# Estimate At Completion (EAC) vs Estimate To Complete (ETC) Formulas in Earned Value Management

EAC vs ETC Formulas in EVM: Due to popular demand :) I’m covering the four formulas for calculating Estimate At Completion (EAC) in Earned Value Management (EVM). The PMBOK^{®} Guide, 5th Edition mentions four different ways of calculating the EAC. We’ll review each of them and reinforce the concepts with the help of a case study.

## What is Estimate at Completion (EAC)?

EAC is a “forecast” of the project cost, as the project progresses. Before the start of the project, EAC is the same as Budget At Complete (BAC). However, as the project progresses, EAC may differ from BAC depending upon the project performance.

### Case Study

You are a project manager on a really large construction project. Your project requirement is to build a shopping mall on a square piece of land. However, due to economic crisis, the project is scaled down and reduced to building just the boundary walls!! The height of the wall needs to be a staggering 2m. As per the original estimate, it will take 1 week to build one side of the boundary and cost $1000 per side. So, your original budget (BAC) is $4000 and you have 4 weeks to complete the project. Without further ado, let’s get on with laying the bricks.

## Four Formulas to calculate Estimate at Completion (EAC)

Now let’s look at 4 scenarios and the corresponding equations to calculate EAC.

### 1. Original estimate is no longer valid

```
EAC = AC + bottom-up ETC
```

Either the original estimate was fundamentally flawed or is no longer valid due to change in circumstances (for example change in scope).

Let’s say at the end of the Week 1, you completed one side of the wall and the cost came out to be exactly $1000. However, your customer asks you to raise the height of the walls by another 0.5m, but still complete the project within 4 weeks. You re-estimate the costs. You need to buy more raw material and hire more workers. For the side already completed, you need another $500 to raise its height by another 0.5m. For the remaining 3 sides, you need $1500 per side.

```
AC = $1000
Bottom-up ETC of the remaining work = $500 + 3 * $1500 = $5000
EAC = $1000 + $5000 = $6000
```

### 2. The current cost performance (CPI) will continue in the future

```
EAC = BAC / CPI
```

Let’s say after completing the first side, you spent $1200 instead of the original estimate of $1000/side. The increased cost was due to the fact that it required more raw material to build the wall than what you originally estimated. You think that you are likely to spend $1200 for each of the remaining 3 sides as well.

```
BAC = 4 * $1000 = $4000
CPI = EV / AC = $1000 / $1200 = 0.833
EAC = $4000 / 0.833 = $4800
```

### 3. The current cost performance is atypical for future project work

```
EAC = AC + (BAC - EV)
```

In other words, future cost performance will be in line with the original estimate.

Let’s say after completing the first side, you spent $1200 instead of the original estimate of $1000/side. However, the extra $200 were spent because of an accidental damage to the first side. You implement a risk mitigation plan to avoid this risk for the remaining work. You still believe that $1000/side is a good estimate for the remaining 3 sides.

```
AC = $1200
BAC = 4 * $1000 = $4000
EV = $1000
EAC = $1200 + ($4000 - $1000) = $1200 + $3000 = $4200
```

### 4. Project needs to meet a deadline

```
EAC = AC + (BAC - EV) / (SPI * CPI)
```

This following equation takes into consideration the schedule performance (Schedule Performance Index) and cost performance (Cost Performance Index) to date.

Let’s say by the end of Week 1, you built only 1.6m (instead of 2m) of the first side (or 80%) and you spent $1200 on it. So, you completed $800 (EV) of work, spent $1200 (AC) on it, when you were supposed to complete $1000 (PV) worth of work. However, you still need to complete all 4 sides in 4 weeks. You might even have to hire extra workers to meet the original schedule of 4 weeks.

```
AC = $1200
BAC = 4 * $1000 = $4000
EV = $800
SPI = EV / PV = $800 / $1000 = 0.8
CPI = EV / AC = $800 / $1200 = 0.66
EAC = $1200 + ($4000 - $800) / (0.8 * 0.66) = $7200
```

As you can see, EAC can be calculated in various ways. Any of these approaches may be appropriate for a project at any given point in time, depending upon the circumstances.

Image credit: Flickr / 79286287@N00

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