Estimate At Completion – 5 EAC Formulas for The PMP Exam

estimate at completion eac formula

I have written this post to provide a detailed explanation of Estimate At Completion (EAC). In this post you will find definition, example, formulas, and calculations related to EAC. The PMBOK Guide describes 4 different Estimate At Completion formulas. In this post, I have extended the concept further to describe a generic equation and 5 EAC formulas.

This is a good resource for people who are preparing for the PMP certification exam and want to understand cost forecasting in project management.

This is a complementary article to my other article on Estimate To Complete (ETC). You should read both the articles together to understand the concept clearly and to find the difference between EAC and ETC.

You can skip to the next section if you already understand the basics of Earned Value Management (EVM). Otherwise, you should read the following articles before going ahead:

Estimate At Completion Definition

The expected total cost of completing all work expressed as the sum of the actual cost to date and the estimate to complete.

PMBOK Guide

The estimated total amount of money needed to finish the Project is called Estimate At Completion.

PMbyPM

You can also refer to Max Wideman Glossary to read some other standard definitions.

In EVM, the original budget is depicted by Budget at Completion (BAC). But, as the project progresses, the original budget may no longer be valid due to cost variances. The the budget forecast may change. The project team can analyze the project’s past performance, find the reason(s) for variance and come out with a new budgetary forecast to finish the project. This new budgetary forecast, which could be based on project’s past performance, is called Estimate At Completion. After Sponsor’s approval this also becomes the Revised Project Budget.

Generic Formula Or Equation For Determining EAC

If we go with the above definition(s), estimate at completion can be simply expressed by the following equation

EAC = (Actual Expenditure Till Date) + (Estimated Future Expenditure)

Let us analyze and solve this further. Refer to Basics of Earned Value Analysis or Earned Value Management System Explained in Easy Language, to understand the terms used for deriving the Generic Equation.

Actual Expenditure Till Date = AC

Estimated Future Expenditure = ETC

So the above expression can be written as

EAC = AC + ETC

This is the only equation that we need to solve the PMP exam questions. It can be used to derive all the other estimate at completion formulas.

EAC Formulas

  1.  EAC = AC + ETC
  2.  EAC = AC + (BAC – EV)
  3.  EAC = AC + (BAC – EV)/CPI
  4.  EAC = BAC/CPI
  5.  EAC = AC + [(BAC – EV)/(CPI * SPI)]

Four of these formulas listed in the PMBOK Guide. Most of the PMP study guides also talk about these same formulas. But, I have explained one more here.

The PMBOK Guide lists Formula II but does not talk about Formula III. I have listed both these formulas separately as the former is a special case of the latter. In fact Formula IV is also a special case of Formula III.

Each of these formulas can be mathematically derived by suitably replacing ETC figure in our generic equation with a ETC formula from my article on Estimate To Complete.

Let us derive each one of them. For all the scenarios and examples, you should read the article on ETC.

Formula I

First one is same as our Generic Equation.

EAC = AC + ETC

In the PMBOK Guide and in some other books you will find it written as

EAC = AC + Bottom-up ETC

So, what is “Bottom-up ETC”?

Refer to Scenario IV of ETC article. The term “Bottom-Up” has no specific significance.  It just means that a fresh ETC should be determined by using Work Breakdown Structure (WBS). It can by found by determining the cost of remaining (unfinished) work components (work packages and activities) at the bottom of WBS and then aggregating them Upwards.

Formula II

To derive the second one, let’s replace ETC with ETC Formula II (project’s past performance was atypical project’s past performance was atypical but the future work will be accomplished at the planned rate) in our generic equation; the resultant expression will be

EAC = AC + (BAC – EV)

Formula III

To derive the third one, let’s replace ETC with ETC Formula I (project’s past performance was typical) in our generic equation; the resultant expression will be

EAC = AC + (BAC – EV) / CPI

Note: If we use ETC Formula III for replacing, it will give us yet another formula. The resulting expression would look similar to the above one. However, it would use projected future CPIp instead of past CPI to calculate ETC.

Formula IV

Let us mathematically solve Formula III above.

EAC = AC + (BAC – EV) / CPI

EAC = AC + (BAC / CPI) – (EV / CPI)

Refer to Basics of Earned Value Analysis. Let us replace CPI in above expression with (EV/AC). The above expression reduces to

EAC = AC + (BAC / CPI) – EV/(EV/AC)

EAC = AC + (BAC / CPI) – AC

EAC = BAC / CPI

Formulas III and IV are, sometimes, also referred to as Independent Estimate at Completion or IEAC.

Formula V

Consider the following scenario.

The Sponsor wants to know the budgetary cost to complete the project work within the Original Schedule and at the current CPI.

None of the above expressions will work in this case.

We already know that project’s current efficiency is measured by two indices – Cost Performance Index (CPI) and Schedule Performance Index (SPI). If CPI is ‘C’, then it means that $C worth of work was done for each dollar spent. If SPI is ‘S’, then it means that ‘S’ units of work was done in each duration unit (e.g. a day).

To determine the budgetary cost to complete the project work within original schedule, we have to consider both CPI and SPI.

Refer to Formula III – it uses only CPI. If we modify it to include SPI also, then it becomes

EAC = AC + (BAC – EV) / (CPI * SPI)

There is another variant of the above expression, which can sometimes used for calculation. In the following formula x & y are weights given to CPI & SPI respectively. The sum of x & y should be 1, e.g. 0.2 & 0.8 or 0.5 & 0.5.

EAC = AC + (BAC – EV) / (x*CPI + y*SPI)

Which Estimate At Completion Formula Should Be Used For the PMP Exam Calculations?

When future work will be completed at the budgeted rate (at planned efficiency – atypical)

EAC = AC + BAC – EV

When future work will be completed at the current rate (at current CPI – typical)

EAC = AC + (BAC – EV) / CPI

Or

EAC = BAC / CPI

When future work will be completed at current rate within the original Schedule (considering both present CPI & SPI)

EAC = AC + (BAC – EV) / (CPI * SPI)

EVM Formulas In Project Management

There are number of other formulas in EVM. You can read Earned Value Management Formulas for a quick snapshot of all of them. You need to understand the these to answer PMP questions correctly. A mere memorization of the formulas would not help – you may not be able to apply the correct one. It is better understand the concept and then apply the formula(s) as required.

Over To You

EVM is difficult topic. Do you still have any confusion about Estimate At Completion? You can write a comment and I will respond to it.

Related Articles

To Complete Performance Index
EVM – Is it Useful?

PMP Exam Formulas

I have also compiled a PMP Formulas Cheat Sheet. It will help you in your exam prep. You can read more about it and directly download it free by joining PMP prep linkedin group. It is the best and most comprehensive cheat sheet based on the PMBOK Guide 6th edition.

If you are looking beyond a cheat sheet, then I would suggest you to buy detailed PMP Exam Formula Study Guide by Cornelius Fichtner. It contains detailed explanations of all the formulas along with examples and 105 practice questions.

Disclosure: This article contains affiliate links - it means that, if you buy from any of these links, then I will receive a small commission that would help me in maintaining this blog for free. However, for you, there is no extra cost. I recommend only those products that I believe will definitely help the certification aspirants.

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Praveen Malik, PMP

​Praveen Malik ​is a certified Project Management Professional (PMP®) with a rich 23+ years of experience. He is a leading Project Management Instructor, Coach and ​Advisor. He ​has successfully trained thousands of aspirants for the PM certification exams.

Click Here to Leave a Comment Below

Ahmed AMIN Reply

Thank You Very very Much

    Praveen Malik, PMP Reply

    Thanks Ahmed

VJBaskar Reply

Nice blog with nice info. been using prmavera for a long time. Never realized that primavera supports all this.

    Praveen Malik, PMP Reply

    Thanks.

MarcusMic Reply

Good read. project management cannot be done with formulas – formulas help decision making.

    Praveen Malik, PMP Reply

    Thanks Marcus

Brianbab Reply

This was great. Hey! Can you make a detailed guide with some examples – even at a cost.

Shepard Aria Reply

Pmbok mentions only 4 formulas, but no explanation. This was crystal clear. Tks.

    Praveen Malik, PMP Reply

    Thanks Shepard.

Shawn Reply

On page 224, the PMBOK states “If future work will be accomplished at the planned rate, use: EAC = AC + BAC – EV” which is different from the you stated for formula II “project’s past performance was atypical” the resultant expression will be EAC = AC + (BAC – EV). If “Atypical does mean that work will not continue at the same rate.”, then we shouldn’t use EAC = AC + (BAC – EV) per PMBOK?

    Praveen Malik, PMP Reply

    Hi Shawn,

    Thanks.

    Both PMBOK Guide and my article say the same thing; language is bit different. PMBOK Guide talks about the “future” (future work will be accomplished at the planned rate) while my article talks about the “past” (project’s past performance was atypical) while explaining the formula.

    After reading your comment, I think, a more appropriate statement would be “project’s past performance was atypical but the future work is forcasted to be accomplished at the planned rate”. Let me make this change.

    BR
    Praveen.

Ilenia Reply

Hi, interesting article!
I wondered what was the best formula to calculate the costs to finish when you want the project to end as soon as possible and your activities are late at the actual date.
Moreover I have studied that there are some formulas for the calculation of completion time (Actual complation date). In particular, I know the formula
AC = T + (BAC-EV) x (BC-T) / (BAC-AC) -> original estimate approach
and
AC = BC / SI -> revise approach.
I understood that cost calculated with formula II corresponds to a completion time given by AC original and cost calculated with formula IV corresponds a time given by AC revise. Is it right?

    Praveen Malik, PMP Reply

    Hi Ilenia,

    To answer your Q about “costs to finish when you want the project to end as soon as possible”, you have to define what is “as soon as possible”. But if you want to finish the project within original schedule, then you can consider using Formula V. Regarding the other things that you have written, they are not part of EVM. Probably you are reading about earned schedule which is not part of PMBOK Guide.

    BR
    Praveen.

Andreas Åhwall Reply

Dear Praveen,

Could you please provide me with a further explanation of the fifth formula? Why is the project expected to be more expensive then planned if the SPI is less then 1? Consider the following simple example:

A two month project of totally 2000h planned (1000h in each month)
After 1 month the project has achieved an EV of 500h with the exact same amount of reported hours (AC=500h)

The CPI = 1 and the SPI = 0.5
According to the formula the estimated cost at completion will be:
EAC = AC + (BAC – EV) / (CPI * SPI)
= 500 + (2000 – 500) / (1 * 0.5) = = 500 + 1500 / 0.5 = 500 + 3000 = 3500h
That is the remaining 1500h of planned work are expected to take 3000h.

If the delay in the first month was solely due to a lack of manpower, which is now available in the second month, I would expect the remaining 1500h to be completed in 1500h (since that reflects the previous cost performance).
Why is not this the case?

Thanks a lot for your help!

    Praveen Malik, PMP Reply

    Hi Andreas,

    Good Q. Ans to your Q is in last part of your comment – “…delay in the first month was solely due to a lack of manpower…”.
    Your statement could mean 2 things:
    1. Manpower was not planned initially and additional manpower was added in second month – Additional manpower will make the project more expensive.
    2. Manpower was planned initially but was not available. In second month requisite manpower is available – If this is the case then you are applying the formula incorrectly. SPI will be substantially more than 0.5.
    You would have noticed that Formula V is an extension of Formula III. Just read the note associated with Formula III again. For calculating EAC, you can either use current SPI or future projected SPI.
    For this particular case SPI cannot be the current SPI. It will be future projected SPI.

    Hope it helps.

      Andreas Ahwall Reply

      Thanks for your clarification Praveen!

      I think the problem at my workplace is that we always use the current SPI for future estimates, regardless of the specific reason for a very low SPI. I take your comment ”If this is the case then you are applying the formula incorrectly. SPI will be substantially more than 0.5.”, as that the incorrect usage you are referring to is that I use the current SPI instead of the projected future SPI, and that you mean that ”THE PROJECTED FUTURE SPI is substantially higher than 0.5″. Is this a correct interpretation?

      With regards to your answer nr.1 I do understand that additional manpower MAYBE and PROBABLY causes extra costs, but I still don’t see how this is directly related to the SPI? In my example above we have planned 1000h to be performed each month, but due to non-availability only 500h were performed in month 1. This could for example be recovered by hiring extra (perhaps external) manpower to perform the ”500h lost hours of month 1″ in month 2. If these hours (for example) are charged with a 40% premium compared to the normal manpower, it will only affect the total cost at project completion with 10% (500/2000*40%). With the formula V proposed above though, the impact will be as high as 75% (3500-2000 / 2000). Also, I interpret the EAC as the expected number of hours consumed at the project completion, not the actual monetary cost of them. Can you please provide further explanation on this topic?

        Praveen Malik, PMP Reply

        Hi Andreas

        EVM is more than formulas. The formulas mentioned this article work in specific scenario (as described in the article). In addition, if you apply formula with incorrect values then the answer will come out to be incorrect.

        Having said that, you have not given the complete problem statement in your comment above. e.g. BAC and total number of months are missing. So, at best, I can speculate to answer your Q.

        I would suggest you to go back to drawing board and understand the definition of EVM terms.
        1. CPI is cost efficiency (cost of work)/(funds). Current efficiency is EV/AC whereas future (projected) efficiency is (BAC-EV)/(BAC-AC). Refer to my article on TCPI https://www.pmbypm.com/to-complete-performance-index to understand more.
        2. SPI is similar. It is schedule efficiency (work)/(planned work). Current efficiency is EV/PV whereas future (projected) efficiency is (BAC-EV)/(BAC-PV).
        3. EAC is not hours but hard $. Although, you can represent it in terms of hours (specifically person hours) but it is factually incorrect. Read more about it in https://www.pmbypm.com/difference-project-effort-and-duration/ and https://www.pmbypm.com/earned-value-management-system-explained-easy-language/

        Lastly, as I gather from your problem statement, both projected SP & CPI are different from the current efficiencies. So, in order to to apply Formula V correctly, you will have to put projected efficiencies.

        Hope it helps.

        BR
        Praveen.

Andreas Ahwall Reply

Hi Praveen!
Have you had the time to look into my second comment above?

ecouter musique Reply

nice content. thanks.

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