While preparing an earned value analysis (EVA) for the sponsor, the project manager provided this...

To answer this question, we need to calculate the earned value (EV), the planned value (PV), and the actual cost (AC) of the project based on the given information. Then, we can compare them to determine the project status in terms of schedule and cost performance.

The earned value (EV) is the monetary value of the work completed so far. It can be calculated by multiplying the percent complete of the project by the budget at completion (BAC), which is the total approved budget for the project. The BAC can be obtained by adding the approved work package cost estimates, the contingency reserves, and the management reserves. In this case, the BAC is:

BAC=9500+500+(10%×500)=10550

The EV is then:

EV=50%×10550=5275

The planned value (PV) is the monetary value of the work that was planned to be completed by a certain date. It can be calculated by multiplying the planned percent of the project by the BAC. In this case, the PV is:

PV=40%×10550=4220

The actual cost (AC) is the monetary value of the work actually performed. It is given as:

AC=4500

To determine the project status, we can use the cost variance (CV) and the schedule variance (SV) formulas. The CV is the difference between the EV and the AC, and it indicates whether the project is under budget or over budget. A positive CV means the project is under budget, while a negative CV means the project is over budget. The CV is:

CV=EV−AC=5275−4500=775

The SV is the difference between the EV and the PV, and it indicates whether the project is ahead of schedule or behind schedule. A positive SV means the project is ahead of schedule, while a negative SV means the project is behind schedule. The SV is:

SV=EV−PV=5275−4220=1055

From the CV and SV values, we can conclude that the project is under budget and ahead of schedule. To find the percentage of deviation from the planned cost and schedule, we can use the cost performance index (CPI) and the schedule performance index (SPI) formulas. The CPI is the ratio of the EV to the AC, and it measures the cost efficiency of the project. A CPI greater than 1 means the project is under budget, while a CPI less than 1 means the project is over budget. The CPI is:

CPI=ACEV​=45005275​=1.17

The SPI is the ratio of the EV to the PV, and it measures the schedule efficiency of the project. A SPI greater than 1 means the project is ahead of schedule, while a SPI less than 1 means the project is behind schedule. The SPI is:

SPI=PVEV​=42205275​=1.25

From the CPI and SPI values, we can calculate the percentage of deviation from the planned cost and schedule by subtracting 1 and multiplying by 100. The percentage of deviation from the planned cost is:

(CPI−1)×100=(1.17−1)×100=17%

The percentage of deviation from the planned schedule is:

(SPI−1)×100=(1.25−1)×100=25%

Therefore, the project cost is 17% lower than planned, and the project schedule is 25% ahead of planned. Among the given options, the closest one is B. The project cost is 10% lower than planned.