ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C White Emerson Process Management


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1 ECONOMICS OF PLANT ENERGY SAVINGS PROJECTS IN A CHANGING MARKET Douglas C Whte Emerson Process Management Abstract Energy prces have exhbted sgnfcant volatlty n recent years. For example, natural gas prces ranged from $4 to $15 per MM BTU s n calendar years 2005 through Future prces are uncertan but are lkely to retan a hgh level of volatlty. Ths volatlty complcates analyss of potental plant captal nvestments to reduce energy usage, n partcular those that nvolve consderaton of alternate energy sources, snce tradtonal fnancal nvestment valuaton assumes that future cash flows are known exactly. Yet, ths s clearly not the case for many energy savng nvestments. In addton, future prce probablty functons may be best characterzed as non symmetrc and economc objectve functons as nonlnear further complcatng nvestment analyss. Falure to recognze these effects can result n ncorrectly valung the potental fnancal return of the nvestment. In ths paper, approprate technques to evaluate such nvestments are presented along wth case studes llustratng the approach. Keywords Energy Savng Project Investment Analyss; Rsk; Uncertanty; Monte Carlo Analyss Introducton For most plants n the process ndustres, energy s the second largest operatng cost component after the cost of raw materals. The rsng cost of energy has ncreased the nterest n process nvestments to reduce energy usage. However, evaluaton of the potental fnancal return of these nvestments s complcated by the volatlty n energy prces whch makes t dffcult to determne what prce or prces to use a bass for the fnancal analyss. Natural gas s the sngle largest type of external purchased fuel for the process ndustres and fgure 1 shows natural gas prcng n dollars per mllon BTU s ($/MMBTU) (EIA, 2011) for the perod 1993 to nvestment analyss, whch sgnfcantly ncreases project rsk. It can also be observed that the prce volatlty tends to be nonsymmetrc wth a skew toward postve devatons. Wth the volatlty n prcng t s attractve to consder nvestments that wll allow use of multple energy sources so that usage can swtch perodcally from a more expensve to a cheaper source. The graph below shows natural gas and fuel ol prcng on equvalent bass for the same perod as the prevous graph. Fgure 2 Comparson Natural Gas and Fuel Ol Prce, 2000 to 2011 Fgure1 Natural Gas Prces, 2000 to 2011 The volatlty s apparent as s the assocated dffculty n forecastng future prcng to be used as the bass for It can be seen that there have been perods when natural gas s cheaper and perods when fuel ol s cheaper. A smlar skewness toward postve devatons s apparent n the fuel ol prcng as wth the natural gas prcng.
2 The subject of ths paper s then analyss of energy nvestments when there s sgnfcant uncertanty n the fuel prces wth the uncertanty best represented by nonsymmetrc dstrbutons and cases where there s potental swtchng between fuels. Background and Prevous Work A corporaton always has more potental nvestments than captal and t s necessary to rank the possble nvestments n terms of attractveness, generally n terms of fnancal return. The fnancal analyss requres valuaton models of the nvestment whch are based on a comparson of the tme based ncome stream generated by the nvestment wth ts cost. There are varous metrcs to use for ths comparson ncludng payback perod and Internal Rate of Return (IRR). From a rgorous fnancal pont of vew the preferred approach s to use the net present value (NPV) of the future sequence of after tax cash flows (ATCF) generated, dscounted back to the present tme (Brealey and Myers, 2003) compared wth the dscounted NPV of the nvestment. If the ATCF evoluton wth tme s known exactly ths can be expressed as: NPV(ATCF) = ATCF CoV = n n+ 1 + n + 1 = 1 rc+ r r) rc+ r r) Where: ATCF = ncremental after tax cash flow n perod (year) due to the nvestment n perod (year) 0 n = number fnancal evaluaton perods for the nvestment CoV n+1 = contnung value of the nvestment n perod n+1 r c = corporate weghted average after tax cost of captal r r = rsk premum to be appled to the expected returns from a partcular nvestment. The NPV of the cash flows s compared wth the NPV of the nvestment sequence IC to rank relatve nvestments. = = n IC NPV(IC) (2) = 0 rc) If NPV(ATCF) s greater than NPV(IC) then the nvestment has a postve return. The rato of ths dfference to the nvestment requred s known as the Proftablty Index and can be used to rank dfferent nvestments. However, ths famlar result s, n fact, only applcable when the projected cash flows are known wth very hgh probablty,.e. f the nvestment s essentally equvalent to a bond (Luenberger, 1998). Some energy nvestments n the past were made wth guaranteed fuel costs and guaranteed demands. The equatons above would be sutable for analyss of such stuatons. For most nvestments today n the process ndustres and most (1) partcularly for energy savng nvestments, ths s not the case. Energy projects have many rsk factors that lead to uncertanty n the calculaton of expected return both nternal n terms of equpment techncal performance, project executon effcency and user acceptance; and external n terms of demand, materal and labor costs, fnancng costs and energy prces. Of these, prces are typcally the largest rsk factor and are the subject of ths paper. To perform an analyss t s necessary to quantfy the rsk. For prcng, and other varables that can be consdered to be contnuous n nature, rsk s represented n the statstcal dstrbuton that s used for the future predcton of the varable evoluton over the lfe of the nvestment. At the same projected future mean value for the varable, a projecton wth hgher varance s consdered to be rsker or more uncertan than one wth a lower varance. In fnancal markets, t s desred to arrve at a sngle number whch values an nvestment, even wth the nvestment has hgh rsk. For example, t s desred to calculate the prce that would be approprate to purchase an opton. There are two generally accepted ways of arrvng at a sngle number whch s the value for such nvestments the rsk adjusted dscount rate and the certanty equvalence method. In the rsk adjusted dscount rate approach, the expected value of the cash flows s dscounted at a rate whch ncludes a rsk premum. The hgher the rsk, the hgher the rsk premum. In the certanty equvalence method, the expected cash flow s reduced by a penalty amount dependent agan on the rskness of the cash flow. It should not be surprsng that these two methods, f performed consstently, gve the same result (Obermaer, 2002) However, for project nvestment analyss, management s not just nterested n the most lkely value for the expected return but also n the dstrbuton. Even f the mean s postve, what s the probablty of a negatve return? If the prce dstrbuton s normal there s an analytc soluton for the mean and the varance of the NPV formula. For more general dstrbutons there s no analytc soluton. Evaluatng swtchng between fuels ntroduces a nonlnear element nto the objectve functon further complcatng the analyss. When there s no analytc soluton, the most common forms of project rsk analyss are senstvty analyss and Monte Carlo smulaton. In senstvty analyss the end ponts (hgh, low) of the ranges of possble outcomes s used as the bass for specfc fnancal case evaluaton. If the worst case stll has an adequate return then the nvestment can be approved. However, for many stuatons ths wll not be the result and t s of nterest to evaluate the probablty dstrbuton. Hertz (1968) s an early reference to the use of Monte Carlo smulaton for project nvestment evaluaton. The book by Dxt and Pendyck (1994) s an examnaton of nvestment analyss
3 when the tmng of the nvestment s one of the prmary uncertantes. The paper by Mlls et al (2006) dscusses performance rsk evaluaton for energy projects and quanttatvely settng the approprate project rsk premum. Van Groenendaal (1998) presents an analyss of the rsk n energy projects va senstvty analyss. Kulatlaka (1993) presented an analyss of the expected return for nvestments usng multple fuels when there was uncertanty n the tmng of the nvestment. Sngle Fuel, Prce Volatlty The ntal case evaluated was that for an nvestment n a new heater that would utlze a sngle fuel,.e. natural gas, wth a hgher effcency than that of the heater t replaced. The frst step was then to model natural gas prces from fgure 1. Consstent wth the Brce and Yucel (2005) prce modelng assumptons, the seres s splt nto two regons, one before January 1, 2000 and one after. The least square lnear trend lne for the post 2000 seres s calculated (see fgure 3) and the resduals from the trend lne used for dstrbuton analyss as shown n fgure 4 below. Fgure 3, Natural Gas Prcng Trend Lne, 2000 to 2011 The postve skewness s apparent from the hstogram and from the lack of ft of the normal dstrbuton. Varous standard nonsymmetrc statstcal dstrbutons, ncludng lognormal, nverse normal and Gumbel, were evaluated on the bass of mnmzng the weghted least square error of the predcted versus actual cumulatve dstrbuton functon of the resduals. The lowest mean square error was produced by the Gumbel dstrbuton (Kotz and Nandarajah (2000)) and t was used for subsequent evaluaton. The sample mean square error for the Gumbel dstrbutons was approxmately 40% of the equvalent measure for the Normal dstrbuton. Fgure 4 Natural Gas Prce Volatlty  Resduals From Trend, 2000 to 2011 As a specfc case study to llustrate the ssues, consder nvestment n a new heater whch has a hgher effcency than the heater t replaces. Table 1 below gves the parameters used for the case study. Table 1 Assumptons For Investment Analyss Table 1  Assumptons Assumptons Process Demand MMBTU/ Hr New Heater Investment Cost $ 13,000,000 Mantenance Costs Per Year, % Investment 2% Gas Prce Intal Gas Prce, $/ MMBTU $ 7 Increase Per Year, $ Old Equpment, Equpment Effcency, % 75 Lfe, Years 15 New Equpment, Effcency, % Operatng 90 Days/ Year Fxed Costs/ Yr $ 15,000 Cost of Capta 10% Deprecaton/Yr $ 866,667 Tax Rate 33% The base case analyss assumes an nvestment cost of $13, 000,000 and a gas cost of $7 per MMBTU s n the frst year ncreasng lnearly on the same trend lne as found for the 2000 to 2011 perod. It can be seen n Fgure 5 that the expected cash flow generates a postve net value compared wth the nvestment.
4 stuatons s more complcated. Flexblty requres nvestment now for an uncertan future payout. There are defnte costs but only potental benefts. As an extenson of the prevous case, purchase of equpment that can process a second fuel, for example fuel ol. In the analyss of ths case, t s necessary to develop a model of fuel ol prcng. A quadratc curve was ft to the prce data for the perod 2000 to 2011 as shown n fgure 7 below. Fgure 5 Investment Analyss, No Prce Volatlty The same case s then analyzed wth prce uncertanty. The natural gas prce statstcal dstrbuton s modeled wth the Gumbel dstrbuton wth a mean equal to the same value as the base case shown,.e. one that ncreases lnearly wth the year. The predcted future statstcal varance can then be adjusted and the resultng dstrbuton of the expected NPV examned. For example, the dstrbuton at the observed value for the varance for the perod 2000 to 2011 s shown below. Fgure 7 Fuel Ol Prcng Trend Lne, 2000 to 2011 The resduals from the trend lne were analyzed and agan found to be best modeled by the Gumbel non symmetrc dstrbuton wth a postve skewness as shown n Fgure 8. Fgure 6 NPV Dstrbuton, Prce Volatlty The smulaton ndcates an expected net NPV of $ However, ths s not the only nformaton receved. From a rsk management vewpont t s mportant to observe that the probablty of a negatve return for the nvestment s approxmately 22% and conversely the probablty of a return greater than $200,000 s 10%. These are mportant consderatons for comparatve nvestment analyss. Two Fuels, Uncorrelated Prce Volatlty As mentoned prevously, wth the volatlty n natural gas prcng t s desrable to consder nvestments that can use multple fuels, allowng the equpment to swtch and always use the cheaper fuel. Investment analyss of such Fgure 8 Ol Prce Resduals From Trend, 2000 to 2011 The fnancal model for the replacement heater was modfed to have two fuel optons, natural gas and fuel ol. The base fuel cost lne was assumed to be the lnear natural gas relatonshp from the prevous secton. The varance of the natural gas and the fuel prce around the trend lne was modeled wth ndependent and uncorrelated Gumbel statstcal dstrbutons wth the varance of the fuel ol dstrbuton at ten tmes that of the fuel gas. Agan the mean value for both fuel costs was the same for each perod. It was assumed that an ncreased nvestment of approxmately $300,000 was requred to add the dual
5 frng capabltes. Trals were then run wth ncreasng varance assumed for the prcng. The results are llustrated n fgure 9. At the case of low uncertanty n the prcng the NPV of the nvestment s negatve and t s not justfed. However, as the assumed prce volatlty ncreases the expected NPV ncreases. The concluson s then that expectatons of ncreased prce volatlty at the same mean ncrease the expected payback of the nvestment. Ths effect of varance on the mean s not normally consdered n nvestment analyss. Increased prce volatlty s consdered to be a negatve factor for an nvestment. Yet t can be seen that n the case of potental fuel swtchng t actually ncreases the expected return. Fgure 9 Effect of Assumed Prce Varance on Expected Investment NPV Dxt, A. K. and R. S. Pndyck (1994); Investment Under Uncertanty; Prnceton Unversty Press (EIA); Energy Informaton Agency; US Department of Energy; Short Term Energy Outlook; webste Table 2. US Energy Prces ; December 11, 2011 release Hertz, D.B.(1968) Investment Polces That Pay Off, Harvard Busness Revew; 46; pp (January February, 1968) S. Kotz, S. Nadarajah (1999); Extreme Value Dstrbutons; Imperal College Press Kulatlaka, N. (1993); The Value of Flexblty: The Case of a Dual Fred Industral Steam Boler, Fnancal Management: 22(3); pp (1993) Luenberger, D. G. (1998); Investment Scence; Oxford Unversty Press, 1998 Mlls, E.; et al (2006); From volatlty To value: analyzng and managng performance rsk n energy savng projects; Energy Polcy; (34); pp Obermaer, R.(2002); Comment on Rsk analyss n nvestment apprasal based on the Monte Carlo smulaton technque by A. Hacura, M. JadamusHacura and A. Kocot; European Physcs Journal (B); (30); pp ; (2002) van Groenendaal, W.J.H. (1998); Estmatng NPV varablty for determnstc models; European Journal of Operatonal Research; (107), pp ; Concluson In ths paper, prce data for natural gas and fuel ol are analyzed for the perod 2000 to 2011 and found to be best modeled by nonsymmetrc statstcal dstrbuton wth a postve skewness. Prce dstrbutons are often assumed to be symmetrc Normal or Gaussan dstrbutons for the purpose of analyss and ths assumpton s not supported by ths data. Volatlty of the fuel prces ncreases the rsk of potental energy savng nvestments and the postve skewness further complcates the analyss. Monte Carlo analyss s used to provde a more complete analyss of the nvestment rsk profle. Addng flexblty to the potental nvestment to permt burnng alternate fuels ncreases the nvestment cost and adds nonlnearty to the nvestment objectve functon. By case study t s shown that ncreasng the predcted volatlty of the fuel prces at the same mean prce value ncreases the expected payout of the nvestment an effect that s not generally recognzed n nvestment analyss n ths area. References Brealey, R. A. and S.C. Myers (2003); Prncples of Corporate Fnance, 7 th Ed.; McGrawHll Irwn Brown, S.PA. and M.K. Yucel; (2005) What Drves Natural Gas Prces; Federal Reserve Bank of Dallas; Research Note; February, 2005
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