Projects often overrun their cost estimates, sometimes by staggering amounts. This occurs even with carefully-constructed bottom-up cost estimates completed to a very detailed level by experienced project teams.

The problem with the usual way of constructing a project estimate at completion (EAC) is that adding the estimates for all work breakdown structure (WBS) components does not produce the most likely cost of the entire project. In fact, a recent article emphasized the folly of adding up single-point most likely estimates in its title!²

A cost risk analysis provides a more accurate, realistic and honest estimates of project costs. 
"A formal risk analysis is putting on the table those problems and fears which heretofore were recognized but intentionally hidden."³

Why Conduct a Project Cost Risk Analysis?
"The purpose of a cost uncertainty analysis is to provide the project manager with a cost that has an acceptable probability of being exceeded."⁴ The notion that there is a probability of exceeding an EAC is a difficult one for some people.  But, the fact is that every project has risk, and ignoring risk does not make it go away.

A risk analysis can determine what is the most likely cost for the total project.  In addition, it can compute the contingency needed to provide the project explicitly with different measures of protection against cost overruns.  It can also provide the project manager with a list of the most risky WBS elements leading to better risk management strategies.

Project Cost Risk Analysis - The Risk Data
"Initial cost and schedule estimates for major projects have invariably been over-optimistic.  The risk that cost and schedule constraints will not be met cannot be determined if cost and schedule estimates are given in terms of single points rather than distributions."⁵

A cost risk analysis starts with the WBS.  The next step is to collect data on the extreme optimistic and pessimistic ranges of cost for each of the risky elements. The data collection is the most important phase of a cost risk analysis, and the most difficult. It involves interviewing the team leaders about the risks they see in their own areas of expertise and responsibility.

It helps to use a case study to illustrate these points. The low, most likely and high ranges for each element of a simple construction project shows the results of the interviews (see Table 1).

Table 1

Ranges for Risk Analysis     WBS Category Value for EAC   Low Most Likely   High             ($ thousands)         Project Design 1,500   1,400 1,500   3,000     Equipment 5,000   4,750 5,000   6,500     Foundation, Structure 7,000   6,700 7,200   9,500     Piping, Elect. HVAC 1,000   800 1,000   1,600     Labor 4,700   4,700 5,000   6,700     Indirects 6,000   5,650 6,000   8,200       __________     __________             25,200     25,700

(Notice that two of the EAC estimates are not actually the most likely costs for their WBS category. This can happen and is important in conducting an accurate risk analysis.)
 

After developing the 3-point range estimates, the next step is to choose a probability distribution for each element.  Often a triangular distribution is used.  An example is shown in Figure 1, below.

Figure 1

This triangular distribution implies a 75% likelihood of overrunning the $1 million estimate for this element. Also, the average cost of a triangular distribution is found by the equation (low + most likely + high) / 3 which in this case is $3,400 / 3 = $1,133.  So, an overrun of $133 on average can be expected for this component alone without further risk management.  This example is not extreme.   In many cases the worst case scenario implies overruns of 200% -- 400%, e.g. if a test fails and the component has to be redesigned or reprocured and retested.

• Should we believe the EAC of $25.2 million? 
• How much contingency is needed to provide an acceptable level of confidence?
• If the amount is greater than our budget, where should risk management steps be focused?
   

The Cost Risk Simulation - Results for Project Management
Using the risk ranges of the WBS categories and assuming triangular distributions, we perform a Monte Carlo simulation.  The answers refute the common-sense notion that the sum of WBS cost estimates is the total project cost.

Figure 2

The most likely cost is a little over $28.4 million. The results reveal the need for a 13% contingency just to accommodate the median cost.  And there is a 50% likelihood of overrunning the median.

The cumulative likelihood estimate developed from the frequency distribution shown in Figure 2, provides the contingency levels for each degree of overrun risk.

Table 2

The table shows that the EAC of $25.2 million is not on the radar screen.  Also, the contingency can be calculated and interpreted correctly using this table.  For instance, a conservative company might require a contingency, which leaves only 20% likelihood of overrun as shown in the box.  The contingency would be $29.337 million or 16.4% of the EAC.

Further Steps in a Cost Risk Analysis
Often costs of WBS elements are correlated with each other.  Positive correlation increases the needed contingency if the company's or agency's target exceeds 50%.  Correlation is very important in cost risk analyses and must be explored in the risk interviews.

Also, a cost risk can provide information about the location of risk in the project. In a 6-element WBS, the priorities for the project manager can be identified by inspection. If there are hundreds of WBS elements, this can pose serious problems for risk management.  Cost risk assumptions can be used to reveal the highest-risk areas for risk management.  The chart below shows the highest risk elements in red, the moderate risk elements in yellow and the low risk element in green.

Table 3

Finally, the contingency or "risk dollars" can be allocated to the WBS elements, which cause most of the overall project cost risk.  Such allocation, if desired, is affected by any correlation that might exist.

Summary
Adding up estimates at completion for WBS components is the traditional way to build up a project cost estimate. Adding single-point cost estimate is easy and appealing, but it is only the beginning of computing a realistic cost estimate. 

To get a more accurate picture of the costs of a project, a cost risk should be conducted. The cost contingency that results is easy to interpret. If the initial results from the cost risk implies project costs that are not what the customer or owner desires, risk management can be conducted to reduce the risk in the project cost.

The risk analysis can indicate where in the project cost risk is greatest.

 ¹ © 1999 by David Hulett.  The author is Principal, Hulett & Associates, Project Management Consultants of
   Los Angeles, CA. Hulett & Associates can be reached at (310) 476-7699 or info@projectrisk.com.

² Steve Book, "Do Not Sum 'Most Likely' Cost Estimates" presented at the Space Systems Cost
   Analysis Group (SSCAG) in 1994 and available from the Aerospace Corporation.

 ³ Final Report of the USAF Risk Analysis Study Team, August, 1971

⁴ Paul Garvey, "A General Analytic Approach to a System Cost Uncertainty Analysis," in
   Greer & Nussbaum, Cost Analysis and Estimating, 1991.

 ⁵ Final Report of the USAF Risk Analysis Study Tea

For more information:

David T. Hulett, Ph.D.
Principal

Phone: (310) 476-7699
       Cell: (310) 283-3527  
   FAX: (310) 472-8846

E-mail: info@projectrisk.com

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