PMP, RMP Exam: Estimate to Complete (ETC) Calculation – Formulas for ETC (Composite)

I received this question from one of my readers. 

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Hello Satya, 
I am a project management instructor for Sacramento State University College of Continuing Education and one of the areas I teach is earned value management.  I found your article written on June 23, 2015 about calculating EAC and ETC when I was looking for a formula to use when calculating ETC with weighted SPI and CPI.  PMBOK refers to this proportional variation but provides no formula to calculate it.  You provided the following formula which makes sense:

            ETC = (BAC - EV) / (CPI * CPIweight) + (SPI * SPIweight)

Both in PMBOK and in your example, there is an implication, but not explicitly stated, that the CPI and SPI weight must equal 1.0.  For example, if the CPIweight is .8, the SPIweight must equal .2.  Therefore, the non-weighted formula,  

           ETC = (BAC – EV) / (CPI * SPI)

would be used when the CPI and SPI have equal influence on the ETC, whereas if they are disproportionate, you would use an 80/20 or other appropriate weighting with your formula.  Using this logic, it would seem that if you used a 50/50 proportion with the weighted formula, it should render the same result as the non-weighted formula.  However, in practice the results are vastly different.

This was causing me a great deal of confusion where I couldn’t determine whether it was my logic or the formula that was incorrect.  Eventually, I came to the conclusion that the formula is correct, but that my logic was flawed.  I’d like your input as to whether my conclusion is accurate.  It is not logical to make the weighting of CPI and SPI a function of each other, but solely a judgement of how much each index influences the remaining cost independently.  In other words, and for example, if the CPI is weighted at .8, that simply means that only 80% the CPI is only influencing the ETC; it doesn’t mean that only 20% of the SPI is influencing the ETC.  In fact, the SPI could also have an 80% influence.  This would mean that the 80 of the cost overruns will continue to influence the remaining cost and that 80% of the schedule delays will be an influence as well. 

This means that the non-weighted formula is basically stating that 100% of the cost factors and 100% of the schedule factors are influencing the ETC.  Part of the past cost overruns may be from atypical factors which could reduce the CPI weight (perhaps to 60%) and the schedule delays may only have a slight impact (perhaps 10%).  In this example, the formula would be:

            ETC = (BAC - EV) / (CPI * .60) + (SPI * .10) 

Clearly, the weights do not add up to 1.0, but this would appear to be appropriate in this scenario.
I’d appreciate your input on my analysis.  Essentially, my theory is that CPI and SPI should be weighted independently based on their respective influence rather than proportionately as a function of one another and do not necessarily need to be something like 80/20, 70/30, or the like.  If fact, they could be 60/50, 10/30, 75/75, etc.

Thank you for taking the time to read this and for any feedback you have.  I hope you are safe and well during this pandemic.  All of my courses are now being taught virtually.  I’m anxious to be able to return to the classroom in person when it is safe. 

Kindest regards,
Gary R. Slavit, PMP
gary@slavitconsulting.com

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It’s a very good question and a discussion on it will clarify a number of things on Estimate to Complete (ETC) calculation in earned value management (EVM). The question and subsequent explanation by Gary are very thoughtful and analytical.

Indeed, it confuses many – particularly when the weighted values of CPI and SPI are considered.

Hence, I’m putting it as a separate post and explaining the concepts with ETC (Composite) and ETC (CPI), with focus on the former.

First, let me put the formulas for ETC. As noted in the article (June 23, 2015), it is actually the ETC which changes. This in turn impacts the Estimate at Completion (EAC). Now, ETC is calculated with many assumptions. They are noted in the below table.

In the below table:

• CPI stands for Cost Performance Index.
• SPI stands for Schedule Performance Index.
• BAC is for Budget at Completion.
• EV is for Earned Value.

Table - ETC Assumptions and Formulas

The content of this table is from the previous article and I've added a few notes, information and classifications of ETC, i.e., ETC (Composite), ETC (CPI) and ETC (Management). All the assumptions are also from the previous mentioned article.

ETC (CPI) and ETC (Composite)

The above table has been divided into three sections. Let's understand them.

• ETC (CPI): For ETC calculation, only the cost performance index is in consideration. Hence, in the name, "CPI" word is appended.
• ETC (Composite): For ETC calculation, both cost and schedule performance indices are considered. As both are considered, it’s called “composite”.
• ETC (Management) or ETC (Formal): Neither CPI nor SPI is explicitly taken in a formula for ETC. Rather, the calculation is a bottom-up and manual one. This is what the management commonly uses and hence appended with word "management".

These naming conventions will be useful to remember the formulas.

The question raised in the beginning directly relates to these assumptions - Assumption # 3 and Assumption # 4. Both of these assumptions fall under ETC (Composite). The calculations for ETC (CPI) are quite straight-forward. 

Hence, in this post we will check on ETC (Composite), i.e., when both CPI and SPI are involved. The related assumptions and formulas are light-yellow highlighted in the above table.

Now let’s check on the questions raised in the beginning. 


Questions and Answers

Question – 1: When CPI and SPI are both considered in proportions, do the proportions together equal 1.0 or 100%? 

Answer: 
In this case, we consider giving certain weightage to CPI and certain weightage to SPI. Based on it, ETC - or as I've named ETC (Composite) - will be calculated. The actual formula is:

ETC 
= (Work Remaining)/Future cost efficiency
= (BAC – EV)/ Future cost efficiency 

When the future cost efficiency with weightage values of CPI and SPI are taken, e.g., 80% and 20% for CPI and SPI, respectively, the formula for ETC will be:

ETC 
= (BAC – EV)/ ((80% × CPI) + (20% × SPI))

Can there be other proportions? For example, can be it 60% of CPI and 10% for SPI?

This is indeed a confusing part and as Gary has rightly mentioned in the query, there is an implicit assumption, i.e., together the proportions equal 1.0 or 100%.

Yes. It can be any other proportion and it need not be 1.  

For example, considering for 60% CPI and 10% SPI, ETC will be:

ETC 
= (BAC – EV)/ ((60% × CPI) + (10% × SPI))
= (BAC - EV)/ ((0.6 × CPI) + (0.1 × SPI))

As you can see, together the proportions for CPI and SPI equal 0.7 (0.6 + 0.1), not 1.0.

Hence, it means the proportions together need not equal to 100% or 1.0. 

Question – 2: Is the non-weighed formula same as equal weighted formula for ETC (composite)?

Answer: 
The non-weighted formula is:  
ETC = (BAC – EV) / (CPI × SPI)

The equal weighted formula, on the other hand, is:
ETC = (BAC – EV) / (50% × CPI) + (50% × SPI)

Mathematically, the value of (CPI × SPI) is not equal to ((50% × CPI) + (50% × SPI)).

Example: Let’s say CPI is 0.6 and SPI is 0.8. Hence,

CPI × SPI 
= 0.6 × 0.8 = 0.48

However, if I use the weighted one, it comes as:
 (50% × CPI) + (50% × SPI)
= (50% × 0.6) + (50% × 0.8)
= (0.3) + (0.4) = 0.7

As you can see the results are different and hence the ETC values will be different. 

So, what does it mean?

It means that for the non-weighted formula of ETC, i.e., (BAC – EV) / (CPI × SPI), the future cost performance/efficiency will also be (additionally) influenced by schedule performance. It does not mean both will have equal weightage.

For example, it’s possible that a bad schedule performance in the future can impact the cost performance and add-up more cost. The reverse is also true.

On the other hand, with the weighted formula, the project manager and management team examine and take a judgement call on how much weight they want to assign to CPI and SPI. 

Again, as noted earlier, together it need not be 1 or 100%.


How to Proceed?
I agree when you take with weighted values for ETC (Composite), it creates confusion. On the other hand, the calculations for ETC (CPI) are straight. Hence, I look at it differently, while considering both ETC (Composite) and ETC (CPI). Instead of saying the formula for ETC as:

ETC 
= (BAC – EV)/ Future cost efficiency,

I would put would it as: 
[Considering both ETC (Composite) and ETC (CPI) ]

ETC 
= Inverse Performance Factor × (Work Remaining)
= Inverse Performance Factor × (BAC – EV)
= IPF × (BAC – EV)

Other than inverse performance factor (IPF), you can call it future performance factor or performance-future, performance-forecast or any other name. 

The key point note here is this: Putting "cost efficiency" or "cost performance" or only "CPI-future" in the ETC equations, gives you an an impression that only CPI and(/or) cost are involved. But it is not the case - because both CPI and SPI can be there in the case of ETC (Composite). However, going with IPF altogether removes this impression of "cost-only efficiency" or "CPI-only future performance".

Now, for non-weighted one, the value of IPF will be:

• IPF = 1/ (CPI × SPI)

For weighted one, the value of IPF will be:

• IPF = 1/ (%age × CPI) + (%age × SPI)

Important Notes on IPF:

• If IPF > 1, it is bad and ETC will be more. Hence EAC will be more.
• If IPF < 1, it is good and ETC will be less. Hence, EAC will be less.
• The concept of IPF applies both to ETC (Composite) and ETC (CPI). It does not apply to ETC (Management).

Using IPF in ETC Formulas

Next, let's apply IPF to calculate the ETC formulas. Remember when IPF is used, I'm considering both ETC (Composite) and ETC (CPI).

Assumption # 1: Future performance will be same as the past performance 

In this case, IPF = 1/CPI.

ETC 
= IPF × (BAC – EV) 
= (1/CPI) × (BAC – EV) 
= (BAC – EV)/CPI

And, EAC = AC + [ (BAC – EV)]/CPI
AC stands for actual cost.

Assumption # 2:  Future performance will be same as planned rate or budgeted rate  

In this case IPF = 1/CPI = 1/1 = 1.
ETC 
= IPF × (BAC – EV)
= 1 × (BAC – EV) 
= BAC – EV

And, EAC = AC + BAC – EV.

Assumption # 3:  Future performance will be influenced by both CPI and SPI.  

In this case, IPF = 1/(CPI × SPI).

ETC 
= IPF × (BAC – EV)
= [1/(CPI × SPI)] × (BAC – EV) 
= (BAC – EV)/(CPI × SPI)

And, EAC = AC + (BAC - EV)/(CPI × SPI)

Assumption # 4:  Future performance will be influenced by some proportion of cost performance (CPI) as well as schedule performance (SPI).  

In this case, IPF = 1/[CPI × CPI (weight) + (SPI × SPI (weight)].

ETC 
= IPF × (BAC – EV)
= [1/(CPI × CPI (weight) + SPI × SPI (weight)] × (BAC – EV) 
= (BAC – EV)/[CPI × CPI (weight) + SPI × SPI (weight)]

And EAC = AC + (BAC - EV) / [CPI × CPI (weight) + SPI × SPI (weight)]

Again, taking an example:

• If IPF is 1.2, it is bad. ETC will be more and hence EAC will be more.
• If IPF is 0.8, it is good. ETC will be less and hence EAC will be less.

Advantages with this Approach

The advantages of this approach are quite a few:

• The complexities associated with ETC formulas go away. 
• If you are calculating using a simulation software or a spreadsheet, then you just have to multiply the IPF value with the ETC value. The value of IPF can be separately set. In fact, I’ve seen project management software calculating this way for ETC and hence Estimate at Completion (EAC).
• The impression of "cost-only efficiency" or "CPI-only future performance" while calculating ETC doesn't arise. As we have seen, ETC can be ETC (Composite), ETC (CPI) and of course, ETC (Management).
• It’s easy to remember the ETC formula(s) this way. 

Conclusion
In conclusion, in the weighted/proportioned approach or in the case of ETC (composite), both CPI and SPI are can be proportioned separately and when combined, it need not be 1.0 or 100%. As we saw, the proportions for CPI and SPI, respectively, can be 50%:50%, 80%:20% or it can be 60%:10%, 60%:70%. It can also be 120%:130%!


References:
[1] Article: PMP® Prep: Calculating EAC and ETC for Forecasting, first published by MPUG.com, written by Satya Narayan Dash

[2] Book - I Want To Be A PMP, The Plain and Simple Way, 2nd Edition, by Satya Narayan Dash

[3] Book - I Want To Be A RMP, The Plain and Simple Way, 2nd Edition, by Satya Narayan Dash

[4] The Standard for Earned Value Management (EVM), 2nd Edition, by Project Management Institute (PMI).