According to the PMBOK® Guide and the Standard for Project Management, the Cost Performance Index (CPI) is the specific earned value management (EVM) metric that measures the cost efficiency of budgeted resources. It is expressed as the ratio of Earned Value (EV) to Actual Cost (AC).
As per PMI standards, the CPI is considered the most critical EVM metric because it indicates the value of work completed compared to the actual amount spent. It is a primary indicator of project cost performance and is used to predict the final project cost. The formula is:
$$\text{CPI} = \frac{\text{EV}}{\text{AC}}$$
Interpretation of CPI values:
CPI > 1.0: Indicates that the project is under budget (performing better than planned).
CPI < 1.0: Indicates that the project is over budget (performing worse than planned).
CPI = 1.0: Indicates that the project is exactly on budget.
The other options are incorrect based on the following PMI definitions:
Cost Variance (CV): This is a measure of cost performance expressed as the difference between earned value and actual cost ($\text{CV} = \text{EV} - \text{AC}$). While it measures efficiency, it is an absolute value (currency), not a ratio.
Budget at Completion (BAC): This is the total planned budget for the project. It is the sum of all budgets established for the work to be performed and serves as the baseline, not a measure of current efficiency.
Variance at Completion (VAC): This is a projection of the amount of budget deficit or surplus, expressed as the difference between the BAC and the Estimate at Completion (EAC) ($\text{VAC} = \text{BAC} - \text{EAC}$).
As per the PMI Lexicon of Project Management Terms, the Cost Performance Index is a fundamental component of the Control Costs process, allowing project managers to determine if corrective action is needed to bring the project back within financial constraints.
