Earned Value

Earned Value

Earned Value, Forecasting and Earned Schedule

Three curves

Earned value management integrates scope, schedule and cost by pricing every piece of planned work in the same money and tracking three cumulative curves against time. The planned value PV (budgeted cost of work scheduled, BCWS) is the baseline: the budget that should have been earned by each date if the work went to plan, rising to the budget at completion BAC at the planned duration PD. The earned value EV (budgeted cost of work performed, BCWP) is the budget of the work actually done, measured by the same rules that built the plan (milestones, percent complete, units delivered), so it can never exceed BAC. The actual cost AC (ACWP) is what the work done so far has cost. Everything else is arithmetic on the three curves at a status date, the actual time AT counted in reporting periods from the start. The tool takes the three values period by period, either as running totals or as the amounts of each period, and evaluates the status at a chosen row.

Variances and indices

The cost variance CV = EV − AC says whether the work done cost more or less than it was budgeted to cost; the schedule variance SV = EV − PV says whether more or less work was done than planned. Both are in money, favourable when positive, and both are usually read as percentages, CV % = CV/EV and SV % = SV/PV. The cost performance index CPI = EV/AC is the value earned per unit of money spent (1.02 means 1.02 of budget earned per 1.00 spent), and the schedule performance index SPI = EV/PV the value earned per unit planned. Their product CPI × SPI, the cost-schedule or critical-ratio index, compounds the two. Percent scheduled PV/BAC, percent complete EV/BAC and percent spent AC/BAC place the status on the whole project. These are the definitions of the DAU and DOE Gold Cards, which the page follows.

A cumulative CPI is a stable statistic: on large defence programmes it has been found to vary by less than 10 % after the project is 20 % complete, and to get worse rather than better from there. That stability is what makes the forecasts below credible, and the reason a CPI of 0.9 at one-third complete is a problem to be acted on and not a transient.

Forecasting the cost at completion

Every estimate at completion is EAC = AC + (BAC − EV)/PF: the money spent plus the budgeted work remaining WR = BAC − EV priced at an assumed performance factor PF for the rest of the project. Four factors are standard:

• PF = 1: the remaining work costs exactly its budget, EAC = AC + BAC − EV. This is the optimist's figure; it assumes the variance to date was a one-off.
• PF = CPI: the remaining work runs at the efficiency achieved so far, EAC = AC + (BAC − EV)/CPI, which is identical to BAC/CPI. This is the usual forecast and the one the Gold Cards print first.
• PF = CPI × SPI: schedule slip is assumed to drive cost further (overtime, extended overheads), EAC = AC + (BAC − EV)/(CPI × SPI). It is the most pessimistic of the index forms while SPI is below 1.0 and becomes meaningless as SPI returns to 1.0 near completion.
• A bottom-up estimate to complete ETC from a re-estimate of the remaining work, EAC = AC + ETC: the project's own figure, informed by what is now known about the remaining tasks.

For each the estimate to complete is ETC = EAC − AC and the variance at completion VAC = BAC − EAC, positive for a projected underrun. The spread between the formulas is itself information: when the CPI and CPI × SPI figures bracket the bottom-up estimate the three stories agree; when the bottom-up figure sits below BAC/CPI the re-estimate assumes an improvement that the record does not show.

To-complete performance index

TCPI turns the forecast round: what efficiency must the remaining work achieve to land on a target? TCPI(BAC) = (BAC − EV)/(BAC − AC) is the CPI needed on the rest of the work to finish on budget; TCPI(EAC) = (BAC − EV)/(EAC − AC) is the efficiency needed to finish on a stated EAC. Against the CPI-based EAC the latter equals CPI by construction, which is the check that the forecast is self-consistent; against a bottom-up EAC it tests the re-estimate. A TCPI more than about 0.10 above the cumulative CPI calls for a sustained improvement that projects rarely deliver, and the budget target should then be treated as lost.

Why the money-based schedule measures fail

SV and SPI are built from EV and PV, and at completion EV = PV = BAC whatever the finish date, so SV returns to zero and SPI to 1.0 for a project that finished late, and they begin to drift that way over the final third of the project (Lipke 2003). They also report in money, which answers "how much work is behind" but not "how late". The measures remain useful early in a project and for the cost forecast, but a time measure is needed for the schedule.

Earned schedule

Lipke's earned schedule projects the earned value onto the baseline: ES is the time at which the PV curve reaches the EV earned to date. With cumulative PV known at the end of each period (PV₀ = 0), find the number of whole periods n whose PV_n is at or below EV and interpolate within the next one,

ES = n + (EV − PV_n)/(PV_n+1 − PV_n),

so that in Lipke's August example, EV = 1,900 lying between PV(Jul) = 1,805 and PV(Aug) = 2,135, ES = 7 + 95/330 = 7.288 months. The schedule variance in time is SV(t) = ES − AT and the time-based index SPI(t) = ES/AT, both referred to the actual time just as CV and CPI are referred to the actual cost. For a late project ES stops at the planned duration while AT keeps counting, so SV(t) ends at the lateness in periods and SPI(t) at PD/(actual duration) rather than at 1.0; for an early project SV(t) ends at the time gained. A plateau in the baseline (PV constant over several periods) gives ES the end of the last rising period, and an earned value above every baseline value, which can only happen when the pasted baseline does not reach BAC, is capped at the last period and flagged. When the baseline is coarse (quarterly totals), ES is the linear interpolation the data allow; a finer baseline gives a finer ES.

Duration forecasts

With the planned duration PD, read from the baseline as the first period at which the cumulative PV reaches BAC or entered directly, the planned duration of the work remaining is PDWR = PD − ES and the independent estimate at completion in time is the long form IEAC(t) = AT + PDWR/PF(t) for a chosen time performance factor (Lipke and Henderson 2006). PF(t) = SPI(t) gives the short form IEAC(t) = PD/SPI(t), the schedule analogue of BAC/CPI; PF(t) = 1 assumes the rest runs to plan; PF(t) = CPI × SPI(t) lets the cost trend drag the schedule. The variance at completion in time is VAC(t) = PD − IEAC(t), and the to-complete schedule performance index TSPI = PDWR/(PD − AT) is the time efficiency the remaining work must reach to finish on the planned duration, read against SPI(t) like TCPI against CPI. The page also lists the money-based forms PD/SPI and PD/(CPI × SPI) that were in use before earned schedule, for comparison: on the two real projects of Lipke and Henderson's Table 1 only PD/SPI(t) reproduced both the early and the late finish, the money forms failing on at least one because SPI tends to 1.0.

Reading the results

The status section gives the cumulative values and every variance and index at the chosen period with the formulas substituted. The forecast section tabulates the four EACs with their ETC, VAC and the TCPI to each, and a sentence compares the TCPI to BAC with the achieved CPI. The earned-schedule section shows the interpolation, SV(t), SPI(t), the duration forecasts and TSPI. The period table repeats the indices for every row of the pasted data so the trend can be seen, with the status row in bold; after the planned duration the money-based SV and SPI are seen drifting back to 0 and 1.0 while SV(t) and SPI(t) keep measuring the lateness, which is the whole point of the method. Figure 1 is the S-curve, with the rows after the status drawn dashed and the cost forecast drawn as a straight line from the status point to EAC at the IEAC(t) date; Figure 2 is the index chart.

Conventions and limits

• Money is one currency throughout and time is the reporting period of the table; the tool carries no units. Use consistent periods (all months or all weeks) and no thousands separators in the pasted table.
• PV must be non-decreasing and reach BAC for the planned duration to be read; EV cannot exceed BAC. A decreasing EV (credit taken back) is allowed with a note.
• The status period is a row of the table; a status part-way through a period is handled by Lipke's fraction-of-period convention in the actual time, which the tool does not implement: enter whole periods.
• The forecasts are index projections, not schedule-network analyses. Earned schedule gives the time the earned work was planned to take; it does not see the critical path, so a project that has earned off-critical work early can show a healthy SPI(t) while its critical path slips. Lipke's later schedule-adherence measure (the P factor) addresses that and is not implemented here.
• Management reserve, undistributed budget and over-target baselines are outside the tool: BAC is taken as the performance measurement baseline total.
• Statistical confidence limits on the forecasts (Lipke's later work on prediction with confidence) are not included; the spread between the four EACs and between the duration forms is the indication of uncertainty offered.