In the previous post, I covered the formulas that cover those quantities dealing with the forecasting of the project’s cost at the completion of the project. As a review, here is the definition of the relevant terms.
1. Review of BAC, EAC, VAC, ETC
Figure 1. Definitions of BAC, EAC, VAC, and ETC.
Quantity  Formula  Definition 
Budget at Completion (BAC)  (Related to PV)  Authorized budget amount of the total project, i.e. what the project was supposed to cost 
Estimate at Completion (EAC)  (several formulas)  Estimated cost of the project at completion, i.e., what the project is now expected to cost 
Variance at Completion (VAC) 
BAC – EAC  The difference between what the project was supposed to cost (BAC) and what is now expected to cost (EAC).

Estimate to Complete (ETC)  EAC – AC  How much more it is estimated it will cost to complete the project, i.e., the difference between what the total project is now expected to cost (EAC) and how much it has cost until now (AC). 
Here are the formulas for VAC and ETC, which are simply derived from the simple definition of what they mean.
Figure 2. Formulas for VAC and ETC (via definition)
Variance at Completion (VAC)  VAC = BAC – EAC 
Estimate to Complete (ETC)  ETC = EAC – AC 
Here are the various formulas for EAC, which vary depending on the REASON for the variance from the budget at completion or BAC.
Figure 3. Formulas for EAC (based on reason for variance from schedule and/or budget)
Formula No. 
Formula 
Formula Name 
Formula Explanation 
1 
EAC = AC + ETC 
New estimate 
ETC is new bottomup estimate

2 
EAC = AC + (BAC – EV) 
Original estimate 
Reason for variance is onetime occurrence

3 
EAC = AC + (BAC – EV)/CPI Or EAC = BAC/CPI

Performance estimate low 
Reason for cost variance will continue at same rate 
4 
EAC = AC + (BAC – EV)/CPI*SPI 
Performance estimate high 
Reason for cost variance will continue and effect schedule performance as well 
.
2. To Complete Performance Index–concept
The formulas I will discuss in this post are those for the To Complete Performance Index or TCPI.
First, a minireview of the formulas so far.
a. PV, EV, and AC tell us about the project NOW. It is like giving a snapshot of where we are.
b. CV, SV, CPI, and SPI tell us whether we are behind/ahead of schedule, and under/over budget NOW. They compare where we are compared to where we are supposed to be.
c. BAC and EAC tell us where we are supposed to be and where we WILL be at the end of the project, respectively. The latter has several formulas that can be used to derive it depending on the reason for our deviance from the place we are supposed to be.
Now, finally the TCPI tells us the following: given where we are now, how will we have to perform with regards to costs in order to be AT BUDGET by the time the project is done?
Think of an analogy. You’re supposed to go from St. Louis to Chicago along a route that has a 65 mph speed limit. You calculate that it will take 5 hours to get there if you drive nonstop at that speed limit. You get halfway there and you realize that, according to records of the time and the mileage actually driven, that you have been going an average of 55 mph speed limit, 10 mph BELOW the speed limit.
How fast will you have to drive the second half of the way in order to get there within the 5 hour projected time? Well, you will have to go 10 mph ABOVE the speed limit for the AVERAGE to equal 65 mph over the entire length of the trip. This is what TCPI tells you for project management.
3. To Complete Performance Index—formula
There are two formulas for the TCPI:
i. Based on the budget at completion (BAC)
TCPI = (BAC – EV)/(BAC – AC)
ii. Based on the estimate at completion (EAC)
TCPI = (BAC – EV)/(EAC – AC)
Rather than memorizing these formulas as collections of random letters, let us understand the quantities in them.
(BAC – EV) is a familiar term from the formulas for EAC, namely the remaining budget. (BAC – AC) is a similar term which represents not the remaining budget, but since it uses AC, it is the remaining cost as per budget. If we substitute EAC for BAC, we get (EAC – AC) or the remaining cost as per estimate.
TCPI in formula i. is thus the remaining budget divided by the remaining cost as per budget.
TCPI in formula ii. is thus the remaining budget divided by the remaining cost as per estimate.
Here is a diagram showing the different quantities we have covered in all of the formulas to show how they relate to each other. Those in BLUE are budgeted values, , those in GREEN deal with the actual costs, and those in YELLOW are estimated values.
Project  START 
NOW 
END 

Budget  ß 
PV 
à 

ß  BAC 
à 

ß EV à  
ß 
BAC – EV 
à 

(remaining  budget)  
Actual  ß 
AC 
à 
ß BAC–AC à  
(remaining costs as per budget)  
ß 
EAC–AC 
à 

(remaining costs as per estimate)  
Estimate 
ß  EAC 
à 

ß 
ETC 
à 

ßVACà 
4. TCPI—example
Okay, let’s use a scenario from a previous post and calculate TCPI to see what it’s significance is in this example.
Scenario 1: Let’s say you are a contractor that gets the job of painting the outside of the Pentagon. Your company can finish each side in a single day at a cost of $10,000 per day. The total budget for the project is 5 X $10,000 = $50,000. (Assume that you are painting one side at a time, waiting for one side to dry before going on to the next.)
At the end of day 4, only three walls are completed. The amount spent by your company to accomplish the work so far comes to $30,000. Assume that the reason for being overbudget and behind schedule will continue until the end of the project.
a. What are PV, EV, and AC?
PV = $40,000, EV = $30,000, and AC = $40,000.
b. What are CV, SV, CPI, and SPI?
CV = EV – AC = $30,000 – $40,000 = $10,000
SV = EV – PV = $30,000 – $40,000 = $10,000
CPI = EV/AC = $30,000/$40,000 = 0.75
SPI = EV/PV = $30,000/$40,000 = 0.75
c. What is BAC?
BAC = $50,000, the total budgeted amount of the project at completion.
d. What is EAC?
First of all, you need to figure out which formula to use for EAC. We are told in the scenario that the COST and SCHEDULE variance will continue to the end of the project, so formula 4 is the most appropriate. Here’s the calculation, using the values derived in a, b, and c above.
EAC = AC + (BAC – EV)/(CPI * SPI) = $40,000 + ($50,000 – $30,000)/(0.75)(0.75)
= $40,000 + ($20,000)/(0.75)(0.75) = $40,000 + $35,556 = $75,556.
e. What is TCPI? (based on BAC)
According to formula i.
TCPI = (BAC – EV)/(BAC – AC) = ($50,000 – $30,000)/($50,000 – $40,000) = $20,000/$10,000 = 2.0
This means that, based on the BAC or budget at completion, we would have to go from a cost performance index of 0.75 which is where we are now, and increase it to 2.0 from now until the rest of the project in order to get to the end of the project WITHIN THE BUDGET.
This makes sense in that we would have to have good cost performance from now until the end of the project in order to make up for the poor cost performance up until now.
This concludes the discussion of these formulas. They are not in the “cheat sheet” handed out by the PMIOC chapter for its PMP exam prep class because they are considered too elaborate to be on the test. I include them for completeness sake so you can understand where they come from.
The next and last post deals with some other random formulas from various areas of knowledge other than cost (i.e., not earned value analysis).
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Hi, thanks for great guide, but not clear why:
AC = $40,000 in a.
According to your statement before “The amount spent by your company to accomplish the work so far comes to $30,000.”