07-Str-B2 · December 2018

Question 6 of 6: Estimating — completing an R.S. Means brick-veneer line and pricing the job

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

Paper format: National Exams, December 2018 — 07-Str-B2 Management of Construction. Three hours, closed book, one approved Casio or Sharp calculator permitted. Six questions of equal value (20 marks each); any five constitute a complete paper and only the first five that appear in the answer book are marked. All six are worked below so the paper serves as a complete revision set whichever five a candidate elects.

Reference texts: Hegazy, T., Computer-Based Construction Project Management (Prentice Hall) — activity-on-arrow and activity-on-node networks, forward and backward passes, total and free float, and the contractor cash-flow / overdraft model with mark-up, retention and payment lag; these chapters carry Questions 1 and 3. Hendrickson, C. & Au, T., Project Management for Construction (2nd ed., Carnegie Mellon) — Chapter 5 (cost estimation and unit-cost data), Chapter 8 (construction contracts and the allocation of risk), Chapter 10 (fundamental scheduling procedures) and Chapter 12 (cost control, monitoring and accounting, including project financing). Halpin, D.W. & Senior, B.A., Construction Management (4th ed., Wiley) — delivery systems, crew productivity and quantity take-off, surety bonding and lien law. R.S. Means, Building Construction Cost Data (annual) — the anatomy of a unit-price line (crew, daily output, labour-hours per unit, bare material / labour / equipment / total, and total including overhead and profit) and of the related crew table, behind Question 6. Sullivan, W.G., Wicks, E.M. & Koelling, C.P., Engineering Economy (17th ed., Pearson) — Chapters 4 and 5, the uniform-series present-worth factor and deferred annuities, used in Question 4. Canadian Construction Documents Committee, CCDC 2 Stipulated Price Contract (2020), CCDC 4 Unit Price Contract, CCDC 3 Cost Plus Contract, CCDC 14 Design-Build Stipulated Price Contract, and CCDC 220 Bid Bond, CCDC 221 Performance Bond and CCDC 222 Labour and Material Payment Bond — the Canadian contract and surety machinery behind Questions 2 and 5. Provincial lien statutes — the British Columbia Builders Lien Act (SBC 1997 c.45) and the Ontario Construction Act (RSO 1990 c.C.30, as amended 2018) — supply the Canadian equivalent of the American “mechanics lien” named in Question 5.

Check — how the two printed figures on page 2 were read. Network (Question 1): nine numbered event circles and eleven arrows, every arrow carrying a letter and a duration — A(4) 1→2, B(6) 1→4, C(2) 1→7, D(8) 2→3, E(4) 3→6, F(10) 4→5, G(16) 4→8, H(8) 5→6, I(6) 6→9, J(6) 7→8, K(10) 8→9. There is no dummy arrow on this drawing, so the translation to activity-on-node in part (c) is exact and needs no extra logic. Budget S-curve (Question 3): the six labelled markers fall squarely on months 1 to 6 of the printed axis (ticks 0 to 7). The project therefore runs six months and the budget (cost) at completion is $127,000.

Question 6: Estimating — completing an R.S. Means brick-veneer line and pricing the job (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. One R.S. Means unit-price line and its related crew table, with a quantity of work and a labour overhead-and-profit rate:

Data taken from the printed tables and the question stem
Item	Value
Quantity of brick veneer	6,000 S.F.
Labour-hours per unit (printed)	0.129 L.H./S.F.
Bare material cost (printed)	$3.54 / S.F.
Book crew D-8	3 bricklayers at $35.25/h + 2 helpers at $26.90/h = 40 L.H./day
Local wages printed beside the crew rows	bricklayer $40/h, helper $30/h (bare)
Labour overhead and profit	60 per cent on the bare labour rate
Crew actually used on the job	5 bricklayers + 3 helpers, 8 h/day

Find. The missing cells of both printed tables, and then the duration and total cost of laying 6,000 S.F. with a crew of five bricklayers and three helpers.

Approach. Everything on an R.S. Means line hangs off one invariant — the labour-hours per unit — so recover the crew's cost per labour-hour from the wage table, use it to fill the labour and total columns of the unit line, back out the daily output from the crew day, and then re-apply the same labour-hours per unit to the larger job crew, whose wages replace the book rates.

Check — how the two round figures in the crew table are read. The printed crew table shows $40 and $30 in the Bare Daily column beside the bricklayer and helper rows. They cannot be daily crew costs: three bricklayers at $35.25 per hour for eight hours is $846.00 a day, not $40, and 60 per cent overhead and profit on $35.25 gives $56.40 an hour, not $40 either. They are read here as the local bare hourly wages to be used for the crew the question tells you to employ. The local-to-book ratios are 40/35.25 = 1.135 and 30/26.90 = 1.115. Both readings are carried below — the book tables are completed with the printed $35.25 and $26.90, and the job is then priced at the local $40 and $30, with the book-rate figure given as a cross-check at Step 7.

Establish the crew day and its bare cost. Crew D-8 is three bricklayers and two helpers, five workers at eight hours, which is the printed “40 Total Hours”. Its bare daily cost is the sum of the two trade lines: $$3\times35.25\times8=846.00,\qquad 2\times26.90\times8=430.40$$ $$\text{Bare daily total}=846.00+430.40=1{,}276.40\ \text{dollars}$$ Dividing by the 40 labour-hours in that day gives the figure the unit line actually needs: $$\text{bare cost per L.H.}=\frac{1{,}276.40}{40}=31.91\ \text{dollars/L.H.}$$
Apply the 60 per cent overhead and profit to labour. The question fixes labour O&P at 60 per cent, so each trade's billing rate is its bare rate multiplied by 1.60: $$35.25\times1.60=56.40\ \text{dollars/h},\qquad 26.90\times1.60=43.04\ \text{dollars/h}$$ giving daily figures of $3\times56.40\times8=1{,}353.60$ and $2\times43.04\times8=688.64$ dollars, a crew daily total of $2,042.24, and hence $$\text{cost per L.H. incl. O\&P}=\frac{2{,}042.24}{40}=51.06\ \text{dollars/L.H.}$$ which is of course $31.91\times1.60$ — the multiplier survives the averaging because it is applied to every trade alike.
Recover the daily output. Daily output and labour-hours per unit are two views of the same productivity, tied together by the crew day: $$\text{Daily output}=\frac{\text{crew L.H. per day}}{\text{L.H. per unit}}=\frac{40}{0.129}=310.1$$ $$\boxed{\text{Daily Output}=310\ \text{S.F./day}}$$ This is the cell the printed table leaves blank, and recovering it rather than guessing it is the whole trick of the question.
Fill the bare cost columns of the unit line. Bare labour per square foot is the labour-hours per unit priced at the crew's bare rate: $$\text{Labor}=0.129\times31.91=4.12\ \text{dollars/S.F.}$$ Crew D-8 contains no equipment, so the equipment column is nil, and the bare total is $$\text{Total}=3.54+4.12+0=7.66\ \text{dollars/S.F.}$$
Fill the Total Incl. O&P column. The two components are marked up differently: the labour rate already carries its 60 per cent, while material carries the standard 10 per cent handling and profit allowance R.S. Means applies to purchased materials. Hence $$\text{Total incl. O\&P}=1.10\times3.54+0.129\times51.06=3.894+6.586$$ $$\boxed{\text{Total incl. O\&P}=10.48\ \text{dollars/S.F.}}$$ Both printed tables are now complete; the filled values are collected in the results table below.
Size the job with the crew the question specifies. Labour-hours per unit is a property of the work, not of the crew, so it carries straight over to a crew of five bricklayers and three helpers: $$H=6{,}000\times0.129=774\ \text{labour-hours}$$ $$\text{crew day}=(5+3)\times8=64\ \text{L.H./day}$$ $$\text{Duration}=\frac{774}{64}=12.09\ \text{days}$$ $$\boxed{\text{Duration}\approx12.1\ \text{days, i.e. 13 working days on site}}$$ The larger crew has raised the daily output to $64/0.129=496$ S.F./day from the book's 310, and $6{,}000/496=12.1$ days confirms the duration from the other direction.
Price the job at the local wages. The blended bare rate for a crew of five bricklayers at $40 and three helpers at $30 is $$\bar{w}=\frac{5\times40+3\times30}{8}=\frac{290}{8}=36.25\ \text{dollars/L.H.}$$ and with 60 per cent overhead and profit, $36.25\times1.60=58.00$ dollars per labour-hour. The two cost components are then $$\text{Labour}=774\times58.00=44{,}892\ \text{dollars}$$ $$\text{Material}=6{,}000\times3.54\times1.10=21{,}240\times1.10=23{,}364\ \text{dollars}$$ $$\boxed{\text{Total cost incl. O\&P}=44{,}892+23{,}364=68{,}256\ \text{dollars}}$$ that is $11.38 per square foot, against the book line's $10.48 — the difference being entirely the dearer local labour. Priced instead at the book crew rates the same job would come to $6{,}000\times10.48=62{,}881$ dollars, which is the cross-check that Steps 5 and 7 are internally consistent. The bare cost, before any overhead and profit, is $774\times36.25+21{,}240=49{,}298$ dollars.

Question 6 — completed R.S. Means tables and job estimate
Item	Value
Crew D-8, bare daily cost	$1,276.40 (846.00 + 430.40)
Crew D-8, daily cost incl. O&P	$2,042.24 (1,353.60 + 688.64)
Bricklayer / helper hourly rate incl. O&P	$56.40 / $43.04
Cost per labour-hour, bare / incl. O&P	$31.91 / $51.06
Daily Output (unit line)	310 S.F./day
Bare Labor / Equip / Total per S.F.	$4.12 / nil / $7.66
Total $/S.F. incl. O&P	$10.48
Total labour-hours for 6,000 S.F.	774 L.H.
Duration with 5 bricklayers + 3 helpers	12.1 days (13 working days)
Blended local rate, bare / incl. O&P	$36.25 / $58.00 per L.H.
Labour / material cost incl. O&P	$44,892 / $23,364
Total job cost incl. O&P	$68,256 ($11.38 per S.F.)

Topic. Unit-price estimating from R.S. Means data: labour-hours per unit, crew cost per labour-hour, daily output, and the conversion of a book line into a job-specific cost and duration.

Key relations. Daily output $=\dfrac{\text{crew L.H. per day}}{\text{L.H. per unit}}$; bare cost per labour-hour $=\dfrac{\text{crew bare daily cost}}{\text{crew L.H. per day}}$; bare labour per unit $=$ L.H./unit $\times$ bare cost per L.H.; total incl. O&P per unit $=1.10\times$ material $+$ L.H./unit $\times$ (cost per L.H. incl. O&P); duration $=\dfrac{\text{quantity}\times\text{L.H. per unit}}{\text{workers}\times8}$.

Why this works. An R.S. Means line is fully determined by three numbers — labour-hours per unit, material cost per unit, and the crew — so any one blank cell can always be recovered from the others. Labour-hours per unit is the productivity constant: it says how much human effort the work absorbs and is independent of how many people are applied to it or what they are paid. Daily output is the same constant expressed against a particular crew day, which is why doubling the crew doubles the output and halves the duration but leaves the labour cost per unit unchanged. Wages enter only through the cost per labour-hour, which is why substituting local rates for book rates re-prices the job without touching the quantity of effort or the schedule. The asymmetric mark-up — 60 per cent on labour, 10 per cent on material — reflects what the two components actually consume: labour carries payroll burden, supervision, small tools and the contractor's profit, whereas purchased material carries only handling and a thin margin.

Common pitfall. The largest single error is applying the 60 per cent to the whole unit cost, material included, which over-states the Total Incl. O&P by about $1.77 per square foot here. The next is assuming that a bigger crew somehow works faster per person — labour-hours per unit is invariant, and only the calendar shrinks. A third is to leave the answer as a fractional 12.09 days: crews are mobilised in whole days, so 13 working days is the schedulable figure, and the estimator should say which is which. Finally, always cross-check the recovered daily output against the crew day (40 divided by 0.129 must land back on 310) before carrying it into a schedule — a mis-read daily output is the one error in this family of questions that propagates into both the cost and the duration.

Source. R.S. Means, Building Construction Cost Data, “How to Use the Cost Data” front matter (crew tables, daily output, bare costs and Total Incl. O&P) and Division 04 Masonry unit-price lines; Hendrickson & Au, Project Management for Construction, Chapter 5 (Cost Estimation), sections on unit-cost methods and labour productivity; Halpin & Senior, Construction Management, chapters on estimating and crew-based productivity.

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