12.2 To-Complete Performance Index (TCPI) & Variance at Completion (VAC)

12.2 To-Complete Performance Index (TCPI) & Variance at Completion (VAC)

Beyond the forecasting mathematics, this section carries 4.M recommend performance improvements (e.g., change orders, performance to-date). TCPI is precisely the tool the blueprint has in mind: it converts "we are behind" into the specific efficiency the remaining work must achieve, which is what a defensible recommendation has to state.

In Earned Value Management, generating an Estimate at Completion (EAC) is only half of the forecasting equation. Project managers, cost engineers, and executive sponsors must validate whether a proposed EAC is operationally achievable or represents wishful thinking.

Under the AACE International Total Cost Management framework, this validation is performed using Variance at Completion (VAC) and the To-Complete Performance Index (TCPI). TCPI is widely recognized by project controls professionals as the ultimate reality check in cost engineering, converting abstract financial forecasts into actionable productivity targets for project execution teams.

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1. Variance at Completion (VAC) Fundamentals

Variance at Completion (VAC) represents the forecasted financial variance between the total approved budget and the expected final cost at the completion of all authorized project scope.

+-----------------------------------------------------------------------------+
|                        VARIANCE AT COMPLETION (VAC)                         |
|                                                                             |
|   Mathematical Formula:       VAC = BAC - EAC                               |
|                                                                             |
|   VAC Percentage:             VAC% = (VAC / BAC) * 100                      |
|                                                                             |
|   INTERPRETATION:                                                           |
|   - VAC > 0 (Positive):       Favorable (Projected Final Cost Underrun)     |
|   - VAC = 0 (Zero):           On Target (Projected to Finish Exactly on BAC)|
|   - VAC < 0 (Negative):       Unfavorable (Projected Final Cost Overrun)    |
+-----------------------------------------------------------------------------+

Distinction Between Cost Variance ($CV$) and Variance at Completion ($VAC$)

• Cost Variance ($CV = EV - AC$): A backward-looking, historical metric that measures cost efficiency from project inception to the current status date. It reflects the sunk cost overrun or underrun realized to date.
• Variance at Completion ($VAC = BAC - EAC$): A forward-looking, predictive metric that projects the net financial delta at the conclusion of 100% of the project scope. If $EAC > BAC$, $VAC$ is negative, indicating that the project will require additional authorization of funds.

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2. To-Complete Performance Index (TCPI) Mechanics

The To-Complete Performance Index (TCPI) is defined as:

The calculated ratio of remaining work to remaining available financial resources, representing the cost performance efficiency that must be maintained on all remaining uncompleted work to achieve a specific management financial target.

$\text{Conceptual Formula:}\quad \text{TCPI} = \frac{\text{Budgeted Cost of Work Remaining (BCWR)}}{\text{Estimated Available Funds Remaining}} = \frac{\text{Work Remaining}}{\text{Funds Remaining}}$

While the historical Cost Performance Index ($CPI = EV / AC$) measures what the project team has achieved, the $TCPI$ defines what the team must achieve from the status date forward.

+-----------------------------------------------------------------------------+
|                        THE TWO TCPI TARGET FORMULATIONS                     |
|                                                                             |
|   TARGET 1: ORIGINAL BASELINE BUDGET (BAC)                                  |
|             TCPI_BAC = (BAC - EV) / (BAC - AC)                              |
|             Used when management requires full recovery of past overruns.   |
|                                                                             |
|   TARGET 2: REVISED ESTIMATE AT COMPLETION (EAC)                            |
|             TCPI_EAC = (BAC - EV) / (EAC - AC)                              |
|             Used when BAC is unachievable and a new financial ceiling is set|
+-----------------------------------------------------------------------------+

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Target 1: Meeting the Original Budget at Completion ($TCPI_{\text{BAC}}$)

When executive management, owners, or government agencies refuse to authorize budget increases, the project team is mandated to complete all remaining work within the original approved $BAC$.

$TCPI_{\text{BAC}} = \frac{BAC - EV}{BAC - AC}$

• Numerator ($BAC - EV$): The baseline budgeted value of all remaining, uncompleted work packages.
• Denominator ($BAC - AC$): The remaining unspent funds within the original budget allocation.

The Singularity Condition ($AC \ge BAC$):

If a project experiences severe cost overruns such that actual expenditures equal or exceed the total budget ($AC \ge BAC$) before all work is earned ($EV < BAC$):

• The denominator becomes zero or negative ($BAC - AC \le 0$).
• Mathematically, $TCPI_{\text{BAC}}$ is infinite or negative.
• Operationally, this indicates that completing the project within the original BAC is 100% physically and financially impossible, because zero baseline funds remain to execute the remaining unearned scope. In such cases, $TCPI_{\text{BAC}}$ ceases to be meaningful, and project controls must transition to $TCPI_{\text{EAC}}$.

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Target 2: Meeting an Approved Revised Forecast ($TCPI_{\text{EAC}}$)

When a project overruns its original budget and management acknowledges that $BAC$ cannot be recovered, an approved revised Estimate at Completion ($EAC$) is established as the new financial baseline. The cost engineer must determine the required efficiency to meet this revised ceiling:

$TCPI_{\text{EAC}} = \frac{BAC - EV}{EAC - AC}$

• Numerator ($BAC - EV$): The baseline budgeted value of all remaining work.
• Denominator ($EAC - AC$): The revised remaining funds available to complete the project ($ETC$).

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3. Interpreting TCPI Values & The Feasibility Threshold Matrix

Understanding how to interpret numerical TCPI values is a core competency tested on the CCP exam:

+-----------------------------------------------------------------------------+
|                     TCPI VALUE INTERPRETATION SPECTRUM                      |
|                                                                             |
|   TCPI < 1.00   --> LESS EFFICIENT THAN PLANNED                             |
|                     Remaining work can be executed at lower efficiency than |
|                     originally budgeted. Project has financial cushion.     |
|                                                                             |
|   TCPI = 1.00   --> EXACT BASELINE PLANNED RATE                             |
|                     Remaining work must achieve exactly $1.00 of EV for     |
|                     every $1.00 spent to hit the target.                    |
|                                                                             |
|   TCPI > 1.00   --> MORE EFFICIENT THAN PLANNED                             |
|                     Remaining work must achieve higher efficiency than      |
|                     originally planned ($1.00 EV requires < $1.00 spend).   |
|                                                                             |
|   TCPI > 1.10   --> EMPIRICAL UNFEASIBILITY THRESHOLD                       |
|                     Demands > 10% efficiency improvement over baseline.     |
|                     Historically unachievable without scope reduction.      |
+-----------------------------------------------------------------------------+

The CPI vs. TCPI Gap Analysis (The Feasibility Reality Check)

In professional cost auditing (e.g., Defense Contract Management Agency / DCMA, Department of Energy, and AACE project reviews), cost analysts compare the historical cumulative $CPI$ against the forward-looking $TCPI_{\text{EAC}}$ to test the validity of a contractor's proposed EAC:

$\text{Feasibility Gap} = TCPI_{\text{EAC}} - CPI_{\text{cumulative}}$

+-----------------------------------------------------------------------------+
|                        EAC FEASIBILITY DECISION RULES                       |
|                                                                             |
|   1. |TCPI_EAC - CPI_cum| <= 0.05:                                          |
|      EAC is highly realistic and mathematically consistent with current     |
|      performance trends.                                                    |
|                                                                             |
|   2. 0.05 < (TCPI_EAC - CPI_cum) <= 0.10:                                   |
|      EAC is moderately aggressive; requires specific management corrective  |
|      action plans (e.g., labor re-tooling, process improvement) to justify. |
|                                                                             |
|   3. (TCPI_EAC - CPI_cum) > 0.10:                                           |
|      EAC is UNREALISTIC / OVERLY OPTIMISTIC. Empirical data indicates that  |
|      troubled projects cannot improve cost efficiency by > 10 percentage    |
|      points without fundamental re-scoping or contract modification.        |
|                                                                             |
|   4. TCPI_EAC == CPI_cum:                                                   |
|      Occurs when EAC = BAC / CPI (The Typical Forecast). The required future|
|      efficiency exactly equals the demonstrated past efficiency.            |
+-----------------------------------------------------------------------------+

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4. Statistical EAC Range Analysis & Independent Estimates at Completion (IEAC)

To prevent reliance on a single point forecast, cost engineers develop an Independent Estimate at Completion (IEAC) range using statistical formulas to define the bounds of financial risk:

+-----------------------------------------------------------------------------+
|                        STATISTICAL IEAC BOUNDING RANGE                      |
|                                                                             |
|   BEST-CASE FLOOR (IEAC_min)   = AC + (BAC - EV)        [Atypical Model]    |
|   MOST LIKELY     (IEAC_mid)   = BAC / CPI              [Typical Model]     |
|   WORST-CASE CEIL (IEAC_max)   = AC + (BAC - EV)/(CPI*SPI) [Composite]     |
+-----------------------------------------------------------------------------+

Schedule-Adjusted Forecasting: Earned Schedule ($ES$) & $EAC_t$

In modern EVM standards, forecasting is extended to project duration using Earned Schedule (ES) metrics:

• Schedule Performance Index (Time) ($SPI_t$): $SPI_t = ES / AT$, where $AT$ is Actual Time.
• Time-Based Estimate at Completion ($EAC_t$): $EAC_t = \text{Planned Duration} / SPI_t$.

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5. Comprehensive Worked Step-by-Step Engineering Case Study

Refinery Hydrocracker Revamp Project Data:

• Approved Baseline Budget ($BAC$): $40,000,000
• Status Date (Month 10 of 18):
  • Planned Value ($PV$): $25,000,000
  • Earned Value ($EV$): $20,000,000
  • Actual Cost ($AC$): $25,000,000
• Contractor Proposal: Contractor submits a revised EAC of $44,000,000.

Step 1: Compute Current Historical Performance Indices

1. Cost Performance Index ($CPI$): $CPI = \frac{EV}{AC} = \frac{\$20,000,000}{\$25,000,000} = 0.800$
2. Schedule Performance Index ($SPI$): $SPI = \frac{EV}{PV} = \frac{\$20,000,000}{\$25,000,000} = 0.800$
3. Cost Variance ($CV$): $CV = EV - AC = \$20,000,000 - \$25,000,000 = -\$5,000,000$
4. Work Remaining ($BAC - EV$): $\text{Work Remaining} = \$40,000,000 - \$20,000,000 = \$20,000,000$

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Step 2: Evaluate Feasibility of Finishing Within Original $BAC$

$\text{Available Funds Remaining under BAC} = BAC - AC = \$40,000,000 - \$25,000,000 = \$15,000,000$ $TCPI_{\text{BAC}} = \frac{BAC - EV}{BAC - AC} = \frac{\$20,000,000}{\$15,000,000} = \mathbf{1.333}$

Engineering Interpretation:

• To finish within the original $40,000,000 budget, the craft labor force must execute all remaining work at a cost efficiency of 1.333 ($1.33 of earned value for every $1.00 spent).
• Compared to current performance ($CPI = 0.800$), this requires an efficiency improvement of: $\Delta \text{Efficiency} = 1.333 - 0.800 = +0.533 \quad \text{(A 66.6\% productivity increase)}$
• Audit Conclusion: Finishing within the original $BAC$ is completely unachievable.

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Step 3: Evaluate Feasibility of Contractor's Proposed EAC ($EAC = $44,000,000$)

$\text{Available Funds Remaining under Proposed EAC} = EAC - AC = \$44,000,000 - \$25,000,000 = \$19,000,000$ $TCPI_{\text{EAC}} = \frac{BAC - EV}{EAC - AC} = \frac{\$20,000,000}{\$19,000,000} = \mathbf{1.0526}$

Gap Analysis:

$\text{Feasibility Gap} = TCPI_{\text{EAC}} - CPI = 1.0526 - 0.8000 = +0.2526 \quad \text{(25.3 percentage points)}$

• Audit Conclusion: Although $TCPI_{\text{EAC}} = 1.053$ appears modest in isolation, achieving it requires improving labor efficiency from $0.800$ to $1.053$. Because the gap (+0.253) far exceeds the empirical 0.10 feasibility threshold, the contractor's proposal is statistically invalid and overly optimistic.

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Step 4: Compute Realistic EAC Using Typical CPI & Variance at Completion

1. Empirical Typical EAC: $EAC_{\text{typical}} = \frac{BAC}{CPI} = \frac{\$40,000,000}{0.800} = \mathbf{\$50,000,000}$
2. Validation via $TCPI_{\text{EAC}}$: $TCPI_{\text{EAC=50M}} = \frac{\$20,000,000}{\$50,000,000 - \$25,000,000} = \frac{\$20,000,000}{\$25,000,000} = \mathbf{0.800}$ (Notice that $TCPI_{\text{EAC}} = CPI = 0.800$, representing zero required change in demonstrated productivity).
3. Variance at Completion ($VAC$): $VAC = BAC - EAC = \$40,000,000 - \$50,000,000 = -\mathbf{\$10,000,000}$ $VAC_{\text{percent}} = \left(\frac{-\$10,000,000}{\$40,000,000}\right) \times 100 = -25.0\%$

[!IMPORTANT] Cardinal Exam Rule for TCPI:

• Whenever $EAC = BAC / CPI$, then $TCPI_{\text{EAC}} = CPI$.
• If an owner accepts an EAC such that $TCPI_{\text{EAC}} > CPI + 0.10$, the owner is accepting an unvalidated schedule/cost recovery plan that is virtually guaranteed to overrun.