Earned Value definition by the example

Written by Arnaud Bonneville

In order to let you understand how you can use the Earned Value concept in your daily job, I will take a concrete example that will help you understanding its helpfulness. This article will progressively introduce all notions and formulas used in the Earned Value Management.

Definition of the Planned Value

Let's assume that you want to develop a small web site for one of your customers.

By applying basic project methodology skills (see my article on Open Workbench), you will first define the list of tasks you need to perform, in other words your WBS.

Let's assume you have defined five tasks for your schedule:

Specification
General web design
Contents feed
Graphic resources & CSS
Web automation & javascript

Once this list is defined, you will apply your resource and calendar constraints in order to come to your baseline project schedule. Let's assume here that all tasks have the same duration, each task having a 1 man-week effort.

Assuming you will be alone, your baseline schedule will be the following :

Task	Week 1	Week 2	Week 3	Week 4	Week 5
Specification	•
General web design		•
Contents feed			•
Graphic resources & CSS				•
Automation & Javascript					•

The total effort on the project has been estimated to $1000 for the five weeks. We can then consider that the forecasted cost will be $200 per task, as each task has the same duration. At this stage, we can now draw our first curve : the Planned Value (PV).

How to read this curve? At the end of the first week, the work done should be equivalent to $200, i.e. the first task should be completed.

Now let's introduce the Actual Cost and the Earned Value.

At the end of the first week, you will have to check two parameters:

How much time did I spent on the project?
How complete are my project tasks?

You will then notice that:

You have worked during five days out of five days planned, you can deduce that your Actual Cost (AC) is $200
You have actually completed 75% of the specification task. The specification task was estimated to $200, so the value of the work realized is $200*75%=$150. This figure is the Earned value (EV) of your project.

Let's complete our graph and put two plots that show the Actual Cost and the Earned Value:

With these two new plots on the graph, you can now evaluate your project performance :

If you compare the Earned Value and the Actual Cost, you will deduce if your project is on budget or not, by using the Cost Variance CV=EV-AC. If CV is less than zero, your project is over budget. In this case CV=150-200 = $-50.
If you compare the Earned Value and the Planned Value, you will deduce if your project is on time or behind schedule, by using the Schedule Variance SV=EV-PV. If SV is less than zero, your project is behind schedule. In this case SV=150-200=$-50.

To summarize, we can deduce a first definition of the Earned Value : the Earned Value is the value of the work accomplished. In its former PMI definition, the Earned Value was called BCWP (Budgeted Cost of Work Performed).

Now that you know where you are: it's time to react!

Now let's continue our example by adding the week 2. As you saw the variance from the baseline, you have decided to react and hired one employee to help you.

You will then notice that for the second week:

You have worked during five days with two people (10 man days), you can deduce that your Actual Cost for the week is $400. The cumulated AC is now $200+$400=$600.
With this additional resource, you have reached to complete the specification task, the Web Design Task and you already performed 40% of the Contents Feeds task . The cumulated Earned Value is then equal to $200 (specification) + $200 (Design) + $200*40% (Contents) = 480.

Then we can plot, on the second week, these two values :

At the end of week two, you can now check the project status :

Schedule Variance SV = EV-PV = $480-$400 = $80 : your project is ahead schedule as you performed more work than initially planned.
Cost Variance CV=EV-AC = $480-$600 = $-120 : your project exceeds your budget.

What will be the total cost of the project?

What benefits can you have of using the Earned Value ? As we already saw it, Earned Value can be used to see if the project is on the track for a given point of time, both on schedule and costs points of view.

But we can also use the Earned Value to evaluate the remaining needed costs to finish the project, the so-called Estimated to Complete (ETC) and the Estimate At Completion (EAC).

There are different ways to calculate these two values, it depends on how you "feel" the rest of the project.

Let's stick with our example. If you consider that the additional resource was just an "extra" and that you plan to finish the web site alone, you will not consider the Cost Variance for the rest of the project. In this case, the Estimate to Complete will be $120 (60% remaining of Contents task) + $200 + $200 (2 last tasks not started yet). At the end, the Estimate At Completion will be $600 (AC)+$520 (ETC)=$1120.

So the first way to get the Estimate At Completion is: EAC = AC + ETC

As the Estimate To Complete is calculated by difference of the Budget At Completion (BAC) and the Earned Value, you can also replace ETC in the previous formula by (BAC-EV). So an alternative way to calculate EAC is: EAC = AC + (BAC-EV)

But if you think that the extra resource must continue to help you because you globally underestimated the work to perform, you will include the Cost Variance impact for the rest of the project.

We will then use a new concept, the Cost Performance Index (CPI) that shows, for 1 consumed $, how many dollars you achieved to produce. In our case, at the end of week 2, CPI = $480 (EV) / $600 (AC) = 0.8

Now we have to consider that to finish the project, we will consume the first cost estimation updated by the Cost Performance Index.

In this second case, EAC = $600 (AC) + $520 (ETC) / 0.8 = $1250
So the second way to get the Estimate At Completion is: EAC = AC + ETC/CPI

By replacing ETC by its calculation using the project Budget At Completion, you get:
EAC = AC + (BAC-EV)/CPI

What will be the global duration of the project?

By applying the same philosophy on the Schedule Variance, you may revise your schedule by using the effects of the Schedule Variance. For that purpose you may calculate the Schedule Performance Index (SPI) by applying the following formula: SPI = EV / PV.

You will then be in position to extrapolate the time adjustment and calculate the date when 100% of the job will be done. Or, if your deadline is not moveable, you can calculate what will be the tasks completion rate at this fixed date by using this index.

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