Chapter 30 — Exercises

Work these with a pencil, a calculator, and a table. Earned value is four subtractions and four divisions; the arithmetic will never be the hard part. The hard part is knowing which question each number answers and which question it cannot touch. Selected answers are in Appendix J; the rounding conventions used throughout are in Appendix A.

Difficulty legend: ⭐ basic · ⭐⭐ applied · ⭐⭐⭐ advanced judgment · ⭐⭐⭐⭐ extension / research

Conventions. All dollar figures are rounded to whole dollars. Indices are carried to six decimal places in intermediate steps and reported to three. Every measure is stated as of a data date — if an exercise gives you a table without one, the first thing you write down is that you cannot use it. CD = calendar days, WD = work days, MH = man-hours.

Part A — Conceptual Understanding ⭐

A1. Define PV, EV, and AC in one sentence each, without using the words "budgeted cost of work" in any of them. Then state which one of the three a conventional cost report is missing, and what that absence makes impossible.

A2. Your budget prices drywall at $2.85 per square foot. You have hung 100,000 SF and it cost you $340,000. State the earned value. Then state what your earned value would have been if the same 100,000 SF had cost $250,000, and explain in one sentence why the answer does not change.

A3. Schedule variance goes to exactly zero at completion on every project, including one that finishes fourteen months late. Explain the mechanism in two sentences, using only the endpoints of the PV and EV curves.

A4. State the four standard EAC formulas from §30.5 and, for each, the assumption it makes about the remaining work — in plain English, not in symbols. Then say which one can never forecast a problem that has not already happened, and why that makes it attractive to the wrong person.

A5. Write the TCPI formula for a target of BAC and for a target of a stated EAC. Then explain what it means, physically, when TCPI to BAC comes out at 1.170 on a job that has run at 0.890 for eight months.

A6. §30.8 lists eight ways to claim earned value. Name the one with almost no built-in bias, name the one with the largest bias, and name the one that guarantees an SPI of exactly 1.000 forever.

A7. Why is a CPI of 1.000 on a subcontracted package usually a measurement failure rather than good news? Name the two inputs that came from the same document.

A8. Define accrual in the context of actual cost, and state what happens to CPI when you stop accruing. Which direction does the error run, and who does it flatter?

Part B — Applied Analysis ⭐⭐

B1. A superintendent tells you the enclosure package is "about 70 percent done." Your cost report shows 74 percent of the budget spent. Write the three questions you ask before you write either number into an earned-value report, and say what document you would ask to see for each one.

B2. Two packages on the same job have identical CV, SV, CPI, and SPI. One of them is on the critical path with zero float; the other has 45 days of total float. Explain what earned value can and cannot tell you about the difference, and name the single report that resolves it.

B3. A project's CPI has read 0.955, 0.954, 0.956, 0.955, 0.954 for five consecutive months. A second project's CPI has read 1.030, 1.015, 1.001, 0.992, 0.986. Both are at roughly 55 percent complete. Which project would you rather be running, and what would you do first on the other one?

B4. Northgate's specialties package at month 11 shows EV of $23,000 against AC of $29,000 — a CPI of 0.793 and a CPI-extrapolated EAC of $1,563,478 on a $1,240,000 budget. Explain why that $323,478 of forecast overrun should not be reported, what you should report instead, and what would have to change before you started believing the index.

B5. Kestrel's rule on Northgate is a month-end data date and a report on Nadia Haddad's desk on the fifth working day. A colleague proposes moving to the twelfth working day so that more subcontractor invoices have landed and fewer accruals are needed. Evaluate the trade in dollars, using Northgate's $10,650 per calendar day of exposure, and give your answer.

B6. Curtain wall at Northgate is 54 percent complete at a CPI of 0.857, and §30.6 gives the cause: the deck-edge geometry moved during the steel acceleration, so unitized panels are meeting embeds that are not where the model said they were. Argue why EAC formula #1 is the honest choice here and formula #2 is not — in terms of the physical condition, not the arithmetic.

Part C — Calculations and Deliverables ⭐⭐–⭐⭐⭐

C1 — Build PV, EV, and AC from raw field data ⭐⭐

You are at the month-6 data date on the Willow Street Community Center — day 182 of a 425-calendar-day contract. Below are six of your cost codes as they actually arrive: a budget, a budgeted quantity, the quantity the baseline said would be installed by today, the quantity your foremen actually reported installed, and the cost charged to the code. Nothing here is called PV, EV, or AC. That conversion is the exercise.

(a) Compute the budget unit rate for each code. (b) Compute PV, EV, and AC for each code, and roll all three up to a six-code total. (c) Compute CV, SV, CPI, and SPI for each code and for the rollup. (d) Rank the six codes by cost variance and by schedule variance. Do the two rankings agree? Name the code that appears healthy on one list and sick on the other, and say which list you would act on first. (e) Code 02-220 and code 05-120 both show a positive cost variance. One of them is a buyout win and one of them is a production win. Which is which, and what evidence would you need to be sure?

C2 — All four EACs, VAC, and TCPI on one dataset ⭐⭐

Same job, same data date. Here is Willow Street at the project level. The cost of the work — not the $6,800,000 contract sum — is your BAC.

(a) Compute CV, SV, CPI, SPI, and percent complete. (b) Compute all four EACs. Show the assumption each one makes in a phrase. (c) Compute VAC using formula #1 as the baseline forecast. (d) Compute TCPI to BAC. Is that a number this job has demonstrated? (e) State the spread between the highest and lowest EAC. Your internal contingency on this lump-sum job is $148,000. Which of the four forecasts fit inside it and which do not? (f) Write the single sentence you would put in the narrative justifying whichever forecast you choose to report.

C3 — The TCPI credibility test on four competing forecasts ⭐⭐⭐

Return to code 04-200, the Willow Street CMU package: BAC $397,600, EV $277,200, AC $302,800, CPI 0.915, SPI 0.868. Four people give you four numbers in the same week.

(a) Compute the TCPI to each of the four targets. (b) Compute EAC formulas #1 and #3 for this package and their implied TCPIs. Confirm that the TCPI for formula #1 comes out equal to the current CPI — that is your spreadsheet check. (c) Rank all six forecasts from most to least credible, and state the demonstrated performance each one requires as a percentage improvement or decline against the 0.915 achieved to date. (d) Your project executive's number requires a TCPI you should be able to state in one line. Write the two-sentence reply you would send.

C4 — The question earned value cannot answer ⭐⭐⭐

The City of Rivermont's project representative reads your month-6 Willow Street report, sees SPI 0.940, and writes you this:

"So you are running about six percent behind. Six percent of 425 calendar days is roughly 25 days. Should we be telling the Parks Board that the building opens 25 days late?"

(a) Explain, in language a non-construction reader will follow, why that arithmetic does not work. Use the fact that SV and SPI are denominated in dollars of work volume. (b) State the complete list of additional information you need in order to answer the question the City actually asked. Be specific: name the document, name the fields on it, and name who produces it. (c) Suppose the CPM update at the same data date shows the controlling path at minus 13 calendar days. Write the three-sentence answer you send. It must give the City a date, say where the date came from, and say plainly what the SPI does and does not mean. (d) Willow Street's exposure is $2,800 per calendar day ($1,600 extended general conditions + $1,200 liquidated damages). Compute the dollar exposure of the 13-day slip. Then state where that number appears in your earned-value report — and if the answer is "nowhere," say why, in terms of what BAC contains. (e) Give one condition under which SPI would be a reasonable proxy for schedule position, and one under which it would be actively misleading. Northgate and the job in §30.9 are your two examples; say which is which and why.

C5 — Period indices versus cumulative indices ⭐⭐⭐

Take the Northgate S-curve table in §30.7. The CPI and SPI columns in that table are cumulative — every one of them measures the whole job from NTP to the data date. That is the right number for forecasting and the wrong number for asking "how did we do last month?"

Compute the period (incremental) CPI and SPI for months 8, 9, 10, and 11 by differencing the cumulative curves: period PV = PV(n) − PV(n−1), and the same for EV and AC.

(a) Build the table. (b) Months 9 and 10 have a distinctive signature: one index above 1.000 and the other below. Name the position from the four-quadrant table in §30.7 and name the event that produced it. (c) Month 11's period CPI is better than the cumulative CPI. Explain what that means and why it does not entitle anyone to forecast a recovery. (d) In eleven months the job has never posted a period CPI at or above 1.000. State the best month and its value, and explain what that single fact does to the credibility of EAC formula #2.

C6 — What the measurement method is worth ⭐⭐⭐

Cost code 12-350, exam-room casework — a $960,000 line inside Northgate's interior finishes package, at the month-15 data date. Thirty-two identical exam rooms at $30,000 each. The baseline scheduled 15 rooms complete by the data date. The field reports 12 rooms complete, 9 rooms started and physically about 40 percent installed, 11 not started. Cost charged to the code: $492,000.

(a) Compute EV four ways: units complete (using the physical percentage on the started rooms), 0/100, 25/75, and 50/50. (b) Compute PV, then CPI and SPI under each of the four methods. (c) State the spread between the highest and lowest EV, in dollars and as a percentage of the package. (d) Under which method does this package look like it is in trouble, and under which does it look fine? Nothing physical changed between those two readings. Write one sentence explaining what did. (e) §30.8 gives a rule: the measurement method is chosen and written down before the work starts and does not change afterward. Using your own numbers from (b), explain what that rule is actually protecting against.

C7 — Earned schedule, and the number you actually report ⭐⭐⭐

Willow Street's baseline cumulative PV curve, months 1 through 6, against a BAC of $5,712,000:

Actual EV at the month-6 data date is $2,148,000. Contract time is 425 calendar days.

(a) Compute earned schedule (ES) by finding where $2,148,000 falls on the PV curve. Interpolate linearly between the two bracketing months. (b) Compute SV(t) and SPI(t), and convert SV(t) to calendar days. (c) Forecast the contract duration as 425 CD ÷ SPI(t). How many calendar days late is that? (d) Now do the crude conversion from §30.3 instead: divide SV by the planned burn rate in month 6. Compare the two answers. (e) The CPM update at the same data date puts the controlling path at minus 13 calendar days. You now have three numbers. State which one you give the City, which ones you keep in your own file, and write the one sentence that explains the discrepancy without undermining any of the three. (f) Multiply your reported slip by Willow Street's $2,800 per calendar day. That number is the reason this exercise exists.

Part D — Judgment and Ethics ⭐⭐⭐

D1. §30.6 shows that Kestrel's choice of EAC formula on one job in one month was worth $223,203 to Kestrel through the 75/25 contingency share. Ray is the project manager and his performance is measured on that job. Write the policy you would adopt at a mid-size contractor to keep that conflict from deciding the number, and identify what your policy costs — because every real control costs something.

D2. You are the project manager. Your CPI is 0.94 at 18 percent complete. Your project executive tells you to report EAC formula #2 this month "because we'll have the recovery plan in place by next month and there's no point alarming the owner twice." The contract is an open-book GMP under which the owner has audit rights over the cost of the work. Identify what is at stake beyond your own comfort, name the one sentence you would need to be able to write to use formula #2 honestly, and state what you do if you cannot write it.

D3. A subcontractor's pay application claims 68 percent complete on a package your field engineer counts at 61 percent. Approving the higher number makes your CPI look better this month, keeps the subcontractor's cash flow healthy, and avoids a fight. Work through the consequences of approving it: to your own earned-value report, to your retention exposure, to your pay application under Chapter 32, and to what happens if the subcontractor defaults in month sixteen.

D4. §30.9 describes a project reporting an SPI of 1.020 while its critical path is 34 days late, and §30.6 carries a ⚠️ warning that a bad index communicated as a demand rather than as a problem to be solved is how schedule pressure gets installed as a hazard. Take both seriously at once: write the half-page you would give a superintendent whose package reads CPI 0.857, in a form that produces a plan rather than a crew working faster on a scaffold nobody re-inspected. Then say what you would do differently if the same number went to that superintendent from the owner instead of from you.

D5. A colleague proposes modestly front-loading the schedule of values on your next job — "just enough to cover real mobilization." Where is the line between defensible and not? Give a test somebody could actually apply, and then state the argument that has nothing to do with ethics: what front-loading does to your own ability to see your own project.

Part M — Mixed and Interleaved Practice ⭐⭐–⭐⭐⭐

M1. (with Chapter 28) Take your month-6 Willow Street cost report and its bottom-up cost-to-complete. Independently compute ETC = EAC − AC using EAC formula

1. Put the two numbers side by side. If they differ by more than a few percent, write the half-page

that finds out which one is wrong — naming the codes where the two methods disagree most and the evidence that would settle each one.

M2. (with Chapter 14) Cost-load twelve activities of your Willow Street CPM so they sum exactly to a stated BAC. Then deliberately break it: move $180,000 of value from a late activity to an early one. Recompute PV and EV at month 6 under both loadings and report what happens to SPI, to EV ÷ BAC, and to your EAC. State in one sentence what front-loading does to SPI and what it does to the meaning of EV — they are not the same answer.

M3. (with Chapter 20) Jamal Foster's self-perform concrete at Northgate closed at 7,363 earned man-hours against 7,570 actual, for a productivity factor of 0.973, while the labor CPI was 0.950. Take one self-perform code from your own Willow Street estimate and do the same decomposition: productivity variance, rate variance, total. Then answer the question that decomposition exists to answer — who in your organization owns each of the two variances?

M4. (with Chapter 29) Put your month-6 Willow Street schedule update and your month-6 earned-value report on the same page. For each of your five worst packages by SV, state the total float on its controlling activities. Sort the list by float, not by dollars. How different is that list from the one you would have escalated using SV alone?

M5. (with Chapter 31 and Chapter 32) A $214,000 change order is executed on Willow Street in month 7 and its work spans months 8 through 11. Show exactly what has to move: BAC, the PV curve month by month, the schedule of values, and the baseline log entry. Then compute what your month-11 CPI would have read if you had added the cost to AC and forgotten to add the budget to BAC — the single most common baseline-maintenance failure there is.

M6. (with Chapter 34) Your EAC is $5,860,916 against a $5,712,000 budget on a $6,800,000 lump-sum contract, and you are 37.6 percent complete by EV. Explain how that forecast flows into a WIP schedule, what it does to earned revenue and to the over/under billing position, and why a company that ignores its project-level EACs discovers the problem at the year-end audit instead of in month six.

Part E — Research and Extension ⭐⭐⭐⭐

E1. Find a real, publicly posted solicitation from a federal, state, or large institutional owner that requires a cost-loaded schedule or earned-value reporting. Public purchasing portals, state DOT sites, university facilities offices, and school district procurement pages all publish them. Locate the actual requirement and summarize, in one page: whether it requires a validated earned-value management system or simply a cost-loaded CPM with monthly updates; who defines the data date; what measurement methods are permitted or prohibited; whether progress payments are computed from earned value; and what the specification says about baseline maintenance when change orders are executed. Compare it to what §30.8 recommends and note every place they differ. Do not rely on any threshold or clause number quoted in a secondary source, including this book — read the solicitation.

E2. The observation that CPI tends to stabilize early in a project is repeated constantly in the project-controls world and is presented in §30.4 as a widely reported practitioner finding, not a law, because its origins are in large government acquisition programs rather than commercial construction. Go and test it on data you can actually get: ask a contractor, an owner, or a public agency for the monthly cost-performance history of two or three completed projects. Plot cumulative CPI against percent complete for each. Does it stabilize? At what percentage? Does it ever improve materially after it does? Write up what you find, including the sample size, and be explicit about what three projects can and cannot establish.

E3. Interview a project controls manager or a scheduler for thirty minutes. Ask: (1) does their company run earned value in dollars, in man-hours, or both, and on which kinds of work; (2) which EV measurement methods they permit and which they have banned; (3) how they handle subcontracted packages where CPI is 1.000 by construction; (4) whether they have ever seen a project report a healthy SPI while the critical path was late, and what happened; and (5) which EAC formula their company reports as standard, and who decides. Write up the answers against §30.5 and §30.8. Where the practitioner disagrees with the book, say who you think is right and what evidence would settle it.