The Earned Value Formulas

Earned Value is a method of calculating project status.  It does this from two perspectives:  Time (schedule) and Cost.  After applying the earned value method the project manager will know whether the project is:

• behind or ahead of schedule.
• over or under budget.

In this post we will outline each formula in the earned value management system.  The first three are inputs obtained from project data, and the rest are outputs calculated by the project manager which give various indications of project status.

Planned Value (PV)

Also known as Budgeted Cost of Work Scheduled (BCWS), Planned Value is the amount of the task that is supposed to have been completed, in terms of the task budget.  It is calculated from the project budget.

For example, if it’s Feb. 12 today, and the task is supposed to last from Feb. 10 to Feb. 20, it should be 20% complete.  If the task budget is $10,000, PV = 20% x $10,000 = $2,000.

Earned Value (EV)

Also known as Budgeted Cost of Work Performed (BCWP), Earned Value is the amount of the task that is actually completed.  It is also calculated from the project budget.

For example, if the actual percent complete is 25% and the task budget is $10,000, EV = 25% x $10,000 = $2,500.

Actual Cost (AC)

Also known as Actual Cost of Work Performed (ACWP), Actual Cost is the actual to-date cost of the task.

For example, if the actual cost is $3,500, AC = $3,500.

Schedule Variance (SV)

In this, the first output calculated in the earned value analysis, the project manager obtains a value which tells you the amount that the task is ahead or behind schedule.

• If SV is negative, the task is behind schedule.
• If SV is zero, the task is on schedule
• If SV is positive, the task is ahead of schedule.

In our example, SV = $2,500 – $2,000 = $500.  This task is ahead of schedule.

Schedule Performance Index (SPI)

The SPI, similar to the SV, also indicates ahead or behind schedule but gives the project manager a sense of the relative amount of the variance.  If you told me your project had a $500 schedule variance, this would mean drastically different things if your project was for building a backyard fence versus constructing a highrise building.

• If SPI < 1, the task is behind schedule
• If SPI = 1, the task is on schedule
• If SPI > 1, the task is ahead of schedule

In our example, SPI = $2,500 / $2,000 = 1.25.  Therefore, the task is 25% ahead of schedule.

Cost Variance (CV)

Similar to the schedule variance, the Cost Variance tells the project manager how far the task is over or under budget.

• If CV is negative, the task is over budget
• If CV is zero, the project is on budget
• If CV is positive, the project is under budget

In our example, CV = $2,500 – $3,500 = -$1,000.  The task is over budget.  Note that the task can be ahead of schedule but over budget.  Too much money has been spent compared to the amount of work that is currently complete.

Cost Performance Index (CPI)

The CPI, similar to the CV, also indicates over or under budget but gives the project manager a sense of the relative amount of the variance.

• If CPI < 1, the task is over budget
• If CPI = 1, the task is on budget
• If CPI > 1, the task is under budget

In our example, CPI = $2,500 / $3,500 = 0.71.  Therefore, the task is 29% over budget.

Budget at Completion (BAC)

This one is easy.  It is simply the total project budget, which is the aggregate of all of the task budgets.

In our example, if we assume the project has just that one task, BAC = $10,000.

Estimate at Completion (EAC)

This value tells the project manager what the overall project budget will be if everything else went according to plan.  It is the extrapolation of the current project status to the end of the project.  Because it is an extrapolation, it can be legitimately calculated in several ways:

• The reason for the variance is likely to continue.
  EAC = BAC / CPI
• The reason for the variance is not likely to continue.  The project performance is expected to return to planned levels.
  EAC = AC + (BAC – EV)
• When you feel the project’s future cost performance is likely to be impacted by the past schedule performance as well as cost, you can use a hybrid.
  EAC = AC + [(BAC – EV) / (SPI x CPI)]
• When you need to change the estimate because the initial assumptions were wrong.
  EAC = AC + ETC

In our example, let’s say the reason for the negative cost variance is a snowstorm that delayed the project.  It is not likely to affect the rest of the project, therefore EAC = $3,500 + ($10,000 – $2,500) = $11,000.  This is the expected final budget.

Estimate to Complete (ETC)

This value tells the project manager how much money must be spent from this point forward, to complete the project.  Sometimes the project assumptions have changed and a new estimate must be produced instead of old performance metrics assumed.

• The project is expected to continue with the same performance in the future as the past.
  ETC = EAC – AC
• The past project performance cannot be expected to continue.  A new estimate is required.
  ETC = new estimate

Variance at Completion (VAC)

This value tells the project manager the forecasted cost variance (CV) at the completion of the project.  It is the extrapolation of the current project status, using the EAC method chosen.

• If VAC is negative, you need that much more money to complete the project.
• If VAC is positive, you will finish the project with that much of a surplus.

In our example, VAC = $10,000 – $11,000 = -$1,000.  You will need an additional $1,000 to complete the project.

To Complete Performance Index (TCPI)

This value tells the project manager what CPI would be necessary to finish the project on budget.  It gives an indication of how much efficiency needs to be found in the remainder of the project to make up for past negative variances.

If the project is required to finish within the original budget:

If the project budget is flexible to accommodate the past variance:

In our example, let’s assume there is no new money.  The original budget is fixed and the project must make up the current negative cost variance.  TCPI = ($10,000 – $2,500) / ($10,000 – $3,500) = 1.15.  This means the project needs to find 15% efficiencies for the remainder to finish on budget.

Summary Table

Symbol	Name	Formula	Description	Interpretation of Result
Inputs
PV	Planned Value		The value of the portion of the task that is supposed to have been completed
EV	Earned Value		The value of the portion of the task that is actually completed
AC	Actual Cost		The actual cost of the task to date
BAC	Budget at Completion		Total overall project budget (planned)
Outputs – Current Status
SV	Schedule Variance	SV = EV – PV	The amount that the task is ahead or behind schedule, expressed as a task value	SV < 0 = behind schedule SV > 0 = ahead of schedule
SPI	Schedule Performance Index	SPI = EV/PV	The amount that the task is ahead or behind schedule, expressed as a percentage of the task	SPI < 1 = behind schedule SPI > 1 = ahead of schedule
CV	Cost Variance	CV = EV – AC	The amount that the task is over or under budget, expressed as a task value	CV < 0 = over budget CV > 0 = under budget
CPI	Cost Performance Index	CPI = EV/AC	The amount that the task is ahead or behind schedule, expressed as a percentage of the task	CPI < 1 = over budget CPI > 1 = under budget
Outputs – Forecast
EAC	Estimate at Completion	EAC = BAC/CPI EAC = AC + (BAC – EV) EAC = AC + [(BAC – EV)/(SPI x CPI)] EAC = AC + ETC	The estimated project budget at the end of the project, given current project budget status
ETC	Estimate to Complete	ETC = EAC – AC ETC = new estimate	The expected cost to finish the project
VAC	Variance at Completion	VAC = BAC – EAC	The expected cost variance at the end of the project, given current project status	VAC < 0 = over budget VAC > 0 = under budget
TCPI	To Complete Performance Index	TCPI = (BAC – EV) / (BAC – AC) TCPI = (BAC – EV) / (EAC – AC)	The CPI required to complete the project on budget	TCPI < 1 = under budget TCPI > 1 = over budget