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Problem concerning BCWP earned value and ACWP actual value
Question

Hello.
I saw a previous topic that is kind of the same problem as me but I still doesn't fully understand. I am doing this exercise:
"A contract to erect a large oil tank is expected to last 6 weeks. The tank requires welding 360 steel slabs. Estimated total man hours are 1080, with cost of 20$/h. All slabs are available on site on first day and erection starts immediately.
During the first week, 50 slabs are erected, using 200 hours.
Second week additional 60 slabs, using 200 hours (accumulated 110 slabs, 400 hours).
Third week additional 90 slabs, using 200 hours (accumulated 200 slabs, 600 hours).
At the time now, four full weeks into the project, 280 slabs are installed with 800 hours consumed so far (so, +80 slabs in 200 hours)
Assume the contract provides for the project to be compensated based on cost plus a 4k$ fixed fee payment scheme. Also, either savings or cost overrun between the original budget and the actual cost must be shared equally.
Compute the BEAC budget estimes at completion and the TEAC time estimates at completion"
So, we have:
BAC budget at completion = 1080*20 = 21.6K $
D duration project = 6 weeks
At the end of week 4 : 280/360 = 78% slabs erected and 800/1080 = 74% of time spent.In order to find BEAC = BAC / cost of variance performance index CI
I need to find CI = earned value BCWP / actual value ACWP
Same goes for TEAC = BC / schedule performance index SI
I need to find SI = BCWP / BCWS
Seems pretty clear so far.
However I am confused when it comes to find BCWP and ACWP, because I think I don't fully understand the difference even with a definition.
BCWS is quite easy to find here. As there are 6 weeks, at the 4th week we are expected to perform 66% of the work, 66% of the expenditures, i.e., 720 hours over 1080 = 67%, so as we have 20$/h, BCWS = 720*20 = 14.4K$.
But what about BCWP and ACWP ?
If we use the hours spent performed so far, i.e. 800 hours, is it correct to compute ACWP = 800*20 = 16k$ ?
In this case, how do we compute BCWP ? We still didn't use the data 280 slabs erected over 360 = 78%, I thought maybe compute BCWP = 78%*BAC = 78%*21.6K= 16848$
That would mean CI = 1.053 and SI = 1.17
I thought of these results as wrong because considering 800 hours over 1060 at week 4, it is more than scheduled (720/1080) that means we should be behind schedule but we have SI > 1 !!!!
Please help me on that one I feel a bit lost !!!!
PS: I am quite in a hurry lol please correct me quickly :S
All replies

Well, normally, I don't do people's homework for them.
When I sat down at my computer this morning I was supposed to be calculating the results for my yacht club, which is urgent. But I saw your question and thought I would give it a go using MS Project.
So I made a calendar with M  F working days, 06:00  18:00, 360 tasks, each task 1 hour duration, 3 welder resources assigned to each task.
Total duration is 30 working days, work = 1080 hours, cost = $21600.
Then I baselined it.
Then I tracked the progress after (status date =) 5 days, 10 days, 15 days, 20 days etc.
Assume the project (the first task) started as scheduled at 06:00 on 25/02/2018.
At status date = end of day 5, 02/03/2018, the first 50 tasks are actually finished.
etc. will have an answer for you soon.

Thank you for your reply.
I simply wanted to know if my answers look correct especially for BCWP and ACWP. The exercise does not specify extra data like you just assumed. Moreover I am training myself for the exam of Project Management, it is not really a homework. So I should not be able to use MS Project for this exercise.

Ok. That will save me a lot of work.
BCWP is what you thought, when you planned it, what it would cost to perform the tasks that you actually performed. The tasks that you actually performed come from tracking the progress. The cost of them comes from your baseline.
ACWP is what it actually cost to perform the tasks that you actually performed. This comes from the invoices and other records of actuals.
The "WP" in both of these stand for work performed. I think this is something of a misnomer, and it would be better if it was "TP", meaning tasks performed
In your example, at the end of week 4, 238 tasks were scheduled to be finished, with 714 hours of work and cost = $14280. That is the BCWS.
But you have said that you have actually finished 280 tasks (slabs) for 800 hours of work, and if those hours cost $20 each the cost is $16000. That is the ACWP. If the 800 actual hours of work actually cost something other than $20, say $21 so that he cost was $16800, then that is the ACWP.
280 tasks were scheduled to have 1083 hours of work and cost $21660. That is the BCWP, the planned cost of what you actually did.
I think working in percentages just confuses the picture/story.

Well let's start from the beginning.
At the end of the week 4, 240 slabs were scheduled with 720 hours of work and cost 720*20 = 14400 $ (just correcting the data) which is, I agree, the BCWS.
I also agree about the ACWP which should be, with 280 slabs, 800 hours, 20$/h, ACWP = 16800$.
However it is wrong to say "280 tasks were scheduled to have 1083 hours of work and cost 21660$"
I don't think this cost is the BCWP. The text suggests 360 tasks to be completed in 1080 hours of work, that is to say a cost of 21600$ with 20$/h, and this cost should be the BAC "budget at completion" right?
I suggested the following BCWP:
BCWP = percentage progress in terms of slabs erected * budget at completion
that is to say
BCWP = (280/360)*21600
BCWP = 16800$
My concern with this BCWP, which is in my opinion obtained from a logical point of view, does not match with the schedule performance index SI because
SI = BCWP/BCWS = 16800/16000 = 1.05 > 1 which means ahead of schedule (good!) but if we compare the total time spent so far at week 4 we spent 800 hours / 1080 which is 74%, and we normally scheduled at that time 4/6 of 1080 (since there are 6 weeks in total) i.e. 720 hours. Consequently just based on this it should be possible to say that we are behind schedule (720<800) no? Do you get my point and my doubts?

I checked, and I have to correct myself. What can I say? It was late.
280 x 1 hour tasks were scheduled to take 280 hours of duration, with 3 hours of work per task, so 840 hours of work, at $20/hour = $16800. This is the "budgeted cost of work performed", BCWP. There is no need to arrive at this any other way. I don't think that you should multiply the total cost by the ratio of actual tasks to total tasks. It should be the ratio of the costs. It only works out the same in this case because all of the tasks are identical.
238 tasks were scheduled to be done by end of week 4, but 280 tasks were actually done, so you are "ahead of schedule", taskwise.
BCWS is the budgeted cost of the 238 tasks that were scheduled to be done by end of week 4, 238 x 3 x 20 = $14280.
BCWP/BCWS = 16800/14280 = 1.18
"total time spent so far at week 4" is not quite correct. The "time spent" is the duration, and that is 4 weeks (20 working days in my program). The work was 840 (man) hours. It looks like "time" but it is not. It's work.