According to the PMBOK® Guide, specifically within the Control Costs process, 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.
$$CPI = \frac{EV}{AC}$$
Where:
EV (Earned Value): The value of the work actually performed expressed in terms of the approved budget assigned to that work.
AC (Actual Cost): The total cost actually incurred and recorded in accomplishing work performed for an activity or work breakdown structure component.
The Calculation:
Given the values from the question:
$CPI = 1.25$
$AC = \$10,000$
We rearrange the formula to solve for EV:
$$EV = CPI \times AC$$
$$EV = 1.25 \times 10,000$$
$$EV = 12,500$$
Interpretation: A CPI of 1.25 means that for every dollar spent on the project, the project has earned $1.25 worth of work. Since the CPI is greater than 1.0, the project is currently under budget (performing efficiently).
Comparison with Other Options:
A. US$8,000: This would be the result if the CPI were 0.8 ($0.8 \times 10,000$). A CPI less than 1.0 indicates the project is over budget.
B. US$9,500: This would be the result if the CPI were 0.95.
C. US$10,000: This would be the result if the CPI were 1.0 ($EV = AC$), indicating the project is exactly on budget.
D. US$12,500: This is the correct mathematical result of the provided CPI and Actual Cost.
