## Estimate At Completion Formulas Explained

Which formula should be used for calculating **Estimate At Completion (EAC)**?

This question is often asked by the PMP aspirants. They are usually confused about different **EAC formulas**. In my opinion, this confusion has been mainly perpetrated by the PMP Study Guides. Earned Value Management (EVM) is not explained well in many of these books. They just list & document the formulas without really explaining the true utility of EAC formula. Rather, they focus on memorization for answering the PMP exam questions.

The purpose of formulas is not to solve mathematical questions. The EVM concepts are important project management concepts. The formulas can be used to gauge project’s performance and take corrective action. In my opinion, it is difficult to answer the exam questions correctly without understanding the underlying concepts.

## Project Forecasting using Estimate At Completion

In this post, I will talk about project forecasting. We will look at the concept of forecasting, understand Estimate At Completion, and discuss a generic EAC Formula. This article is complementary to my article on Estimate To Complete (ETC). You should read these two articles together to understand EAC and ETC completely.

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

### EAC and BAC – The Difference

Consider the following scenario.

You are in middle of a project. Your Project Sponsor comes and asks you – *how much would it cost to complete the project*? The Sponsor wants you to *forecast & estimate the project budget*.

You can make an educated guess and answer the question. But, would that be a good Forecast? Probably not.

Instead, we can take a more scientific approach to answer the question. This is where Estimate At Completion comes into the picture. EAC is the estimated **forecast of total budget to complete the project**.

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 estimate to complete the project. This **new budgetary estimate**, which is based on project’s past performance, is called **Estimate At Completion (EAC)**. EAC can become the** Revised Project Budget** only after the Sponsor’s approval.

If we wanted, we can write a simple definition of EAC as

Based on project’s past performance, the estimated total amount of money needed to complete the Project is called Estimate At Completion.

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

## Generic EAC Formula

In my opinion, EVM is more about common sense and less about mathematical formulas. If we go with the above definition, EAC can be simply expressed by the following equation

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

Let us analyze and solve this equation.

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 EAC equation can be written as

EAC = AC + ETC

This is the only Formula that we need. Let us call it Generic EAC Formula – it can be used to derive other formulas.

## 5 Formulas Derived from the Generic EAC Formula

- Formula I – EAC = AC + ETC
- Formula II – EAC = AC + (BAC – EV)
- Formula III – EAC = AC + (BAC – EV)/CPI
- Formula IV – EAC = BAC/CPI
- Formula V – EAC = AC + [(BAC – EV)/(CPI * SPI)]

There are 4 formulas listed in the PMBOK Guide 5th Edition. Most of the PMP study guides also list the same 4 formulas. But, I have listed 5 formulas here. The PMBOK Guide lists Formula II but does not list Formula III. I have listed both these formulas as Formula II is a special case of Formula III. In fact Formula IV is also a special case of Formula III. Let us take a close look at all the formulas.

Let me explain each one of them in detail.

### Formula I

Formula I is same as our Generic EAC Equation.

EAC = AC + ETC

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

EAC = AC + Bottom-up ETC

#### What is “Bottom-up ETC”?

Refer to Scenario IV of my article on Estimate to Complete. The term “Bottom-Up” has no specific significance in the EAC formula. ETC can be either derived mathematically by using the ETC formulas or it can be estimated afresh. A fresh ETC can by found by estimating the cost of remaining (unfinished) work in the Work Breakdown Structure (WBS). You can re-estimate the cost of remaining (unfinished) work components (work packages and activities) and then total them Upwards in the WBS to determine a fresh ETC.

### Formula II

Refer to my article on Estimate to Complete. By replacing ETC Formula II (project’s past performance was **atypical**) in the EAC Equation, the EAC Equation reduces to

EAC = AC + (BAC – EV)

### Formula III

Refer to my article on Estimate to Complete. By replacing ETC Formula I (project’s past performance was **typical**) in the EAC Equation, the EAC Equation reduces to

EAC = AC + (BAC – EV) / CPI

**Note**: We can also use Formula III of ETC in the EAC Equation. It will give us another formula which would be similar to EAC Formula III. However, the resulting formula would use projected future CPI instead of past CPI.

### Formula IV

Let us mathematically solve EAC Formula III.

EAC = AC + (BAC – EV) / CPI

EAC = AC + (BAC – EV) / CPI

EAC = AC + (BAC / CPI) – (EV / CPI)

Refer to Basics of Earned Value Analysis. Let us replace CPI in above Equation with (EV/AC). The above Equation 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 forecast of budgetary estimate to complete the project work within the Original Schedule and at the current CPI. None of the above formulas will work in this case – to complete the project work withing original schedule, we should consider Schedule Performance Index (SPI) as well.

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’, it means that $C worth of work was done for each money unit (e.g. $1). If SPI is ‘S’, it means that ‘S’ units of work was done for each duration unit (e.g. day).

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

EAC = AC + (BAC – EV) / (CPI * SPI)

There is another variant of the above formula, which is sometimes used by the project team. In the following formula x & y are weights given to CPI & SPI respectively – the sum of x & y is 1 e.g. 0.2 & 0.8 or 0.5 & 0.5.

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

### Summary

EAC Formula when future work will be completed at budgeted rate (at planned efficiency – atypical)

EAC = AC + BAC – EV

EAC Formula when future work will be completed at current rate (at current CPI – typical)

EAC = AC + (BAC – EV) / CPI

Or

EAC = BAC / CPI

EAC Formula when future work will be completed within original Schedule at current rate (considering both present CPI & SPI)

EAC = AC + (BAC – EV) / (CPI * SPI)

#### Note For PMP Aspirants

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

I have also compiled a PMP Formulas Pocket Guide. You can download it free for exam prep. It is the most comprehensive pocket guide that is based on the PMBOK Guide 5th Edition. If you are looking for more, you can also buy detailed PMP Exam Formula Study Guide by Cornelius Fichtner. It contains explanations of all the formulas along with examples & 105 PMP practice questions.

EVM is difficult topic. If you still have any confusion on EAC or EVM, you can write a comment and I will respond to it.

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