7.1 Earned Value Foundations: PV, EV, AC, and Variances

7.1 Earned Value Foundations: PV, EV, AC, and Variances per earned-value management practice

AACE Professional Context: Under Total Cost Management (TCM) and earned-value management practice (Earned Value Analysis Practicing Skills), Earned Value Management (EVM) is not merely a cost-reporting mechanism—it is an integrated project management methodology that unifies technical scope, CPM schedule logic, and resource budgets into a single objective baseline. On the Planning and Scheduling Professional (PSP) examination, candidates must demonstrate complete fluency with the foundational tripartite data architecture of EVM, understand how baseline early and late dates shape the Performance Measurement Baseline (PMB), and master the computation and interpretation of Schedule Variance ($SV$) and Cost Variance ($CV$).

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earned-value management practice and the EVM Practitioner Competencies

AACE International published Recommended Practice 54R-07 to delineate the competencies required of project controls practitioners who design, implement, and analyze earned value management systems. Unlike simplistic accounting systems that compare actual expenditures against budget allocations, an ANSI/EIA-748-compliant EVM system incorporates work accomplished (physical performance).

                   TRADITIONAL ACCOUNTING vs. EARNED VALUE ANALYSIS

     Traditional Accounting (Flawed)             Earned Value Management (earned-value management practice)
   ┌────────────────────────────────┐         ┌─────────────────────────────────────┐
   │  Budget:       \$1,000,000      │         │  Planned Value (PV):  \$600,000      │
   │  Actual Spend:   \$550,000      │         │  Earned Value (EV):   \$450,000      │
   │  "Variance":   +\$450,000 Under!│         │  Actual Cost (AC):    \$550,000      │
   │  (False sense of security)     │         │  SV = -\$150,000 (Behind Schedule!) │
   │                                │         │  CV = -\$100,000 (Cost Overrun!)    │
   └────────────────────────────────┘         └─────────────────────────────────────┘

Under traditional cost accounting, spending $550,000 against a $1,000,000 budget appears to show a $450,000 "surplus." In reality, if only $450,000 worth of physical work was accomplished when $600,000 was planned, the project is both over budget by $100,000 and significantly behind schedule! earned-value management practice provides the rigorous framework to eliminate this blind spot.

Key Practitioner Competencies Codified in earned-value management practice

1. Baseline Architecture Integration: Structuring the Work Breakdown Structure (WBS) and Organizational Breakdown Structure (OBS) into Control Accounts (CAs) that tie directly to schedule activities.
2. Time-Phasing of Budgets: Allocating direct labor hours, material dollars, equipment costs, and indirect charges across CPM network activities using baseline early start and finish distributions.
3. Objective Progress Measurement: Selecting appropriate Earned Value Measurement Techniques (EVMT) that represent true physical progress rather than elapsed calendar time or money spent.
4. Contemporaneous Variance Analysis: Evaluating root causes of cost and schedule deviations, calculating variance thresholds, and formulating corrective recovery actions.

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The Performance Measurement Baseline (PMB)

The Performance Measurement Baseline (PMB) is the approved, integrated time-phased plan against which project execution is monitored and controlled. It represents the sum of all authorized control account budgets, summary-level planning packages, and undistributed budget.

Components of Total Project Budget

In standard cost engineering architecture, project funds are divided into distinct contractual and managerial categories:

$\text{Total Allocated Budget (TAB)} = \text{Performance Measurement Baseline (PMB)} + \text{Management Reserve (MR)}$

$\text{PMB} = \sum \text{Control Accounts} + \text{Summary-Level Planning Packages} + \text{Undistributed Budget (UB)}$

$\text{Budget at Completion (BAC)} = \text{Total Value of the PMB}$

Exam Trap Alert: Management Reserve (MR) is never part of the Performance Measurement Baseline (PMB) or Budget at Completion (BAC). Therefore, spending MR requires a formal baseline change request and baseline budget increase. Contingency Reserve, however, is part of the PMB and can be distributed to control accounts to mitigate modeled technical risks.

Early-Dates vs. Late-Dates PMB Envelope (The Banana Curve)

When time-phasing baseline activity budgets across the CPM network, two bounding S-curves emerge:

• Early-Dates PMB: Cumulative planned value generated when every activity executes at its Early Start ($ES$) and Early Finish ($EF$). This represents the most aggressive cash flow and resource burn profile.
• Late-Dates PMB: Cumulative planned value generated when every activity is delayed to its Late Start ($LS$) and Late Finish ($LF$), consuming all available total float.
• The "Banana Envelope": The area bounded between the early curve and the late curve. If actual cumulative earned value falls below the late-dates curve, project completion will inevitably be delayed unless the critical path is accelerated through crashing or re-sequencing.

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Core EVM Data Pillars: PV, EV, AC, and BAC

EVM relies on three fundamental data values measured periodically at each Data Date (Status Date):

                                   BAC (Budget at Completion)
                                            │
   Cumulative Dollars (\$)                  ▼
        │                                  ┌─┐
        │                                ┌─┘ │
        │                              ┌─┘   │   ◄── Performance Measurement
        │                            ┌─┘     │       Baseline (PV Curve)
        │                          ┌─┘       │
        │                 AC ───► *          │
        │                        /│          │
        │                 PV ──► *│          │
        │                       / │          │
        │                EV ──►*  │          │
        │                     /   │          │
        │                    /    │          │
        └───────────────────┴─────┴──────────┴────────────────────────►
                          Project Data     Target Completion
                           Start   Date         Date (PD)

1. Planned Value (PV) / Budgeted Cost for Work Scheduled (BCWS)

Planned Value is the approved time-phased budget assigned to scheduled work up to the Data Date. It defines what work should have been completed according to the baseline schedule.

• Historical terminology: BCWS (Budgeted Cost for Work Scheduled).
• Formally: $PV = \sum \text{Baseline Budget of scheduled activities and work packages up to the Data Date}$.
• At project start: $PV$ = $0.
• At scheduled completion date: $PV = BAC$.

2. Earned Value (EV) / Budgeted Cost for Work Performed (BCWP)

Earned Value is the measure of physical work accomplished expressed in terms of the baseline budget authorized for that work. It quantifies the genuine value earned regardless of how much money was actually spent.

• Historical terminology: BCWP (Budgeted Cost for Work Performed).
• Formally: $EV = \sum [\text{Baseline Budget (BAC}_i\text{)} \times \text{Physical \% Complete}_i]$.
• Earned Value can never exceed the total BAC of an activity; once an activity reaches 100% physical completion, its $EV = BAC_i$.

3. Actual Cost (AC) / Actual Cost of Work Performed (ACWP)

Actual Cost is the total direct and allocable indirect expenditure incurred in accomplishing the work performed up to the Data Date.

• Historical terminology: ACWP (Actual Cost of Work Performed).
• Encompasses booked labor timesheets, subcontractor invoices, purchase order receipts, material disbursements, and accrued liabilities.
• Cutoff alignment: Actual cost and earned value should use compatible cutoff periods, with accruals or reconciliation where accounting and schedule dates differ. Recording invoices received after the Data Date, or failing to record accruals for work earned prior to the Data Date, destroys the mathematical validity of EVM.

4. Budget at Completion (BAC)

Budget at Completion is the total authorized baseline budget for the entire project, control account, or work package. It represents the final value of the Planned Value curve ($PV_{\text{final}} = BAC$).

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Schedule Variance ($SV$) and Cost Variance ($CV$)

From these three foundational pillars, EVM computes two primary dollar-denominated variance metrics:

Schedule Variance ($SV$)

$\mathbf{SV = EV - PV}$

• Measures the dollar (or work-hour) difference between the physical work completed and the work scheduled to be completed.
• $SV > 0$ (Positive): Ahead of plan. The project has accomplished more work (in budget terms) than scheduled.
• $SV = 0$ (Zero): On plan. The volume of earned work equals the planned work.
• $SV < 0$ (Negative): Behind plan. Less work has been earned than scheduled.

Cost Variance ($CV$)

$\mathbf{CV = EV - AC}$

• Measures the financial difference between the earned value of work completed and the actual cost incurred to achieve it.
• $CV > 0$ (Positive): Under budget (Favorable). The work accomplished cost less than budgeted.
• $CV = 0$ (Zero): On budget. The cost incurred matches the baseline budget value earned.
• $CV < 0$ (Negative): Over budget (Unfavorable). The work accomplished cost more than budgeted.

                         THE FOUR VARIANCE QUADRANTS

             Cost Variance (CV = EV - AC)
                         ▲
                         │
             QUADRANT II │ QUADRANT I
             Ahead of Schedule (SV > 0) │ Ahead of Schedule (SV > 0)
             Over Budget (CV < 0)       │ Under Budget (CV > 0)
             [High Burn, Fast Pace]     │ [Ideal Project Condition]
                         │
  ───────────────────────┼───────────────────────► Schedule Variance (SV = EV - PV)
                         │
             QUADRANT III│ QUADRANT IV
             Behind Schedule (SV < 0)   │ Behind Schedule (SV < 0)
             Over Budget (CV < 0)       │ Under Budget (CV > 0)
             [Severe Distress / Delay]  │ [Slow Start / Resource Starved]
                         │
                         ▼

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Progress Measurement Integration with CPM Networks

A critical requirement of earned-value management practice is establishing objective Earned Value Measurement Techniques (EVMT) that link directly to Critical Path Method schedule activities. Choosing the wrong measurement method introduces severe reporting distortions.

Exam caution: Duration percent complete is not objective evidence of physical accomplishment for discrete work; use the authorized earned-value technique and measurable completion evidence. Duration percent complete reflects only elapsed calendar time. If an excavation crew sits idle on site for 10 days out of a 20-day planned duration, duration percent complete reports 50%, generating 50% earned value even though zero cubic yards of earth were moved! earned-value management practice mandates physical quantity or discrete milestone tracking.

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Worked Calculation: Gas Turbine Compressor Foundation Package

An industrial EPC project includes Control Account CA-CVI-02: Gas Turbine Compressor Foundation.

• Budget at Completion (BAC): $800,000
• Planned Scope: 1,600 cubic yards (CY) of reinforced structural concrete
• Baseline Planned Production Rate: 160 CY per week over a 10-week planned duration (Weeks 1 to 10)

Performance Status at Data Date = End of Week 5:

• Baseline Planned Value ($PV$): At Week 5, the baseline schedule called for 50% of the volume to be placed (800 CY). $PV = \text{\textdollar}800{,}000 \times 0.50 = \text{\textdollar}400{,}000$
• Field Measurement: Quality control sign-off records confirm that 600 CY of concrete have been placed, cured, and inspected.
• Accounting Ledger: General ledger records confirm total direct and accrued costs for labor, concrete batches, and formwork rental equal $480,000 ($AC$).

Step-by-Step Variance Computation:

1. Compute Physical Percent Complete: $\text{Physical } \% = \frac{600 \text{ CY installed}}{1,600 \text{ CY total}} = 37.50\%$

2. Compute Earned Value ($EV$): $EV = BAC \times \text{Physical } \% = \text{\textdollar}800{,}000 \times 0.3750 = \text{\textdollar}300{,}000$

3. Compute Schedule Variance ($SV$): $SV = EV - PV = \text{\textdollar}300{,}000 - \text{\textdollar}400{,}000 = -\text{\textdollar}100{,}000$ Interpretation: The work package has accomplished $100,000 less work than scheduled by the baseline. (Behind schedule).

4. Compute Cost Variance ($CV$): $CV = EV - AC = \text{\textdollar}300{,}000 - \text{\textdollar}480{,}000 = -\text{\textdollar}180{,}000$ Interpretation: The project has spent $180,000 more than the baseline budget earned for the work accomplished. (Over budget).

5. Executive Summary for Project Controls: The work package resides in Quadrant III (Behind Schedule and Over Budget). Notice that if the project had relied on Duration Percent Complete ($5 \text{ weeks elapsed} / 10 \text{ weeks} = 50\%$), $EV$ would have been falsely reported as $400,000, masking $100,000 of schedule variance and understating the cost overrun by $100,000!