After collecting the control information on a light rail project within an original budget of 200.000 work hours, the construction contractor is…

The Cost Performance Index (CPI) is a key metric in Earned Value Management (EVM) that measures 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). Using the data provided: BCWP (earned) = 105,000 work hours ACWP (paid) = 110,000 work hours The formula is: CPI = BCWP / ACWP CPI = 105,000 / 110,000 = 0.9545, which rounds to 0.95. A CPI less than 1.0 indicates a cost overrun, meaning the project is costing more than planned for the work completed.

B. This option incorrectly inverts the standard CPI formula, calculating ACWP/BCWP. This ratio does not represent the standard Cost Performance Index.
C. This option incorrectly uses the Budgeted Cost for Work Scheduled (BCWS) instead of BCWP in the numerator, which does not measure performance against work actually completed.
D. This option is the inverse of the incorrect formula in option C. It uses BCWS instead of BCWP and inverts the standard ratio.

1. AACE International, Recommended Practice No. 10S-90, "Cost Engineering Terminology" (June 28, 2019).

Page 31: Defines Cost Performance Index (CPI) as "A measure of cost efficiency on a project. It is the ratio of earned value (EV) to actual cost (AC). CPI = EV/AC." The document equates EV with BCWP and AC with ACWP.

2. AACE International, Skills & Knowledge of Cost Engineering, 6th ed. (Morgantown, WV: AACE International, 2015).

Chapter 7, Section 7.3, "Progress and Cost Control": This section details the fundamentals of Earned Value Management, explicitly stating the formula for the Cost Performance Index as CPI = BCWP / ACWP. It explains that this index measures the value of work accomplished for every unit of cost incurred.

3. Humphreys, K. K., Project and Cost Engineers' Handbook, 4th ed. (New York: Marcel Dekker, 2005), sponsored by AACE International.

Chapter 11, "Cost Control," Page 268: The text provides the formula for cost performance: "Cost Performance Index (CPI) = BCWP/ACWP." It further explains that a value less than 1.0 indicates that costs are higher than budgeted.