11.4 Forecasting: EAC, ETC, VAC & TCPI

11.4 Forecasting: EAC, ETC, VAC & TCPI

Quick Summary: Historical variances and indices ($CV, SV, CPI, SPI$) describe past performance. However, executive project governance requires predictive forecasting: How much will the project ultimately cost, how much additional cash is needed to finish, and how efficiently must the remaining work be executed? EVM answers these questions through Estimate at Completion (EAC), Estimate to Complete (ETC), Variance at Completion (VAC), and the To-Complete Performance Index (TCPI). Selecting the correct EAC formula depends strictly on management's assumptions regarding whether past performance was typical (will persist), atypical (one-off event), or constrained by immovable schedule deadlines ($CPI \times SPI$). When evaluated against current CPI, TCPI provides an indispensable mathematical "reality check" on baseline feasibility.

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1. Principles of Predictive Cost Forecasting

In capital projects, waiting until project closeout to recognize an overrun is professional negligence. Earned Value Management provides statistical forecasting mechanisms that project final financial outcomes early in the project lifecycle.

+-----------------------------------------------------------------------------------+
|                         EVM FORECASTING TERMINOLOGY                               |
|                                                                                   |
|  - BAC:  Budget at Completion       --> The original authorized baseline budget   |
|  - EAC:  Estimate at Completion     --> The forecasted final total project cost   |
|  - ETC:  Estimate to Complete       --> Forecasted additional funds needed to end |
|  - VAC:  Variance at Completion     --> Projected final overrun or surplus        |
|  - TCPI: To-Complete Perf. Index    --> Required efficiency on remaining work     |
+-----------------------------------------------------------------------------------+

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2. Estimate at Completion (EAC) Formulations & Assumptions

There is no single "universal" EAC equation. Cost engineers select from four primary formulations based on explicit, defensible assumptions regarding future project conditions.

+-----------------------------------------------------------------------------------+
|                            THE FOUR EAC FORMULATIONS                              |
+-----------------------------------------------------------------------------------+
|  CASE 1: TYPICAL FUTURE PERFORMANCE (Default / Continuing Trend)                  |
|          Assumption: Future work will proceed at the current cumulative CPI.      |
|          $$\mathbf{EAC = \frac{BAC}{CPI}} = AC + \frac{BAC - EV}{CPI}$$           |
+-----------------------------------------------------------------------------------+
|  CASE 2: ATYPICAL FUTURE PERFORMANCE (One-Off Past Variances)                     |
|          Assumption: Past variances were anomalies; remaining work proceeds at    |
|                      the planned baseline budget rate (Future CPI = 1.0).         |
|          $$\mathbf{EAC = AC + (BAC - EV)}$$                                       |
+-----------------------------------------------------------------------------------+
|  CASE 3: COMBINED COST & SCHEDULE CONSTRAINTS (Hard Fixed Deadlines)              |
|          Assumption: Both cost efficiency and schedule delays will impact the     |
|                      cost of remaining work (e.g., crashing to meet firm date).   |
|          $$\mathbf{EAC = AC + \frac{BAC - EV}{CPI \times SPI}}$$                   |
+-----------------------------------------------------------------------------------+
|  CASE 4: COMPREHENSIVE BOTTOM-UP RE-ESTIMATE (Fundamental Re-forecast)            |
|          Assumption: Original baseline assumptions are invalid; fresh QTO done.   |
|          $$\mathbf{EAC = AC + \text{Bottom-Up ETC}}$$                              |
+-----------------------------------------------------------------------------------+

Detailed Analysis of EAC Assumptions

Case 1: Typical Performance ($EAC = BAC / CPI$)

• Operational Context: The default standard across AACE and DoD projects. It assumes that the organizational, labor, environmental, and commercial productivity experienced to date represents the "new normal" for the remainder of the project.
• Mathematical Identity: Notice that: $EAC = AC + \frac{BAC - EV}{CPI} = AC + \frac{BAC}{CPI} - \frac{EV}{CPI}$ Because $EV / CPI = EV / (EV / AC) = AC$, the actual costs cancel out: $EAC = AC + \frac{BAC}{CPI} - AC = \frac{BAC}{CPI}$ Both formulations yield the exact same mathematical result.

Case 2: Atypical Performance ($EAC = AC + [BAC - EV]$)

• Operational Context: Used only when past variances were caused by non-recurring, isolated "black swan" events (e.g., a one-time Category 5 hurricane, an isolated supplier bankruptcy, or an unforeseen geotechnical sinkhole that has been fully remediated).
• Mechanism: The project absorbs the actual cost incurred to date ($AC$), and assumes all remaining physical scope ($BAC - EV$) will be executed exactly at the original budgeted rate ($CPI_{future} = 1.00$).

Case 3: Combined Cost and Schedule ($EAC = AC + [(BAC - EV) / (CPI \times SPI)]$

• Operational Context: Applied when a project has an immovable contractual completion date with severe delay damages. When a project is behind schedule ($SPI < 1.0$), the project manager must accelerate remaining work through overtime, second shifts, and expedited freight. These corrective measures inflate labor inefficiency, compounding the existing cost distress ($CPI < 1.0$). Dividing remaining work by the Critical Ratio ($CPI \times SPI$) produces the most conservative (highest cost) forecast.

Case 4: Bottom-Up Re-estimate ($EAC = AC + \text{Bottom-Up ETC}$)

• Operational Context: When actual site conditions deviate so drastically from baseline assumptions that statistical index projections become useless, the project team executes a complete bottom-up re-estimate of remaining work packages (new quantity takeoffs, crew builds, and vendor bids). This becomes the Bottom-Up ETC.

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3. Estimate to Complete (ETC) & Variance at Completion (VAC)

Estimate to Complete (ETC)

Estimate to Complete (ETC) represents the expected additional cash outlay required to finish all outstanding project scope from the status date onward: $\mathbf{ETC = EAC - AC}$

If calculating ETC directly based on typical future performance: $\mathbf{ETC_{typical} = \frac{BAC - EV}{CPI}}$

Variance at Completion (VAC)

Variance at Completion (VAC) projects the final monetary surplus or deficit at project closeout: $\mathbf{VAC = BAC - EAC}$

+-----------------------------------------------------------------------------------+
|                         VAC INTERPRETATION MATRIX                                 |
|                                                                                   |
|   VAC > 0 (+)  --> Favorable Cost Surplus (Project will finish UNDER budget)       |
|   VAC = 0      --> On Budget (Project will finish exactly at approved baseline)   |
|   VAC < 0 (-)  --> Unfavorable Cost Overrun (Project will EXCEED approved budget) |
+-----------------------------------------------------------------------------------+

[!CAUTION] The VAC Subtraction Trap: Notice that $VAC = BAC - EAC$. It is not $EAC - BAC$. If your project has a $BAC = $1,000,000$ and an forecasted $EAC = $1,200,000$, the calculation is: $VAC = \$1,000,000 - \$1,200,000 = -\$200,000$ The negative sign correctly indicates an unfavorable overrun of $200,000.

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4. To-Complete Performance Index (TCPI)

The To-Complete Performance Index (TCPI) is the efficiency benchmark of future project performance. It defines the cost efficiency that the project team must achieve on all remaining work to meet a specified management financial goal.

$\mathbf{TCPI = \frac{\text{Work Remaining}}{\text{Funds Remaining}} = \frac{BAC - EV}{\text{Target Ceiling} - AC}}$

Depending on whether management's target ceiling is the original budget ($BAC$) or an approved revised forecast ($EAC$), cost technicians use one of two distinct TCPI formulations:

+-----------------------------------------------------------------------------------+
|                         THE TWO TCPI FORMULATIONS                                 |
+-----------------------------------------------------------------------------------+
|  1. TCPI BASED ON BAC (Target: Finish within Original Authorized Budget):         |
|     $$\mathbf{TCPI_{BAC} = \frac{BAC - EV}{BAC - AC}}$$                           |
|                                                                                   |
|  2. TCPI BASED ON EAC (Target: Finish within Approved Revised Forecast):          |
|     $$\mathbf{TCPI_{EAC} = \frac{BAC - EV}{EAC - AC}}$$                           |
+-----------------------------------------------------------------------------------+

Practical Interpretation of TCPI Values

Unlike CPI (where higher is better), TCPI represents a required hurdle rate:

• $TCPI > 1.0$ (Demanding): The team must operate more efficiently than originally budgeted to meet the target. E.g., $TCPI = 1.25$ means the remaining work must achieve $1.25 of progress for every $1.00 spent (a 25% productivity improvement).
• $TCPI = 1.0$ (Baseline): The remaining work can be executed exactly at the original baseline efficiency.
• $TCPI < 1.0$ (Lenient): The team can perform less efficiently than budgeted and still meet the target. This occurs when an expanded $EAC$ budget envelope has been approved.

The TCPI Feasibility "Reality Check" (The Rule of 0.10)

Cost technicians evaluate the operational credibility of project recovery plans by comparing $TCPI_{BAC}$ against the current cumulative $CPI$:

+-----------------------------------------------------------------------------------+
|                        THE TCPI FEASIBILITY REALITY CHECK                         |
|                                                                                   |
|   If:  TCPI_BAC - CPI_cumulative > 0.10 (10 Percentage Points)                   |
|   --> The target BAC is STATISTICALLY AND OPERATIONALLY UNREALISTIC.              |
|   --> Management cannot achieve the plan; a formal EAC rebaseline is required.    |
+-----------------------------------------------------------------------------------+

Example: If a contractor has a cumulative $CPI = 0.82$, and the calculated $TCPI_{BAC} = 1.15$, the contractor is claiming they will improve craft productivity from $0.82$ to $1.15$ (a delta of $+0.33$, or a 40% leap in productivity). In construction and engineering, sustained 40% productivity spikes never happen. The plan is a statistical delusion.

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5. Master Numerical Case Study: Complete EVM Project Lifecycle

The Project: Constructing a regional electrical transmission switching station.

• Authorized Budget at Completion (BAC): $5,000,000
• Project Duration: 10 Months
• Status Cutoff Date: End of Month 5 (Midpoint)

Status Date Financial & Schedule Data:

• Scheduled Progress: The baseline schedule planned for 60% of total scope to be completed by Month 5.
• Actual Physical Progress: Independent field engineering surveys verify that exactly 50% of the physical scope has been installed and inspected.
• Cumulative Accounting Costs: The project job ledger records total cumulative actual costs of $3,000,000 ($AC$) incurred through the end of Month 5.

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Step 1: Calculate the Four Core Parameters

1. $BAC = \mathbf{$5,000,000}$ (Authorized budget)
2. $PV = BAC \times % \text{ Scheduled} = $5,000,000 \times 0.60 = \mathbf{$3,000,000}$
3. $EV = BAC \times % \text{ Physical Complete} = $5,000,000 \times 0.50 = \mathbf{$2,500,000}$
4. $AC = \mathbf{$3,000,000}$ (Recorded expenditures)

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Step 2: Calculate Absolute and Percentage Variances

• Cost Variance ($CV$): $CV = EV - AC = \$2,500,000 - \$3,000,000 = -\mathbf{\$500,000} \quad (\text{Unfavorable / Over Budget})$
• Schedule Variance ($SV$): $SV = EV - PV = \$2,500,000 - \$3,000,000 = -\mathbf{\$500,000} \quad (\text{Unfavorable / Behind Schedule})$
• Cost Variance Percentage ($CV%$): $CV\% = \left(\frac{CV}{EV}\right) \times 100 = \left(\frac{-\$500,000}{\$2,500,000}\right) \times 100 = -\mathbf{20.0\%}$
• Schedule Variance Percentage ($SV%$): $SV\% = \left(\frac{SV}{PV}\right) \times 100 = \left(\frac{-\$500,000}{\$3,000,000}\right) \times 100 = -\mathbf{16.67\%}$

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Step 3: Calculate Performance Indices

• Cost Performance Index ($CPI$): $CPI = \frac{EV}{AC} = \frac{\$2,500,000}{\$3,000,000} = \mathbf{0.8333}$ (The project earns only $0.833 of value for every $1.00 spent).
• Schedule Performance Index ($SPI$): $SPI = \frac{EV}{PV} = \frac{\$2,500,000}{\$3,000,000} = \mathbf{0.8333}$ (Work is progressing at only 83.3% of the planned schedule pace).
• Critical Ratio ($CR$): $CR = CPI \times SPI = 0.8333 \times 0.8333 = \mathbf{0.6944}$ (Severe distress: $CR < 0.80$ indicates immediate corrective action required).

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Step 4: Forecast Final Costs Across EAC Scenarios

Calculate work remaining: $\text{Work Remaining} = BAC - EV = $5,000,000 - $2,500,000 = \mathbf{$2,500,000}$.

Scenario A: Typical Future Performance (Cumulative CPI will continue)

$EAC_{typ} = \frac{BAC}{CPI} = \frac{\$5,000,000}{0.8333} = \mathbf{\$6,000,000}$ $ETC_{typ} = EAC - AC = \$6,000,000 - \$3,000,000 = \mathbf{\$3,000,000}$ $VAC_{typ} = BAC - EAC = \$5,000,000 - \$6,000,000 = -\mathbf{\$1,000,000} \quad (\text{Overrun of } \$1.0\text{M})$

Scenario B: Atypical Future Performance (Past variance was an isolated event; remaining work at budget)

$EAC_{atyp} = AC + (BAC - EV) = \$3,000,000 + \$2,500,000 = \mathbf{\$5,500,000}$ $ETC_{atyp} = EAC - AC = \$5,500,000 - \$3,000,000 = \mathbf{\$2,500,000}$ $VAC_{atyp} = BAC - EAC = \$5,000,000 - \$5,500,000 = -\mathbf{\$500,000} \quad (\text{Overrun of } \$500\text{k})$

Scenario C: Combined Cost and Schedule Constraints (Hard deadline / Overtime acceleration)

$EAC_{comb} = AC + \frac{BAC - EV}{CPI \times SPI} = \$3,000,000 + \frac{\$2,500,000}{0.8333 \times 0.8333} = \$3,000,000 + \frac{\$2,500,000}{0.6944} = \mathbf{\$6,600,000}$ $ETC_{comb} = EAC - AC = \$6,600,000 - \$3,000,000 = \mathbf{\$3,600,000}$ $VAC_{comb} = BAC - EAC = \$5,000,000 - \$6,600,000 = -\mathbf{\$1,600,000} \quad (\text{Overrun of } \$1.6\text{M})$

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Step 5: Evaluate To-Complete Performance Indices (TCPI)

1. TCPI to Achieve the Original Baseline Budget ($BAC = $5,000,000$):

$\text{Work Remaining} = BAC - EV = \$5,000,000 - \$2,500,000 = \$2,500,000$ $\text{Funds Remaining in BAC} = BAC - AC = \$5,000,000 - \$3,000,000 = \$2,000,000$ $TCPI_{BAC} = \frac{BAC - EV}{BAC - AC} = \frac{\$2,500,000}{\$2,000,000} = \mathbf{1.25}$

Feasibility Reality Check:

• Current cumulative $CPI$ is 0.833.
• Required future $CPI$ is 1.250.
• $\Delta = TCPI_{BAC} - CPI = 1.250 - 0.833 = +\mathbf{0.417}$ (a 50% productivity leap!).
• Because $\Delta = 0.417 \gg 0.10$, achieving the original $5,000,000 BAC is statistically impossible under the Christensen stability rule. Management cannot recover.

2. TCPI to Achieve the Realistic Revised Forecast ($EAC_{typ} = $6,000,000$):

$\text{Funds Remaining in EAC} = EAC - AC = \$6,000,000 - \$3,000,000 = \$3,000,000$ $TCPI_{EAC} = \frac{BAC - EV}{EAC - AC} = \frac{\$2,500,000}{\$3,000,000} = \mathbf{0.8333}$

Feasibility Reality Check:

• Required future efficiency ($TCPI_{EAC} = 0.8333$) matches the current cumulative performance ($CPI = 0.8333$).
• This target is highly achievable because the team only needs to maintain its existing operating rhythm without further degradation.

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Step 6: Master Summary Matrix of Forecasting Results

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

[!WARNING] The EAC Formula Selection Trap: Exam questions will state: "Variances experienced to date are considered non-recurring and future work will proceed as originally planned. What is the EAC?" Candidates who reflexively calculate $BAC / CPI$ will get the question wrong! When variances are non-recurring/atypical, use $EAC = AC + (BAC - EV)$.

[!CAUTION] The TCPI Denominator Confusion: In $TCPI_{BAC}$, the denominator is $(BAC - AC)$. In $TCPI_{EAC}$, the denominator is $(EAC - AC)$. The numerator is always the identical work remaining: $(BAC - EV)$. Never put $(EAC - EV)$ in the numerator!

[!TIP] VAC Sign Conventions: A positive VAC ($VAC > 0$) is favorable (finishing under budget with a cash surplus). A negative VAC ($VAC < 0$) is unfavorable (finishing over budget with an overrun). Always evaluate VAC as $BAC - EAC$.