Question 1 of 6: Project Control — earned value and the 20/80 rule

Question 1: Project Control — earned value and 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 read at a data date of day 12, in which the darker bar of each pair is the planned duration and the lighter bar is the time actually spent so far. Every activity consumes $\$1{,}000$ of cost for each day it is worked, and credit is taken under the 20/80 rule: an activity earns 20 % of its budget the moment it starts and the remaining 80 % only when it finishes.

Find. The cost performance index of each of the four activities and of the project as a whole, at the data date.

[Figure not reproduced: Figure 1.1 — the bar chart as printed, redrawn to scale. Light bars are time actually spent, dark bars are planned durations, and the red line is the data date at day 12. Activity A overran, B matched plan, C has started but is unfinished, and D lies entirely in the future. See the official exam paper.]

Approach. Convert each planned bar into a budget and each actual bar into an incurred cost at $\$1{,}000$ per activity-day, credit earned value from the 20/80 milestone rule rather than from elapsed time, and divide earned value by actual cost for each activity and for their totals.

1. Budget each activity from its planned bar. The budget at completion of an activity is its planned duration multiplied by the daily cost, $BAC_i = d_{plan,i}\times c$ with $c = \$1{,}000$ per day:$$BAC_A = BAC_B = BAC_C = 4\times\$1{,}000 = \$4{,}000,\qquad BAC_D = 1\times\$1{,}000 = \$1{,}000$$The four budgets sum to a project budget of $\$13{,}000$.
2. Charge the actual cost from the light bars up to the data date. Cost is incurred only for days actually worked, so $AC_i = d_{act,i}\times c$:$$AC_A = 6\times\$1{,}000 = \$6{,}000,\quad AC_B = \$4{,}000,\quad AC_C = 1\times\$1{,}000 = \$1{,}000,\quad AC_D = \$0$$The project has therefore spent $\$11{,}000$ so far. Note that activity A kept charging for the two days it overran, which is exactly the effect the index has to expose.
3. Credit earned value under the 20/80 rule. The rule is a two-milestone rule: a started activity is credited with 20 % of its budget and nothing more until it is complete, when it takes the full 100 %. Progress inside an activity is deliberately not measured, which removes the optimism that continuous percent-complete reporting introduces:$$EV_A = 1.00\times\$4{,}000 = \$4{,}000,\qquad EV_B = 1.00\times\$4{,}000 = \$4{,}000$$Activity C has started but is unfinished, so it earns only the opening milestone, $EV_C = 0.20\times\$4{,}000 = \$800$; activity D has not started and earns $EV_D = \$0$. The project earned value is $\$8{,}800$.
4. Form the activity cost performance indices. The index is earned value divided by actual cost, $CPI = EV/AC$, so a value below unity means the work in place cost more than it was budgeted to cost:$$CPI_A = \frac{\$4{,}000}{\$6{,}000} = 0.67,\qquad CPI_B = \frac{\$4{,}000}{\$4{,}000} = 1.00,\qquad CPI_C = \frac{\$800}{\$1{,}000} = 0.80$$Activity D has neither earned nor spent anything, so its index is the indeterminate ratio $0/0$ and is reported as not applicable rather than as zero — an unstarted activity carries no cost performance information at all.
5. Roll the totals up to a project index. Project performance is the ratio of the summed quantities, never the average of the activity indices:$$CPI_{proj} = \frac{\sum EV}{\sum AC} = \frac{\$8{,}800}{\$11{,}000}\;\Rightarrow\; \boxed{CPI_{proj} = 0.80}$$Averaging the three defined activity indices would have given 0.82, which is wrong because it weights a $\$1{,}000$ activity equally with a $\$6{,}000$ one.
6. Read the result against the other control indices. The planned value at day 12 is what the plan says should have been earned by now: A and B complete and C started, so $PV = \$4{,}000+\$4{,}000+0.20\times\$4{,}000 = \$8{,}800$. The schedule performance index is therefore $SPI = EV/PV = 1.00$ and the cost variance is $CV = EV-AC = -\$2{,}200$. The project is on schedule and 20 % over cost, and the overrun is entirely attributable to activity A. If the present efficiency persists, the forecast at completion is $EAC = BAC/CPI = \$13{,}000/0.80 = \$16{,}250$, a projected overrun of $\$3{,}250$.