For a Project Manager and especially for a PMP, Earned Value calculations are not new. Almost all of us know about the estimate forecasts and we utilize these calculations in our projects all the time. The most commonly used formula to calculate Estimate At Completion is
EAC=BAC/CPI
Unfortunately, this computation is not that simple. For every scenario and level of accuracy we may have to use a different formula. PMI in its standard PMBOK Guide 4th and 5th Editions gives a number of formula to compute EAC with barely enough explanation and reasoning, as follows:-
EAC=BAC/CPI, if CPI is expected to be same for the remainder of the project
EAC=BAC/CPIC, if cumulative CPI is expected to be same for the remainder of the project
EAC=BAC/(CPIxSPI), if cumulative effect of CPI and SPI is likely to affect remainder of the project
EAC=BAC/(0.8xCPI+0.2xSPI), if a ratio of CPI and SPI is collectively likely to affect remainder of the project
EAC=AC+BAC-EV, if future work will be accomplished at the planned rate
EAC=AC+Bottom-up ETC, if the initial plan is no more valid
EAC=AC+((BAC-EV)/CPIC), probably the best ever way to find EAC
EAC=AC+((BAC-EV)/(CPIxSPI)), if both CPI and SPI affect the remainder of the work
EAC=AC+((BAC-EV)/(CPICxSPIC)), If cumulative values CPIC and SPIC affect remainder of the work
EAC=AC+((BAC-EV)/((0.8xCPIC)+(0.2xSPIC))), if remainder of the work is affected by CPIC and SPIC in a specific ratio like 80:20
How can you predict the Estimated Duration of the project, looking at past Earned Value variables?
There are at least three methods.
Simplest way would be to divide the project duration with SPI.

Estimated Time for Completion = EtAC= Total Planned Duration / SPI

But it might be important to do trend analysis and try the impact of cumulative SPI if you have a history of varied performances.

Cumulative SPI or SPIC= (EV1+EV2+....+EVn)/(PV1+PV2+....+PVn)
So your Estimated Time = EtAC = BAC/SPIC

If you want to be further accurate about your estimated duration then find the estimated time to do the remaining work first.

Estimated Time to complete Remaining Work = EtTC = (BAC-EV)/SPIC
Estimated Time for Completion of the Project = EtAC = Time Spend so far + EtTC

Another dimension and the most accurate method to calculate the Estimated Time for Completion of the Project would be to translate the effect on time axis graphically.

New Perspectives from Bayesian Approach
Refer to the Research Paper "A Bayesian Approach to Improve Estimate at Completion in Earned Value Management" by Fanco Caron, Fabrizio Ruggeri and Alessandro Merli in Project Management Journal of Feb 2013.

The research mostly agrees with what we have already discussed with a little bit more and better explanation and reasoning. They have also justified a progressive CPI and SPI which is the basis of their research.

I will once again list down various methods in order of importance from lowest to highest, with the reasoning given in this research paper. According to the paper, two new terms are introduced SAC (Schedule At Completion) and SCI (Schedule Cost Index) = CPI x SPI. Remember EtAC means Estimated time at Completion.

Ordered List of Methods
APPLICATION OF AUTOMATIC ADJUSTMENT
Method 1. EAC=BAC & EtAC=SAC
There will be NO effect of cost and schedule variances or performance indices as deviations registered during the project will be absorbed by suitable corrective measures. Whatever has gone well or wrong will be automatically adjusted and the overall project will complete as per original plan.

VARIANCES
Based on the Cost and Schedule variances, we can predict EAC (Estimate at Completion), considering there will be no more variances in the project.
CV = EV-AC
SV = EV-PV
APPLICATION OF VARIANCES

Method 2. EAC=BAC-EV & EtAC=SAC-SV
The deviations CV and SV reported at any point in time will not affect the rest of the project. Whatever has gone well or wrong will not be repeated and the rest of the project will go as per plan.

INDICES
In the previous two methods, there was no application of any indices and EAC was calculated based on no change in the plan. In earned value calculations we have two indices CPI (Cost Performance Index) and SPI (Schedule Performance Index).
CPI=EV/AC & SPI=EV/PV
Sometimes we used the combined or joint effect of these two indices together and for that a new index has been developed SCI (Schedule Cost Index) which is simple multiplication if these two indices CPI and SPI.
SCI=CPIxSPI

APPLICATION OF INDICES ON WHOLE PROJECT
Method 3. EAC=BAC/CPI & EtAC=SAC/SPI
The indices CPI and SPI reported at a point in time will remain constant until project completion. Whatever has gone well or wrong at the point of taking the readings, will be repeated for the whole project.

Method 4. EAC=BAC/SCI=BAC/(CPIxSPI) & EtAC=SAC/SCI=SAC/(CPIxSPI)
The joint effect of cost and schedule performance will be considered in calculating the estimate at completion. Whatever has gone well or wrong in cost and schedule performance at the point of taking the readings, will be jointly affecting the whole project.

CUMULUTAIVE INDICES
As the current vale of CPI and SPI may not be a true representative of all past performances and therefore cannot be applied squarely to predict future, therefore cumulative indices CPIC (Cost Performance Index Cumulative) and SPIC (Schedule Performance Index Cumulative) were to be found.
CPIC=((EV1+EV2+....+EVn)/(AC1+AC2+....+ACn))
SPIC=((EV1+EV2+....+EVn)/(PV1+PV2+....+PVn))

As we will require some new variables for calculating EtAC (Estimated Time At Completion), following terms are introduced here:-
TN= Time Now
ES= Earned Schedule

APPLICATION OF CUMULATIVE INDICES ON REMAINING WORK

Method 5. EAC=AC+(BAC-EV)/CPIC
where CPIC=((EV1+EV2+....+EVn)/(AC1+AC2+....+ACn))

& EtAC=TN + (SAC - ES)/SPIC
where TN= Time Now, ES= Earned Schedule, and
SPIC=((EV1+EV2+....+EVn)/(PV1+PV2+....+PVn))

Future performance significantly differs from past performance so remaining work is affected by cumulative performance indices. The trend of whatever indices we historically had on this project will be projected on the rest of the project.

Method 6. EAC=AC+(BAC-EV)/(CPICxSPIC)
where CPIC=((EV1+EV2+....+EVn)/(AC1+AC2+....+ACn))
and SPIC=((EV1+EV2+....+EVn)/(PV1+PV2+....+PVn))

& EtAC=TN + (SAC - ES)/(CPICxSPIC)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of cumulative performance indices. The joint trend of whatever indices we historically had on this project will be projected on the rest of the project.

Method 7. EAC=AC+(BAC-EV)/(0.8xCPIC+0.2xSPIC)
where CPIC=((EV1+EV2+....+EVn)/(AC1+AC2+....+ACn))
and SPIC=((EV1+EV2+....+EVn)/(PV1+PV2+....+PVn))

& EtAC=TN + (SAC - ES)/(0.8xCPIC+0.2xSPIC)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of cumulative performance indices CPIC:SPIC in the ratio of 80:20. The joint trend of whatever indices we historically had on this project will be projected on the rest of the project on the 80:20 ratio. The ratio could be altered to 70:30, 60:40 or whatever combination.
CURRENT CUMULATIVE INDICES
To further make the forecast more accurate, it was analysed that the cumulative indices do represent all the previous periods but still last few periods are more predictive of future performance than the older records. Therefore indices CPIcc (CPI Current Cumulative) and SPIcc (SPI Current Cumulative) were introduced.
CPIcc=((EVn+EV(n-1)+EV(n-2)/(ACn+AC(n-1)+AC(n-2)))
SPIcc=((EVn+EV(n-1)+EV(n-2))/(PVn+PV(n-1)+PV(n-2)))

These indices take into account the latest 3 or 4 periods and no further backwards. The calculations here show only three periods but they could be extended to more periods.
APPLICATION OF ONLY CURRENT CUMULATIVE INDICES ON REMAINING WORK

Method 8. EAC=AC+(BAC-EV)/CPIcc
where CPIcc=CPI Current Cumulative
CPIcc=((EVn+EV(n-1)+EV(n-2)/(ACn+AC(n-1)+AC(n-2)))

& EtAC=TN + (SAC - ES)/SPIcc
where TN= Time Now, ES= Earned Schedule, and SPIcc = SPI Current Cumulative
SPIcc=((EVn+EV(n-1)+EV(n-2))/(PVn+PV(n-1)+PV(n-2)))

Future performance significantly differs from past performance so remaining work is affected by current cumulative performance indices. The trend of latest indices we had on this project will be projected on the rest of the project.

Method 9. EAC=AC+(BAC-EV)/(CPIccxSPIcc)
where CPIcc=((EVn+EV(n-1)+EV(n-2)/(ACn+AC(n-1)+AC(n-2)))
and SPIcc=((EVn+EV(n-1)+EV(n-2))/(PVn+PV(n-1)+PV(n-2)))

& EtAC=TN + (SAC - ES)/(CPIccxSPIcc)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of current cumulative performance indices. The joint trend of latest indices we had on this project will be projected on the rest of the project.

Method 10. EAC=AC+(BAC-EV)/(0.8xCPIcc+0.2xSPIcc)
where CPIcc=((EVn+EV(n-1)+EV(n-2)/(ACn+AC(n-1)+AC(n-2)))
and SPIcc=((EVn+EV(n-1)+EV(n-2))/(PVn+PV(n-1)+PV(n-2)))

& EtAC=TN + (SAC - ES)/(0.8xCPIcc+0.2xSPIcc)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of current cumulative performance indices CPIcc:SPIcc in the ratio of 80:20. The joint trend of latest indices we had on this project will be projected on the rest of the project on the 80:20 ratio. The ratio could be altered to 70:30, 60:40 or whatever combination.

PROGRESSIVE INDICES

To be on the cutting edge, we can use the progressive indices, just taking into account the current and last values. Apply following values of CPIp (CPI Progressive) and SPIp (SPI Progressive)

These progressive indices contribute towards formulating Bayesian Approach, establishing a monthly trend.

APPLICATION OF P|ROGRESSIVE INDICES ON REMAINING WORK

Method 11. EAC=AC+(BAC-EV)/CPIp
where CPIp=CPI Progressive
CPIp=(EVn-EV(n-1))/(ACn-AC(n-1))

& EtAC=TN + (SAC - ES)/SPIp
where TN= Time Now, ES= Earned Schedule, and SPIp = SPI Progressive
SPIp=(EVn-EV(n-1))/(PVn-PV(n-1))

Future performance significantly differs from past performance so remaining work is affected by current and last performance indices. The trend of latest two indices we had on this project will be projected on the rest of the project.

Method 12. EAC=AC+(BAC-EV)/(CPIpxSPIp)
where CPIp=(EVn-EV(n-1))/(ACn-AC(n-1))
and SPIp=(EVn-EV(n-1))/(PVn-PV(n-1))

& EtAC=TN + (SAC - ES)/(CPIpxSPIp)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of last two performance indices. The joint trend of latest two indices we had on this project will be projected on the rest of the project.

Method 13. EAC=AC+(BAC-EV)/(0.8xCPIp+0.2xSPIp)
where CPIp=(EVn-EV(n-1))/(ACn-AC(n-1))
and SPIp=(EVn-EV(n-1))/(PVn-PV(n-1))

& EtAC=TN + (SAC - ES)/(0.8xCPIp+0.2xSPIp)
where TN= Time Now, ES= Earned Schedule, and

Future performance significantly differs from past performance so remaining work is affected by the joint effect of last two performance indices CPIp:SPIp in the ratio of 80:20. The joint trend of latest two indices we had on this project will be projected on the rest of the project on the 80:20 ratio. The ratio could be altered to 70:30, 60:40 or whatever combination.

APPLICATION OF GRAPHICAL METHOD FOR EtAC
Method 14. The most accurate method to calculate the EtAC (Estimated Time for Completion) of the Project would be to translate the effect on time axis graphically.

On the Cost baseline graph, draw a line originating from the current EV horizontally to the cost baseline. It would be backwards if you are ahead of schedule and forwards if you are behind schedule. Record the exact point on cost baseline where the line intersects it and draw a line perpendicularly downwards to see the exact time when this much work should have been completed. Note the difference between this point and the current time, call it x. You are this much behind or ahead of schedule in terms of time. Time which has so far been spent, call it y, and the total planned time for the project, call it z. Now find if you are x time behind/ahead of schedule in y time then how much behind/ahead of schedule you would be for z time? This will give you a time duration which if added/subtracted from the total planned time of the project (z) would give you EtAC.

I think this pretty much concludes the discussion on ESTIMATE-AT-COMPLETION.

To calculate EtAC (Estimated Time At Completion), we have similarly deduced methods but the difference would be another dimension and that is graphics. I will try to put them all together for the next topic of discussion. Saving Changes...

Bala S DuvvuriProject Manager| ShellBangalore, Karnataka, India

I never knew that these many formulas are there in EV.Thanks for sharing. Saving Changes...

Howard LaiBEng, MEng, MSc, CEng, CPEng, NER, IntPE(Aust), MIET, PMP, CSSBB, CISA, ISO9001| AWBrisbane, Queensland, Australia

Good explanation and a quick reference for PM work. Thanks! Saving Changes...