Project controls × Research note
Forecasting final cost: when the CPI formula works, and when it doesn’t
Earned value’s favourite shortcut assumes that a project’s cost efficiency settles early and stays put. That holds on some projects and not on others. Here is what the research says, and where machine learning adds something real.
Key takeaways
- The standard forecast, EAC = BAC ÷ CPI, assumes the cost efficiency to date will continue for the rest of the job.
- On 155 large defence contracts, cumulative CPI barely moved after 20% complete. That result is the basis of the “CPI stability” rule.
- It does not transfer automatically: on 136 environmental remediation projects, CPI did not settle until 41% complete, and it is rarely stable on smaller commercial projects.
- Construction front-loads procurement, change orders and subcontract packages, which is exactly what breaks the assumption.
- ML can learn from completed projects which early patterns predict overrun, but only if it is tested on later projects and compared honestly with the CPI baseline.
01The formula everyone uses
Earned value management compares three numbers at any point in a project: the budgeted cost of work planned, the budgeted cost of work actually performed (earned value, EV) and the actual cost of that work (AC). The cost performance index, CPI = EV ÷ AC, says how much budgeted work you get for each unit spent. A CPI of 0.9 means every ₹100 spent has earned ₹90 of planned work.
The most common forecast of final cost divides the budget at completion by the CPI to date: EAC = BAC ÷ CPI. It is simple, explainable and built into most project controls software. It also carries a strong assumption: the efficiency of the work done so far is the efficiency of the work still to do.
02The evidence for CPI stability
The assumption has a respectable origin. In 1993, David Christensen and Scott Heise analysed cost performance reports from 155 government defence contracts across 44 programmes from 1971 to 1991: aircraft, missiles, electronics, ships, software and more. They found that from the 20% completion point to contract completion, the range of the cumulative CPI was less than 0.20 on every contract[1]. That is usually summarised as “after 20% complete, cumulative CPI does not change by more than ±0.10”.
If that holds, the CPI formula gives a usable forecast early in a project, and a CPI of 0.85 at 20% complete is an early warning that is unlikely to fix itself.
03The evidence against assuming it
Later research tested whether the rule transfers to other kinds of projects. It often doesn’t.
- Clayson, Thal and White studied monthly earned value data for 136 environmental remediation projects at a government agency (fiscal years 2012–2013). CPI did not stabilise until the projects were 41% complete by duration, and stability depended on factors such as contractor qualifications, communication, stakeholder engagement and contracting strategy[2].
- Research by Henderson and Zwikael, discussed by Patrick Weaver, found CPI stability is not a given and rarely exists on smaller commercial projects. Where stability does appear, it is better read as a sign of a good plan, stable scope and effective management than as a law of nature[3].
Figure
Completion point after which cumulative CPI settled
CPI stability is better read as a sign of a good plan and stable scope than as a law of nature.
04Why construction breaks the assumption
A building project’s cost curve is not a steady stream of similar work. Several features common in construction make early CPI a weak guide to late CPI:
- Front-loaded commitments. Early packages such as piling, frame and long-lead procurement are often bought competitively and may perform well, while finishes and services come later with more interfaces and more variation.
- Change orders. Scope added mid-project changes both the budget and the actual cost; if the budget isn’t updated promptly, CPI moves for reasons unrelated to productivity.
- Subcontract timing. Cost is often recognised when a subcontractor bills, not when the work happens, which moves AC relative to EV.
- Price movement. Material escalation during the job raises actual cost without any change in site efficiency.
None of this makes the CPI formula useless. It makes it a baseline: the forecast any better method has to beat.
05Where machine learning genuinely helps
A model trained on completed projects can learn which early patterns preceded overruns: the mix of cost codes, the pace of commitments, variation history, the gap between billed and certified work. It can also output a range rather than a single number. But three disciplines separate a useful forecast from an impressive-looking one:
- Test on later projects. Train on projects that finished earlier and test on projects that came later. A random split lets the model see the future.
- Beat the baseline where it matters. The early stage, below about 30% complete, is where a forecast is most useful and where CPI is least reliable. Report accuracy there separately.
- Stay explainable. A cost manager needs to see why the forecast moved (which packages, which codes), or they won’t act on it.
06Case study: Project Cost & Margin Intelligence
From my portfolio · project 06 of 15
Synthetic data- Problem
- Final cost and margin are forecast with the CPI formula, which is least reliable early on.
- Decision supported
- Where margin is at risk, and next quarter’s spend.
- Data
- 30 live projects plus 239 completed projects (2016–2023), monthly cost history.
- Method
- Ridge, Random Forest, XGBoost, MLP and LSTM against the CPI formula; quantile ranges with conformal calibration.
- Result
- 2.8% error below 30% complete vs 4.6% for CPI; next-quarter spend error 14% vs 36%.
- Limits
- Synthetic data; the P10–P90 band held 76% of outcomes against an 80% target.
07Ranges and next-quarter spend
A final-cost forecast is only half of what a cost manager needs. The other half is how sure the forecast is, and how much cash the project will draw next. In my Cost & Margin project, the same model family produces both[4]:
Figure
Next-quarter spend forecast error (WAPE, lower is better)
- Margin accuracy. At about 50% complete, the forecast margin was off by 1.9 percentage points of contract value, against 2.8 for the CPI formula, and closer on 14 of 20 projects.
- Range honesty. The P10–P90 band held the final cost 76% of the time against an 80% target, with a median width of 7% of budget. Slightly too narrow, and reported as such.
08How strong is the evidence?
Not every finding in this note rests on the same kind of evidence. This is how I would weigh each one before acting on it.
| Finding | Evidence | Strength | Main caveat |
|---|---|---|---|
| Cumulative CPI settles by 20% complete | 155 defence contracts, 1971–1991 | Moderate | Defence programmes with mature EVM |
| CPI can take much longer to settle elsewhere | 136 environmental remediation projects | Moderate | One agency, two fiscal years |
| CPI stability is rare on smaller commercial work | Later research, summarised by a practitioner | Indicative | Secondary summary of the studies |
| ML beats the CPI formula early in a project | My test on 239 completed projects | Indicative | Synthetic data; validate on real history |
09A practical forecasting routine
- Report CPI-based EAC as the baseline, and say how stable CPI has been over the last few periods.
- Add at least one independent forecast: bottom-up estimate to complete, a model, or both, and explain any gap.
- Keep budgets current. Approve and load change orders promptly so CPI reflects performance, not paperwork.
- Show a range. P10–P90 on final cost is more honest than one EAC figure, especially early.
- Track forecast accuracy over time on completed projects, by project stage, so you know which method to trust when.
NotesSources
- Christensen, D. S. and Heise, S. R. (1993). Cost performance index stability. Paper analysing 155 US defence contracts, 1971–1991.
- Clayson, D. S., Thal, A. E. and White, E. D. (2018). Cost performance index stability: insights from environmental remediation projects. Journal of Defense Analytics and Logistics, 2(2).
- Weaver, P. The CPI stability myth. Mosaic Projects.
- Iwale, A. (2026). Project Cost & Margin Intelligence. GitHub.
Figures are quoted from the sources above as published; where a source reports a range or a survey estimate, it is described that way. Results from my own projects say whether they use real public data or synthetic data.