Cost performance index (CPI) is defined by AACE International as: (assume no change in budgeted quantities)

The Cost Performance Index (CPI) is a fundamental Earned Value Management (EVM) metric used to measure the cost efficiency of the work accomplished. It is calculated as the ratio of the Budgeted Cost of Work Performed (BCWP), also known as Earned Value (EV), to the Actual Cost of Work Performed (ACWP), also known as Actual Cost (AC). A CPI value greater than 1.0 indicates a favorable condition (under budget), while a value less than 1.0 indicates an unfavorable condition (over budget). The formula is CPI = BCWP / ACWP.

A. ACWP/BCWS: This ratio compares the actual cost to the planned value. It is not a standard, meaningful performance index in EVM as it mixes actual performance cost with planned schedule value.
B. BCWS/BCWP: This is the inverse of the Schedule Performance Index (SPI). The correct formula for SPI is BCWP/BCWS, which measures schedule efficiency.
C. ACWP/BCWP: This is the inverse of the CPI. It represents the cost per unit of earned value, but it is not the standard definition of the Cost Performance Index.

1. AACE International. (2022). Recommended Practice 10S-90: Cost Engineering Terminology.

Page 41: Defines COST PERFORMANCE INDEX (CPI) as "A measure of cost efficiency on a project. It is the ratio of earned value (EV) or budgeted cost of work performed (BCWP) to actual cost (AC) or actual cost of work performed (ACWP). CPI = EV/AC = BCWP/ACWP."

2. Hollmann, J. K. (Ed.). (2015). AACE International's Skills & Knowledge of Cost Engineering (6th ed.). AACE International.

Chapter 7.3, "Earned Value Management," Page 7.3.5: Explicitly states the formula for the Cost Performance Index: "Cost Performance Index (CPI) = BCWP/ACWP". This text is the official body of knowledge for the CCP certification.

3. Fleming, Q. W., & Koppelman, J. M. (2016). Earned Value Project Management (4th ed.). Project Management Institute.

Chapter 4, "The Five Core Data Elements," Page 33: Although a PMI publication, it is a foundational academic text on EVM, universally recognized and aligned with AACE principles. It defines CPI as the ratio of the budgeted cost of the work performed (BCWP) to the actual cost of the work performed (ACWP). "Formula: CPI = BCWP/ACWP".