According to the PMBOK® Guide, specifically within the Control Costs process, Earned Value Management (EVM) is used to forecast the project ' s financial outcome based on current performance.
The Scenario: The question provides a Cost Performance Index (CPI) and an Estimate at Completion (EAC), while stating that the current performance is expected to continue for the remainder of the project.
The Formula: When the current $CPI$ is expected to continue, the formula for $EAC$ is:
$$EAC = \frac{BAC}{CPI}$$
Solving for BAC: To find the original budget (Budget at Completion or $BAC$), we must rearrange the formula:
$$BAC = EAC \times CPI$$
$$BAC = \$1000 \times 0.80$$
$$BAC = \$800$$
This result indicates that the project was originally budgeted for $\$800$, but because it is performing inefficiently (spending $\$1.00$ to get $\$0.80$ worth of work), it is now expected to cost $\$1000$ to complete.
Analysis of Other Options:
B. $1000: This is the $EAC$ (the forecasted total cost), not the $BAC$ (the original budget).
C. $1250: This would be the result if you incorrectly divided $EAC$ by $CPI$ ($\$1000 / 0.80 = \$1250$), which does not align with the standard EVM mathematical relationships for this scenario.
D. $1800: This number has no mathematical basis in the provided EVM data.
