 1998; Howe and Whie, 1999) advocae he evaluaion of measures based on uni cos of conserved waer, known as levelised cos. Oher auhors frame heir evaluaions' in erms of he ne cos or ne benefi derived from a given measure (Macy and Maddaus 1987). The advanage of a levelised cos approach is ha measures can hen be ranked on relaive uni cos and compared direcly o he avoided cos of conservaion. This allows an immediae comparison of he coss of conservaion o he avoided cos and he price of waer paid by consumers. There is also he advanage ha presening measures in a ranked order of cos effeciveness can be illusraed in he form of a conservaion supply curve (Meier, 1982; Sof, 1995). A conservaion supply curve shows a series of seps wih each represening a conservaion measure (Meier, 1982). The widh of each sep is he esimaed conservaion oucome and he heigh, he levelised cos of ha measure. The levelised cos (however calculaed) is compared o avoided cos of conservaion. Despie general accepance ha he levelised cos of measures be compared o he avoided cos of conservaion, disagreemen exiss as o he appropriae mehods for calculaing hese criical parameers. Calculaing he avoided cos of waer conservaion In IRP he avoided cos of conservaion is he incremenal or marginal cos saving associaed wih no producing an addiional uni of supply (Beecher, 1995). Mos auhors use he marginal cos of supply, also know as he long run marginal cos (LRMC), as he avoided cos of conservaion alhough some sudies also accoun for furher avoidable coss, including exernaliies. In heory he marginal cos of supply should accoun for all he prediced direc and indirec coss of fuure supply. Herringon, (1987) saes ha his would cover boh quaniaive and qualiaive coss, in he form of exernaliies, operaing and capial coss. In pracice however, Hanke s (1981) definiion of LRMC as a meric of he cos impac of incremenal use on a supply sysem is more commonly adhered o. This covers only hose direc coss o he uiliy from producion and bulk augmenaion. The average producion cos of supply, also known as he shor run marginal cos (SRMC), is relaively easy o accoun for wih he operaing coss of supply simply averaged per kilolier produced. Calculaing he fracion of fuure bulk augmenaion cos, know as he marginal capaciy cos, o assign o incremenal use is, however, more difficul. Ambiguiy arises due o he 'lumpiness' in coss and differen mehods available for spreading hese coss over ime. A leas four mehods are possible for esimaing he marginal capaciy cos of uiliy supply (Mann, e al, 1980). The wo mos commonly cied in he lieraure on marginal cos of waer supply are Turvey's mehod and he average incremenal cos (AIC) mehod. Turvey (1969) described a mehod for calculaing marginal capaciy cos based on he cos in ne presen value erms of moving he nex planned capaciy augmenaion forward by a single year. This 'cos' is hen divided by he one-off volumeric increase, or incremen, in curren demand ha would require he planned capaciy augmenaion o be moved forward in such a manor. Wih Turvey's mehod he LRMC is generaed by adding he SRMC o he calculaed marginal capaciy cos. A number of auhors, have described a mehod of calculaing he marginal cos for waer supply using he erm AIC (Mann, e al, 1980; Herringon 1987). Average incremenal cos is calculaed by "discouning all incremenal coss which will be incurred in he fuure o provide for esimaed addiional demand over a specified period, and dividing ha by he discouned value of incremenal oupu over he period" (Mann, e al, 1980). In oher words, he AIC for a supply sysem is he presen value of he sream of capial and operaing coss needed o saisfy he projeced demand divided by he presen value of he sream of demand iself. Average incremenal cos gives an esimae of he LRMC. Wih eiher Turvey's or AIC mehods, he evaluaion is herefore only as precise as he demand projecion. Turvey's mehod or he use of AICusually are applied wih reference o a subse of he possible avoidable coss due o waer conservaion. Maddaus (1999) idenified wo oher capaciy coss poenially avoidable when waer is conserved. These are waer reamen plan and reaed waer sorage capaciy coss and pumping saion capaciy coss, which are dependen on peak day and peak hour waer demand, or fire fighing requiremens respecively.

3 Avoidable coss o agens oher han he urban waer uiliies can also be considered. Avoidable coss due o waer conservaion may be eviden in wasewaer sysems (Whie, 1998). These coss are limied mosly o operaional coss of wasewaer reamen. Those capaciy coss which can be avoidable hrough household sewage volumes reducions are mosly resriced o eriary sewage reamen or land disposal capaciy (Howe and Whie 1999). Waer conservaion measures can save consumers in erms of heir waer bills, and heir energy bills for waer heaing. Some measures, such as washing machine rebaes, may also save consumers in he cos of deergen. Savings made on waer bills should no be included in avoidable coss as his represens a direc financial cos of conservaion o he waer supply uiliy and is a ransfer paymen (Whie, 1998). Oher savings, on energy for example, can be included. The value of avoidable exernaliies, such as reduced greenhouse gas emissions due o pumping and waer heaing (Howe and Whie, 1998) or increased river flows can be esimaed in moneary erms and are included in he avoided cos of conservaion by some auhors. udies differ in wheher hese oher avoidable coss are included in he avoided cos. In pracice he impac of differen waer conservaion measures across he urban waer sysem will vary. Differences will be eviden beween he avoided cos of oudoor and indoor use, measures which disproporionaely impac on peak demands, and measures which provide long erm and shor erm conservaion. I can be argued ha in any supply sysem a number of specific locaional poins of high avoided coss exiss. Calculaing he uni cos of waer conservaion The erm levelised cos has been used by various auhors o describe he uni cos of conserved waer (Menke and Woodwell, 1990; Dziegielewski e al 1993; Howe and Whie, 1999). Oher auhors don' use he erm bu do define mehodologies for calculaing an esimaed uni cos of 'supply' from a conservaion measure. The esimae of he uni cos of conservaion measures is useful in IRP as i allow immediae comparison of he relaive coss of conservaion o he avoided cos. The levelised coss of measures can hen be presened in ranked order of cos effeciveness and represened in a supply curve of waer conservaion. In his hesis on 'supply curves of conserved energy', Meier (1982) provided he original discussion of his concep, and describes he cos of conserved energy (CCE) as equal o: C * r CCE = (1) n S[1 (1 + r) ] Where C is he cos of he measure, S is he annual (energy) saving r is he discoun rae and n is he life ime of he opion. The Rocky Mounain Insiue (Menke and Woodwell, 1990) describes his same formula as he 'Lawrence Berkeley Laboraory mehod' for calculaing levelised cos for use in he evaluaing waer conservaion measures. Menke and Woodwell (1990) define C in equaion 1 as he presen value of all coss associaed wih a conservaion measure including any hardware, insallaion, adminisraion and mainenance coss. The significan problem wih his mehod is ha only one single figure for annual saving can be used. Applied o boh conservaion measures and bulk supply his mehod does no accoun for he fac ha large scale measures will produce significan over capaciy in he shor erm. The mehod is sysemaic bias owards large scale supply opions and does no accoun for he advanages provided by disribued resources in incremenally meeing demand (Fane e al., 2002). Dziegielewski e al (1993), and he NSW Waer Demand Managemen Forum (1996) independenly defined he levelised cos (LC) of conserved waer as: C /(1 + r) LC = S (2) Where C is he cos (capial and operaing) of he opion in he year, S is he saving in year and r is he real discoun rae. The sum is aken over he life of he program or some oher defined period. The California Urban Waer Conservaion Council (2000) advocae using his formula based on oal volume of waer

4 conserved. Wih his mehod he period over which analysis is conduced will have significan impacs on he cos oucome due o he lack of discouning. If a long assessmen period is aken, such as he life of a dam, hen no discouning oupu will give an inappropriaely low uni cos of supply. For shorer assessmen periods as prescribed in CUWCC (2000) or WDMF (1996), large scale waer supply projecs would no approach heir capaciies. LC Skeel,e al (1998), and Whie (1998) define he levelised cos of conserved waer as: = C /(1 + r) S /(1 + r) (3) Where C is he cos (capial and operaing) of he opion in he year, S is he saving in year and r is he real discoun rae. The sum is aken over he same lengh of ime for numeraor and denominaor. This approach generaes a uni cos of waer which is equivalen o he 'consan price' of waer from ha measure (see Secion 4 below). Equaion 3 is also idenical o he formula given for AIC by Mann, e al. (1980) and Herringon (1987) excep ha for average incremenal cos, S is se equal o oupu in year raher han savings. The same formula (equaion 3) herefore has applicaion o boh bulk supply and conservaion opions, and i is argued is consisen wih he aims of 'equivalence beween supply and conservaion'. However, comparing he levelised cos of a conservaion measure o he AIC marginal cos of supply needs furher explanaion, and his is underaken in Secion 6. Firsly he issue of discouning waer demand is addressed. 3. Discouned waer demand explained There is opposiion o he levelised cos mehod represened by Equaion 3. This opposiion comes from he concepually problemaic idea of discouning a sream of fuure waer. Opponens indicae ha discouning physical quaniies is nonsensical. This apparen anomaly can be explained by correcly idenifying he variable S in equaion 3. Previously his variable has been idenified as waer saved (Whie, 1998; Skeel, e. al.1999). Howe and Whie, (1999) however accuraely idenified he variable S as been "annual reducion in demand for waer resuling from ha opion. This variable, despie being measured in kiloliers or kilowa hours, is no a physical quaniy, bu an esimae of he fuure demand saisfied by a given measure. I represens he sream of saisfied demand provided by ha conservaion measure and is herefore a meric of uiliy, in he economic sense. Discouning his quaniy over ime is herefore reasonable, in order o accoun for consumer s ime preference for consumpion. The definiion given by Howe and Whie (1999) for S in Equaion 3 can easily be broadened o include boh demand supplied and demand conserved. 4. Levelised cos as consan price Equaion 3 generaes a levelised cos ha equivalen o he 'consan price' of conserved or supplied demand from an opion. This consan price is equal o he income per uni ha would need o be received from each uni of supply/conservaion for ha opion o break even in presen value erms. A similar argumen based on consan price has been presened by Sof (1995) in jusificaion for he discouning of energy conserved over ime. The consan price for any opion is ha value of a uni price which if held consan over ime and paid for each kilolire saved or supplied, would yield he same presen value for ha opion as i's presen value cos. To demonsrae his, noe ha he presen value cos for an opion is given by he expression: PV (cos ) = C /(1 + r)

5 Where C is he cos (capial and operaing) of he opion in he year, and r is he discoun rae o be applied. Therefore if levelised cos is he same value of a consan uni price of waer over ime hen: PV (cos ) = LC * W /(1 + r) Where W is he waer supplied or conserved in year. Expanded, his equaion provides: PV(coss) = LC*Wyear 1 /(1+r) 1 + LC*Wyear 2 /(1+r) 2 LC*Wyear x /(1+r) x Where Wyear 1 Wyear 2 Wyear x is he demand for waer supplied or conserved in year 1, year 2 and year x respecively. This can hen be easily rearranged o give: PV(coss) = LC * PV (demand for waer supplied or conserved) an equivalen expression o he formula for levelised cos given in equaion Ranking opions on levelised coss Equaion 3 wih S defined as demand saisfied (demand supplied or demand conserved) provides a meric which allows any supply or conservaion opion o be compared. The formula can be applied in an equivalen manner o boh demand managemen measures and new bulk supplies. Calculaing levelised cos by Equaion 3 for a given opion requires boh an esimaed sream of coss and he esimaed sream of demand conserved or supplied by ha opion. From hese sreams a uni cos equal o he 'consan price' of supply from ha opion (a presen value) can be calculaed. The levelised cos for an opion including a bulk supply opion is calculaed as he cos of immediaely implemening ha opion. In a siuaion where here is no remaining bulk waer supply capaciy, hen Equaion 3 may hen be used o rank any finie number of opions in an order in which hey should be implemened which will minimise he presen value cos o sociey. In oher words he leas cos schedule of conservaion and supply opions is provided by ranking opions in order of levelised coss as calculaed by Equaion 3. The fac ha Equaion 3 will generae he leas cos schedule of opions is illusraed hrough considering he following argumen. If here are only wo supply or conservaion opions, A and B, currenly available, Opion A will mee increasing demand for x years and opion B for y years. The presen value cos of A and B, PV (cos A) and PV (cos B), canno be compared meaningfully because hey do no saisfy equivalen demand scenarios. There are hen wo possibiliies for meeing demand over he period x + y years. The opions can be scheduled eiher, A hen B (AB) or B hen A (BA). The presen value of scheduling A before B and scheduling B before A can be represened respecively by: PV (cos AB) = PV (D1*LCA, D2*LCA,..Dx*LCA, Dx+1*LCB,..Dx+y*LCB) and PV (cos BA) = NPV (D1*LCB, D2*LCB,..Dy*LCB, Dy+1*LCA,..Dx+y*LCA Where he levelised cos for opions A and B are LCA and LCB respecively and D1 equals he difference beween demand in year 1 and year 0, D2 equals he difference beween demand in year 2 and year 1. If he levelised cos of opion A is less han he levelised cos of opion B hen he presen value cos of scheduling A before B mus be less han he presen value cos of scheduling B before A. This is because coss in laer years are proporionally diminished in presen value erms hrough discouning for all posiive discoun raes. 6 Comparing Levelised cos o Average Incremenal Cos In many IRP sudies he avoided cos of conservaion is aken as a given, ouside he boundary of he sudy. Ofen he mehods used for he cos of conservaion and he avoided cos of conservaion are herefore no consisen. As IRP aims o rea supply and conservaion in an equivalen manner his lack of consisency is problemaic.

6 Using Equaion 3, boh individual conservaion and supply opions can be compared and scheduled on he basis of relaive uni cos. As bulk augmenaion can be considered as jus anoher opion i can be argued ha all opions wih a levelised cos ha is less han ha of bulk augmenaion should be implemened before ha augmenaion occurs. As highlighed previously, Equaion 3 is he same as ha used for esimaing he AIC from he curren sysem. The AIC is a represenaion of he marginal cos of supply from he exising supply sysem and he planned bulk augmenaion. I has been suggesed ha any disribued resource wih a levelised cos less han his AIC should be implemened immediaely. However he AIC should represen he leas cos schedule of opions for meeing demand (Mann, e al, 1980; Herringon 1987). If disribued resources are reaed as equivalen o bulk supply hen he rue leas cos schedule should include hese measures. Only for hose opions ha have a levelised cos less han his 'rue AIC' can i be argued ha immediae implemenaion is warraned. A mehodology for generaing he 'rue AIC' and he leas cos schedule is given below. I should be noed ha only disribued resources wih a fixed or long erm capaciy impac can be compared using his mehodology. This means ha he capaciy of hese measures in erms of supply or conservaion does no decrease before bulk augmenaion needs o be considered. Measures wih a ransien impac or he proporion of he impac of a measures ha is ransien should be compared o he shor run marginal cos. AIC/ levelised cos mehodology oulined The AIC/levelised cos mehodology for developing he leas cos scenario for conservaion and supply and rue AIC is oulined below: i) Develop a deailed model of fuure demand for waer services based on end-use analysis. ii) iii) iv) Projec he base case demand for bulk supply based on he assumpion ha here is no governmen or uiliy acion o manage he bulk demand. Develop poenial demand managemen and secondary supply measures based on he deailed enduse model and esimae conservaion poenial for each measure. Calculae he levelised cos for demand managemen measures, local secondary supply and bulk supply opions using equaion 3 wih S defined as he demand me in year. v) Accoun for any oher avoided coss included in he analysis o give ne levelised cos for each opion. These avoided cos may come from wasewaer savings, peak demand savings and he avoided cos of exernaliies. vi) vii) viii) ix) Rank all opions in erms of ne levelised cos. Consuling his ranking on ne levelised cos, derive a revised augmenaion schedule based on implemening hose opions ha have a lower ne levelised cos and can be feasibly implemened in he fuure before bulk augmenaion. Calculae a 'rue AIC' based of he leas cos conservaion/supply schedule Compare he 'rue AIC' o he ranked order of opions on ne levelised cos o idenify opions which should be implemened immediaely. x) Implemen furher opions over ime as he 'rue AIC' increase o he poin equal wih heir ne levelised cos. 7. Conclusion Inegraed resource planning needs an evaluaion mehodology which is applicable o boh supply or conservaion opions and accouns for he advanages of disribued resources. The advanage of a levelised cos approach is ha measures can be ranked on relaive uni cos and compared o he avoided cos of

7 conservaion. This allows immediae comparison of conservaion coss o he avoided cos and o he price of waer. This paper argues ha he levelised cos should be calculaed by he mehod used previously by Skeel,e al (1998), and Whie (1998) and ha his mehod can be made applicable o any supply or conservaion opion. This mehod, unlike hose oher suggesed by oher auhors, provides an equiable and consisen comparison of relaive cos across sysem scales. The waer oupu sream variable mus however be defined as he fuure demand which is me by he opion. Discouning he waer oupu sream in he calculaion of boh levelised cos and average incremenal cos is hen valid and appropriae o accoun for he ime preference of consumpion. I is also argued ha levelised cos, so calculaed, is he equivalen o he 'consan price' of a conservaion or supply opion. Furher, i is argued ha avoidable coss o agens oher han he waer supply uiliy can be included in a ne levelised cos for each opion. The ranking of opions on ne levelised cos will hen provide he leas cos schedule for implemenaion of conservaion and supply opions. The AIC/levelised cos mehodology oulined is similar o ha uilised by previous auhors bu differs in he manor in which he avoided cos of conservaion is deermined and handled in he analysis. Furher, ha all opions wih a levelised cos less ha he levelised cos of bulk augmenaion should be implemened before augmenaion has no previously made explici. In AIC/levelised cos mehodology, he ne levelised coss of conservaion measures are compared o an avoided cos of conservaion idenifies as he 'rue AIC'. This figure represens he marginal cos of supply or conservaion for a supply sysem. For only hose measures ha have a levelised cos less han his marginal cos can i be argued ha immediae implemenaion is warraned. 8. References Beecher, J. (1996) Inegraed Resource Planning for Waer Uiliies, Waer Resources Updae, Issue Number 104, Summer. Beecher, J (1995) Inegraed Resource Planning Fundamenals. AWWA Journal v87 (6) California Urban Waer Conservaion Council (2000) A guide o he daa and mehods for cos effeciveness analysis of urban waer conservaion bes managemen pracices. CUWCC, Sacrameno CA. Dziegielewski B., Opiz E., Kiefer J., and Baumann D. (1993). Evaluaing Urban Waer Conservaion Programs: A Procedures Manual, AWWA Carbondale IL, USA. Fane Whie and Robinson, (2002), The Use of Levelised Cos in Comparing Supply and Demand Side Opions, Proceedings of he World Waer Congress Melbourne. Greenberg V. and Harshbarger S. (1993). Leas cos selecion of energy conservaion measures for regulaed gas uiliies. Energy Economics. July 93 Hanke S., (1981), On he Marginal Cos of Waer Supply, Waer Engineering and Managemen, Vol. 120, Herringon P. (1987). Pricing of Waer Services. OECD, Paris. Howe C. and Whie S. (1999). Inegraed Resource Planning for Waer and Wasewaer: Sydney Case Sudies. Waer Inernaional, 24 (4) Macy and Maddaus (1987), Cos-Benefi analysis of conservaion programs AWWA Journal, v81, Mar Maddaus, W (1999) Esimaing benefis from waer conservaion, Proceedings of Conserv99. Mann, P., R.. Saunders, and J. Warford, (1980), A Noe on Capial Indivisibiliy and he Definiion of Marginal Cos, Waer Resources Research, Vol. 16, June 1980,

8 Meier, (1982 ), hesis 'supply curves of conserved energy', 'Lawrence Berkeley Menke and Woodwell (1990) Waer efficiency, repor by he Rocky Mounain Insiue. NSW Waer Demand Managemen Forum (1996) Waer Demand Managemen: a Framework for Opion Assessmen, Whie, S. (ed), Repor of he NSW Waer Demand Managemen Forum o he Independen Pricing and Regulaory Tribunal of New Souh Wales, Sydney Skeel T, (1999) Waer conservaion poenial assessmen : a ool for sraegic resource, managemen Efficien use and managemen of waer for urban supply, Sof, S. (1995) The economics of conserved energy supply curves, Energy Journal, 16 (4). Turvey, R. (1969) Marginal Cos Economics Journal 79(314) Vickers A. (2001) Handbook of waer use and conservaion, Waerplow Press, Amhers, Massachuses Whie and Fane, (2002), Designing Cos Effecive Waer Demand Managemen Programs in Ausralia, Waer Science & Technology, Volume 46 Number 6. Whie, S. (1998) Wise Waer Managemen : A Demand Managemen Manual for Waer Auhoriies, Waer Services Associaion of Ausralia.