Earned value at month 12 of a building contract, three ways to forecast the outturn, and the input that hides an overrun.
Earned value compares three numbers at the same date: the value of work planned (PV), the budgeted value of work actually done (EV) and the cost actually incurred (AC). CPI is EV divided by AC, SPI is EV divided by PV, and the standard estimate at completion is the budget divided by CPI. On an illustrative 26,000,000 project at month 12, EV of 11,160,000 against AC of 12,090,000 gives a CPI of 0.92, an SPI of 0.90 and an EAC of 28,166,667, a forecast overrun of 2,166,667 or 8.3 per cent.
Worked in full in Construction Cost Control by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The method is simple; the difficulty on a construction project is getting EV right. A valuation, a payment certificate and a cost report all describe progress in money, and only one of them is earned value. The worked example below runs the formulas, then shows what the wrong input does to the forecast.
| Input | Meaning | Value |
|---|---|---|
| Budget at completion (BAC) | Approved cost budget, including approved changes | 26,000,000 |
| Planned value (PV) | Budget of the work the programme says should be done by now | 12,400,000 |
| Earned value (EV) | Budget of the work actually in place, measured at budget rates | 11,160,000 |
| Actual cost (AC) | Cost incurred for that work, including accruals | 12,090,000 |
Cost variance CV = EV − AC = 11,160,000 − 12,090,000 = −930,000
Schedule variance SV = EV − PV = 11,160,000 − 12,400,000 = −1,240,000
Both are negative: the work in place cost 930,000 more than its budget, and 1,240,000 of budgeted work that should have been done by now has not been. The planned position was 47.7 per cent complete; the project has earned 42.9 per cent and spent 46.5 per cent of the budget.
CPI = EV ÷ AC = 11,160,000 ÷ 12,090,000 = 0.923
SPI = EV ÷ PV = 11,160,000 ÷ 12,400,000 = 0.900
In Excel, with BAC, PV, EV and AC in B1 to B4: CPI =B3/B4, SPI =B3/B2. A CPI of 0.923 means each 1.00 of budgeted work is costing 1.083, an overrun of 8.3 per cent on everything done so far.
There is no single EAC. Each formula is a statement about what will happen to the remaining 14,840,000 of budgeted work, and the cost report should say which statement it is making.
| Method | Assumes | EAC | Variance at completion | Over budget |
|---|---|---|---|---|
| BAC ÷ CPI | The cost performance so far continues | 28,166,667 | -2,166,667 | 8.3% |
| AC + (BAC − EV) | The overrun was a one-off; the rest goes to budget | 26,930,000 | -930,000 | 3.6% |
| AC + (BAC − EV) ÷ (CPI × SPI) | Cost and delay both persist and compound | 29,952,963 | -3,952,963 | 15.2% |
The middle line is the most tempting to report and the hardest to justify. It requires a reason the overrun will stop: a re-procured package, a resolved design issue, a productivity problem fixed. The third line uses a combined index of 0.831 and fits a building job where the delay itself costs money, because time-related site costs keep running while the work is late; that cost of time is worked in how to calculate prolongation costs for an extension of time.
TCPI = (BAC − EV) ÷ (BAC − AC) = 14,840,000 ÷ 13,910,000 = 1.067
To finish on the original budget, every remaining 1.00 of budget has to buy 1.067 of work, after the work done so far bought 0.923. A swing from 0.92 to 1.07 almost never happens on a building contract without a scope reduction. When the TCPI to the budget is well above the CPI achieved so far, the budget is no longer a forecast and the report should say so.
Dividing the 24-month programme by an SPI of 0.90 suggests 26.7 months. That is a rough guide only, because SPI is measured in money and always returns to 1.00 at completion, however late the job finishes. Earned schedule converts it to time: EV of 11,160,000 equals the planned value at 11.14 months (PV was 10,950,000 at month 11 and 12,400,000 at month 12), so the job is 0.86 of a month behind, an SPI(t) of 0.929 and a projected duration of 25.8 months. Neither replaces the critical path programme, but earned schedule does not decay as the job nears the end.
| CPI | EAC | Overrun | Over budget |
|---|---|---|---|
| 1.000 | 26,000,000 | 0 | 0.0% |
| 0.970 | 26,804,124 | 804,124 | 3.1% |
| 0.950 | 27,368,421 | 1,368,421 | 5.3% |
| 0.923 | 28,166,667 | 2,166,667 | 8.3% |
| 0.900 | 28,888,889 | 2,888,889 | 11.1% |
| 0.850 | 30,588,235 | 4,588,235 | 17.6% |
The curve steepens as CPI falls: from 0.970 to 0.950 the outturn moves by 564,297, from 0.900 to 0.850 by 1,699,346. A CPI rounded to one decimal place is not good enough for a board report.
On a construction contract the obvious progress figure is the gross valuation. It is not earned value. It includes variations that may not yet be in the budget, materials on site not yet built in, and whatever the contractor managed to get valued early. Suppose the month 12 gross valuation is 12,350,000. Used as EV against the same 12,090,000 of cost, it gives a CPI of 1.02 and an EAC of 25,452,632, an apparent saving. The real forecast is 28,166,667: the wrong input has hidden 2,714,035. Measure EV as the budget value of the work physically in place, add approved changes to BAC and PV before they enter EV, and keep unapproved changes out of both.
CPI 0.92, SPI 0.90, EAC 28,166,667 by the standard formula, between 26,930,000 and 29,952,963 depending on what you believe about the remaining work. State the assumption, and check the TCPI before promising the budget. Construction Cost Control follows one contract from the contract sum to the final account, and the free workbooks for this case show where the movement between the two comes from line by line. Escalation on the remaining work is worked in construction cost escalation to the midpoint.
A CPI of 1.00 means work is costing exactly its budget; above 1.00 is under budget. Many cost managers treat anything below about 0.95 as a warning, because research on large defence contracts found the cumulative index rarely recovers much once a job is about a fifth complete. In the example a CPI of 0.923 at month 12 of 24 projects an 8.3 per cent overrun, 2,166,667 on a 26,000,000 budget.
EAC, the estimate at completion, is the total forecast cost of the project. ETC, the estimate to complete, is what is still to be spent: EAC minus actual cost to date. With an EAC of 28,166,667 and 12,090,000 already spent, the ETC is 16,076,667. The cost report should show both, with the ETC built up from the remaining packages where possible.
The to-complete performance index is the efficiency the remaining work must achieve to finish on a target. A TCPI of 1.067 to the original budget means each remaining 1.00 of budget must deliver 1.067 of work, after the work so far has delivered 0.923. A gap that wide signals the budget is unattainable without a scope change.
This article is one calculation from Construction Cost Control. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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