PMP Prep: Range of Incentive Effectiveness (RIE) - How to Derive the Formulas?

We have understood the Range of Incentive Effectiveness (RIE) with the basics and the associated formulas in the earlier article. 

Now, let’s go a bit deeper and see how RIE is represented graphically in the cost-profit curve. This you need to know, before we derive the formulas for RIE. This will give you a better understanding.


The content of this article has been taken from: PMP Live Lessons – Guaranteed Pass

You can read the previous article on RIE here: 
Range of Incentive Effectiveness in Procurement Management


Cost-Profit Curve in CPIF Contracts
The cost-profit curve is widely used by Contract Administrators or Procurement Managers. This is a two-dimensional (2D) graph and pictorially shows:

• RIE (min) point,
• RIE (max) point,
• Profit or Fee (max) point,
• Profit or Fee (min) point, and of course,
• Range of Incentive Effectiveness (RIE).

The cost-profit curve for a Cost Plust Incentive Fee (CPIF) contact is depicted in the below figure. 

Range of Incentive Effectiveness (RIE): Cost-Profit Curve

As shown above, in the X-axis we have cost, whereas profit is shown in the Y-axis. At RIE (minimum) cost point, the profit is maximum or it’s Fee (max). At RIE (maximum) cost point, the profit is minimum or it’s Fee (min). These are shown in red dotted lines.

Finally, RIE – the range in which the incentive is effective – is the range between RIE (min) and RIE (max). 

The target cost is shown with blue dotted line and target cost/profit point is shown with a blue circle.The blue dotted lines are projected to X-axis giving you the target cost (TC) value and projected to Y-axis giving you the target profit (TF) value. 

Below are few key points to note by looking at the above graph:

• At RIE (min), the profit is maximum or Fee (max).
  RIE (min) in cost curve = Fee (max) in profit curve
• At RIE (max), the profit is minimum or Fee (min).
  RIE (max) in cost curve = Fee (min) in profit curve
• Target Profit or Target Fee (TF) is less than the Fee (max), but more than Fee (min).
  TF < Fee (max); TF > Fee (min)
• Target Cost (TC) is less than RIE (max), but more than the RIE (min).
  TC < RIE (max); TC > RIE (min)

With these key points, let’s derive the formulas.

Deriving RIE Formulas
First, we will check upon the formula for RIE (min).

I. Formula for RIE (min) – Cost Underrun
RIE (min) will be during cost underrun. During cost underrun, the actual cost (AC) will be less than the target cost (TC). This is obvious. Hence:

Cost Underrun is the subtraction of actual cost from target cost, i.e.,
Cost Overrun = Target Cost (TC) - Actual Cost (AC)

Now, the actual fee (AF) will be an addition to the target (TF), along with the seller’s share of cost gain because of cost underrun. This is added, because the seller performed well from cost perspective and seller is entitled to gets it extra share. 

But do note: the total fee given to the seller can NOT be more than the Fee (max).

Hence, from the seller’s perspective: 
Actual Fee (AF) = Target Fee (TF) + (Cost Underrun) × SSR
= Target Fee (TF) + [Target Cost (TC) – Actual Cost (AC)] × SSR …. [1]

We already know at RIE (min) point from the earlier graph, the fee is at maximum or it is Fee (max). This is when you project the profit it into the Y-axis of the above graph. In an equation:

Actual Fee (AF) = Fee (max) …. [2]

Also, we know at this stage actual cost (AC) is in fact the RIE (min). This is when you project the cost it into the X-axis of the above graph. In an equation:

Actual Cost (AC) = RIE (min) …. [3]

Hence, considering equation [2] and equation [3] and putting these values in equation [1], we will have:

Fee (max) = Target Fee (TF) + [Target Cost (TC) – RIE (min)] × SSR
=> Fee (max) = TF + [TC- RIE (min)] × SSR
=> Fee (max) - TF = [TC- RIE (min)] × SSR
=> [ Fee (max) – TF ] / SSR = TC- RIE (min)
=> RIE (min) = TC – ( [ Fee (max) – TF ] / SSR )

This what I mentioned in earlier piece of RIE as the formula for cost underrun.

Next, we will derive the formula for RIE (max).

II. Formula for RIE (max) – Cost Overrun 
RIE (max) will be during cost overrun. During cost overrun, the actual cost (AC) will be more than the target cost (TC). This is also obvious. Hence:

Cost Overrun is the subtraction of target cost from actual cost, i.e.,
Cost Overrun = Actual Cost (AC) - Target Cost (TC)

For the actual fee (AF), we have to subtract seller’s share ratio of cost overrun from the target fee (TF). This is subtracted, because the seller performed badly from cost perspective and seller will have to pay its share. 

But do note: the total fee given to the seller can NOT be less than the Fee (min).

Hence, from the seller’s perspective: 

Actual Fee (AF) = Target Fee (TF) – (Cost Overrun) × SSR
= Target Fee (TF) - [Actual Cost (AC) - Target Cost (TC)] × SSR …. [4]

We already know at RIE (max) point from the earlier graph, the fee is at minimum or it is Fee (min). This is when you project the profit it into the Y-axis of the above graph. In an equation:

Actual Fee (AF) = Fee (min) …. [5]

Also, we know at this stage actual cost (AC) is in fact the RIE (max). This is when you project the cost it into the X-axis of the above graph. In the equation:

Actual Cost (AC) = RIE (max) …. [6]

Hence, considering equation [5] and equation [6] and putting these values in equation [4], we will have:

Fee (min) = Target Fee (TF) - [Actual Cost (AC) - Target Cost (TC)] × SSR
=> Fee (min) = TF - [RIE (max) - TC] × SSR
=> [RIE (max) - TC] × SSR = TF – Fee (min)
=> RIE (max) - TC = [ TF - Fee (min) ] / SSR
=> RIE (max) = TC + [ (TF - Fee (min)] / SSR ] 

This what I mentioned in earlier piece of RIE (max) as the formula for cost overrun.

III. Formula for RIE

Finally, the formula for RIE will be:

Conclusion
As noted in earlier part for RIE, questions on PTA have been coming in the PMP exam for quite some time. A related concept to know is Range of Incentive Effectiveness (RIE), which is used in CPIF contracts. 

I don’t expect many questions on Range of Incentive Effectiveness (RIE) in the PMP exam. Like the concept of Point of Total Assumption (PTA), questions will be very few, if it comes. However, it is an excellent one to know and understand Procurement Management better.

You may also like:

• Range of Incetive Effectiveness (RIE) in Procurement Management
• Point of Total Assumption in Procurement (PTA) Management

References:

[1] PMP Live Lessons - Guaranteed Pass or Your Money Back, by Satya Narayan Dash

[2] PMP 35 Contact Hours Online Course - Full Moneyback Guarantee, by Satya Narayan Dash

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

[4] Project Management Body of Knowledge (PMBOK) Guide, 6th Edition, by Project Management Institute (PMI)

PMP Prep: Range of Incentive Effectiveness in Procurement Management

Recently, I wrote an article on Point of Total Assumption (PTA), which is used in Fixed Price with Incentive Fee (FPI/FPIF) contracts. 

One of the biggest misconceptions I’ve seen – PTA can surely be used in Cost Plus Incentive Fee (CPIF) – has been dispelled in the article. I’ve mentioned the reason for it. I’ve also mentioned that Range of Incentive Effectiveness (RIE) is used in Cost Plus Incentive Fee (CPIF) contracts.

Article: Point of Total Assumption in Procurement Management

Questions on PTA have been coming in the PMP exam. In a recent success story, a successful PMP mentioned questions are there on PTA in the exam. In other success stories also, PMPs have mentioned on PTA questions. Another candidate recently asked on the Range of Effectiveness (RIE). As questions on PTA (at most one or two) come, I believe it’s good to know on the RIE concept as well. If you understand PTA well, you can easily understand RIE.

Hence, this post. In this article, we will know more about RIE.


RIE Definition 
The range of incentive effectiveness in a CPIF contract can be defined as follows:

“Range of incentive effectiveness is simply the range of costs in which the incentive is effective. Below this range or above this range, the contract behaves like a Cost Plus Fixed Fee (CPFF) contract.”

In other words, below this range of incentive effectiveness (RIE), after paying a fixed fee to the seller, the buyer share is 100% and sellers share is 0%, i.e., the sharing ratio between buyer and seller is 100%:0%. Similarly, above RIE, after paying a fixed fee to the seller, the sharing ratio between buyer and seller is 100%:0%.

The fee is paid to the seller, because the contract behaves as a CPFF contract, as the previous definition informs. Also, when the CPIF contract becomes a CPFF contract, the fee for the seller becomes fixed.

If there is profit below the RIE, then this profit is taken up by the buyer, after paying the fixed fee to the seller. Similarly, if there is a loss above the RIE, then the loss is also taken by the buyer, after paying the fixed fee to the seller. This concept of RIE is displayed in the below figure.

RIE - Simplified Image, One-Dimentional (Cost)

As shown above, the RIE is basically the cost range – from a minimum RIE cost point to a maximum RIE cost point. You see, in the name itself we have the term “range”!

In case of cost underrun, the buyer takes all the share after the fixed fee of the seller is given. Similarly, during cost overrun, a fixed fee is given to the seller and the buyer has to take all the share. Remember outside RIE zone, the CPIF contract behaves as a CPFF contract!

Hence, beyond RIE, incentive has no effectiveness.

We will understand more of it with an example shortly, but first let’s understand the terms related to RIE in CPIF contracts.

I’ll also strongly recommend that you read the concepts of cost, profit, fee and incentive in the article earlier mentioned. It’s under section: “Price, Cost, Profit, Incentives”.


Terms Related to RIE
When I say terms related to RIE, I mean terms related to CPIF contracts. As noted earlier, RIE is usually the case in CPIF contracts. The terms are:

• Target Cost (TC): The amount taken by a seller to create or develop an item.
• Target Fee (TF): It is the profit taken by the seller on top of cost. It is also known as margin or fee.
• Target Price (TP): Target Price is a combination Target Cost and Target Fee. The formula for TP is Target Price (TP) = Target Cost (TC) + Target Fee (TF).
• Share Ratio (SR): This is the sharing ratio between buyer and seller, e.g., 80:20. The first percentage is for the buyer, and the second is for the seller. It means for every $1 cost overrun; 80 cents will be paid by the buyer and 20 cents by the seller.
• Buyer Share Ratio (BSR): This is the share ratio for the buyer. In the above case, the buyer share is 80%. It means for every $1 cost overrun; 80 cents will be paid by buyer. Also, for every $1 cost underrun; 80 cents will be taken by the buyer.
• Seller Share Ratio (SSR): This is obviously the difference from 100%. In the above case of 80:20, the seller share ratio is 20%. It means for every $1 cost overrun; 20 cents will be paid by seller. Also, for every $1 cost underrun; 20 cents will be taken by the seller.

As you would have noticed the terms are very similar to the ones used in Fixed Price with Incentive Fee (FPIF) contracts. Now, I’ll introduce four more related terms to understand RIE. These are particularly applicable to CPIF contracts.

• Maximum Fee or Fee (max): In CPIF contract, the fee is incentivized and the maximum fee informs the maximum amount that can be taken as a profit or fee. It is typically +3% or +4% above the target fee (TF).
• Minimum Fee or Fee (min): The minimum fee informs the minimum amount that can be taken as a profit or fee. It is typically -3% or -4% below the target fee (TF).

Both maximum and minimum fee limit is set by the buyer for the seller.

• RIE (max): This is the cost at minimum fee or Fee (min). In the range of incentive effectiveness, the cost is at its maximum point; hence simply named as RIE (max). This cost point is reached in the cost-profit curve, when the profit or fee is minimum.
• RIE (min): This is the cost at maximum fee or Fee (max). In the range of incentive effectiveness, the cost is at its minimum point; hence simply named as RIE (min). This cost point is reached in the cost-profit curve, when the profit or fee is maximum.

Do note again: in the profit-cost curve, we have the following key points.

• When cost is at RIE (min), we have Fee (max).
• When cost is at RIE (max), we have Fee (min).

With this understanding, I’ve expanded the previous figure, and showing only the cost part, in one-dimensional (1D) format.

RIE - Explanatory Image, One-Dimentional (Cost)

As shown in the above figure:

• At RIE (min), the fee is maximum. In other words, when the Fee is maximum, in the range of effectiveness, we are at RIE (minimum) cost point.
• At RIE (max), the fee is minimum. In other words, when the Fee is minimum, in the range of effectiveness, we are at RIE (maximum) cost point.

Also, the figure informs that the target cost (TC) is somewhere between the RIE (min) and RIE (max) cost points.


RIE Formulas
Now we have two RIE points – RIE (min) and RIE (max). And at RIE (min), the fee is maximum and at RIE (max), the fee is minimum.

It’s obvious that when the fee/profit is maximum, then there is cost underrun, whereas when the fee/profit is minimum, there is cost overrun.

Hence, there will be two formulas for RIE.

RIE (min) Formula – Cost Underrun
RIE (min) will be during cost underrun. The formula for RIE (min) is depicted below.

RIE (max) Formula – Cost Overrun
RIE (max) will be during cost overrun. The formula for RIE (max) is noted in the below figure.

RIE Formula
As the Range of Incentive Effectiveness (RIE) is the cost range between RIE (min) and RIE (max), obviously, the formula for RIE will be the one shown below.

Example
Let’s take an example to understand. I’ll reuse the same example given in PTA for FPIF contracts. This will make your understanding easier and also easy to solve.
An Example of RIE

Question: In a CPIF contract, the buyer and seller agreed to a cost of $300,000 and a fee (or profit) of $30,000, which is 10% of the cost. Because it’s a CPIF contract, the maximum fee is set at 13% and the minimum fee is set at 7% of the cost. The share ratio between the buyer and seller will be 60%:40%. Determine the RIE (max) and RIE (min) values, along with the range of incentive effectiveness (RIE).

Solution:
From this example, let’s find out the values.

• Target Cost (TC): $300,000
• Target Fee (TF): $30,000
• Target Price (TP): $300,000 + $30,000 = $330,000
• Sharing Ratio (SR): 60:40
• Buyer Sharer Ratio (BSR): 60% or 0.6
• Seller Sharer Ratio (SSR): 40% or 0.4
• Maximum fee or Fee (max): 13% of TC, i.e., 13% of $300,000
  Fee (max): $39,000
• Minimum fee or Fee (min): 7% of TC, i.e., 7% of $300,000
  Fee (min): $21,000

We will first calculate the case for RIE (min), which is for cost underrun.

Calculation for RIE (min)
RIE (min) = TC - [ Fee (max) – TF ] / SSR
=> RIE (min) = $300,000 – [($39,000 - $30,000)] / 0.4           40% is 0.4
= $300,000 – [$9,000]/0.4
= $300,000 – $22,500
= $277,500

Next, let’s calculate the case for RIE (max), which is for cost overrun.

Calculation for RIE (max)
RIE (max) = TC + [ (TF - Fee (min)] / SSR ]
=> RIE (max) = $300,000 + [($30,000 - $21,000)] / 0.4           40% is 0.4
= $300,000 + [$9,000]/0.4
= $300,000 + $22,500
= $322,500

Calculation for Final RIE
Hence RIE = RIE (max) – RIE (min) = $322,500 - $277,500
RIE = $45,000


Conclusion
In this range of incentive effectiveness, i.e., $45,000, the CPIF contract is effective. Beyond this range – above RIE (max) of $322,500 or below RIE (min) of $277,500 – the CPIF contract no longer behaves like an incentivized contract. Rather, it behaves like a CPFF contract.

For the PMP exam, you need to know these basics to answer questions. The questions are most likely to be direct in nature for RIE and for that you need to just remember the formulas. Sometimes the questions can be a bit tricky, e.g., it might give you just the Fee (max) and Fee (min) values and you will be asked to calculate RIE.

You may also like:

• Range of Incentive Effectiveness - How to Derive the Formulas?
• Point of Total Assumption in Procurement (PTA) Management

References:

[1] PMP Live Lessons - Guaranteed Pass or Your Money Back, by Satya Narayan Dash

[2] PMP 35 Contact Hours Online Course - Full Moneyback Guarantee, by Satya Narayan Dash

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

[4] Project Management Body of Knowledge (PMBOK) Guide, 6th Edition, by Project Management Institute (PMI)

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

I received this question from one of my readers. 

*****

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

*****

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).