NOTICE:¬This¬standard¬has¬either¬been¬superseded¬and¬replaced¬by¬a¬new¬version¬or

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Designation: E 1946 – 98
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM

Standard Practice for

Measuring Cost Risk of Buildings and Building Systems1
This standard is issued under the fixed designation E 1946; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.

1. Scope construction projects.3 Specifically, BCRA helps answer the

1.1 This practice establishes a procedure for measuring cost following questions:
risk for buildings and building systems, using the Monte Carlo 5.1.1 What are the probabilities for the construction contract
simulation technique as described in Guide E 1369. to be bid above or below the estimated value?
1.2 A computer program is required for the Monte Carlo 5.1.2 How low or high can the total project cost be?
simulation. This can be one of the commercially available 5.1.3 What is the appropriate amount of contingency to use?
software programs for cost risk analysis, or one constructed by 5.1.4 What cost elements have the greatest impact on the
the user. building’s cost risk exposure?
5.2 BCRA can be applied to a building project’s contract
2. Referenced Documents cost, construction cost (contract cost plus construction change
2.1 ASTM Standards: orders), and project cost (construction cost plus owner’s cost),
E 833 Terminology of Building Economics2 depending on the users’ perspectives and needs. This practice
E 1369 Guide for Selecting Techniques for Treating Uncer- shall refer to these different terms generally as “building cost.”
tainty and Risk in the Economic Evaluation of Buildings
6. Procedure
and Building Systems2
E 1557 Classification for Building Elements and Related 6.1 Identify Critical Cost Elements:
Sitework - UNIFORMAT II2 6.1.1 A building cost estimate consists of many variables.
Even though each variable contributes to the total building cost
3. Terminology risk, not every variable makes a significant enough contribu-
3.1 Definitions—For definition of terms used in this guide, tion to warrant inclusion in the cost model. Identify the critical
refer to Terminology E 833. elements in order to simplify the cost risk model.
6.1.2 A critical element is one which varies up or down
4. Summary of Practice enough to cause the total building cost to vary by an amount
4.1 The procedure for calculating building cost risk consists greater than the total building cost’s critical variation, and one
of the following steps: which is not composed of any other element which qualifies as
4.1.1 Identify critical cost elements. a critical element. This criterion is expressed as:
4.1.2 Eliminate interdependencies between critical ele- IF VY . VCRIT (1)
ments. AND Y contains no other element X where VX. VCRIT
4.1.3 Select Probability Density Function.
THEN Y is a critical element
4.1.4 Quantify risk in critical elements.
4.1.5 Create a cost model. where:
4.1.6 Conduct a Monte Carlo simulation. VY 5 (2)
4.1.7 Interpret the results. ~Max. percentage variation of the element Y! * ~Y’s anticipated cost!
4.1.8 Conduct a sensitivity analysis. Total Building cost
5. Significance and Use
5.1 Building cost risk analysis (BCRA) provides a tool for VCRIT 5 Critical Variation of the Building Cost.
building owners, architects, engineers, and contractors to 6.1.3 A typical value for the total building cost’s critical
measure and evaluate the cost risk exposures of their building variation is 0.5%4. By experience this limits the number of
critical elements to about 20. A larger VCRIT will lead to fewer

1 3
This practice is under the jurisdiction of ASTM Committee E-6 on Performance This practice is based, in part, on the article, “Measuring Cost Risk of Building
of Buildings and is the direct responsibility of Subcommittee E06.81 on Building Projects,” by Douglas N. Mitten and Benson Kwong, Project Management Services,
Economics. Inc., Rockville, MD, 1996.
4
Current edition approved April 10, 1998. Published June 1998. Curran, Michael W., “Range Estimating—Measuring Uncertainty and
2
Annual Book of ASTM Standards, Vol 04.11. Reasoning With Risk,” Cost Engineering, Vol 31, No. 3, March 1989.

1
 NOTICE:¬This¬standard¬has¬either¬been¬superseded¬and¬replaced¬by¬a¬new¬version¬or
discontinued.¬Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
E 1946
critical elements and a smaller VCRIT will yield more. A risk represents the anticipated increase in the project cost for
analysis with too few elements is over-simplistic. Too many change orders beyond the signed contract value, if total
elements makes the analysis more detailed and difficult to construction cost, instead of contract cost, is used.
interpret. A BCRA with about 20 critical elements provides an 6.1.9 The sample project represents a BCRA conducted
appropriate level of detail. Review the critical variation used from the owner’s perspective to estimate the construction
and the number of critical elements for a BCRA against the contract value at final design. General conditions, profits, and
unique requirements for each project and the design stage. A escalation are identified as critical elements. Since the design
higher critical variance resulting in fewer critical elements, is documents are 100 % complete, there is no design contingency.
more appropriate at the earlier stages of design. The contingency in the cost element represents the risk element
6.1.4 Arrange the cost estimate in a hierarchical structure and is therefore eliminated from the cost model. There is no
such as UNIFORMAT II (Classification E 1557). Table 1 construction contingency in the model since this model
shows a sample project cost model based on a UNIFORMAT II estimates construction contract cost only. If total project cost is
Levels 2 and 3 cost breakdown. The UNIFORMAT II structure desired, add other project cost items to the cost model, such as
of the cost estimate facilitates the search of critical elements for construction contingency, design fees, and project management
the risk analysis. One does not need to examine every element fees.
in the cost estimate in order to identify those which are critical. 6.2 Eliminate Interdependencies Between Critical
6.1.5 Starting at the top of the cost estimate hierarchy (that Elements:
is, the Group Element level), identify critical elements in a 6.2.1 The BCRA tool works best when there are no strong
downward search through the branches of the hierarchy. interdependencies between the critical elements identified.
Conduct this search by repeatedly asking the question: Is it Highly interdependent variables used separately will
possible that this element could vary enough to cause the total exaggerate the risk in the total construction cost. Combine the
building cost to vary, up or down, by more than its critical highly dependent elements or extract the common component
variation? Terminate the search at the branch when a negative as a separate variable. For example, the cost for ductwork and
answer is encountered. Examine the next branch until all the cost of duct insulation are interdependent since both depend
branches are exhausted and the list of critical elements on the quantity of ducts, which is a highly uncertain variable in
established. Table 1 and Fig. 1 show the identification of most estimates. Combine these two elements as one critical
critical elements in the sample project using the hierarchical element even though they both might qualify as individual
search technique. critical elements. As another example, if a major source of risk
is labor rate variance, then identify labor rate as a separate
6.1.6 In the sample project, Group Element Superstructure
critical element and remove the cost variation associated with
has an estimated cost of $915,000 with an estimated maximum
labor rates from all other cost elements.
variation of $275,000, which is more than $50,000, or 0.5 % of
6.2.2 In the sample project, a percentage escalation is
the estimated total building cost. It is therefore a candidate for
treated as a separate cost element, instead of having the
a critical element. However, when we examine the Individual
escalation embedded in each cost element. The escalations for
Elements that make up Superstructure, we discover that Floor
all cost elements are highly correlated because they all depend
Construction has a estimated maximum variation of $244,500,
on the general escalation rate in material and labor. Therefore
qualifying as a critical element; whereas Roof Construction
the model is more accurate when taking escalation as a separate
could only vary as much as $40,000, and does not qualify.
cost element. Treat escalation as a critical element if it causes
Since Floor Construction is now a critical element, we would
the total cost to vary by more than 0.5 %.
eliminate Superstructure, its parent, as a critical element.
6.3 Select Probability Density Function (PDF):
6.1.7 Include overhead cost elements in the cost model, 6.3.1 Assign a PDF to each critical element to describe the
such as general conditions, profits, and escalation, and check variability of the element. Select the types of PDFs that best
for criticality as with the other cost elements. Consider time describe the data. These include, but are not restricted to, the
risk factors, such as long lead time or dock strikes for imported normal, lognormal, beta, and triangular distributions. In the
material, when evaluating escalation cost. construction industry, one does not always have sufficient data
6.1.8 Contingency, as commonly used in the building cost to specify a particular distribution. In such a case a triangular
estimates, includes both the change element and the risk distribution function has some advantages5. It is the simplest to
element. The change element in contingency covers the construct and easiest to conceptualize by the team of design
additional cost due to incomplete design (design contingency) and cost experts. The triangular PDF assumes zero probability
or construction change orders (construction contingency). The below the low estimate and above the high estimate, and the
risk element in contingency covers the additional cost required highest probability at the most likely estimate. Straight lines
to reduce the risk that the actual cost would be higher than the connect these three points in a probability density function,
estimated cost. However, the risk element in contingency is forming a triangle, thus giving the name triangular distribution.
rarely identified separately and usually included in either 6.3.2 Because the triangular distribution function is only an
design or construction contingencies. When conducting approximation, the low and high estimates do not represent the
BCRA, do not include the risk element in contingency cost
since that will be an output of the risk analysis. Include design
contingency only to the extent that the design documents are 5
Biery, Fred, Hudak, David, Gupta, Shishu, “Improving Cost Risk Analysis,”
incomplete. Include construction contingency, which Journal of Cost Analysis, Spring 1994.

2
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E 1946
TABLE 1 Sample Uniformat II Cost Model
GROUP INDIVIDUAL EST MAX/
ITEM GROUP ELEMENT INDIVIDUAL ELEMENT ELEMENT ELEMENT VARIATION
COST COST
A10 FOUNDATIONS $150,000 $45,000
A1010 Standard Foundations $100,000
A1030 Slab on Grade $50,000
A20 BASEMENT CONSTRUCTION $70,000 $30,000
A2010 Basement Excavation $20,000
A2020 Basement Walls $50,000
B10 SUPERSTRUCTURE $915,000 $275,000
B1010 Floor Construction $815,000 $244,500 *
B1020 Roof Construction $100,000 40,000
B20 EXTERIOR ENCLOSURE $800,000 $250,000
B2010 Exterior Walls $576,000 $172,800 *
B2020 Exterior Windows $204,000 $102,000 *
B2030 Exterior Doors $20,000 $8,000 *
B30 ROOFING $54,000 $20,000
B3010 Roof Coverings $54,000
C10 INTERIOR CONSTRUCTION $240,000 $72,000 *
C1010 Partitions $132,000 $45,000
C1020 Interior Doors $108,000 $30,000
C20 STAIRS $95,000 $40,000
C2010 Stair Construction $75,000
C2020 Stair Finishes $20,000
C30 INTERIOR FINISHES $916,000 $300,000
C3010 Wall Finshes $148,000 $45,000
C3020 Floor Finishes $445,000 $178,000 *
C3030 Ceiling Finishes $323,000 $129,200 *
D10 CONVEYING $380,000
D1010 Elevators & Lifts $380,000 $228,000 *
D20 PLUMBING $142,000 $45,000
D2010 Plumbing Fxtures $70,000
D2020 Domestic Water Distribution $30,000
D2030 Sanitary Waste $22,000
D2040 Rain Water Drainage $20,000
D30 HVAC $1,057,000 $550,000
D3010 Energy Supply $20,000 $8,000
D3020 Heat Generating Systems $80,000 $30,000
D3030 Cooling Generating Systems $275,000 $137,500 *
D3040 Distribution Systems $500,000 $300,000 *
D3050 Terminal & Package Units $60,000 $30,000
D3060 Controls and Instrumentation $217,000 $130,200 *
D3070 System Testing & Balancing $20,000 $10,000
D40 FIRE PROTECTION $270,000 $100,000
D4010 Sprinklers $220,000 $88,000 *
D4020 Standpipes $50,000 $15,000
D50 ELECTRICAL $985,000 $500,000
D5010 Electrical Service & Distribution $180,000 $108,000 *
D5020 Lighting & Branch Wiring $685,000 $411,000 *
D5030 Communication & Security $120,000 $45,000 *
G10 SITE PREPARATION $120,000 $45,000
G1030 Site Earthwork $120,000
G20 SITE IMPROVEMENT $800,000 $450,000
G2030 Pedestrian Paving $420,000 $252,000 *
G2050 Landscaping $380,000 $228,000 *
G30 SITE MECHANICAL UTILITIES $420,000 $126,000 *
G3010 Water Supply $120,000 $40,000
G3020 Sanitary Sewer $120,000 $42,000
G3030 Storm Sewer $140,000 $46,000
G3060 Fuel Distribution $40,000 $20,000
G40 SITE ELECTRICAL UTILITIES $200,000 $100,000 *
G4010 Electrical Distribution $100,000 $45,000
G4020 Site Lighting $25,000 $15,000
G4030 Site Communications & Security $75,000 $42,000

SUBTOTAL $7,729,000
GENERAL CONDITIONS $823,000 $411,500 *
SUBTOTAL $8,552,000
PROFITS (10 %) $855,200 $427,600 *
SUBTOTAL $9,407,200
ESCALATION (5 %) $470,360 $188,144 *
SUBTOTAL $9,877,560
CONTINGENCY (5 %) $493,878
$10,371,438
TOTAL CONSTRUCTION CONTRACT COST
* Meets criteria for critical elements

3
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discontinued.¬Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
E 1946

FIG. 1 Identification of Critical Elements in the Sample Project

4
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E 1946
absolute lowest and highest probable value. As compared to the TABLE 2 Sample Critical Element Input List
more realistic “normal distribution,” these values represent
CRITICAL ELEMENT LOW MOST LIKELY HIGH
about the first and 99th percentiles, respectively. In other words,
there is a 1 % chance that the value will be lower than the low B1010 Floor Construction $652,000 $815,000 $1,059,500
estimate (point “a” on Fig. 2) and another 1 % chance that it B2010 Exterior Walls $460,800 $576,000 $748,800
B2020 Exterior Windows $142,800 $204,000 $306,000
will be higher than the high estimate (point “b” on Fig. 2). The C10 Interior Construction $192,000 $240,000 $312,000
triangular distribution is a reasonably good approximation of C3020 Floor Finishes $333,750 $445,000 $623,000
C3030 Ceiling Finishes $226,100 $323,000 $452,200
the normal distribution except at the extreme high or low ends. D1010 Elevators & Lifts $228,000 $380,000 $608,000
However, for building estimates, there is rarely a requirement D3030 Cooling Generating Systems $192,500 $275,000 $412,500
for values below the 5th and above the 95th percentile. D3040 Distribution Systems $300,000 $500,000 $800,000
D3060 Controls & Instrumentation $108,500 $217,000 $347,200
Therefore, there is no significant loss of model accuracy in D4010 Sprinklers $154,000 $220,000 $308,000
using the triangular distribution. D5010 Electrical Service & $108,000 $180,000 $228,000
Distribution
6.4 Quantify Risks in Critical Elements: G5020 Lighting & Branch Wiring $411,000 $685,000 $1,096,000
6.4.1 Quantify the risk for each element by a most likely G2030 Pedestrian Paving $210,000 $420,000 $672,000
G2050 Landscaping $228,000 $380,000 $608,000
estimate, a low estimate, and a high estimate. Table 2 shows the G30 Site Mechanical Utilities $336,000 $420,000 $546,000
list of critical elements identified in the sample project, with G40 Site Electrical Utilities $140,000 $200,000 $300,000
General Conditions $493,800 $823,000 $1,234,500
the associated three point estimates. As discussed in the Profits 4% 10 % 15 %
previous section, the high and low estimates should capture the Escalation 3% 5% 7%
middle 98 % of the probable outcome for the element. The
most likely estimate, on the other hand, represents value with
highest probability of occurrence, and is the peak of the where:
triangular distribution. This may not coincide with the single MLE 5 most likely estimate,
value cost estimate since the single value is most often HE 5 high estimate on the triangular distribution,
interpreted as the mean or median, rather than the mode. On a LE 5 low estimate on the triangular distribution,
skewed triangular distribution, the mean (average), median, HE’ 5 high estimate given an alternative percentile,
LE’ 5 low estimate given an alternative percentile,
and mode (most likely) values are all different (Fig. 3). r 5 adjustment factor which can be calculated using the
6.4.2 There may be a tendency to select low estimates that inverse normal cumulative function, and
are not low enough, and high estimates that are not high r 5 1.82 for 10th and 90th percentiles.
enough. In part this is a result of not being able to envision 6.4.3 The coefficients of variation (standard deviation
lowest and highest possible outcomes. It may be helpful to divided by the mean) for line items in trade estimates range
quantify the high and low estimates in a narrower band (for from 13 % to 45 %6, with a weighted average of 22 %. These
example, 10th and 90th percentiles). Then adjust these estimates are based on rates on selected items from the lowest bidders of
to get the two extreme points on the triangular distribution. similar projects. Note that the middle 98 % of normal
HE 5 MLE 1 ~HE’ – MLE! * r (3)
distribution’s value occur within 6 2.3 standard deviations of
the mean. This corresponds to an average range estimate of 2.3
LE 5 MLE – ~MLE– LE’! * r (4)

6
Beeston, Derek T., “One Statistician’s View of Estimating,” Property Services
Agency, Department of Environment, London, UK, July 1974.

FIG. 2 Comparison of Triangular PDF to Normal Distribution Function

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E 1946

FIG. 3 Skewed Triangular Probability Distribution Function

3 22 % 5 50 %. Therefore, the typical high estimate shoud be 6.6 Conduct a Monte Carlo Simulation:
about 150 % of the most likely estimate; and the low estimate 6.6.1 Run a Monte Carlo simulation once the risk in the
about 50 % of the most likely estimate. This serves as a check critical elements are quantified and the model set up. The
on the range estimates. Monte Carlo method builds up a PDF for the bottom line
6.5 Create a Cost Model: building cost by repeatedly running the model with randomly
6.5.1 The cost model is essentially the hierarchical cost generated numbers for the critical elements according to the
estimate. Treat all non-critical elements as constants. Simplify individual PDFs. Each Critical element will use a separate
the cost model by combining constants. random number for the calculation. Each time the model is run,
6.5.2 In the sample project, the cost model becomes: one point is generated for the total building cost risk PDF. The
~( COSTCE 1 $1,249,000! * ~1 1 Profit! * ~1 1 Escalation! (5) process is repeated until the total building cost risk PDF
“converges” or settles into a final shape, which often requires
where: 1,000 or more iterations. See Guide E 1369, section 7.7, for a
COSTCE 5 variable cost for the critical more detailed description of the simulation technique.
elements 1 through 18,
$1,249,000 5 total cost for all the non-critical 6.6.2 To implement a BCRA, use commercial software
elements; programs or write your own simulation software code.
Profit and Escalation 5 variable percentages. 6.7 Interpret the Results:
6.5.3 For triangular PDFs, the random cost of each critical 6.7.1 By inspecting the converged PDF for the bottom line
element is calculated by the formula: construction cost and its corresponding Cumulative
COSTCE 5 LE 1 @RV * ~MLE – LE! * ~HE – LE!#0.5 (6) Distribution Function (CDF), obtain the following information:
if COSTCE # MLE 6.7.1.1 Expected (mean) total cost, which is the average of
all the data points generated by the simulation.
COSTCE 5 HE – @~12RV! * ~HE – MLE! * ~HE– LE!#0.5 (7)
6.7.1.2 Standard deviation on the total cost, which is the
if COSTCE . MLE standard deviation of all the data points generated by the
where: simulation.
RV 5 a random variable between 0 and 1. 6.7.1.3 The confidence level, which is the cumulative
Use the same random variable for each formula. After percentage corresponding to those data points generated by the
calculating both formulas, use the one which satisfies the simulation which are less than or equal to the estimated amount
corresponding condition on the right. on the CDF. Fig. 2 illustrates the concept of a confidence level.
6.5.4 For example, for the critical element Floor Denote the low estimate as point “a” and the high estimate as
Construction, if RV 5 0.3, the two equations become: point “b.” Because point a corresponds to the 1st percentile of
the normal distribution, only 1 % of all occurrences of actual
COST ~Floor Const.! 5 $652,000 1 @0.3 * ~$815,000 – (8)
costs will fall below point a. The confidence level associated
0.5
$652,000! * ~$1,059,500 – $652,000!# with point a is therefore 1 %. Similarly, point b corresponds to
5 $793,162, which satisfies the condition COST # $815,000 the 99th percentile of the normal distribution, which implies
COST ~Floor Const.! 5 $1,059,500 – @0.7 * ~$1,059,500 – (9) that 99 % of all occurrence of the actual cost will fall below
0.5
point “b.” The confidence level associated with point “b” is
$815,000! * ~$1,059,500 – $652,000!# therefore 99 %.
5 $795,410, which does not satisfy the condition COST . $815,000 6.7.1.4 Cost estimate for a given confidence level, which is
The result from the first equation will be used since it the total cost estimate corresponding to the desired confidence
satisfies the corresponding condition. level on the CDF. This cost estimate is designated as
6
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E 1946
COST(CL), where CL indicates the confidence level (for VAR~A 1 c! 5 VAR ~A! (13)
example, 10 %). 2
VAR~c*A! 5 c * VAR~A! (14)
6.7.1.5 Contingency, which is the difference between the
total cost estimate for the desired confidence level and the base where:
cost estimate. The contingency is designated as CONT(CL). VAR 5 variance,
6.7.2 Fig. 4 and Fig. 5 show the PDF and CDF for the A, B 5 function of independent random variables,
sample project, respectively. The Monte Carlo simulation c 5 constant.
generated 4,000 data points using a computer spreadsheet. The 6.8.3 Calculate the contribution of each critical element to
results are as follows: the total variance by holding all other variables constant.
6.7.2.1 The expected (mean) total contract cost is Multiply the variance of that element by the square of the
$10,246,000, which is higher than the deterministic cost multiplication factors. In the sample project, the variance
estimate of $9,877,560. contributed by the critical elements is calculated with the
6.7.2.2 The standard deviation of the sample of total following formulas and the results for the sample project are
contract cost is $430,000, or 4.19 % of the mean. tabulated in Table 3.
6.7.2.3 The contingency used in the deterministic cost
estimate (that is, $493,878) corresponds to a confidence level VARTBC ~COSTCE! 5 VAR~COSTCE!* @~1 1 Profit! (15)
of 63.0 % (that is, COST(63 %) – $9,877,560). * ~1 1 Escalation!# 2

6.7.2.4 The total cost estimate for each confidence level is: VARTBC ~Profit! 5 VAR~Profit! * @~( COSTCE 1 (16)
COST(10 %) 5 $9,706,000
2
COST(25 %) 5 $9,951,000 $1,249,000! * ~1 1 Escalation!#
COST(50 %) 5 $10,240,000 VARTBC ~Escalation! 5 VAR ~Escalation! * @~( COSTCE 1 (17)
COST(75 %) 5 $10,526,000 2
$1,249,000! * ~1 1 Profit!#
COST(90 %) 5 $10,809,000
COST(95 %) 5 $10,983,000 where:
6.7.2.5 Given the deterministic cost estimate in Table 1, the VARTBC 5 contribution to the Total Building Cost
contingencies by confidence level are as follows: Variance.
CONT(50 %) 5 $362,000 (3.7 %) 6.8.4 In the sample project, for Floor Construction:
CONT(75 %) 5 $648,000 (6.6 %)
CONT(90 %) 5 $931,000 (9.4 %) VAR~Floor Construction! 5 ~1,059,5002 1 815,0002 1 652,0002
(18)
CONT(95 %) 5 $1,105,000 (11.2 %)
6.8 Conduct a Sensitivity Analysis: – 1,059,500*652,000 – 815,500*652,000 –815,000*1,059,500!/ 18
6.8.1 Use sensitivity analysis to determine the relative 5 7,010,000,000
contribution of each critical element to the total building cost
VARTBC ~Floor Construction! 5 7,010,000,000* @~1.10! * ~1.05!#2
risk.
6.8.2 The mean and variance for the triangular distribution 5 9,350,000,000
are: And for profits:
Mean 5 ~HE 1 MLE 1 LE! / 3 (10)
VAR~Profit! 5 ~0.152 1 0.102 1 0.042 – 0.15*0.04 – (19)
Variance 5 ~HE2 1 MLE2 1 LE2 – HE*LE – MLE*LE – MLE*HE! / 18 0.10*0.04 – 0.10*0.15! / 18
(11)
5 0.000506
See Eq 3 and Eq 4 for the variable definitions. The arithmetic
for variance of a function of independent random variables are: VARTBC ~Profit! 5 0.000506 * @$8,552,000 * 1.05#2
VAR~A 1 B! 5 VAR~A! 1 VAR~B! (12) 5 40,800,000,000

FIG. 4 Sample Probability Density Function Resulting from Monte Carlo Simulation

7
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discontinued.¬Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
E 1946

FIG. 5 Sample Cumulative Distribution function Resulting from Monte Carlo Simulation

TABLE 3 SAMPLE SENSITIVITY ANALYSIS

ITEM CRITICAL ELEMENT LOW MOST LIKELY HIGH MEAN VARIANCE VARIANCE % OF TOTAL
CONTRIBUTION VARIANCE
B1010 Floor Construction $652,000 $815,000 $1,059,500 $842,167 7.01E+09 9.35E+09 5%
B2010 Exterior Walls $460,800 $576,000 $748,800 $595,200 3.50E+09 4.67E+09 3%
B2020 Exterior Windows $142,800 $204,000 $306,000 $217,600 1.13E+09 1.51E+09 1%
C10 Interior Construction $192,000 $240,000 $312,000 $248,000 6.08E+089 8.11E+08 0%
C3020 Floor Finishes $333,750 $445,000 $623,000 $467,250 3.55E+09 4.73E+09 3%
C3030 Ceiling Finishes $226,100 $323,000 $452,200 $333,767 2.14E+09 2.86E+09 2%
C1010 Elevators & Lifts $228,000 $380,000 $608,000 $405,333 6.10E_09 8.13E+09 4%
D3030 Cooling Generating Systems $192,500 $275,000 $412,500 $293,333 2.06E+09 2.75E+09 2%
D3040 Distribution Systems $300,000 $500,000 $800,000 $533,333 1.06E+10 1.41E+10 8%
D3060 Controls & Instrumentation $108,500 $217,000 $347,200 $224,233 2.38E+09 3.18E+09 2%
D4010 Sprinklers $154,000 $220,000 $308,000 $227,333 9.95E+08 1.33E+09 1%
D5010 Electrical Service & Distribution $108,000 $108,000 $288,000 $192,000 1.37E+09 1.82E+09 1%
G5020 Lighting & Branch Wiring $411,000 $685,000 $1,096,000 $730,667 1.98E+10 2.64E+10 14 %
G2030 Pedestrian Paving $210,000 $420,000 $672,000 $434,000 8.92E+09 1.19E+10 7%
G2050 Landscaping $228,000 $380,000 $608,000 $405,333 6.10E+09 8.13E+09 4%
G30 Site Mechanical Utilities $336,000 $420,000 $546,000 $434,000 1.86E+09 2.48E+09 1%
G40 Site Electrical Utilities $140,000 $200,000 $300,000 $213,333 1.09E+09 1.45E+09 1%
General Conditions $493,800 $823,000 $1,234,500 $850,433 2.30E+10 3.06E+10 17 %
Profits 4% 10 % 15 % 9.67 % 5.06E-04 4.08E+10 22 %
Escalation 3% 5% 7% 5.00 % 6.67E-05 5.90E-09 3%

TOTAL $7,303,000 $7,647,317 1.83E+11

The sum of all VARTBC are 1.85 3 1011. The percentage of phase. Instead of a single value of building cost, the owner has
total variance are: the range and probability of possible building cost and uses this
%VAR~Floor Construction! 5 9.35 3 109/ 1.83 3 1011 5 5 %
information for contingency planning.
(20) 7.2 Alternative Evaluation—BCRA allows the owner and
10
%VAR~Profits! 5 4.08 3 10 / 1.83 3 10 5 22 % 11
(20) the architect/engineer to evaluate the project alternatives based
on cost risk exposures as well as building cost. An alternative
6.8.5 Note that there is no simple expression for VAR (A *
with a higher cost but lower cost risk exposure than another
B). The variance contribution for the variables that are
will be preferable to some owners since the likely amount of
multiplied together (for example, escalation and profit in the
cost overrun will be lower. An example is a stalemate in the
example) is therefore not additive and the sum of all VARTBC
labor negotiation with the local sheetmetal workers union,
will exceed 100 %. However, the individual VARTBC provides
which has a potential impact on the cost and availability for the
a good relative measure of cost risk.
labor to install HVAC distribution systems during the project.
6.8.6 Table 3 shows that the major contributors of cost
variance are Profits (22 %), General Conditions (17 %), The owner/project manager reduces cost risk by using factory
Lighting and Branch Wiring (14 %), and HVAC Distribution preformed ductwork, which has a higher material cost but
System (8 %). These are the items that should be investigated significantly lower field labor requirement.
if reduction in contract cost risk is desired. 7.3 Competitive Bidding—Contractors use BCRA to
identify the acceptable risk exposure on a project and make an
7. Applications informed decision on the bid amount.
7.1 Budgetary Control—BCRA allows an owner to examine 7.4 Negotiation—BCRA informs the negotiating parties of a
the cost risk exposure of the project starting from the planning construction contract on the magnitude of cost risk and helps
8
 NOTICE:¬This¬standard¬has¬either¬been¬superseded¬and¬replaced¬by¬a¬new¬version¬or
discontinued.¬Contact¬ASTM¬International¬(www.astm.org)¬for¬the¬latest¬information.¬
E 1946
them allocate risk between the owner and the contractor as unacceptably high, then explore alternative design or
appropriate. construction methods, or both, to reduce the risk. In the sample
7.5 Project Management—BCRA helps the project manager project, an investigation shows that the main light fixture type
pinpoint the source of cost risk, monitor the remaining cost risk is a historical replication and therefore a custom item, with a
exposure, and reduce total building cost risk. The options are to high cost risk. To manage the risk, the owner/project manager
accept or mitigate the risks. If the risks are acceptable, no changes the requirements so that off-the-shelf fixtures are
further action needs to be taken, except to assure sufficient acceptable.
funding to cover the required contingency. If the risks are

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