What is the Cost Performance Index (CPI) of the project under the conditions listed below? | Project Budget (BAC) | 100,000 dollars Project Duration | 4 months Elapsed Time | 1 month Actual Cost (AC) | 20,000 dollars Project Progress | As planned

ITPEC FE Subject A April 2024 Question 42

What is the Cost Performance Index (CPI) of the project under the conditions listed below?

Project Budget (BAC)	100,000 dollars
Project Duration	4 months
Elapsed Time	1 month
Actual Cost (AC)	20,000 dollars
Project Progress	As planned

a)0.25b)0.8c)1.0d)1.25

Explanation

1.25 — progress as planned means the earned value equals the planned value, which is then divided by the actual cost.

•Planned value after 1 of 4 months: 100,000 × 1 ÷ 4 = 25,000 dollars
•Earned value: progress is as planned, so EV = PV = 25,000 dollars
•CPI: EV ÷ AC = 25,000 ÷ 20,000 = 1.25

A CPI above 1 means the work done so far cost less than its budget.

Answer (d)

Why not others:

•(a) 0.25 — 25,000 ÷ 100,000, EV over the total budget: the share of work completed, not cost efficiency
•(b) 0.8 — 20,000 ÷ 25,000, the formula inverted as AC ÷ EV
•(c) 1.0 — the schedule performance index, EV ÷ PV, which is 1 because progress is as planned; the cost index compares EV with AC

Key rule: CPI = EV ÷ AC and SPI = EV ÷ PV; above 1 is favourable for both, and "as planned" settles only the SPI.

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