11.2 Cost & Schedule Variances

11.2 Cost & Schedule Variances

Quick Summary: Variance analysis is the primary diagnostic mechanism in Earned Value Management. Variances isolate whether project performance deviations stem from cost inefficiency, schedule pacing issues, or both. The two fundamental absolute variance formulas are Cost Variance ($CV = EV - AC$) and Schedule Variance ($SV = EV - PV$). For all standard EVM variances, Earned Value ($EV$) always leads the equation, and the sign convention is absolute: Positive is Favorable (Good), Negative is Unfavorable (Bad), and Zero is Exactly on Plan. Crucially, Schedule Variance is measured in currency or labor hours—not calendar days—and inevitably collapses to zero at project finish, masking schedule delays unless paired with Critical Path analysis.

---

1. Absolute Variance Formulations & Sign Conventions

In project controls, absolute variances indicate the raw monetary or resource deviation from the authorized plan.

+-----------------------------------------------------------------------------------+
|                       FUNDAMENTAL EVM VARIANCE EQUATIONS                          |
|                                                                                   |
|   COST VARIANCE (CV):       CV = EV - AC        (Earned Value - Actual Cost)      |
|   SCHEDULE VARIANCE (SV):   SV = EV - PV        (Earned Value - Planned Value)    |
|                                                                                   |
|   RULE: EV is ALWAYS the first term! Never subtract EV from AC or PV.             |
+-----------------------------------------------------------------------------------+
|                              SIGN CONVENTION MATRIX                               |
|                                                                                   |
|   METRIC      RESULT > 0 (+)              RESULT = 0            RESULT < 0 (-)    |
|   -----------------------------------------------------------------------------   |
|   CV          Under Budget (Favorable)    On Budget             Over Budget (Bad) |
|   SV          Ahead of Schedule (Good)    On Schedule           Behind Sched (Bad)|
+-----------------------------------------------------------------------------------+

The Directional Logic of EVM Math

Why does Earned Value come first? In cost engineering, you evaluate performance by comparing what you earned against what you spent or planned:

• If what you earned ($EV$) exceeds what you spent ($AC$), you have a positive balance ($EV - AC > 0$), meaning you accomplished more work than you paid for (Favorable Cost Variance).
• If what you earned ($EV$) is less than what you planned to accomplish ($PV$), you have a negative balance ($EV - PV < 0$), meaning you delivered less work than scheduled (Unfavorable Schedule Variance).

Reversing the subtraction order (e.g., calculating $AC - EV$) produces opposite mathematical signs that contradict international standards and lead to failing scores on the CCT exam.

---

2. Percentage Variances ($CV%$ and $SV%$)

While absolute dollar variances quantify financial impact, they fail to convey the relative severity of an overrun. An unfavorable Cost Variance of -$50,000 is catastrophic on a small $100,000 control account (a 50% overrun), but negligible on a $50,000,000 industrial facility (a 0.1% blip). To enable cross-project comparisons, cost engineers calculate percentage variances.

Formulations & Denominator Rules

$\mathbf{CV\% = \left(\frac{CV}{EV}\right) \times 100 = \left(\frac{EV - AC}{EV}\right) \times 100}$ $\mathbf{SV\% = \left(\frac{SV}{PV}\right) \times 100 = \left(\frac{EV - PV}{PV}\right) \times 100}$

[!CRITICAL] The Denominator Rule: Notice the fundamental difference in denominators:

• In $CV%$, the denominator is $EV$ (Earned Value)—measuring cost overrun relative to physical work delivered.
• In $SV%$, the denominator is $PV$ (Planned Value)—measuring schedule deviation relative to the work that was scheduled to be completed. (Note: While some legacy corporate handbooks divide CV by BAC, the ANSI/EIA-748 standard and AACE International explicitly mandate EV in the denominator for operating CV%).

---

3. Critical Nuances & Limitations of Schedule Variance (SV)

Schedule Variance is one of the most frequently misunderstood metrics in cost engineering. Candidates must master two vital technical limitations:

Nuance 1: SV Measures Volume of Work, Not Calendar Time

Schedule Variance is expressed in currency units (dollars, euros) or craft labor hours, never in calendar units (days, weeks, or months).

• If a project reports $SV = -$120,000$, it indicates that the project has completed $120,000 less physical work than planned by the status date.
• It does not mean the project is 120 days late, nor does it tell you when the project will finish.
• Converting volume of work to calendar delay requires either Earned Schedule (ES) analysis (which maps EV back to the time axis of the PV curve) or Critical Path Method (CPM) schedule analysis.

Nuance 2: The "SV Anomaly at Project Completion"

A major mathematical limitation of EVM occurs at the end of a project. Examine what happens as a late project approaches completion:

1. As long-delayed activities are finally finished, $EV$ eventually reaches the total budget: $EV = BAC$.
2. Because the original scheduled finish date has long passed, all planned work has matured: $PV = BAC$.
3. When the project finally completes—even if it is two years late—the Schedule Variance equation becomes: $SV = EV - PV = BAC - BAC = \mathbf{\$0}$ $SV\% = \left(\frac{BAC - BAC}{BAC}\right) \times 100 = \mathbf{0\%}$

THE SV ANOMALY GRAPHICAL PROGRESSION:
  Status at Planned Finish: EV = $800k, PV = $1,000k --> SV = -$200k (Severe Lag)
  Project Continues 6 Months Late...
  Final Project Delivery:   EV = $1,000k, PV = $1,000k --> SV = $0      (Appears "On Schedule"!)

[!WARNING] An uninformed stakeholder looking at an EVM report at project closeout will see $SV = $0$ and conclude the project finished on schedule! Cost technicians must recognize this anomaly: Schedule Variance loses its predictive reliability as a project approaches and passes its scheduled completion date.

Nuance 3: Critical Path Blindness

Schedule Variance measures total volume of work performed across all activities, irrespective of whether those activities lie on the Critical Path.

• If a project team expends massive effort over-performing on non-critical activities with months of total float, they will generate massive Earned Value, resulting in a positive (favorable) Schedule Variance ($SV > 0$).
• Simultaneously, if the single critical path activity driving the project completion milestone is stalled, the actual calendar completion of the project is slipping.
• Therefore, a positive SV never guarantees that the project is on track to meet its contractual milestone date. EVM must always be cross-referenced with CPM network logic.

---

4. Graphical Representation of Variances on the S-Curve

When cumulative Planned Value ($PV$), Earned Value ($EV$), and Actual Cost ($AC$) are plotted against time on an S-curve, variances appear as direct vertical distances between the curves at the status date:

CUMULATIVE S-CURVE VARIANCE GEOMETRY:

Cost ($) ^
         |                                     BAC - - - - - - - - [Finish]
         |                                         /            /
         |                                  AC    /      PV    /
         |                                 /     /      /     /
         |                                /     /      /     /
         |                               /     /      /     /
         |                              *     /      /     /
         |                             /     /      /     /
         |                            /     *      /     /
         |                           /     /      /     /
         |                          /     /      *     /
         |                         /     /      /     /
         |                        /     /      /     /
         |                       /     /      /     /
         |                      /     /      /     /
         |---------------------+-----+------+-----+------------------------>
                             Time = Status Date (T)

  VERTICAL DELTAS AT STATUS DATE (T):
  - [AC to EV Delta]:  Cost Variance (CV = EV - AC). Here AC is above EV --> CV < 0 (Over Budget)
  - [PV to EV Delta]:  Schedule Variance (SV = EV - PV). Here PV is above EV --> SV < 0 (Behind Sched)

The Four Operating Quadrants of Project Health

By evaluating the combination of CV and SV signs, cost controllers classify project status into four distinct operational quadrants:

---

5. Step-by-Step Worked Calculation: Multi-Account Variance Analysis

Scenario: An industrial piping and instrumentation project has an overall Budget at Completion (BAC) of $500,000. The project controller evaluates performance at the end of Quarter 2 across four primary Control Accounts:

CONTROL ACCOUNT BASELINE DATA AT STATUS DATE:
- CA-01 (Site Earthwork & Grading):     BAC = $60,000  | PV = $60,000  | % Comp = 100% | AC = $54,000
- CA-02 (Foundation & Concrete):        BAC = $140,000 | PV = $140,000 | % Comp = 90%  | AC = $150,000
- CA-03 (Structural Steel Erection):    BAC = $180,000 | PV = $120,000 | % Comp = 50%  | AC = $110,000
- CA-04 (Mechanical Piping & Valves):   BAC = $120,000 | PV = $30,000  | % Comp = 15%  | AC = $25,000

Step 1: Calculate Earned Value (EV) for Each Account

Apply the Cardinal Rule ($EV = BAC \times % \text{ Complete}$):

• $\text{EV}_{01} = $60,000 \times 1.00 = \mathbf{$60,000}$
• $\text{EV}_{02} = $140,000 \times 0.90 = \mathbf{$126,000}$
• $\text{EV}_{03} = $180,000 \times 0.50 = \mathbf{$90,000}$
• $\text{EV}_{04} = $120,000 \times 0.15 = \mathbf{$18,000}$

Step 2: Calculate Absolute Variances (CV and SV)

• $\text{CA-01: } CV = $60,000 - $54,000 = +\mathbf{$6,000}; \quad SV = $60,000 - $60,000 = \mathbf{$0}$
• $\text{CA-02: } CV = $126,000 - $150,000 = -\mathbf{$24,000}; \quad SV = $126,000 - $140,000 = -\mathbf{$14,000}$
• $\text{CA-03: } CV = $90,000 - $110,000 = -\mathbf{$20,000}; \quad SV = $90,000 - $120,000 = -\mathbf{$30,000}$
• $\text{CA-04: } CV = $18,000 - $25,000 = -\mathbf{$7,000}; \quad SV = $18,000 - $30,000 = -\mathbf{$12,000}$

Step 3: Calculate Percentage Variances (CV% and SV%)

• $\text{CA-01: } CV% = (+$6,000 / $60,000) \times 100 = +\mathbf{10.0%}; \quad SV% = ($0 / $60,000) \times 100 = \mathbf{0.0%}$
• $\text{CA-02: } CV% = (-$24,000 / $126,000) \times 100 = -\mathbf{19.05%}; \quad SV% = (-$14,000 / $140,000) \times 100 = -\mathbf{10.0%}$
• $\text{CA-03: } CV% = (-$20,000 / $90,000) \times 100 = -\mathbf{22.22%}; \quad SV% = (-$30,000 / $120,000) \times 100 = -\mathbf{25.0%}$
• $\text{CA-04: } CV% = (-$7,000 / $18,000) \times 100 = -\mathbf{38.89%}; \quad SV% = (-$12,000 / $30,000) \times 100 = -\mathbf{40.0%}$

Step 4: Total Project Roll-Up & Summary Table

$\text{Project } CV = \sum EV - \sum AC = \$294,000 - \$339,000 = -\mathbf{\$45,000}$ $\text{Project } SV = \sum EV - \sum PV = \$294,000 - \$350,000 = -\mathbf{\$56,000}$ $\text{Project } CV\% = \left(\frac{-\$45,000}{\$294,000}\right) \times 100 = -\mathbf{15.31\%}$ $\text{Project } SV\% = \left(\frac{-\$56,000}{\$350,000}\right) \times 100 = -\mathbf{16.00\%}$

Analytical Takeaway:

Overall, the project is in Quadrant IV distress—experiencing an overall cost overrun of $45,000 (15.31%) and lagging its scheduled production by $56,000 (16.00%). Although Earthwork finished favorably under budget, heavy cost overruns and lagging physical installation in Concrete, Steel, and Piping threaten the overall completion date and budget.

---

6. Exam Watch: High-Yield Traps & Rules of Thumb

[!WARNING] The Reversed Subtraction Trap: Exam questions often test whether you know which parameter comes first. If you memorize that "Cost Variance is Actual Cost minus Earned Value," you will calculate $CV = $339,000 - $294,000 = +$45,000$ and mistakenly select "$45,000 favorable under budget." Always remember: Earned Value always leads the subtraction ($EV - AC$ and $EV - PV$).

[!CAUTION] The Calendar Days Fallacy: If a multiple-choice question presents a project with $SV = -$30,000$ and asks: "What is the status of the project schedule?", avoid options stating "The project is 30 days behind schedule." The correct answer must state that the project is behind schedule by $30,000 worth of planned work, because EVM Schedule Variance does not measure calendar time.

[!TIP] The Zero SV at Completion Trap: If an exam question describes a project that finished 8 months after its contractual baseline completion date and asks for the final Schedule Variance (SV), the answer is $0. Do not calculate an arbitrary financial penalty. At project finish, all scope has been earned, making $EV = BAC$ and $PV = BAC$, resulting in $SV = 0$.