Hi Simon,
If you are a customer of the PM PrepCast I highly recommend that you watch the earned value management videos on this (L07.05.1 , L07.05.2). It is very clear and contains all the information you need for the exam, also it will make you understand the formulas.
ETC is the Estimate to Complete, it is the estimated cost to finish all the remaining project work.
calculating ETC has 2 formulas:
1. Assuming work is proceeding on plan, ETC = EAC – AC
where EAC is the Estimate at Completion and AC is the Actual Cost.
2- assuming work is not going as planned in such case ETC is simply the re-estimate of the remaining work. ETC = Re-Estimate.
Regarding the EAC, you will need to calculate this to come up with ETC, it is the expected total cost of completing all work expressed as the sum of the actual cost to date and the estimate to complete. based on the situation and the current project status, EAC has the below formulas.
1. If the CPI is expected to be the same for the remainder of the project, EAC = BAC/CPI
2. If the future work will be accomplished at the planned rate, EAC = AC + BAC – EV
3. If the initial plan is no longer and you will have to estimate, EAC = AC + Bottom-up ETC
4- If both the CPI and SPI influence the remaining work, EAC = AC + [(BAC – EV)/ (CPI x SPI)]
In the example you referred to
ETC = EAC - AC
where EAC = AC + [(BAC – EV)/ (CPI x SPI)] and
if we substitute both equations you will come up with
ETC = (BAC-EV) / (CPI x SPI)
and for some reason your example assumed SPI is 1 or just ignored it and came up with ETC = (BAC-EV) / CPI
I hope this will help you understand these formulas.