Estimate At Completion

How to Calculate Estimate At Completion (EAC) for the PMP Exam

This post is about how to calculate the Estimate At Completion. Otherwise known as EAC.


Estimate At Completion is used to predict the cost of the project at its completion.

In other words,the Estimate At Completion predicts the total cost of your project.

Estimate At Completion Formula

The Estimate At Completion formula is more complicated than most.

This is because there are actually four formulas.

Each formula tackles a different scenario that you may face on your project.

***Note: When doing the calculation in exam try to use 4 digits after decimal so that your answers are more accurate.

Scenario 1 – Original estimate is no longer valid

You might discover that the original estimates for your project were fundamentally floored.
Or circumstances may have changed so much that the estimates you have are no longer valid.

In this case you would use the following formula:

EAC = AC + Bottom up ETC

You might be wondering how you calculate the Bottom-up Estimate To Complete. According to the PMBOK® there is no formula.
Instead this is a prediction by the team of how much work is left to complete the project.

Scenario 2 – CPI will stay the same for the rest of the project

This scenario assumes that the Cost Performance Index (CPI) experienced by the project will stay the same until the project is completed.

EAC = BAC/CPI

In this scenario you assume that the project will continue to perform to the end as it was performing until now. Simply put, your future performance will be same as the past performance; i.e. the CPI will remain the same for the rest of the project.

Scenario 3 – Current CPI is abnormal

In this case you need to calculate the Estimate At Completion but discover that your current CPI is abnormal.
Here, you say that until now you have deviated from your budget estimate; however, from now on you can complete the remaining work as planned.

Usually this happens when, due to some unforeseen conditions, an incident happens and your cost elevates. However, you are sure that this will not happen again and you can continue with the planned cost estimate.

That is why in this formula, to calculate the EAC you will simply add the money spent to date (i.e. AC) to the budgeted cost for the remaining work.

EAC = AC + (BAC – EV)

Why could the current CPI be abnormal? An example might be that you have estimated $50,000 to install a new generator.
During the installation the generator is accidentally damaged and $5,000 has is spent on repairs.

You have three more generators to install but you are confident that the accident won’t happen again as you have a risk mitigation plan (and you yelled at the people who caused the damage!).

In this case it is appropriate to believe that your original estimates for installing the generators are still good.

It’s also appropriate that the current CPI (which reflects the accidental damage) does not reflect how the project will progress.

In this case you should use a formula that ignores the CPI. The formula is:
EAC = AC + (BAC – EV)

Scenario 4 – Project has to meet a deadline

We’ve all worked on projects where the boss or a customer demand that a project be delivered by a certain date.
To calculate the Estimate At Completion for such a project you need to take into account the Schedule Performance Index and Cost Performance Index.

You are over budget, behind schedule, and the client is insisting you complete the project on time. In this case, both the cost and the schedule need to be taken into consideration.

In other words, you can say that if your cost performance is poor, you are also behind schedule and you must complete your project on time. In this case you will use the formula for Case-III.

The formula is:

EAC = AC + (BAC – EV)/(CPI*SPI)

What does EAC mean?

After calculating the EAC you’ll have an amount in dollars, pounds, yen or whatever currency your project is using.

But what does this amount mean? The EAC predicts what you expect the total cost of the project to be.

Example of Calculating Estimate At Completion

Lets see some examples.

Example 1

Frank is the project manager for a software development company based in London. He is managing a project to create a new recipe sharing social network.

The project recently hit problems when the development team discovered that the software architecture they were going to use is not valid. After discussions the team has decided on a new approach.

The PMO has asked for a new estimate of the total cost of the project.

The project has already spent $210,000 and has a CPI of 1.1.

After talking with the teams on the project, he determined that the remaining costs are development – $50,000, quality assurance – $30,000 and documentation – $10,000.

What is the Estimate At Completion?


Answer: The Estimate At Completion is $300,000.



How did we calculate this?

In this example, the original estimates are bad because they are based on a flawed architecture approach.

Therefore, we will calculate Estimate At Completion using the formula from scenario one:

Estimate At Completion = Actual Cost + Bottom-up Estimate To Complete

Knowing this we can calculate: $210,000 + ($50,000 + $30,000 + $10,000) = $300,000

Example 2

Tim is the project manager for an undersea cable company based in Cyprus. He is managing a project to lay an optical fiber cable from Naples to Palermo.

The PMO has asked for an updated estimate of the total cost of the project.

At the start of the project, the costs of the project were estimated as $1,600,000 for design and permitting, $18,750,000 for optical fiber costs, $4,500,000 for installation and $2,300,000 for testing of the cable.

The Cost Performance Index of the project is currently 1.08.

What is the Estimate At Completion?


Answer: The Estimate At Completion is $25,138,888.89



How did we calculate this?

In this example, the CPI is not considered abnormal.

Therefore, a formula using CPI can be used.

So we will calculate Estimate At Completion using the formula from scenario two:

Estimate At Completion = Budget At Completion / Cost Performance Index

Knowing this we can calculate: ($1,600,000 + $18,750,000 + $4,500,000 + $2,300,000) / 1.08 = $25,138,888.89

Example 3

Gill is the project manager for a software company based in New York. She is managing a project to create a new accounting software package.

During construction, the team realized that mistakes were made while collecting requirements.

The mistake has now been fixed and a risk mitigation plan put in place.

During a review of the project, the PMO has asked for an updated estimate of the total cost of the project.

At the start of the project, the costs of the project were estimated as $200,000 for design, $300,000 for development, $200,000 for quality assurance.

The project has spent $400,000 so far. The value of the work completed is $500,000.

What is the Estimate At Completion?


Answer: The Estimate At Completion is $600,000



How did we calculate this?

In this example, the CPI is considered abnormal.

So we will calculate Estimate At Completion using the formula from scenario three:

Estimate At Completion = Actual Cost + (Budget At Completion – Earned Value)

Knowing this we can calculate: $400,000 + ($700,000 – $500,000) = $600,000

Example 4

Rajesh is working on a project to create a new inventory management system for a food manufacturer in Sheffield, England.

The CEO has told the shareholders that the new system will be in place in six months, without discussing this first with the PMO.

At the start of the project, the costs of the project were estimated as $150,000 for design, $700,000 for development, $225,000 for quality assurance.

The project has spent $450,000 so far. The value of the work completed is $375,000. The CPI for the project is 0.83 (CPI = $375,000 / $450,000) and the SPI is 0.8.

What is the Estimate At Completion?


Answer: The Estimate At Completion is $1,510,606.06



How did we calculate this?

In this example, the project has to meet a deadline.

So we will calculate Estimate At Completion using the formula from scenario three:

Estimate At Completion = Actual Cost + [(Budget At Completion - Earned Value) / (Cost Performance Index X Schedule Performance Index)]
Knowing this we can calculate:

= $450,000 + [($1,075,000 - $375,000) / (0.83 X 0.8)]

= $450,000 + [$700,000 / 0.66]

= $450,000 + $1,060,606.06

= $1,510,606.06

TCPI

 

How to Calculate To-Complete Performance Index (TCPI) for the PMP Exam

• 
  

TCPI is an estimate of the performance needed to achieve a goal.

What does TCPI mean?

You can calculate the TCPI by dividing the remaining work by the remaining funds; i.e.
TCPI = (Remaining Work)/(Remaining Funds)

Remaining work: You can calculate the remaining work by subtracting the earned value from the total budget; i.e. (BAC – EV).

Remaining funds:However, there are two cases to determine the remaining funds on hand.
In the first case, when you are on or under budget. BAC - AC
In the second case when you are over budget. EAC - AC

Imagine you are the driver of a freight train 5506. You are due in Boston by 4:00pm.
It is now 2:40pm and you have 80 miles to go.
Your TCPI is the speed you need to squeeze out of 5506 to arrive in Boston by 4:00pm.

To Complete Performance Index (TCPI) is used in Earned Value Measurement (EVM). It is one of the common indices used along with Schedule Performance Index (SPI) and Cost Performance Index (CPI) in EVM.

Difference between TCPI and CPI:
Simply put, TCPI is a a future performance measurement for your project based on your past performance, whereas CPI is current performance measurement based on the project's past performance.  TCPI is a forecasting technique, where as CPI is a budgetary measurement or cost efficiency measurement technique.

With CPI you can ask: Is my project within budget or is my project over budget? How is the project doing with respect to spent cost so far? With TCPI, you can ask: What performance level has to be achieved on the remaining work in order to meet the financial commitment - going forward? Both TCPI and CPI are used in EVM. When used together they are indeed very powerful in project-portfolio management.

To-Complete Performance Index Formula

As with EAC, there is more than one formula for TCPI.

One formula is based on the BAC; the other is based on EAC.

Scenario 1 – BAC is valid  (Project is on or under budget)

We know that BAC is an estimate of the project cost that you created at the start of the project.

If this estimate is still valid, use this formula:

(Budget At Completion – Earned Value) / (Budget At Completion – Actual Cost)

How do you know if the BAC is still valid? Remember that the BAC is estimated at the start of the project based on certain assumptions.

If any of those assumptions aren’t valid anymore, don’t use this formula.

For example, one of those assumptions for the tablet project was probably that you need x people working x hours a day to finish the project on time. (EG I need 200 people working 6 hours per day to finish this project in four months).

If the project now has to be complete in two months, then you will probably need more people or to work longer hours. (Actually it will most likely be both…)

So in this case the BAC is no longer valid and this formula should not be used.

Scenario 2 – BAC is no longer valid (Project is over budget)

If the BAC is invalid, use this formula:

(Budget At Completion – Earned Value) / (Estimate At Completion – Actual Cost)

Example of Calculating To-Complete Performance Index

Scenario 1 – BAC is valid

John is the project manager on a project to install new light fixtures in a hotel in Houston. The hotel is currently closed and the light fixtures are being replaced as part of a refurbishment. The project is estimated to last for six months.

The project is due to be completed in two months. At the start of the project, John estimated that the project would cost $120,000 to complete. The costs incurred by the project so far are $80,000. John has also estimated that the value of the work completed so far is $85,000.

At a recent meeting with the stakeholder, he was informed that the hotel will be opening ahead of schedule and that the project needs to be completed in one month.

What is the To-Complete Performance Index?


Answer: The To-Complete Performance Index is 0.875.


How did we calculate this?

In this example, the BAC is $120,000. The EV is $85,000 and the AC is $80,000.

The BAC can be considered valid.

Why? The BAC was estimated to be $120,000. The project is two thirds complete (four months work has been completed on a six month project).

The AC is $80,000 which is exactly what you would expect two thirds of the way through the project.

So we will calculate the TCPI using the formula from Scenario 1:

To-Complete Performance Index = (Budget At Completion – Earned Value) / (Budget At Completion – Actual Cost)

To-Complete Performance Index = ($120,000 – $85,000) / ($120,000 – $80,000)

To-Complete Performance Index = $35,000 / $40,000

To-Complete Performance Index = 0.875

Scenario 2 – BAC is no longer valid

Greg is the project manager on a project to create a new mobile sharing app. The project is due to go live in twelve months.

The project is due to be completed in four months. At the start of the project, Greg estimated that the project would cost $2,400,000 to complete. The costs incurred by the project so far are $2,100,000. John has also estimated that the value of the work completed so far is $1,200,000.

At a recent meeting with the stakeholder, he was informed that the project must now go live in two months. After the meeting John estimated that the total project will cost $2,700,000.

What is the To-Complete Performance Index?


Answer: The To-Complete Performance Index is 2.



How did we calculate this?

In this example, the BAC is $2,400,000. The EV is $1,200,000 and the Actual Costs are $2,100,000.

The BAC cannot be considered valid. Why? The BAC was estimated to be $2,400,000. The project is three quarters complete (eight months work has been completed on a twelve month project).

So you would expect the AC to be $1,600,000. However the AC is $2,100,000 – a discrepancy of $500,000.

So we will calculate the TCPI using the formula from Scenario 2:

To-Complete Performance Index = (Budget At Completion – Earned Value) / (Estimate At Completion – Actual Cost)

To-Complete Performance Index = ($2,400,000 – $1,200,000) / ($2,700,000 – $2,100,000)

To-Complete Performance Index = $1,200,000 / $600,000

To-Complete Performance Index = 2



========================================================================

What is TCPI? (Further elaboration)
When will be the Budget At Completion (BAC) be used and/or when will be the Estimate At Completion (EAC) will be used?
Is it that when TCPI is less than 1, it means good and vice versa?
What is its relationship with Cost Performance Index (CPI) in performance measurement?
What it has got to do with other calculations such as Net Present Value (NPV), Internal Rate of Return (IRR) etc.?

1. The Fundamentals - TCPI and CPI:

To Complete Performance Index (TCPI) is used in Earned Value Measurement (EVM). It is one of the common indices used along with Schedule Performance Index (SPI) and Cost Performance Index (CPI) in EVM.

Simply put, TCPI is a a future performance measurement for your project based on your past performance, whereas CPI is current performance measurement based on the project's past performance.  TCPI is a forecasting technique, where as CPI is a budgetary measurement or cost efficiency measurement technique.

With CPI you can ask: Is my project within budget or is my project over budget? How is the project doing with respect to spent cost so far? With TCPI, you can ask: What performance level has to be achieved on the remaining work in order to meet the financial commitment - going forward? Both TCPI and CPI are used in EVM. When used together they are indeed very powerful in project-portfolio management.

Note: Earned Value Measurement (EVM) is with respect to your defined baseline and your status date. Without baseline, you are not measuring anything. And in EVM, your measurement is "now" - on the status date. Re-read the just completed para again - it is important!

Mathematically put:
TCPI =  "Work Remaining"/"Funds Remaining",
 whereas,
CPI = "Work Done"/"Funds Spent"

Considering the formula:
TCPI = (Budget At Completion - Earned Value) / (Budget At Completion - Actual Cost)
           = (BAC - EV)/ (BAC - AC)
CPI    = (Earned Value) / (Actual Cost)
           = (EV) / (AC)

Both CPI and TCPI are Indices, and hence the values will be one of these - "1" or "< 1" or "> 1".

Cost Performance Index is a measure of the value of work completed compared to the actual cost incurred. It is the cost efficiency of the project till date, i.e., with respect to the status date - the day on which you are measuring.

For CPI:
 - If less than one means bad. (i.e., You are over budget)
 - If more than one means good. (i.e., You are under budget)
 - If equal to one means you are on budget. (i.e., Your funds spent is perfectly alright or you are on budget)


CPI at a project level becomes cumulative CPI, which in plain terms is the add-up values of CPI for individual activities or work packages that you are measuring fully at a project level.

For TCPI:
 - If less than one means good. (i.e., It is easier to complete)
 - If more than one means bad. (i.e., It is harder to complete)
 - If equal to one means it is perfectly alright. (i.e., It is same to complete)

Mark the words - for CPI while I am saying over or under budget; for TCPI, I am saying it is easier or harder to complete.

So, how and where TCPI and CPI help? Here it is.
Say you have a cumulative CPI of 0.5 and TCPI is coming at 1.5. It means based on your past performance, you are getting 50 cents for every $1 spent. But going forward, to meet the financial commitment, you need to have $1.5 in return for every $1 spent.  Now, that is highly unlikely. At best you can have 80 or 90 cents return, going forward. It means  you need to have a index of value 0.8 or 0.9 to meet your goal.

This is also where the formula for TCPI changes - when your cumulative CPI has fallen below the baseline. Now your BAC (the budget that has been planned, authorized and baselined), as shown in the above data, is not going to help you, as your project's current cost performance (CPI) is low.  And as we saw, the predicted TCPI is difficult to achieve. Hence, EAC - the Estimate At Completion - is the new viable one. Once it is approved, EAC becomes the cost performance goal  in place of BAC. Simply put, EAC is your new baseline, once approved.

Here, the formula for TCPI will be:
TCPI = (Work remaining) / (Funds Remaining) = (BAC - EV) / (EAC - AC)



2. An Example:

Let me take a simple example. You have 2 tasks each taking 2 days and executed by two resources - say R1 and R2. For each day, you are paying $100 to the resources. After 1 day, you are checking the status. As you are measuring at the end of 1 day, it is your status date. This is what you found:

Status For Task - 1:
- 1 day over. But R1 needs 2 more days.
- So the total duration now becomes 3 days. There is an increase of 1 day.
Status For Task - 2:
- 1 day over. But R2 needs 0.75 day more.
- So, the total duration becomes 1.75 days. There is a reduction of .25 day.

Now quickly, let us check the EVM related metrics.

TCPI and CPI For Task -1:
BAC = Budget At Completion (This is what you planned when you started) = 2 days * $100 = $200
EAC = Estimate At Completion (This is going to be your new estimate) = $300 (as resource R1 is now taking 1 day more)
PV = Planned Value (when you started off, what you have planned by end of 1 day) =  % Planned Complete * BAC = 1/2 * $200 = $100
AC = Actual Cost (what is the money spent as on today) = $100
EV = Earned Value (what you have actually done till end of 1st day) = % Actual Complete * BAC = 1/3 * BAC = 1/3 * $200 = $66.67
What is the value of CPI?
CPI = Earned Value/Actual Cost = EV/AC = 0.67

What is the value of TCPI?
TCPI = (BAC - EV)/ (BAC-AC) = ($200 - $66.67) / ($200 - $100) = 1.33

But this TCPI value is no longer to be used, as CPI has fallen below the baseline. In other words, going from 0.67 to 1.33, as explained earlier, is going to be a tough one - harder to complete.  So, EAC has to be new approved one and on that we will calculate the TCPI.

So the TCPI, for this over budget task will be:
TCPI = (BAC-EV)/(EAC-AC) = ($200 - $66.67) / ($300 - $100) = 0.67

So, for the first time, TCPI and CPI will match. And it must be noted that TCPI is not the inverse of CPI, i.e., 1/CPI. Also, TCPI is not (1-CPI).

TCPI and CPI For Task -2:
BAC = Budget At Completion (This is what you planned when you started) = 2 days * $100 = $200
EAC = Estimate At Completion (This is going to be your new estimate) = $175 (as resource R2 is now taking 1.75 days in total)
PV = Planned Value (when you started off, what you have planned by end of 1 day) =  % Planned Complete * BAC = 1/2 * $200 = $100
AC = Actual Cost (what is the money spent as on today) = $100
EV = Earned Value (what you have actually done till end of 1st day) = % Actual Complete * BAC = 1/1.75 * BAC = 1/1.75 * $200 =  $114.28
What is the value of CPI?
CPI=Earned value/Actual Cost = EV/AC = 1.14

What is the value of TCPI?
TCPI = (BAC - EV)/ (BAC-AC) = ($200 - $114.28) / ($200 - $100) = 0.86

Here, for Task-2, the first formula of TCPI with BAC is used, unlike for Task-1 where the EAC related formula is used.

3. A Set of Questions and Answers:

When I started  this post, I noted on certain questions. Let me address the answers here, now that it has been discussed:
Can TCPI be 0? Yes it can be. When you have not baselined, the value will be 0.
Can TCPI be 1? Yes it can. When you baseline first time and before tracking, the value is 1. At this point, the BAC and EAC are same.
Is TCPI the reverse of CPI? No. We have seen that.
Is TCPI the value is -> 1-CPI? No. We have seen that.
Has TCPI anything to do while we measure NPV or IRR? No. TCPI is a performance measurement or forecasting technique based on money you have to spend, where as NPV or IRR drives investment decisions, based on the value you are going to get.