The definitions above are circular on their own: EAC is actual cost plus what is left to spend, and what is left to spend is EAC minus actual cost. To get from data to a number you need earned value. Three inputs, measured at the same moment:
- BAC - Budget at Completion. The approved budget.
- EV - Earned Value. Budget value of the work actually finished: percent complete × BAC.
- AC - Actual Cost. What has been spent to date.
From those, the standard earned-value formulas:
CPI = EV / AC cost performance index
EAC = BAC / CPI the variance so far continues
= BAC x AC / EV same thing, no rounded divisor
EAC = AC + (BAC - EV) the rest goes to plan
EAC = AC + (BAC - EV) / (CPI x SPI) cost and schedule both slipping
ETC = EAC - AC what is still to spend
VAC = BAC - EAC the overrun, if negative
TCPI = (BAC - EV) / (BAC - AC) efficiency needed to still hit BAC
Worked example. A fixed-fee engineering study is budgeted at BAC = $400,000. Halfway through the schedule, the team has completed 45% of the work and spent $220,000.
- EV = 45% × $400,000 = $180,000
- AC = $220,000
- CPI = EV / AC = $180,000 / $220,000 = 0.8181... (a recurring decimal - never round it before dividing by it)
You are getting about 82 cents of work for every dollar spent. If that rate continues, EAC = BAC / CPI - but CPI is a recurring decimal here, so use the equivalent form that has no divisor to round: EAC = BAC × AC / EV = $400,000 × $220,000 / $180,000 = $488,888.89. Round CPI first and you get a different answer at every number of digits - $487,805 at 0.82, $488,878 at 0.8182 - which is exactly the trap this form avoids. The project lands about $89,000 over budget. That is VAC = $400,000 − $488,888.89 = −$88,888.89, and it comes straight out of the fee.
If instead you believe the overrun was a one-off and the remainder will run to plan, EAC = $220,000 + ($400,000 − $180,000) = $440,000. The gap between those two EACs - $488.9k against $440k - is the decision you actually have to make: was this a blip, or is it how the project runs?
Either way, ETC = EAC − AC, so between $220,000 and $269,000 remains to be spent. And TCPI = ($400,000 − $180,000) / ($400,000 − $220,000) = $220,000 / $180,000 = 1.2222...: to still finish at budget, every remaining dollar has to buy about 22% more work than every dollar so far. That is the number that tells you whether recovery is realistic or whether the conversation is about scope and fee instead.