5 Keeping Score: Earned Value Management

“What gets measured gets managed.” — Peter Drucker

Imagine you’re three months into a six-month project and you’ve spent exactly half the budget. That might sound encouraging, but the more useful question is: how much work did you actually get done? If you’ve completed 30% of the project, the budget situation looks very different than if you’ve completed 55%.

This is the fundamental insight behind Earned Value Management (EVM): you can’t judge project health by money spent alone. You need to compare three things: what you planned, what you actually did, and what it cost you to do it.

Learning Objectives

By the end of this chapter, you will be able to:

Compute PV, EV, and AC from project data
Calculate and interpret CPI and SPI performance indices
Produce an EAC forecast using all three methods and choose the right one
Calculate ETC, VAC, and TCPI
Read and construct an EVM trend chart

5.1 The Three Core Numbers

PV, EV, AC: The Foundation of Everything

Quantity	What it measures
PV: Planned Value	The budget authorized for work scheduled through today
EV: Earned Value	The budget value of work actually completed
AC: Actual Cost	Total cost incurred to date

Every EVM metric, variance, index, or forecast, derives from these three numbers. If you know PV, EV, and AC, you know everything EVM can tell you.

EVM integrates scope, schedule, and cost into these three core quantities (Fleming and Koppelman 2010). From them, all the other EVM metrics flow, with every performance index, every forecast, and every variance coming back to PV, EV, and AC.

5.2 Key Metrics

Metric	Formula	Interpretation
CV: Cost Variance	EV − AC	> 0: under budget; < 0: over budget
SV: Schedule Variance	EV − PV	> 0: ahead of schedule; < 0: behind schedule
CPI: Cost Performance Index	EV / AC	> 1: efficient; = 1: on target; < 1: over-spending
SPI: Schedule Performance Index	EV / PV	> 1: ahead; = 1: on target; < 1: behind
EAC: Estimate at Completion	See below	Forecast of total project cost
ETC: Estimate to Complete	EAC − AC	Remaining cost to finish the project
VAC: Variance at Completion	BAC − EAC	Expected surplus (positive) or overrun (negative)
TCPI: To-Complete Performance Index	(BAC−EV) / (BAC−AC)	Efficiency required on remaining work

5.3 Example Setup

library(PRA)

We will track a project with a total budget of $500,000 over a 5-period schedule.

bac      <- 500000
schedule <- c(0.10, 0.25, 0.50, 0.75, 1.00)
time_period <- 3

5.3.1 Planned Value (PV)

PV is the authorized budget for work planned through the current period.

pv_val <- pv(bac, schedule, time_period)
cat("Planned Value (PV): $", format(pv_val, big.mark = ","), "\n")

Planned Value (PV): $ 250,000

The project was planned to be 50% complete by period 3, so PV = $250,000.

5.3.2 Earned Value (EV)

EV reflects the budget value of work actually completed.

actual_per_complete <- 0.40
ev_val <- ev(bac, actual_per_complete)
cat("Earned Value (EV): $", format(ev_val, big.mark = ","), "\n")

Earned Value (EV): $ 2e+05

Only 40% of work is done despite 50% being planned, so we are behind schedule.

5.3.3 Actual Cost (AC)

AC is the cumulative cost incurred through period 3.

period_costs <- c(45000, 110000, 135000)
ac_val <- ac(period_costs, time_period, cumulative = FALSE)
cat("Actual Cost (AC): $", format(ac_val, big.mark = ","), "\n")

Actual Cost (AC): $ 290,000

5.3.4 Performance Indicators

sv_val  <- sv(ev_val, pv_val)
cv_val  <- cv(ev_val, ac_val)
spi_val <- spi(ev_val, pv_val)
cpi_val <- cpi(ev_val, ac_val)

cat("Schedule Variance (SV):           $", format(sv_val, big.mark = ","), "\n")

Schedule Variance (SV):           $ -50,000

cat("Cost Variance (CV):               $", format(cv_val, big.mark = ","), "\n")

Cost Variance (CV):               $ -90,000

cat("Schedule Performance Index (SPI):", round(spi_val, 3), "\n")

Schedule Performance Index (SPI): 0.8

cat("Cost Performance Index (CPI):    ", round(cpi_val, 3), "\n")

Cost Performance Index (CPI):     0.69

Interpretation: SPI < 1 means we are behind schedule, earning only 80 cents of planned value per dollar of schedule. CPI < 1 means we are over budget, earning only 69 cents of value per dollar spent. Both are below 1.0: this project is in trouble.

5.4 Forecasting: Estimate at Completion (EAC)

EAC forecasts the total cost at project completion. Three methods are available, each making a different assumption about future performance:

Method	Formula	When to use
Typical	BAC / CPI	Current cost inefficiency is expected to continue
Atypical	AC + (BAC − EV)	Cost overrun was a one-time event; future work at planned rate
Combined	AC + (BAC − EV) / (CPI × SPI)	Both cost and schedule performance will influence future costs

eac_typical  <- eac(bac, method = "typical", cpi = cpi_val)
eac_atypical <- eac(bac, method = "atypical", ac = ac_val, ev = ev_val)
eac_combined <- eac(bac,
  method = "combined", cpi = cpi_val, ac = ac_val,
  ev = ev_val, spi = spi_val
)

cat("EAC (typical):  $", format(round(eac_typical),  big.mark = ","), "\n")

EAC (typical):  $ 725,000

cat("EAC (atypical): $", format(round(eac_atypical), big.mark = ","), "\n")

EAC (atypical): $ 590,000

cat("EAC (combined): $", format(round(eac_combined), big.mark = ","), "\n")

EAC (combined): $ 833,750

The typical method gives the most conservative (highest cost) estimate because it assumes the current CPI persists. The atypical method is the most optimistic.

5.4.1 EAC Comparison Table

eac_table <- data.frame(
  Method     = c("Typical", "Atypical", "Combined"),
  EAC        = c(round(eac_typical), round(eac_atypical), round(eac_combined)),
  Overrun    = c(
    round(eac_typical  - bac),
    round(eac_atypical - bac),
    round(eac_combined - bac)
  ),
  Assumption = c(
    "Current CPI continues",
    "Future work at planned rate",
    "CPI and SPI both factor in"
  )
)
knitr::kable(eac_table,
  format.args = list(big.mark = ","),
  caption = "EAC Comparison by Method"
)

EAC Comparison by Method
Method	EAC	Overrun	Assumption
Typical	725,000	225,000	Current CPI continues
Atypical	590,000	90,000	Future work at planned rate
Combined	833,750	333,750	CPI and SPI both factor in

5.5 Additional Metrics

etc_val  <- etc(bac, ev_val, cpi_val)
vac_val  <- vac(bac, eac_typical)
tcpi_bac <- tcpi(bac, ev_val, ac_val, target = "bac")
tcpi_eac <- tcpi(bac, ev_val, ac_val, target = "eac", eac = eac_typical)

cat("Estimate to Complete (ETC):  $", format(round(etc_val), big.mark = ","), "\n")

Estimate to Complete (ETC):  $ 435,000

cat("Variance at Completion (VAC): $", format(round(vac_val), big.mark = ","), "\n")

Variance at Completion (VAC): $ -225,000

cat("TCPI (to meet BAC):          ", round(tcpi_bac, 3), "\n")

TCPI (to meet BAC):           1.429

cat("TCPI (to meet EAC):          ", round(tcpi_eac, 3), "\n")

TCPI (to meet EAC):           0.69

Interpretation: TCPI > 1 means the team must work more efficiently than they have been to meet the target. A TCPI above 1.2 is a widely-cited practitioner rule of thumb for “unrealistic” (not a formal PMBOK standard), a useful warning signal. If you need to be 30% more efficient for the rest of the project, it probably isn’t going to happen. Using the EAC target gives a more realistic benchmark.

5.6 Performance Trend Chart

The chart below shows cumulative PV, AC, and EV over time, with reference lines for BAC and EAC.

time_periods <- c(1, 2, 3)
actual_pct   <- c(0.08, 0.22, 0.40)
p_costs      <- c(45000, 110000, 135000)

pv_vals <- sapply(time_periods, function(t) pv(bac, schedule, t))
ac_vals <- cumsum(p_costs)
ev_vals <- sapply(actual_pct, function(a) ev(bac, a))

trend_data <- data.frame(
  Period = time_periods,
  PV = pv_vals, AC = ac_vals, EV = ev_vals
)

p <- ggplot2::ggplot(trend_data, ggplot2::aes(x = Period)) +
  ggplot2::geom_line(ggplot2::aes(y = PV, color = "Planned Value (PV)"), linewidth = 1.2) +
  ggplot2::geom_line(ggplot2::aes(y = AC, color = "Actual Cost (AC)"), linewidth = 1.2) +
  ggplot2::geom_line(ggplot2::aes(y = EV, color = "Earned Value (EV)"), linewidth = 1.2) +
  ggplot2::geom_point(ggplot2::aes(y = PV, color = "Planned Value (PV)"), size = 3) +
  ggplot2::geom_point(ggplot2::aes(y = AC, color = "Actual Cost (AC)"), size = 3) +
  ggplot2::geom_point(ggplot2::aes(y = EV, color = "Earned Value (EV)"), size = 3) +
  ggplot2::geom_hline(yintercept = bac, linetype = "dashed", color = "black", linewidth = 0.8) +
  ggplot2::geom_hline(yintercept = eac_typical, linetype = "dotted", color = "darkred", linewidth = 0.8) +
  ggplot2::annotate("text", x = 2.8, y = bac + 12000, label = "BAC = $500K", size = 3.5) +
  ggplot2::annotate("text", x = 2.8, y = eac_typical + 12000, label = "EAC (typical)", size = 3.5) +
  ggplot2::scale_color_manual(values = c(
    "Planned Value (PV)" = "steelblue",
    "Actual Cost (AC)"   = "tomato",
    "Earned Value (EV)"  = "forestgreen"
  )) +
  ggplot2::scale_y_continuous(labels = scales::label_dollar(scale = 1e-3, suffix = "K")) +
  ggplot2::labs(
    title = "Earned Value Management: Performance Trend",
    x     = "Time Period", y = "Value", color = NULL
  ) +
  ggplot2::theme_minimal() +
  ggplot2::theme(legend.position = "bottom")

print(p)

EVM trend chart. When EV falls below PV, you’re behind schedule. When AC rises above EV, you’re over budget. Both conditions here, a project in the red on both dimensions.

Reading the chart: The gap between PV and EV shows the schedule gap, with EV below PV. The gap between AC and EV shows the cost overrun, as we’ve spent more than the value we’ve earned.

5.7 Summary

Key Takeaways

EVM combines scope, schedule, and cost into three numbers (PV, EV, AC) from which all performance metrics flow.
CPI < 1 means over-budget; SPI < 1 means behind schedule. Both below 1 signals a project in serious trouble.
The Typical EAC (BAC / CPI) is the most conservative forecast; use it when current inefficiency is expected to persist.
TCPI > 1.2 is a common practitioner rule of thumb for “unrealistic” (not a formal standard), flag it as a signal to revise the budget rather than chase an unachievable efficiency target.
The trend chart (PV, EV, AC over time) is your single most powerful communication tool for project status.

EVM tells you where the project stands right now. For forward-looking updates that incorporate new information as the project evolves, Bayesian methods in Chapter 6 provide a complementary approach to cost forecasting.

5.8 Exercises

Diagnosis. If SPI < 1 and CPI > 1, what does that tell you about the project? Describe the scenario in plain English and give an example of how this might happen on a real project.
Forecast comparison. Compute EAC using all three methods for a new project with BAC = $200K, PV = $80K, EV = $60K, AC = $70K. Which method produces the highest estimate? The lowest? Which would you recommend reporting to the client?
TCPI reality check. For the same project (BAC = $200K, PV = $80K, EV = $60K, AC = $70K), calculate TCPI to meet BAC. Is it realistic? At what TCPI would you advise the client to revise the budget rather than try to recover?
The optimistic mistake. A project manager always uses the atypical EAC method, regardless of what’s happening. In what circumstances would this be dangerously wrong? Write a 2–3 sentence warning label for the atypical method.
Build your own trend. ★ Create a 5-period EVM dataset where the project starts over budget but recovers over time (CPI < 1 in periods 1–2, CPI ≥ 1 in periods 3–5). Plot the trend chart. Does the “typical” EAC improve as the project recovers?

# Keeping Score: Earned Value Management {#sec-evm} > *"What gets measured gets managed."* > — Peter Drucker Imagine you're three months into a six-month project and you've spent exactly half the budget. That might sound encouraging, but the more useful question is: how much work did you actually get done? If you've completed 30% of the project, the budget situation looks very different than if you've completed 55%. This is the fundamental insight behind **Earned Value Management** (EVM): you can't judge project health by money spent alone. You need to compare three things: what you planned, what you actually did, and what it cost you to do it. ::: {.callout-note icon=false} ## Learning Objectives By the end of this chapter, you will be able to: 1. Compute PV, EV, and AC from project data 2. Calculate and interpret CPI and SPI performance indices 3. Produce an EAC forecast using all three methods and choose the right one 4. Calculate ETC, VAC, and TCPI 5. Read and construct an EVM trend chart ::: ## The Three Core Numbers ::: {.callout-note} ## PV, EV, AC: The Foundation of Everything | Quantity | What it measures | |----------|-----------------| | **PV**: Planned Value | The budget authorized for work *scheduled* through today | | **EV**: Earned Value | The budget value of work *actually completed* | | **AC**: Actual Cost | Total cost *incurred* to date | Every EVM metric, variance, index, or forecast, derives from these three numbers. If you know PV, EV, and AC, you know everything EVM can tell you. ::: EVM integrates scope, schedule, and cost into these three core quantities [@flemming2010]. From them, all the other EVM metrics flow, with every performance index, every forecast, and every variance coming back to PV, EV, and AC. ## Key Metrics | Metric | Formula | Interpretation | |--------|---------|----------------| | **CV**: Cost Variance | EV − AC | > 0: under budget; < 0: over budget | | **SV**: Schedule Variance | EV − PV | > 0: ahead of schedule; < 0: behind schedule | | **CPI**: Cost Performance Index | EV / AC | > 1: efficient; = 1: on target; < 1: over-spending | | **SPI**: Schedule Performance Index | EV / PV | > 1: ahead; = 1: on target; < 1: behind | | **EAC**: Estimate at Completion | See below | Forecast of total project cost | | **ETC**: Estimate to Complete | EAC − AC | Remaining cost to finish the project | | **VAC**: Variance at Completion | BAC − EAC | Expected surplus (positive) or overrun (negative) | | **TCPI**: To-Complete Performance Index | (BAC−EV) / (BAC−AC) | Efficiency required on remaining work | ## Example Setup ```{r setup} #| code-fold: false library(PRA) ``` We will track a project with a total budget of \$500,000 over a 5-period schedule. ```{r} bac <- 500000 schedule <- c(0.10, 0.25, 0.50, 0.75, 1.00) time_period <- 3 ``` ### Planned Value (PV) PV is the authorized budget for work planned through the current period. ```{r} pv_val <- pv(bac, schedule, time_period) cat("Planned Value (PV): $", format(pv_val, big.mark = ","), "\n") ``` The project was planned to be 50% complete by period 3, so PV = \$250,000. ### Earned Value (EV) EV reflects the budget value of work actually completed. ```{r} actual_per_complete <- 0.40 ev_val <- ev(bac, actual_per_complete) cat("Earned Value (EV): $", format(ev_val, big.mark = ","), "\n") ``` Only 40% of work is done despite 50% being planned, so we are behind schedule. ### Actual Cost (AC) AC is the cumulative cost incurred through period 3. ```{r} period_costs <- c(45000, 110000, 135000) ac_val <- ac(period_costs, time_period, cumulative = FALSE) cat("Actual Cost (AC): $", format(ac_val, big.mark = ","), "\n") ``` ### Performance Indicators ```{r} sv_val <- sv(ev_val, pv_val) cv_val <- cv(ev_val, ac_val) spi_val <- spi(ev_val, pv_val) cpi_val <- cpi(ev_val, ac_val) cat("Schedule Variance (SV): $", format(sv_val, big.mark = ","), "\n") cat("Cost Variance (CV): $", format(cv_val, big.mark = ","), "\n") cat("Schedule Performance Index (SPI):", round(spi_val, 3), "\n") cat("Cost Performance Index (CPI): ", round(cpi_val, 3), "\n") ``` **Interpretation:** SPI < 1 means we are behind schedule, earning only 80 cents of planned value per dollar of schedule. CPI < 1 means we are over budget, earning only 69 cents of value per dollar spent. Both are below 1.0: this project is in trouble. ## Forecasting: Estimate at Completion (EAC) EAC forecasts the total cost at project completion. Three methods are available, each making a different assumption about future performance: | Method | Formula | When to use | |--------|---------|-------------| | **Typical** | BAC / CPI | Current cost inefficiency is expected to continue | | **Atypical** | AC + (BAC − EV) | Cost overrun was a one-time event; future work at planned rate | | **Combined** | AC + (BAC − EV) / (CPI × SPI) | Both cost and schedule performance will influence future costs | ```{r} eac_typical <- eac(bac, method = "typical", cpi = cpi_val) eac_atypical <- eac(bac, method = "atypical", ac = ac_val, ev = ev_val) eac_combined <- eac(bac, method = "combined", cpi = cpi_val, ac = ac_val, ev = ev_val, spi = spi_val ) cat("EAC (typical): $", format(round(eac_typical), big.mark = ","), "\n") cat("EAC (atypical): $", format(round(eac_atypical), big.mark = ","), "\n") cat("EAC (combined): $", format(round(eac_combined), big.mark = ","), "\n") ``` The typical method gives the most conservative (highest cost) estimate because it assumes the current CPI persists. The atypical method is the most optimistic. ### EAC Comparison Table ```{r} eac_table <- data.frame( Method = c("Typical", "Atypical", "Combined"), EAC = c(round(eac_typical), round(eac_atypical), round(eac_combined)), Overrun = c( round(eac_typical - bac), round(eac_atypical - bac), round(eac_combined - bac) ), Assumption = c( "Current CPI continues", "Future work at planned rate", "CPI and SPI both factor in" ) ) knitr::kable(eac_table, format.args = list(big.mark = ","), caption = "EAC Comparison by Method" ) ``` ## Additional Metrics ```{r} etc_val <- etc(bac, ev_val, cpi_val) vac_val <- vac(bac, eac_typical) tcpi_bac <- tcpi(bac, ev_val, ac_val, target = "bac") tcpi_eac <- tcpi(bac, ev_val, ac_val, target = "eac", eac = eac_typical) cat("Estimate to Complete (ETC): $", format(round(etc_val), big.mark = ","), "\n") cat("Variance at Completion (VAC): $", format(round(vac_val), big.mark = ","), "\n") cat("TCPI (to meet BAC): ", round(tcpi_bac, 3), "\n") cat("TCPI (to meet EAC): ", round(tcpi_eac, 3), "\n") ``` **Interpretation:** TCPI > 1 means the team must work more efficiently than they have been to meet the target. A TCPI above 1.2 is a widely-cited practitioner rule of thumb for "unrealistic" (not a formal PMBOK standard), a useful warning signal. If you need to be 30% more efficient for the rest of the project, it probably isn't going to happen. Using the EAC target gives a more realistic benchmark. ## Performance Trend Chart The chart below shows cumulative PV, AC, and EV over time, with reference lines for BAC and EAC. ```{r} #| fig-cap: "EVM trend chart. When EV falls below PV, you're behind schedule. When AC rises above EV, you're over budget. Both conditions here, a project in the red on both dimensions." time_periods <- c(1, 2, 3) actual_pct <- c(0.08, 0.22, 0.40) p_costs <- c(45000, 110000, 135000) pv_vals <- sapply(time_periods, function(t) pv(bac, schedule, t)) ac_vals <- cumsum(p_costs) ev_vals <- sapply(actual_pct, function(a) ev(bac, a)) trend_data <- data.frame( Period = time_periods, PV = pv_vals, AC = ac_vals, EV = ev_vals ) p <- ggplot2::ggplot(trend_data, ggplot2::aes(x = Period)) + ggplot2::geom_line(ggplot2::aes(y = PV, color = "Planned Value (PV)"), linewidth = 1.2) + ggplot2::geom_line(ggplot2::aes(y = AC, color = "Actual Cost (AC)"), linewidth = 1.2) + ggplot2::geom_line(ggplot2::aes(y = EV, color = "Earned Value (EV)"), linewidth = 1.2) + ggplot2::geom_point(ggplot2::aes(y = PV, color = "Planned Value (PV)"), size = 3) + ggplot2::geom_point(ggplot2::aes(y = AC, color = "Actual Cost (AC)"), size = 3) + ggplot2::geom_point(ggplot2::aes(y = EV, color = "Earned Value (EV)"), size = 3) + ggplot2::geom_hline(yintercept = bac, linetype = "dashed", color = "black", linewidth = 0.8) + ggplot2::geom_hline(yintercept = eac_typical, linetype = "dotted", color = "darkred", linewidth = 0.8) + ggplot2::annotate("text", x = 2.8, y = bac + 12000, label = "BAC = $500K", size = 3.5) + ggplot2::annotate("text", x = 2.8, y = eac_typical + 12000, label = "EAC (typical)", size = 3.5) + ggplot2::scale_color_manual(values = c( "Planned Value (PV)" = "steelblue", "Actual Cost (AC)" = "tomato", "Earned Value (EV)" = "forestgreen" )) + ggplot2::scale_y_continuous(labels = scales::label_dollar(scale = 1e-3, suffix = "K")) + ggplot2::labs( title = "Earned Value Management: Performance Trend", x = "Time Period", y = "Value", color = NULL ) + ggplot2::theme_minimal() + ggplot2::theme(legend.position = "bottom") print(p) ``` **Reading the chart:** The gap between PV and EV shows the schedule gap, with EV below PV. The gap between AC and EV shows the cost overrun, as we've spent more than the value we've earned. ## Summary ::: {.callout-tip icon=false} ## Key Takeaways - EVM combines scope, schedule, and cost into three numbers (PV, EV, AC) from which all performance metrics flow. - **CPI < 1** means over-budget; **SPI < 1** means behind schedule. Both below 1 signals a project in serious trouble. - The **Typical EAC** (BAC / CPI) is the most conservative forecast; use it when current inefficiency is expected to persist. - **TCPI > 1.2** is a common practitioner rule of thumb for "unrealistic" (not a formal standard), flag it as a signal to revise the budget rather than chase an unachievable efficiency target. - The trend chart (PV, EV, AC over time) is your single most powerful communication tool for project status. ::: EVM tells you *where the project stands right now*. For forward-looking updates that incorporate new information as the project evolves, Bayesian methods in @sec-bayes provide a complementary approach to cost forecasting. ## Exercises 1. **Diagnosis.** If SPI < 1 and CPI > 1, what does that tell you about the project? Describe the scenario in plain English and give an example of how this might happen on a real project. 2. **Forecast comparison.** Compute EAC using all three methods for a new project with BAC = \$200K, PV = \$80K, EV = \$60K, AC = \$70K. Which method produces the highest estimate? The lowest? Which would you recommend reporting to the client? 3. **TCPI reality check.** For the same project (BAC = \$200K, PV = \$80K, EV = \$60K, AC = \$70K), calculate TCPI to meet BAC. Is it realistic? At what TCPI would you advise the client to revise the budget rather than try to recover? 4. **The optimistic mistake.** A project manager always uses the atypical EAC method, regardless of what's happening. In what circumstances would this be dangerously wrong? Write a 2–3 sentence warning label for the atypical method. 5. **Build your own trend.** ★ Create a 5-period EVM dataset where the project starts over budget but recovers over time (CPI < 1 in periods 1–2, CPI ≥ 1 in periods 3–5). Plot the trend chart. Does the "typical" EAC improve as the project recovers?