Earned value management on a worked project

Four months into a ten-month warehouse automation project, 11,300 thousand has been spent and the plan expected 11,225 by now: on the face of it, the project is on budget. Earned value says otherwise, because only 10,020 worth of the planned work is done, so the project is both over cost and behind schedule.

You will compute the three numbers of earned value from four control accountsA part of the project's work with one responsible manager and its own budget and plan, where actual costs are collected and earned value is measured., turn them into variances and indices, and read the S-curve they draw; then you will forecast the final cost from them and see where the method misleads.

Earned value adds a third number to the plan and the actual

Comparing spending with the plan mixes two questions: how much work is done, and what it cost. Earned value management separates them with three numbers taken at one status date, all in money:

• Planned valueplanned value (PV): The budget of the work the plan scheduled to be done by the status date, also called the budgeted cost of work scheduled. (PV), the budgeted cost of work scheduled: the budget of the work the plan said would be done by now, 11,225.
• Earned valueearned value (EV): The budget of the work actually done by the status date, also called the budgeted cost of work performed; it measures progress in money. (EV), the budgeted cost of work performed: the budget of the work actually done, 10,020.
• Actual costactual cost (AC): What the work done by the status date really cost, also called the actual cost of work performed. (AC), the actual cost of work performed: what that work cost, 11,300.

Each is measured against the budget at completionbudget at completion (BAC): The total budget of all the work in the performance baseline: the sum of the control accounts' budgets, without the management reserve. (BAC), 24,000, the sum of the control accounts’ budgets. The program builds the three from the accounts’ status and prints their monthly totals:

"""Earned value at the month-4 status date of an invented warehouse-automation project (budget at completion 24,000).

Money is in thousands. Four control accounts, each with a budget and a monthly plan; for each the team reports the
work performed, valued at its budget (earned value), and what it actually cost. Planned value is the budget of the
work scheduled up to the status date. Decimal arithmetic, rounded half up for printing.
CV = EV - AC, SV = EV - PV, CPI = EV / AC, SPI = EV / PV.
"""

from decimal import ROUND_HALF_UP, Decimal

STATUS_MONTH = 4
# Control account: (name, budget, planned spend per month {month: amount}, EV by month, AC by month, cumulative)
ACCOUNTS = [
    ("Racking and civil works", 6000, {m: 1500 for m in range(1, 5)},
     {1: 1200, 2: 2700, 3: 4300, 4: 6000}, {1: 1150, 2: 3000, 3: 4800, 4: 6600}),
    ("Conveyor and sorter", 9600, {m: 1600 for m in range(3, 9)},
     {3: 800, 4: 2400}, {3: 1100, 4: 2900}),
    ("Warehouse software", 5400, {m: 675 for m in range(2, 10)},
     {2: 450, 3: 1000, 4: 1620}, {2: 500, 3: 1150, 4: 1800}),
    ("Training and handover", 3000, {m: 1000 for m in range(8, 11)}, {}, {}),
]


def cumulative(by_month, month):
    """The latest cumulative value reported at or before this month (0 before the first report)."""
    known = [m for m in by_month if m <= month]
    return Decimal(by_month[max(known)]) if known else Decimal(0)


def planned(plan, month):
    return sum((Decimal(v) for m, v in plan.items() if m <= month), Decimal(0))


def r(x, places="1"):
    return x.quantize(Decimal(places), rounding=ROUND_HALF_UP)


BAC = sum(Decimal(a[1]) for a in ACCOUNTS)
assert all(sum(a[2].values()) == a[1] for a in ACCOUNTS), "each plan spreads its whole budget"

print(f"Status at the end of month {STATUS_MONTH}, budget at completion {r(BAC)}")
print(f"{'Control account':<24} {'Budget':>6} {'PV':>6} {'EV':>6} {'AC':>6} {'CV':>6} {'SV':>6}")
tot = {"pv": Decimal(0), "ev": Decimal(0), "ac": Decimal(0)}
for name, budget, plan, ev_m, ac_m in ACCOUNTS:
    pv, ev, ac = planned(plan, STATUS_MONTH), cumulative(ev_m, STATUS_MONTH), cumulative(ac_m, STATUS_MONTH)
    tot["pv"] += pv
    tot["ev"] += ev
    tot["ac"] += ac
    print(f"{name:<24} {budget:>6} {r(pv):>6} {r(ev):>6} {r(ac):>6} {r(ev - ac):>6} {r(ev - pv):>6}")
pv, ev, ac = tot["pv"], tot["ev"], tot["ac"]
print(f"{'Project':<24} {r(BAC):>6} {r(pv):>6} {r(ev):>6} {r(ac):>6} {r(ev - ac):>6} {r(ev - pv):>6}")
print()
print(f"CPI = EV / AC = {r(ev)} / {r(ac)} = {r(ev / ac, '0.001')}: each 1.00 spent earned {r(ev / ac, '0.01')} of planned work")
print(f"SPI = EV / PV = {r(ev)} / {r(pv)} = {r(ev / pv, '0.001')}: {r(ev / pv * 100, '0.1')} % of the work planned by now is done")
print(f"Percent complete = EV / BAC = {r(ev / BAC * 100, '0.01')} %; percent spent = AC / BAC = {r(ac / BAC * 100, '0.01')} %")
print()
print("The S-curve, cumulative (PV for every month of the plan; EV and AC up to the status date):")
print(f"{'Month':<6} {'PV':>6} {'EV':>6} {'AC':>6}")
for month in range(1, 11):
    pvm = sum(planned(a[2], month) for a in ACCOUNTS)
    if month <= STATUS_MONTH:
        evm = sum(cumulative(a[3], month) for a in ACCOUNTS)
        acm = sum(cumulative(a[4], month) for a in ACCOUNTS)
        print(f"{month:<6} {r(pvm):>6} {r(evm):>6} {r(acm):>6}")
    else:
        print(f"{month:<6} {r(pvm):>6}")

Status at the end of month 4, budget at completion 24000
Control account          Budget     PV     EV     AC     CV     SV
Racking and civil works    6000   6000   6000   6600   -600      0
Conveyor and sorter        9600   3200   2400   2900   -500   -800
Warehouse software         5400   2025   1620   1800   -180   -405
Training and handover      3000      0      0      0      0      0
Project                   24000  11225  10020  11300  -1280  -1205

CPI = EV / AC = 10020 / 11300 = 0.887: each 1.00 spent earned 0.89 of planned work
SPI = EV / PV = 10020 / 11225 = 0.893: 89.3 % of the work planned by now is done
Percent complete = EV / BAC = 41.75 %; percent spent = AC / BAC = 47.08 %

The S-curve, cumulative (PV for every month of the plan; EV and AC up to the status date):
Month      PV     EV     AC
1        1500   1200   1150
2        3675   3150   3500
3        7450   6100   7050
4       11225  10020  11300
5       13500
6       15775
7       18050
8       21325
9       23000
10      24000

The racking is finished and has earned its whole 6,000, but it cost 6,600. The conveyor should have earned 3,200 by now and has earned 2,400 for 2,900 spent. Drawn over time, PV is the S-curve of the cost baseline, with EV and AC drawn against it up to the status date:

The vertical gap between AC and EV is cost; the gap between PV and EV is schedule, measured in money.

Variances and indices say how far off the project is

Two subtractions and two divisions turn the three numbers into a verdict. GAO’s cost guide uses the usual signs: negative variances and indices below 1.0 are unfavourable.

In words, the cost variancecost variance (CV): Earned value minus actual cost. A negative value means the work done cost more than its budget. is −1,280 and the schedule varianceschedule variance (SV): Earned value minus planned value, in money. A negative value means less work is done than the plan scheduled by now. −1,205. The cost performance indexcost performance index (CPI): Earned value divided by actual cost: the budgeted work bought by each unit of money spent. Below 1.0 is unfavourable. of 0.887 says each 1.00 spent bought 0.89 of planned work, and the schedule performance indexschedule performance index (SPI): Earned value divided by planned value: the share of the scheduled work that is done. Below 1.0 is unfavourable. of 0.893 says 89.3 % of the work planned by now is done. Step through how each figure follows, then two accounts:

An index travels better than a variance: −1,280 is serious in a budget of 24,000 and trivial in one of 2,400,000, while 0.887 means the same in both. The racking shows why cost and schedule are read together: a finished account always has SV 0, whenever it finished, so only the racking’s CV of −600 shows its overrun.

Four more tools complete the method. An estimate at completionestimate at completion (EAC): A forecast of the final cost of the work: the actual cost so far plus the remaining work, re-priced with an efficiency index. (EAC) re-prices the remaining work with an efficiency index to forecast the final cost. The to-complete performance indexto-complete performance index (TCPI): The cost efficiency the remaining work would need for the project to finish at a target, such as the budget or a forecast. (TCPI) is the efficiency the remaining work needs to finish at a target. Earning rulesearning rule: The rule that decides how much of a work package's budget counts as earned at each stage of its work, such as 0/100 or 50/50. such as 0/100 and 50/50 decide how much of a started work package counts as earned. Earned scheduleearned schedule: An extension of earned value management that states schedule performance in units of time, such as months, instead of money. restates the schedule gap in months.

Forecasting the final cost, with GAO's tests Pro: opens with a Pro, Premium or Ultimate pass

Where earned value misleads, reproduced in numbers Pro: opens with a Pro, Premium or Ultimate pass

Practise: the three numbers and their indices

The questions use the warehouse project’s month-4 status and a few new accounts. Work out each number before you choose:

Interview questions

Warm-up: what do a CPI and an SPI below 1.0 mean?

A CPI below 1.0 means the work done so far cost more than its budget: at 0.887, each 1.00 spent earned 0.89 of planned work. An SPI below 1.0 means less work is done than the plan scheduled by now: at 0.893, 89.3 % of it. Both use earned value, the budget of the work actually done, which is what makes them comparable across projects.

Three harder questions follow, about a report that looks green, a supplier’s optimistic forecast and progress that is estimated rather than measured. Decide what you would check first, then open each first step:

Key takeaways

• Planned value, earned value and actual cost, taken at one status date, separate how much work is done from what it cost.
• The cost and schedule variances are EV − AC and EV − PV, and the CPI and SPI divide EV by AC and by PV, with values below 1.0 unfavourable.
• Indices compare across projects of any size, and a finished account always shows a schedule variance of 0, so cost and schedule are read together.
• On an S-curve, the gap between AC and EV is the cost problem and the gap between PV and EV is the schedule problem.