## 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) (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. [^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.

t6lPERT 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 a and & 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.

t^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.

["^Fleming, Quentin W. and Koppelman, Joel M., Appendix I, pp. 157-181 and Appendix II, pp. 183-188.

Team LiB

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