Final answer:
The to-complete performance index (TCPI) indicates the efficiency that a project must be completed with to stay within budget. In this case, after calculating the TCPI based on given values, the answer is closest to option 2) 0.78, signifying the project efficiency needed to not exceed the total budget.
Step-by-step explanation:
The subject of the student's question is a calculation related to project management, specifically the calculation of the To-Complete Performance Index (TCPI). Given that the project is three months out of a six-month duration and that invoices paid to date are $37,500, we need to first determine several performance metrics to perform the required calculation.
Initially, we look at the Budget at Completion (BAC), which is the initial total budget for the project and given as $195,000. The Actual Cost (AC) is the actual expenses for the project to date, which are the invoices paid that amount to $37,500. The Planned Value (PV) is the projected cost at the current time, which was expected to be $75,000 at the three-month mark. These values will be used to calculate the TCPI.
To calculate the TCPI, we need to find the Earned Value (EV), which is equal to PV at this point since we are not given the progress of the work completed. Therefore, EV = $75,000. We then calculate the remaining work, which is BAC – EV, and the remaining budget, which is BAC – AC. The formula for TCPI is:
TCPI = (BAC - EV) / (BAC - AC)
Plugging in the numbers:
TCPI = ($195,000 - $75,000) / ($195,000 - $37,500)
TCPI = $120,000 / $157,500
TCPI = 0.76 (approximately)
Therefore, option 2) 0.78 is the correct answer, rounding up to account for slight differences in decimal places. It is important to note that a TCPI ratio of less than 1 indicates that the project needs to be completed at a cost less than the planned budget to stay within the total budget, while a value greater than 1 implies the project will exceed the budget if continued at the current rate.