Path7/11

Process — Earned Value (EVM) & Key Calculations

Process · 41%Course 7/114 chapters

The Process domain is 41% of the exam (2026 ECO) and holds almost all calculation questions. This module covers Earned Value Management (EVM) — the go-to method to measure cost AND schedule at a glance — plus PERT estimation, the critical path, and the other must-know formulas (communication channels, EMV).

Estimated time : 65 min

Assess and manage project valueMeasure project progress and performancePlan and manage budget and schedule

Learning objectives

Compute and interpret PV, EV, AC, the variances (SV, CV) and the indices (SPI, CPI).
Build forecasts at completion: EAC, ETC, VAC, TCPI, and pick the right formula for the context.
Estimate a duration/cost with the three-point method (beta PERT and triangular) and the standard deviation.
Determine the critical path, the float, and apply the key formulas (communication channels, EMV).

Key concepts

Planned Value (PV): The authorized budget for the work PLANNED by a given date (a.k.a. BCWS). The schedule baseline reference.; PMBOK — Earned Value Analysis
Earned Value (EV): The budgeted value of the work ACTUALLY done = BAC × actual % complete (a.k.a. BCWP). The pivot of all EVM.; PMBOK — Earned Value Analysis
Actual Cost (AC): The cost actually incurred for the work performed (a.k.a. ACWP).; PMBOK — Earned Value Analysis
Budget at Completion (BAC): The total approved budget for the whole project (the PV at the end).; PMBOK — Earned Value Analysis
Critical path: The longest sequence of activities in the network; it sets the project's minimum duration. Its activities have zero float.; PMBOK — Schedule / Critical Path Method
Total Float: How long an activity can slip without delaying the project end: Float = LS − ES = LF − EF. Zero on the critical path.; PMBOK — Schedule

1. EVM: measuring cost and schedule

Earned Value Management (EVM) combines scope, schedule and cost into a few numbers. It all rests on three measures at a point in time: what we PLANNED to do (PV), what we ACTUALLY did in budgeted value (EV), and what we SPENT (AC).

EV = BAC × % d'avancement réel

Earned value: the heart of EVM.

Variances

SV = EV − PV CV = EV − AC

Schedule Variance (SV) and Cost Variance (CV). Negative = bad.

Performance indices

SPI = EV / PV CPI = EV / AC

Schedule (SPI) and Cost (CPI) Performance Indices. < 1 = bad.

Quick reading of the results

Indicator	> 0 or > 1	< 0 or < 1
SV / SPI (schedule)	Ahead of schedule	Behind schedule
CV / CPI (cost)	Under budget	Over budget

At "now": EV < PV → behind (SV < 0); EV < AC → over budget (CV < 0).

EVM S-curve: PV (planned), EV (earned), AC (actual cost).

Example — mid-project diagnosis

BAC = $100,000. By now 50% should be done (PV = $50,000). Actually 40% is done (EV = $40,000) and AC = $45,000 has been spent.

SV = EV − PV = 40,000 − 50,000 = −$10,000 (behind schedule).
CV = EV − AC = 40,000 − 45,000 = −$5,000 (over budget).
SPI = EV / PV = 40,000 / 50,000 = 0.80 (progressing at 80% of plan).
CPI = EV / AC = 40,000 / 45,000 = 0.89 ($0.89 of value per dollar spent).

Project is behind AND over budget (SPI and CPI < 1). Corrective action needed.

Sign memo

All variances start with EV and subtract (EV − …). All indices have EV on top (EV / …). Negative or < 1 = bad. Always.

SV/SPI near closeout

As the project nears the end, EV approaches BAC, and since PV also ends at BAC, SV → 0 and SPI → 1 — automatically, even if delivery was late. So SV and SPI lose meaning at closeout: to judge timing late in the project, rely on CPI (still valid on cost) and a classic schedule-method analysis (critical path, remaining milestones).

Artifact → decision → PMI action map

Artifact

Cost/schedule baseline + EVM + vendor register

Decision

Is the variance cost, schedule, quality, or vendor-related?

PMI action

Calculate variance, forecast impact, propose correction, and update plans.

Avoid: Correcting the schedule without understanding the variance cause.

Recommendations

Always jot down PV, EV, AC, BAC before computing: half the errors come from misreading.
EV is almost always "BAC × actual % complete": spot the % complete in the statement.

Tips

Variance = subtraction (result in $); Index = division (unitless result).

Chapter quiz

1.EV = 40,000, AC = 50,000. What is the CPI and what does it indicate?

2.A project has SV = +$5,000. What can you conclude?

3.BAC = $80,000, actual progress 25%. What is EV?

2. EVM: forecasts at completion

Once performance is measured, EVM lets you FORECAST the end: total cost (EAC), remaining cost (ETC), final variance (VAC), and the efficiency you must hold to finish on budget (TCPI).

The 4 EAC formulas — pick by the wording

When to use	EAC formula
Current variances will continue (current rate)	EAC = BAC / CPI
The variance was a one-off (rest at budget)	EAC = AC + (BAC − EV)
Both cost AND schedule will keep weighing	EAC = AC + (BAC − EV) / (CPI × SPI)
New detailed estimate of the rest	EAC = AC + ETC (bottom-up)

ETC = EAC − AC VAC = BAC − EAC

Estimate To Complete (ETC) and forecast final variance (VAC).

TCPI = (BAC − EV) / (BAC − AC)

Efficiency required to finish within BAC. > 1 = must outperform past (hard).

Example — forecast at the current rate

Continuing: BAC = $100,000, EV = $40,000, AC = $45,000, CPI = 0.89. Current variances are expected to persist.

EAC = BAC / CPI. To dodge rounding error, compute unrounded: EAC = BAC × AC / EV = 100,000 × 45,000 / 40,000 = $112,500 (equivalent to CPI = 0.8889).
ETC = EAC − AC = 112,500 − 45,000 = $67,500 (left to spend).
VAC = BAC − EAC = 100,000 − 112,500 = −$12,500 (forecast overrun).
TCPI (to BAC) = (100,000 − 40,000) / (100,000 − 45,000) = 60,000 / 55,000 ≈ 1.09.

The project will end ~$12,500 over budget; to hold the BAC it would need 1.09 efficiency (vs 0.89 now) — unrealistic.

Common trap

Mixing up the two TCPIs: "to finish within BAC" → divide by (BAC − AC); "to finish within the revised EAC" → divide by (EAC − AC). Read the target.

The three EACs side by side

Example — same situation, three EAC formulas

Running case: BAC = $100,000, EV = $40,000, AC = $45,000 (so CPI = 0.8889 and SPI = 0.80). Which EAC, depending on the assumption?

Assumption 1 — the cost variance is TYPICAL and will persist: EAC = BAC / CPI = 100,000 / 0.8889 = $112,500.
Assumption 2 — the variance was a ONE-OFF, the rest runs at budget: EAC = AC + (BAC − EV) = 45,000 + (100,000 − 40,000) = 45,000 + 60,000 = $105,000.
Assumption 3 — both cost AND schedule (SYSTEMIC) will weigh on the rest: CPI × SPI = 0.8889 × 0.80 = 0.711; EAC = AC + (BAC − EV) / (CPI × SPI) = 45,000 + 60,000 / 0.711 ≈ 45,000 + 84,375 ≈ $129,375.

Three legitimate forecasts — $105,000 (one-off), $112,500 (typical cost), $129,375 (systemic cost + schedule). The wording dictates the formula: "one-off" → the 2nd; "at the current rate" → the 1st; "the delay and overrun will keep compounding" → the 3rd.

Example — TCPI to BAC vs to EAC

Same case: BAC = $100,000, EV = $40,000, AC = $45,000. We adopted EAC = $112,500 (typical cost). What efficiency must the remaining work hold?

Shared numerator = remaining work in value = BAC − EV = 100,000 − 40,000 = $60,000.
TCPI to BAC: denominator = budget remaining = BAC − AC = 100,000 − 45,000 = $55,000; TCPI = 60,000 / 55,000 ≈ 1.09.
TCPI to EAC: denominator = forecast money remaining = EAC − AC = 112,500 − 45,000 = $67,500; TCPI = 60,000 / 67,500 ≈ 0.89.

Hitting the BAC demands 1.09 (do BETTER than the past — demanding); hitting the revised EAC only needs 0.89 (keep the current pace). Only the denominator changes: budget remaining (BAC − AC) vs forecast money remaining (EAC − AC).

EVM near closeout

Near closeout, EV → BAC, so SV → 0 and SPI → 1 mechanically, even if the project finished late: EVM schedule analysis loses meaning late in the project. Favor CPI (still reliable) and classic schedule-method analysis (critical path, milestones) to judge timing.

Artifact → decision → PMI action map

Artifact

Cost/schedule baseline + EVM + vendor register

Decision

Is the variance cost, schedule, quality, or vendor-related?

PMI action

Calculate variance, forecast impact, propose correction, and update plans.

Avoid: Correcting the schedule without understanding the variance cause.

Recommendations

The EAC formula choice hinges on one word in the prompt: "current rate", "one-off", "cost and schedule".
Negative VAC = overrun; positive VAC = saving. Same sign logic as other variances.

Tips

Default EAC on the exam, if nothing is specified: EAC = BAC / CPI.

Chapter quiz

1.BAC = $200,000, CPI = 0.80, and variances will continue. What is the EAC?

2.EAC = $250,000, AC = $90,000. What is the ETC?

3.A TCPI (to BAC) of 1.15 means…

4.BAC = $100,000, EV = $40,000, AC = $45,000 (CPI = 0.8889, SPI = 0.80). The prompt says the delay AND the overrun will keep compounding together. Which EAC?

5.Remaining work in value = $60,000. We now target the revised EAC, with EAC − AC = $67,500. What TCPI?

3. Three-point estimation (PERT)

Instead of a single guess, three-point estimation uses Optimistic (O), most Likely (M) and Pessimistic (P) scenarios to reduce bias. Two variants exist.

PERT (bêta) : tE = (O + 4M + P) / 6

Weights the most likely scenario heavily.

Triangulaire : tE = (O + M + P) / 3

Simple average of the three scenarios.

Écart-type σ = (P − O) / 6 Variance = σ²

Measures the estimate's uncertainty (beta distribution).

Example — task duration

For a task: O = 8 days, M = 10 days, P = 18 days.

Beta PERT: tE = (8 + 4×10 + 18) / 6 = (8 + 40 + 18) / 6 = 66 / 6 = 11 days.
Std dev σ = (18 − 8) / 6 = 10 / 6 ≈ 1.67 days.
~68% range (±1σ, assuming a near-normal approximation): 11 ± 1.67 → between 9.3 and 12.7 days.

Expected duration ≈ 11 days, with about ±1.67 days of uncertainty.

Which formula?

If the prompt says "PERT" or "beta", use (O + 4M + P)/6. If it says "triangular" or "simple average", use (O + M + P)/3.

PERT at the path level

Example — path duration and uncertainty

Three activities in series on one path. X: O=8, M=10, P=18. Y: O=4, M=6, P=8. Z: O=6, M=12, P=18. What is the path's expected duration and confidence range?

tE per activity: X = (8+40+18)/6 = 11; Y = (4+24+8)/6 = 6; Z = (6+48+18)/6 = 12. Path duration = Σ tE = 11 + 6 + 12 = 29 days.
Variances σ² = ((P−O)/6)²: X = (10/6)² ≈ 2.78; Y = (4/6)² ≈ 0.44; Z = (12/6)² = 4.00.
Sum the VARIANCES (never the standard deviations): Σ σ² ≈ 2.78 + 0.44 + 4.00 = 7.22. Path σ = √7.22 ≈ 2.69 days.
~68% range (±1σ, assuming a near-normal approximation): 29 ± 2.69 → about 26.3 to 31.7 days.

Expected path duration ≈ 29 days, σ ≈ 2.69 days, with a ~68% chance of finishing between 26.3 and 31.7 days (subject to near-normality).

Add variances, not the σ

To combine the uncertainty of several activities on a path, add the VARIANCES (σ²) then take the root: path σ = √(Σ σ²). Never sum the standard deviations directly. The "68% at ±1σ" rule assumes a near-normal approximation — each activity's beta distribution is skewed, so treat these ranges as ballpark figures, not exact probabilities.

Artifact → decision → PMI action map

Artifact

ECO + PMBOK 8 + study plan

Decision

Which ECO competency does this chapter strengthen?

PMI action

Connect concept, scenario, counterexample, and explained question.

Avoid: Memorizing without linking the concept to a project decision.

Recommendations

The factor 4 ALWAYS goes on M (most likely), never on O or P.

Tips

σ and variance use only O and P (the extremes), never M.

Chapter quiz

1.O = 6, M = 12, P = 24. PERT (beta) estimate?

2.O = 10, P = 28. What is the standard deviation (beta)?

3.Two activities in series on a path have standard deviations σ = 3 and σ = 4 days. What is the standard deviation of the whole path?

4. Critical path, float & other calculations

Critical path & float

The critical path is the LONGEST path through the network; it sets the project's minimum duration. Activities off it have float.

Marge totale = LS − ES = LF − EF

Possible slip without moving the end. Zero on the critical path.

Critical path A-C-D = 14 d (red) > A-B-D = 10 d. Float of B = 4 d.

Activity network: the critical path is the longest (in red).

Example — find the critical path

Two paths run start to end: Path 1 = A(3) → B(5) → D(2); Path 2 = A(3) → C(9) → D(2).

Path 1 duration = 3 + 5 + 2 = 10 days.
Path 2 duration = 3 + 9 + 2 = 14 days.
The longest (14) is the critical path; float of B = 14 − 10 = 4 days.

Critical path = A-C-D (14 days). Project duration = 14 days; B has 4 days of float.

Forward/backward pass (ES, EF, LS, LF)

To get each activity's dates and float, run a FORWARD pass (earliest: ES, EF) then a BACKWARD pass (latest: LS, LF). Convention: EF = ES + duration; LS = LF − duration. At a merge, take the MAX of upstream EFs (forward) and the MIN of downstream LSs (backward).

Example — forward/backward pass on an AON network

AON network (durations in parentheses). Top path: A(3) → B(4) → D(2). Bottom path: A(3) → C1(1) → C2(1) → D(2). A is the start, D the end.

FORWARD pass (ES/EF), start at 0: A ES=0/EF=3; B ES=3/EF=7; C1 ES=3/EF=4; C2 ES=4/EF=5; D merges → ES = max(EF_B=7, EF_C2=5) = 7, EF=9. Project duration = 9 days.
BACKWARD pass (LS/LF), set LF_D = 9: D LF=9/LS=7; B LF=7/LS=3; C2 LF=LS_D=7/LS=6; C1 LF=LS_C2=6/LS=5; A LF=min(LS_B=3, LS_C1=5)=3/LS=0.
Total float = LS − ES (= LF − EF). A, B, D: 0 (critical path A-B-D = 9). C1: 5 − 3 = 2. C2: 6 − 4 = 2.
Free float of C1 = successor's ES − EF = ES_C2(4) − EF_C1(4) = 0: slipping C1 would delay C2. Free float of C2 = ES_D(7) − EF_C2(5) = 2.

Critical path A-B-D = 9 days. The C1-C2 chain has 2 days of TOTAL float, but C1 has 0 FREE float: it shares its float with C2, so only C2 can slip without affecting another task.

Total float vs free float

TOTAL float = how long an activity can slip without delaying the PROJECT END (LS − ES). FREE float = slip without delaying the EARLIEST START of the immediate SUCCESSOR (successor's ES − EF). Free float is always ≤ total float; along a chain of non-critical activities the total float is shared, but the free float usually sits on the last activity before the merge.

Communication channels

Canaux = n (n − 1) / 2

n = number of stakeholders. Don't forget to count yourself.

Example — adding members

A team grows from 8 to 10 people. By how much do communication channels increase?

Before: 8 × 7 / 2 = 28 channels.
After: 10 × 9 / 2 = 45 channels.
Increase = 45 − 28 = 17 channels.

+17 channels. Complexity grows far faster than headcount.

Expected Monetary Value (EMV)

EMV = Probabilité × Impact (somme sur les risques)

Threat = negative impact; opportunity = positive impact.

Example — contingency reserve

Risk A: 30% probability, impact −$10,000. Opportunity B: 20%, impact +$20,000.

EMV(A) = 0.30 × (−10,000) = −$3,000.
EMV(B) = 0.20 × (+20,000) = +$4,000.
Total EMV = −3,000 + 4,000 = +$1,000.

Net EMV = +$1,000: the risk portfolio is slightly favorable.

Example — decision tree (choosing an option)

Two ways to deliver a component. Option A "in-house": certain cost $50,000, plus a 40% risk of $20,000 rework. Option B "outsource": certain cost $52,000, plus a 20% risk of a $15,000 penalty. Which branch to pick?

Expected cost = certain cost + risk EMV. Branch A: 50,000 + 0.40 × 20,000 = 50,000 + 8,000 = $58,000.
Branch B: 52,000 + 0.20 × 15,000 = 52,000 + 3,000 = $55,000.
Compare: $55,000 (B) < $58,000 (A). Since this is a COST, the LOWEST EMV wins.

Pick Option B (outsource), expected EMV $55,000 vs $58,000 in-house. The decision tree here is a CHOICE TOOL between options, not just reserve summation: the option with the lowest expected cost (or highest expected payoff) wins.

Artifact → decision → PMI action map

Artifact

Cost/schedule baseline + EVM + vendor register

Decision

Is the variance cost, schedule, quality, or vendor-related?

PMI action

Calculate variance, forecast impact, propose correction, and update plans.

Avoid: Correcting the schedule without understanding the variance cause.

Recommendations

Critical path = the LONGEST (not the shortest); it constrains the project end.
For channels, count ALL stakeholders, including yourself, before applying n(n−1)/2.

Tips

A threat's EMV is negative; an opportunity's is positive. Sum them for the reserve.

Chapter quiz

1.A project has 6 stakeholders. How many communication channels?

2.Paths: A-B-C = 12 days; A-D-C = 16 days; A-E-C = 9 days. Project duration?

3.Risk: 40% probability, impact −$25,000. What is the EMV?

4.An activity has ES=5, EF=8, LS=9, LF=12, and its single successor has ES=8. What are its total and free float?

5.Decision tree. Option X: certain cost $40,000 + 50% risk of $20,000. Option Y: certain cost $45,000 + 10% risk of $10,000. Which to choose?

Decision toolkit

PMP decision trees & running case

Use this when two answers look right: qualify the context, choose the artifact, then act.

Change request

A sponsor, customer, or user asks to change scope, cost, schedule, or quality.

1. Predictive approach with an approved baseline.
Decision: Analyze impact before acting.
Action: Document the request, assess impacts, then route it through integrated change control/CCB.
2. Agile approach with a product backlog.
Decision: Do not disrupt the current sprint.
Action: Add it to the backlog, clarify value, and reprioritize with the Product Owner.
3. Urgent compliance/safety-related change.
Decision: Protect compliance and transparency.
Action: Analyze quickly, inform governance authorities, and record the decision.

Trap: Implementing directly because the sponsor asked bypasses governance.

Risk vs issue

An event may happen or has just happened.

1. The event is uncertain.
Decision: Treat it as a risk.
Action: Qualify probability/impact, choose response, owner, and reserve.
2. The event has occurred.
Decision: Treat it as an issue.
Action: Create corrective action, assign an owner, and track to closure.
3. The issue creates new risks.
Decision: Update both logs/registers.
Action: Issue log for immediate action, risk register for remaining uncertainty.

Trap: A materialized risk is no longer just monitored: action is required.

Vendor delay

A vendor announces a delay, quality issue, or resource unavailability.

1. The contract defines SLAs, milestones, or penalties.
Decision: Check commitments before negotiating.
Action: Compare contract, actual performance, and project impacts.
2. The delay impacts the critical path or value.
Decision: Evaluate alternatives and reserve.
Action: Analyze fast tracking, replanning, another vendor, or scope trade-off.
3. The vendor relationship is recoverable.
Decision: Collaborate without losing contractual control.
Action: Dated action plan, checkpoints, and risk register update.

Trap: Threatening the vendor before analyzing contract and impact is a poor first response.

Construction project: industrial site expansion

Charter

Objective: add a production line without interrupting existing operations.

Backlog / WBS

WBS, critical path, quality/HSE plans, inspection milestones, and RACI matrix.

Stakeholders

Industrial sponsor, HSE, procurement, EPC vendor, production, local authorities.
Success measured by safety, schedule, compliance, and operational readiness.

Risks

Permit delay, HSE incident, critical vendor unavailability.
Poorly defined interfaces between works and ongoing production.

Change

Request: material change after baseline. Response: cost/schedule/quality impact, CCB, plan updates.

EVM

Classic EVM: PV/EV/AC by work package, CPI/SPI, and EAC forecast.

Closure

Punch list, issue closure, as-built documentation, maintenance handover, and formal acceptance.

Practical examples

Progress report to the sponsor

Scenario : The sponsor asks "where do we stand?" at mid-project. You have PV, EV, AC.

Project manager's action : Compute SPI and CPI to summarize schedule and cost in two numbers, then EAC to project the final cost — a factual, shared language.

Compressing a late schedule

Scenario : The project is behind (SPI < 1) and the date is fixed.

Project manager's action : Act on the CRITICAL PATH (the only one that moves the end) via fast-tracking (parallelize) or crashing (add resources) — not on tasks with float.

Exam strategy

Memorize the sign convention: a NEGATIVE variance (SV/CV < 0) or an index < 1 is always BAD (behind / over budget).
All variance formulas start with EV (EV − PV, EV − AC). All index formulas have EV on top (EV/PV, EV/AC).
Read the wording: "at the current rate" → EAC = BAC/CPI ; "the variance was a one-off" → EAC = AC + (BAC − EV).
Write down your data (PV, EV, AC, BAC) before computing; most errors come from misreading, not from the math.

Module assessment

1.PV = 60,000, EV = 55,000, AC = 50,000. The project is…

2.Which formula gives the forecast total cost if the current rate persists?

3.To shorten a project, which activities should you act on?

4.O = 4, M = 6, P = 14. Beta PERT estimate?