The majority of the formulas that have to be memorized come from the Cost Management knowledge area, in particular from Earned Value Management. Rather than simply memorizing formulas in terms of random arrangements of letters in an equation, our study group found it better to understand the underlying reasoning behind the formulas. This will help one recreate any particular formulas if one happens to forget it.
The first part of this series of blog posts will be on the three fundamental quantities or values that tell you where you are at any given moment of the project with respect to a) the schedule, b) the budget, or c) both.
These quantities are the Planned Value (PV), Earned Value (EV), and Actual Costs (AC).
Quantity | Measures | Also known as | Definition |
Planned Value (PV) | Schedule | Budgeted Cost of Work Scheduled | Authorized budget amount assigned to the work scheduled to be accomplished |
Earned Value (EV) | Schedule AND Budget | Budgeted Cost of Work Performed | Authorized budget amount assigned to the work actually accomplished |
Actual Cost (AC) | Budget | Actual Cost of Work Performed | Actual costs incurred to complete workactually accomplished |
Let’s take an example to make this clearer. Let’s say you are a contractor that gets the job of painting the outside of the Pentagon. Your company can finish each side in a single day at a cost of $10,000 per day. The total budget for the project is 5 X $10,000 = $50,000. (Assume that you are painting one side at a time, waiting for one side to dry before going on to the next.)
The purpose of these three quantities is to tell you how you are doing with respect to this plan which includes a budget of $50,000 and a schedule of 5 days. Let’s pick a scenario where the project is partially finished.
Scenario 1: At the end of day 4, only three walls are completed. The amount spent by your company to accomplish the work so far comes to $40,000.
It’s obvious that you are behind schedule, because you are supposed to have four walls done by the end of day 4. Also, if you’ve spent four days worth of the budget, but only have completed three days worth of the work, you have overspent your budget somehow.
What are the three quantities above in this scenario?
1) PV = $40,000. The work scheduled to be accomplished by the end of day 4 is four walls, and the amount authorized in the budget to complete that amount of work is 4 x $10,000 = $40,000. This is the planned value or the value of the work that is scheduled to be done by this time in the project.
2) EV = $30,000. The work actually accomplished by the end of day 4 is only 3 walls, and the amount authorized in the budget to complete that amount of work is 3 x $10,000 = $30,000. This is the earned value or the budgeted value of the work that is actually done by this time in the project.
3) AC = $40,000. This number comes from the fact given in the scenario. This is the actual cost of the work that is actually done by this time in the project.
“Planned value” tells you where you are supposed to be in the budget if you are on schedule. “Actual costs” tells you exactly what the costs were based on the work that was actually performed, as the name would tell you. “Earned value” is the lynchpin which links these concepts together, because it gives you information on the plan or budget (what the work was supposed to cost), but it also gives you information on the actual work done. So all of the formulas start with EV and either relate it to PV or AC. These four formulas derived from these three basic quantities tell you whether you are a) ahead or behind schedule, or b) under or over budget, respectively. The Schedule Variance (SV) or Schedule Performance Index (SPI) tell you whether you are ahead or behind schedule, and the Cost Variance (CV) or Cost Performance Index (CPI) tell you whether you are under or over budget.
Here are the steps to memorize the formula.
Step 1: All formulas start with EV.
Derived Quantity |
Formula |
Cost Variance (CV) | EV |
Schedule Variance (SV) | EV |
Cost Performance Index (CPI) | EV |
Schedule Performance Index (SPI) | EV |
Step 2: If the formula has the word “Variance” in it, the EV is followed by a – (subtraction) sign.
If the formula has the word “Index” in it, the EV is followed by a / (division) sign.
Derived Quantity |
Formula |
Cost Variance (CV) | EV – |
Schedule Variance (SV) | EV – |
Cost Performance Index (CPI) | EV / |
Schedule Performance Index (SPI) | EV / |
This should be clear because a “variance” means that one thing is greater than the other, and the way to tell the difference is by subtracting one from the other. An index, such as a refractive index or other such physical quantity is measured by a ratio, and so involves division.
Step 3: If the formula has the word “Cost” in it, then insert “AC” because it has the word “Cost” as well.
If the formula has the word “Schedule” in it, then insert “PV” because it has the word “planned” in it which means according to schedule.
Derived Quantity |
Formula |
Cost Variance (CV) | EV – AC |
Schedule Variance (SV) | EV – PV |
Cost Performance Index (CPI) | EV / AC |
Schedule Performance Index (SPI) | EV / PV |
And that is it! Those are the four basic formulas you have to memorize for telling you “where you are” in the project.
Let’s bring back our scenario about the Pentagon and see what kind of numbers our example yields. Just to repeat:
Scenario 1: At the end of day 4, only three walls are completed. The amount spent by your company to accomplish the work so far comes to $40,000.
We know from our earlier discussion that in this case: PV = $40,000, EV = $30,000, and AC = $40,000. We already surmised based on the logic of the scenario that we are a) behind schedule and b) over budget. What do the four formulas tell us?
Derived Quantity |
Formula |
Value (in $) |
Cost Variance (CV) | EV – AC | 30,000 – 40,000 = -10,000 |
Schedule Variance (SV) | EV – PV | 30,000 – 40,000 = -10,000 |
Cost Performance Index (CPI) | EV / AC | 30,000 / 40,000 = 0.75 |
Schedule Performance Index (SPI) | EV / PV | 30,000 / 40,000 = 0.75 |
It gives a negative number in case of the two variances. This means that a negative number for CV or SV is bad, meaning either the cost is over budget or the project is behind schedule, respectively. A positive number would have meant the reverse, either that the cost was under budget or the project was ahead of schedule.
With the indexes, a number less than one for CPI or SPI means either the cost is over budget or the project is behind schedule, respectively. A number greater than one would have meant the reverse, either that the cost was under budget or the project was ahead of schedule.
In the next post, we discuss the next step in earned value analysis. Once you know where you are in relationship to the project plan, if your boss asks you “how long will it take to finish the project, and how much will it cost us?”, there are quantities you need to know that tell you this. The formula for these quantities will be discussed next time.
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