In forecasting, the two primary metrics used are estimate to complete (ETC) and estimate at completion (EAC). ETC is the expected cost to finish the remaining work of the project, whereas EAC is the expected total cost of completing all work for the project. As EAC considers the total expected cost, it is the sum of actual cost incurred so far for the project (AC) and ETC. Putting it into an equation, you get:

*Estimate at completion = Actual cost + Estimate to complete*

*or*

*EAC = AC + ETC*

This is the main formula for EAC, which is derived from AC and EAC.

However, you may come across sources that are confused about EAC. A number of books, articles and journals mention that EAC changes based on certain assumptions. In fact, EAC doesn’t change directly at all on various assumptions. However, ETC does. And as ETC changes, it in turn changes EAC.

**How and why? You’ll see shortly.**

ETC is the cost needed to complete the remaining work. It’s driven by a performance factor or performance index. Putting it into an equation, you get:

*ETC = Work remaining / Performance factor*

*or*

*ETC = (Budget at Completion – Earned Value) / Performance factor*

*or*

*ETC = (BAC – EV) / Performance factor*

The performance factor could be the cost performance factor or the cost performance index (CPI). It can also be combination of CPI and schedule performance index (SPI) or a weighted combination of CPI and SPI.

So why use earned value for ETC calculation? Why not actual cost? Because we’re talking about remaining work — not remaining cost — while calculating ETC. Had it been remaining cost, the formula would have been “BAC – AC.” But for remaining work ETC will equal “BAC – EV”.

**Now, let’s review assumptions based on which the performance factor changes. You’ll see that as the performance factor changes ETC, EAC will also change.**

**Assumption #1: Future Performance Will Be the Same as Past Performance**

*ETC = Work remaining / Performance factor*

*or*

*ETC = Work remaining / Cost performance factor*

*or*

*ETC = (BAC – EV) / CPI*

Why are we taking the CPI by default and not SPI? Because here the calculation is primarily focused on cost and not schedule. Our main formula for EAC, as noted above, is:

*EAC = AC + ETC*

Now, replacing the just-calculated value of ETC on the previous equation, the modified equation becomes:

*EAC = AC + [(BAC – EV) / CPI]*

*or*

*EAC = AC + [(BAC / CPI)] – [(EV / CPI)]*

*or*

*EAC = AC + [(BAC / CPI)] – [(EV) / (EV / AC)]*

*or*

*EAC = AC + [(BAC / CPI)] – AC*

*or*

*EAC = BAC / CPI*

This is what you would mostly see in almost all the reference material for the PMP® exam — the formula for “Estimate for Completion is EAC = BAC / CPI.” It’s mentioned as the default formula in many books and plainly written as BAC / CPI, but hardly ever is it explained clearly. As we just saw, this formula is simply derived by ETC.

**Assumption #2: Future Performance Will Be the Same as Planned Rate or Budgeted Rate**

When you first plan and baseline, it’s assumed that the performance factor will be “one” or going forward EV and AC will be same. In others words, your CPI will be 1. ETC, as we have already seen, is:

*ETC = Work remaining / Performance factor*

*or*

*ETC = Work remaining / Cost performance factor*

*or*

*ETC = (BAC – EV) / CPI*

Using the CPI value 1, ETC becomes:

*ETC = (BAC – EV) / 1*

*or*

*ETC = BAC – EV*

Our main formula for EAC is:

*EAC = AC + ETC*

Replacing, the value of ETC calculated in this assumption, the equation for EAC becomes:

*EAC = AC + (BAC – EV)*

Here again you’ll see that ETC is driving the formula for EAC based on an assumption.

**Assumption #3: Future Performance Will Be Influenced by Both Cost Performance and Schedule Performance**

In this example, note that we’re talking not only about cost performance but also schedule performance. Why? Imagine that your project is doing well with respect to schedule but not cost. In such a case it’s possible that your final ETC might be less if you consider both SPI and CPI, rather than only CPI.

Applying this to the formula of ETC, we get:

*ETC = Work remaining / Performance factor*

*or*

*ETC = Work remaining / (Cost performance factor * Schedule performance factor)*

*or*

*ETC = (BAC – EV) / (CPI * SPI)*

For the performance factor in the previous equation, we have considered both SPI and CPI.

Again, our equation for EAC is:

*EAC = AC + ETC.*

Now, using the value of ETC listed above, the equation for EAC is:

*EAC = AC + [(BAC – EV) / (CPI * SPI)]*

**Assumption #4: Future Performance Will Be Influenced by Some Proportion of Schedule as well as Cost Performance**

This is a variant of assumption #3. In this instance, weighting is given to CPI as well as SPI while calculating ETC. Giving an 80 percent weighting to CPI and a 20 percent weighting to SPI, the equation for ETC is:

*ETC = Work remaining / Performance factor*

*or*

*ETC = Work remaining / [(0.8 * Cost performance factor) + (0.2 * Schedule performance factor)]*

*or*

*ETC = (BAC – EV) / [(0.8 * CPI) + (0.2 * SPI)]*

Our formula for EAC is:

*EAC = AC + ETC*

Replacing ETC, which we calculated for this assumption, the equation for EAC is:

*EAC = AC + (BAC – EV) / [(0.8 * CPI) + (0.2 * SPI)]*

Other variations in weighting are also possible, such as 50 percent for CPI and 50 percent for SPI. This will be in accordance with the judgment of the project manager.

**Assumption # 5: The Initial Plan Is No Longer Valid**

In this case, you have to recalculate ETC using a bottom-up approach. This is called “Bottom-up ETC.” Hence, for this assumption the equation for EAC will become:

*EAC = AC + Bottom-up ETC*

You can view EAC and ETC graphically as S-curves in the figure below.

**As you prepare for your PMP® exam, you’ll be ready to calculate various formulas related to EAC and ETC by remembering:**

- Don’t assume that EAC changes based on certain assumptions. ETC is what actually changes. You need to focus on ETC and how ETC is calculated based on various assumptions;
- The formula for EAC is “AC + ETC,” and therefore it is EAC which is changing based on ETC because EAC is derived from ETC. It’s not the other way around. ETC doesn’t change based on EAC; and

By focusing on ETC and understanding ETC as the division of work remaining with a performance factor, and it is ETC that drives EAC, a PMP® aspirant can easily calculate various formulae related to EAC and ETC.

This article was first publish by MPUG on 23rd June, 2015.

**You may also like:****To Complete Performance Index (TCPI) and Cost Performance Index (CPI) - Part 1****To Complete Performance Index (TCPI) and Cost Performance Index (CPI) - Part 2**

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