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, with a light bar for time actually spent and a dark bar for the planned duration of each activity. Every activity is charged at $1,000 per day of work, so a bar length in days converts directly into dollars. Activity C has started but is not finished; activity D has not started.

Find. The cost performance index for each of the four activities and for the project as a whole at the data date, crediting progress by the 20/80 rule.

[Figure not reproduced: Figure 1.1 — the examination bar chart redrawn to scale. Light bars are time actually spent, dark bars are planned durations, and the dashed line is the data date at day 12. Activity C’s dark bar runs past the data date because the activity is still in progress; activity D has no light b. See the official exam paper.]

Approach. Convert every bar length to money at $1,000 per day, credit earned value by the 20/80 rule (0 % not started, 20 % started, 100 % finished), then form the ratio of earned value to actual cost activity by activity and once more on the summed totals.

1. Convert planned bar lengths into budgets. The budget at completion of an activity is its planned duration priced at the daily rate, $$BAC_i = d_{\text{planned},i}\times r,\qquad r = 1000\ \text{per day}$$ so A, B and C each carry a four-day budget of $4,000 while D, a one-day activity, carries $1,000. The total project budget is $13,000.
2. Convert the light bars into actual cost to date. Actual cost is time genuinely expended, priced at the same rate, $$AC_i = d_{\text{actual},i}\times r$$ giving $6,000 for A (six days of work against a four-day plan), $4,000 for B, $1,000 for C (one day so far) and nothing at all for D, which has not started. Summing, the project has consumed $11,000 of cash-equivalent effort.
3. Assign percent complete by the 20/80 rule. The rule is a deliberately coarse progress convention: an activity is credited with 20 % of its budget the moment it starts and the remaining 80 % only when it finishes, with nothing in between. Nothing is credited for an activity that has not started. On that basis A and B are at 100 %, C is at 20 % and D is at 0 %. Notice that the rule ignores how long C has actually been running — one day or three, it earns the same 20 % until it is complete.
4. Compute earned value. Earned value is the budgeted cost of the work genuinely performed, $$EV_i = p_i\times BAC_i$$ so A and B each earn their full $4,000, C earns $$EV_C = 0.20\times 4000 = 800$$ and D earns nothing. The project has therefore earned $8,800 of its $13,000 budget.
5. Form the cost performance index activity by activity. The index compares value earned with cash spent, $$CPI_i = \frac{EV_i}{AC_i}$$ which gives $$CPI_A=\frac{4000}{6000}=0.667,\quad CPI_B=\frac{4000}{4000}=1.00,\quad CPI_C=\frac{800}{1000}=0.80$$ Activity D has both a zero numerator and a zero denominator, so its index is indeterminate and is properly reported as not applicable rather than as zero — no work has been bought and none has been earned.
6. Roll the totals up to a project index. A project index is formed from summed dollars, never from an average of the activity indices, because each activity must be weighted by the money flowing through it: $$CPI_{\text{project}}=\frac{\sum EV_i}{\sum AC_i}=\frac{4000+4000+800+0}{6000+4000+1000+0}=\frac{8800}{11000}$$ so that $$\boxed{CPI_{\text{project}} = 0.80}$$ The project is buying 80 cents of earned value for every dollar spent, an overrun of 25 % on work performed to date. Averaging the three defined activity indices would have returned 0.822 and quietly flattered the result.
7. Interpret the numbers. The cost variance is $$CV = EV - AC = 8800 - 11000 = -2200$$ a $2,200 overrun that is entirely attributable to activity A, which took six days against a four-day plan; B ran exactly to plan and C is marginally behind on cost. If the present cost efficiency persists, the estimate at completion is $$EAC = \frac{BAC}{CPI} = \frac{13000}{0.80} = 16250$$ that is $16,250 against a $13,000 budget. Note also that the planned value at day 12 is likewise $8,800 (A and B were both due to be complete, C was due to have started), so $$SPI = \frac{EV}{PV} = \frac{8800}{8800} = 1.00$$ and the project is on schedule but over cost — the classic signature of buying progress with overtime or extra crew.