16-Civ-B8 Management of Construction · May 2014

Question 1 of 6: Estimating and Bidding — RSMeans unit price and a re-priced crew

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

Notes on this paper

Paper format. National Exams, May 2014 — 98-Civ-B8 Management of Construction (the paper now catalogued as 16-Civ-B8). Three hours, closed book; one of two approved calculator models permitted. Six questions of equal value (20 marks each); the rubric states that any five constitute a complete paper and that only the first five presented in the answer book will be marked. All six are worked here, because this set is a study resource rather than an exam script.

Reference texts.

Halpin, D. W. and Senior, B. A., Construction Management, 4th ed., Wiley — unit-price estimating and crew productivity, precedence diagramming with lags, labour relations, project control.
Hendrickson, C. and Au, T., Project Management for Construction, 2nd ed. — Ch. 5 (cost estimation from productivity data), Ch. 10 (scheduling with activity relationships and resource constraints).
Project Management Institute, A Guide to the Project Management Body of Knowledge (PMBOK Guide) — §6.5 Develop Schedule (leads, lags, critical path, float), §7 Cost Management.
RSMeans, Building Construction Cost Data — front matter on crew tables, daily output, labour-hours per unit and the overhead-and-profit columns.
Fraser, N. M. et al., Global Engineering Economics: Financial Decision Making for Engineers, Canadian ed., Pearson — Ch. 3–4 (present worth, uniform series, deferred annuities).
Canadian Construction Documents Committee, CCDC 2 — Stipulated Price Contract (2020) — GC 6.5 delays and extensions of time; and Society of Construction Law, Delay and Disruption Protocol, 2nd ed. — concurrency, time-slice and as-built but-for analysis.
Hinze, J. W., Construction Safety, 2nd ed.; WorkSafeBC, Occupational Health and Safety Regulation (Parts 4, 8, 11, 18, 20) and the BC Ministry of Transportation Traffic Management Manual for Work on Roadways.

Question 1: Estimating and Bidding — RSMeans unit price and a re-priced crew (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. The printed RSMeans line and the crew D-7 table are the whole data set; the two cells marked “?” are what part (a) asks for.

Line 095 800 — item 0100 Wood composition gym floor (2014 bare costs, per m²)
Crew	Daily output	Labour-hours	Unit	Mat.	Labour	Equip.	Total	Total incl. O&P
D-7	13.94	?	m²	48.5	27	—	75.5	?

Crew D-7 — bare costs and costs including subcontractor overhead and profit
Crew D-7	Bare $/h	Bare $/day	Incl. O&P $/h	Incl. O&P $/day
1 Tile Layer	26.10	208.80	38.60	308.80
1 Tile Layer Helper	21.00	168.00	31.05	248.40
16 L.H., daily totals	—	376.80	—	557.20
Cost per labour-hour	23.55	—	34.83	—

Find. (a) The labour-hours per m² and the total unit price including overhead and profit for the published line; (b) for a 1250 m² job executed by a crew of three tile layers and two helpers at local bare wages of $30 and $23 per hour, the construction cost and the activity duration.

Approach. An RSMeans line item is internally self-checking: daily output multiplied by labour-hours per unit must equal the crew’s daily labour-hours, and labour-hours per unit multiplied by the crew’s bare cost per labour-hour must reproduce the printed labour column — so recover the crew size and shift length from the crew table first, fill the two missing cells from those identities, then re-price only the labour slice at local wages while material passes through untouched.

Recover the shift length and crew size the question never states. Each worker’s daily rate is exactly eight times the hourly rate, $\$208.80 / \$26.10 = 8.00$ h and $\$168.00 / \$21.00 = 8.00$ h, and the crew is one tile layer plus one helper, so $$\text{crew LH/day} = n_{\text{crew}} \times t_{\text{shift}} = 2 \times 8 = 16\ \text{LH/day},$$ which is precisely the “16 L.H., Daily Totals” line. The daily totals confirm it: $\$208.80 + \$168.00 = \$376.80$ and $\$376.80 / 16 = \$23.55$ per labour-hour bare, $\$557.20 / 16 = \$34.83$ per labour-hour including O&P.
First missing cell — labour-hours per unit. The crew delivers 13.94 m² in a day while expending 16 labour-hours, so $$LH_{\text{unit}} = \frac{\text{crew LH/day}}{\text{daily output}} = \frac{16}{13.94} = \boxed{1.148\ \text{LH/m}^2}.$$
Check that value against the printed labour column. Multiplying the recovered productivity by the bare cost per labour-hour must reproduce the labour cost RSMeans printed: $$c_{\text{lab}} = LH_{\text{unit}} \times r_{\text{bare}} = 1.1478 \times \$23.55 = \$27.03/\text{m}^2,$$ against the printed $27 — agreement to 0.1 %, which confirms both the 1.148 figure and the eight-hour, two-person reading of the crew.
Second missing cell — total including overhead and profit. The O&P columns are built up element by element, not by scaling the bare total. Labour carries the crew table’s own O&P rate, and material carries the standard RSMeans 10 % handling-and-profit allowance: $$c_{\text{lab}} = 1.1478 \times \$34.83 = \$39.98/\text{m}^2, \qquad c_{\text{mat}} = 1.10 \times \$48.50 = \$53.35/\text{m}^2.$$ There is no equipment component, so the total unit price including overhead and profit is $$\text{Total} = 53.35 + 39.98 = \boxed{\$93.33/\text{m}^2 \approx \$93.50/\text{m}^2}$$ as RSMeans would print it. Note that the labour markup is a ratio, $k = 34.83/23.55 = 1.47898$, and that scaling the whole bare total of $75.5 by that ratio would give $111.7 — wrong, because it would inflate material by 48 % instead of 10 %.
Part (b): capacity of the enlarged crew. Three tile layers plus two helpers is five workers on the same eight-hour shift, so $$\text{LH/day} = 5 \times 8 = 40\ \text{LH/day}, \qquad \text{daily output} = \frac{40}{1.1478} = \boxed{34.85\ \text{m}^2/\text{day}}.$$ Equivalently the published output scales with crew size, $Q_d = 13.94 \times 5/2 = 34.85$ m²/day — the two routes agree because productivity per labour-hour is what the RSMeans line actually measures.
Duration of the activity. With 1250 m² to place, $$D = \frac{Q}{\text{daily output}} = \frac{1250}{34.85} = 35.87\ \text{days} \Rightarrow \boxed{36\ \text{working days}}.$$ The same answer follows from the labour content: $Q\,LH_{\text{unit}} = 1250 \times 1.1478 = 1434.7$ LH divided by 40 LH/day is again 35.87 days. A partial final day cannot be sold to the owner as a half-day of crew time, so the estimate is rounded up.
Weighted local wage rate. The crew mix is not one-to-one any more, so the average cost of a labour-hour must be weighted by head count: $$r_{\text{local}} = \frac{3(\$30) + 2(\$23)}{5} = \frac{\$136}{5} = \boxed{\$27.20\ \text{per labour-hour}}.$$ Using a simple average of $30 and $23 ($26.50) would understate the labour cost by 2.6 %.
Labour cost, material cost, and the bare construction cost. Only the labour slice is re-priced; the material rate is a supplied-and-delivered price and is unaffected by local wages: $$C_{\text{lab}} = 1434.7\ \text{LH} \times \$27.20 = \$39\,024, \qquad C_{\text{mat}} = 1250 \times \$48.50 = \$60\,625,$$ $$C_{\text{bare}} = 39\,024 + 60\,625 = \boxed{\$99\,649 \approx \$99\,600\ \ (\$79.72/\text{m}^2)}.$$
Carry the markups if a sell price is wanted. Applying the same two markups recovered in step 4 — 1.47898 on labour and 1.10 on material — gives the price the activity would carry in a bid: $$C_{\text{sell}} = 60\,625(1.10) + 39\,024.39(1.47898) = 66\,688 + 57\,716 = \$124\,404 \ \ (\$99.52/\text{m}^2).$$ The bare figure is the correct answer to “construction cost”; this line is what the owner would see.

Check: three engineering assumptions carry these numbers. (i) Material overhead and profit is taken at the RSMeans standard 10 %, which is the convention the published O&P columns are built on but is not printed on this extract. (ii) Productivity per labour-hour is assumed unchanged when the crew is enlarged from two to five — on a gym floor of this size that is defensible, but crowding, a single grout-bed mixing station or a single material hoist would depress it, and a 10 % productivity loss would add about four days and $3,900. (iii) The local $30 and $23 are bare wages; statutory burden (CPP, EI, WorkSafeBC premiums, vacation pay) and small tools are not included and would typically add 25–35 % to the labour slice before profit.

Question 1 — results
Quantity	Value
(a) Labour-hours per unit	1.148 LH/m²
(a) Total including O&P	$93.33/m² (RSMeans would print $93.50)
(b) Crew capacity (3 layers + 2 helpers)	40 LH/day → 34.85 m²/day
(b) Activity duration for 1250 m²	35.87 → 36 working days
(b) Weighted local labour rate	$27.20 per labour-hour
(b) Labour cost / material cost	$39,024 / $60,625
(b) Bare construction cost	$99,649 ($79.72/m²)
(b) Price if RSMeans O&P markups are carried	$124,404 ($99.52/m²)

Topic. Unit-price estimating from published productivity data, and the adjustment of a published line item to local wages and a non-standard crew.

Key relations. Crew labour-hours per day $= n_{\text{crew}} t_{\text{shift}}$; labour-hours per unit $LH_{\text{unit}} = (\text{crew LH/day})/(\text{daily output})$; bare labour cost per unit $= LH_{\text{unit}} r_{\text{bare}}$; duration $D = Q/(\text{daily output})$; weighted crew rate $r = \sum n_i r_i / \sum n_i$; and the O&P transfer ratios (labour $r_{\text{O\&P}}/r_{\text{bare}}$, material 1.10).

Why this works. A published line item does not record a price so much as a productivity: the pairing of daily output with labour-hours per unit fixes how much human effort a square metre of finished work absorbs, and that quantity is portable between cities in a way that a dollar figure is not. Everything else in the line is arithmetic on top of it. Because the crew table also prints both a bare and an O&P cost per labour-hour, the two are locked into a fixed ratio, and that ratio — not any absolute dollar amount — is what travels when the wages change. Re-pricing therefore touches exactly one term, $LH_{\text{unit}} \times r$, and leaves material and equipment alone. The same identity run backwards is the estimator’s audit: if $LH_{\text{unit}} r_{\text{bare}}$ does not reproduce the printed labour column, either the crew has been misread or the line has been transcribed wrongly.

Common pitfall. Two errors dominate. The first is scaling the whole bare total by the wage ratio, which silently inflates the material component — here it would turn $75.5 into $111.7 instead of $93.3. The second is averaging the two local wages instead of weighting them by head count, which for a 3:2 crew mix misprices every labour-hour by seventy cents. A third, subtler error is assuming that adding people shortens the job in proportion without asking whether the work face, the material supply or the setting bed can absorb the extra hands.

Source. Halpin & Senior, Construction Management, 4th ed., Ch. 6–7 (labour productivity and unit-price estimating); Hendrickson & Au, Project Management for Construction, 2nd ed., Ch. 5 §5.4–5.6; RSMeans Building Construction Cost Data, “How to Use the Cost Data” front matter (crew tables, daily output, the O&P columns).

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