Question 5 of 6: Project Control — earned value and the cost performance index under the 20/80 rule

Question 5: Project Control — earned value and the cost performance index under the 20/80 rule (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A four-activity bar chart in which the darker bar of each pair is the planned duration and the lighter bar is the time actually spent, with a vertical line marking the current date; one day of work on any activity costs 1,000 CAD. The bar endpoints below are read against the printed tick spacing, each tick being one day, and the current date falls on day 12.

Find. The cost performance index of each activity and of the project as a whole at the current date, with earned value credited by the 20/80 rule.

[Figure not reproduced: Figure 5.1 — The examination bar chart redrawn from the printed figure. Dark bars are planned durations, light bars are time actually spent, and the vertical line is the current date at day 12. Activity D has no light bar because it has not started. See the official exam paper.]

Approach. Convert each bar into money at 1,000 CAD per activity-day — planned duration gives the budget, elapsed time gives the actual cost — credit earned value by the 20/80 rule according to each activity’s status, and form $CPI = EV/AC$ activity by activity and then for the project from the totals.

1. State the 20/80 crediting rule. An activity is credited with 20 percent of its budget as soon as it starts and the remaining 80 percent only when it finishes; nothing is credited for partial progress in between. Formally, the earned value of activity $i$ is $$EV_i = BAC_i \times \begin{cases} 0 & \text{not started} \\ 0.20 & \text{started, not finished} \\ 1.00 & \text{finished} \end{cases}$$ The rule exists so that progress can be reported without asking the crew to estimate percentage complete, which is the least reliable number on any site.
2. Convert planned durations into budgets. At 1,000 CAD per activity-day, $BAC_A = BAC_B = BAC_C = 4(1{,}000) = 4{,}000$ and $BAC_D = 1(1{,}000) = 1{,}000$, so the budget at completion for the project is $$BAC = 4{,}000+4{,}000+4{,}000+1{,}000 = \boxed{13{,}000\ \text{CAD}}$$
3. Convert elapsed time into actual cost. The lighter bars give six days on A, four on B, one on C and none on D, so $AC_A = 6{,}000$, $AC_B = 4{,}000$, $AC_C = 1{,}000$ and $AC_D = 0$, and the actual cost of work performed to the data date is $$AC = 6{,}000+4{,}000+1{,}000+0 = \boxed{11{,}000\ \text{CAD}}$$
4. Credit the earned value. A and B are finished and are credited in full at 4,000 CAD each. C has started but has not finished, so it earns only $0.20 \times 4{,}000 = 800$. D has not started and earns nothing. Hence $$EV = 4{,}000+4{,}000+800+0 = \boxed{8{,}800\ \text{CAD}}$$ Note that C has consumed 1,000 CAD to earn 800 CAD, which is a feature of the rule rather than a sign of poor performance on C.
5. Cost performance index, activity by activity. With $CPI = EV/AC$, $$\begin{aligned} CPI_A &= \frac{4{,}000}{6{,}000} = \boxed{0.667} \\ CPI_B &= \frac{4{,}000}{4{,}000} = \boxed{1.000} \\ CPI_C &= \frac{800}{1{,}000} = \boxed{0.800} \end{aligned}$$ Activity D has incurred no cost, so its index is undefined and is properly reported as “not applicable” rather than as zero.
6. Cost performance index for the project. The project index is formed from the totals, never by averaging the activity indices: $$CPI = \frac{EV}{AC} = \frac{8{,}800}{11{,}000} = \boxed{0.800}$$ with a cost variance of $CV = EV - AC = 8{,}800 - 11{,}000 = -2{,}200$ CAD. The project is earning eighty cents of value for every dollar spent.
7. Forecast the outturn. If the performance to date is representative, the estimate at completion is $$EAC = \frac{BAC}{CPI} = \frac{13{,}000}{0.800} = \boxed{16{,}250\ \text{CAD}}$$ a forecast overrun of 3,250 CAD on a 13,000 CAD budget. Two-thirds of that overrun is already banked in activity A, which is the item to investigate first.
8. Separate the schedule question from the cost question. Applying the same 20/80 rule to the plan at day 12 gives A and B planned complete at 4,000 CAD each, C planned started but not finished at 800 CAD, and D not yet planned to start, so the planned value is $PV = 8{,}800$ CAD. The schedule performance index is therefore $SPI = EV/PV = 8{,}800/8{,}800 = 1.000$ with $SV = 0$. The project is exactly where it planned to be in value terms while spending 25 percent more than it should have to get there — a pure cost problem, not a schedule problem, which is precisely the distinction the earned-value method exists to make.