
The basis of project control is still the WBS because it defines the project scope and describes the effort necessary to accomplish the project objectives. Earned value, which is a technique for tracking progress against actual accomplishment, is based on the WBS budget and schedule estimates. The Gantt chart facilitates the earned value analysis by providing a quick reference for percentage completion, a necessary input to the earned value formulas.
An earned value analysis is not particularly difficult from a mathematical viewpoint. The formulas are simple and require only straightforward arithmetic manipulations to arrive at a snapshot of how well the project is progressing. The difficulty is that it uses terms that are not familiar to us, and schedule is measured in terms of dollars instead of time. Since measuring schedule in this fashion goes against intuition and experience, some people focus on the language rather than the concepts of earned value, making learning to use the technique harder than it should be.
The key to understanding earned value is in understanding three terms: planned value (PV), actual cost (AC), and work performed (EV). These three terms previously were known, respectively, as budgeted cost of work scheduled (BCWS), actual cost of work performed (ACWP), and budgeted cost of work performed (BCWP). EV is also known as the earned value, hence the origin of the name of this technique.
Once these three terms and the concepts behind them are mastered, the rest of earned value analysis is easy to understand and use.
PV is simply the task or project budget. Each task of the project has an estimated cost, so its PV is the amount of money identified for the expected or scheduled work to be done during execution. Each task has its own planned value. The accumulation of all these individual PV amounts equals the total budgeted cost for the project. Again, PV is an estimated amount and represents the cost that one expects to pay for part of a task, the whole task, or the project, depending on when in time the analysis is accomplished.
AC is simply the amount of money that is actually paid out in the accomplishment of a task or the project. This figure is derived from labor, material, vendor, and subcontractor costs of the tasks as work on them progresses. Usually, the project manager is provided these figures from an accounting process that tracks invoices, accounts payable from vendors or subcontractors, and the salaries of personnel assigned to the tasks.
Before the earned value technique was developed in the late 1960s, AC and PV were the figures used to track project progress. In other words, the project manager would compare actual and budgeted costs. If the actual costs were higher than expected expenditures, then it was assumed the project was in trouble. However, comparing actual and planned budget figures alone does not take schedule into account, so the project might actually be better off than expected. For example, if a project plan included the purchase of a number of computers during month five of the schedule, but the vendor offered them at a cheaper price to take them out of inventory earlier, then the actual costs for that period would be significantly higher than originally planned. Comparing only those figures would show the project to be over budget, but all else being equal, at month five the AC would be below the planned budget. In other words, more was spent at a point in time, but the project was way ahead of schedule. This concept introduces EV, the next and most difficult term to understand.
EV is the value of the work actually completed and measured against the planned completion amount for that period. Consider, for example, that a project is estimated to cost $20,000 and, for ease of calculation, that the cost across the project duration is linear. That is, at 25 percent completion, the project should cost $5,000; at 50 percent completion, $10,000; and so on. If the task progresses according to the planned schedule, then at the 25 percent progress point, the PV and the actual work accomplished is $5,000. That is, the budget for 25 percent of the work was planned to be $5,000 (PV), and since the task was on schedule at that point, then the budget for a completed 25 percent of work was also $5,000 (EV). But suppose at the time that this project was planned to be 25 percent completed, it was only 20 percent completed, or only 20 percent of the budgeted amount had been earned. Then the PV is $5,000 (25 percent of $20,000), and the EV is $4,000 (20 percent of $20,000). Hence, EV is a measure of schedule because it shows project progress—how much was accomplished against the plan.
Measurement or calculation of these three terms provides a basis for determining whether there is a cost and schedule variance from the project baseline.
Cost variance (CV) is the difference between the earned value and the actual cost of work performed. Mathematically, this relationship is expressed as:
CV = EV  AC
Schedule variance (SV) is the difference between the earned value and the planned value. The equation for SV is:
SV = EV  PV
Note that in both these equations, the first term on the right side of the equation is EV. EV is the key component for both these equations because this is the earned value term, or the amount earned toward completion of the project.
An example will better demonstrate the use of these formulas. Suppose at the planned 60 percent point for the $20,000 project, we actually have only completed 50 percent of the work. At this point, then, the PV is $12,000 and EV is $10,000. Suppose further that the actual moneys expended for the work accomplished is $8,000. The cost variance is:
CV = EV  AC  
or  CV = 10,000  8,000 
and  CV = $2,000 
A positive CV indicates that the project is under budget. A negative CV then indicates that the project is over budget. Of course, if the CV equals zero, then we are on budget.
The SV for this task is:
SV = EV  PV  
or  SV = 10,000  12,000 
and  SV =  $2,000 
A negative SV indicates that the project is behind schedule, a positive SV indicates that we are ahead of schedule, and a SV equal to zero means that we are exactly on schedule.
There are several other mathematical terms and equations important to the earned value techniques. These are the cost performance index (CPI), the schedule performance index (SPI), the budget at completion (BAC), the estimate to complete (ETC), and the estimate at completion (EAC). Each of these terms and their representative equations are discussed in detail below.
The SPI and CPI provide the same information as the SV and CV measures, except they are shown in terms of efficiency as opposed to pure numbers. This way of presenting the project status has some distinct advantages.
SPI is calculated by dividing the earned value by the planned value. Notice that these are the same components used to calculate schedule variance. Mathematically, SPI is represented by:
SPI = EV/PV
Or, using the previous example:
SPI = 10,000/12,000
SPI = 0.83 (rounded to the nearest 100th)
If the SPI is less than 1.0, then it is behind schedule. If it is greater than 1.0, then it is ahead of schedule, and if it is 1.0, then it is exactly on track. Another way of looking at SPI is that for every dollar of physical work that the project planned to accomplish, only eightythree cents was actually completed.
CPI is a measure of how much of the task or project value is earned against its actual cost to that point. It is calculated by dividing the earned value by the actual cost. Again, these are the same components used in the previous example to calculate the cost variance. Mathematically, CPI is described by:
CPI = EV/AC  
or  CPI = 10,000/8,000 
CPI = 1.25 
The interpretation of CPI is that for every project dollar spent, $1.25 of physical work is accomplished. That is, the project is earning more than it is spending.
Clearly, if CPI is less than 1.0, then the project is over budget (i.e., spending more to accomplish less). Likewise, if CPI is greater than 1.0, then the project is under budget, and a CPI equal to 1.0 shows the project is exactly on budget.
Both these indexes are more useful than the variance calculations for communicating progress to the stakeholders. A pure number (e.g., CV =  $100) has no meaning to someone not intimately acquainted with the project and its finances because $100 more or less gives no indication of how good or bad the project is doing. For example, if the EV is $2,000 and the AC is $2,100, the CV is still  $100. But the CPI is now 0.95 (2,000/ 2,100), which indicates that the project is under budget, but not by very much relative to total amount earned or spent—and certainly not so much as to require drastic recovery actions. That is not true in a case where CV  equals $100 and the CPI = 0.67, which occurs when EV is $200 and AC is $300. In the latter case, the project can only survive if drastic measures are not taken, and even then, the project will most likely not ever recover to a point of finishing on budget. Thus, the SPI and CPI indicators are excellent for use in status reporting and managing projects because they more accurately portray the true project status. These indexes also are important in predicting how much additional time or money may be needed to complete a project.
The SPI and CPI are used to calculate final schedule and budget figures. For instance, suppose in our example the task originally was estimated to require ten weeks to complete. A new or latest schedule estimate (LSE) at completion can be calculated by dividing the original schedule at completion (SAC) estimate by the SPI. The latest schedule estimate is represented by:
LSE = SAC/SPI  
or  LSE = 10/0.83 
LSE = 12.05 (rounded to nearest 100th) 
Hence, the new schedule requirement is just over twelve weeks if nothing is done to improve the schedule from this point forward.
Likewise, a latest revised budget estimate (LRE) is calculated by dividing the original budget at completion (BAC) by the CPI. Mathematically this calculation is provided by the equation:
LRE = BAC/CPI  
or  LRE = 20,000/1.25 
LRE = $16,000 
So the new estimated cost of the total task is now $4,000 less than originally estimated. However, the CPI and SPI must be interpreted together. That is, the indication is that the project is under budget but behind schedule. This might be because some of the scheduled tasks are not completed or, worse, have not begun. The project manager's task is to determine not only why the project is under budget, but also why it is behind schedule and what the impacts to the project are.
Some practitioners use CPI and SPI together to obtain worst and bestcase budget estimates at completion. That is, the CPI alone will provide the bestcase estimate. The product of multiplying CPI and SPI provides the worst case, since multiplying two fractions yields a smaller fraction and includes the schedule impact. To demonstrate, multiply our CPI of 1.25 and SPI of 0.83 to obtain 1.04 (rounded to the nearest 100th). Then calculate a new LRE as follows.
LRE = BAC/1.04  
or  LRE = 20,000/1.04 
LRE = $19,230.77 
Hence, the new budget estimate falls within the range of approximately $16,000 and $19,000. In actuality, the new estimate at completion for the budget will probably not be as good as the $15,000, nor as bad as the $19,000, but rather something in between, depending on how well the schedule recovers with project management intervention.
One final calculation is important in the earned value analysis process, and that is the estimate to complete.
ETC provides the project manager with an estimate of the amount of money required from a point in time to the estimated end of the project. This figure is important for two reasons. First, the project manager has to know how much additional funding may be required. If nothing can be done to improve the budget picture, then either the customer must agree to additional funding, or the organization must absorb the loss. Naturally, the project manager will endeavor to get the project back on track, but knowing how badly the project is faring will provide insight into what actions need to be taken for recovery. The second reason ETC is important is that the financial organization needs the information for planning future cash flow requirements.
The ETC is calculated by subtracting the actual amount expended on the project from the latest budget estimate at completion. Mathematically, ETC is calculated by this equation:
ETC = LRE  AC  
or  ETC = 16,000  3,000 
ETC = $13,000 
Exhibit 211 is a useful table of the most important earned value formulas and their definitions. Exhibit 212 is a graphical depiction of the earned value analysis.
Exhibit 211: Earned value terms, definitions, and formulas.
Term  Definition  Formula 

PV  Planned value of the work scheduled or the estimated cost of each task or project.  PV for project = Total budgeted cost for each of the project tasks. PV for a task is total task budget. 
AC  Actual cost to accomplish the work. Money expended to accomplish the EV.  AC = Total of all actual costs (labor, materials, vendor, and subcontractor costs) at time of status checkpoint. 
EV  The budgeted amount "earned" or completed against the planned amount.  EV = (% of tasks completed) PV of project or task as appropriate. 
CV  Cost Variance. The difference between the amount earned, that is EV, and the actual expenditures, AC.  CV = EV  AC 
SV  Schedule Variance. The difference between the amount accomplished or earned, EV, and PV, the amount planned.  SV = EV  PV 
CPI  Cost Performance Index. A measure of the amount earned per each dollar expended.  CPI = EV/AC 
SPI  Schedule Performance Index. A measure of the physical work accomplished per each dollar expended.  SPI = EV/PV 
SAC  Schedule At Completion. The total project schedule duration.  SAC = Total project schedule 
BAC  Budget At Completion. The total project cost.  BAC = Total project cost 
ETC  Estimate To Complete. The amount of money needed to finish the project from the point of each status checkpoint.  ETC = BAC (or LRE)  AC 
LRE  Latest Revised Estimate. The most recent budget estimate for total project cost.  LRE = BAC (or previous LRE)/CPI 
LRS  Latest Revised Schedule. The most recent total project duration estimate.  LRS = SAC (or previous LRS)/SPI 
Exhibit 212: Earned value graph.
