Alternative approach to estimating crash costs for cost-benefit analysis using Monte Carlo simulation

Transcription

1 Australasan Transport Research Forum 2018 Proceedngs 30 October 1 November, Darwn, Australa Publcaton webste: Alternatve approach to estmatng crash costs for cost-beneft analyss usng Monte Carlo smulaton Surya Prakash BITRE, Department of Infrastructure, Regonal Development and Ctes, Canberra, Australa Unversty of Canberra, Australa Unversty of the South Pacfc, Fj Emal for correspondence: Surya.prakash@nfrastructure.gov.au Abstract Cost-beneft analyss (CBA) s used as a tool to nform nvestment decsons n both the government and prvate sectors. An essental part of any CBA for road nfrastructure projects s the calculaton of crash cost savngs. Currently, crash cost savngs are typcally addressed va determnstc methods, as the product of projected future traffc volumes and the expected accdent rate of the road after project completon. Road traffc crashes, especally fatalty and casualty crashes, typcally occur only nfrequently, and at unpredctable ntervals, ths doesn t naturally accord wth the determnstc model. Ths paper demonstrates how probablstc methods can be appled to better account for crash cost savngs n CBAs. The benefts of ths approach are demonstrated va an example. 1. Introducton A Cost-beneft analyss (CBA) s usually conducted to nform decsons makers of the net economc benefts of a project ahead of ts constructon. It provdes nformaton about whether the project benefts outwegh costs, and f so, by how much. It s mportant to note that the cost and benefts beng compared are forecast values and hence nvolve uncertantes, whch should be addressed as effectvely as possble so as to ensure that the comparson s vald. The uncertantes nherent n a project wll mean that there wll be separate dstrbutons of possble cost and benefts outcomes, whch are not adequately captured n a sngle number. Probablstc methods, or quanttatve rsk analyss approaches, are now wdely utlsed to quantfy the uncertantes of the predcted outcomes and produce a probablty dstrbuton across all possble outcomes (Galloway et al. 2012, Baccarn 2005) as opposed to a sngle value produced by determnstc approaches. Probablstc methods, utlsng approaches lke Monte Carlo smulaton, are becomng ncreasngly popular to produce project-related estmates, because they mprove the overall understandng of the estmates by explctly addressng the potental rsks of the tem(s) beng estmated. Quantfyng rsk and uncertanty s a cost estmatng best practce addressed n many gudes and References (GAO 2009, p. 154). 1

2 In Australa, project proposals for road projects submtted for fundng applcatons/requests are requred to submt, amongst other thngs, a probablstc cost estmate along wth a beneft cost rato (BCR) (Infrastructure 2014). Currently there s no requrement for the estmated benefts or overall beneft-cost rato (BCR) to be probablstc. The Department of Infrastructure, Regonal Development and Ctes requres a probablstc cost estmate for all projects exceedng $25 mllon n out-turn costs. Smlar to cost estmates, the estmated benefts of projects wll also be more nformatve f based on probablstc methods. Ths paper bulds on Prakash & Mtchell (2015), whch consdered dervaton of probablstc BCRs, by demonstratng how probablstc methods could be appled to better estmatng the crash cost savngs element of expected projects benefts. The crash cost element was chosen because the probablty of road crashes s hghly probablstc and more readly lends tself to the applcaton of probablstc methods. The motvaton for ths paper also comes from a recent ex-post economc evaluaton report of Natonal Road Investment projects (BITRE 2018), recommendng that Reportng of probablty dstrbutons of BCR and NPV should be encouraged due to large uncertantes accompanyng the determnstc estmates of BCR and NPV. 2. Probablstc estmaton methods Probablstc estmaton methods, or quanttatve rsk analyss, usually nvolves usng Monte Carlo smulaton (the predomnant method used) to generate a probablty dstrbuton for all possble outcomes or scenaros. Ths s acheved by accountng for every possble value that an tem, nvolved n the estmate, and the probablty of occurrence of that value, and combnng across all other tems. Boardman et al. (1996) outlnes the general stages nvolved n performng CBA (see Fgure 1). Fgure 1: CBA stages 1 Specfy the set of alternatve projects 2 Decde the benefts and costs to be ncluded 3 Lst all costs and benefts ncludng tems over the lfe of project 4 Monetze the costs and benefts 5 Apply dscount rates to obtan present values 6 Compute the preferred beneft over cost, [BCR, NPV etc], for each opton 7 Assess rsks and uncertanty (senstvty analyss) Source: Adapted from Boardman et al. (1996). If a probablstc approach s adopted, the steps shown n Fgure 1, would be modfed from stage 6 onwards to account for the range of possble outcomes, as shown n Fgure 2. In partcular, note that the orgnal stage 7 senstvty analyss may not be necessary by the applcaton of probablty dstrbutons to all lkely possble outcomes. 2

3 Fgure 2: Probablstc CBA stages 1 Specfy the set of alternatve projects 2 Decde the benefts and costs to be ncluded 3 Lst all costs and benefts ncludng tems over the lfe of project 4 Monetze all dentfed tems (costs and benefts) 5 Apply dscount rates to obtan present values 6 Assgn approprate probablty dstrbutons to all tems 7 Account for correlatons between tems, f any Generate a probablty dstrbuton for the requred tem (NPV, BCR etc) usng Monte 8 Carlo smulaton The step of assessng senstvtes rsks s not requred snce a Monte Carlo smulaton produces senstvty analyss by default. Durng a Monte Carlo smulaton, values are sampled at random from the nput probablty dstrbutons of the nherent and contngent tems, and the results combned to obtan an outcome for each teraton. For the purposes of ths paper, nherent tems are referred to tems that wll defntely contrbute to the overall estmate. In other words, the lkelhood of occurrence of ths tem s 100%. I defne contngent tems, on the other hand, as tems that may or may not contrbute to the overall estmate. In other words, the lkelhood of occurrence s less than 100%. Ths process s repeated hundreds or thousands of tmes. Ths resultant probablty dstrbuton of possble outcomes produces not only the range of possble outcomes, but also the lkelhood of those outcomes. The detals on the changes made to Fgure 1 as shown n Fgure 2 are explaned below: Assgnng approprate probablty dstrbutons to all tems (step 6) Ths step s to assgn approprate probablty dstrbutons to each of the nherent and contngent tems, and to also assgn probabltes to the occurrence of each contngent tem. The probablty dstrbuton chosen for each cost or beneft tem should account for all possble project outcomes and are typcally determned usng lowest, most lkely and hghest possble values. Carefully approxmatng the range of possble outcomes s crtcal because use of napproprate or unrealstc ranges can lead to unrelable results. The assgned probablty dstrbuton represents the shape of the rsk tem and the tals of the dstrbuton reflect the best and worst case scenaro. The choce of dstrbuton functon s beyond the scope of ths paper however there s an extensve lterature avalable on the type of dstrbuton functons to use, and crcumstances under whch to apply them, n project rsk evaluaton (see, for example, Vose 2009). Accountng for correlaton between cost elements (step 7) Correlaton between tems needs to be gven consderaton. When modellng, t s mportant to consder the mpact of nter-relatonshps (correlaton) between tems to generate accurate and sensble outputs. Falure to sutably account for correlaton can result n artfcally tght project cost/beneft dstrbutons, and an ncorrect assessment of the true estmate. 3

4 Generatng a probablty dstrbuton usng Monte Carlo smulaton methods (step 8) The most common technque for combnng the ndvdual elements and ther dstrbutons s by usng Monte Carlo smulaton. Monte Carlo smulaton s a computersed mathematcal technque that facltates accountng for rsks n quanttatve analyss and decson makng. A number of easy-to-use propretary tools exst for mplementng Monte Carlo smulatons to ncorporate rsk n project evaluaton the most wdely used ones and Oracle s Crystal Ball. In ths was used for all smulatons. 3. Crash Cost Savngs n a BCA For a road-related project, the estmated savngs due to expected reductons n crashes s extremely mportant potental beneft, and has great socetal mpacts due to the loss of lfe and serous njury of those nvolved n serous crashes. Estmated reductons n the cost of road crashes are classfed as part of the safety benefts of a road project. Calculatng the crash cost savngs nvolves the followng steps (TIC 2018a): Estmatng the expected number of crashes by crash type for each year under the base case and the project case Multply the crash numbers for each type by ther respectve unt costs The expected number of crashes durng a perod of tme s typcally obtaned by multplyng expected crash rates by forecast traffc volumes. The relevant crash rate for estmatng future crash numbers n the base and project optons s a number of crashes per year to unt of traffc (vehcles, trans, cyclsts and pedestrans) or traffc-klometre. Road crash rates are typcally expressed per 100 mllon vehcle klometres travelled (VKT). Crashes may be consdered at dfferent severty levels such as fatal, serous njury, mnor njury or property damage only. The levels are dependent on the data avalablty. For a specfed perod, where: crash cost, cc = N μ (1) N s the estmated crash number for crash type severty level of accdent; and μ s the unt crash cost of severty type. To derve the crash cost savngs (beneft) for a project case, ether: ) project case crash costs are subtracted from base case crash costs; or ) the base crash cost s multpled by the crash cost reducton factor for the dentfed project opton ( TIC 2018a). For a specfed perod, crash cost savngs for severty type, for opton, j of a project s where: crash cost savngs, cc j = N α j μ j N s the estmated crash number for the base case for crash type severty level of accdent; α j s the crash cost reducton factor wth project opton j mplemented; and μ j s the unt crash cost of severty type wth project opton j mplemented. (2) 4

5 4. Probablstc Crash Cost Savngs n a BCA To better account for the uncertantes nvolved n calculatng crash cost savngs, I apply the relevant steps as shown n Fgure 2, prmarly to consder the varables as probablty dstrbutons nstead of a sngle number. Hence, Equaton 2 s transformed as below: prob. dst(crash cost savngs, cc j ) = prob. dst(n ) prob. dst(α j ) prob. dst(μ j ) (3) Notce that all the three quanttes, estmated crash number, crash cost reducton factor and unt crash cost, n Equaton 2 are represented as separate probablty dstrbutons, because all these three quanttes have uncertantes assocated wth them. The next step would be to consder any correlatons between these tems and perform a Monte Carlo smulaton to obtan a probablty dstrbuton for crash cost savngs. The followng secton llustrates ths method to a worked example provded n (TIC 2018b) and compares the generated results. For the purposes of ths paper, I focus on the crash cost calculaton and leave the other tems as determnstc. 5. Worked example Ths example has been adapted from (TIC 2018b) on Pedestran/cycle sgnalzed crossng or overpass Problem descrpton The scenaro presented s that currently pedestrans and cyclsts are crossng a major subarteral road. The crossng s not presently sgnalsed but there s pedestran refuge n the roadway medan. The annual average daly traffc (AADT) s 5,000 vehcles growng at 2% per annum. On average, 150 walkers and 100 cyclsts use the crossng each day, makng an average of two crossngs per day per person. Actve travel trps are growng at 2% pa. The problem statement: facltate safer pedestrans and cyclsts crossng Optons There are two optons (Optons 1 and 2) beng nvestgated wth the base case beng Do Nothng. Opton 1: Provde sgnals at the crossng to allow actve travellers to cross safely; and Opton 2: Provde a pedestran and cycle overpass Inputs and assumptons The nputs requred for an analyss are as lsted n Table 1. Table 1: Inputs Base year and prce year: 2015 Constructon perod years: 2016 Real dscount rate 7% Apprasal perod: constructon perod plus 30 years of operaton 5

6 Ref Item Base Case Opton 1 Opton 2 A Constructon costs $250,000 $4,250,000 B Asset (economc) lfe 30-year lfe 40-year lfe C Resdual value $1,062,500 1 D Mantenance costs $4,000 per year $25,000 per year E Number of crossng trp/day walkers F Number of crossng trp/day cyclsts G Actve transport trps 2 as % of total trps 60% 60% 60% H Annual average daly traffc (AADT) (2015) % prvate car % busness car % commercal 80% 15% 5% 80% 15% 5% 80% 15% 5% I Average delay walkers/cyclsts (secs) J Average delay all vehcles (secs) (F) K Days per year L Average crash cost fatal (2013 values) $7,573,412 $7,573,412 $7,573,412 M Average crash cost serous njures (2013 values) N Crash cost reducton factor relatve to medan refuge $526,606 $526,606 $526, % 77% O Fatal crashes per year P Serous njury crashes Q Weghted average value of travel tme - $31.34 per hr $31.34 per hr $31.34 per hr vehcles R Average value of travel tme actve travellers $14.99 per hr $14.99 per hr $14.99 per hr S CPI June T CPI June U Growth rate 2% 2% 2% 1 Shown as a beneft n the fnal year of apprasal. Based on: straght lne deprecaton method, 10 years of 40- year lfe remanng at end of apprasal perod (40 30). 2 Actve trps mples walkng and cyclng wth a purpose and not for recreatonal purposes. For more detals and other assumptons, please refer to TIC (2018b) The benefts and costs for the BCR calculaton can be classfed as follows: Benefts: Travel tme savngs (dsbeneft) Crash cost savngs Resdual value 6

7 Costs: Constructon costs Mantenance costs See below for the values of these tems derved va dfferent approaches Determnstc Approach The calculatons were performed as follows (TIC 2018b). Note: All dollar values are multpled by CPI June 2015 / CPI June 2013 to nflate the 2013 unt cost parameter values to the prce year of 2015; Upper case letters n the formulas refer to the reference labels (Ref) appearng n Table 1; Benefts for 2018 and onwards are calculated by applyng the growth rate (2% each Growth rate year from 2017 onwards.e. multply by (1 + ). 100 All values have been dscounted rate at a 7% dscount rate. Crash cost savngs for base year (ths s the combned cost of fatal and serous njury crashes saved due to the ntatve): where: 2 crash cost savngs, cc j = N α =1 j μ j = (O*L+P*M)*N (4) N s the estmated crash number for the base case for crash type severty level of accdent; α j s the crash cost reducton factor wth project opton j mplemented; μ j s the unt crash cost of severty type wth project opton j mplemented; 1, severty level: Fatal = { 2, severty level: serous njury 1, Opton 1 j = { 2, Opton 2 Tme travel beneft (dsbeneft): Resdual value: and; Tme travel beneft = (E + F) G R I ( K U ) ( )2 Table 2: Total cost, dscounted, $,000 Resdual value = C Opton 1 Opton 2 Total cost (captal and mantenance) Table 3 shows the calculatons for these quanttes usng the determnstc approach as suggested n (TIC 2018b). 7

8 Table 3: Determnstc calculatons ($,000) Year Crash reducton Opton 1 Opton 2 Travel tme savngsactve travellers Travel tme savngs - cars, trucks Total benefts Crash reducton Travel tme savngsactve travellers Travel tme savngs - cars, trucks Total benefts The total values of benefts as shown n Table 3 after applyng dscount rates s provded n Table 4. Table 4: Total benefts, dscounted, $,000 Opton 1 Opton 2 Total crash reducton dscounted at 7% Total travel tme savngs actve travellers Total travel tme savngs cars, trucks Resdual value Total

9 Usng the values of the total cost (Table 2) and the total benefts (Table 3) for the two optons, the BCR 1 values (rounded to one decmal place) are then 22.7 (Opton 1) and 2.1 (Opton 2): Opton 1: BCR = Total Benefts Total Costs = = 22.7 Opton 2: BCR = Total Benefts Total Costs = = 2.1 Table 5: BCA calculatons BCR= Total Benefts Total Costs Opton 1 Opton NPV= Total Benefts - Total Costs Probablstc Approach As detaled n Secton 4, to account for uncertantes, all varables should be treated as probablty dstrbutons nstead of a sngle number. In ths followng example, all varables have an assocated probablty dstrbuton. Benefts: Costs: Travel tme savngs: there s uncertanty n the value of travel tme savngs due to uncertanty n the underlyng tems such as dollar value of travel tme and number of crossngs, etc; Crash cost savngs: There s uncertanty n the expected number of crashes and expected crash severty; and Resdual value: Uncertanty n the estmated resdual dollar value. Constructon costs: Uncertanty n estmated costs; and Mantenance costs: Uncertanty n estmated mantenance costs Bascally, when relyng on estmates, t cannot be sad that there s no uncertanty, ncludng the uncertanty n the acceptance of the solutons brought about by the projects. For nstance, for opton 2 of the project beng consdered n the paper, there could be a tendency for pedestrans and cyclsts to not use the overhead pass bult. Ths would then mean that the crash cost reducton factor would not be as predcted,.e., accdents stll occurrng at the prevous rate. Uncertanty s nherent n all estmates and the estmatng processes hence t s hghly msleadng to represent an estmate as a sngle number. Ideally, all the tems for the costs and benefts calculaton should be replaced wth approprate dstrbutons and modelled. The probablty dstrbuton utlzed depends on the characterstcs of the quantty to be represented. For nstance, beneft due to travel tme savngs s dependent upon number of 1 Ths BCR corresponds to BCR1 n Australan and Infrastructure Councl (2018b). 9

10 crossngs per day by walkers/cyclsts and the average value of tme savngs. The possble values of the former varable can only be whole numbers, e {0,1,2,3, }, therefore the use of a dscrete dstrbuton s approprate where the latter varable, ncludes values (dollar amounts) upto two decmal places where a contnuous dstrbuton s requred. Contnuous dstrbutons, unlke dscrete ones, can take any value over a contnuous range of values. For more detals, see Baccarn (2018). For the purposes of ths paper, I focus only on the crash costs calculaton and then only on uncertanty n the estmated number of crashes, smply assumng that average crash costs are certan, and model the benefts by treatng the estmated number of crashes as a dstrbuton. Hence, after these assumptons, Equaton 3 transforms to: where: prob. dst(crash cost savngs, cc j ) = prob. dst(n ) α j μ j N s the estmated crash number for the base case for crash type severty level of accdent; α j s the crash cost reducton factor wth project opton j mplemented; and μ j s the unt crash cost of severty type wth project opton j mplemented. From the nformaton provded, N, for both severty types (fatal and serous njures) was taken as 0.1. In other words, the probablty for a crash for both severty types s 0.1. Ths value has been used n the calculatons as shown n Secton 5.4. Notce that the determnstc approach, as per Equaton 4, the crash reducton beneft for 2017, for opton 1,s calculated as below: crash cost savngs, cc 1 = N α j μ j 2 =1 After multplcaton by CPI adjustment factor ( = (0.1 7,573, ) + ( , ) 494,101 CPI June 2015 CPI June 2013 ), the crash cost savngs for 2017 s $0.52 mllon as also provded n Table 3. Note that ths fgure s an approxmated average and s not representng the possble realty. For a possble crash n 2017, for both severty types (fatal and serous njury), the crash cost savngs would be $5.2 mllon and not one tenth of t. To overcome ths approxmaton, I model N by usng the prob. dst(n ) as a bnomal dstrbuton (Baccarn 2018). A bnomal dstrbuton has only two values wth each havng an assocated probablty. In ths case, the two values would be ether 0 or 1. I assgn 0 for the crash not happenng and 1 for a crash happenng wth the assocated probabltes as 0.9 and 0.1 respectvely. It s mportant to pont out that, for any gven year, the realty s that ether the cost s gong to be zero or the cost s gong to be the cost of crash f t happens. Ths s how the crash number s modelled and the Monte Carlo smulaton done. Ths functon s provded software as RskBernoull and Fgure 3 depcts prob. dst(n ). 10

11 Fgure 3: Probablty dstrbuton functon of estmated crash number per year, N Monte Carlo results Monte Carlo smulaton then nvolves takng repeated random draws from the dstrbuton, for each year and for each severty case ether a 0 (no crash) or 1 (crash) and multpled by the respectve cost to obtan the crash cost for that year. For nstance, for a random teraton for opton 1, f the crash number for a fatal crash s drawn as 1, then ths s multpled to the crash cost of $7,573,412 and the reducton factor of opton 1, 0.61 to obtan the crash cost savngs of approxmately $4.6 mllon (before any CPI or dscount rate adjustment); on the other hand, f the crash number for a fatal crash s drawn as 0 then the crash cost savngs s $0 as expected. The results of the Monte Carlo smulaton are presented n Table 6 and Fgures Table 6: Summary of Monte Carlo smulatons results Opton 1 Opton 2 P(>= breakeven*) P50** P90 P(>= breakeven) P50 P90 BCR 95.5% % NPV 95.5% % * refers to the breakeven ponts of 1 for BCRs and 0 for NPVs. ** P50 value s the value wth a 50 per cent lkelhood that t wll not be exceeded For nstance, refer to Fgures 4 & 5 whch depct the dstrbuton of the total crash reducton savngs. The determnstc total for ths tem as provded n Table 4 was $7,408,000 and $9,326,000 for optons 1 and 2 respectvely. The addtonal nformaton that Fgures 4 and 5 provde s that the probablty of achevng these totals or less s 54%. Snce ths s related to benefts, the other way to look at ths would be to state that the probablty of achevng a crash cost savng of at least $7,408,000 for opton 1 and $9,326,000 for opton 2 s 46% for both. Whch therefore ndcates that there s a bgger chance of the total crash cost savngs beng less than the dentfed totals for both the optons. 11

12 Fgure 4: Total crash reducton, dscounted for Opton 1 Fgure 5: Total crash reducton, dscounted for Opton 2 The effects of the consderaton of probablty for a crash as a probablty dstrbuton also flows onto the total benefts. The extra detals that can be extracted from the probablty dstrbutons of the total benefts (Fgures 6 and 7) are that the probablty of achevng a negatve beneft are 4.0% and 0.5% respectvely for optons 1 and 2. Also that the probabltes of gettng at least the determnstc fgures of total benefts (Table 4) of $6,351,000 for opton 1 and $9,138,000 for opton 2 are approxmately 46% for both. Smlar to the concluson drawn for the total crash savngs, the results ndcate there s a bgger chance of the total benefts beng less than the dentfed totals for both the optons. 12

13 Fgure 6: Total benefts, dscounted for Opton 1 Smlar observatons can be made from the BCR dstrbutons (Fgures 8 and 9). The probablty of a negatve BCR due to negatve benefts for opton 1 s 4% whle t s 0.5% for opton 2. The probabltes of gettng the determnstc values of BCR (Table 5) of at least for opton 1 and 2.14 for opton 2 are about 46% for both and therefore there s a bgger chance of the BCR values beng less than the dentfed values for both the optons. In relaton to the breakeven pont of BCR beng 1, Opton 1 has a 95.5% of achevng at least a 1 as compared to Opton 2 s 82.4%. The Net Present Value (NPV) dstrbutons are shown n Fgures 10 and 11. The probablty for gettng a negatve NPV due to negatve benefts for opton 1 s 4.5% whle t s 17.6% for opton 2. The probabltes of gettng the determnstc values of NPV (Table 5) of at least $6.07 mllon for opton 1 and $4.88mllon for opton 2 are about 46% for both and therefore there s a bgger chance of the NPV values beng less than the dentfed values for both the optons. Preferred Opton The dstrbutons of BCRs and NPVs (Fgures 8-11) can be used to nform the decson makng process when choosng between Opton 1 and Opton 2, f decson s to be made on these ndcators and not for poltcal reasons. In ths case, Opton 1 has a greater BCR and NPV values for a chosen pont of comparson, for nstance a chosen P value. For nstance, a P50 value s the value wth a 50 per cent lkelhood that t wll not be exceeded. Usually for a determnstc BCR, the expected value or mean s utlzed for the computatons. Havng these dstrbutons provdes one wth more nformaton to facltate the decson makng process. For nstance, also avalable s the probablty of an Opton breakng even. In the example presented Opton 2 has a 17.6% chance of not achevng a BCR of 1 as compared to 4.5% chance for Opton 1. Smlarly Opton 2 has a greater chance (17.6%) of achevng a NPV of less than 0 as compared to 4.5% for Opton 1. Hence Opton 1 would be the project to pursue because t has greater BCR and NPV values for a chosen P value and t also shows a greater chance of achevng a greater than or equal to the breakeven pont. 13

14 Fgure 7: Total benefts, dscounted for Opton 2 Fgure 8: BCR for Opton 1 Fgure 9: BCR for Opton 2 14

15 Fgure 10: NPV for Opton 1 Fgure 11: NPV for Opton 2 6. Conclusons In ths paper, I have presented a probablstc approach to calculatng the crash cost benefts, as part of performng a CBA, n a road project. The nfrequent and uncertan nature of road crashes lend themselves to probablstc methods. As shown va a demonstrated example, a probablstc approach provdes more nformaton, as compared to a determnstc approach, to assst decson makers to choose between projects. The addtonal nformaton provdes decson makers wth an dea as to the nature of the rsks nvolved n projects, ncludng extreme outcomes, whch can be very useful when comparng projects. Ths paper presented the results by replacng the determnstc crash cost savngs wth ts probablstc equvalent. Ths analyss would be better f all tems were substtuted by ther respectve dstrbutons and hence provded deeper analyss whch possbly renders separate the senstvty analyss unnecessary because the probablty dstrbuton generated by the Monte Carlo smulatons contan the senstvty analyss and more. 15

16 7. Acknowledgements The author wshes to acknowledge Davd Mtchell (BITRE) for valuable dscusson and comments. Any opnons expressed n the paper are those of the author and do not necessarly reflect the vews of the Department of Infrastructure, Regonal Development and Ctes. Responsblty of any errors remans the author s. 8. References Baccarn, D. 2005, Estmatng project cost contngency Beyond the 10% syndrome. In Australan Insttute of Project Management Natonal Conference. Baccarn D. 2018, Project Uncertanty Management, e-book. Bureau of Infrastructure, Transport and Regonal Economcs (BITRE), 2018, Ex-post Economc Evaluaton of Natonal Road Investment Projects, Report 145, Volume 1 Synthess Report. Boardman, A, Greenberg, D, Vnng, A and Wemer, D 2014, Cost-Beneft Analyss: Concepts and Practce Concepts and Practce, Pearson Educaton. Department of Infrastructure and Regonal Development (Infrastructure), 2014, Notes on Admnstraton for Land Transport Infrastructure Projects to , Department of Infrastructure and Regonal Development, Canberra Galloway P D, Nelsen, K R and Dgnum, J L, 2012, Managng Ggaprojects: Advce from Those Who've Been There, Done that, Amercan Socety of Cvl Engneers. Prakash, S & Mtchell, D 2015, Probablstc Beneft Cost Rato A Case Study., n Australasan Transport Research Forum 2015 Proceedngs. Transport and Infrastructure Councl (TIC) 2018a, Australan Transport and Assessment (ATAP) Gudelnes - T2 Cost Beneft Analyss, Commonwealth Department of Infrastructure and Regonal Development, Canberra Transport and Infrastructure Councl (TIC) 2018b, Australan Transport and Assessment (ATAP) Gudelnes Worked Examples: W4 Actve Travel, Commonwealth Department of Infrastructure and Regonal Development, Canberra Unted States Government Accountablty Offce (GAO), 2009, GAO Cost Estmatng and Assessment Gude: Best Practces for Developng and Managng Captal Program Costs, GAO, Washngton D.C. Vose D.,2009, Rsk Analyss: A Quanttatve Gude, John Wley & Sons Ltd. 16