PE Exam (Civil) Earned Value Management: CV, SV, CPI, SPI
Last updated: May 2, 2026
Earned Value Management: CV, SV, CPI, SPI questions are one of the highest-leverage areas to study for the PE Exam (Civil). This guide breaks down the rule, the elements you need to recognize, the named traps that catch most students, and a memory aid that scales to test day. Read it once, then practice the same sub-topic adaptively in the app.
The rule
Earned Value Management (EVM) compares three measurements at a status date: Planned Value ($PV$, the budgeted cost of work scheduled), Earned Value ($EV$, the budgeted cost of work performed), and Actual Cost ($AC$, the actual cost of work performed). From those three numbers, derive variances $CV = EV - AC$ and $SV = EV - PV$, and indices $CPI = \frac{EV}{AC}$ and $SPI = \frac{EV}{PV}$. Negative variances and indices below $1.0$ are unfavorable; the construction PE expects you to read these signs correctly and forecast completion using $EAC = \frac{BAC}{CPI}$ when current cost performance is assumed to continue. EVM is governed by ANSI/EIA-748 and is the standard project-controls framework in construction project management literature (PMBOK Guide, AACE International RPs).
Elements breakdown
The three primary measurements
Every EVM calculation starts from these three numbers, all expressed in dollars at the status date.
- $PV$ — budgeted cost of scheduled work
- $EV$ — budgeted cost of performed work
- $AC$ — actual cost of performed work
- All three are cumulative through status date
- $EV$ uses the BUDGETED rate, not actual
- $BAC$ — total budget at completion
Variances (subtraction form)
Variances tell you the dollar gap; sign convention: positive is favorable, negative is unfavorable.
- $CV = EV - AC$ (cost variance)
- $SV = EV - PV$ (schedule variance)
- $CV < 0$: spending more than work earned
- $SV < 0$: less work done than scheduled
- $VAC = BAC - EAC$ (variance at completion)
- Units are dollars, not percent
Performance indices (ratio form)
Indices express performance as a unitless ratio; index of $1.0$ is on plan.
- $CPI = \frac{EV}{AC}$ (cost efficiency)
- $SPI = \frac{EV}{PV}$ (schedule efficiency)
- $CPI > 1.0$: under budget for work done
- $SPI > 1.0$: ahead of schedule
- Both share $EV$ in the numerator
- Indices, not variances, used for forecasting
Forecasting completion
Once you have a $CPI$, project the final cost.
- $EAC = \frac{BAC}{CPI}$ — assumes current $CPI$ continues
- $EAC = AC + (BAC - EV)$ — assumes remaining work runs on plan
- $EAC = AC + \frac{BAC - EV}{CPI \times SPI}$ — both indices continue
- $ETC = EAC - AC$ — estimate to complete
- $VAC = BAC - EAC$ — projected over/under run
- Pick the formula matching the assumption stated in the prompt
Reading the dashboard
Translate the four numbers into a one-sentence project diagnosis.
- $CV<0$ and $SV<0$: over budget AND behind
- $CV<0$ and $SV>0$: over budget but ahead
- $CV>0$ and $SV<0$: under budget but behind
- $CV>0$ and $SV>0$: under budget and ahead
- $CPI \times SPI$ — sometimes used as a single health index
- Always state status date with the numbers
Common patterns and traps
The $EV$-vs-$AC$ Swap
The single most-engineered distractor in construction EVM problems. The candidate plugs the actual dollars spent ($AC$) into a formula that calls for the earned-value dollars ($EV$), or vice versa, because both numbers are reported "to date" and both relate to completed work. The result is an index or variance that is plausible-looking but inverted in meaning.
A choice equal to $\frac{AC}{EV}$ when $CPI = \frac{EV}{AC}$ was asked, or a $CV$ equal to $AC - EV$ instead of $EV - AC$ (sign flipped).
Index Inversion
Candidates who memorize "$CPI$ involves cost" without anchoring on $EV$ in the numerator sometimes write $CPI = \frac{AC}{EV}$. The numerical result is the reciprocal of the right answer, which is itself often offered as a distractor. The same trap exists for $SPI = \frac{PV}{EV}$ (wrong) versus $\frac{EV}{PV}$ (right).
Two choices that multiply to approximately $1.0$ — one is the correct index, the other is its reciprocal.
Schedule-Cost Cross-Substitution
Because the structure of $CV$/$SV$ and $CPI$/$SPI$ is parallel, a candidate rushing the question may compute the schedule metric when asked for the cost metric (or vice versa). $PV$ and $AC$ both sit in the second position of their respective formulas, making this swap easy to miss.
A choice equal to $SPI$ when the question asks for $CPI$ — values often differ by only a few hundredths, making the wrong answer look correct.
Wrong $EAC$ Assumption
There are at least three accepted $EAC$ formulas, each tied to a specific assumption about how the rest of the work will run. Picking $EAC = AC + (BAC - EV)$ when the prompt says "current cost performance continues" yields a number that is too optimistic; picking $EAC = \frac{BAC}{CPI}$ when the prompt says "the remaining work will run as originally planned" yields a number that is too pessimistic. The exam writer always tells you which assumption to use — read carefully.
Two $EAC$ values differing by exactly the variance to date, one matching the stated assumption and one matching the other common assumption.
Sign Convention Drift
Variances follow a strict sign convention: positive is favorable, negative is unfavorable. Candidates who remember the magnitude but flip the sign report a $CV$ of $+\$70{,}000$ when the project is actually $\$70{,}000$ over budget. The exam offers both signs as distractors, sometimes with the correct magnitude.
Two choices with the same dollar magnitude but opposite signs — one is the correct variance, the other is the absolute value swapped or computed as $AC - EV$.
How it works
Take a paving package with $BAC = \$1{,}000{,}000$, scheduled to be $40\%$ complete by week 4. At week 4 you have actually placed $35\%$ of the work and spent $\$420{,}000$. Then $PV = 0.40 \times \$1{,}000{,}000 = \$400{,}000$, $EV = 0.35 \times \$1{,}000{,}000 = \$350{,}000$, and $AC = \$420{,}000$. Cost variance is $CV = EV - AC = \$350{,}000 - \$420{,}000 = -\$70{,}000$, schedule variance is $SV = EV - PV = \$350{,}000 - \$400{,}000 = -\$50{,}000$, and the indices are $CPI = \frac{350}{420} = 0.833$ and $SPI = \frac{350}{400} = 0.875$ — over budget AND behind schedule. If cost performance holds, $EAC = \frac{BAC}{CPI} = \frac{\$1{,}000{,}000}{0.833} = \$1{,}200{,}000$, projecting a $\$200{,}000$ overrun at completion.
Worked examples
You are the project controls engineer on the Aldridge Drainage Improvement Project, a stormwater package with a budget at completion of $BAC = \$1{,}000{,}000$ and a planned duration of 100 working days. At the day-60 status review the schedule shows the work should be $60\%$ complete. The superintendent's quantity walkdown confirms the package is actually $50\%$ complete, and the cost-loaded resource report shows $\$620{,}000$ in committed and incurred costs to date. There are no scope changes. Compute the three primary EVM measurements, then derive the cost performance index.
Most nearly, what is the cost performance index ($CPI$) at day 60?
- A $0.81$ ✓ Correct
- B $0.83$
- C $1.24$
- D $0.97$
Why A is correct: From the data: $PV = 0.60 \times \$1{,}000{,}000 = \$600{,}000$, $EV = 0.50 \times \$1{,}000{,}000 = \$500{,}000$, and $AC = \$620{,}000$. Then $CPI = \frac{EV}{AC} = \frac{\$500{,}000}{\$620{,}000} = 0.806 \approx 0.81$. The dollar units cancel, leaving a unitless ratio less than $1.0$, confirming the package is over budget for work performed.
Why each wrong choice fails:
- B: This is $SPI = \frac{EV}{PV} = \frac{500}{600} = 0.833$, the schedule performance index — the candidate computed the right structural formula but with $PV$ in the denominator instead of $AC$. (Schedule-Cost Cross-Substitution)
- C: This is the reciprocal of $CPI$: $\frac{AC}{EV} = \frac{620}{500} = 1.24$. The candidate inverted the ratio, putting the actual cost in the numerator. (Index Inversion)
- D: This is $\frac{PV}{AC} = \frac{600}{620} = 0.968$, a non-standard ratio. The candidate substituted $PV$ for $EV$ in the numerator — using planned work instead of earned work. (The $EV$-vs-$AC$ Swap)
The Korhonen Bridge Deck Replacement Project has a $BAC = \$2{,}400{,}000$ and a 16-week schedule. At end of week 8, the baseline schedule indicates $\$1{,}200{,}000$ of work should be complete. The site engineer reports the deck demolition and rebar placement total $45\%$ of the contract value, and the cost ledger shows $\$1{,}150{,}000$ in actual costs incurred to date. Determine whether the project is ahead of, behind, or on schedule, and report the schedule variance.
Most nearly, what is the schedule variance ($SV$) at week 8?
- A $-\$120{,}000$ ✓ Correct
- B $-\$70{,}000$
- C $+\$120{,}000$
- D $-\$50{,}000$
Why A is correct: Compute $EV = 0.45 \times \$2{,}400{,}000 = \$1{,}080{,}000$ and use the planned $PV = \$1{,}200{,}000$. Then $SV = EV - PV = \$1{,}080{,}000 - \$1{,}200{,}000 = -\$120{,}000$. The negative sign indicates the project is behind schedule by $\$120{,}000$ of budgeted work at the status date.
Why each wrong choice fails:
- B: This is $CV = EV - AC = \$1{,}080{,}000 - \$1{,}150{,}000 = -\$70{,}000$, the cost variance — the candidate computed the wrong variance (cost instead of schedule), substituting $AC$ for $PV$. (Schedule-Cost Cross-Substitution)
- C: Correct magnitude but wrong sign — the candidate computed $PV - EV$ instead of $EV - PV$, flipping the sign convention so an unfavorable variance reads as favorable. (Sign Convention Drift)
- D: This is $AC - PV = \$1{,}150{,}000 - \$1{,}200{,}000 = -\$50{,}000$, a meaningless quantity in EVM. The candidate ignored $EV$ entirely and subtracted the actual cost from the planned value. (The $EV$-vs-$AC$ Swap)
You are forecasting completion cost for the Patel Highway Rehabilitation Project, a mill-and-overlay package with a budget at completion of $BAC = \$4{,}500{,}000$. At the third quarterly review, the project controls report shows $EV = \$1{,}800{,}000$ and $AC = \$2{,}000{,}000$ to date. The owner has asked for the estimate at completion ($EAC$) under the assumption that the current cost performance will continue through the remainder of the project (typical CPI-based forecast).
Most nearly, what is the estimate at completion ($EAC$)?
- A $\$4{,}050{,}000$
- B $\$4{,}700{,}000$
- C $\$5{,}000{,}000$ ✓ Correct
- D $\$4{,}500{,}000$
Why C is correct: First compute $CPI = \frac{EV}{AC} = \frac{\$1{,}800{,}000}{\$2{,}000{,}000} = 0.90$. Under the assumption that current cost performance continues, $EAC = \frac{BAC}{CPI} = \frac{\$4{,}500{,}000}{0.90} = \$5{,}000{,}000$. The variance at completion is $VAC = BAC - EAC = -\$500{,}000$, signaling a projected $\$500{,}000$ overrun.
Why each wrong choice fails:
- A: This multiplies $BAC \times CPI = \$4{,}500{,}000 \times 0.90 = \$4{,}050{,}000$ instead of dividing. The candidate inverted the forecasting formula, producing an under-run when the data indicate an over-run. (Index Inversion)
- B: This uses $EAC = AC + (BAC - EV) = \$2{,}000{,}000 + (\$4{,}500{,}000 - \$1{,}800{,}000) = \$4{,}700{,}000$, which assumes the remaining work runs at the original budget rate — the WRONG assumption for this problem, which specifies CPI-based forecasting. (Wrong $EAC$ Assumption)
- D: This simply restates $BAC$, ignoring cost performance to date. The candidate did not perform the forecast at all, defaulting to the original budget. (Wrong $EAC$ Assumption)
Memory aid
"EV on top, EV in front": every index has $EV$ in the numerator ($CPI = \frac{EV}{AC}$, $SPI = \frac{EV}{PV}$), and every variance has $EV$ as the lead term ($CV = EV - AC$, $SV = EV - PV$). If $EV$ is not in front, you wrote it backward.
Key distinction
$EV$ uses the BUDGETED cost of the work physically completed — it is the percent complete times the budget, NOT the dollars actually spent. The single most common error on the construction PE is plugging $AC$ where $EV$ belongs because both are tied to work that is finished.
Summary
$EV$ leads every formula: variances subtract from it, indices divide into it, and $EAC = \frac{BAC}{CPI}$ projects how the job will land if today's cost performance continues.
Practice earned value management: cv, sv, cpi, spi adaptively
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Start your free 7-day trialFrequently asked questions
What is earned value management: cv, sv, cpi, spi on the PE Exam (Civil)?
Earned Value Management (EVM) compares three measurements at a status date: Planned Value ($PV$, the budgeted cost of work scheduled), Earned Value ($EV$, the budgeted cost of work performed), and Actual Cost ($AC$, the actual cost of work performed). From those three numbers, derive variances $CV = EV - AC$ and $SV = EV - PV$, and indices $CPI = \frac{EV}{AC}$ and $SPI = \frac{EV}{PV}$. Negative variances and indices below $1.0$ are unfavorable; the construction PE expects you to read these signs correctly and forecast completion using $EAC = \frac{BAC}{CPI}$ when current cost performance is assumed to continue. EVM is governed by ANSI/EIA-748 and is the standard project-controls framework in construction project management literature (PMBOK Guide, AACE International RPs).
How do I practice earned value management: cv, sv, cpi, spi questions?
The fastest way to improve on earned value management: cv, sv, cpi, spi is targeted, adaptive practice — working questions that focus on your specific weak spots within this sub-topic, getting immediate feedback, and revisiting items you missed on a spaced-repetition schedule. Neureto's adaptive engine does this automatically across the PE Exam (Civil); start a free 7-day trial to see your sub-topic mastery climb in real time.
What's the most important distinction to remember for earned value management: cv, sv, cpi, spi?
$EV$ uses the BUDGETED cost of the work physically completed — it is the percent complete times the budget, NOT the dollars actually spent. The single most common error on the construction PE is plugging $AC$ where $EV$ belongs because both are tied to work that is finished.
Is there a memory aid for earned value management: cv, sv, cpi, spi questions?
"EV on top, EV in front": every index has $EV$ in the numerator ($CPI = \frac{EV}{AC}$, $SPI = \frac{EV}{PV}$), and every variance has $EV$ as the lead term ($CV = EV - AC$, $SV = EV - PV$). If $EV$ is not in front, you wrote it backward.
What's a common trap on earned value management: cv, sv, cpi, spi questions?
Confusing $EV$ (budgeted cost of performed work) with $AC$ (actual cost of performed work)
What's a common trap on earned value management: cv, sv, cpi, spi questions?
Inverting index ratios — $CPI$ is $\frac{EV}{AC}$, not $\frac{AC}{EV}$
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