## Generic Estimate At Completion Equation And Formulas Explained

Which formula should be used for **calculating Estimate At Completion (EAC) in the PMP Exam**?

This question is often asked by the exam aspirants. They are usually confused about different **Estimate At Completion formulas**. There are 4 different formulas explained in the **PMBOK Guide 5th edition**. In this post, I have extended the concept a bit further and described **5 EAC formulas** with the help of a** generic equation**.

If you want to understand the concept clearly and get every PMP exam question right, then read on.

## Before You Read Ahead

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 to understand the basics, before going ahead:

- Fundamentals of Earned Value Analysis Using An Example
- Simple Explanation of Earned Value Management Terms

This article is complementary to my article on Estimate To Complete (ETC). You should read that article along with this one to understand the concept clearly.

## Estimate At Completion Definition

In EVM, the original budget is depicted by **Budget at Completion (BAC)**. But the budget forecast may change as the project progresses – the original budget may no longer be valid due to cost variances. You can analyze the project’s past performance 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**.

If we wanted, we can write a simple definition as

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

Or follow the definition from the PMBOK Guide 5th Ed.

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

You can refer to Max Wideman Glossary to read some other standard definitions. Let us now look at the generic Estimate At Completion equation.

## Generic EAC Equation

In my opinion, EVM is more about common sense and less about mathematics. 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

Actual Expenditure Till Date = AC

Refer to my article on Estimate to Complete or Earned Value Management System Explained in Easy Language

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 formulas.

## EAC Formulas

- EAC = AC + ETC
- EAC = AC + (BAC – EV)
- EAC = AC + (BAC – EV)/CPI
- EAC = BAC/CPI
- EAC = AC + [(BAC – EV)/(CPI * SPI)]

Four of these formulas listed in the PMBOK Guide 5th Edition. 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 CPI_{p} 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)

### Summary

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

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.

### 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 5th 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.

### Over To You

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

#### Related Articles

**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.

Thank You Very very Much

Thanks Ahmed

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

Thanks.

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

Thanks Marcus

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

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

Thanks Shepard.

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?

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.

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?

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.