Forecasting cost at completion

Every month the project team must answer the question management cares about most: what will this job finally cost? Lesson 6 built that answer line by line, from commitments and judgement. Earned value offers a second set of answers, from formulas that project current performance forward. Neither is right on its own. The formulas are fast, objective and hard to argue with, but they assume the future will resemble the past in a particular way. The bottom-up forecast captures what the team knows about the remaining work, but it is open to optimism. This lesson sets out the standard estimate at completion (EAC) formulas, the to-complete performance index (TCPI) that tests whether a forecast is believable, and how to combine the methods into a forecast that holds up.

Estimate to complete and estimate at completion

The estimate at completion is the expected final cost of the work. It is always actual cost to date plus an estimate to complete (ETC) for the remaining work. The formulas differ only in how they estimate the ETC.

The remaining work, in budget terms, is BAC minus EV. The question is how efficiently that remaining budget will be converted into cost.

The standard formulas

The second formula is algebraically the same as AC + (BAC − EV) ÷ CPI. Because CPI tends to be stable after the early part of a job (Lesson 8), BAC ÷ CPI is often treated as a reasonable lower bound on the final cost of a project already performing below budget: experience suggests outcomes better than BAC ÷ CPI are uncommon once a job is well under way. The third formula, using CPI × SPI, gives a higher figure on a late job and is often treated as a reasonable upper bound when there is schedule pressure.

# EAC by four methods, Riverbend Commons at month 8 (amounts $)
BAC, EV, AC, PV = 16_124_000, 7_907_000, 8_163_000, 8_860_000
CPI, SPI = EV / AC, EV / PV
remaining = BAC - EV
bottom_up_etc = 8_352_000          # from the line-by-line cost report (Lesson 6 method)
methods = {
    "At budget rates  AC + (BAC - EV)": AC + remaining,
    "At cumulative CPI  BAC / CPI": BAC / CPI,
    "CPI x SPI  AC + rem / (CPI*SPI)": AC + remaining / (CPI * SPI),
    "Bottom-up  AC + ETC": AC + bottom_up_etc,
}
print(f"CPI {CPI:.3f}  SPI {SPI:.3f}  remaining budget {remaining:,}")
for name, eac in methods.items():
    print(f"{name:<36} EAC {eac:>12,.0f}   VAC {BAC - eac:>+11,.0f}")

CPI 0.969  SPI 0.892  remaining budget 8,217,000
At budget rates  AC + (BAC - EV)     EAC   16,380,000   VAC    -256,000
At cumulative CPI  BAC / CPI         EAC   16,646,037   VAC    -522,037
CPI x SPI  AC + rem / (CPI*SPI)      EAC   17,668,464   VAC  -1,544,464
Bottom-up  AC + ETC                  EAC   16,515,000   VAC    -391,000

The four methods give a range from about $16.4 million to $17.7 million. The budget-rate figure is the most optimistic: it assumes every remaining dollar will be spent exactly as planned, which nothing in the trend supports. The CPI × SPI figure is the most pessimistic, because it lets the 11 % schedule shortfall inflate the cost of all remaining work. The bottom-up forecast sits between BAC ÷ CPI and the budget-rate figure.

Variance at completion

The variance at completion (VAC) is the budget at completion minus the estimate at completion. A negative VAC is a forecast overrun. VAC is the number that tells management how much of the contingency and fee the job is expected to consume.

The to-complete performance index

The to-complete performance index (TCPI) asks the reverse question: what cost efficiency must the remaining work achieve to finish at a given target? It divides the work remaining by the money remaining.

TCPI is a credibility test. If the project has been working at a CPI of 0.97 and the bottom-up forecast requires a TCPI of 1.10 for the rest of the job, the forecast is assuming a dramatic improvement that should be explained by specific changes. A common rule of thumb is that a TCPI more than about 0.05 to 0.10 above the cumulative CPI deserves serious scrutiny.

BAC, EV, AC = 16_124_000, 7_907_000, 8_163_000
cpi = EV / AC
for label, target in [("Finish on budget (BAC)", BAC), ("Bottom-up EAC", 16_515_000), ("BAC / CPI", BAC / cpi)]:
    tcpi = (BAC - EV) / (target - AC)
    print(f"{label:<24} target {target:>12,.0f}  TCPI {tcpi:.3f}  (cumulative CPI {cpi:.3f})")

Finish on budget (BAC)   target   16,124,000  TCPI 1.032  (cumulative CPI 0.969)
Bottom-up EAC            target   16,515,000  TCPI 0.984  (cumulative CPI 0.969)
BAC / CPI                target   16,646,037  TCPI 0.969  (cumulative CPI 0.969)

To finish on budget, the remaining work would have to run at a TCPI of 1.032, well above the 0.969 achieved so far; that is not credible without major changes. The bottom-up EAC requires 0.984: better than to date, but within reach if the corrective actions on forming work. The BAC ÷ CPI figure requires exactly the current CPI, by definition.

Building a defensible forecast

Experienced project teams use the formulas to frame the forecast rather than to produce it. The line-by-line bottom-up forecast remains the primary number, because only it can reflect commitments, known changes and specific plans. The formulas then act as checks.

This example illustrates a general point about index-based formulas on building projects: they apply the project's average performance to all remaining work, but the mix of remaining work may be very different from the work done so far. A job whose overrun came from self-performed concrete early on, and whose remaining work is mostly bought-out subcontracts, will usually finish better than BAC ÷ CPI. A job whose remaining work is the riskiest part (a complex mechanical fit-out, say) may finish worse. Applying the formulas at the control account level and summing the results often gives a better project EAC than applying them once at the top.

# EAC by control account, then summed (amounts $1000)
accounts = {  # name: (BAC, EV, AC, method)
    "Site and foundations": (1_420, 1_420, 1_455, "complete"),
    "Structure": (3_160, 2_780, 2_960, "cpi"),
    "Envelope": (2_740, 1_370, 1_390, "cpi"),
    "Mechanical and electrical": (3_310, 1_210, 1_200, "budget"),
    "Interiors": (2_880, 175, 180, "budget"),
    "General conditions": (1_904, 952, 978, "time"),
    "Close-out and site works": (710, 0, 0, "budget"),
}
gc_etc = 973                     # time-based, from Lesson 6
total = 0
for name, (bac, ev, ac, how) in accounts.items():
    if how == "complete": eac = ac
    elif how == "cpi": eac = bac / (ev / ac)
    elif how == "time": eac = ac + gc_etc
    else: eac = ac + (bac - ev)
    total += eac
    print(f"{name:<27} {how:<9} EAC {eac:>7,.0f}")
print(f"Project EAC from accounts: {total:,.0f}; whole-project BAC/CPI: {16_124 / (7_907 / 8_163):,.0f}")

Site and foundations        complete  EAC   1,455
Structure                   cpi       EAC   3,365
Envelope                    cpi       EAC   2,780
Mechanical and electrical   budget    EAC   3,300
Interiors                   budget    EAC   2,885
General conditions          time      EAC   1,951
Close-out and site works    budget    EAC     710
Project EAC from accounts: 16,446; whole-project BAC/CPI: 16,646

Summing account-level forecasts gives about $16.45 million, slightly below the bottom-up figure and about $200,000 below the whole-project BAC ÷ CPI, because the subcontracted accounts are forecast at budget rates and only the self-performed and troubled accounts carry their own CPI.

Forecasting the completion date

Cost and time forecasts must be consistent. If the cost forecast assumes the project finishes in month 17, the general conditions, equipment and supervision in the forecast must run to month 17. Earned schedule (Lesson 8) gives an independent estimate of duration, PD ÷ SPI(t); the scheduler's updated critical path gives another. The forecast completion date used for cost should be stated in the cost report and reconciled with the schedule.

Presenting the forecast

Management and owners need a forecast they can act on, not a single number with false precision. A good presentation gives the most likely EAC from the bottom-up forecast, the range from the formula methods, the TCPI the most likely forecast requires, the forecast completion date, and the main risks and opportunities that could move the outcome, with contingency remaining against them. On cost-reimbursable and GMP contracts, the owner will usually receive this information monthly; on lump sum contracts it stays internal, but the same discipline applies.

The projected fee in the table follows from the forecast: the contract value of $16,850,000 less the most likely EAC of $16,515,000 leaves about $335,000. That is less than half the fee bid, and it makes the case for the recovery actions and change pricing that Lessons 10 and 12 discuss.