# PMP Training Kit: Cost Management

This section contains the answers to the questions for the “Exercises” and “Chapter review” sections in this chapter.

### Exercises

1. (A) You are the project manager on a project to build 10 identical offices. You expect to spend \$50,000 per office to complete the work and take 20 months to finish. You are 12 months into the work and have completed five offices and spent \$310,000 in total. Use this information to calculate the following:

1. Budget at completion (BAC): 10 offices × \$50,000 each = \$500,000

2. Actual cost (AC): You have spent \$310,000 in total so this is your actual cost.

3. Planned value (PV): You are 12 months into a 20-month work program, so you planned to have created value equivalent to 12/20, or 60%, of your total planned value, or budget at completion. Therefore, your planned value (PV) is \$500,000 × 60% = \$300,000.

4. Earned value (EV): You have built five offices, each with a value to you of \$50,000, so your earned value is 5 × \$50,000 = \$250,000.

5. Cost variance (CV): CV = EV – AC: \$250,000 – \$310,000 = –\$60,000

6. Cost performance index (CPI): CPI = EV/AC: \$250,000/\$310,000 = 0.81

7. Schedule variance (SV): SV = EV – PV: \$250,000 – \$300,000 = –\$50,000

8. Schedule performance index (SPI): SPI = EV/PV: \$250,000/\$300,000 = 0.83

9. Estimate at completion (EAC)

1. EAC= BAC/CPI: \$500,000/0.81 = \$617,283.95

2. EAC = AC + ETC: \$310,000 + \$307,283.95 = \$617,283.95

3. EAC = AC + (BAC – EV): \$310,000 + (\$500,000 – \$250,000) = \$560,000

4. EAC = AC + ((BAC–EV)/(CPI × SPI)): \$310,000 + ((\$500,000 – \$250,000)/(0.81 × 0.83)) = \$681,857.80

10. Estimate to complete (ETC): The estimate to complete answer will depend on which estimate at completion figure you choose to use in the formula ETC = EAC – AC. If you use the estimate at completion (EAC) from the BAC/CPI formula, the answer is \$307,283.95.

11. Variance at completion (VAC): The variance at completion answer will depend on which estimate at completion you choose to use in the formula VAC = BAC – EAC. If you use the estimate at completion (EAC) from the BAC/CPI formula, the answer is –\$117,283.95.

12. To-complete performance index (TCPI): The to-complete performance index answer will depend on whether your target is your budget at completion (BAC) or the estimate at completion (EAC), and if it is the estimate at completion (EAC), it will depend on which formula you use to calculate that. The following example uses BAC/CPI to calculate EAC.

1. TCPI for EAC = (BAC – EV)/(EAC – AC) = 0.81

2. TCPI for BAC = (BAC – EV)/(BAC – AC) = 1.31

(B) Based on the information gained from the calculations you have performed, how is the project performing in terms of both cost and time?

Based on the information calculated, the project is over budget because the cost variance (CV) is negative and the cost performance index (CPI) is less than 1. The project is behind schedule, because the schedule variance (SV) is negative and the schedule performance index (SPI) is less than 1.

2. (A) You are the project manager on a project to complete 15 miles of road. Your approved budget for the project is \$930,000, and you have forecast that the project will take 35 weeks to complete. You are 13 weeks into the project, and have constructed seven miles of road at a cost of \$58,000 per mile. Use this information to calculate the following:

1. Budget at completion (BAC): \$930,000

2. Actual cost (AC): You have built seven miles of road at a cost of \$58,000 so your actual cost is 7 × \$58,000 = \$406,000.

3. Planned value (PV): You are 13 weeks into a 35-week work program, so you planned to have created value of 13/35, or 37%, of your total planned value, or budget at completion. Therefore, your planned value (PV) is \$930,000 × 37% = \$344,100.

4. Earned value (EV): You are building 15 miles of road for \$930,000, so each mile of road has a value of \$930,000/15 = \$62,000. You have built seven miles of road each with a value to you of \$62,000, so your earned value is 7 × \$62,000 = \$434,000.

5. Cost variance (CV): CV = EV – AC: \$434,000 – \$406,000 = \$28,000

6. Cost performance index (CPI): CPI = EV/AC: \$434,000/\$406,000 = 1.07

7. Schedule variance (SV): SV = EV – PV: \$434,000 – \$344,100 = \$89,900

8. Schedule performance index (SPI): SPI = EV/PV: \$434,000/\$344,100 = 1.26

9. Estimate at completion (EAC)

1. EAC= BAC/CPI: \$930,000/ 1.07 = \$869,158.88

2. EAC = AC + ETC: \$406,000 + \$464, 158.88 = \$870,158.88

3. EAC = AC + (BAC – EV): \$406,000 + (\$930,000 – \$434,000) = \$902,000

4. EAC = AC + ((BAC – EV)/(CPI × SPI)): \$406,000 + ((\$930,000 – \$434,000)/(1.07 × 1.26)) = \$773,407.41

10. Estimate to complete (ETC): The estimate to complete answer will depend on which estimate at completion figure you choose to use in the formula ETC = EAC – AC. If you use the estimate at completion (EAC) from the BAC/CPI formula, the answer is \$463,158.88.

11. Variance at completion (VAC): The variance at completion answer will depend on which estimate at completion you choose to use in the formula VAC = BAC – EAC. If you use the estimate at completion (EAC) from the BAC/CPI formula, the answer is \$60,841.12.

12. To-complete performance index (TCPI): The to-complete performance index answer will depend on whether your target is your budget at completion (BAC) or the estimate at completion (EAC), and if it is the estimate at completion (EAC), it will depend on which formula you use to calculate that. The following example uses BAC/CPI to calculate EAC.

1. TCPI for EAC = (BAC – EV)/(EAC – AC) = 1.07

2. TCPI for BAC = (BAC – EV)/(BAC – AC) = 0.95

(B) Based on the information gained from the calculations you have performed, how is the project performing in terms of both cost and time?

Based on the information from the earned value calculations, the project is ahead of schedule because the schedule variance (SV) is positive and the schedule performance index (SPI) is greater than 1. The project is also under budget because the cost variance (CV) is positive and the cost performance index (CPI) is greater than 1.

### Chapter review

1. Correct: First plan your approach to cost management, then estimate costs, then determine your budget, then control the costs.

2. Incorrect: Estimate Costs occurs before Determine Budget.

3. Incorrect: Control Costs occurs after Determine Budget.

4. Incorrect: Control Costs occurs after Determine Budget.

1. Incorrect: Activity cost estimates are an output from the Estimate Costs process.

2. Incorrect: The cost baseline is an output from the Determine Budget process.

3. Correct: The cost management plan is the sole output from the Plan Cost Management process.

4. Incorrect: Cost forecasts are an output from the Control Costs process.

1. Incorrect: A description of the accuracy of estimating would be included in the cost management plan.

2. Incorrect: A description of the cost reporting formats to be used would be included in the cost management plan.

3. Incorrect: A description of the units of measure used to estimate costs would be included in the cost management plan.

4. Correct: The dates each activity will occur would be included as part of your project schedule, not the cost management plan.

1. Correct: Analogous estimating uses similar activities from the past and extrapolates from them a likely current cost estimate.

2. Incorrect: Parametric estimating multiplies a known quality by a known dollar amount to arrive at a cost estimate.

3. Incorrect: Three-point estimating takes the weighted average of a most likely, optimistic, and pessimistic cost estimate.

4. Incorrect: Bottom-up estimating aggregates lower-level cost estimates.

1. Incorrect: Analogous estimating uses similar activities from the past and extrapolates from them a likely current cost estimate.

2. Incorrect: Parametric estimating multiplies a known quality by a known dollar amount to arrive at a cost estimate.

3. Incorrect: Three-point estimating takes the weighted average of a most likely, optimistic, and pessimistic cost estimate.

4. Correct: Bottom-up estimating aggregates lower-level cost estimates up to higher levels to arrive at a total project cost estimate.

1. Incorrect: The contingency reserve is for known unknowns on the project.

2. Incorrect: The funding limit reconciliation is an output from the Determine Budget process.

3. Correct: The management reserve is available for truly unforeseen costs that arise on a project and is controlled by senior management.

4. Incorrect: Cost aggregation is the technique of adding up lower-level costs to obtain higher-level cost estimates.

1. Incorrect: The project would need a CPI less than 1 and an SPI less than 1 to be over budget and behind schedule.

2. Correct: A CPI less than 1 and an SPI greater than 1 indicate that the project is over budget and ahead of schedule.

3. Incorrect: The project would need a CPI greater than 1 and an SPI less than 1 to be under budget and behind schedule.

4. Incorrect: The project would need a CPI greater than 1 and an SPI greater than 1 to be under budget and ahead of schedule.

1. Incorrect: \$70,000 is the budget at completion.

2. Incorrect: You would arrive at this figure if you reversed the calculation for cost performance index (CPI).

3. Correct: If you calculate the cost performance index (CPI) first by dividing the earned value (EV) by the actual cost (AC), then divide the budget at completion (BAC) by the cost performance index (CPI), this is the answer you get.

4. Incorrect: This is the answer you get if you add the earned value (EV) to the actual cost (AC).

1. Incorrect: There is a variance at completion, according the formula VAC = BAC – EAC.

2. Incorrect: This is the answer you arrive at if you calculate estimate at completion (EAC) incorrectly.

3. Correct: Variance at completion (VAC) equals budget at completion (BAC) minus estimate at completion (EAC), which is -\$4 468.08.

4. Incorrect: If you got this answer, you probably guessed or used the wrong equation.

1. Incorrect: A to-complete performance index (TCPI) of 1.1 is a bad thing and means you need to work faster or more efficiently to achieve your goal of either budget at completion (BAC) or estimate at completion (EAC).

2. Incorrect: A to-complete performance index (TCPI) of 1.1 shows that the project is not on track.

3. Correct: A to-complete performance index (TCPI) of 1.1 means that you have to work harder or more efficiently to achieve the goal of the budget at completion (BAC).

4. Incorrect: A to-complete performance index (TCPI) of 1.1 means that you must pay attention to both schedule and spending, but neither one is in a good position because the index is greater than 1.