To Complete Performance Index (TCPI) and Cost Performance Index (CPI) - Part 1

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Last month in a PMP session, on "To Complete Performance Index (TCPI)", a number of questions came forward. Some of them are: 

• What exactly is TCPI?
• When will be the Budget At Completion (BAC) be used and/or when will be the Estimate At Completion (EAC) will be used?
• Is it that when TCPI is less than 1, it means good and vice versa?
• What is its relationship with Cost Performance Index (CPI) in performance measurement? 
• What it has got to do with other calculations such as Net Present Value (NPV), Internal Rate of Return (IRR) etc.?

These were all discussed in the session. Here in addition, I'll share some more insight into TCPI and CPI. I'll also show with a simple example how a software (MS Project 2013) handles CPI and TCPI. 

1. The Fundamentals - TCPI and CPI:

To Complete Performance Index (TCPI) is used in Earned Value Measurement (EVM). It is one of the common indices used along with Schedule Performance Index (SPI) and Cost Performance Index (CPI) in EVM. To understand very quickly on SPI and CPI, I have given a simple example, which is available here (What is the Health of Your Project.)

Simply put, TCPI is a a future performance measurement for your project based on your past performance, whereas CPI is current performance measurement based on the project's past performance.  TCPI is a forecasting technique, where as CPI is a budgetary measurement or cost efficiency measurement technique. 

With CPI you can ask: Is my project within budget or is my project over budget? How is the project doing with respect to spent cost so far? With TCPI, you can ask: What performance level has to be achieved on the remaining work in order to meet the financial commitment - going forward? Both TCPI and CPI are used in EVM. When used together they are indeed very powerful in project-portfolio management. 

Note: Earned Value Measurement (EVM) is with respect to your defined baseline and your status date. Without baseline, you are not measuring anything. And in EVM, your measurement is "now" - on the status date. Re-read the just completed para again - it is important!

Mathematically put:
TCPI =  "Work Remaining"/"Funds Remaining",
 whereas, 
CPI = "Work Done"/"Funds Spent"

Now, Work Remaining = Total Work Planned - Work Done, where work done is as on the status date.
Similarly, Funds Remaining = Total Budget Planned - Funds Spent, where funds spent is again on the status date.

Total Work Planned = Budget At Completion (BAC)
Work Done = Earned Value (EV)
Hence, work remaining = BAC - EV

Total Budget/Funds Planned = Budget At Completion (BAC)
Funds Spent = Actual Cost (AC)
Hence, funds remaining = BAC - AC

Considering these, the formula for TCPI comes as: 
TCPI = (Budget At Completion - Earned Value) / (Budget At Completion - Actual Cost) 
           = (BAC - EV)/ (BAC - AC)
CPI    = (Earned Value) / (Actual Cost) 
           = (EV) / (AC) 

Both CPI and TCPI are Indices, and hence the values will be one of these - "1" or "< 1" or "> 1".

Cost Performance Index is a measure of the value of work completed compared to the actual cost incurred. It is the cost efficiency of the project till date, i.e., with respect to the status date - the day on which you are measuring.

For CPI:
 - If less than one means bad. (i.e., You are over budget)
 - If more than one means good. (i.e., You are under budget)
 - If equal to one means you are on budget. (i.e., Your funds spent is perfectly alright or you are on budget)

It is depicted in the figure below.

Figure - Cost Performance Index 

CPI at a project level becomes cumulative CPI, which in plain terms is the add-up values of CPI for individual activities or work packages that you are measuring fully at a project level. 

For TCPI:
 - If less than one means good. (i.e., It is easier to complete)
 - If more than one means bad. (i.e., It is harder to complete)
 - If equal to one means it is perfectly alright. (i.e., It is same to complete)

Mark the words - for CPI while I am saying over or under budget; for TCPI, I am saying it is easier or harder to complete. 

So, how and where TCPI and CPI help? Here it is. 
Say you have a cumulative CPI of 0.5 and TCPI is coming at 1.5. It means based on your past performance, you are getting 50 cents for every $1 spent. But going forward, to meet the financial commitment, you need to have $1.5 in return for every $1 spent.  Now, that is highly unlikely. At best you can have 80 or 90 cents return, going forward. It means  you need to have a index of value 0.8 or 0.9 to meet your goal. 

This is also where the formula for TCPI changes - when your cumulative CPI has fallen below the baseline. Now your BAC (the budget that has been planned, authorized and baselined), as shown in the above data, is not going to help you, as your project's current cost performance (CPI) is low.  And as we saw, the predicted TCPI is difficult to achieve. Hence, EAC - the Estimate At Completion - is the new viable one. Once it is approved, EAC becomes the cost performance goal  in place of BAC. Simply put, EAC is your new baseline, once approved. 

Here, the formula for TCPI will be:
TCPI = (Work remaining) / (Funds Remaining) = (BAC - EV) / (EAC - AC)

It is depicted in the figure below.

Figure - To Complete Performance Index
(Reference Source: PMI-PMBOK Guide 5th Edition)

2. An Example:

Let me take a simple example. You have 2 tasks each taking 2 days and executed by two resources - say R1 and R2. For each day, you are paying $100 to the resources. After 1 day, you are checking the status. As you are measuring at the end of 1 day, it is your status date. This is what you found:

Status For Task - 1:
- 1 day over. But R1 needs 2 more days.
- So the total duration now becomes 3 days. There is an increase of 1 day. 
Status For Task - 2:
- 1 day over. But R2 needs 0.75 day more.
- So, the total duration becomes 1.75 days. There is a reduction of .25 day.

Now quickly, let us check the EVM related metrics. 

TCPI and CPI For Task -1:

• BAC = Budget At Completion (This is what you planned when you started) = 2 days * $100 = $200
• EAC = Estimate At Completion (This is going to be your new estimate) = $300 (as resource R1 is now taking 1 day more)
• PV = Planned Value (when you started off, what you have planned by end of 1 day) =  % Planned Complete * BAC = 1/2 * $200 = $100
• AC = Actual Cost (what is the money spent as on today) = $100
• EV = Earned Value (what you have actually done till end of 1st day) = % Actual Complete * BAC = 1/3 * BAC = 1/3 * $200 = $66.67 

What is the value of CPI?
CPI = Earned Value/Actual Cost = EV/AC = 0.67

What is the value of TCPI?
TCPI = (BAC - EV)/ (BAC-AC) = ($200 - $66.67) / ($200 - $100) = 1.33

But this TCPI value is no longer to be used, as CPI has fallen below the baseline. In other words, going from 0.67 to 1.33, as explained earlier, is going to be a tough one - harder to complete.  So, EAC has to be new approved one and on that we will calculate the TCPI.

So the TCPI, for this over budget task will be:
TCPI = (BAC-EV)/(EAC-AC) = ($200 - $66.67) / ($300 - $100) = 0.67

So, for the first time, TCPI and CPI will match. And it must be noted that TCPI is not the inverse of CPI, i.e., 1/CPI. Also, TCPI is not (1-CPI).

TCPI and CPI For Task -2:

• BAC = Budget At Completion (This is what you planned when you started) = 2 days * $100 = $200
• EAC = Estimate At Completion (This is going to be your new estimate) = $175 (as resource R2 is now taking 1.75 days in total)
• PV = Planned Value (when you started off, what you have planned by end of 1 day) =  % Planned Complete * BAC = 1/2 * $200 = $100
• AC = Actual Cost (what is the money spent as on today) = $100
• EV = Earned Value (what you have actually done till end of 1st day) = % Actual Complete * BAC = 1/1.75 * BAC = 1/1.75 * $200 =  $114.28 

What is the value of CPI?
CPI=Earned value/Actual Cost = EV/AC = 1.14

What is the value of TCPI?
TCPI = (BAC - EV)/ (BAC-AC) = ($200 - $114.28) / ($200 - $100) = 0.86

Here, for Task-2, the first formula of TCPI with BAC is used, unlike for Task-1 where the EAC related formula is used.

3. A Set of Questions and Answers:

When I started  this post, I noted on certain questions. Let me address the answers here, now that it has been discussed:

1. Can TCPI be 0? Yes it can be. When you have not baselined, the value will be 0.
2. Can TCPI be 1? Yes it can. When you baseline first time and before tracking, the value is 1. At this point, the BAC and EAC are same.
3. Is TCPI the reverse of CPI? No. We have seen that.
4. Is TCPI the value is -> 1-CPI? No. We have seen that. 
5. Has TCPI anything to do while we measure NPV or IRR? No. TCPI is a performance measurement or forecasting technique based on money you have to spend, where as NPV or IRR drives investment decisions, based on the value you are going to get. 

Next with a software tool, which you will use in real life as a project or portfolio manager.

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