Appendix J — Answers to Selected Exercises

What this appendix is, and what it deliberately is not

Every chapter in this book ends with an exercise set built in six parts: A conceptual, B applied, C calculations and deliverables, D judgment and ethics, M mixed and interleaved, and E research and extension. A great many individual exercises already carry their answers with them, hidden in a <details> block right under the question, so that you can attempt the problem and check yourself without leaving the page.

This appendix covers the ones that do not. For each chapter I have picked the three to six exercises whose answers a reader working alone most needs and cannot get anywhere else — almost always the Part C calculations, plus the occasional Part B item that has a determinate answer. Where a chapter's Part C is already answered in place, the section here says so and spends its space on something you cannot get from the chapter.

Part D and Part E have no answer key here, and that is on purpose. Part D asks you to make a judgment call about money, safety, or somebody's reputation. Part E sends you out to find a real contract, a real wage determination, or a real practitioner. Printing an "answer" to either one would teach you the single worst habit in this profession: the belief that there is a back-of-the-book result waiting behind every hard decision. There is not. On a job site you will be the back of the book.

How to use this

Attempt first. Then check.

I am going to be blunt about why, because this is the part readers skip. Reading a worked solution produces a warm, immediate feeling of understanding that is almost entirely false. Your brain recognizes each step as sensible and mistakes recognition for the ability to generate. Two weeks later, standing in front of a schedule with a superintendent waiting, recognition gives you nothing. The learning is in the retrieval — in the twenty uncomfortable minutes where you cannot remember whether the backward pass takes the minimum or the maximum, and you have to reason it out from what is physically happening on the job.

So: work the problem badly, on paper, with your own assumptions written down, before you open this appendix. A wrong answer you generated yourself is worth more than a right answer you read.

What a strong Part D answer contains

Since Part D has no key, here is the standard I would hold you to if I were grading it. A strong answer has three things and a weak answer has none of them.

One — it engages the strongest version of the opposing position. Not the caricature. If the question is whether to disclose the non-monetary cost of acceleration to the owner, the strong counter-argument is not "the owner might get mad." It is: a written admission that acceleration degrades safety and quality is a document that will be read aloud in a deposition, and disclosing it may make the owner refuse an acceleration that is genuinely in everyone's interest. Beat that argument, or concede to it. Do not pretend it is not there.

Two — it names a trade-off in specific terms. Not "there are pros and cons." Something like: I am accepting $43,650 of unrecovered cost in exchange for keeping a relationship with an owner who awards $30 million a year, and I am willing to say that out loud to my CFO. A trade-off you can put a number and a name on is a trade-off you have actually made. A list of considerations is a trade-off you are avoiding.

Three — it ends in a decision you are willing to defend. Survey answers — "it depends on the circumstances," "reasonable people could differ," "both approaches have merit" — are how people avoid being wrong. They are also how people avoid being useful. Pick one. Say why. Say what would change your mind.

If your Part D answer contains all three, it is a good answer even if I would have decided the other way.

A note on arithmetic, and on being "wrong"

Construction arithmetic is a professional skill, not a test. An answer that differs from the one printed here is not automatically wrong.

Before you conclude you made an error, check two things. First: do your assumptions differ from mine? Most of the numbers in this book depend on an assumption somebody chose — a swell factor, a production rate, a work-day-to-calendar-day conversion, a burdened labor rate, whether a weather allowance is counted in work days or calendar days. Change the assumption and the number changes legitimately. Second — and this is the one that matters — did you write your assumptions down?

Here is the professional standard, and it is the same standard on a bid, an estimate, a change-order proposal, and a delay claim: the documented assumption is the deliverable. A number with a written basis can be reviewed, argued, corrected, and defended. A number without one is a rumor with a dollar sign in front of it. In more than one place in these solutions I have deliberately shown two defensible answers to the same question and told you which assumption separates them, because that is what the work actually looks like.

Money is rounded to whole dollars unless cents genuinely matter. Units are labeled every time: CY cubic yards, SF square feet, LF linear feet, MH man-hours, CD calendar days, WD work days, SFCA square feet of contact area. Contract time and liquidated damages run in calendar days; crew productivity runs in work days; conversions between the two are stated wherever one is made.

Where an exercise statement itself contains an inconsistency, I have solved it exactly as written and added an Editor's note identifying the problem. Those notes are listed together at the end of this appendix.

Chapter 1 — What Is Construction Management?

Answered in place: C1, C2, C3, C6, C7, C8 and the arithmetic in M1(d). Those are the daily-exposure, dollars-per-square-foot, truck-count, triage, fee and price-a-day items — work them there.

C4 — Five measurable success criteria for Willow Street. The test is that a stranger could evaluate each one on a Tuesday without arguing with you.

The quality line is the one people get wrong. "High quality" is a slogan; 72 items is a criterion, and it is falsifiable — which is exactly why it is uncomfortable to write down.

C9 — Turn a slogan into a measurement.

Every rewrite has three things: a number, a document, and a name for the document. If you cannot name the document, you have written another slogan. That is the whole exercise.

Chapter 2 — The Construction Industry

All of Part C is answered in place — fee versus profit, bonding capacity, backlog and hit rate, the subcontractor's working capital, delay cost, the developer's pro forma, and the sector table. It is the most completely answered exercise set in the book. Use it.

B1 — A 2.4 percent net margin and a "four to five point" fee are not in conflict. They measure different things. The fee is gross — the markup on the cost of the work, before the contractor pays for anything at the home office. Net margin is what survives after general and administrative overhead, unrecovered job cost, and fade. Trace one hundred dollars of revenue:

What you ask to see: an income statement showing revenue, gross profit and G&A on separate lines, and the WIP schedule with its fade column. Gross profit tells you what the jobs earned; G&A tells you what the company cost; the fade column tells you whether the first number is real. A contractor who will show you the first two and not the third has told you something.

Chapter 3 — Project Delivery Methods

Answered in place: C1 (build a GMP), C2 (savings split), C3 (the schedule carry), C4 (reconciling a GMP to a hard bid) and B8.

C6 — Rewrite the design-build criteria line. The original — "Concrete slab on grade shall be suitable for warehouse operations, minimum 8 inches thick, 4,000 psi" — fails because "suitable for warehouse operations" is a performance requirement with no performance in it, and because it never says who supplies the loading data or when. Three sentences:

The slab on grade shall be designed and constructed to support a maximum rack-post load of 14,000 lb on a 6-inch by 6-inch base plate at 8-foot on-center spacing and a maximum wheel load of 9,000 lb, with a minimum thickness of 8 inches, a minimum compressive strength of 4,000 psi at 28 days, and an overall floor flatness and levelness of FF 35 / FL 25 measured in accordance with the referenced standard. The Owner shall furnish the final racking layout, equipment cut sheets, and rack-post and wheel loading data no later than sixty (60) calendar days after the Notice to Proceed. If that information is furnished after that date, or differs materially from the loading stated above, the Contract Sum and Contract Time shall be adjusted in accordance with the Changes article.

Three things changed: a number replaced an adjective, an owner obligation acquired a date, and the consequence of missing that date became a contract term instead of an argument.

C5 — what the sensitivity test is actually for. If moving one weight by two points changes which method wins, the model did not decide anything; you decided, and the weights are where you hid it. That is not a reason to abandon the worksheet. It is a reason to publish the weights, defend them out loud in front of the owner, and stop presenting the total as though it fell out of the arithmetic.

Chapter 4 — Construction Contracts

Answered in place: C1, C2, C3, C5, C6, C7, C8 and B10 — the GMP build-up, the extended-GC rate, one scope priced four ways, the allowance reconciliation, escalation exposure, cost-plus with and without a cap, and the honest time-related general-conditions rate.

C4 — Unbalance a bid, then measure it. First, the balanced total on the estimated quantities:

Now read the actual quantities against the estimates before you price anything. Excavation underruns (14,200 to 11,100 CY, down 21.8%) and the drilled shaft overruns (3,240 to 3,910 LF, up 20.7%). So you load the shaft and starve the excavation. Set the shaft at $520.00/LF — an increase of $349,920 on the estimated quantity — and drop excavation by the same amount over 14,200 CY, which is $24.64/CY, giving $13.86/CY:

The unbalanced bid total lands $32 above the balanced total, comfortably inside $2,000. The balanced bid, paid at the same actual quantities, collects $4,712,550. The unbalanced bid collects $148,776 more.

Check it from the deltas: shaft overrun gain (3,910 − 3,240) × ($520.00 − $412.00) = $72,360; excavation underrun gain `(14,200 − 11,100) × ($38.50 − $13.86) = $76,384`; plus the $32 of bid-total difference — $148,776. ✓

Why an agency rejects it. The excavation price is 64% below the engineer's estimate and the shaft price is 26% above it. That is materially unbalanced on its face, and most public procurement rules let the agency declare such a bid nonresponsive because the low total no longer predicts the lowest ultimate cost. Second, the agency can see what you saw: the bid is a wager on the agency's own quantity error, disclosed to nobody.

The common wrong reading of this exercise is to treat it as a technique. It is a demonstration. The honest version of the same insight is a written question during the question period, which corrects the quantity for every bidder and makes you the contractor who found the problem.

Chapter 5 — Construction Law

Answered in place: C1 (bond premium — but see the Editor's note at the end of this appendix), the numeric part of C2, C5 (the default arithmetic), C7 (bonding around a lien) and B8. C3 and C6 are research exercises against your own jurisdiction and have no key by design.

C2 (ii) and (iii) — the waiver matrix for Willow Street pay application #7. Net payable to the masonry subcontractor is $148,000 × 0.95 = $140,600. The documents that must change hands:

The pattern to memorize: conditional for the money you are about to pay, unconditional for the money you already paid. Every tier that has given notice is in the exchange, and every waiver carries a through date — a waiver without one waives nothing you can identify.

(iii) If the supplier's conditional waiver does not arrive with the application, you do not delete the line and you do not simply pay. You either hold the $52,000 attributable to that supplier out of the subcontractor's payment until the waiver arrives, or you issue a joint check to the subcontractor and the supplier against delivery of the waiver — and you say which, in writing, the same day. Silence is the only option that reliably costs money.

Chapter 6 — Risk Management

All seven Part C items are answered in place: expected monetary value, PERT on duration and on price, contingency sized top-down and bottom-up, drawdown and burn ratio, deductible versus premium, and schedule risk converted to dollars. B8's merge-point arithmetic is there too.

B2 — What the owner actually bought by deleting the differing-site-conditions clause. Not a transfer at no cost. The owner bought a subsurface contingency from the lowest bidder — priced by the party with the least information about the ground — and paid for it in the contract sum whether or not a single unexpected shovel of rock ever appears.

The mechanism has three steps, and the third is the one that hurts. First, every honest bidder prices the unknown: a percentage on the earthwork, a rock allowance, or a higher unit price. Second, the bidder who prices it correctly loses to the bidder who ignores it, so the owner systematically awards to whoever mispriced the risk it just handed over. Third, when the condition appears, that contractor has no contractual remedy and no money, so it goes looking for one — in change-order pricing, in a schedule claim, in a substitution request, in the quality of what gets covered up. A risk you transfer to a party that cannot absorb it does not leave the project. It changes form.

Chapter 7 — Reading the Construction Documents

Answered in place: C1 (pricing a discrepancy), C2 (the same conflict found twice, 13 times apart), C3 (the corridor), C4 (counting openings), C7 (the ten-minute section read) and B11.

C8 — Crosswalk both formats, and find the seams. Take one UniFormat element — B2010 Exterior Walls, brick veneer over cold-formed metal stud backup — and list what it takes to specify it and to buy it:

Six seams, and every one is a scope gap until some subcontract says the word:

1. Through-wall flashing at the shelf angle — mason or sheet metal? Routinely excluded by both.
2. Shelf angles and lintels — steel furnishes; who installs, shims and grouts?
3. Where the air barrier stops and the roof membrane starts, at the parapet. This is the most common enclosure gap in commercial construction, and it is Chapter 9's RFI exercise.
4. Perimeter sealant at windows — the glazier's joint or the caulker's? Both usually exclude the second one.
5. Masonry anchors that attach to the light-gauge stud: the framer sets the stud, the mason needs the anchor, and neither carries it.
6. Fire-safing and smoke seal at the slab edge — framer, fireproofer, or firestop contractor?

That list is your buyout agenda. Closing a seam at buyout costs a sentence; closing it in month ten costs roughly 2.4 times the work plus everything it disrupts. See Chapter 16, C3.

C9(d) — the decision rule for 6:40 a.m. Whatever your contract's precedence article says, the rule you hand a superintendent is the same three sentences: "If two documents disagree, do not pick one. Do not build the cheaper one and do not build the more expensive one — photograph both, mark the sheet and the section, and call me before anybody installs anything. We will have an answer in writing before the work goes in, and if we cannot get one, we will move the crew." Contracts differ — some rank the documents, some say they are complementary and that what is required by one is as binding as if required by all, and some say the more stringent requirement governs — but none of them authorizes a foreman to resolve a conflict by choosing.

Chapter 8 — Sitework and Structure

All eight Part C items are answered in place, including swell and shrinkage, excavator and fleet production, the concrete takeoff, the quarter-inch problem, the steel back-schedule that produces the canonical 23-day slip, the form-cycle resource check, and unit-price quantity variation.

B5 — Quantify the 5-day/6-day cycle mismatch nobody noticed. Fourteen typical floors, one day of difference per floor:

14 floors × 1 WD    =  14 work days
14 WD ÷ 5 × 7       =  19.6  →  20 calendar days
20 CD × $4,900/CD   =  $98,000 of extended general conditions alone

That is before crane and hoist time, formwork rental, the trades that cannot start, and any acceleration you buy later. On a job carrying Northgate's total daily exposure it would be 20 × $10,650 = $213,000.

The meeting: before the first floor is formed, in the trailer, with the formwork subcontractor's superintendent and its project manager, your general superintendent, your self-perform concrete superintendent, and the scheduler. The agenda is not "whose schedule is right." It is C7's arithmetic — carpenter-hours per cycle divided by hours available per carpenter equals the crew the cycle requires. One of the two schedules is supported by a crew that exists and the other is not, and fifteen minutes of division settles which.

Chapter 9 — Enclosure and Interiors

Answered in place: C1 (the honest slip cost), C3 (ponding load), C4 (the gypsum finish decision), C5 (the failed above-ceiling inspection) and the guidance on C7.

C2 — Back-schedule the curtain wall. The chain from award to first unit set is 38 weeks = 266 calendar days.

(a) First unit set January 5, Year 2, minus 266 CD: the latest subcontract award is April 14, Year 1.

(b) Notice to proceed is March 3, Year 1; the actual award was April 9, Year 1. NTP to the deadline is 42 CD; the team used 37 and left 5 calendar days of float — on a 266-day chain. That is a 1.9% margin on the longest procurement chain on the job. It is not comfort. It is the same margin that the anchor-bolt submittal on this project consumed and did not have.

(c) With design assist completing the transition details during design, the resubmittal-and-re-review cycle of 4 weeks disappears: 34 weeks = 238 CD, and the latest award moves to May 12, Year 1 — four weeks later, converting 5 days of float into 33. Note what bought the float. Not a faster fabricator: a decision made during design about which drawings exist before award.

Chapter 10 — Building Systems (MEP)

Answered in place: C1 (the level-3 cavity budget), C2 (the plan width check), C3 (the switchgear back-schedule that lands on NTP day one) and C4 (pricing the schedule consequence).

C7 — Draft the access-panel schedule. Ninety feet of hard gypsum ceiling, and every device above it needs a way in:

Sixteen access panels in ninety feet — one every 5.6 feet. That number is the answer, and it should prompt a design question before it prompts a cost question: is a hard ceiling the right ceiling here?

What it costs to find this at commissioning rather than at coordination sign-off, and who pays. Cutting sixteen openings in a finished, painted ceiling means framing sixteen rough openings, buying and setting sixteen panels (the six at fire/smoke dampers must be rated and labeled), patching, re-taping, and repainting the corridor ceiling end to end, because a patch will not match — with a lift working in a finished corridor, probably at night. And there is no change order, because nobody added anything: the panels were always required by the code and the specification. The drawings simply never showed them. It lands on the contractor as a coordination failure. The access-panel schedule is a coordination deliverable, not a design deliverable — the size, location and rating of each panel cannot be known until the systems above the ceiling are coordinated, which is why it belongs on the coordination sign-off checklist and nowhere else.

Chapter 11 — Preconstruction Services

Answered in place: C1 (escalation to the midpoint), C2 (historical cost adjustment), C3 (the burden multiplier), C5 (life-cycle comparison, and why simple payback fails it), C7 (skin-to-floor ratio) and B11. C6 and C8 are deliverables with no single answer.

C4 — the part of the elemental estimate that has a checkable answer: is the result believable? Two seeds and one test.

Seed one, the geometry. 58,000 SF over two stories is 29,000 SF per floor; a square plate is √29,000 = 170.3 ft on a side, so the perimeter is 681 LF. At 14'-0" floor to floor with a 3'-6" parapet, enclosure area is (681 × 14 × 2) + (681 × 3.5) = 19,068 + 2,384 = 21,452 SF, and the skin-to-floor ratio is 21,452 ÷ 58,000 = 0.370. Write that ratio down. It is the number a reviewer checks first, and it is why Northgate's 0.451 told Tomás something before he priced a single element.

Seed two, the test. Anchor your dollars per square foot against buildings whose numbers you already have. Willow Street is $6,800,000 ÷ 24,000 SF = $283.33/SF for a simple municipal building on public wages. Northgate is $360/SF for outpatient healthcare. A two-story municipal library sits between them and closer to the bottom — heavier floor framing for stack loads, more glazing, real millwork, but no medical gas, no imaging shielding, no surgery. A believable band is roughly $300 to $340/SF, or $17.4M to $19.7M.

If your elemental build-up lands outside that band, do not scale it to fit. Find the element that is the outlier and check its ratio — enclosure area, partition LF per SF, or MEP as a percentage of the cost of work. One line is usually wrong by a factor, and forcing the total hides it.

Chapter 12 — Estimating Fundamentals

All seven Part C items are answered in place: volume conversions, earthwork with swell and shrinkage, building a burdened rate, building a unit cost, formwork takeoff in SFCA, markup versus margin in both directions, and stress-testing a derived quantity.

B7 — Quantify the double-counted waste. A 5% waste factor applied to the quantity and a unit price that already includes waste:

412,000 SF × 5%       =  20,600 SF of phantom board
20,600 SF × $0.42/SF  =  $8,652 of cost you will never incur

On a hard bid that is $8,652 you are high by, on one material line, for no reason at all. On a GMP it inflates the number the owner is comparing against another contractor's. And it is invisible, because each decision was individually reasonable.

The one-sentence policy that makes it structurally impossible: "Waste is applied to quantity, never to price; every unit price in the cost database carries a field stating whether waste is included, and every takeoff sheet carries the waste factor on its own line." Two places to look, one answer in each, and a reviewer can check it in ten seconds.

Chapter 13 — Detailed Estimating

All seven Part C items are answered in place — reconciling a GMP, building a general-conditions estimate from staff and facilities, leveling three roofing bids, own-versus-rent with the utilization flip, the iterative markup stack, the self-perform decision, and the bid-day plug summary.

B2 — The daily exposure, and what it licenses you to spend.

$2,240,000 ÷ 640 CD   =  $3,500.00/CD  general-conditions burn
+ $3,900/CD liquidated damages
=  $7,400/CD  total daily exposure

What the number tells you: any action that reliably saves one calendar day and costs less than $7,400 is money-positive, and you should be able to say that out loud in a meeting without asking permission. Expediting a submittal, paying overtime to a detailer, renting a second hoist, adding a project engineer whose only job is the submittal log — measure each against $7,400 a day.

The common wrong instinct is to compare the cost of the fix against the general-conditions line item, where it looks expensive and unbudgeted. Compare it against the day.

Chapter 14 — Scheduling: Critical Path Method

Answered in place: C1 (the Willow Street fragnet, 67 WD, and its surprising critical path), C5 (perturbing the Northgate network, and why rising float on a parallel path is bad news) and C8 (line of balance at Harbor Ridge).

C2 — Durations from quantities. Duration = quantity ÷ (production rate × crews), then add the non-production days the rate does not cover.

Item 1 cross-checks against C1's activity F, which is 8 WD. ✓

Assumptions that would change these: for #3, that two crews have two independent work faces — if they share one, the second crew does not double production and the duration is 20 WD, not 10. For #6, that the slab has cured and the building is conditioned to the flooring manufacturer's temperature and humidity limits before day one. A wood gym floor laid over a slab that has not dried is not a six-day activity; it is a six-day activity plus a warranty claim.

C3 — Calendar and money.

(a) 425 CD − 121 weekend days − 9 holidays − 14 weather days = **281 work days**. State the weather assumption: this treats the 14-day allowance as work days. If your contract expresses it in calendar days, roughly ten of the fourteen are work days and you have 285 WD. Both are defensible; only the undocumented one is wrong.

(b) $680,000 ÷ 425 CD = **$1,600.00/CD**.

(c) $1,600 + $1,200 = **$2,800/CD** of total daily exposure.

(d) 281 WD − 268 WD = **13 work days of project float**. Converted, 13 × 7 ÷ 5 = 18.2 → 18 CD, worth 18 × $2,800 = **$50,400** if you had to buy it back.

(e) Refuse. Here is the trap. Nine work days of extension on a critical activity does not move substantial completion, because you hold 13 work days of float — so the immediate exposure looks like zero and the $14,000 credit looks free. It is not. You are selling 9 WD, about 13 CD, of protection worth 13 × $2,800 = $36,400 for $14,000, and the four work days you keep are worth only $11,200. Float is a project asset you can spend exactly once. Counter at a number that covers the exposure, or take the credit only if you can name what you intend to buy with the remaining four days.

C4 — Auditing a schedule for phantom float.

(a) Corrected total float: 2 work days. The schedule reported thirteen times more cushion than it has.

(b) Finding 4 — durations roughly 12% longer than the subcontractor's own manpower commitments support — does not change the CPM arithmetic at all. The network computes exactly what its durations say. It matters because the subcontractor has buried contingency inside durations instead of declaring it. Float hidden in a duration cannot be seen, cannot be allocated, and cannot be managed by anyone but the party hiding it — and it will be spent on that party, not on the project.

(c) The email, three sentences:

Your schedule reports 26 work days of total float on the driving path. Our review finds a Finish On constraint set 15 days beyond the subcontract completion date, three activities with no successor that add 5 days when tied in, and an FS−8 lag between hang and finish that adds 4 days when modeled as a start-to-start with a realistic offset — corrected, total float is 2 days, not 26. Please reissue with the constraint removed, the open ends tied, and the negative lag replaced, and include the manpower curve that supports your durations; we will review within five working days.

No adjectives, four facts, one number, one deadline.

C6 — Cost-load the schedule and draw the S-curve. Spreading each summary activity evenly across the months it spans:

(b) It is an S. Steepest in months 5 and 6 at $908,214 a month, 13.4 points each, because structure, enclosure and MEP rough-in all run at once. That is also when peak manpower, peak cash outflow and peak trade-stacking risk arrive together, which is not a coincidence.

(c) Cumulative billing first exceeds 50% in month 6. Retention held at 5%: 0.05 × $3,492,856 = **$174,643**.

(d) Twelve percent below the curve through month 7 is a shortfall of $4,038,570 × 0.12 = $484,628, and there are three completely different explanations. You are behind — distinguish with the CPM update and a physical measure of quantities in place. You are on schedule but under-billing — stored material not billed, a line the architect disputed, an application submitted short; distinguish with the continuation sheet against a field measure. The curve was wrong — MEP does not spread evenly across seven months, it ramps; distinguish by comparing the even-spread assumption against an activity-level cost loading. Only the first is a problem you fix in the field, and it is the one people assume without checking.

Chapter 15 — Bidding and Proposals

Answered in place: C1 (the recovery arithmetic), C3(a)(b), C4 (expected value of a pursuit), C8 (unbalanced unit prices, both directions) and C9(a)–(c). C2, C5 and C6 are your own firm's numbers.

C7 — The bid-day plan, backward from an 11:00 a.m. deadline.

Justifying the lock at 45 minutes out. Every minute after lock buys a small price improvement and costs a rising probability of a transcription error made under pressure. Past a point the second is worth more than the first, and 45 minutes is where most firms find it. Late quotes go into a separate post-lock column and are used only if the bid would otherwise be uncompetitive and two people re-check the affected line.

Chapter 16 — Procurement and Buyout

Answered in place: C1 (gross versus net buyout variance), C2 (the air-handler back-schedule), C3 (pricing a scope gap twice), C4 (bond versus subcontractor default insurance), C6 (the escalation clause), B3 and B5.

C7 — The award memo that recommends the second-low bidder at $76,000 above low. The memo has one job: to convert a preference into an arithmetic statement somebody can disagree with.

Break-even days  =  $76,000 ÷ $10,650/CD  =  7.14 calendar days

So the recommendation sentence writes itself: "We are recommending Meridian Acoustical at $76,000 above low. That premium is worth it if the low bidder would have finished the grid more than seven calendar days late. Their manning letter commits four installers to a sequence our own look-ahead says needs seven, and the ceiling grid carries zero float into MEP above-ceiling sign-off."

If instead the low bidder's crew is adequate and the grid carries fifteen days of float, the same arithmetic says award low and stop talking. The memo is not an argument about quality. It is a purchase of a specific number of calendar days at a stated price, and once it is written that way your operations executive can make the decision rather than ratify your instinct.

Chapter 17 — Preconstruction Planning

Answered in place: C1 (pricing a gating permit, 375:1), C8 (the oversail decision re-run) and C9 (gate throughput at peak).

C7 — Derive Willow Street's daily rate. State the assumption first: general conditions at 10% of contract value, $680,000, which is the figure Chapter 13 establishes and the book uses everywhere.

$680,000 ÷ 425 CD   =  $1,600.00/CD  extended general conditions
+ $1,200/CD          liquidated damages
=  $2,800/CD         total daily exposure

A one-week permit delay costs 7 CD × $2,800 = **$19,600**. The application takes a project engineer about half a day; at the roughly $500 of fully burdened cost C1 assumes for half a day, the return is 39 to 1. At ten times that labor cost it is still 3.9 to 1. Notice the shape of the number: it is the same shape as Northgate's 375:1, one order of magnitude smaller, on a job one-seventh the size. The ratio survives the change of scale, which is why this arithmetic is worth doing on every job you run.

C6 — What the mobilization float costs. Mobilization is spent across three weeks, so the average dollar goes out about day 11; the first application goes in on the 25th and is paid 30 days later, about day 55. Call it 45 calendar days between the average expenditure and the cash for it. At 9%:

Every $100,000 of mobilization  ×  0.09  ×  (45 ÷ 365)  =  $1,110

Multiply by your own C5 total. Two legitimate ways to shrink it: a mobilization line in the schedule of values, billed on application #1 against costs actually incurred and substantiated; and payment for stored material on long-lead items with the owner's written consent, bill-and-hold documentation and insurance in place. One illegitimate way: front-loading the schedule of values, which is Chapter 32's subject and reliably costs more than it earns.

C3 — the method, worked once. Date required in hand − review − resubmittal allowance − preparation = file-by date. For a building permit needed in hand at NTP (March 3, Year 1), assuming a 45-CD review and a 21-CD resubmittal allowance with 14 CD to prepare: 45 + 21 + 14 = 80 CD before NTP, so you file by December 14, Year 0. And the answer to "is it the one you would have guessed?" is usually no. The earliest file-by date is almost always the utility service application or the land-disturbance and stormwater permit — because those sit in an agency queue you do not control and have a prerequisite (an approved SWPPP, a recorded easement) that is itself a submittal with its own review.

Chapter 18 — Site Management

All seven Part C items are answered in place: the cost of standing still, double handling, hoist capacity, the pour-or-don't-pour decision, the crane pick schedule, temporary heat, and the sanitation arithmetic that nobody puts on a cost report.

B5 — Just-in-time versus stockpiling, three cases.

(a) Hollow-metal frames, congested urban site, reliable local supplier: JIT, by floor. Frames are bulky, easily damaged, and installed in a known sequence; there is nowhere to put them and every day they sit is a day something hits them. The supplier's reliability is what makes JIT safe here — remove it and the answer changes.

(b) Imported porcelain tile, 16-week lead, three acres of laydown: stockpile. The constraint is not space, it is the lead time and the dye lot. Order early, take the full delivery, verify that the whole quantity comes from one run, and store it indoors. A 16-week reorder in month ten is not a delivery problem; it is a schedule event.

(c) Ready-mix concrete: JIT, always, everywhere. There is no stockpiling option. Its shelf life is measured in about ninety minutes, and the entire discipline of a pour plan exists because of that fact.

Chapter 19 — Subcontractor Management

Answered in place: C1 (reading the curve, $138,450), C2(a), C3(a)(b), C4(a)–(c) (the measured mile), C5(a)(b) (diagnosing the manpower table) and C6's arithmetic.

C8 — The six-rung escalation procedure.

Why skipping a rung voids the remedy. Every remedy in a subcontract — supplementation, backcharge, termination — is conditioned on notice and an opportunity to cure. A backcharge issued without a written cure notice and documented failure to cure is not a weak backcharge; it is one you lose in the first hour, which is exactly what C2(b) is showing you. And check the bond form: notice to the surety is often required before you supplement, not after.

Chapter 20 — Labor and Productivity

Answered in place: C1 (the burdened electrician), C2 (productivity factor and forecast), C3 (six tens, correctly loaded), C6 (apprentice ratio), C7 part 1 (the learning curve) and C8 (the Thursday diagnosis).

C4 — The optimum crew. Burdened rates: foreman $63.32, journeyman $54.12, apprentice $40.70, laborer $41.51; 10-hour days.

The optimum is seven, at $6.58/LF. Marginal cost per linear foot of each step up:

5→6  $541.20 ÷ 100 LF =  $5.41      8→9   $415.10 ÷ 40 LF = $10.38
6→7  $407.00 ÷  90 LF =  $4.52      9→10  $541.20 ÷ 20 LF = $27.06
7→8  $541.20 ÷  70 LF =  $7.73

The marginal cost first exceeds the optimum's average cost at the 7→8 step, $7.73 against $6.58 — the eighth worker is the first one who costs more than the average he dilutes. That is what "optimum" means; it is not a judgment.

When you staff past it anyway. On Willow Street's 6,200 LF of partition: seven workers take 6,200 ÷ 530 = 11.7 → 12 WD at 12 × $3,485.90 = $41,831. Nine workers take 6,200 ÷ 640 = 9.7 → 10 WD at 10 × $4,442.20 = $44,422. You pay $2,591 to save two work days — about three calendar days, worth 3 × $2,800 = $8,400. Buy the days. Unit cost is the right number when the activity has float and the wrong number the moment it does not.

C5 — Certified payroll, two classifications in one week. Ironworker structural: $37.90 base, $22.40 fringe. Laborer Group 1: $26.40 base, $13.10 fringe. Assume Monday–Thursday as ironworker (32 hr), Friday 8 hr and Saturday 4 hr as laborer, so hours 41–44 are laborer hours.

Had the four overtime hours fallen in the ironworker classification instead, the gross would be $2,479.40 — a difference of $23.00 for one worker in one week, decided entirely by which hours the daily record says were which classification.

The record that must exist is a daily time record showing hours by classification by day, created contemporaneously by the person who supervised the work: the foreman. Not payroll, not the project manager, and not a reconstruction on Friday afternoon. That is why classification discipline is a field problem — and why the misclassification arithmetic in §20.4 scales to $68,292 before anybody notices.

C9 — The blended prevailing-wage rate. Packages from §20.4: carpenter $52.05, cement mason $50.35, laborer Group 1 $39.50.

Foreman (carpenter + $3.10)  $55.15  |  4 carpenters   $208.20
2 cement masons              $100.70 |  2 laborers      $79.00
Crew                         $443.05/hr  →  blended $49.23 per person-hour
10-hour day                  $4,430.50
Unit labor cost              $4,430.50 ÷ 780 SFCA = $5.68/SFCA

Reduces unit cost: add a tenth person, a second laborer, if the carpenters are handling their own material. Daily cost rises to $4,825.50 (up 8.9%); if production rises to 880 SFCA (up 12.8%), unit cost falls to $5.48/SFCA. Reduces total daily cost but raises unit cost: drop one carpenter. Daily cost falls to $3,910.00 (down 11.7%) but production falls to about 650 SFCA, and unit cost rises to $6.02/SFCA.

The difference between the two objectives is the point. Total daily cost is a cash and manpower question; unit labor cost is a productivity question. A superintendent told to cut this week's labor bill will cut heads and make every square foot more expensive. You need both numbers, and confusing them is how a job runs "under budget this week" all the way to a loss.

Chapter 21 — Equipment Management

All seven Part C items are answered in place: production four ways, fleet matching, ownership cost, break-even utilization, running a pick, ground bearing, and planning a pour.

B1 — The skid steer, diagnosed. Two crossovers, both from division:

Daily → weekly:   $940 ÷ $340   = 2.76  →  at 3 days the weekly rate is cheaper
Weekly → 4-week:  $2,600 ÷ $940 = 2.77  →  at 3 weeks the 4-week rate is cheaper

Four days at the daily rate is $1,360 against a $940 week — $420 already wasted this week, and "another week or two" puts him at three weeks. Call the rental house today, ask them to rebill this week at the weekly rate (most will), and convert to the four-week rate. Against continuing at day rates for two more weeks ($1,360 + 10 × $340 = $4,760) the four-week rate saves about $2,160; even against weekly rates it saves $640. "Day by day so we stay flexible" is a preference being paid for in cash by somebody who has not divided two numbers.

B8 — Idle fuel. 9,600 engine hours at 34% idle is 3,264 idle hours; idle burn is about one third of 4.1 gal/hr, or 1.37 gal/hr.

3,264 hr × 1.37 gal/hr = 4,461 gal  ×  $4.15/gal  =  ≈ $18,500 a year

Two non-fuel costs: hour-meter hours, which consume warranty, accelerate every scheduled maintenance interval and reduce resale value, so ownership cost per productive hour rises; and engine wear at low load, which on modern diesels also drives regeneration and diesel exhaust fluid consumption. A third, quieter one: those idle hours get charged to cost codes as though they were production, so your own unit-cost history is being poisoned by them.

Chapter 22 — Temporary Structures

Answered in place: C1 (lateral pressure), C2 (the cycle and the money), C3 (buy or rent), C4 (average versus marginal dewatering cost), C7 (temporary heat) and C8 (the stopped pump, 5.7:1).

C5 — the two sentences that govern modification, which is the part of the procedure that actually prevents the week-34 near-miss:

No scaffold on this project is erected, altered, moved or dismantled by anyone other than the erecting contractor's competent person. Any scaffold found modified is immediately taken out of service, its tag pulled, and it stays out of service until that competent person re-inspects and re-tags it — and the modification is written up as a near-miss whether or not anybody was hurt.

The second half is what makes it work. Milo Serrano's plank was moved by a trade that did not erect the scaffold, and the tag was two days stale. Both failures are addressed by a rule that treats an unauthorized modification as a reportable event rather than as housekeeping.

C6 — The temporary-structures register. Eight rows for Willow Street, with the column that matters most on the right:

Assume three to four weeks for a delegated design plus the engineer of record's review period, and back-schedule from the day the bracing is needed — not from the day the wall goes up. The register's real value is the last column: it converts "somebody will handle it" into three submittals with dates.

Chapter 23 — Quality Management

Answered in place: C1 (pricing the wrong letter), C3 (cost of quality, 2.00), C6(a)(b) (the mockup back-schedule and its $1,192,800) and C7 (punch arithmetic).

C4 — the four dispositions and their approvers, which is the part of the NCR most people get wrong:

Rework, and do it in the two days before finishing starts. The window is the answer. A listed fire- rated assembly has no discretion in it, and the cheapest moment to fix it is the only moment when the board edges are still visible.

C5 — Price it now versus at the fire marshal's final.

Now: 3,100 SF × $0.42 = $1,302 + $1,200` inspection and documentation + `$1,900 finishing resequencing = $4,402.

Eleven months later, shaft finished, corridors finished, elevator installed:

Ratio: 17.9 to 1. And that is the cheap version of the late answer, because the fire marshal's final sits on the certificate-of-occupancy chain: ten days of slip at Northgate's $10,650/CD adds $106,500, more than the repair itself. Every line above is defensible in front of a client, which is the standard the exercise sets.

Chapter 24 — Safety Management

Answered in place: C1 (fall clearance, and why the "easier" anchor is far worse), C2 (TRIR and DART, and why short-horizon movement is noise) and C3 (EMR and the prequalification door).

C5 — Price the controls on the acceleration. Eighteen finish workers onto a floor already occupied by two trades, five weeks, priced at $62,000. State every assumption:

All-in: $62,000 + $56,638 = $118,638 — the controls nearly double the priced cost of the acceleration, and none of them is optional.

How many of the promised days it delivers: fewer than promised. Three crews on one floor is trade stacking, and stacking costs productivity across all three crews, not just the new one. At a conservative 15% loss, a package sold as recovering ten days delivers six or seven. The evidence is on this project: the steel acceleration in weeks 34–36 produced trade stacking, a deck-edge rework event, and a spike in near-misses that ended with a plank shifting under a mason tender. Price the controls before you price the acceleration, and discount the days before you promise them.

Chapter 25 — Submittals, RFIs and Document Control

Answered in place: C1 (back-scheduling the gym floor), C2 (aging and ball-in-court, and the switchgear sitting in your own office), C4 (levelling the submission curve, 62 items) and C5 ($550 a minute).

C3 — The RFI, written out. This is the model for every RFI in the book.

RFI WS-047 · Issued: [date] · Response required by: [date, 5 CD] · Discipline: Plumbing / Structural · Location: Commercial kitchen, first floor, grids C-4 to D-5

References: P-201 rev. 2 (grease interceptor GI-1, invert elevation shown); S-101 rev. 3 (footing F-12, bottom-of-footing elevation shown); Specification Section 22 13 19.

Question. The grease interceptor GI-1 shown on P-201 has an invert 14 inches below the bottom of adjacent footing F-12 as shown on S-101. The structural drawings show no undercut, step, or underpinning at F-12. Please direct which of the following is intended: (1) relocate GI-1 outside the building footprint, or (2) deepen or step footing F-12 to clear the interceptor.

Suggested resolution. Option 1. It removes a structural modification from the critical path and keeps the interceptor accessible for pumping.

Cost impact. Option 1 approximately $11,000 plus a civil revision and a possible permit revision; Option 2 approximately $6,500 plus structural direction. Neither is included in the Contract Sum.

Schedule impact. Option 2 carries an estimated 5 CD impact to the kitchen slab. Activity C-1220 (slab on grade, 96 CY) is scheduled in 12 calendar days. A response received later than [pour date minus 7 CD] will delay the pour regardless of which option is selected.

The required response date is justified, not asserted: twelve days to the pour, minus five days to procure direction and materials, minus two days to reschedule the crew and the pump, leaves five. Notice what is not in the RFI: no argument, no blame, and no request for a change order. Those are a different document on a different clock.

C7 — Rewrite the field note. The original is a paragraph of feelings. Here is the same day, written so that it is worth money:

North corridor, Level 2, grids 4–9. Coastline Drywall's crew of 6 carpenters was unable to close the corridor ceiling from 12:15 p.m. to 3:30 p.m. because overhead mechanical and electrical work above the corridor ceiling is incomplete between grids 6 and 9. Ceiling closure is held by RFI 118 (transmitted 9/14, response due 9/28, open) and by the coordination sign-off for this zone, which remains outstanding. Crew was redeployed at 12:15 p.m. to hang board in Rooms 2-114 through 2-118, which absorbed 4 of the 6 workers; 2 workers × 3.25 hours = 6.5 man-hours lost. Photographs 0912-01 through 0912-06 taken at 12:20 p.m. Notified S. Marchetti (Cardinal) and D. Achebe (Halcyon) by email at 12:40 p.m., copy to D. Whitcomb (H+P), requesting a completion date for the zone. Third occurrence in this zone; see daily reports 8/29 and 9/5.

Four things changed. Every fact is quantified and datable. Mitigation is recorded, which is what makes the 6.5 hours recoverable rather than arguable. Notice is documented, with a time and a recipient list. And there is not one sentence a lawyer could read aloud to embarrass its author.

Chapter 26 — Meetings and Field Documentation

Answered in place: C1's crane-standby arithmetic (26 labor hours) and the warning not to blend two different impacts into one entry.

C3 — Verify CO #14, then price the writing.

Actual cost incurred                    $186,400
Substantiable with contemporaneous records  121,000
Documentation gap                        $65,400  ✓
Negotiated settlement                    142,750
Unrecovered                              $43,650  ✓

The settlement recovered `$142,750 − $121,000 = $21,750` of the $65,400 gap — exactly one third, which is the same relationship premium Chapter 25's C5 assumes. That is not a coincidence; it is the book showing you the same behavior from two directions.

At 4.1 hours of writing:

Against the unrecovered cost:  $43,650 ÷ 4.1 hr  =  $10,646 per hour
Against the full gap:          $65,400 ÷ 4.1 hr  =  $15,951 per hour

No other hour of a project manager's week returns anything close to that, and the reason is structural: the price of a change is set by what you can document, not by what it cost you.

C4 — Two of the five rewrites, as models. Each must carry all five elements — what, where, when, who was affected, and what it cost.

"Waiting on the architect" becomes: "Ceiling grid installation in Rooms 2-204 through 2-209 did not start today. RFI 094 (transmitted 10/2, response due 10/16) governs the soffit dimension at the mechanical chase and is 6 days past its response date. Two ceiling installers stood down at 9:40 a.m. and were redeployed to Room 2-215; 1 installer × 5.5 hours = 5.5 man-hours lost. Followed up by email to D. Whitcomb at 9:55 a.m., copy to the owner's representative."

"Concrete came late" becomes: "Placement of footings F-8 through F-14 (34 CY, activity C-1140) was scheduled to begin at 7:00 a.m.; first truck arrived 9:20 a.m. Crew of 7 plus one pump operator stood by 2 hours 20 minutes = 18.7 man-hours plus 2.3 pump-hours at standby. Cause per Rivermont Ready-Mix dispatch: plant breakdown, confirmed by phone at 7:35 a.m. Placement completed at 2:10 p.m.; no overtime. Notified the supplier in writing at 3:00 p.m. that standby time will be backcharged under the purchase order."

What each rewrite is worth that the original is not: a number somebody else can verify, and a name to send it to. The original is a mood. The rewrite is an invoice waiting to be issued.

Chapter 27 — Lean Construction and the Last Planner System

Answered in place: C1 (chain reliability, and why shortening the chain beats raising reliability), C2 (PPC arithmetic and the raw-count check) and C3 (takt calculation).

C5 — The money check. At 0.6 CD of slip per week with 18 weeks remaining: 0.6 × 18 = **10.8 CD** still to come, on top of the 0.6 × 8 = 4.8 CD already banked — about 16 CD total at substantial completion. Using the canonical general-conditions budget of $680,000 (10% of contract value, the middle of the defensible 8–12% band):

Extended GC only:      10.8 CD × $1,600/CD  =  $17,280   (16 CD → $25,600)
With liquidated damages: 10.8 CD × $2,800/CD  =  $30,240   (16 CD → $44,800)

The make-ready effort: one person, 12 hours a week, 18 weeks = 216 hours at a fully burdened project engineer rate of $86/hr = $18,576.

Break-even on general conditions alone:  $18,576 ÷ $1,600/CD  =  11.6 CD
Break-even on total exposure:            $18,576 ÷ $2,800/CD  =   6.6 CD

Read that honestly. On general conditions alone it is a close call — the effort must save nearly the entire projected remaining slip to pay for itself. The moment liquidated damages are live it is not close at all, at under seven days. That asymmetry is why make-ready looks like overhead on a job with float and like the cheapest thing on the page on a job without it.

C7 — Reason-code Pareto.

Material and submittals are exactly half of all misses. Material is owned by the procurement and expediting system (Chapter 16): purchase orders, confirmed delivery dates, an expediting log. Submittals are owned by the submittal log and its back-scheduled release gates (Chapter 25). Both are office systems. Half of this job's field misses are being manufactured in the trailer.

Two countermeasures, each with a name and a date: "Wei Chen reissues the submittal log by Friday with every item back-scheduled from its release gate; the ten items with the least float go on the six-week look-ahead as activities with need-by dates." And: "Dani Okonkwo builds a delivery-confirmation call sheet — every material required in the next six weeks gets a written ship date from the supplier, re-confirmed ten days out; anything unconfirmed is a constraint and its activity does not enter the weekly work plan. First pass by the 15th, standing every Tuesday."

(d) A profile dominated by material and submittals says the field is ready and the office is not. A profile dominated by prerequisite work and space-and-access says the office is fine and the production sequence is wrong. The two jobs need opposite interventions and could post identical PPC numbers, which is precisely why the reason code, not the PPC, is the useful output.

Chapter 28 — Cost Control

All six Part C items are answered in place, and they are the densest set in the book: decomposing an actual unit rate, forecasting one code four ways with a $155,200 spread, the believability thresholds, reading a stranger's cost report and moving it $182,000 with two lines of arithmetic, the accrual schedule, and contingency drawdown against percent complete.

B2 — What a negative cost to complete asserts. In plain language: finishing this work will give us money back — the job gets cheaper by doing more of it. No physical process on a construction site does that.

Cost systems display it anyway because the default cost-to-complete is a formula, budget − cost to date, and the formula has no floor. When a code overruns its budget before it finishes, the subtraction goes negative and the software prints it without complaint. The fix is a rule, not a setting: on any code that is physically complete, the forecast is the cost to date and the variance is real and already earned. The reason this matters beyond tidiness is that a negative cost to complete silently offsets a genuine overrun somewhere else in the rollup, and the total looks better than the job is — which is the same failure the C4 report commits twelve lines at a time.

Chapter 29 — Schedule Control

Answered in place: C1 (running the update, and the 8 negative days that existed in the accepted baseline) and C3 (crashing, 17 CD for $110,000).

C2 — Float absorption, and the smallest number in the table.

Net impact: 19 calendar days late.

Now the counterfactual. Transmit on time and the chain arrives at the release date with 5 CD of float instead of zero — so the release lands three days inside the die-run window instead of two days outside it. The 28-day penalty never happens, and the chain finishes with 5 days of float intact. Impact: zero.

The general contractor's own 5-day administrative delay is the smallest number on the page and is responsible for all 19 days, because it is the one that crossed a threshold. The architect's 7-day overrun consumed float and crossed nothing. That is the whole lesson about float: it is not a cushion that absorbs delay proportionally, it is the distance to the next cliff.

C7 — The decision page. Exposure is $3,000 + $2,600 = $5,600/CD.

Do nothing is financially optimal. Marginal cost per day bought: $9,000, $11,167 and $13,813 — every package costs more per day than a day is worth. Spread between the best and worst acceleration options: $237,800 − $126,800 = $111,000, or 0.79% of a $14,000,000 contract.

The two columns not denominated in dollars are peak trades stacked and rework exposure, and you cannot invent either: you would have to go get the manpower histograms from each subcontractor's recovery plan, and your own project's nonconformance count and cost per week during the last acceleration.

Recommendation, no dollar sign: "None of the three packages returns more schedule than it consumes, so we do not accelerate; we go to the owner this week with the time-extension request the update supports, and we put the recovery effort into the two controlling activities where the constraint is information rather than manpower."

Chapter 30 — Earned Value Management

Answered in place: C1, C2, C3, C5, C6 and C7 — building PV/EV/AC from field data, all four EACs, the TCPI credibility test, period versus cumulative indices, what the measurement method is worth, and earned schedule.

C4 — The question earned value cannot answer.

(a) SPI 0.940 does not convert to days because SV and SPI are denominated in dollars of work volume, not time. It says you have completed 94% of the budget value the baseline placed by today. It says nothing about which 6% is missing. That 6% could be spread thinly across every activity and cost you nothing; it could be one activity on the controlling path and cost you forty days; it could be entirely off the critical path and cost you zero. Multiplying a dollar ratio by contract duration assumes every dollar of work occupies the same amount of critical-path time, which is false in every building ever built. And because EV converges on BAC by construction, SPI drifts back toward 1.000 as a job finishes — including a job that finishes sixty days late.

(b) What you need to answer the question actually asked: the CPM schedule update at the same data date, from Wei Chen — specifically its controlling path with early and late dates, the total float on that path, the data date, the list of logic changes and out-of-sequence progress since the last update, and the narrative naming the driving activities. Plus the contract completion date to measure against.

(d) 13 CD × $2,800/CD = **$36,400** — and it appears in the earned-value report nowhere. BAC is the cost of the work: the budget for building the building. Extended general conditions on thirteen additional days is a cost you have not incurred and never budgeted, and liquidated damages are a contract remedy, not a work package. Earned value cannot show you a number that is not inside the budget it measures against.

Chapter 31 — Change Order Management

All six Part C items are answered in place: pricing a change from first principles, the cascading second-tier markup, time and the money attached to it, the measured mile, the deletion that costs money, and the change log with its aging report.

B4 — Reading the ratio. $36,050 ÷ $111,273 = **32.4%** of CO #015 is time, not work. Check the rate: $36,050 ÷ 7 CD = $5,150/CD — the contract's extended-GC rate exactly.

Why the person who prices only the work feels good: they negotiated the $75,223 of physical work hard and won; they hold a signed change order; and the seven days they gave away appear on no invoice, in no cost code, and in no variance column. The cost surfaces eleven months later as extended general conditions in a report nobody connects back to CO #015. A concession that generates no document feels free, and that is exactly why it is the one people make.

Chapter 32 — Progress Payments

Answered in place: C1 through C6 — building a schedule of values that foots, completing and independently checking an application, rolling it forward, modelling retention, finding the cash trough, and pricing a front-loading decision.

C8 — Count the days from the work to the subcontractor's cleared funds. Work performed on the 2nd of month M falls in period M, which is billed by the 5th of month M+1:

Work performed                                     day 0
Application submitted by the 5th of the next month day 34
Architect certifies, 14 days                       day 48
Owner pays, 30 days from certification             day 78
  + 3 days to clear                                day 81
You pay the subcontractor, 10 days from receipt    day 91
  + 3 days to clear                                day 94

About 94 calendar days, and 5% retention on that work is not in the number at all.

The memo for a new subcontractor writes itself from the ladder: "Plan your cash on a 90-day cycle from the day the work is performed, not the day you invoice. To be in an application you must be in our office by the 20th with your billing, continuation sheet, certified payroll and conditional waiver — an item that arrives on the 21st is not paid four days late, it is paid a month late. Retention is not in the 90 days. If you have a cash constraint, tell us before you sign, not in month four."

Chapter 33 — Claims and Delay Analysis

Answered in place: C2 (the concurrent period, and the $9,600 that turns on one float figure), C3 (the windows analysis Curtis could have run), C4 (four ways to derive an extended-GC rate) and C5 (a measured mile stress-tested, and what the $24,411 disclosure buys).

C1 — Classify eight delays.

Two rows change entirely without contemporaneous float data: 2 and 8. Row 2 is harmless only because 14 days of float existed on the day the delay began, and that number lives in one place — the total-float column of the update in effect. Row 8's concurrency finding is a float question and nothing else. One row changes without timely notice: 7. A differing site condition is the classic notice-barred claim; the condition must be reported in writing, within the contractual period, before it is disturbed.

C7 — Pursue, negotiate, or absorb. Midpoint of the honest range is $225,000. Discount at 12%.

Recommend C. It is the highest net, the fastest, and the only one that does not put a repeat public owner across a table from your lawyers. Two facts that would flip it: if the substantiated damages are materially higher than $225,000, path A's expected value rises while its cost does not; and if this agency will never award you another dollar, the relationship value that justifies discounting a $620,000 claim to a $160,000 ask disappears.

For the CFO: "Filing this has a negative expected value of about fifty thousand dollars. A four-month executive negotiation at a reduced ask is worth about sixty-four thousand and keeps a public owner that has awarded us work three times. I want one phone call from you before anybody bills an hour to it."

Chapter 34 — Construction Finance

All five Part C items are answered in place, and they build on one another: completing the WIP schedule, footing it, naming the job that should worry you, the ratios and months of backlog, and the bonding effect of a fade.

B1 — The month she left the forecast alone.

Reported:  $14,700,000 ÷ $35,000,000 = 42.0% complete  →  revenue $15,750,000, GP $1,050,000
Correct:   $14,700,000 ÷ $36,750,000 = 40.0% complete  →  revenue $15,000,000, GP $300,000

$750,000 of revenue recognized and not earned, and because cost to date does not move, the entire $750,000 is also overstated gross profit. Who relies on the difference outside the company: the surety, which sets bonding capacity off these statements; the bank, whose revolver covenants are computed from them; and the CPA who will have to stand behind the reviewed or audited financials. "Seeing whether the sub eats part of it" is a hope. A forecast is not the place to keep one.

B7 — Who is financing whom. $9,180,000 − $5,880,000 = **$3,300,000** net retention receivable, carried by the general contractor. At an 8.5% revolver rate that is $280,500 a year — real interest, on money already earned, paid so that owners can hold cash. The contractor passes two thirds of the burden down to companies with smaller balance sheets and higher borrowing rates, so the project's true cost of the retention provision is higher than $280,500, and every dollar of it eventually returns as price.

Chapter 35 — BIM for Construction

All six Part C items are answered in place: triaging a raw clash report, the Willow Street kitchen cavity budget, building LOD matrix rows, reading the funnel and the trade matrix as diagnostics, pricing the same conflict twice, and reconciling a model extraction against a hand takeoff.

B5 — The model 1,140 feet northeast and rotated 21 degrees. Two ways it gets "fixed."

The right way: the trade republishes from a corrected project base point and survey point on the project's shared coordinate system, so the file's own coordinates are true. The dangerous way: apply a transform inside the coordination software only. That fixes the picture and not the file — every export, every fabrication file, every total-station layout point, and every scan-to-model comparison still carries the offset, and it will surface as a field error weeks later with no obvious cause.

How to detect it afterward: pick a known survey control point, export its coordinates from the trade's own model in a neutral format, and compare against the surveyor's control. Ninety seconds, and it is the only test that distinguishes the two fixes.

Chapter 36 — Sustainable Construction

Answered in place: C1 and C2 (diversion rate, and losing 4.4 points because a dispatcher changed a route), C3 (effective R-value), C4 (the three discovery points, 1 : 13.5 : 42.9) and C6 (the SCM schedule trade-off).

C8 — The scorecard. Estimated points total 54. Do not carry a threshold out of this book; look up the certification levels for the rating-system version your project is actually registered under, and notice that 54 is close enough to a boundary that two points decide it — which is why the confidence column matters more than the total.

Contractor-owned or contractor-influenced: Materials and Resources (8) and Indoor Environmental Quality (9) are yours outright — 17 points. Add Sustainable Sites (6), Energy and Atmosphere (14, because you build the envelope), Innovation (3) and Regional Priority (2), and 42 of the 54 points are ones you can affect. That is your contractual exposure, because the contract almost certainly obliges you to achieve a level rather than to try. The number for your risk register is not 54; it is the 42 you can move and the 12 you cannot.

C9 — Cost of quality, applied to certification.

The second air test and the documentation chase are classified as failure, not appraisal, on purpose: a retest exists only because the first test failed, and chasing material documentation you should have collected at buyout is rework of a records process. Reasonable people classify them the other way, and saying which you chose is the professional part.

Exchange rate: $308,110 ÷ $118,000 = **2.61 to 1** — $2.61 of failure for every dollar of prevention. And sharper: the $8,600 mockup extension that was never bought sits against $236,710 of slab-edge remediation, a ratio of 27.5 to 1 on a single decision. To the executive who wants to cut the coordinator: "We spend $118,000 preventing and $308,110 fixing. The largest failure on the list is the one an $8,600 mockup would have caught. Cutting the coordinator removes the only full-time person whose job is to find the next $8,600 decision before it becomes the next $236,710."

Chapter 37 — Residential Construction Management

All five Part C items are answered in place, and they are among the best arithmetic in the book: cycle time and Little's Law, the crew that costs a day versus the crew that costs the line, reading the production chart to find the throttle, the draw schedule and the working capital it strands, and what thirty days costs a spec house.

B2 — Why starting houses is not production, in three sentences with no jargon.

Starting a house does not finish a house. Our output is set by the slowest trade on the line — right now that is interior trim, which can turn about 45 houses a year against the 43.6 we need, and adding starts does not make the trim carpenter faster. If you want more output, buy more trim capacity; if you want more houses standing half-built with our money in them, start four more.

Every sentence is a number the regional manager can check, and the last one names the actual consequence of the instruction rather than arguing with it.

Chapter 38 — Heavy Civil Construction

Answered in place: C1 through C5 — building a unit price from production, the measurement clause, quantity variation and stranded fixed cost, the mass-haul diagram, and pay factors.

C7 — The differing-site-conditions notice. Its six required elements, in order: the location by station and elevation; the specific contract document the condition differs from, named by title, date and sheet; a factual description of what was found, with no argument and no adjectives; a statement that work in the affected area has stopped and is undisturbed; a request for inspection before the condition is disturbed; and a reservation of rights to time and cost under the named articles.

Why there is no dollar figure, in two sentences. You do not yet know the cost, and the first number you write down is the number the other side will hold you to for the rest of the dispute — a low guess caps your recovery and a high guess destroys your credibility on every line that follows. The notice's only jobs are to preserve the right and to get the condition inspected before it is destroyed; pricing is a separate document on a separate clock, and the contract almost always gives you a separate period for it.

Chapter 39 — Construction Technology

All five Part C items are answered in place: scoring three proposals on A/B/C/D, designing a pilot with a kill criterion, the drone earthwork volume that correctly declined to buy a survey, the maturity-sensor float test, and break-even versus return on investment.

B1 — Five vendor sentences, five failure modes.

Chapter 40 — Project Closeout

Answered in place: C1 (the closeout chain, 69 CD and three outside dates), C2 (rolled forward, June 25 and $82,237), C4 (the carrying cost of a delayed final completion) and C5 (what the retention-reduction request is worth). C7's punch arithmetic is there too.

C3 — Sort the list, name the payer.

(a) Seven can prevent substantial completion — 2, 4, 5, 7, 9, 13, 15 — and item 6 conditionally. What they share: every one is a life-safety system, a required regulatory test or certificate, or a performance requirement the space cannot function without. None is about appearance and none is a matter of judgment, because in each case a third party — the fire marshal, the health department, the elevator authority — has to sign something. Punch items are deferrable by definition; these are not.

(b) Item 14 is added scope. Close it silently and you have performed work with no directive, no price and no time — CO #14 in miniature, plus the precedent that the punch list is where scope goes to hide. Instead: strike it from the punch list, log it as a change request the same day, price it, and tell the owner in writing that you are glad to do it and here is the number.

(c) Items 8, 11 and 16 turn on three separate questions: is it inside the applicable warranty period (each has its own — a one-year general warranty, longer where the specification required an extended roofing or sealant warranty); is it a defect or is it maintenance and misuse (a condensate stain may be a pan nobody cleaned); and whose warranty is it (a manufacturer's material warranty and your workmanship warranty are different instruments, with different periods and different claimants). All three go in the warranty log; item 16 also belongs in the envelope commissioning record, because sealant failing at six locations on one elevation at month eleven is a pattern, not an incident.

Chapter 41 — Leading People

Answered in place: C1 (the cost of being right, 23.6:1 and 42.3:1 once it touches the critical path), C2 (six tens, worked, at three efficiency assumptions), C3 (turnover priced) and C8 (the $441 that was really $2,520).

C4 — The escalation decision, five situations. Test 1 (safety or code) stands alone; otherwise two or more must be true.

(a) Fire lane, asked twice. Tests 1 and 4. Escalate today — in writing to the subcontractor's project manager — and fix the physical condition now. Escalation starts at the rung that can actually fix it, not at your VP.

(b) Load-bearing CMU grouted without reinforcing, wall closed. Tests 1, 2 and 3. Escalate immediately, issue the nonconformance report, and notify the engineer of record the same hour. Let nobody propose a repair before the EOR rules — a repair to a load-bearing element is the engineer's call, not the mason's.

(c) Two subs arguing over $2,400 of cleanup. No test is met. Do not escalate. Resolve it in twenty minutes with the two-trade method, and if the scope sheets are genuinely silent, split it or absorb it and fix the scope sheet on the next subcontract. Escalating this teaches both subs that you cannot decide anything.

(d) Owner's rep called your project engineer directly asking for scope. Tests 2 and 3. Escalate today, but laterally first: call the owner's representative, thank them, restate the single-point-of- contact rule in writing, and then tell your own VP it happened — so that if it happens twice there is a record that you addressed it the first time. And protect the project engineer; the failure is a process gap, not their mistake.

(e) Scissor lift with the guardrail chain removed. Test 1, alone. Stop the work now, then escalate the same day to the subcontractor's safety representative and your safety director. Then apply Chapter 24's threshold: ask why the chain is in the way. The honest answer is usually that the lift is the wrong machine for the reach, and the next crew will remove it too.

Chapter 42 — The CM Career

Answered in place: C1 (the bonus pool and how to game it), C2 (the cash trough at 46.6% of contract), C3 (comparing two offers on deltas) and C6 (sizing the first job at two sets of contract terms). C4, C5 and C7 are about you, and this appendix has nothing useful to say about you.

C7 — the model the résumé rewrite is built on. Scope, size, outcome, in that order, using your own Willow Street notebook if you have no projects yet:

Before: "Built a CPM schedule."

After: "Built and maintained the CPM schedule for a $6.8M, 24,000 SF municipal community center on a 425-calendar-day design-bid-build contract — 268 work days of computed critical path against 281 available — and I can tell you which two activities consumed the 13 days of float and what buying them back would have cost at $2,800 a day."

The follow-up an experienced interviewer will ask is always the same shape: "Which two, and what did you do about it?" Have the answer, and make it name a mechanism rather than an effort — "we back-scheduled every submittal from its release gate and put the ten with the least float on the six-week look-ahead as activities with need-by dates" beats "we watched it closely" every time. That is the difference between a line that survives an interview and a line that ends one.

Where the answers are

Two chapters deserve a note. Chapter 2 and Chapter 28 have the most completely worked exercise sets in the book; if you are teaching yourself and want to know what "showing your work" looks like at a professional standard, start there. And Appendix B is twenty more scheduling problems with full solutions — if Chapter 14 is where the critical path stopped making sense, that is where it starts making sense again.

Editor's notes

These are the places where an exercise statement, or an answer printed with it, does not hold up. I have solved each item exactly as written above and flagged the problem here rather than quietly correcting it, because on a real job the discrepancy is the finding.

1. Chapter 5, C1(a) — arithmetic error in the printed answer. The sliding scale is first $500,000 at 2.500%, next $2,000,000 at 1.500%*, so a $1,850,000 contract has $1,350,000 in the second tier, not $1,000,000. The premium is `$12,500 + ($1,350,000 × 1.5% = $20,250) = $32,750`, an effective rate of 1.770%* — not the $27,500 and 1.486% printed. Items (b), (c) and (d) are correct as printed.

The correction strengthens the chapter's own argument rather than weakening it. The spread between (a) and (d) becomes 1.770% − 0.820% = **0.950 percentage points**, and the small job pays 1.770 ÷ 0.820 = **2.16 times** as much per dollar of contract — about 116% more, not 81%. On that $1,850,000 job with a 4% fee of $74,000, the extra bond cost relative to the large-project rate is $32,750 − $15,170 = **$17,580**, roughly 24% of the entire fee. Bonding is more regressive than the printed number says.

2. Willow Street's general-conditions budget is $680,000 — one figure, everywhere. It is established in Chapter 13 and used unchanged in Chapters 1, 14, 17, 25, 27, 31, 33, 35, 36 and Appendix K: $680,000 over 425 CD = $1,600/CD, giving the $2,800/CD total daily exposure that is the Willow Street counterpart to Northgate's $10,650/CD. If an exercise ever fails to supply a rate, use those two numbers.

3. Northgate's general-conditions rate appears as two numbers, on purpose. `$2,900,000 ÷ 565 CD = $5,132.74`, which Chapter 1's C1 rounds to $5,132 and Chapter 33's C4 carries as $5,132.74. The contractually agreed extended-GC rate is $5,150/CD, and that is the number every exposure calculation in the book uses. They are not the same figure and neither is wrong: one is a quotient, the other is a contract term. When you are computing exposure, use $5,150.

4. Chapter 3, C4 does not reconcile — deliberately. The stated $19,600,000 GMP is $187,980 above the sum of its own stated components ($19,412,020). That is the exercise, not an error, and the printed answer says so. It is listed here so that you do not spend twenty minutes hunting for your own mistake.

5. Chapter 18, C2 uses the number 48 for two different things in consecutive lines — 48 SF per 4-foot by 12-foot sheet, and 48 sheets moved per crew-hour. Both are correct and the coincidence makes the solution hard to follow. Write the units next to each one and it resolves immediately: 268,000 SF ÷ 48 SF/sheet = 5,583 sheets, then 5,583 sheets ÷ 48 sheets/crew-hour = 116.3 crew-hours.

If you find an error in this appendix, you have done the exercise correctly. Write down the arithmetic that disagrees with mine, write down the assumption that separates us, and then decide which of us is right — because that is the entire skill this book is trying to teach, and it does not stop being the skill just because the number is printed in a book.