# How To Use Estimate At Completion (EAC) Formulas In Project Management?

Do you think **Estimate At Completion (EAC)** is a misnomer? I think it is. How can you estimate anything when it is already complete?

Well! That is Earned Value Management (EVM) for you. It has many confusing terms. But you don’t have to worry. You are at the right place.

You will find detailed explanation of EAC in this post. After reading it, you will have complete understanding of EAC definition and meaning. You will learn about EAC formulas, calculations, and examples. You will know how Estimate At Completion formulas can be used in Project Management (PM). You will see detailed exposition of the EVM forecasting concepts and understand the difference between EAC and Estimate To Complete (ETC). Lastly, this post will be extremely helpful for you if you are confused about the EAC formulas for PMP exam.

## Estimate At Completion (EAC) In Project Management

### What Is EAC 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

Even though the PMBOK Guide’s definition is appropriate, it is somewhat confusing. Let’s consider the following situation.

You are managing a project. A part of the work has been completed. Your Sponsor comes and asks you how much money would be needed to complete the project.

How will you respond to the Sponsor’s question?

It is simple. You just have to calculate Estimate At Completion and share the number with the Sponsor.

Estimate At Completion is the estimated total amount of money needed to finish a project. It is the sum of the Actual Cost (expenditure already incurred) till the control date and Estimate to Complete (expected cost of remaining work).

PMbyPM

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

### Estimate At Completion (EAC) vs Budget At Completion (BAC)

In EVM, the original and expected project budget is expressed as BAC and EAC respectively. BAC is approved budget at the start of a project. EAC is determined periodically at different control points as the project progresses.

The funds requirement of a project may change after the project starts. The original budget may no longer be valid. The project team may need more or less funds to complete the project. This can happen due to various reasons like cost variances, risks, incorrect assumptions etc. The team can analyze the reasons for the change and estimate or forecast a new budget. The new budgetary forecast is called Estimate At Completion. It becomes revised project budget after the Sponsor’s approval.

### Estimate At Completion (EAC) vs Estimate To Complete (ETC)

ETC is the expected cost of completing the remaining project work whereas EAC is the estimated budget to complete all the project work.

In my experience, most professionals are confused about the difference between EAC and ETC. I think PM books have not treated this topic well. The books describe EAC and then derive ETC. But, it should be done the other way. EAC should be derived after finding ETC. It will be much simpler to understand.

Let’s read the PMBOK Guide’s definition of EAC again. EAC is the sum of the actual cost to date and the estimate to complete. So, EAC should be calculated only after computing ETC.

You should read my other article on Estimate To Complete before reading this article. I have taken many references from that article to explain EAC formulas.

## Generic Estimate At Completion Formula

Let’s read the EAC definition again and give it mathematical form. We can be write the following equation:

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

Let us solve this further by replacing Actual Expenditure Till Date with AC and Estimated Future Expenditure with ETC. The above expression can be re-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.

I will derive and explain following formulas in the subsequent section.

- EAC = AC + ETC
- EAC = AC + (BAC – EV)/CPI
- EAC = AC + (BAC – EV)
- EAC = BAC/CPI
- EAC = AC + (BAC – EV)/CPI
_{p} - EAC = AC + Bottom-up ETC
- EAC = AC + [(BAC – EV)/(CPI * SPI)]
- EAC = AC + [(BAC – EV)/(x*CPI + y*SPI)]

The PMBOK Guide lists only 4 formulas. Most of the PMP study guides also talk about these same formulas. But, I have provided a more rounded view.

Let us derive each one of them. You should read my article on ETC in parallel for all the scenarios and examples.

## Calculating EAC Formulas

The above 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.

### Formula I

First one is same as our Generic Equation.

EAC = AC + ETC

### Formula II – Typical Performance

To derive the this, let’s replace ETC with ETC Formula I in our generic equation. Project’s past performance was typical and future work will be accomplished at the same rate. The resultant expression becomes

EAC = AC + (BAC – EV) / CPI

### Formula III – Atypical Performance

The PMBOK Guide lists Formula III but does not talk about Formula II. 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.

To derive this, let’s replace ETC with ETC Formula II in our generic equation. Project’s past performance was atypical but the future work will be accomplished at the planned rate. The resultant expression becomes

EAC = AC + (BAC – EV)

### 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 II and IV are also referred to as **Independent Estimate at Completion (IEAC)**.

### Formula V

To derive the this, let’s replace ETC with ETC Formula III in our generic equation. The resultant expression becomes

EAC = AC + (BAC – EV) / CPI_{p}

This expression is similar to the Formula II above. However, it uses projected future CPI_{p} instead of past CPI to calculate ETC.

### Formula VI – Bottom-up ETC

Refer to Scenario V in The ETC article. To derive the this, let’s replace ETC with Bottom-up ETC in our generic equation. The resultant expression becomes

EAC = AC + Bottom-up ETC

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 VII

Consider the following scenario.

The Sponsor wants to know the budgetary cost estimate for finishing the project work within the original schedule at current CPI.

None of the above expressions will work in this case. We need to factor in schedule performance as well.

We already know that project’s current efficiency is measured by two indices – Schedule Performance Index (SPI) and Cost Performance Index (CPI).

A SPI of ‘S’ means that ‘S’ units of work was done in each duration unit (e.g. a day).

A CPI of ‘C’ means that $C worth of work was done for each dollar spent.

We have to consider both CPI and SPI to determine the budgetary cost to complete the project work within original schedule at current CPI.

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)

### Formula VIII

There is another variant of the above expression, which can also be used for calculations. In the following formula x & y are weights given to CPI & SPI respectively. These weights signify how much importance the project team is willing to give to each performance factor. 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)

## How To Use EAC Formulas In The PMP Exam?

The PMBOK Guide describes only 4 formulas. In this post, I have extended the concept further to describe a generic equation and 8 different formulas.

If you are preparing for the PMP exam, only PMBOK Guide’s formulas should be sufficient. Here is my brief take on how you should solve the PMP questions.

You can use one of the following formulas depending the situation described in the exam question

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)

## Final Thoughts On EAC

EAC provides an revised estimate to complete the project work. It is a derived from ETC. EAC and ETC are important metrics to gauge the health of a project. They should be revised periodically as project progresses and moves towards the completion.

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 the PMP questions correctly. A mere memorization of the formulas is not useful. You may not be able to apply the correct formula in the exam question. 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 your question in the comments section below 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 contains 45 formulas and 57 abbrviations. It will help you in your exam prep. You can freely download the PMP Formulas Sheet for your studies. 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.

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