Chapter 30 — Quiz

B — $169,280. 9,200 LF × $18.40 = $169,280. Earned value is measured at budget rates, never at actual cost. The $196,000 is actual cost, and if it ever leaks into your EV your CPI becomes exactly 1.000 forever and the report stops measuring anything. The planned quantity is needed for PV, not for EV.

B. CV = EV − AC = 24,970,000 − 25,642,000 = −$672,000, and SV = EV − PV = 24,970,000 − 25,760,000 = −$790,000`. The "$118,000 under budget" isPV − AC` — arithmetically correct and completely meaningless, because it compares what you spent to what you planned to spend without asking how much building you got. Being behind looks exactly like being under budget until the month you catch up.

C — dollars of work volume. SV = EV − PV, and both of those are dollar figures. It measures how much work you are short, not how much time you are late. This single fact is the difference between using earned value well and standing in an owner's meeting saying something you will regret.

B. CPI = EV ÷ AC = 455,000 ÷ 511,000 = 0.890. SPI = EV ÷ PV = 455,000 ÷ 520,000 = 0.875. Both indices use EV as the numerator — everything in earned value is anchored on what you actually built. Option A is the classic error: swapping the two denominators.

B. Formula #2 assumes the remaining work performs exactly to budget, so its VAC always equals the cost variance already incurred and nothing else. On Northgate at month 11 its VAC is exactly −$672,000, which is exactly the CV. That is its entire appeal to a project manager who does not want to deliver bad news, and it is why "we'll hold the rest to budget" is the most common sentence in a bad monthly report. It is legitimate only when you can name a closed, non-recurring event and show the remaining work is unaffected.

B. TCPI = (BAC − EV) ÷ (BAC − AC) — remaining work divided by remaining money. 15,030,000 ÷ 14,358,000 = 1.047. TCPI does not predict anything; it converts a forecast into a testable claim about future performance, which you then check against demonstrated performance. If the required index is far above anything the job has posted, the forecast is a wish with a decimal point.

A. LOE sets EV equal to PV by definition, so its SPI is permanently 1.000 and it drags the aggregate SPI toward 1.000 from whichever side the aggregate is on. Its effect on CPI depends on whether the LOE work is itself running over or under. On Northgate, folding in the $2,900,000 of general conditions moved SPI from 0.969 to 0.971 and CPI from 0.974 to 0.972 — and neither movement reflects a single thing that happened in the field. Keep LOE in its own bucket and out of the index you forecast from.

C. On a subcontract package, EV is usually the percentage on the subcontractor's pay application and AC is what you approved for payment. Two numbers from the same document produce a CPI of approximately 1.000 by construction. Kestrel does not have Cardinal's labor hours and never will. The 0.997 is a rounding artifact from a small backcharge. What is real on a subcontract package is the SPI, because PV comes from your schedule and EV comes from their billing.

B. Half the value is released at start. That is convenient and it is a systematic overstatement. Prefer 25/75 if you need a fixed formula, prefer 0/100 for activities shorter than a reporting period, and prefer units complete — the one method with almost no built-in bias — wherever the work can be counted. And whichever you pick, pick it before the work starts and write it down.

B. At completion all the work is done, so EV = BAC, and the baseline eventually runs out of planned work, so PV = BAC. Therefore SV = BAC − BAC = 0 and SPI = 1.000. Any two curves that start at zero and end at BAC must converge. The metric does not know what a calendar is. Cost variance behaves completely differently — it converges to the final overrun, not to zero.

B. Work earned versus money spent — 62.4 against 64.1 — is EV against AC, and it is $672,000 wide. The first gap (59.1 against 62.4) says the job is producing slightly faster than the calendar, which is good news of a limited kind. Reading those three percentages in that order is the fastest possible read of any job.

True. EV and PV both end at BAC, so their difference must be zero at completion. SV is a useful early- and mid-project indicator and a useless late-project one; on a 19-month job, stop trusting it somewhere around month 14 and use the CPM.

False. Verify before celebrating. On construction, a CPI above 1.05 is more often an EV measurement error, a padded baseline, or unaccrued actual cost than a triumph. The most common cause is invoices that have not landed yet — an AC that understates cost inflates CPI directly.

False, and that is the whole point of the extension. If a 565-day job finishes at day 576, earned schedule stops accumulating at 565 while actual time keeps running, so SPI(t) correctly reports lateness at the end. Northgate at month 11: ES = 10.79 months, AT = 11.00, SPI(t) = 0.981 — a more meaningful number than the SPI($) of 0.969. Be honest about adoption, though: earned schedule is well established in the project-controls literature and is not widely used in building construction.

True, and it is a free spreadsheet check. Formula #1 assumes current performance continues, so the performance the remainder must achieve to land there is exactly current performance. Similarly, TCPI against formula #2 is always exactly 1.000. If either check fails, your arithmetic is wrong, not your project.

False. Pending changes stay out of BAC until executed; only executed changes move the performance measurement baseline, and every baseline change gets a log entry with a date, an amount, and an authorizing document. A baseline you can silently move is a baseline you can always hit — and if the baseline is not maintained properly the indices become meaningless within about four months.

You do not have the subcontractor's actual hours. Earned value in man-hours needs earned hours (installed quantity × your budgeted unit rate) and actual hours charged, and a subcontractor's hours are their internal cost data — you are buying a result, not hours. What you can do on subcontracted work is count installed quantities against your schedule, which gives you a genuine units-complete EV and a genuine SPI even though the CPI stays approximately 1.000. Count the terminal units. Count the panels. Count the linear feet.

Because two methods computed different ways converged. Two-tenths of one percent of agreement between a bottom-up-style package sum and a top-down index extrapolation is evidence. One method by itself is an opinion. Note also what produced the agreement: applying the discipline of not extrapolating packages below 20 percent complete. The naive sum was $41,623,447, and $623,768 of that was pure extrapolation noise from two packages at 15 percent and 1.9 percent complete.

Unaccrued cost means AC is understated while EV is not, so CPI = EV ÷ AC comes out too high. The report says you are more efficient than you are. It is the single most common way an earned-value report lies by accident. It flatters the project manager, and if you do not accrue uninvoiced work you are not measuring performance — you are measuring your accounts-payable department's turnaround time.

Earned value is a cost-performance instrument: it gives an early, honest read on efficiency and a defensible, testable forecast of final cost. It is a poor schedule instrument — SV and SPI are denominated in dollars of work volume and converge to zero and 1.000 at completion regardless of how late the job is — so the completion date comes from the CPM, and the honest answer to "give me one number" is that there are two, and here is why.

Variances and indices

CV = 1,116,000 − 1,203,000 = −$87,000 SV = 1,116,000 − 1,240,000 = −$124,000 CPI = 1,116,000 ÷ 1,203,000 = 0.928 SPI = 1,116,000 ÷ 1,240,000 = 0.900 Percent complete = 1,116,000 ÷ 1,860,000 = 60.0% — well above any do-not-forecast-yet threshold

Remaining budgeted work = 1,860,000 − 1,116,000 = $744,000

VAC = 1,860,000 − 2,005,000 = −$145,000 — a 7.8 percent overrun TCPI to BAC = 744,000 ÷ (1,860,000 − 1,203,000) = 744,000 ÷ 657,000 = **1.132**

Recoverable? No. The remaining $744,000 would have to run at 1.132 — about 22 percent better than the 0.928 this crew has demonstrated over ten months — merely to break even. There is no version of "try harder" that produces a 22 percent improvement.

The most useful thing you can do is contain it, and containment is worth real money: lifting the remainder from 0.928 to 0.970 pulls the EAC from $2,005,000 to $1,203,000 + ($744,000 ÷ 0.970) = $1,970,010, saving about $35,000 on work you had already lost. Notice also that the foreman's own bottom-up ($2,031,000) lands between formulas #2 and #1 — bottom-up re-estimates prepared by the party responsible for the overrun tend to land optimistic. Ask what production rate the $828,000 assumes and compare it to the rate actually achieved.

(a) The project SPI of 1.009 says the job is marginally ahead of plan on work volume. It is averaging a fire and an icebox: −$555,000 on the only work that can move the completion date against +$630,000 on work that cannot, plus $900,000 of level of effort permanently pinned at 1.000 and dragging the aggregate toward the middle. The net of +$75,000 describes nothing that exists.

(b) Planned critical-path burn = $460,000 ÷ 30 CD = $15,333 per calendar day. SV ÷ rate = −555,000 ÷ 15,333 = **−36.2 calendar days**.

(c) You defend the CPM's 35 days, always, because it is built from logic — a forward pass, a backward pass, and total float — and it is the only one of the two that survives cross-examination. The agreement between 36.2 and 35 does not prove earned value can measure schedule. It proves something narrower and more useful: at the right level of aggregation, on a single serial chain with a roughly linear planned burn, earned value is a legitimate corroborating indicator. Note also that you only knew which rows to isolate because you had already read the CPM.

(d) Report the controlling path as its own line in the earned-value table, every month, above the project total — and never publish a project SPI without the CPM's controlling-path total float printed next to it.