Understanding Planned Value (PV), Earned Value (EV), and Actual Cost (AC)
Every calculation in the Earned Value Management CAPM framework relies on three fundamental data points: Planned Value (PV), Earned Value (EV), and Actual Cost (AC). These values are snapshots in time that allow a project manager to compare what was supposed to happen against what has actually occurred. PV represents the authorized budget assigned to scheduled work; it is the value of the work that should have been completed by a specific date according to the Performance Measurement Baseline (PMB).
EV is the measure of work performed expressed in terms of the budget authorized for that work. It is essentially the "physical work completed" translated into currency. If a task budgeted at $1,000 is 50% complete, the EV is $500, regardless of how much was actually spent. AC is the total cost incurred and recorded in accomplishing the work performed. On the CAPM exam, these three variables are usually provided in a scenario, and your task is to identify which is which. A common mistake is confusing PV with the total project budget (Budget at Completion or BAC). Remember that PV is time-phased, whereas BAC is the total value of the project at its conclusion.
Once the three foundational values are established, they are used to calculate variances and indices. Variances, such as Cost Variance (CV) and Schedule Variance (SV), provide a raw number (usually in currency) that indicates the magnitude of deviation from the plan. Indices, specifically the Cost Performance Index (CPI) and Schedule Performance Index (SPI), provide a ratio of efficiency. These indices are critical for the CAPM because they allow for comparison across projects of different sizes.
In the PMI scoring system, understanding the relationship between these numbers is as important as the calculation itself. A variance is always calculated as EV minus another value (EV - AC for cost, EV - PV for schedule). If the result is negative, the project is in trouble (over budget or behind schedule). Conversely, indices are calculated as EV divided by another value (EV/AC for cost, EV/PV for schedule). An index of 1.0 means the project is exactly on plan. This standardized approach allows project managers to communicate status objectively to stakeholders without subjective bias.
Interpretation is where many candidates lose points. The CAPM exam will often provide a CPI of 0.8 and ask what this means for the project. You must recognize that a CPI of 0.8 indicates that for every dollar spent, only 80 cents of value was earned. This is a clear indicator of cost inefficiency. Similarly, an SPI of 1.2 suggests the project is progressing at 120% of the planned rate, meaning it is ahead of schedule.
When evaluating project health, the CPI is often considered the most critical metric because it reflects the actual burn rate of the budget. If a project has a high SPI but a very low CPI, it might be moving fast only because the team is over-spending on overtime or premium resources. This relationship is often tested through CAPM math questions that require you to choose the best corrective action based on these numbers. For example, if CV is negative but SV is positive, a project manager might look for ways to reduce costs even if it means slowing down the schedule slightly to get back to the budget baseline.
Core Earned Value Management (EVM) Calculations
The schedule variance formula CAPM candidates must use is SV = EV - PV. This formula measures the difference between the work actually performed and the work planned. If the result is $0, the project is exactly on schedule. A positive value indicates the project is ahead of schedule, while a negative value indicates a delay. However, SV is limited because it is expressed in currency, which doesn't always translate intuitively to time.
To solve this, we use the Schedule Performance Index (SPI), calculated as SPI = EV / PV. This ratio is a measure of schedule efficiency. For example, if a project has an EV of $4,000 and a PV of $5,000, the SPI is 0.8. On the exam, this might be presented in a word problem where you must determine if the project will finish on time. An SPI of 0.8 suggests the project is only progressing at 80% of the planned rate. If this trend continues, the project will inevitably finish late unless the Critical Path is shortened through crashing or fast-tracking.
The cost performance index CPI is perhaps the most vital calculation in the EVM suite. The formula is CPI = EV / AC. It measures the value of work completed against the actual costs spent to achieve that work. If your CPI is 1.1, you are performing under budget; if it is 0.9, you are over budget. The corresponding variance formula is CV = EV - AC.
Exam questions frequently ask for the "cumulative CPI," which is the total EV for all tasks divided by the total AC for all tasks. This provides a more stable view of performance than looking at a single period. It is important to note that CV and CPI specifically help identify "cost leakage." If a project has a CV of -$5,000, it means the project has spent $5,000 more than the value of the work produced. This information is used to trigger a Change Request if the variance exceeds the established threshold in the Cost Management Plan.
The To-Complete Performance Index (TCPI) is a unique formula that calculates the efficiency required to finish the project within a specific goal, such as the original BAC or a new EAC. Unlike CPI, which looks at past performance, TCPI looks at the future. The formula for TCPI based on the BAC is (BAC - EV) / (BAC - AC). This represents the "remaining work" divided by the "remaining funds."
If the TCPI is greater than 1.0, the project team must work more efficiently than they have in the past to meet the budget goal. For instance, a TCPI of 1.2 means the team must generate $1.20 of value for every $1.00 spent from this point forward. If the TCPI is less than 1.0, the team can afford to be less efficient and still meet the target. This metric is a reality check for project managers; if the required TCPI is significantly higher than the current CPI, the project's budget goal may be unattainable.
The estimate at completion EAC formulas are used to predict the total cost of the project at its conclusion based on current performance. There are four distinct scenarios the CAPM tests:
- Standard/Typical Variance:
EAC = BAC / CPI. Use this if you expect the current cost performance to continue until the end of the project.
- Atypical Variance:
EAC = AC + (BAC - EV). Use this if the current variances were caused by a "one-time" event and you expect future work to be performed at the budgeted rate.
- Flawed Initial Estimates:
EAC = AC + Bottom-up ETC. Use this if the original plan is no longer valid and a new estimate for all remaining work is required.
- Cost and Schedule Impact:
EAC = AC + [(BAC - EV) / (CPI * SPI)]. Use this if the project is over budget and has a firm completion date that must be met, requiring both cost and schedule efficiency to be factored into the forecast.
Estimate to Complete (ETC) and Variance at Completion (VAC)
While EAC predicts the total final cost, the Estimate to Complete (ETC) predicts how much more money is needed from this point forward. The simplest formula for ETC is EAC - AC. This is used when you have already calculated the forecasted total and simply want to know the remaining balance. If you are asked to calculate ETC from scratch based on current performance, you would use (BAC - EV) / CPI.
Variance at Completion (VAC) is the forecasted version of Cost Variance. It is calculated as VAC = BAC - EAC. A positive VAC indicates the project is expected to finish under budget, while a negative VAC indicates an expected budget overrun. On the CAPM, VAC is a vital communication tool for the Sponsor. If the VAC is negative, the project manager may need to request additional funding or reduce the project scope to bring the final costs back in line with the authorized budget.
The difficulty in CAPM math questions regarding EAC lies in selecting the right formula. The exam will provide a narrative description of the project's status. If the prompt says, "The project experienced a strike that is now resolved," you are dealing with an atypical variance, and you should use the formula that assumes future work returns to the planned rate. If the prompt says, "The current cost trends are expected to continue," you must use the CPI-based formula.
Identifying keywords is essential. Terms like "one-time event," "atypical," or "anomaly" point toward the additive formula. Terms like "representative of the future" or "current rate" point toward the division formula. If the question mentions that both cost and schedule are lagging and the deadline is fixed, the complex formula incorporating both CPI and SPI is the correct choice. Mastering these situational triggers is the key to scoring high on the forecasting portion of the exam.
PERT (Three-Point Estimation) and Standard Deviation
Outside of EVM, the PERT (Program Evaluation and Review Technique) formula is a staple of the CAPM exam. It is used to calculate a weighted average for activity duration or cost, accounting for uncertainty. The formula is (Optimistic + 4*Most Likely + Pessimistic) / 6. This "Beta distribution" gives more weight to the most likely estimate than a simple triangular average.
You may also be asked to calculate the Standard Deviation of a single task to measure risk. The formula is (Pessimistic - Optimistic) / 6. A larger standard deviation indicates higher uncertainty. In a Normal Distribution, there is a 68% probability that the actual result will fall within one standard deviation of the mean, and a 95% probability it will fall within two. Understanding these percentages is crucial for answering questions about the "confidence level" of a project estimate.
Communications Channel Calculation
Communication complexity grows exponentially as the number of stakeholders increases. The CAPM tests this using the Communications Channel formula: n(n - 1) / 2, where n is the number of stakeholders. For example, if a project has 10 stakeholders, there are 45 potential channels of communication.
A common exam trap involves a scenario where the number of stakeholders increases. If a project grows from 5 stakeholders to 8, the question will ask how many new channels were added. You must calculate the channels for 5 (which is 10) and the channels for 8 (which is 28), then find the difference (18). This formula highlights the importance of a formal Communications Management Plan to prevent information overload as the project team expands.
Return on Investment (ROI) and Payback Period
While usually part of the Business Case or project selection process, basic financial metrics can appear on the CAPM. Return on Investment (ROI) is the net profit divided by the cost of the investment, expressed as a percentage. A higher ROI is generally preferred. The Payback Period is the time it takes for a project to recover its initial investment.
If Project A costs $100,000 and returns $25,000 per year, its payback period is 4 years. If Project B costs the same but returns $50,000 per year, its payback period is 2 years. In a selection scenario, Project B would typically be chosen. Candidates should also be familiar with the concept of Present Value (PV), though complex calculations are rare. The core principle is that money today is worth more than money in the future due to inflation and earning potential, a concept known as the Time Value of Money.
Cost of Quality (COQ): Prevention, Appraisal, Failure Costs
Quality management involves balancing the costs of achieving quality against the costs of non-conformance. The Cost of Quality (COQ) is divided into three categories. Prevention Costs are spent to keep defects out of the process (e.g., training, equipment maintenance). Appraisal Costs are spent to find defects through testing and inspection.
Failure Costs are divided into internal (found before the customer sees the product, like rework) and external (found by the customer, like warranty claims). The CAPM exam expects you to categorize these costs correctly. A key rule of thumb in quality management is that prevention is almost always cheaper than failure. Therefore, spending more on "appraisal" and "prevention" during the project lifecycle reduces the "Total Cost of Ownership" and protects the organization's reputation.
Point of Total Assumption (PTA) in Fixed-Price Incentive Fee Contracts
In procurement, specifically for Fixed-Price Incentive Fee (FPIF) contracts, the Point of Total Assumption (PTA) is the cost level at which the seller bears all the loss for every dollar of overspend. It is the point where the contract effectively turns into a Firm Fixed Price contract for the buyer. The formula is [(Ceiling Price - Target Price) / Buyer's Share Ratio] + Target Cost.
This calculation is used to determine the financial risk threshold for the seller. If the actual cost exceeds the PTA, the seller's profit begins to erode rapidly because they are responsible for 100% of the costs above this point up to the ceiling price. On the CAPM, you might not be asked to perform the full calculation often, but you must understand that the PTA is a measure of Seller Risk. The higher the PTA, the less risk the seller carries relative to the buyer.
The most effective way to handle the CAPM exam formulas list is to use the "brain dump" method. As soon as the exam begins and the timer starts, use the provided digital notepad or physical scratch paper to write down every formula you have memorized. This offloads the information from your working memory, allowing you to focus on the logic of the questions without worrying about forgetting a specific ratio.
Your cheat sheet should include all EVM formulas (SV, CV, SPI, CPI, EAC, ETC, VAC, TCPI), the PERT formula, and the communication channels formula. Group them by their function—variance, index, or forecasting—to make them easier to find during the test. Practice writing this list from memory every day for two weeks leading up to the exam until you can reproduce it in under five minutes.
Practice Problems and Interpretation Scenarios
Calculation is only half the battle; interpretation is the other. When practicing, don't just stop once you find the numerical answer. Ask yourself: "What does this mean for the project?" If your answer is a CPI of 1.05 and an SPI of 0.92, you should immediately think: "Under budget but behind schedule." This mental habit will prepare you for the situational questions that PMI favors.
Use practice exams to identify which formulas you struggle with. If you consistently miss forecasting questions, focus on the four EAC scenarios and the logic behind choosing one over the other. Remember that the PMBOK Guide—or the relevant exam reference—emphasizes that these formulas are tools for decision-making. In a real-world scenario, a project manager uses these numbers to justify a request for more resources or to explain a delay to the Project Management Office (PMO).
Common Exam Traps and How to Avoid Them
A common trap on the CAPM is the inclusion of "irrelevant data." A question might provide the PV, EV, AC, and the name of the Project Manager, then ask for the Cost Variance. If you aren't careful, you might try to incorporate the PV into the calculation, even though CV only requires EV and AC. Always identify exactly what the question is asking for before you start calculating.
Another trap involves units. Ensure you aren't mixing up percentages and decimals. An SPI of 0.9 is the same as saying the project is at 90% efficiency. Finally, be wary of "negative" vs "positive" logic. In EVM, negative is bad. In some other areas of life, negative might be good, but for the CAPM, a negative variance or an index less than 1.0 is always a signal that the project is performing worse than the baseline. Stay disciplined with these rules, and the quantitative portion of the exam will become a source of easy points rather than a source of stress.