## Doubt in Estimate At Completion (EAC) Calculations

Today, I got a question from our friend, PMP aspirant. He wanted me to explain the answer to the PMP question. He said that his answer is not matching the right answer given. The question is given below:
You are the project manager of a \$5 billion dollar construction project. Your project is doing extremely well in terms of cost performance, which is indicated by the Cost Performance Index value of 1.25. But, you have reasons to believe that the current variances were due to extraneous factors, and you do not expect similar variances to occur in future. The original estimated budget at completion is \$250,000. What should be the estimate at completion (EAC) for your project if AC = \$ 100,000 and EV = \$ 125,000?
OK, before going into the question, I would like to explain the various ways of calculating the Estimate At Completion (EAC). There are three different scenarios you will encounter in the EAC calculations. They are:

1. Current project performance is typical; you expect the project to perform similarly till end of the project
EAC = BAC/ CPI
Let me give you an example. Say, your original budget is \$1000. The actual cost as of now is \$200, but the earned value is only \$100. It means that you are spending \$2 for every \$1 of work. So, if the same performance continues till end of the project, you would be spending \$2000 instead of \$1000.

In terms of calculations, CPI = EV/ AC = 100/200 = 0.5
So, your EAC = BAC/ CPI = 1000/0.5 = \$2000

2. Current project performance is atypical; you expect the project to perform to original expectation from now on.
EAC = AC + (BAC-EV)
Let us use the above example in case 1. You have spent \$200 so far for an earned value of \$100. So, you still have \$900 (BAC-EV = \$1000-\$100) worth of work to be completed. Since you are expected to fall back in line with the original estimate, you need only \$900 to complete the project from now on. Add the amount you have already spent on the project (\$200).

So, EAC = 200 + (1000-100) = \$1100

3. You need to complete the project in time, irrespective of what has happened so far.
EAC= AC + (BAC-EV) / (SPI * CPI)
Let us again use the example from case 1. You have spent \$200 so far for an earned value of \$100.  But, as per schedule, you should have completed \$400 value of work.

So, PV = \$400, EV = \$100, AC = \$200
SPI = EV/PV = 100/400 = 0.25
CPI = EV/AC = 100/200 = 0.50

EAC = 200 + (1000-100)/(0.25*0.75) = \$5000.

EAC = 200 + (1000-100)/(0.25*0.50) = \$7400.

The revised estimate now is too high compared to the original estimate; this is because of the very slow progress (SPI =0.25). You may have to spend more money (using schedule compression techniques) to bring back the project on schedule.

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### Solution to the given problem

I hope you understand the different scenarios given here. Now, let me come back to the question sent by our friend, PMP Aspirant. The project manager believes that the current variances are not typical and does not expect similar variances to occur in the future. The scenario given falls under case 2. So, let us the relevant formula to compute the EAC value.

EAC = AC + (BAC-EV)
In the given problem, AC = \$100,000; BAC = \$250,000; EV = \$125,000

EAC = 100000 + (250000-125000) = \$225000

Is that clear? Do you still have any doubts? Please feel free to share your thoughts. If you need help on any other problem, I would be glad to help.

## Doubt in Schedule Network Diagram

Network Diagram is the most interesting concept in project scheduling. But, it can also become tricky if you do not understand it clearly. Today, I got a query from one of my PMP candidates. He sent me the following table of activities.

Activity  Predecessor  Duration (days)
AStart6
DA8
BStart3
EB5
CStart9
EC6
EndD3
EndE4

He was confused why activity E is appearing twice in the table with different duration. He also wanted to know the critical path, duration of the critical path and the total float of activity B.

### Solution

Now, let us look at the solution for the above problem. I will draw the network diagram using Precedence Diagramming Method (PDM)/ Activity On Node (AON) diagram. To avoid confusion, I will just draw the relationship without showing the duration of the activities.

So, we have no problem in drawing the network. You can check the relationship against the table and everything looks fine.

Now, let us start including the duration for each activity. This is where it gets troublesome. Activity E's duration is shown as 5 days in one row and as 6 days in another. Why does activity E appears twice with different duration?

Since activity E appears twice, this problem cannot be represented using Precedence Diagramming Method (PDM)/ Activity On Node (AON) diagram or even Arrow Diagramming Method (ADM)/ Activity On Arrow (AOA) diagram. In both approaches, the activity appears only once. So, we need to interpret the problem a little bit differently.

Instead of reading that duration of activity E is 5 days, let us read it as the duration of activity E-B is 5 days. Similarly, let us interpret that the duration of E-C is 6 days. With this interpretation, I am going to draw the network with a combination of both PDM and ADM. The activity is placed in the node as in PDM while the duration is placed on the arrow as in ADM. Let us see how the network diagram looks like.

So, I believe we have correctly represented the problem in the network diagram. Now, it is simple to answer the questions.

Question 1: Identify the Critical Path. What is the duration of the critical path?
We have three paths in the network, namely Start-A-D-End, Start-B-E-End and Start-C-E-End. Let us find out the duration of each path.

Duration of Start-A-D-End: 17 days
Duration of Start-B-E-End: 12 days
Duration of Start-C-E-End: 19 days

So, it is clear that the path Start-C-E-End with the longest duration of 19 days is the critical path.

Question 2: What is the total float of activity B?
We know the duration of the critical path is 19 days. Activity B appears in only one path, Start-B-E-End, which takes 12 days. So, the total float of activity B is 19-12 = 7 days.

That's it. Hope the above explanation gives you a better picture of the problem and its solution. What is your opinion? Is it clear? Do you have any other doubts? Please feel free to leave your comments.