# Applying Three-Point Statistical Estimates to Cost

## Applying Three-Point Statistical Estimates to Cost

The P&L statement that we have just discussed is deterministic. The P&L statement is a product of the business accounting department. The P&L is not based on statistics. However, the project cost estimates are probabilistic and require three-point estimates of most pessimistic, most optimistic, and most likely, as was discussed in the chapter on statistical methods. Once the three-point estimates are applied to a distribution and the expected value determined, the expected value could then be used in the earned value concept, which will be discussed in the balance of this chapter.

### Statistical Distributions for Cost

We actually use the same statistical distributions discussed earlier for all probabilistic problems in projects, whether cost, schedule, or other. It is up to the project manager and the project team to select the most appropriate distribution for each cost account on the WBS. Often the project manager applies three-point estimates only to selected cost accounts on the WBS simply because of the "80-20" rule (80% of problems arise from 20% of the opportunities).

The Uniform distribution would be applied when there is no central tendency around a mean value. There may indeed be some cases where the cost is estimated equally likely between the pessimistic and optimistic limits. However, if there is a central tendency and the likelihood of pessimistic or optimistic outcomes is about equal, then the Normal distribution would be appropriate. We know, of course, that the BETA and Triangular distributions are applicable when the risk is asymmetrical.

### Three-Point Estimates

When doing the cost estimates leading to the summarized project cost, three-point distributions should be applied to the WBS. We will discuss in Chapter 7 that the ultimate cost summarization at the "top" of the WBS will be approximately Normal regardless of the distributions applied within the WBS. The fact that the final outcome is an approximately Normal distribution is a very significant fact and a simplifying outcome for the project manager. Nevertheless, in spite of the foregone result of a Normal distributed cost summation, applying three-point estimates to the WBS will add information to the project that will help establish the degree of cost risk in the project. The three-point estimates will provide the information necessary to estimate the standard deviation and the variance of the final outcome and quantify the risk between the project side and the business side of the project balance sheet.

## The Earned Value Concept

The earned value concept is about focusing on accomplishment, called earnings or performance, and the variance between the dollar value and the dollar cost of those accomplishments. Perhaps focusing on the dollar value of accomplishment is what you thought you have always been doing, but that probably is not so. More often, the typical financial measure employed by project managers is the variance between period budget and period cost. Such a variance works as follows: if we underspend the budget in a period, regardless of accomplishment, we report a favorable status, "budget less cost > \$0," for the period. Such would not be the case in the earned value system: if accomplishment does not exceed its cost, the variance of "accomplishment less cost < \$0" is always reported as an unfavorable status.

The earned value concept is not exclusively about minimizing the variance and interchanging the word value for the word budget in the equations. All of that calculation is historical and an explanation of how the project got to where it is at the time the variance is measured. Earned value also provides a means to forecast performance. The forecast is a tool to alert the project manager that corrective action may be required or to expose upside opportunity that might be exploited. For instance, if the forecast is for an overrun in cost or schedule, then obviously the project manager goes to work to effect corrections. However, if the cost or schedule forecast is for an underrun, then what? Such an underrun may present an opportunity to implement a planned phase earlier or bring forward deferred functionality. Whether or not the opportunity is acted on, the earned value forecast identifies the possibility to the project team.

### Earned Value Standards and Specifications

The earned value system has been around since the late 1960s in its formal state, but the idea of "getting your money's worth" is a concept as old as barter. A brief but informative history of the earned value system is provided by Quentin Fleming and Joel Koppelman in their book, Earned Value Project Management, Second Edition. [5] Earned value as it is known today originated around 1962 in the Department of Defense, originally as an extension of the scheduling methodology of the era, PERT, [6] but became its own methodology in 1967 with the introduction of the Cost/Schedule Control Systems Criteria [7] (C/SCSC for short, and pronounced "c-speck") into the Defense Department's instructions (DoDI) about systems acquisition. [8] The Defense Department C/SCSC has evolved over time to the present ANSI/EIA 748 standard. [9] Along the way, some of the acronyms changed and a few criteria were combined and streamlined, but nothing has changed in terms of the fundamentals of earning value for the prescribed cost and schedule.

In the original C/SCSC, the requirements for measuring and reporting value were divided into 35 criteria grouped into five categories. [10] The ANSI/EIA 748 has fewer criteria, only 32, but also the same five categories, albeit with slight name changes. The five categories are explained in Table 6-2. Quentin and Koppleman [11] provide detail on all of the criteria from both standards for the interested reader.

Table 6-2: Earned Value Management Categories

Category

General Content and Description

Number of Criteria in Category

Organization

Define the WBS, the program organizational structure, and show integration with the host organization for cost and schedule control.

5

Planning, scheduling, and budgeting

Identify the work products, schedule the work according to work packages, and apply a time-phased budget to the work packages and project. Identify and control direct costs, overhead, and time and material items.

10

Accounting considerations

Record all direct and indirect costs according to the WBS and the chart of accounts; provide data necessary to support earned value reporting and management.

6

Analysis and management reports

Provide analysis and reports appropriate to the project and the timelines specific to the project.

6

Revisions and data maintenance

Identify and manage changes, updating appropriate scope, schedule, and budgets after changes are approved.

5

### Earned Value Measurements

Earned value measurements are divided roughly between history and forecast. The history measures by and large involve variances. Variances are computed by adding and subtracting one variable from another:

• \$Variance = \$Expectation of performance - \$Actual performance

Forecasts require performance indexes. Indexes are ratios of one variable divided by another of like dimension. Indexes are historical; numerator and denominator both come from past performance. These indexes, which are dimensionless, are used as a factor to amplify or discount remaining future performance. Forecasts are computed by multiplying performance remaining by a historical performance factor that amplifies or discounts remaining performance based on performance to date:

 \$Forecast = \$Performance remaining * Historical performance factor Historical performance factor = Value obtained/Value expectation

It is evident from the components of variance and forecast that three measures are needed to construct an earned value system of performance evaluation:

• Planned value (PV): The dollar value planned and assigned to the work or the deliverable in the WBS. PV is the expectation project sponsors have for the value embodied in the project. PV is a quantity on the left side, or sponsor's side, of the project balance sheet. PV assignments are made by decomposing the overall project dollar value, in other words the budget, into dollar values of the lowest work package. PV assignments are made before work begins; the aggregate of the PV assignments makes up the dollar value of the performance measurement baseline (PMB) that is, in turn, the budget for the project. The PMB is on the right side of the project balance sheet and should reconcile with the PV on the sponsor's side. If there is a mismatch, the difference is made up in risk.

 Σ (All PV \$assignments) = \$PMB Σ (All PV \$assignments) = Project manager's \$budget for the project \$Value of the project = Σ (All PV assignments) + \$Risk

• Actual cost (AC): The cost of performance to accomplish the work or provide the deliverable on the WBS. AC should reconcile with the expenses reported on the project P&L. Now is where our discussion of depreciation, fixed and variable, and direct and indirect costs comes into play. In the category of "Accounting Considerations" in the ANSI/EIA 748 standard, criteria 16–19 (of 32 criteria) address handling direct and indirect costs. Generally, the criteria can be interpreted as requiring direct costs to be identified at the work package level, with indirect costs allocated appropriately. Such guidance can be applied two ways: either the work package manager tracks indirect costs or the project manager tracks indirect costs at the project level. The important idea for the cost account and work package managers is to have a consistent approach that can be used to systematically align with the project P&L.

• Earned value (EV): A measure of the project value actually obtained by the work package effort. EV could be more than, equal to, or less than the PV for the work package for the period being measured. Of course, the same could be said for the AC: AC could be more than, equal to, or less than the PV.

The acronyms PV, AC, and EV are new with the ANSI/EIA 748 standard. The old acronyms that they replace, along with other comparisons between the old and new standards, are given in Table 6-3.

Table 6-3: Earned Value Acronyms

ANSI/EIA 748 Standard

DoD C/SCSC Standard

Description

Planned Value, PV

Budgeted Cost of Work Scheduled, BCWS

The time-phased budget for the project that is allocated to the cost accounts on the WBS.

Earned Value, EV

Budgeted Cost of Work Performed, BCWP

The dollar value of the work accomplished in each cost account in the evaluation period, whether the work is scheduled for that period or not. The dollar value of the work is found in the PV for the cost account.

Actual Cost, AC

Actual Cost of Work Performed, ACWP

The dollar value paid for the work accomplished in each cost account in the evaluation period, whether the work is scheduled for that period or not. The dollar value of the payment is independent of the dollar value of the work as set in the PV for the cost account.

Cost Performance Index, CPI

Cost Performance Index, CPI

An index of efficiency relating how much is paid for a unit of value. Optimally, \$1 is paid for \$1 of value earned, CPI = 1.

Schedule Performance Index, SPI

Schedule Performance Index, SPI

An index of efficiency relating how much value that is scheduled to be accomplished really is accomplished. Optimally, \$1 of scheduled value is earned in the period scheduled for that \$1, SPI = 1.

Cost Variance

Cost Variance

A historical measure to indicate whether the actual cost paid for an accomplishment exceeds, equals, or does not exceed the value of the accomplishment. Variance = EV - AC.

Schedule Variance

Schedule Variance

A historical measure to indicate whether value is being accomplished on time. This variance can also be thought of as a "value variance." Variance = EV - PV.

### The Bicycle Project Example

As a simple example to illustrate the principles explained so far, let us assume the following project situation. The project is to deliver a bicycle to the project sponsor. Let us say that the sponsor has placed a value on the bicycle of \$1,000 (PV = \$1,000). Within the \$1,000 value, we must deliver a complete and functioning bicycle that conforms to the usual understanding of a bicycle: frame, wheels, tires, seat, brakes, handlebars, chains and gears, pedals and crank, all assembled and finished appropriately.

Ordinarily, the project manager will spread the \$1,000 of PV to all of the bicycle work packages in the WBS. The sum of all the PV of each individual work package then equals the PV for the whole project. We call the distributing of PV into the WBS the PMB. For simplicity, we will skip that step in this example.

What happens if at the end of the schedule period all is available as prescribed except the pedals? Because of the missing pedals, the project is only expensed \$900 (AC = \$900). How would we report to the project sponsor? By the usual reckoning, we are okay since we have not overspent the budget; in fact, we are \$100 under budget (Variance to budget = \$1,000 - \$900 = \$100). The variance to budget is "favorable." If we have not run out of time, and the bicycle is not needed right away, perhaps we could get away with such a report.

In point of fact, we have spent \$900 and have no value to show for it! If the pedals never show up, we are not \$100 under budget; we are \$900 out of luck with nothing to show for it. A bicycle without pedals is functionally useless and without value. We should report the EV as \$0, PV as \$1,000, and the AC as \$900. Our variances for the first period are then:

 Planned value1 = PV1 = \$1,000 Cost variance1 = EV1 - AC1 = \$0 - \$900 = -\$900 (unfavorable) Value variance1 = EV1 - PV1 = \$0 - \$1,000 = -\$1,000 (unfavorable)

Now here is an interesting idea: the value variance has the same functional effect as a schedule variance. That is to say, the value variance is the difference between the value expected in the period and the value earned in the period. So, in the case cited above, the project has not completed \$1,000 of planned work and thus is behind schedule in completing that work. We say in the earned value management system that the project is behind schedule by \$1,000 of work planned and not accomplished in the time allowed.

 \$Schedule variance = \$Value variance = EV - PV \$SV = EV - PV

What is the reporting if in the next period the pedals are delivered, the project is expensed \$100 for the pedals, and the assembly of the bicycle is complete in all respects? The good news is that the project manager can take credit for earning the value of the bicycle. The EV is \$1,000 in the second period. The PV for the second period is \$0; baselines do not change just because there is a late-performing work package. We did not intend to have any work in the second period, so the PV for the second period is \$0. The project AC in the second period is \$100. We calculate our variances as follows:

 Cost variance2 = EV2 - AC2 = \$1,000 - \$100 = \$900 (favorable) Value variance2 = EV2 - PV2 = \$1,000 - \$0 = \$1,000 (favorable) Schedule variance2 = EV2 - PV2 = \$1,000 - \$0 = \$1,000 (favorable)

As a memory jogger, note the pattern in the equations. The EV is always farthest to the left, and both the AC and the PV are subtracted from EV.

Now, let's take a close look at this second period. The second period was never in the plan, so the PV for this period is \$0. However, any value earned in an unplanned period always creates a positive value or schedule variance in that period. The cost variance does not have a temporal dependency like the PV. The cost variance is simply the difference between the claimed value and the cost to produce it. The cost variance in an unplanned period might be positive or negative. Overall, the project at completion, considering Period 1 and 2 in tandem, has the following variances:

 Project variances = Σ (All period variances) Value (schedule) variance = -\$1,0001 + \$1,0002 = \$0 Cost variance = -\$9001 + \$9002 = \$0

### Earned Value Equations for Variances and Indexes

From the bicycle example, we have developed some experience with the two most important earned value equations that address project history: the cost variance and the schedule or value variance. Table 6-4 provides all the equations associated with the earned value measurements that are important to project managers. You can see that they are quite simple mathematically. In this table you will find not only the equations that address history but also the equations necessary to understand the potential outcome of the project. You will also see some of the other acronyms associated with the process; for instance, ETC stands for estimate to complete and EAC stands for estimate at completion.

Table 6-4: Earned Value Equations

Metric

Equation

Comment

Cost variance

CV = EV - AC

Historical measurement of past cost performance.

Schedule variance

SV = EV - PV

Historical measurement of past scheduled work accomplishment performance; can also be viewed as a variance on value.

Cost performance index (CPI)

CPI = EV/AC

Index of cost efficiency of past cost performance. A figure less than 1 indicates more actual cost is being paid than is value being earned.

Schedule performance index (SPI)

SPI = EV/PV

Index of scheduled-work efficiency of past scheduled performance. A figure less than 1 indicates more actual time is being consumed than was planned for the value earned. Can also be thought of as an index on value accumulation in the project.

COST estimate to complete (ETC)

ETC = PVR/CPI

ETC is equal to remaining or unearned value normalized to the historical cost performance. A CPI less than 1 will inflate the ETC to greater than the remaining budget. PVR = PV remaining.

COST estimate at completion (EAC)

EAC = AC + ETC

EAC is the total forecasted funds needed to do the project.

To complete performance index (TCPI)

TCPI = PVR/ETC

TCPI less than 1 means the project will overrun the remaining budget for the work remaining.

SCHEDULE estimate to complete (STC)

STC = (SR) * (EVR)/(PVR)

SR = schedule remaining.

EVR = EV remaining.

SCHEDULE estimate at completion (SAC)

SAC = STD + (SR) * (EVR)/(PVR)

STD = schedule to date.

It is self-evident from Table 6-4 that the mathematics are not the challenging part of the earned value process. The equations are simple formulas involving relatively few and easily understood variables. The challenges arise, as is often the case, from application of theory to real practice. We will address these practice problems in the subsequent paragraphs.

[5]Fleming, Quentin W. and Koppelman, Joel M., Earned Value Project Management, Second Edition, Project Management Institute, Newtown Square, PA, 2000, chap. 3, pp. 25–33.

[6]PERT is an acronym for Program Evaluation Review Technique. PERT is a network scheduling methodology that employs expected value for the duration estimate. The expected value is estimated from three-point estimates of duration applied to the BETA distribution. The α and β parameters of the BETA distribution are such that the distribution is asymmetric with the mode closer to the optimistic value than to the pessimistic value.

[7]Under Secretary of Defense (Acquisition), DoDI 5000.1 The Defense Acquisition System, Department of Defense, Washington, D.C., 1989; and its predecessor instruction: DoD Comptroller, DoDI 7000.2 Performance Measurement for Selected Acquisitions, Department of Defense, Washington, D.C., 1967.

[8]In 1967, the earned value standard was under the executive control of the DoD comptroller (the chief accountant) because it was seen chiefly as a financial reporting tool. Not until 1989 did the executive control pass to the systems acquisition chief in the Pentagon, thereby recognizing the importance of the tool to the overall management of the project.

[9]ANSI/EIA is an acronym for two standards organizations: the American National Standards Institute and the Electronic Industries Association. The ANSI/EIA 748 standard can be obtained, for a fee, from the sponsoring organizations.

[10]Kemps, Robert R., Project Management Measurement, Humphrey's and Associates, Inc., Mission Viejo, CA, 1992, chap. 16, pp. 97–107.

[11]Fleming, Quentin W. and Koppelman, Joel M., Appendix I, pp. 157–181 and Appendix II, pp. 183–188.