A Simple Method for Consumers to Address Uncertainty When Purchasing Photovoltaics

Transcription

1 A Simple Mehod for Consumers o Address Uncerainy When Purchasing Phoovolaics Dr. Thomas E. Hoff Clean Power Research 10 Glen C. Napa, CA Dr. Rober Margolis Naional Renewable Energy Laboraory 901 D Sree, SW, Suie 903 Washingon, DC Chrisy Herig Segue Consuling Firs S. E. Redingon Shores, FL Execuive Summary Invesmen under uncerainy is a complex subjec and has been he focus of much research. Financial ools, real opions, decision analysis and oher approaches quanify he uncerainy based on marke daa and/or he decision maker s beliefs and he invesmen decision is made wihin his conex. I is difficul o idenify all uncerainies and solici he decision maker s beliefs abou hem. An alernaive is o idenify he minimum se of beliefs a decision maker needs o have in order o inves in a given echnology. This enables a decision maker o have confidence in heir decision based on a few key issues. This paper examines he consumer s decision o inves in phoovolaics (PV). I concludes ha consumers are economically beer off invesing immediaely han waiing if: (1) he sysem has posiive economic value; (2) PV prices will decline less han X% per year; and (3) elecriciy raes will decline less han Y% per year where X and Y are cusomer- and locaion-dependen. For example, a residenial consumer in San Jose, CA needs o believe ha PV prices will decline less han 7 percen per year and elecric raes will no drop more han 20 percen in order o jusify purchase of a 5 kw PV sysem ha saisfies half of heir elecriciy needs.

2 Background There is a growing ineres among individuals and companies in considering disribued resources as an alernaive o convenional uiliy elecric supply. These resources include enhanced energy efficiency, phoovolaics (PV), fuel cells, gas urbines, ec. Moivaed by a desire o reduce uiliy bills and o help he environmen, consumers wan o know if hese alernaives are good invesmens. While one could evaluae all alernaives, his paper limis he analysis o an invesmen in PV. This is done for he following reasons: I simplifies he analysis, hus providing a beer faciliaion of he meaning of he resuls An imporan compeior is energy efficiency and i is assumed ha all efficiency invesmens have already been made PV is he simples commercially available echnology o own and operae and hus is likely o become more widely available han some of he oher echnologies PV is he only commercially available disribued generaion echnology ha provides consumers wih relaive cerainy in heir fuure elecric prices because i does no use fossil fuels Inroducion When evaluaing a marke invesmen such as a sock or bond, he price ha one should be willing o pay is he same for everyone regardless of where hey live and he deails of heir personal circumsances. In addiion, he marke price is unaffeced by he purchase of any one invesor on he scale a which mos individuals purchase socks and bonds. Furhermore, hese invesmens are no muually exclusive and are only limied by he amoun of money a person wans o inves. Cusomer-owned PV sysems, however, differ from socks and bonds in several ways. There is he obvious difference ha an invesmen in PV is an invesmen in propery ha depreciaes over ime while he value of socks and bonds is expeced o increase over ime. Beyond his basic difference are he following differences: 1. The price a consumer should be willing o pay is siuaion-dependen. This is because incenives, elecriciy prices, solar resource, and curren energy consumpion differ by locaion and cusomer. 2. The price a consumer should be willing o pay for fuure invesmens in PV is based on pas PV invesmens because he PV invesmen opporuniy is depleable. Tha is, a paricular consumer has a limied amoun of PV hey can purchase before he marginal elecriciy savings value goes o $0. 1 The opion of purchasing a PV sysem is los for he fuure by purchasing a PV sysem now. 1 This is magnified in areas wih iered rae srucures (such as California) where he value of he firs kw can be subsanially higher han he value of addiional kws. 2

3 3. An invesmen ha reduces coss requires a differen analyical reamen han an invesmen ha produces revenue. This is because delaying he purchase of a PV sysem resuls in he loss of cos savings (i.e., reduced uiliy bills). Assumpions Sample Cusomer A sample consumer is used hroughou his paper in order o provide concree resuls. The consumer has he characerisics as presened in Table 1. Table 1. Characerisics of sample cusomer. Locaion San Jose, California Cusomer Type Residenial Annual Uiliy Bill $2,650 2 PV Sysem Cos $8,000/kW DC (before incenives) PV Sysem Life 30 Years Paymen Mehod Loan w/ ax-deducible ineres Loan Terms 30-year, 7% loan Analyical Tool The Esimaor (also referred o as he Clean Power Esimaor) 3 is used o perform he analysis. The Esimaor is an Inerne-based compuer program, designed o help cusomers evaluae he cos-effeciveness of clean energy sysems such as phoovolaic (solar elecric), solar hermal, wind, and efficiency invesmens. I provides a personalized esimae of he coss and benefis of a sysem for a specific residenial or commercial cusomer and akes ino accoun he characerisics of he specific cusomer purchasing he sysem in order o provide he mos relevan analysis. These cusomer characerisics may include he ype of sysem being purchased as well as he cusomer s locaion, rae srucure, ax saus and oher informaion. The Naional Renewable Energy Laboraory (NREL) has funded he developmen of a version of he Esimaor o perform marke and policy analysis. I is called he Marke and Policy Analysis ool. The Marke and Policy Analysis ool is used in his paper o perform he analysis. 4 Invesmen Crierion The financial communiy ofen uses ne presen value (NPV) as he sandard economic framework o make invesmen decisions. NPV is he sum of he discouned cash flows over he life of he projec. The ypical es is ha he invesmen is a good one if he 2 he $2,650 annual bill is seleced because he consumer can saisfy all heir needs wih a 10 kw DC sysem 3 More informaion is available abou he Clean Power Esimaor a 4 The ool can be used accessed a 3

4 NPV is greaer han $0. This paper will show ha, while his is a necessary condiion, i is no a sufficien condiion. Criical Inpus The firs sep in he analysis is o idenify inpus ha have he greaes effec on he economic value. Consider changes o he following inpus: cos, elecric raes, PV oupu, and ineres rae. Figure 1 presens he change in ne presen value for he sample cusomer wih parameer changes of ± 50 percen. The figure suggess ha increasing elecric raes (or PV oupu) is comparable o decreasing cos, while ineres rae changes have a lower impac. $20 $15 $10 NPV ($K) $5 $0 -$5 -$10 -$15 Cos Raes or Oupu Ineres Rae -$20-50% 0% 50% Change From Base Case Figure 1. Sensiiviy of ne presen value o inpu assumpions (based on 5 kw PV sysem for sample cusomer presened in Table 1). Uncerainies ha are of he mos concern from he consumer s perspecive are he ones ha have he larges economic effec and he ones o which consumers are unable o respond. Consider he four uncerainies lised above: cos, elecriciy raes, sysem oupu, and ineres raes. PV sysem oupu is very closely relaed o equipmen performance and equipmen performance is covered by sysem warranies. I is assumed ha he warrany is wrien such ha consumers have sufficien confidence ha performance is of concern primarily o he pary offering he warrany raher han he consumer. In addiion, while ineres raes may change over ime, a consumer could respond o ineres rae declines by refinancing heir PV sysem in he same way ha hey would refinance heir house. 4

5 The remaining wo criical uncerainies are he ne sysem cos afer incenives and elecriciy raes. These uncerainies have a large economic effec and canno be miigaed by fuure acions. The consumer mus decide wheher o inves immediaely or o wai o inves wih he hope ha he ne cos will decrease significanly (due o echnological breakhroughs, general price reducions, or changes in incenive programs). Similarly, he consumer mus also decide wheher hey believe ha elecriciy prices will increase or decrease in he fuure. Consumer Decision Consumers considering an invesmen in PV mus conend wih a variey of decisions and uncerainies. A a broad level, purchasing PV means no purchasing oher disribued resources, including ones ha are currenly available (such as energy efficiency measures ha hey have no implemened) as well as ones ha migh be available in he fuure (such as residenial fuel cells, ec.). In addiion, here are uncerainies abou he cos and value of he PV sysem. For he reasons saed earlier, his paper focuses only on he PV invesmen. As saed above, a sandard economic crierion is o inves when he ne presen value is posiive. I is necessary ha he NPV of an invesmen in PV exceeds $0 in order for he invesmen o be a good one. I is no sufficien, however, because one may no obain he same value from purchasing a uni of PV now and hen purchasing anoher uni of PV laer. As a resul, raher han answering he quesion, Should I purchase a PV sysem? consumers are faced wih he following quesion: How much PV should I purchase and when should I make he purchase? Tha is, do hey purchase any PV now or do hey wai unil laer (perhaps indefiniely)? Figure 2 presens a simplified descripion he consumer s decision: buy now or wai. If hey buy now, hey face he possibiliy of elecric raes going down (bu here is no decision o make even if his occurs). If hey wai, hey face he possibiliy of elecric raes increasing and coss increasing as well. 5

6 NOW FUTURE Up Buy Raes Wai Down Up Raes Up Cos Down Up Buy Wai Buy Wai Buy Wai Down Cos Down Buy Wai Figure 2. Consumer Decision. Problem Formulaion The problem can be formulaed mahemaically as follows. The consumer s objecive is o purchase he opimal amoun of PV over ime such ha he expeced NPV of he invesmen sream (i.e., PV can be purchased incremenally over ime) is maximized. Since NPV equals he sum of he discouned value minus cos, his is mahemaically formulaed as: max E ~ ( PVn ) C ( PV ) n= max ( S,0) PV PV PV = 0 0, 1,... L 1 L ~ V ( ) + r ( 1 ) Consider he meaning of each erm in Equaion ( 1 ). max PV 0, PV1,... PV L means ha he invesor wans o selec he PV sysem size in year (PV ) such ha resul is maximized. E corresponds o he fac ha he consumer is an expeced value decision maker. 5 L represens he number of years ha he consumer expecs o live (while his is uncerain 5 The problem is furher complicaed if he consumer is an expeced uiliy decision maker. 6

7 in realiy, i is assumed o be known wih cerainy; in addiion, consumers ha rea cos and value he same for fuure generaions could subsiue L wih infiniy). V ~ is he value funcion and C ~ is he cos funcion a ime. The squiggly line over V and C denoe he fac ha value and cos are uncerain. The value funcion in year, depends upon he oal amoun of PV insalled o dae excluding PV invesmens made in earlier years ha are no longer acive (i.e., PV n= max( S,0) n, where S is he life of he PV sysem). The value funcion may also depend upon oher facors, such as elecriciy prices, ax effecs, ec. Cos is he ne cos afer incenives. This is wha Equaion ( 1 ) would look like for years 0, 1, and 2 of he invesmen. The E is ouside he square bracke because i is he expecaion over fuure uncerain cash flows. ~ ~ ~ ~ V1 ( ) ( ) ( PV0 + PV1 ) C1( PV1 ) V2 PV0 + PV1 + PV2 C2 PV2 max V 0 PV0 C0 PV0 + E + PV,, PV1 PV L ( 1+ r) 1+ r ( ) ( ) + L ( ) I may be difficul o solve Equaion ( 1 ) because of he uncerainy and shape of he funcions. Thus, in order o simplify he analysis, assume ha cos is proporional o he amoun of PV insalled; value is proporional o he amoun of PV insalled up o a cerain poin and hen 0 afer ha (his implies ha rae srucures are fla); and value is consan over ime (his implies ha fuure elecriciy prices are known wih cerainy and ha he consumer s energy consumpion is consan over ime). Mahemaically, his means ha ~ C ~ V ( PV ) ( PV ) c = uni = v = 0 uni PV PV for PV PVMAX for PV > PVMAX where PVMAX is he maximum amoun of PV a paricular cusomer can purchase and sill have a non-zero marginal value; i.e., here is a limi o he amoun of on-sie power a paricular cusomer can produce. Subsiue hese assumpions ino Equaion ( 1 )and simplify. max L n = max ( S,0) uni PV PV PV = 0 0, 1,... L 1 regrouping he value erms, v PV ( + r) n c uni PV 7

8 max S m= 0 m ( 1+ r) ( + r) PV PV PV = 0 0, 1,... L 1 S v uni c uni ( PV ) and applying he definiion of ne presen value NPV L max PV, PV,... PV = 0 1 L 1 uni ( PV ) ( + r) 0 ( 2 ) The opimum soluion o his linear equaion is ha eiher he full amoun of PV (PVMAX) will be insalled a a single poin in ime or no PV will be insalled a all. Tha is, one calculaes he NPV a each poin in ime and selecs he ime o inves where he presen value of NPV is maximized. Poin of Indifference As saed earlier, he consumer s decision is o purchase now or o wai. Since he soluion o Equaion ( 2 ) is o fully inves a a single poin in ime (or o no inves a all), consumers have a poin of indifference beween invesing now or waiing. The consumer s decision is depiced in Figure 3. NOW FUTURE Buy Now Buy Laer Figure 3. Consumer decision. Suppose ha he decision is o purchase now or o purchase in T years. The consumer is indifferen beween purchasing now or waiing if he NPV of purchasing immediaely equals he NPV of purchasing in T years. 6 Tha is, he consumer is indifferen if 6 The rue poin of indifference would ake ino accoun he value of he opion ha he consumer has o inves in he fuure afer he iniial PV sysem wears ou. This will make he NPV of he curren invesmen opporuniy even more valuable. 8

9 NPV 0 NPV = 1 + T ( r) T ( 3 ) where NPV 0 is he ne presen value of an invesmen in year 0, NPV T is he ne presen value in year T of an invesmen made in year T. (Noe: since he NPV T occurs in he fuure, i mus be discouned o year 0 o make i comparable wih NPV 0. The reason for his is ha, by waiing o inves, he consumer loses he opporuniy o reduce heir uiliy bill for he nex T years. In order o make up for his missed opporuniy, he NPV of he invesmen mus be higher in he fuure han i is oday.) Simple Example Suppose ha he sample cusomer is rying o decide wheher o purchase a 5 kw DC PV sysem now for $40,000 or wai 10 years unil he price comes down. The California Energy Commision s PV buydown of $3,800/kW AC and 15% California sae income ax credi are currenly available. I is assumed ha here will be no incenives in 10 years. Using NREL s Marke and Policy Analysis ool, 7 he incenives reduce he $40,000 sysem cos o a ne cos of $21,189 o he consumer. The NPV of he invesmen is $4,263. As shown by he solid black line in Figure 4, he cusomer pays $2,212 in he firs year ($1,033 uiliy bill plus $1,692 loan paymen minus $512 in income ax savings due o loan ineres wrie-off) as compared o heir curren uiliy bill of $2,650, hus saving $438 in he firs year. Should his cusomer purchase he sysem now or wai 10 years? Equaion ( 3 ) can be used o deermine how much he sysem could cos in 10 years and he cusomer be economically indifferen beween purchasing now or waiing. 8 Assuming a 7% discoun rae, he NPV of he invesmen in year 10 would have o be $8,385 in order for he consumer o be economically indifferen beween invesing now and waiing because $8,385/(1.07) 10 = $4,263. Should his cusomer purchase he sysem now or wai 10 years? NREL s Marke and Policy Analysis ool indicaes ha a 5 kw DC sysem mus cos $16,000 wihou incenives o resul in a NPV of $8,385. The dashed red line in Figure 4 presens he uiliy bill and afer-ax loan paymens associaed wih his alernaive ($2,650 for he firs 10 years followed by he reduced cos in subsequen years). 7 The ool is available a hp:// 8 This is a very conservaive crierion because he consumer will have he opporuniy o inves in PV again in 30 years when he exising sysem needs o be replaced. 9

10 Uiliy Bill & Afer-Tax Loan & Paymen ($/yr.) $4,000 Buy now for $21,189 ($40K w/o incenives) Buy in 10 years for $16,000 $3,000 $2,000 $1,000 $ Figure 4. Example of purchasing a PV sysem now versus waiing 10 years. Figure 5 helps o illusrae why a consumer is economically indifferen beween hese wo alernaives. The ligh red and black lines are he discouned coss for he corresponding buy now and wai 10 year decisions. The decision o buy now saves money for he firs 10 years while he decision o wai 10 years saves money beginning in As can be seen visually in he figure, he area of he Buy in 10 years minus Buy now for he firs 10 years is approximaely equal o he area of he Buy now minus Buy in 10 years for he nex 30 years. This makes he consumer economically indifferen beween he wo alernaives. 10

11 Uiliy Bill & Afer-Tax Loan & Paymen ($/yr.) $4,000 Buy now for $21,189 ($40K w/o incenives) Buy in 10 years for $16,000 $3,000 $2,000 $1,000 Buy Now & Save Discouned Coss Buy Laer & Save $ Figure 5. Example of purchasing a PV sysem now versus waiing 10 years (Discouned). Discussion The preceding analysis suggess ha a consumer is economically indifferen beween purchasing a $40,000 PV sysem oday ($21,189 afer incenives) or waiing 10 years and purchasing a sysem for $16,000 wih no incenives. PV would have o reduce in price 9 percen every year for he nex 10 years in order for his scenario o occur. The consumer only needs o believe ha PV sysem prices will decrease less han 9 percen per year in order o be beer off invesing immediaely versus waiing 10 years. Exension of Simple Example The previous secion simplified he decision o eiher invesing immediaely or waiing 10 years. In realiy, he consumer could inves a any ime during which a variey of incenive combinaions could occur. This secion expands he simple example o demonsrae how much he price of PV mus decrease in order for he consumer o be beer off waiing o inves over he nex en years under a variey of incenive scenarios. A combinaion of hree scenarios are evaluaed for each year: CEC buydown only; buydown plus 7.5% sae ax credi; and buydown plus 15% sae ax credi. Breakeven NPV The invesmen decision is based on he NPV. As discussed in he previous secion, he NPV mus increase over ime in order for he consumer o wai o inves. Assume ha all he deails are he same as in he simple example. Table 2 presens he NPV ha he 11

12 cusomer mus obain in order o be economically indifferen beween invesing and waiing. Table 2. Required NPV o be Economically Indifferen ( ). Breakeven NPV 2003 $4, $4, $4, $5, $5, $5, $6, $6, $7, $7, $8,386 CEC PV Buydown CEC buydown for sysems under 30 kw was $4,000/kW AC in he firs half of 2003 where he definiion of a kw AC is he module a PVUSA es condiions muliplied by peak inverer efficiency. According o he CEC s Emerging Renewables Program Guidebook, 9 he rebae levels will be reduced by 20 cens per wa every six monhs beginning July 1, 2003 (and every January 1 s and July 1 s hereafer). The declining buydown schedule is shown in Table 3. Noe ha, given he budge uncerainy in California and he speed a which rebae applicaions are occurring, he rebae could reduce a an even faser rae han is presened in he able. This uncerainy is no included in he analysis because i will simply furher early invesmen raher han waiing. 9 Available a hp:// See page 9. 12

13 Table 3. California Energy Commission PV Buydown (Jul ). CEC Buydown ($/kw AC ) 2003 $3, $3, $3, $2, $2, $1, $1, $1, $ $ $0 California Sae Tax Credi A California sae ax credi is available o residenial consumers. According o he California Solar Cener, he ax credi, for ax years , is equal o he lesser of 15 percen of he ne purchase cos of a phoovolaic or wind-driven sysem wih a generaing capaciy of no more han 200 kilowas. The Bill allows a credi for one sysem per each separae legal parcel of propery or per each address of he axpayer in California, and requires recapure of he credi if he sysem is sold or removed from California wihin one year. The credi will be reduced o half ha amoun for ax years , and will sunse on January 1, The credi, however, faced inense scruiny and was almos cancelled during las year s budge proceedings. The budgeary siuaion of California is even worse his year. While here is currenly a predicable decline in he ax credi, here is he possibiliy ha he ax credi could be repealed enirely. Thus, he ax credi could range beween 0% and 15%. Resuls Reurn o he sample cusomer. As shown in Table 2, he NPV of his sysem assuming no rae changes is $4,263. This cusomer would need o obain an NPV of $4,561 in 2004 in order o be indifferen beween invesing and waiing. This is because $4,561 discouned a a 7% discoun rae equals $4,263. Thus, suppose ha he CEC buydown program is reduced as planned (from $3,800/kW in he second half of 2003 o $3,200/kW in July 2004) and ha he ax credi is reduced from 15% in 2003 o 7.5% in How much can a 5 kw sysem cos in July 2004 for he consumer o obain an NPV of $4,561? Using NREL s Marke and Policy Analysis 10 Available a hp:// 13

14 ool, obaining an NPV of $4,561 requires ha he sysem coss $36,500. This is a $3,500, or almos 9% cos reducion from he curren price of $40,000. This process was repeaed for all scenarios. The red circles in Figure 6 are he required cos reducion wih he CEC buydown, he green circles are he required cos reducion wih he buydown and a 7.5% sae ax credi, and he blue circles are he required cos reducion wih he buydown and a 15% sae ax credi. The black circles show he expeced pah based on wha is planned for exising incenives. The shaded area is included for reference purposes o show wha hisorical price reducions have been. The high reducion corresponds o he price reducions experienced in he Japanese residenial marke from 1997 o and he low reducion is a 3% rae. The average price reducion in modules over he pas 25 years has been abou 5% per year. Required Cos Reducion (%/yr) 15% 10% 5% Buydown Buydown & 7.5% Sae Credi Buydown & 15% Sae Credi Expeced Pah High Price Reducion Range Low 0% Figure 6. Required cos reducions o delay invesmen (San Jose, CA residenial cusomer ha mees half heir energy needs wih 5 kw DC PV sysem). Discussion Consumers can use Figure 6 o deermine wha hey need o believe in order o inves immediaely based on wha scenarios hey believe are feasible. For example, suppose he 11 Based on informaion provided couresy of BP Solar. 14

15 consumer believes ha he incenive will follow he expeced pah (colors wih black circles). Excep for 2005, he consumer should inves now unless hey believe ha prices will decline faser han 7 ½ percen per year over he nex decade (i.e., he high rae experienced by he Japanese program). The figure shows ha consumers are beer off invesing now han waiing in many cases. Noe While he focus of his paper is on invesmens from he consumer s perspecive, i should also be noed ha his analysis is beneficial in designing good incenive programs. In paricular, he wo crieria ha a well designed incenive program mus mee are: 1. The NPV is posiive (so he consumer is beer off invesing han no invesing) 2. Consumers are beer off invesing immediaely han waiing relaive o heir expecaions abou fuure PV prices. 3. The incenive should be srucures o reduce o $0 a he ime when sysems are projeced o be economical in ha locaion wihou incenives. Elecriciy Price Uncerainy The firs secion of his paper addressed he issue of how consumers should make invesmen decisions in he face of PV price uncerainy. This secion addresses he issue of elecriciy price uncerainy. Inroducion Risk is a broad and complex opic. Many corporaions have risk managemen deparmens ha use a variey of risk miigaion and evaluaion ools. Some of hese ools include: Financial ools, such as opions, fuures, forward conracs, and swaps Porfolio analysis Real opions Decision analysis Scenario analysis An imporan assumpion upon which hese ools are based is ha here is eiher an implici or explici undersanding of he poenial uncerainies. The financial ools rely on markes and an undersanding of he uncerainy processes o price risk. Porfolio analysis relies on marke condiions (bu has also been applied o elecric generaing porfolios). Real opions and decision analysis rely on he user s belief abou he fuure, boh in erms of wha he uncerainy migh look like as well as he probabiliies of he various occurrences. Scenario analysis relies on he user s belief abou he fuure bu does no require probabiliies of he various possible saes of he world. Use of hese ools requires an undersanding of he uncerainy. In order o apply many of hese ools o elecriciy rae uncerainy, however, one needs o undersand he uncerain process ha he raes could follow as well as being able o assign probabiliies o he various saes of he world. 15

16 This may be a difficul ask when i comes o elecriciy prices. While elecriciy prices do no end o be volaile over he shor erm (e.g., days), changes can be complex and can occur in a variey of ways. Some of he changes may have been predicable while i would have been very difficul o predic some of he rae srucure changes. Change could occur o he rae srucure componens, including energy prices by monh, period, or ier, demand changes by monh, period, or ier, fixed coss, minimum bills, bill discouns, fuel adjusmen coss, ec. The change could occur suddenly or gradually over ime Raes could increase or decrease The enire rae srucures could change (e.g., residenial cusomers in California moved from a 2-ier o 5-ier rae srucure in 2001; low-ier users experienced no change in heir monhly elecric bill while some high users saw heir bills double overnigh) Approach The same way ha he firs par of he paper deermined how much PV prices mus decline in order o wai, one can deermine how much raes can decrease and he consumer sill be beer off invesing han no invesing. The analysis is somewha differen in his case. The key quesion is o deermine how much of a rae change he consumer can olerae and be beer off invesing han no invesing. The crierion is ha he NPV remain greaer han zero. As saed earlier, rae changes can occur in a variey of ways and a differen imes. The wo exremes considered in his analysis are where all porions of he rae srucure have an immediae, one-ime shif and he oher is a change ha occurs a an annual rae over he life of he PV sysem. The objecive is o deermine how much a rae change he consumer can olerae and sill be beer off waiing han invesing. Simple Example Consider once again o he simple example of he San Jose, CA residenial cusomer wih a 5 kw sysem. The NPV of his sysem wih curren raes is $4,263. Using he NREL s Policy Analysis Tool, an immediae 21 percen rae decrease or an annual decrease of 2½% would resul in an NPV of $0. Thus, if he consumer believes ha any change in raes will occur immediaely and ha change will be less han a 21 percen decrease, hey are beer off invesing now raher han waiing. Sysem Size Due o he fac ha he energy value of he PV sysem is a funcion of is size in a locaion wih iered raes, a furher complicaion ha needs o be considered is he effec of sysem size on he allowable rae change. Figure 7 and Figure 8 presen he allowable rae change versus sysem size. Figure 7 presens he resuls for an immediae, one-ime rae change. Figure 8 presens he resuls for an annually occurring change. For example, he figures sugges ha a consumer purchasing a PV sysem ha provides 20 percen of heir needs could olerae an immediae rae decrease of 25 percen or an 16

17 annual rae decrease of 3 percen per year. As long as he consumer believes ha he raes will decrease by no more han his amoun, hey are beer off invesing now han laer. 40% Immediae Rae Change 20% 0% -20% Purchase Now Wai o Purchase -40% 0% 20% 40% 60% 80% 100% Percen of Energy from PV Figure 7. Allowable immediae, one-ime rae change. 17

18 4.0% Annual Rae Change 2.0% 0.0% -2.0% Purchase Now Wai o Purchase -4.0% 0% 20% 40% 60% 80% 100% Percen of Energy from PV Figure 8. Allowable annual rae change. Conclusions Invesmen under uncerainy is a complex subjec and has been he focus of much research. Financial ools, real opions, decision analysis and oher approaches quanify he uncerainy based on marke daa and/or he decision maker s beliefs and he invesmen decision is made wihin his conex. I is difficul o idenify all uncerainies and solici he decision maker s beliefs abou hem. An alernaive is o idenify he minimum beliefs a decision maker needs o have in order o inves. This enables a decision maker o have confidence in heir decision based on a few key issues. This paper examines he consumer s decision o inves in phoovolaics (PV). I concludes ha consumers are economically beer off invesing immediaely han waiing if: (1) he sysem has posiive economic value; (2) PV prices will decline less han X% per year; and (3) elecriciy raes will decline less han Y% per year where X and Y are cusomer- and locaion-dependen. For example, a residenial consumer in San Jose, CA needs o believe ha PV prices will decline less han 7 percen per year and elecric raes will no drop more han 20 percen in order o jusify purchase of a 5 kw PV sysem ha saisfies half of heir elecriciy needs. 18