Earned value (EVM): SPI and CPI with a worked example
Earned value is a way to measure project performance by comparing three figures at one date: planned value (PV) for the work that should be done, earned value (EV) for the work actually done at budget prices, and actual cost (AC) for what was spent. From them come the schedule performance index SPI = EV ÷ PV and the cost performance index CPI = EV ÷ AC, where a value below 1 means delay or overrun. They also give the forecast of what the project will cost at completion (EAC).
By Ta3mir engineering team · Published · Last updated
The base figures: BAC, PV, EV and AC
| Figure | The question it answers | How it is worked out |
|---|---|---|
| Budget at completion (BAC) | What should the whole project cost per the plan? | The sum of activity budgets on the approved baseline |
| Planned value (PV) | How much should be done by today? | Each activity budget × its planned % to the data date |
| Earned value (EV) | How much is actually done, at budget prices? | Each activity budget × its actual % complete |
| Actual cost (AC) | How much was spent on it? | The costs recorded up to the data date |
The four figures must share one basis: the budget at cost, not at selling price, in one currency, and up to the same data date. If the budget is at selling price and the actual cost at cost, the cost performance index looks better than it is.
Variances and the SPI and CPI indices
Schedule variance SV = EV − PV
Cost variance CV = EV − AC
Schedule performance index SPI = EV ÷ PV
Cost performance index CPI = EV ÷ AC
| Value | SPI | CPI |
|---|---|---|
| Above 1 | Ahead of schedule | Under budget |
| Equal to 1 | On schedule | On budget |
| Below 1 | Behind schedule | Over budget |
A negative variance and an index below 1 say the same thing two ways: the variance measures the gap in money, the index as a ratio that compares projects of different sizes. The schedule variance is also measured in money, so it is not a number of days late; read it together with the critical path in the programme.
Forecasting completion: EAC, ETC and VAC
Estimate at completion EAC = BAC ÷ CPI
Estimate to complete ETC = EAC − AC
Variance at completion VAC = BAC − EAC
The first formula assumes the cost efficiency so far continues to the end, and it is the most used. Other forms exist, such as EAC = AC + (BAC − EV), which assumes the remaining work is done at budget rates and suits an overrun caused by a one-off event. Choose the form by the cause of the variance, and state it with the figure.
How to measure actual progress
Earned value is only as accurate as the progress percentages behind it. Measure each activity's actual % from quantities done or agreed milestones, then multiply by its budget, so project progress is weighted by cost rather than a plain average of percentages.
| Activity | Budget | Planned to date | PV | Actual | EV |
|---|---|---|---|---|---|
| Excavation and backfill | 300,000 | 100% | 300,000 | 100% | 300,000 |
| Reinforced concrete | 1,000,000 | 50% | 500,000 | 40% | 400,000 |
| Masonry and finishes | 700,000 | 0% | 0 | 0% | 0 |
- Do not use money spent as progress: it makes EV always equal AC and hides the overrun.
- Do not use elapsed duration instead of actual progress: an activity half way through its time may be only a quarter done.
- Fix the baseline before measuring and change it only through an approved variation, or the comparison loses its meaning.
- Book costs to the right project and cost code: uncoded cost distorts AC.
Worked example: a three-activity project
Illustrative figures. A project with a budget of EGP 2,000,000 and three activities (tabled in the previous section). At the data date the work planned was worth 800,000, the work actually done at budget prices 700,000, and the actual cost recorded 760,000.
| Figure | Formula | Value |
|---|---|---|
| Budget at completion (BAC) | Sum of activity budgets | 2,000,000 |
| Planned value (PV) | Budget × planned % | 800,000 |
| Earned value (EV) | Budget × physical % | 700,000 |
| Actual cost (AC) | From the books | 760,000 |
| Schedule variance (SV) | EV − PV | -100,000 |
| Cost variance (CV) | EV − AC | -60,000 |
| Schedule performance index (SPI) | EV ÷ PV | 0.875 |
| Cost performance index (CPI) | EV ÷ AC | 0.921 |
| Estimate at completion (EAC) | BAC × AC ÷ EV | 2,171,428.57 |
| Estimate to complete (ETC) | EAC − AC | 1,411,428.57 |
| Variance at completion (VAC) | BAC − EAC | -171,428.57 |
Reading: the project is behind schedule (SPI = 0.875, so 87.5% of the planned work is done) and over cost (CPI = 0.921, so each pound spent produced about 0.921 of work). If the cost efficiency stays the same, the estimate at completion is EGP 2,171,428.57, 171,428.57 over budget.
Steps to apply earned value to your project
- Prepare the programme with activities and their links, and spread the project budget, at cost, across the activities.
- Approve a baseline that freezes dates and budgets as the single reference for measurement.
- Set the data date and record each activity's actual progress from site.
- Total the actual cost to the data date for the same project and in the same currency.
- Work out PV and EV, then the variances and indices, then EAC, ETC and VAC.
- Save a snapshot every period to see the indices' trend on the S-curve, and look into the cause of every index below 1.
How to do it in Ta3mir
In Ta3mir earned value is computed on its own page within the schedule, against the active approved baseline, with the same formulas as this guide.
- BAC is the sum of activity budgets frozen on the baseline, and PV spreads each activity budget linearly over the working days of the baseline calendar.
- EV is each activity budget × its actual % complete; where no actual % exists, duration progress is used instead and the page says so.
- AC is accrual: expenses plus issued purchase and subcontractor invoices, without counting their payments a second time.
- CPI and SPI to three decimals, EAC = BAC ÷ CPI, ETC and VAC, with a snapshot history that draws the S-curve.
Sources
- Project Management Institute (PMI): A Guide to the Project Management Body of Knowledge (PMBOK Guide), the standard earned value formulas
This guide is an explanatory summary written by the Ta3mir engineering team and is not professional advice. Figures in the example are illustrative. If your contract or your project's reporting rules set another way to measure progress or forecast cost, they govern.