Australian Climate Change Adaptation Network for Settlements and Infrastructure. Discussion Paper February 2010

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1 Australa Clmate Chage Adaptato Network for Settlemets ad Ifrastructure Dscusso Paper February 2010 The corporato of ucertaty assocated wth clmate chage to frastructure vestmet apprasal Davd G. Carmchael 1 ad Mara C. A. Balatbat 2 The Uversty of New South Wales, Sydey, 2052, New South Wales, Australa 1 School of Cvl ad Evrometal Egeerg; D.Carmchael@usw.edu.au 2 Australa School of Busess; M.Balatbat@usw.edu.au Abstract Covetoal vestmet apprasal for frastructure teds to be carred out determstcally, assumg that today s codtos wll cotue or tred to the future. Ths mght be supplemeted wth sestvty or scearo aalyss order to corporate possble devatos. However wth clmate chage, such steady state assumptos o loger hold. Ifrastructure, the future due to clmate chage, could be expected to have to deal wth creased temperatures, altered rafall patters, altered frequeces of extreme weather evets ad sea level rse. These tur wll lead, for example, to chaged demad patters, creased mateace ad operato costs, decreased logevty, creased costs of retrofttg, chaged lad use ad demographcs, ad more frequet dsrupto to use. Ad all of these cosequeces are oly kow to wth defed probabltes. Future costs ad beefts for frastructure are ow heretly probablstc, ad ay vestmet apprasal must ecessarly take to accout the ucertaty. Determstc apprasals ca o loger be justfed. Three ma choces for ew frastructure are possble: (I) buld for today s codtos ad abado the future because of clmate chage, whereby the logevty of the frastructure s restrcted; (II) buld for today s codtos wth the vew to beg able to modfy or upgrade the future, such that the frastructure s talored to the chagg clmate or adapts to the chagg clmate; or (III) buld for future codtos whereby the frastructure s overdesged the ear future but adequate for the loger term. Each choce represets dfferet levels of feasblty. The paper explores the dfferet possble mechasms by whch feasblty levels ca be evaluated, cludg the feasblty assocated wth havg flexble ad adaptable frastructure, such that ratoal vestmet decsos ca be made wth the ucertaty troduced by clmate chage. 1. Itroducto Commoly, ecoomc feasblty of ew frastructure s based o a preset worth (et preset value) aalyss, ad ths s doe determstcally whereby all costs ad beefts are assumed kow, ad the future s assumed to be a cotuato of the preset, or tred from the preset. Where varablty s atcpated future costs ad beefts, a sestvty aalyss or scearo aalyss mght also be carred out. 1

2 However wth clmate chage, the future becomes less certa because of the uderlyg complete scece ad assocated lack of cofdece predcto. Future beefts ad costs ad frastructure lfespas caot be predcted wth ay degree of accuracy, because of ucertaty assocated wth atcpated sea level ad temperature rses, ad chaged occurreces ad magtudes of extreme weather evets ad rafall patters. Icreases are expected frastructure mateace, repar ad operato costs, damage, ad surace premums, whle demads o frastructure, eergy, water ad trasport wll chage - both crease ad decrease o a stuato-by-stuato bass. The locatos of frastructure eeds wll also chage as demad chages. The operato of frastructure wll be dsrupted more frequetly. The logevty of frastructure wll decrease ad exteral facades of frastructure wll experece accelerated degradato. Ifrastructure wll eed to be replaced more frequetly. Much has bee wrtte o ths, for example [1], [2] ad [3]. Clmate chage wll expose vulerabltes exstg frastructure ad frastructure establshed alog busess-as-usual les. Ad such vulerablty could be expected to vary betwee locatos. Exstg frastructure could be expected to have lmted ablty or capacty to adapt, ad may be foud to be adequate. Ifrastructure teded for log term use may prove adequate. Clearly future beefts ad costs wll be best modelled as radom varables rather tha determstc quattes as was the commo practce the past. Ths tur meas that preset worth becomes a radom varable, ad feasblty has to be defed terms of the probablty that the preset worth s postve [4], [5]. 2. Backgroud The Natoal Clmate Chage Adaptato Research Pla: Settlemets ad Ifrastructure Cosultato Draft of September 2009 by the Natoal Clmate Chage Adaptato Research Faclty (NCCARF) [3] hghlghts the backgroud to the preset paper. At pp : There s cosderable ucertaty about the tmg ad testy of future clmate chage especally at regoal ad local scales. The ecoomc stuato cotrbutes further ucertaty. Noetheless decsos about developmets, may rreversble, wll cotue to be made, ad these eed to creasgly take to accout a awareess of both clmate chage ad ucertaty about ts specfc local mplcatos. Oe sesble approach for large vestmets s to udertake staged developmets that allow for future expaso or addtoal adaptve features to be mplemeted cotget o certa clmatc thresholds beg surpassed. These so-called real optos allow for learg ad flexblty plag ad desg decsos pror to ay commtmet of scarce resources. Optoalty ca add value to projects a way that ca be prced wth moder facal tools that avod the ptfalls assocated wth tradtoal [determstc] Net Preset Value calculatos, ofte used for costbeeft aalyss. NCCARF rases ths as a sgfcat ssue wth respect to both buldg ad for frastructure facg. Ad at p. 27: Tradtoal [determstc] Beeft/Cost aalyses based o Preset Worth method wth relatvely hgh dscout rate ad short plag perods are ot approprate to the log plag perods heret adaptato to clmate chage over the ext cetury (ad loger). Facal aalyses for assessg frastructure projects eed to be modfed to corporate ad 2

3 take accout of rsks that are lkely to chage wth clmate over a exteded tmele. Alteratve facal ad busess models eed to be vestgated for use by govermet ad prvate sectors for adopto optos assessmet ad vestmet decso makg the ew clmate era. The preset paper addresses the cocers both these quotatos. The methodology advaced ths paper corporates ucertaty ad values optos ad flexblty. 3. Ifrastructure developmet choces Three ma choces for ew frastructure are possble: I. Buld for today s codtos ad abado the future because of clmate chage, whereby the logevty of the frastructure s restrcted. II. Buld for today s codtos wth the vew to beg able to modfy or upgrade the future, such that the frastructure s talored to the chagg clmate or adapts to the chagg clmate. III. Buld for future codtos whereby the frastructure s overdesged the ear future but adequate for the loger term. Each choce represets dfferet levels of feasblty ad value. Mateace, f applcable, o the frastructure for all three cases ca be corporated as a ogog cost, ad as such mateace s ot assumed to be a dstct case IV. The stuato volvg sgfcat rectfcato work ca be corporated uder case II. Where exstg frastructure s beg refurbshed, the same optos apply. The preset worth calculatos for each case ca be made to ft uder oe geeral formulato, whch s gve the ext secto. Costs, beefts ad dsbeefts are coverted to cash outflows ad cash flows. The cash flow dagrams for each of the three cases I, II ad III mght follow somethg lke Fgure 1. Varablty the beefts would remove the regularty mpled by Fgure 1. 3

4 Fgure 1 Schematc example cash flow dagrams (wth varablty beefts removed) for the three possble frastructure vestmet cases. Beefts are above the le. The costs below the le are the order I, II ad III at tme ow, whle the costs are the order I ad II for later tmes. 4. Applcable tools Wth such a probablstc problem, avalable soluto tools clude Mote Carlo smulato (for example, [6]), fuzzy set approaches (for example, [7]) ad secod order momet aalyss ([4] ad [5]). The frst two are umercal ad oly gve a lttle sght to uderlyg behavour. Black-Scholes ad bomal lattces (for example, [8]), as used facal optos theory, could also be used but lack tutve appeal to may. Secod order momet aalyss s used the followg because of ts ease of use ad requres very lttle adjustmet for those famlar wth covetoal dscouted cash flow (DCF) aalyss. The method gves equvalet results to real optos aalyss va Black-Scholes or bomal lattces. Covetoal determstc approaches would commoly use a rsk-adjusted dscout rate, leadg to a hgh dscout rate, whch tur leads to future cash flows havg lttle value preset worth terms. As such, determstc approaches effectvely gore ay log term clmate chage mpacts, ad decsos would favour projects wth short lfespas ad short term returs. Probablstc approaches o the other had, because the ucertaty s already ecapsulated wth the future cash flows, use the lower rsk-free dscout rates, whch gve value ( preset worth terms) to the future. Wth may of clmate chage mpacts beg log term ad frastructure lfespas beg log term, t s accordgly more ratoal to adopt a probablstc approach; ths s o top of the ssue as to what a rsk-adjusted dscout rate meas preset worth calculatos. Determstc approaches hde the fact that there s potetal dowsde to ay vestmet, whle probablstc approaches ackowledge that there s always a fte probablty that the preset worth of ay vestmet ca tur out to be egatve. 5. DCF formulato coverg frastructure choces Ifrastructure choces I, II ad III ca be corporated uder a geeral model that has cash flows at each tme perod. The ature, magtude ad sg of these cash flows wll dffer betwee the three choces. Let the et cash flow at each tme perod, = 0, 1, 2,...,, be the result of a umber of cash flow compoets Y k, k = 1, 2,..., m. The cash flow compoets are beeft, dsbeeft ad cost related. There may be correlato betwee the cash flow compoets at the same perod. The et cash flow X ay perod ca be expressed as, X Y 1 Y 2... Y m (1) where Y k, = 0, 1, 2,..., ; k = 1, 2,..., m, s the cash flow perod due to compoet k, wth mea E[ Y k ] ad varace Var[ Y k ]. 4

5 The expectato ad varace of X become, m E[X ] E[Y k ] (2) k 1 m Var[X ] Var[Y k ] 2 Cov[Y k,y ] (3) k 1 m 1 k 1 m k 1 where Cov[ ] s the covarace. Alteratvely, the varace expresso ca be wrtte terms of the compoet correlato coeffcets, k, betwee Y k ad Y, k, 1, 2,..., m, m m 1 m Var[X ] Var[Y k ] 2 k Var[Y k ] Var[Y ] (4) k 1 k 1 k 1 The preset worth, PW, s the sum of the dscouted X, = 0, 1, 2,...,, accordg to, X PW (1 r) (5) 0 where r s the dscout rate. The expected value ad varace of the preset worth become ([9], [10], [11]), E[X E[PW] ] (6) (1 r) 0 1 Var[X Var[PW] ] Cov[X 2,X j ] (7) (1 r) 2 (1 r) j 0 0 j 1 Alteratvely, the varace expresso ca be wrtte terms of the tertemporal correlato coeffcets betwee X ad X j, amely j, rather tha the covarace of X ad X j, 1 Var[X Var[PW] ] j Var[X ] Var[X j ] 2 (8) (1 r) 2 0 (1 r) j 0 j 1 For depedet cash flows X, Var[X Var[PW] ] (9) (1 r) 2 0 For perfect correlato of the cash flows X, Var[PW] 0 2 Var[X ] (1 r) (10) Var[PW] s smaller for the assumpto of depedece compared wth the assumpto of correlato. 5

6 6. Feasblty ad upsde value Havg characterzed the preset worth terms of ts momets, some measure s eeded to establsh the sutablty of a vestmet. Feasblty s oe approprate measure. Feasblty,, s defed as the probablty that the preset worth s postve ([4], [5]). P[PW 0] (11) Ths may be readly evaluated where preset worth follows a ormal dstrbuto. A ormal dstrbuto s commoly held to be a good represetato of preset worth ([9], [12], [10], [13]) Where competg frastructure choces exst, that wth the largest feasblty mght be preferred. Feasblty s a probablty, ad some people may ot feel comfortable workg wth ths measure. The questo arses as to what s a level of feasblty acceptable to the vestor, that s, what s a acceptable level of probablty that the preset worth wll tur out to be postve. The aswer to ths wll deped o whether the vestor s rsk proe, rsk averse or rsk eutral, ad hece requres kowledge of the vestor s values. A alteratve determstc measure s to use the mea of the preset worth upsde, that s the mea of the porto of the preset worth dstrbuto that s postve. Ths s referred to as the upsde value, UV, ths paper. UV = E[PW upsde] (12) The Black-Scholes formula ad bomal lattces calculate somethg smlar. For a gve Var[PW], a larger E[PW] meas hgher feasblty ad hgher upsde value, whle a lower E[PW] meas a lower feasblty ad lower upsde value. That s for a gve Var[PW], as creases/decreases, so too does UV crease/decrease respectvely. Accordgly the preferred frastructure, where alteratves exst, s that wth the largest UV. Wth a dvdual vestmet, what s cosdered a mmum upsde value wll deped o other crcumstaces ad tagbles surroudg the frastructure. It s oted that there wll always be a upsde value because of the postve tal of the ormal dstrbuto represetg PW. However the upsde value wll approach zero for vestmets wth low feasblty. Ad so vestors mght lke to make a decso based o both the upsde value cojucto wth the feasblty. What feasblty ad the upsde value are tellg s that all vestmets may tur out as losses ad also tur out as gas, wth probabltes attached. 7. Example To demostrate the types of results obtaed, cosder three vestmets of the form show Fgure 1. The umbers ad correlato type assumed are ot mportat; rather t s the methodology that s beg demostrated. Ucertaty the beefts ad costs s assumed to crease wth tme. The stadard devatos of the beefts ad the costs are take to crease 6

7 respectvely at 0.01 ad 0.02 tmes the mea for each addtoal year. Havg basc frastructure s take to cost 1.1 tally wth replacemet costs beg 1.25 ad ad 20 years respectvely; havg adaptable frastructure s take to tally cost 1.5, wth upgrades costg 0.4 ad 0.6; havg frastructure that wll last the full perod s take to cost 1.8. Beefts are 0.2 aually. Beefts ad costs are a ut of moey. A dscout rate of 10% s used. Beefts are assumed correlated. Costs are assumed correlated. Beefts ad costs are assumed ucorrelated. Fgure 2 shows the preset worth dstrbutos for cases I, II ad III. I summary, greatest feasblty s demostrated by II ad least by I (the three values are 0.83, 0.97 ad 0.96 respectvely for I, II ad III); I demostrates hghest upsde value, wth III the lowest (the three values are 0.37, 0.35 ad 0.29 respectvely for I, II ad III);. It s see that wth creasg ucertaty, the upsde value, UV, creases. Ths s cosstet wth optos aalyss. For comparso, a covetoal determstc aalyss (usg expected values oly, ad gorg varablty, but usg the same dscout rate) gves preset worths for I, II ad III of 0.27, 0.33 ad 0.27 respectvely, wth III slghtly greater tha I; that s II performs the best ad I the poorest. The determstc approach hdes the fact that there s potetal dowsde to ay vestmet, whle the probablstc approach ackowledges that there s always a fte probablty that the preset worth of ay vestmet ca tur out to be egatve. Table 1 gves a comparso performace of each of the vestmet choces. Fgure 2. Preset worth desty fuctos (frequecy of occurrece of preset worth versus moey) for frastructure choces I, II ad III; example values. UV E[PW] I II III Table 1. Comparso of choces I, II ad III for the example calculatos. Hghest value preferred for, UV ad E[PW]. 7

8 8. The value of buldg flexblty Buldg flexblty to frastructure may take may forms cludg defedg, modfyg (retrofttg, alterato), retreatg, relocatg ad abadog. The lkely mpacts of clmate chage eed to be recogsed ad a adaptve maagemet approach to desgg ad maagg vestmet s essetal. Clmate codtos wll chage cosderably over the lfe of log-lved frastructure The capacty for such assets to corporate adaptato treatmets or adjustmets to ther mateace regme wll part determe ther reslece to accelerated degradato of materals ad fatgue of structures due to creased testy ad frequecy of extreme evets (storms, wd, rafall, bushfre). Itegratg reewal optos log-lved frastructure would also help eable perodc mprovemets to these assets as kowledge mproves. ([3], p. 23) The value of buldg the capacty to be flexble may be vewed as s doe real optos aalyss. I the real optos lterature, the techques of Black-Scholes ad bomal lattces are used, but ca be crtczed for ther lack of tutve appeal, partcularly eedg to defe a volatlty term, whch has meag a share prce sese but ot a project sese. Istead of Black-Scholes ad bomal lattces, the authors prefer to use the results of the probablstc DCF aalyss outled above, to value the opto to adapt. Cosder the stuato for cases I ad II, at the tme where a frst decso s ecessary (after 10 years the example), but before the secod decso becomes ecessary. Case I volves rebuldg aew; case II volves adaptg the tal frastructure. The preset worth of ths flexblty s show Fgure 3. It has a upsde value of 0.14 for I ad 0.37 for II. Ths s equvalet to the Black-Scholes opto value. The opto to be flexble the future has a value. The total value of the frastructure s based o ts value up to the pot where a decso s ecessary together wth ths opto value. Fgure 3. Probablty desty fuctos of preset worths (frequecy of occurrece of preset worth versus moey) for upsde value calculato for choces I (buld aew) ad II (adapt); example values. 9. Coclusos 8

9 Wth clmate chage comes creasg ucertaty. Wth creased ucertaty comes the eed for rethkg feasblty studes of frastructure vestmets. Flexble ad adaptable frastructure may offer the potetal to gve better facal feasblty over exstg oflexble approaches because of ths ucertaty. The paper offers a soud methodology for ot oly corporatg future ucertaty but also allowg vestors to prce flexblty. The tet of the paper was ot to mply that ay oe of the three choces for frastructure lsted, amely I (desg for today), II (desg for adaptato) or III (over-desg for tomorrow) s better tha ay other. Whch s best wll be determed by the partcular crcumstaces. Rather the paper offers a soud methodology for establshg whch choce s best ay partcular stuato. Ackowledgemet The assstace developg ths dscusso paper provded by Assocate Professor Ro Cox from the School of Cvl ad Evrometal Egeerg at the Uversty of New South Wales, ad the Australa Clmate Chage Adaptato Network for Settlemets ad Ifrastructure s thakfully ackowledged. Refereces [1] IPCC Itergovermetal Pael o Clmate Chage (2007), Clmate Chage 2007, the Fourth Assessmet Report (AR4), Uted Natos, New York. [2] Presto, B. ad Joes R. (2006), Clmate Chage Impacts o Australa ad Beefts of Early Acto to Reduce Global Greehouse Gas Emssos, CSIRO, Caberra. [3] NCCARF Natoal Clmate Chage Adaptato Research Faclty (2009), Natoal Clmate Chage Adaptato Research Pla: Settlemets ad Ifrastructure, Cosultato Draft, September. NCCARF, Grffth Uversty. [4] Carmchael, D. G. ad Balatbat, M. C. A. (2008a), "Probablstc DCF aalyss, ad captal budgetg ad vestmet - A survey", The Egeerg Ecoomst, Vol. 53, No. 1, pp [5] Carmchael, D. G. ad Balatbat, M. C. A. (2008b), The fluece of extra projects o overall vestmet feasblty, Joural of Facal Maagemet of Property ad Costructo, Vol. 13, No. 3, pp [6] Nassar, K. ad Al-Mohase, A. (2006), Smplfed approach to probablstc cost beeft aalyss; Archtectural lghtg example, Cost Egeerg, Vol. 48, No. 1, pp [7] Omtaomu, O. A. ad Badru, A. (2007), Fuzzy Preset Value Aalyss Model for Evaluatg Iformato System Projects, The Egeerg Ecoomst, Vol. 29, No. 2, pp

10 [8] Eschebach, T., Lews, N., Here, M., Baker, E. ad Hartma, J. C. (2007), Real optos ad real egeerg, Egeerg Maagemet, Vol. 19, No. 4, pp [9] Hller, F. S. (1963), The dervato of probablstc formato for the evaluato of rsky vestmets, Maagemet Scece, Vol. 9, No. 3, pp [10] Wagle, B. (1967), A statstcal aalyss of rsk captal vestmet projects, Operatoal Research Socety, Vol. 18, No. 1, pp [11] Caada, J. R. ad Whte, J. A. (1980), Captal Ivestmet Decso Aalyss for Maagemet ad Egeerg, Pretce-Hall, New Jersey. [12] Hller, F. S. (1969), The Evaluato of Rsky Iterrelated Ivestmets, North Hollad, Amsterdam. [13] Tug, Y. K. (1992), Probablty dstrbuto for beeft/cost rato ad et beeft, Joural of Water Resources, Vol. 118, No. 2, pp