A project reports an earned value (EV) of USS45 for work completed with an actual...

According to the PMBOK® Guide, the Cost Performance Index (CPI) is a measure of the cost efficiency of budgeted resources, expressed as the ratio of earned value to actual cost. It is one of the most critical metrics in Earned Value Management (EVM) for determining if a project is under or over budget.

The Formula: The formula for calculating CPI is:

$$CPI = \frac{EV}{AC}$$

Where:

EV (Earned Value): The value of the work actually performed (US$45).

AC (Actual Cost): The actual cost incurred for the work performed (US$40).

The Calculation:

$$CPI = \frac{45}{40} = 1.125$$

Rounding to two decimal places, the result is 1.12.

Interpretation:

A CPI greater than 1.0 (like 1.12) indicates that the project is under budget or performing better than planned regarding costs. For every dollar spent, the project has earned $1.12 worth of work.

A CPI equal to 1.0 indicates the project is exactly on budget.

A CPI less than 1.0 indicates the project is over budget.

Analysis of other options:

A. 0.88: This would be the result if the calculation were inverted ($AC / EV$ or $40 / 45$), which is incorrect. A value below 1.0 indicates poor cost performance.

C. 0.58 and D. 1.58: These values do not correspond to the mathematical relationship between the provided EV and AC figures.

Per PMI standards, the CPI is a primary indicator used to forecast the final project cost at completion (Estimate at Completion), making it a vital tool for the Control Costs process.