# Solving the Estimate At Completion (EAC) Puzzle

In an earlier post, we reviewed four formulas for Estimate At Completion (EAC) mentioned in the PMBOK^{®} Guide, 5th Edition, and when to use each of them. Just when I thought I had it all covered, a keen reader published a question about another EAC formula that I had not mentioned. The formula was EAC = AC + (BAC - EV) / CPI. Sure enough, I didn’t have it covered. If this formula isn’t mentioned in the latest edition of PMBOK Guide, does it even exist or is it a work of imagination? Read the complete article to find the answer.

When I saw the formula, my first reaction was to open the PMBOK Guide, Fourth edition and check whether it’s even legitimate. Of course, it wasn’t there. Otherwise, I would have covered it in my previous article. Next, I called upon my trusted friend, Google. The very first result eradicated my doubt. The formula was indeed legitimate. But, why wasn’t it mentioned in the PMBOK Guide, Fourth Edition? I started looking around for clues. Soon, I found the missing piece of the puzzle. It was lying inside the previous edition of the PMBOK Guide (Third Edition). Now I had the answer. Let’s see what it is.

More important than learning the EV formulas is to understand them. As usual, let’s begin with an example. We’ll use the same simple example we used in the earlier post. The project involves constructing a boundary wall around a square piece of land. The planned cost for each side is $1000 and it’s estimated to take one week to construct each side. Budget At Completion (BAC) is $4000 (= 4 x $1000). Let’s say that at the end of week 1, we completed only 80% of the first side and spent $1200 on it.

```
Planned Value (PV) = $1000
Earned Value (EV) = 80% of $1000 = $800
Actual Cost (AC) = $1200
```

### Formula for Schedule Performance Index (SPI)

```
Schedule Performance Index (SPI) = EV / PV
```

Calculate SPI by substituting EV and PV:

```
SPI = $800 / $1000 = 0.8
```

### Formula for Cost Performance Index (CPI)

```
Cost Performance Index (CPI) = EV / AC
```

Calculate CPI by substituting EV and AC:

```
CPI = $800 / $1200 = 0.66
```

As you can see, we have completed only $800 worth of work in one week and spent $1200 on it. Assuming that the current variances are typical, and are expected to continue for the rest of the project, to accomplish $4000 worth of work, it’s going to take us 5 weeks and cost us $6000 ($1200 x 5). Therefore, our EAC is $6000.

Now, we’ll calculate EAC using a formula. As per PMBOK Guide, Fourth Edition, the EAC formula for ‘typical’ variances is:

```
EAC = BAC / CPI ... (1)
```

Substituting the values, we get:

```
EAC = $4000 / 0.66 = $6000
```

Notice that the value of EAC is the same as we derived without the formula. Now let’s have some fun with this equation. If we add and subtract EV in the numerator of the equation, we get:

```
EAC = (EV + BAC - EV) / CPI
```

Now, split the fraction on the right hand side:

```
EAC = EV / CPI + (BAC - EV) / CPI
```

We also know that `CPI = EV / AC`

. Therefore, `AC = EV / CPI`

. Let’s substitute `EV / CPI`

with `AC`

in the EAC equation above and we get:

```
EAC = AC + (BAC - EV) / CPI ... (2)
```

Hey, wait a minute. Isn’t equation (2) the same as the one our keen reader pointed out? As it turns out, PMBOK Guide, Third Edition specified `EAC = AC + (BAC - EV) / CPI`

for ‘typical’ variances. The fourth edition of the Guide, simplified the equation to `EAC = BAC / CPI`

. Both equations (1) and (2) are the same. I’ve seen lot of confusion around the EAC formulas among PMP aspirants, in online forums too. I hope you find this information useful and pass it along to others who face similar doubts.

Do you have other doubts about Earned Value formulas? Feel free to post your questions.

Image credit: Lumaxart

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