## Estimate At Completion Formula Explained

Which formula should be used for calculating Estimate At Completion?

This question is often asked by the PMP aspirants. They get confused by the different formulas written in the books. On the other hand, a person who regularly uses Earned Value Management would never ask this kind of question. Let me explain.

In my opinion, the aspirants should not be faulted for confusion regarding Estimate At Completion formula. This confusion has been mainly perpetrated by the PMP reference books. Most of the reference books just list & document the formulas. They do not explain them sufficiently. Their focus is mainly on memorizing and answering the exam questions without really explaining the true utility of each formula.

Is it possible to answer the exam questions correctly without understanding the concept? I don’t think so.

In this post, I will talk about project forecasting using Estimate At Completion. I will first explain the concept of forecasting and then I will talk about Estimate At Completion Formula. This article complements my article on Estimate To Complete (ETC). You should read these two articles together.

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:

### Forecasting & Estimate At Completion

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 arrive at the answer.

This is where Estimate At Completion (EAC) comes into the picture. EAC is the estimated forecast of total budget to complete the project.

We already know that, in EVM, original budget is depicted as **Budget at Completion (BAC)**. But in the middle of a Project, the original budget may no longer be valid. This can happen due to if there is are 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.

### A Generic Estimate At Completion 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 Estimate At Completion Formula that we need. It can be used to derive a few other formulas and it can be also used to calculate EAC in any scenario.

### 5 Formulas Derived from the Generic EAC Formula

There are 4 formulas listed in the PMBOK Guide 5th Edition. Most of the PMP reference books 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 me explain each one of them in detail.

#### EAC 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 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 work components at the bottom of WBS and then total then total them Upwards in the WBS to determine a fresh ETC.

#### EAC Formula II

Refer to my article on Estimate to Complete. By replacing ETC Formula II in the EAC Equation, the EAC Equation reduces to

EAC = AC + (BAC – EV)

#### EAC Formula III

Refer to my article on Estimate to Complete. By replacing ETC Formula I 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.

#### EAC 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

#### EAC Formula V

Consider the following scenario.

The Sponsor wants to know the revised budgetary estimate to complete the project work within the Original Schedule at the current CPI. None of the above formulas will work in this case as none of them uses Schedule Performance Index (SPI).

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

Formula III uses only CPI. To give an answer to the Sponsor, we need SPI also. If we can modify the Formula III to include SPI, then it becomes

EAC = AC + (BAC – EV) / (CPI * SPI)

### Summary

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

EAC = AC + BAC – EV

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

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)

While doing the PMP questions, you should avoid memorizing the formulas. Pure memorization does not help. It is better understand the concept and then apply the formula(s) as required.

I have compiled a PMP Formulas Pocket Guide that is based on the PMBOK Guide 5th Edition. You can download the Pocket Guide for free. It is the most comprehensive guide to all the PMP Exam formulas. 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 and 105 PMP practice questions.

Please leave a comment, if you have seen a any other EAC formula and you were not able to understand it.

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Earned Valaue Management Formulas

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