# Estimate At Completion – 5 EAC Formulas for The PMP Exam

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**.

**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

- 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. 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)

### 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.