Designation: E1946 − 12Standard Practice forMeasuring Cost Risk of Buildings and Building Systemsand Other Constructed Projects1This standard is issued under the fixed designation E1946; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This practice covers a procedure for measuring cost riskfor buildings and building systems and other constructedprojects, using the Monte Carlo simulation technique asdescribed in Guide E1369.1.2 A computer program is required for the Monte Carlosimulation. This can be one of the commercially availablesoftware programs for cost risk analysis, or one constructed bythe user.2. Referenced Documents2.1 ASTM Standards:2E631 Terminology of Building ConstructionsE833 Terminology of Building EconomicsE1369 Guide for Selecting Techniques for Treating Uncer-tainty and Risk in the Economic Evaluation of Buildingsand Building SystemsE1557 Classification for Building Elements and RelatedSitework—UNIFORMAT IIE2103 Classification for Bridge Elements—UNIFORMATIIE2168 Classification for Allowance, Contingency, and Re-serve Sums in Building Construction Estimating3. Terminology3.1 Definitions—For definitions of general terms used in thisguide, refer toTerminology E631; and for general terms relatedto building economics, refer to Terminology E833.4. Summary of Practice4.1 The procedure for calculating building cost risk consistsof the following steps:4.1.1 Identify critical cost elements.4.1.2 Eliminate interdependencies between critical ele-ments.4.1.3 Select Probability Density Function.4.1.4 Quantify risk in critical elements.4.1.5 Create a cost model.4.1.6 Conduct a Monte Carlo simulation.4.1.7 Interpret the results.4.1.8 Conduct a sensitivity analysis.5. Significance and Use5.1 Measuring cost risk enables owners of buildings andother constructed projects, architects, engineers, and contrac-tors to measure and evaluate the cost risk exposures of theirconstruction projects.3Specifically, cost risk analysis (CRA)helps answer the following questions:5.1.1 What are the probabilities for the construction contractto be bid above or below the estimated value?5.1.2 How low or high can the total project cost be?5.1.3 What is the appropriate amount of contingency to use?5.1.4 What cost elements have the greatest impact on theproject’s cost risk exposure?5.2 CRA can be applied to a project’s contract cost, con-struction cost (contract cost plus construction change orders),and project cost (construction cost plus owner’s cost), depend-ing on the users’ perspectives and needs. This practice shallrefer to these different terms generally as “project cost.”6. Procedure6.1 Identify Critical Cost Elements:6.1.1 A project cost estimate consists of many variables.Even though each variable contributes to the total project costrisk, not every variable makes a significant enough contribu-tion to warrant inclusion in the cost model. Identify the criticalelements in order to simplify the cost risk model.6.1.2 A critical element is one which varies up or downenough to cause the total project cost to vary by an amountgreater than the total project cost’s critical variation, and one1This practice is under the jurisdiction of ASTM Committee E06 on Perfor-mance of Buildings and is the direct responsibility of Subcommittee E06.81 onBuilding Economics.Current edition approved April 1, 2012. Published April 2012. Originallyapproved in 1998. Last previous edition approved in 2007 as E1946 – 07. DOI:10.1520/E1946-12.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at

[email protected] For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3This practice is based, in part, on the article, “Measuring Cost Risk of BuildingProjects,” by D.N. Mitten and B. Kwong, Project Management Services, Inc.,Rockville, MD, 1996.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1which is not composed of any other element which qualifies asa critical element. This criterion is expressed as:IF VY.VCRIT(1)AND Y contains no other element X where VX.VCRITTHEN Y is a critical elementwhere:VY5 (2)~Max. percentage variation of the element Y!*~Y’s anticipated cost!Total Project CostVCRIT= Critical Variation of the Project Cost.6.1.3 A typical value for the total project cost’s criticalvariation is 0.5 %.4By experience this limits the number ofcritical elements to about 20. A larger VCRITwill lead to fewercritical elements and a smaller VCRITwill yield more. A riskanalysis with too few elements is over-simplistic. Too manyelements makes the analysis more detailed and difficult tointerpret. A CRA with about 20 critical elements provides anappropriate level of detail. Review the critical variation usedand the number of critical elements for a CRA against theunique requirements for each project and the design stage. Ahigher critical variance resulting in fewer critical elements, ismore appropriate at the earlier stages of design.6.1.4 Arrange the cost estimate in a hierarchical structuresuch as UNIFORMATII (Classification E1557 for Buildings orClassification E2103 for Bridges). Table 1 shows a sampleproject cost model based on a UNIFORMAT II Levels 2 and 3cost breakdown for a building. The UNIFORMAT II structureof the cost estimate facilitates the search of critical elements forthe risk analysis. One does not need to examine every elementin the cost estimate in order to identify those which are critical.6.1.5 Starting at the top of the cost estimate hierarchy (thatis, the Group Element level), identify critical elements in adownward search through the branches of the hierarchy.Conduct this search by repeatedly asking the question: Is itpossible that this element could vary enough to cause the totalbuilding cost to vary, up or down, by more than its criticalvariation? Terminate the search at the branch when a negativeanswer is encountered. Examine the next branch until allbranches are exhausted and the list of critical elements estab-lished (denoted by asterisks in the last column of Table 1).Table 1 and Fig. 1 show the identification of critical elementsin the sample project using the hierarchical search technique.6.1.6 In the sample project, Group Element B10 Superstruc-ture has an estimated cost of $915 000 with an estimatedmaximum variation of $275 000, which is more than $50 000,or 0.5 % of the estimated total building cost. It is therefore acandidate for a critical element. However, when we examinethe Individual Elements that make up Superstructure, wediscover that Floor Construction has a estimated maximumvariation of $244 500, qualifying as a critical element; whereasRoof Construction could only vary as much as $40 000, anddoes not qualify. Since Floor Construction is now a criticalelement, we would eliminate Superstructure, its parent, as acritical element.6.1.7 Include overhead cost elements in the cost model,such as general conditions, profits, and escalation, and checkfor criticality as with the other cost elements. Consider timerisk factors, such as long lead time or dock strikes for importedmaterial, when evaluating escalation cost.6.1.8 Allowance and contingency, as commonly used in theconstruction cost estimates, include both the change elementand the risk element. The change element in allowance coversthe additional cost due to incomplete design (design allow-ance). The change element in contingency covers the addi-tional cost due to construction change orders (constructioncontingency). The risk element in contingency covers theadditional cost required to reduce the risk that the actual costwould be higher than the estimated cost. However, the riskelement in allowance and contingency is rarely identifiedseparately and usually included in either design allowance orconstruction contingency. When conducting CRA, do notinclude the risk element in allowance or contingency cost sincethat will be an output of the risk analysis. Include designallowance only to the extent that the design documents areincomplete. Include construction contingency, which repre-sents the anticipated increase in the project cost for changeorders beyond the signed contract value, if total constructioncost, instead of contract cost, is used. See Classification E2168for information on which costs are properly included underallowance and contingency.6.1.9 The sample project represents a CRA conducted fromthe owner’s perspective to estimate the construction contractvalue at final design. General conditions, profits, and escalationare identified as critical elements. Since the design documentsare 100 % complete, there is no design allowance. The contin-gency in the cost element represents the risk element and istherefore eliminated from the cost model. There is no construc-tion contingency in the model since this model estimatesconstruction contract cost only. If total project cost is desired,add other project cost items to the cost model, such asconstruction contingency, design fees, and project managementfees.6.2 Eliminate Interdependencies Between Critical Ele-ments:6.2.1 The CRA tool works best when there are no stronginterdependencies between the critical elements identified.Highly interdependent variables used separately will exagger-ate the risk in the total construction cost. Combine the highlydependent elements or extract the common component as aseparate variable. For example, the cost for ductwork and thecost of duct insulation are interdependent since both depend onthe quantity of ducts, which is a highly uncertain variable inmost estimates. Combine these two elements as one criticalelement even though they both might qualify as individualcritical elements.As another example, if a major source of riskis labor rate variance, then identify labor rate as a separatecritical element and remove the cost variation associated withlabor rates from all other cost elements.4Curran, M.W., “Range Estimating—Measuring Uncertainty and ReasoningWith Risk,” Cost Engineering, Vol 31, No. 3, March 1989.E1946 − 122TABLE 1 Sample UNIFORMAT II Cost ModelGROUP INDIVIDUAL EST MAX/ITEM GROUP ELEMENT INDIVIDUAL ELEMENT ELEMENT ELEMENT VARIATIONCOST COSTA10 FOUNDATIONS $150 000 $45 000A1010 Standard Foundations $100 000A1030 Slab on Grade $50 000A20 BASEMENT CONSTRUCTION $70 000 $30 000A2010 Basement Excavation $20 000A2020 Basement Walls $50 000B10 SUPERSTRUCTURE $915 000 $275 000B1010 Floor Construction $815 000 $244 500 *B1020 Roof Construction $100 000 40 000B20 EXTERIOR ENCLOSURE $800 000 $250 000B2010 Exterior Walls $576 000 $172 800 *B2020 Exterior Windows $204 000 $102 000 *B2030 Exterior Doors $20 000 $8 000B30 ROOFING $54 000 $20 000B3010 Roof Coverings $54 000C10 INTERIOR CONSTRUCTION $240 000 $72 000 *C1010 Partitions $132 000 $45 000C1020 Interior Doors $108 000 $30 000C20 STAIRS $95 000 $40 000C2010 Stair Construction $75 000C2020 Stair Finishes $20 000C30 INTERIOR FINISHES $916 000 $300 000C3010 Wall Finshes $148 000 $45 000C3020 Floor Finishes $445 000 $178 000 *C3030 Ceiling Finishes $323 000 $129 200 *D10 CONVEYING $380 000D1010 Elevators and the lowestimate about 50 % of the most likely estimate. This serves asa check on the range estimates.6.5 Create a Cost Model:6.5.1 The cost model is essentially the hierarchical costestimate. Treat all non-critical elements as constants. Simplifythe cost model by combining constants.6.5.2 In the sample project, the cost model becomes:~(COSTCE1$1 249000!*~11Profit!*~11Escalation! (5)where:COSTCE= variable cost for the critical elements1 through 18,$1 249 000 = total cost for all the non-criticalelements;Profit and Escalation = variable percentages.6.5.3 For triangular PDFs, the random cost of each criticalelement is calculated by the formula:COSTCE5

[email protected]*~MLE 2 LE!*~HE 2 LE!#0.5(6)if COSTCE# MLECOSTCE5 HE 2 @~1 2 RV!*~HE 2 MLE!*~HE 2 LE!#0.5(7)if COSTCE.MLEwhere:RV = a random variable between 0 and 1.Use the same random variable for each formula. Aftercalculating both formulas, use the one which satisfies thecorresponding condition on the right.6.5.4 For example, for the critical element FloorConstruction, if RV = 0.3, the two equations become:COST ~Floor Const.! 5 $6520001[0.3*~$8150002 (8)$652000)*~$1 059500 2 $652000!]0.55$793162, which satisfies the condition COST#$815000COST ~Floor Const.! 5 $1 059500 2 [0.7*~$1 0595002 (9)$815000)*~$1 059500 2 $652000!]0.55$795410, which does not satisfy the condition COST.$815000The result from Eq 8 will be used since it satisfies thecorresponding condition.6.6 Conduct a Monte Carlo Simulation:6.6.1 Run a Monte Carlo simulation once the risk in thecritical elements are quantified and the model set up. TheMonte Carlo method builds up a PDF for the bottom lineproject cost by repeatedly running the model with randomlygenerated numbers for the critical elements according to theindividual PDFs. Each Critical element will use a separaterandom number for the calculation. Each time the model is run,one point is generated for the total project cost risk PDF. Theprocess is repeated until the total project cost risk PDF“converges” or settles into a final shape, which often requires1,000 or more iterations. See Guide E1369, Section 7.7, for amore detailed description of the simulation technique.6.6.2 To implement a CRA, use commercial software pro-grams or write your own simulation software code.6.7 Interpret the Results:6.7.1 By inspecting the converged PDF for the bottom lineconstruction cost and its corresponding Cumulative Distribu-tion Function (CDF), obtain the following information:6.7.1.1 Expected (mean) total cost, which is the average ofall the data points generated by the simulation.6.7.1.2 Standard deviation on the total cost, which is thestandard deviation of all the data points generated by thesimulation.6.7.1.3 The confidence level, which is the cumulative per-centage corresponding to those data points generated by thesimulation which are less than or equal to the estimated amounton the CDF. Fig. 2 illustrates the concept of a confidence level.Denote the low estimate as point “a” and the high estimate aspoint “b.” Because point a corresponds to the 1stpercentile ofthe normal distribution, only 1 % of all occurrences of actualcosts will fall below point a. The confidence level associatedwith point a is therefore 1 %. Similarly, point b corresponds tothe 99thpercentile of the normal distribution, which impliesthat 99 % of all occurrence of the actual cost will fall belowpoint “b.” The confidence level associated with point “b” istherefore 99 %.6.7.1.4 Cost estimate for a given confidence level, which isthe total cost estimate corresponding to the desired confid