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 progress bar chart at a data date of day 12, showing for each of four activities a planned (dark) bar and, where work has been done, an actual (light) bar; work is costed uniformly at $1,000 per activity per day; and progress is claimed under the 20/80 rule, with activity C started but not finished. The bar ends are read from the printed chart.

Find. The Cost Performance Index for each activity and for the project as a whole at the data date.

Approach. Cost every activity's planned duration at $1,000 per day to get its budget, cost its actual duration the same way to get what has been spent, then award earned value by the 20/80 convention — twenty per cent of the budget on starting, the remaining eighty on finishing — and form the ratio of value earned to cost incurred.

1. Budget at completion for each activity. At $1,000 per activity per day, the budget is simply the planned duration priced out: $$BAC_i=d_{\text{plan},i}\times 1000$$ $$BAC_A=BAC_B=BAC_C=4\times 1000=\$4{,}000,\qquad BAC_D=1\times 1000=\$1{,}000$$ Summing, the project budget is $$BAC=4{,}000+4{,}000+4{,}000+1{,}000=\$13{,}000$$
2. Actual cost incurred to the data date. The same rate applied to the time actually spent, which is what the lighter bars measure: $$AC_A=6\times 1000=\$6{,}000,\quad AC_B=4\times 1000=\$4{,}000,\quad AC_C=1\times 1000=\$1{,}000,\quad AC_D=\$0$$ $$AC=6{,}000+4{,}000+1{,}000+0=\$11{,}000$$ Activity C's actual bar runs from day 11 to the data date at day 12, so exactly one day has been spent on it; activity D has not begun and has therefore consumed nothing.
3. Apply the 20/80 rule to get earned value. The 20/80 convention credits an activity with 20 % of its budget as soon as it starts and the remaining 80 % only when it is complete; nothing is earned in between, and nothing at all before it starts. Activities A and B are complete and earn their full budgets; C has started but not finished, so it earns one fifth; D has not started and earns nothing: $$EV_A=1.00\times 4{,}000=\$4{,}000,\qquad EV_B=1.00\times 4{,}000=\$4{,}000$$ $$EV_C=0.20\times 4{,}000=\$800,\qquad EV_D=\$0$$ $$EV=4{,}000+4{,}000+800+0=\boxed{EV=\$8{,}800}$$ It is worth pausing on activity C: one day of its four-day plan has been worked, so a percent-complete measure would have credited $1,000. The 20/80 rule deliberately credits less, $800, because it refuses to reward progress that has not yet reached a verifiable milestone.
4. Cost Performance Index for each activity. By definition $CPI=EV/AC$, the value earned per dollar spent: $$CPI_A=\frac{4{,}000}{6{,}000}=\boxed{CPI_A=0.67}$$ $$CPI_B=\frac{4{,}000}{4{,}000}=\boxed{CPI_B=1.00}$$ $$CPI_C=\frac{800}{1{,}000}=\boxed{CPI_C=0.80}$$ For activity D both the earned value and the actual cost are zero, so the ratio is $0/0$ and the index is undefined, not zero. This must be said rather than glossed over: an activity that has not started is neither performing nor under-performing, and reporting a CPI of zero for it would drag the project average down without any work having gone wrong.
5. Cost Performance Index for the project. The project index is formed from the totals, never by averaging the activity indices: $$CPI=\frac{EV}{AC}=\frac{8{,}800}{11{,}000}=\boxed{CPI=0.80}$$ The equivalent cost variance is $$CV=EV-AC=8{,}800-11{,}000=-\$2{,}200$$ so the project has earned 80 cents of value for every dollar spent and is $2,200 over budget for the work performed to date. Averaging the three defined activity indices would have given (0.67 + 1.00 + 0.80)/3 = 0.82, which is wrong — it weights a $1,000 activity equally with a $6,000 one.
6. Interpret the result, and locate the overrun. Decomposing the $2,200 cost variance by activity: A accounts for $4,000 − $6,000 = $−2,000, C for $800 − $1,000 = $−200, and B contributes nothing. Essentially the entire overrun is activity A, which took six days against a four-day plan; C's small shortfall is an artefact of the 20/80 convention rather than evidence of poor performance, since only one day of a four-day activity has been worked. Extrapolating at the current efficiency gives a forecast at completion of $$EAC=\frac{BAC}{CPI}=\frac{13{,}000}{0.80}=\$16{,}250$$ an overrun of $3,250 if performance does not improve.
7. Check the schedule dimension for completeness. The question asks only for cost, but the same data yields the schedule index and the comparison is instructive. Applying the identical 20/80 convention to the plan at day 12: A and B were planned complete and contribute $4,000 each, C was planned to have started (day 11) but not to have finished (day 15) and contributes 0.20 × $4,000 = $800, and D was not due to start until day 15 and contributes nothing. So $PV=\$8{,}800$ and $$SPI=\frac{EV}{PV}=\frac{8{,}800}{8{,}800}=1.00,\qquad SV=EV-PV=\$0$$ The project is exactly on schedule while being 20 % over cost — the classic signature of an activity that was recovered by spending more, not by working faster. Activity A ran two days long, but B and C absorbed the slippage and started on their planned dates.