# Project Management Central

ETC calculation including SPI
 Network:27
Hello!

PMBok (page 221) mentions two formulas for estimation ETC:

(1) ETC = (BAC-EV) / CPI
(2) ETC = (BAC-EV) / (CPI * SPI)

While (1) is completly clear for me, I don't understand the motivation for including SPI in (2).

Assuming that we can proportionall reduce task duration by adding resources [ money / duration ] , i would expect the total remaining cost [ money / duration ] * [duration] to stay constant.

If the process cannot be speeded by additional resources due to its nature I don't see a point in adding resources.

So basically I don't see why in this case the factor time should be included in the ETC calculation. CPI = EV/AC, this definition is independent if we are ahead or behind shedule. And extrapolation should be indepentently if we increase burn rate or not.
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 Network:406
Any time you add resources to a project it increases the cost. Unless you are compressing the schedule, the duration won't change. For example, if the duration of an activity is 25 days and takes one person to finish the task, it won't matter if you add 2 more people to the task. It will still take 25 days.
However, if you want to include the SPI into the ETC, the second formula could be used especially when that 25 day duration is behind at 35 days, for example.
I think the second formula could be more useful for projects where clients demand delivery in 6 months or maybe the stakeholders and clients are utilizing phase gates and time is the standard measurement.
 Network:27
Dear Ed,

Sorry I cant follow your arguments. I understand that some activites cannot be crashed by adding resources. However why should I as PM should than add resources?

Secondly, a bad SPI might be easily comensated when you are at the beginning of a project. However if you are close to the end of a project it needs much more corrective action to fix it. Assume you have a 100 day activity. After 10 days a SPI of 0.8 would mean 2.5 days of delay which might be not too critical. After 95 days the same SPI would mean a delay of 23,75 day, which cannot be compensated in the remaining 5 days.

Regards, Bernd
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1 reply by Sungjoon Park
Apr 20, 2017 3:12 AM
Sungjoon Park
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I generally agree with you in case that it is applicable only in one activity because we do generally decompose up to the activity level. However, your argument is not applicable over activity level. Some activities of higher value can be finished within shorter period of time without any measures to reduce time.
 Network:252
First, your 1) is not a correct formula because it is not clear of planned value which has been completed or of remaining work to be dome at the time of estimation so that the ETC should be calculated as indicated in PMBOK:
EAC= BAC/CPI, ETC= EAC-AC= BAC/CPI-AC.

Second, the SPI is not fully time related factor by definition but should be seen scope associated, which is more like an emphasis of planned value (scheduled scope to be done) so that if actual work ( earned value) was far from planned work (planned value) regardless of actual cost incurring from the work done, the SPI might be practically considered when you calculate the ETC. See an example below:

1) PV= 50
2) BAC=100
3) AC= 32
4) EV=35

CPI= 1.097 (Cost favorable but unknown whether or not the planned scope of work has been completed by the time of estimation)
SPI= 0.7 (Far behind schedule against planned scope of work to be completed by the time of estimation)

In case of CPI only applicable, the EAC= BAC/CPI, 100/1.097= 91.16, seems to be over-optimistic without consideration of delayed scope of work which was scheduled to be done (if scope(s) is (are) not omitted or changed). And ETC= EAC-AC=91.16-32=58.84 in which it might be hard to see inclusion of the delayed scope of work at the time of estimation.

If both CPI and SPI are used, simply 50:50 ratio, an ETC is (100-35)/(1.097*0.7), approx. 84.65 and EAC= 32+84.65=116.65, seems to be more practical than vale of 91.16, considering the lack of previous performance of scope of work (activities or whatever called).
 Network:252
Apr 20, 2017 1:48 AM
Replying to Bernd Brier
...
Dear Ed,

Sorry I cant follow your arguments. I understand that some activites cannot be crashed by adding resources. However why should I as PM should than add resources?

Secondly, a bad SPI might be easily comensated when you are at the beginning of a project. However if you are close to the end of a project it needs much more corrective action to fix it. Assume you have a 100 day activity. After 10 days a SPI of 0.8 would mean 2.5 days of delay which might be not too critical. After 95 days the same SPI would mean a delay of 23,75 day, which cannot be compensated in the remaining 5 days.

Regards, Bernd
I generally agree with you in case that it is applicable only in one activity because we do generally decompose up to the activity level. However, your argument is not applicable over activity level. Some activities of higher value can be finished within shorter period of time without any measures to reduce time.
 Network:27
I agree with:
ETC= EAC-AC= BAC/CPI-AC

Since: CPI = EV / AC
AV = EV / CPI

ETC= BAC/CPI-AC = BAC/CPI - EV / CPI = (BAC -EV) / CPI

In both formulations, yours and mine there is no need to implement SPI. Because in my understanding SPI is no relevant input factor. So I' supprised to find it in Formula (2)
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1 reply by Sungjoon Park
Apr 20, 2017 3:20 AM
Sungjoon Park
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You're right Bernd.
 Network:252
Apr 20, 2017 3:15 AM
Replying to Bernd Brier
...
I agree with:
ETC= EAC-AC= BAC/CPI-AC

Since: CPI = EV / AC
AV = EV / CPI

ETC= BAC/CPI-AC = BAC/CPI - EV / CPI = (BAC -EV) / CPI

In both formulations, yours and mine there is no need to implement SPI. Because in my understanding SPI is no relevant input factor. So I' supprised to find it in Formula (2)
You're right Bernd.
 Network:27
In the standard "Practice Standard for Earned Value Management" (download for PMI memebers) i have found some additional formulations. E.G.:

(3) ETC = (BAC-EV) / (0.8 CPI + 0.2 SPI)

Seems like, there is some alchemie involved in these estimations.
 Network:785
The formula on page # 221 of the PMBOK Guide is for EAC. Look at the table on page # 224 for all of the equations.

PMBOK Guide Formula: ETC = EAC-AC
EVM Practice Standard: Statistical ETC = (BAC-EV)/CPI

The statistical ETC accounts for efficiency-to-date measured by the CPI.

Just to make things more confusing, if both the CPI and SPI influence the remaining work, you could use ETC = (BAC-EV)/(CPI*SPI). The multiple formulas for EAC create problems the likes of which remind me of a common complaint in higher level math classes - I'm never going to use this in the real world. If only I had known...
 Network:60
There are more ETC estimates possible than the two mentioned in the PMBok, I can think of these five:

ETC1=(BAC-EV)
ETC2=(BAC-EV)/CPI
ETC3=(BAC-EV)/SPI
ETC4=(BAC-EV)/CPI*SPI
ETC5=(BAC-EV)/(w*SPI+(1-w)*CPI)

Where ETC can be used to calculate the EAC=AC+ETC and:

CPI=EV/AC,
SPI=EV/PV.

I find EAC useful for reporting and budget control.

ETC1 is the simplest ETC you devise; it is the remaining budget minus the (total) EV, so the associated EAC1= AC + (BAC-EV). At completion, EV-BAC so the EAC1=AC at completion. You basically record AC and hope it will end up close to BAC at completion. There are no assumptions on cost level and schedule changes factored in this estimation.

But what happens to EAC if the cost level changes throughout the project?

This is not a unlikely scenario. For example the consultants rates where increased in the new year. The question then is how will the costs of the remaining work (BAC-EV) change? Your simplest estimate for the cost change is the CPI, so (BAC-EV)/CPI are the estimated costs for the outstanding work (here named ETC2). So your best estimate for the EAC2 are the AC plus ETC2. Of course, we assume the CPI remains the same until project completion.

Idem if the project schedule performance changes?

For instance the project is ahead of schedule due to a highly productive team. Here we assume actual costs remain unchanged. The ETC3 can be estimated to be (BAC-EV)/SPI. If SPI is larger than 1 you complete the work faster, so you end up with an EAC3 lower than BAC if you extrapolate EAC3 to the planned completion date.

The other metrics, ETC4 and ETC5 are of course a combination of the two above. ETC5 requires some PM discretion to determine the w fudge factor, which I find not very useful in practice. We are dealing with enough uncertainty in our projects already.

I my opinion EAC1, EAC2 or EAC3 are useful metrics that provide some bandwidth of the expected EAC. The other ones can be used to add more detail to the EAC bandwith if you want.

At last, academic research showed us that the CPI and SPI provide some useful information only up to 20% project completion. After 20% completion, they may fluctuate too much to be useful. Moreover, at this stage (20%) of the project you can still make corrections by adding or removing resources. Beyond 20% completion it will become a lot harder to make corrections without making a serious impact on your delivery time and budget at completion.

I hope this helps.