Passing the #PMP Exam—Memorizing Formulas (part 2–Earned Value)


In the previous post, I covered the basic formulas having to do with the three quantities of Planned Value (PV), Earned Value (EV), and Actual Cost (AC).

1. Review of PV, EV, AC

Just for review, here is the definition of the quantities themselves.

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

And here are the simple formulas related to these quantities:

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

These formulas tell you the answer to the question “where are we in relationship to the schedule and budget?” Another question you might get is, “will be finish the project on time and within the budget?” To calculate these quantities, we need to introduce some new terms.

2. Terms dealing with the project cost at completion

Quantity Formula Definition
Budget at Completion (BAC) (Related to PV) Authorized budget amount of the total project, i.e. what the project was supposed to cost
Estimate at Completion (EAC) (several formulas) Estimated cost of the project at completion, i.e., what the project is now expected to cost
Variance at
Completion
(VAC)
BAC – EAC The difference between what the project was supposed to cost (BAC) and what is now expected to cost (EAC).
Estimate to Complete (EAC) EAC – AC How much more it is estimated it will cost to complete the project, i.e., the difference between what the total project is now expected to cost (EAC) and how much it has cost until now (AC).

3. Relationship between PV, AC and the terms of completion (BAC, EAC, ETC, VAC)

Perhaps a diagram would best explain the relationship of these terms.

Project START

NOW

END

Budget ß

PV

à

ß BAC

à

Actual ß

AC

à

Estimate
ß EAC

à

ß

ETC

à

ßVACà

The project starts, the project keeps going until the point where we are doing the earned value analysis, which is listed as NOW and is represented by the solid line down the center. The end of the project is listed above.

Those terms that deal with the point right NOW are the planned value or PV, which is the budgeted value of the work was supposed to done up to now, and the actual cost or AC, which is the actual cost of the work that was actually done up to now. The

If the project were to go as planned, the project would be completed at the amount it was budgeted for, which is the BAC, or Budget at Completion. It is the analogous value for PV if it were measured not NOW at the present moment but at the end or completion of the project. That is why it is in blue like PV to make sure you understand that they are both based on the budget.

AC is in green to let you know that it is based not on the budget, but on the actual costs.

What about the estimate at completion? It is the amount that it is estimated the project will cost at completion. But EAC is made up of AC, which is the actual cost up to now, and the estimated cost to complete, which is ETC. The difference between the BAC, the budgeted amount, and the ETC, the estimated amount at completion, is the VAC or variance at completion.

So two of the formulas that relate to the terms of completion, namely,

Variance at Completion (VAC) VAC = BAC – EAC
Estimate to Complete (ETC) ETC = EAC – AC

can be memorized simply by visualizing the diagram and realizing what the terms mean.

4. Calculating the EAC

So how to you calculate the EAC? As listed in the chart in paragraph 2, there are several formulas, which is always a point of confusion for test takers. How do you know which one to use? Here are the formulas, their characteristics, and an explanation of when they are to be used.

The purpose of each formula for EAC is to estimate how much it will take to complete the project based on the performance to date. If the project is over budget or behind schedule, the key in figuring out the EAC is to analyze WHY it is over budget or behind schedule. This will give you the clue as to which formula to use. I’ll give some examples after explaining the terms in the table.

Formula

No.

Formula

Formula

Name

Formula Explanation

1

EAC = AC + ETC

New estimate

ETC is new bottom-up estimate

2

EAC = AC + (BAC – EV)

Original estimate

Reason for variance is one-time occurrence

3

EAC = AC + (BAC – EV)/CPI

Or

EAC = BAC/CPI

Performance estimate low

Reason for cost variance will continue at same rate

4

EAC = AC + (BAC – EV)/CPI*SPI

Performance estimate high

Reason for cost variance will continue and effect schedule performance as well

Formula 1. If the original budget is considered totally flawed, then one way to estimate the amount it will now take to do the project is to take the amount spent on the project so far (AC) and then do a more accurate bottom-up estimate of the amount it will take to complete the project (ETC). That’s one way to do it. But if you are answering a question from the PMP exam, don’t use this formula unless it specifically states the ETC is a brand-new estimate. In this case, they will have to give you the figure for ETC because it is not derivable from any other formula but from the project’s own WBS (work-breakdown structure).

Formulas 2-4. The rest of the formulas are similar in that they all start with AC, the actual cost up to now, and then they add an amount called the remaining budget or BAC – EV, modified by some other factor.

What is the remaining budget? Take a look at the chart below which adds EV and the BAC – EV or remaining budget figure.

Project START

NOW

END

Budget ß

PV

à

ß BAC

à

ß EV à
ß

BAC – EV

à

Actual ß

AC

à

Estimate
ß EAC

à

ß

ETC

à

ßVACà

In this chart, the assumption is made that the EV is somehow different than the PV, i.e., the project is off schedule somehow. Now the PV is essentially useless for planning purposes because it shows you the value of the work that was supposed to be done, and the assumption is that the EV is somehow different than that. So the logical think to do is to start figuring out how much work actually needs to be completed from now (EV) to the end of the project (EAC), and that difference EAC – EV is the remaining work.

Let’s go back to our Pentagon example from the previous post.

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.

Here the PV = $40,000, and the EV = $30,000. Remember that the total amount budgeted for the project (BAC) = $50,000.

Now what is the remaining budget? Well, there are two walls left to be painted, and that will cost $20,000. So the remaining budget to complete the work is $20,000. You can see how this works with the formula because

Remaining budget = BAC – EV = $50,000 – $30,000 = $20,000

Now let’s take a look at the formulas in more detail using variations of the scenario 1 based on the REASON for the delay.

Formula 2.

Scenario 2: 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 $30,000.

If the reason for the delay in painting the walls is a one-time occurrence, let’s say because it rained that one day and we don’t expect (according to the weather forecast) that it will happen again, that the EAC is simply

EAC = AC + (BAC – EV) = $30,000 + ($50,000 – $30,000) = $30,000 + $20,000 = $50,000.

This makes sense because the work done so far (3 walls) should have cost $30,000, and that’s what is actually cost. So if the rain was a one-time occurrence, and the painters continue at their same pace, it will take 2 days to complete, at a cost of $20,000 (2 x $10,000), so the total estimated cost = $50,000. The project will be one-day late in completion, but not under budget.

Scenario 3. At the end of day 3, three walls are completed. The amount spent by your company to accomplish the work so far comes to $40,000.

In this scenario, the workers are doing the project on time, but their cost is higher than expected. You would expect 3 walls to cost $30,000, not $40,000. So in this case PV = $30,000, EV = $30,000, and the SV = PV – EV = $30,000 – $30,000 = 0, meaning that the project is right on schedule.

But with regards to the cost, AC = $40,000, so CPI = EV/AC = $30,000/$40,000 = 0.75. This means that the project is over budget (by $10,000).

What is the estimate at completion? Assuming that the workers continue to work at the same rate of pay, then the remaining two days should be billed at the same rate as the ones up until now, meaning that the CPI or cost performance index should be the same up until the end of the project. This fits into the “variance continues at the same rate” scenario that fits formula 3.

If you remember the earlier formula 2, EAC = AC + (BAC – EV), and just divide the remaining budget term by CPI, you get

EAC = AC + (BAC – EV)/CPI

Now here’s a shortcut: if you do all the algebra, the above equation simplifies to

EAC = BAC/CPI

Here’s how to remember the shortcut: take the original equation and literally cut in short, i.e., cut out all the terms that are shorter (have 2 letters rather than 3) and you get, as if by magic, the formula above.

In this case,

EAC = BAC/CPI = $50,000/0.75 = $66,667.

Scenario 4. At the end of day 4, three walls are completed. The amount spent by your company to accomplish the work so far comes to $40,000.

So the three walls worth of work are costing $40,000, more than $30,000 than expected. That’s one factor that will continue supposedly at the same rate throughout the project, similar to Scenario 2. But now, you have the added factor that they are doing the work more SLOWLY than anticipated, because they are doing three walls worth of work in the time they were expected to do four. This means that not only the cost, but the schedule is now compromised. Let’s just say it has to do with the type of brushes they are using not being as effective as had originally been thought (they are using hand brushes, let’s say, rather than roller brushes). Now the COST AND SCHEDULE factors will cause a delay, and here we have to use the more complicated formula of

EAC = AC + (BAC – EV)/(CPI * SPI)

I tried the algebra on this equation and it doesn’t simply into anything nice and neat like formula 3. So there’s no alternative but to slog it out.

Here BAC = $50,000, PV = $40,000, EV = $30,000, and AC = $40,000, so

CPI = EV/AC = $30,000/$40,000 = 0.75, SPI = EV/PV = $30,000/$40,000 = 0.75, so

EAC = AC + (BAC – EV)/(CPI * SPI) = $40,000 + ($50,000 – $30,000)/(0.75)(0.75)

= $40,000 + ($20,000)/(0.75)(0.75) = $40,000 + $35,556 = $75,556.

So, if you remember the REASON for the delay in the project, you can figure out whether you are to use formula 2, 3, or 4. No further delay, it’s formula 2. A continued reason for being overbudget, then it’s formula 3. If it’s a continued reason for being overbudget AND behind schedule, then it’s formula 4.

Formula 3 has the advantage of being able to be simplified somewhat.

Tomorrow, there are just two more Earned Value formulas to mention, but they are so complicated that our instructors in our PMP exam prep course didn’t even include them in our list of formulas to memorize because they thought the chance was remote of it being included on the exam. I will list it for the sake of completion, because the concept behind the formula is actually quite important.

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3 Responses

  1. Very well explained. There is a confusion The Remaining budget used in Para 4. Calculating the EAC, at one place its BAC-EV and the other EAC-EV. This can be true at the start of the project but not in the above example where project is at stage NOW.

  2. The estimate to completion in section 2 shows the acroynm as EAC. It should be ETC.

  3. Hi,

    Innovative use of coloured cells for explanation. For your readers here is a comprehensive list of all EVM formulas

    BR
    Praveen Malik

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