Designation: E 1946 – 02

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 5. Significance and Use

1.1 This practice establishes a procedure for measuring cost 5.1 Building cost risk analysis (BCRA) provides a tool for
risk for buildings and building systems, using the Monte Carlo building owners, architects, engineers, and contractors to
simulation technique as described in Guide E 1369. measure and evaluate the cost risk exposures of their building
1.2 A computer program is required for the Monte Carlo construction projects.4 Specifically, BCRA helps answer the
simulation. This can be one of the commercially available following questions:
software programs for cost risk analysis, or one constructed by 5.1.1 What are the probabilities for the construction contract
the user. to be bid above or below the estimated value?
5.1.2 How low or high can the total project cost be?
2. Referenced Documents 5.1.3 What is the appropriate amount of contingency to use?
2.1 ASTM Standards: 5.1.4 What cost elements have the greatest impact on the
E 833 Terminology of Building Economics2 building’s cost risk exposure?
E 1369 Guide for Selecting Techniques for Treating Uncer- 5.2 BCRA can be applied to a building project’s contract
tainty and Risk in the Economic Evaluation of Buildings cost, construction cost (contract cost plus construction change
and Building Systems2 orders), and project cost (construction cost plus owner’s cost),
E 1557 Classification for Building Elements and Related depending on the users’ perspectives and needs. This practice
Sitework - UNIFORMAT II2 shall refer to these different terms generally as “building cost.”
E 2168 Classification for Allowance, Contingency and Re-
serve Sums in Building Construction Estimating3 6. Procedure
6.1 Identify Critical Cost Elements:
3. Terminology 6.1.1 A building cost estimate consists of many variables.
3.1 Definitions—For definition of terms used in this guide, Even though each variable contributes to the total building cost
refer to Terminology E 833. risk, not every variable makes a significant enough contribu-
tion to warrant inclusion in the cost model. Identify the critical
4. Summary of Practice elements in order to simplify the cost risk model.
4.1 The procedure for calculating building cost risk consists 6.1.2 A critical element is one which varies up or down
of the following steps: enough to cause the total building cost to vary by an amount
4.1.1 Identify critical cost elements. greater than the total building cost’s critical variation, and one
4.1.2 Eliminate interdependencies between critical ele- which is not composed of any other element which qualifies as
ments. a critical element. This criterion is expressed as:
4.1.3 Select Probability Density Function. IF VY . VCRIT (1)
4.1.4 Quantify risk in critical elements.
AND Y contains no other element X where VX. VCRIT
4.1.5 Create a cost model.
4.1.6 Conduct a Monte Carlo simulation. THEN Y is a critical element
4.1.7 Interpret the results. where:
4.1.8 Conduct a sensitivity analysis. VY 5 (2)
~Max. percentage variation of the element Y! * ~Y’s anticipated cost!
1
This practice is under the jurisdiction of ASTM Committee E06 on Perfor- Total Building cost
mance of Buildings and is the direct responsibility of Subcommittee E06.81 on
Building Economics.
Current edition approved Oct. 10, 2002. Published November 2002. Originally
4
published as E 1946–98. Last previous edition E 1946–98. This practice is based, in part, on the article, “Measuring Cost Risk of Building
2
Annual Book of ASTM Standards, Vol 04.11. Projects,” by Douglas N. Mitten and Benson Kwong, Project Management Services,
3
Annual Book of ASTM Standards, Vol 04.12. Inc., Rockville, MD, 1996.

Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.

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 E 1946 – 02
The change element in contingency covers the additional cost
due to construction change orders (construction contingency).
VCRIT = Critical Variation of the Building Cost. The risk element in contingency covers the additional cost
6.1.3 A typical value for the total building cost’s critical required to reduce the risk that the actual cost would be higher
variation is 0.5%5. By experience this limits the number of than the estimated cost. However, the risk element in allow-
critical elements to about 20. A larger VCRIT will lead to fewer ance and contingency is rarely identified separately and usually
critical elements and a smaller VCRIT will yield more. A risk included in either design allowance or construction contin-
analysis with too few elements is over-simplistic. Too many gency. When conducting BCRA, do not include the risk
elements makes the analysis more detailed and difficult to element in allowance or contingency cost since that will be an
interpret. A BCRA with about 20 critical elements provides an output of the risk analysis. Include design allowance only to
appropriate level of detail. Review the critical variation used the extent that the design documents are incomplete. Include
and the number of critical elements for a BCRA against the construction contingency, which represents the anticipated
unique requirements for each project and the design stage. A increase in the project cost for change orders beyond the signed
higher critical variance resulting in fewer critical elements, is contract value, if total construction cost, instead of contract
more appropriate at the earlier stages of design. cost, is used. See Classification E 2168 for information on
6.1.4 Arrange the cost estimate in a hierarchical structure which costs are properly included under allowance and con-
such as UNIFORMAT II (Classification E 1557). Table 1 tingency.
shows a sample project cost model based on a UNIFORMAT 6.1.9 The sample project represents a BCRA conducted
II Levels 2 and 3 cost breakdown. The UNIFORMAT II from the owner’s perspective to estimate the construction
structure of the cost estimate facilitates the search of critical contract value at final design. General conditions, profits, and
elements for the risk analysis. One does not need to examine escalation are identified as critical elements. Since the design
every element in the cost estimate in order to identify those documents are 100 % complete, there is no design allowance.
which are critical. The contingency in the cost element represents the risk element
6.1.5 Starting at the top of the cost estimate hierarchy (that and is therefore eliminated from the cost model. There is no
is, the Group Element level), identify critical elements in a construction contingency in the model since this model esti-
downward search through the branches of the hierarchy. mates construction contract cost only. If total project cost is
Conduct this search by repeatedly asking the question: Is it desired, add other project cost items to the cost model, such as
possible that this element could vary enough to cause the total construction contingency, design fees, and project management
building cost to vary, up or down, by more than its critical fees.
variation? Terminate the search at the branch when a negative
6.2 Eliminate Interdependencies Between Critical Ele-
answer is encountered. Examine the next branch until all
ments:
branches are exhausted and the list of critical elements estab-
lished. Table 1 and Fig. 1 show the identification of critical 6.2.1 The BCRA tool works best when there are no strong
elements in the sample project using the hierarchical search interdependencies between the critical elements identified.
technique. Highly interdependent variables used separately will exagger-
6.1.6 In the sample project, Group Element Superstructure ate the risk in the total construction cost. Combine the highly
has an estimated cost of $915,000 with an estimated maximum dependent elements or extract the common component as a
variation of $275,000, which is more than $50,000, or 0.5 % of separate variable. For example, the cost for ductwork and the
the estimated total building cost. It is therefore a candidate for cost of duct insulation are interdependent since both depend on
a critical element. However, when we examine the Individual the quantity of ducts, which is a highly uncertain variable in
Elements that make up Superstructure, we discover that Floor most estimates. Combine these two elements as one critical
Construction has a estimated maximum variation of $244,500, element even though they both might qualify as individual
qualifying as a critical element; whereas Roof Construction critical elements. As another example, if a major source of risk
could only vary as much as $40,000, and does not qualify. is labor rate variance, then identify labor rate as a separate
Since Floor Construction is now a critical element, we would critical element and remove the cost variation associated with
eliminate Superstructure, its parent, as a critical element. labor rates from all other cost elements.
6.1.7 Include overhead cost elements in the cost model, 6.2.2 In the sample project, a percentage escalation is
such as general conditions, profits, and escalation, and check treated as a separate cost element, instead of having the
for criticality as with the other cost elements. Consider time escalation embedded in each cost element. The escalations for
risk factors, such as long lead time or dock strikes for imported all cost elements are highly correlated because they all depend
material, when evaluating escalation cost. on the general escalation rate in material and labor. Therefore
6.1.8 Allowance and contingency, as commonly used in the the model is more accurate when taking escalation as a separate
building cost estimates, include both the change element and cost element. Treat escalation as a critical element if it causes
the risk element. The change element in allowance covers the the total cost to vary by more than 0.5 %.
additional cost due to incomplete design (design allowance). 6.3 Select Probability Density Function (PDF):
6.3.1 Assign a PDF to each critical element to describe the
variability of the element. Select the types of PDFs that best
5
Curran, Michael W., “Range Estimating—Measuring Uncertainty and Reason- describe the data. These include, but are not restricted to, the
ing With Risk,” Cost Engineering, Vol 31, No. 3, March 1989. normal, lognormal, beta, and triangular distributions. In the

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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
PROFIT (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

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FIG. 1 Identification of Critical Elements in the Sample Project

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 E 1946 – 02
construction industry, one does not always have sufficient data TABLE 2 Sample Critical Element Input List
to specify a particular distribution. In such a case a triangular
distribution function has some advantages6. It is the simplest to CRITICAL ELEMENT LOW MOST LIKELY HIGH

construct and easiest to conceptualize by the team of design B1010 Floor Construction $652,000 $815,000 $1,059,500
and cost experts. The triangular PDF assumes zero probability B2010 Exterior Walls $460,800 $576,000 $748,800
below the low estimate and above the high estimate, and the B2020 Exterior Windows $142,800 $204,000 $306,000
C10 Interior Construction $192,000 $240,000 $312,000
highest probability at the most likely estimate. Straight lines C3020 Floor Finishes $333,750 $445,000 $623,000
connect these three points in a probability density function, C3030 Ceiling Finishes $226,100 $323,000 $452,200
forming a triangle, thus giving the name triangular distribution. D1010 Elevators & Lifts $228,000 $380,000 $608,000
D3030 Cooling Generating Systems $192,500 $275,000 $412,500
6.3.2 Because the triangular distribution function is only an D3040 Distribution Systems $300,000 $500,000 $800,000
approximation, the low and high estimates do not represent the D3060 Controls & Instrumentation $108,500 $217,000 $347,200
absolute lowest and highest probable value. As compared to the D4010 Sprinklers $154,000 $220,000 $308,000
D5010 Electrical Service & $108,000 $180,000 $228,000
more realistic “normal distribution,” these values represent Distribution
about the first and 99th percentiles, respectively. In other words, G5020 Lighting & Branch Wiring $411,000 $685,000 $1,096,000
G2030 Pedestrian Paving $210,000 $420,000 $672,000
there is a 1 % chance that the value will be lower than the low G2050 Landscaping $228,000 $380,000 $608,000
estimate (point “a” on Fig. 2) and another 1 % chance that it G30 Site Mechanical Utilities $336,000 $420,000 $546,000
will be higher than the high estimate (point “b” on Fig. 2). The G40 Site Electrical Utilities $140,000 $200,000 $300,000
General Conditions $493,800 $823,000 $1,234,500
triangular distribution is a reasonably good approximation of Profit 4% 10 % 15 %
the normal distribution except at the extreme high or low ends. Escalation 3% 5% 7%
However, for building estimates, there is rarely a requirement
for values below the 5th and above the 95th percentile. There-
fore, there is no significant loss of model accuracy in using the
triangular distribution. 6.4.2 There may be a tendency to select low estimates that
6.4 Quantify Risks in Critical Elements: are not low enough, and high estimates that are not high
6.4.1 Quantify the risk for each element by a most likely enough. In part this is a result of not being able to envision
estimate, a low estimate, and a high estimate. Table 2 shows the lowest and highest possible outcomes. It may be helpful to
list of critical elements identified in the sample project, with quantify the high and low estimates in a narrower band (for
the associated three point estimates. As discussed in the example, 10th and 90th percentiles). Then adjust these estimates
previous section, the high and low estimates should capture the to get the two extreme points on the triangular distribution.
middle 98 % of the probable outcome for the element. The HE 5 MLE 1 ~HE’ – MLE! * r (3)
most likely estimate, on the other hand, represents value with
LE 5 MLE – ~MLE– LE’! * r (4)
highest probability of occurrence, and is the peak of the
triangular distribution. This may not coincide with the single where:
value cost estimate since the single value is most often MLE = most likely estimate,
interpreted as the mean or median, rather than the mode. On a HE = high estimate on the triangular distribution,
skewed triangular distribution, the mean (average), median, LE = low estimate on the triangular distribution,
and mode (most likely) values are all different (Fig. 3). HE’ = high estimate given an alternative percentile,
LE’ = low estimate given an alternative percentile,
r = adjustment factor which can be calculated using the
inverse normal cumulative function, and
6
Biery, Fred, Hudak, David, Gupta, Shishu, “Improving Cost Risk Analysis,” r = 1.82 for 10th and 90th percentiles.
Journal of Cost Analysis, Spring 1994.

FIG. 2 Comparison of Triangular PDF to Normal Distribution Function

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 E 1946 – 02

FIG. 3 Skewed Triangular Probability Distribution Function

6.4.3 The coefficients of variation (standard deviation di- 6.5.4 For example, for the critical element Floor Construc-
vided by the mean) for line items in trade estimates range from tion, if RV = 0.3, the two equations become:
13 % to 45 %7, with a weighted average of 22 %. These are COST ~Floor Const.! 5 $652,000 1 @0.3 * ~$815,000 – (8)
based on rates on selected items from the lowest bidders of 0.5
similar projects. Note that the middle 98 % of normal distri- $652,000! * ~$1,059,500 – $652,000!#
bution’s value occur within 6 2.3 standard deviations of the 5 $793,162, which satisfies the condition COST # $815,000
mean. This corresponds to an average range estimate of 2.3 3 COST ~Floor Const.! 5 $1,059,500 – @0.7 * ~$1,059,500 – (9)
22 % = 50 %. Therefore, the typical high estimate shoud be 0.5
$815,000! * ~$1,059,500 – $652,000!#
about 150 % of the most likely estimate; and the low estimate
about 50 % of the most likely estimate. This serves as a check 5 $795,410, which does not satisfy the condition COST . $815,000
on the range estimates. The result from the first equation will be used since it
6.5 Create a Cost Model: satisfies the corresponding condition.
6.5.1 The cost model is essentially the hierarchical cost 6.6 Conduct a Monte Carlo Simulation:
estimate. Treat all non-critical elements as constants. Simplify 6.6.1 Run a Monte Carlo simulation once the risk in the
the cost model by combining constants. critical elements are quantified and the model set up. The
6.5.2 In the sample project, the cost model becomes: Monte Carlo method builds up a PDF for the bottom line
~( COSTCE 1 $1,249,000! * ~1 1 Profit! * ~1 1 Escalation! (5) building cost by repeatedly running the model with randomly
generated numbers for the critical elements according to the
where: individual PDFs. Each Critical element will use a separate
COSTCE = variable cost for the critical ele- random number for the calculation. Each time the model is run,
ments 1 through 18, one point is generated for the total building cost risk PDF. The
$1,249,000 = total cost for all the non-critical process is repeated until the total building cost risk PDF
elements; “converges” or settles into a final shape, which often requires
Profit and Escalation = variable percentages. 1,000 or more iterations. See Guide E 1369, section 7.7, for a
6.5.3 For triangular PDFs, the random cost of each critical more detailed description of the simulation technique.
element is calculated by the formula: 6.6.2 To implement a BCRA, use commercial software
COSTCE 5 LE 1 @RV * ~MLE – LE! * ~HE – LE!#0.5 (6) programs or write your own simulation software code.
if COSTCE # MLE 6.7 Interpret the Results:
6.7.1 By inspecting the converged PDF for the bottom line
construction cost and its corresponding Cumulative Distribu-
COSTCE 5 HE – @~12RV! * ~HE – MLE! * ~HE– LE!#0.5 (7)
tion Function (CDF), obtain the following information:
if COSTCE . MLE
6.7.1.1 Expected (mean) total cost, which is the average of
where: all the data points generated by the simulation.
RV = a random variable between 0 and 1. 6.7.1.2 Standard deviation on the total cost, which is the
Use the same random variable for each formula. After standard deviation of all the data points generated by the
calculating both formulas, use the one which satisfies the simulation.
corresponding condition on the right. 6.7.1.3 The confidence level, which is the cumulative per-
centage corresponding to those data points generated by the
simulation which are less than or equal to the estimated amount
7
Beeston, Derek T., “One Statistician’s View of Estimating,” Property Services on the CDF. Fig. 2 illustrates the concept of a confidence level.
Agency, Department of Environment, London, UK, July 1974. Denote the low estimate as point “a” and the high estimate as

6
 E 1946 – 02
point “b.” Because point a corresponds to the 1st percentile of 6.8.1 Use sensitivity analysis to determine the relative
the normal distribution, only 1 % of all occurrences of actual contribution of each critical element to the total building cost
costs will fall below point a. The confidence level associated risk.
with point a is therefore 1 %. Similarly, point b corresponds to 6.8.2 The mean and variance for the triangular distribution
the 99th percentile of the normal distribution, which implies are:
that 99 % of all occurrence of the actual cost will fall below
Mean 5 ~HE 1 MLE 1 LE! / 3 (10)
point “b.” The confidence level associated with point “b” is
therefore 99 %.
6.7.1.4 Cost estimate for a given confidence level, which is Variance 5 ~HE2 1 MLE2 1 LE2 – HE*LE – MLE*LE – MLE*HE! / 18
(11)
the total cost estimate corresponding to the desired confidence
level on the CDF. This cost estimate is designated as See Eq 3 and Eq 4 for the variable definitions. The arithmetic
COST(CL), where CL indicates the confidence level (for for variance of a function of independent random variables are:
example, 10 %). VAR~A 1 B! 5 VAR~A! 1 VAR~B! (12)
6.7.1.5 Contingency is the difference between the total cost
estimate for the desired confidence level and the base cost
VAR~A 1 c! 5 VAR ~A! (13)
estimate. The contingency is designated as CONT(CL).
6.7.2 Fig. 4 and Fig. 5 show the PDF and CDF for the
sample project, respectively. The Monte Carlo simulation VAR~c*A! 5 c2 * VAR~A! (14)
generated 4,000 data points using a computer spreadsheet. The where:
results are as follows: VAR = variance,
6.7.2.1 The expected (mean) total contract cost is A, B = function of independent random variables,
$10,246,000, which is higher than the deterministic cost c = constant.
estimate of $9,877,560. 6.8.3 Calculate the contribution of each critical element to
6.7.2.2 The standard deviation of the sample of total con- the total variance by holding all other variables constant.
tract cost is $430,000, or 4.19 % of the mean. Multiply the variance of that element by the square of the
6.7.2.3 The contingency used in the deterministic cost multiplication factors. In the sample project, the variance
estimate (that is, $493,878) corresponds to a confidence level contributed by the critical elements is calculated with the
of 63.0 % (that is, COST(63 %) – $9,877,560 = $493,878). following formulas and the results for the sample project are
6.7.2.4 The total cost estimate for each confidence level is: tabulated in Table 3.
COST(10 %) = $9,706,000
VARTBC ~COSTCE! 5 VAR~COSTCE!* @~1 1 Profit! (15)
COST(25 %) = $9,951,000
2
COST(50 %) = $10,240,000 * ~1 1 Escalation!#
COST(75 %) = $10,526,000 VARTBC ~Profit! 5 VAR~Profit! * @~( COSTCE 1 (16)
COST(90 %) = $10,809,000 2
$1,249,000! * ~1 1 Escalation!#
COST(95 %) = $10,983,000
6.7.2.5 Given the deterministic cost estimate in Table 1, the VARTBC ~Escalation! 5 VAR ~Escalation! * @~( COSTCE 1 (17)
contingencies by confidence level are as follows: $1,249,000! * ~1 1 Profit!# 2

CONT(50 %) = $362,000 (3.7 %)

CONT(75 %) = $648,000 (6.6 %) where:
CONT(90 %) = $931,000 (9.4 %) VARTBC = contribution to the Total Building Cost Vari-
CONT(95 %) = $1,105,000 (11.2 %) ance.
6.8 Conduct a Sensitivity Analysis: 6.8.4 In the sample project, for Floor Construction:

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

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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 %
Profit 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

VAR~Floor Construction! 5 ~1,059,5002 1 815,0002 1 652,0002 %VAR~Profits! 5 4.08 3 1010/ 1.83 3 1011 5 22 %
(18)
6.8.5 Note that there is no simple expression for VAR (A *
– 1,059,500*652,000 – 815,500*652,000 –815,000*1,059,500!/ 18
B). The variance contribution for the variables that are multi-
5 7,010,000,000 plied together (for example, escalation and profit in the
VARTBC ~Floor Construction! 5 7,010,000,000* @~1.10! * ~1.05!#2 example) is therefore not additive and the sum of all VARTBC
5 9,350,000,000
will exceed 100 %. However, the individual VARTBC provides
a good relative measure of cost risk.
And for profits: 6.8.6 Table 3 shows that the major contributors of cost
variance are Profits (22 %), General Conditions (17 %), Light-
VAR~Profit! 5 ~0.152 1 0.102 1 0.042 – 0.15*0.04 – (19) ing and Branch Wiring (14 %), and HVAC Distribution System
0.10*0.04 – 0.10*0.15! / 18 (8 %). These are the items that should be investigated if
5 0.000506 reduction in contract cost risk is desired.
VARTBC ~Profit! 5 0.000506 * @$8,552,000 * 1.05#2
7. Applications
5 40,800,000,000
7.1 Budgetary Control—BCRA allows an owner to examine
The sum of all VARTBC are 1.85 3 1011. The percentage of the cost risk exposure of the project starting from the planning
total variance are: phase. Instead of a single value of building cost, the owner has
%VAR~Floor Construction! 5 9.35 3 109/ 1.83 3 1011 5 5 % the range and probability of possible building cost and uses this
(20) information for contingency planning.

8
 E 1946 – 02
7.2 Alternative Evaluation—BCRA allows the owner and 7.5 Project Management—BCRA helps the project manager
the architect/engineer to evaluate the project alternatives based pinpoint the source of cost risk, monitor the remaining cost risk
on cost risk exposures as well as building cost. An alternative exposure, and reduce total building cost risk. The options are to
with a higher cost but lower cost risk exposure than another accept or mitigate the risks. If the risks are acceptable, no
will be preferable to some owners since the likely amount of further action needs to be taken, except to assure sufficient
cost overrun will be lower. An example is a stalemate in the funding to cover the required contingency. If the risks are
labor negotiation with the local sheetmetal workers union, unacceptably high, then explore alternative design or construc-
which has a potential impact on the cost and availability for the tion methods, or both, to reduce the risk. In the sample project,
labor to install HVAC distribution systems during the project. an investigation shows that the main light fixture type is a
The owner/project manager reduces cost risk by using factory historical replication and therefore a custom item, with a high
preformed ductwork, which has a higher material cost but cost risk. To manage the risk, the owner/project manager
significantly lower field labor requirement.
changes the requirements so that off-the-shelf fixtures are
7.3 Competitive Bidding—Contractors use BCRA to iden-
acceptable.
tify the acceptable risk exposure on a project and make an
informed decision on the bid amount.
7.4 Negotiation—BCRA informs the negotiating parties of a
construction contract on the magnitude of cost risk and helps
them allocate risk between the owner and the contractor as
appropriate.

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