# Earned Value for a task with non proportional costs

I have a question regarding EVM. Suppose I have a task with a 2 weeks duration. PV for week 1 is 800 and PV for week 2 is 200. If the PV is not proportional with the % complete, so each week I expect 50% of the task done, and suppose after the first week the % complete done was 60% of the total task. In this scenario if i use EV as (real % complete * BAC) I would get 600 (60%*1000) and this would mean that I am behind schedule due the 800 PV for week 1, but actually I am ahead of schedule. Ins this case would be better to compute EV as: If 60% is done then my EV is at least 800 because I did what was planned for week 1, plus i did a 10% of the remaining 50%, so i will have 20% of the 200 PV of week 2, obtaining an EV of 800 + (10%/50%)*200 =840, so now my EV would be bigger than PV for week 1 and I could see clearly than I am ahead of schedule.

Based on that, Am I thinking this right or the proportional thing is something we always have to assume.

Hope I made myself clear.

I won't provide you with the answers but I'll help you get there. The chart below represents the project you provided in your problem: The left Y-Axis represents your budget; the right Y-Axis represents physical % complete; and the X-Axis is time over two weeks. The blue line shows your planned rate of completion, which you indicated is 50% for the first week and 50% for the second week.

The red line shows you are planning to spend \$800 for the first week and then \$200 the second, for a total BAC of \$1,000.

At the end of the first week, your physical % complete is 60%, represented by the dotted line going to point A. You should have completed 50% so you are ahead of schedule. You should have spent \$800 but your AC = \$900.

Here is how to find EV. If you are at A, draw a horizontal line until you intersect with your planned value line at point B. That represents where you are physically on your timeline. Draw a vertical line until you intersect your budget plan value line, at point C. This is where you are from a budget perspective. Now, draw a horizontal line to intersect your budget Y-Axis at point D. Where it intersects is your EV. While my drawing is nowhere precise, I estimate your EV to be around \$830 to \$840. Let's use \$835.

So, what do we know?

BAC = \$1,000 EV = \$835 (there are more precise ways to find EV but this is the information you provided) PV = \$800 AC = \$900 CV = EV - AC CPI = EV/AC SV = EV-PV SPI = EV/PV EAC = BAC / CPI (one of many formulae) VAC = BAC - EAC

Let me know how this works for you. Post other questions when you have them.

• Now that I think about it, you can interpolate between known values to find EV more precisely. Let's assume you had 10 units of work. That is one unit a day. You completed six units. In the second week, you were to spend \$40 a day for five days, equaling \$200. So you earned the \$40 for the sixth unit of work. That would make your EV \$840, which is quite visible on the graph. So instead of \$835, use \$840 for your calculations. Nov 21, 2021 at 20:27
• Thanks David for the answer. I believe the way I calculated my EV in my original question is the same as your graphical solution. I just explained it badly I think. I would love some book or documentation with examples that are harder than the ones we usually see on PM books or courses.
– JmML
Nov 21, 2021 at 20:36

You need to claim the proper % complete based on the way you developed the plan. For EV, we calculate the costs of the development of the project's product because EV is a COST control tool. It would be incorrect to simply spread those costs proportionally across the duration because your AC will not be proportional and then your CV would be unusable. While you can calculate SPI and SV with it, it is an unuseful schedule control tool. Use Earned Schedule for that.

But if your focus is the schedule (and assuming you'll calculate your schedule variances using earned schedule), you can build your planned schedule (PS, like PV) not only using dollars (like for EV) but also using days (duration) or physical completion.

When you claim earned schedule (like claiming earned value) you claim it using the same method you used to establish the planned schedule.

Take a look at the graph below. This represents a project where, depending if you are looking at days (straight line obviously), physical % complete, or costs, you get three different curves with three different % complete values despite being at the same place in the project. So if you used physical % to establish your PS, then you use physical % to claim your ES. The math does not care what you use. For the example below, 50% physical complete = 38% duration complete = 12% budget complete.

Just stay consistent. • Thanks for the answer. I am learning EVM first, so if we leave ES methodology aside, what would be the correct values in my example for the EV CV and SV if I had an AC of 900 in the first week ?
– JmML
Nov 21, 2021 at 16:22

Proportional calculation of earned value is a simplification that may assist in making planning and scheduling decisions but it's not always based on reality. The only "true" earned value is the value of your product if you stop right now and don't continue working on it. If an incomplete product is worth nothing then your EV is 0.

For scheduling and planning you need to ask yourself: Given the incomplete state of the product, how much effort needs to be invested to complete it, and how long will that take given the available resources and our current velocity? These predictions can be highly inaccurate if you're not really close to completion.

In your example, you stumble across something that I would intuitively call a misnomer: PV is actually not value, but planned cost of work. If you plan to expend 80% of your budget in the first week and 20% in the second week, there are probably good reasons for doing so (for example, you need an expensive external expert to start up your project) and you should consider how your better-than-expected intermediate result will affect further progress. It's possible that there is indeed less work left to do, which means you may complete a bit early. But it is also possible that the triple-ex boosted your speed by doing all the work while she was present, and that your project will grind to a halt when she leaves at the end of the first week because your internal team isn't capable enough.

• Thanks for the answer, are you saying that I am misinterpreting what PV means and assigning a planned cost to it instead ? How should I calculate PV instead of just assigning weekly estimated costs ?
– JmML
Nov 21, 2021 at 16:29
• I'm not a project manager (as a software developer, my interest in PM stems more from the role as "victim" of weird PM ideas). My naive interpretation is that "V" stands for value as in something valuable to the stakeholders, but the PMBOK definition of the term PV is something different, so I wouldn't say you're misinterpreting the meaning, but the PMBOK definition is counterintuitive. For a much better insight into the interpretation of the numbers look at David Espina's answer. Nov 21, 2021 at 17:20