16-Civ-B8 Management of Construction · December 2016

Question 6 of 6: Estimating

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

Notes on this paper

Paper format. 98-Civ-B8 Management of Construction, National Exams December 2016. Three hours, closed book, one approved calculator (Casio or Sharp). Six questions of equal value (20 marks each); any five constitute a complete paper and only the first five presented in the answer book are marked. All six are solved here, because the set is a study resource rather than an examination script.

Reference texts.

Halpin & Senior, Construction Management, 4th ed. — precedence networks with lags, bonding, project control.
Hendrickson, Project Management for Construction, 2nd ed. — scheduling, cost control, earned value, financing of constructed facilities.
Project Management Institute, A Guide to the Project Management Body of Knowledge (PMBOK Guide), 6th ed. — schedule and cost management, earned value.
Fraser et al., Global Engineering Economics, 5th Canadian ed. — present worth, deferred annuities, maximum justifiable investment.
Canadian Construction Documents Committee: CCDC 2 (stipulated price), CCDC 4 (unit price), CCDC 14 (design-build), CCDC 3 (cost-plus), CCDC 23 Guide to Calling Bids and Awarding Contracts; CCDC 220 / 221 / 222 bond forms.
Builders Lien Act (British Columbia, RSBC 1997 c. 45) and the provincial construction-lien / prompt-payment statutes; RSMeans Residential Square Foot Costs.

Question 6: Estimating (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 R.S. Means “Residential / Average / 2 Story” square-foot cost model printed on page 3 of the paper, together with the specification of the house to be priced.

Given data — the two table rows that apply, in dollars per square foot of living area
Living area (SF)	2,000	2,200	2,500	2,600	3,000
Solid Masonry exterior wall	74.00	71.85	required	67.30	63.15
Finished Basement, Add	10.25	10.05	required	9.70	9.45

The house to be priced is a two-storey single-family dwelling of average quality, 2,500 SF of living area, solid masonry exterior wall, with a finished basement. The base model excludes a basement, which is why the basement appears as an additive adjustment rather than in the base rate.

Find. The estimated construction cost of the house.

Approach. Select the correct row of the square-foot table for the specified exterior wall, interpolate linearly between the two living-area columns that bracket 2,500 SF, add the finished-basement adjustment interpolated the same way, and multiply the combined rate by the living area.

Locate the position of 2,500 SF between the table columns. The table jumps from 2,200 SF to 2,600 SF, so 2,500 SF must be interpolated. The interpolation fraction is $$f = \frac{2{,}500-2{,}200}{2{,}600-2{,}200} = \frac{300}{400} = 0.75,$$ that is, three-quarters of the way from the 2,200 column to the 2,600 column.
Interpolate the base cost on the Solid Masonry row. Reading 71.85 at 2,200 SF and 67.30 at 2,600 SF: $$C_{\text{base}} = 71.85 + 0.75\,(67.30 - 71.85) = 71.85 - 3.4125 = \$68.44 \text{ per SF} .$$ Note that the rate falls as the house grows — fixed elements such as the kitchen, mechanical plant and service connections are spread over more area — so interpolating in the right direction matters.
Interpolate the finished-basement adjustment the same way. Reading 10.05 at 2,200 SF and 9.70 at 2,600 SF: $$C_{\text{bsmt}} = 10.05 + 0.75\,(9.70 - 10.05) = 10.05 - 0.2625 = \$9.79 \text{ per SF} .$$ The unfinished-basement line (3.60 and 3.35 in the same columns) is not used, because the specification calls for a finished basement.
Combine into a single adjusted square-foot rate. The adjustments in this Means model are expressed per square foot of living area, so they add directly to the base rate: $$C_{\text{unit}} = C_{\text{base}} + C_{\text{bsmt}} = 68.44 + 9.79 = \$78.23 \text{ per SF} .$$
Multiply by the living area to obtain the estimate. Carrying the unadjusted values 68.4375 and 9.7875 through the multiplication to avoid a rounding drift: $$C_{\text{total}} = 78.225 \times 2{,}500$$ $$\boxed{C_{\text{total}} = \$195{,}562.50 \;\approx\; \$195{,}600}$$
Confirm the split and bracket the answer. The base structure accounts for $68.4375 \times 2{,}500 = \$171{,}093.75$ and the finished basement for $9.7875 \times 2{,}500 = \$24{,}468.75$, which sum exactly to the boxed total. As a bracket, the same house priced at the 2,200 SF rate would be $(71.85+10.05)\times 2{,}500 = \$204{,}750$ and at the 2,600 SF rate $(67.30+9.70)\times 2{,}500 = \$192{,}500$; the answer lies properly between them and much closer to the 2,600 end, as the interpolation fraction of 0.75 requires.

Check: two conventions for applying the basement adjustment. The interpretation used above — and the one the printed table supports, since its caption reads “Base cost per square foot of living area” and the basement lines sit inside that table under the same living-area columns — applies the $9.79 to the full 2,500 SF of living area. An alternative sometimes taught applies the basement add to the basement’s own footprint, which for a two-storey house of 2,500 SF living area is 1,250 SF, giving $171{,}093.75 + 9.7875\times 1{,}250 = \$183{,}328$. State whichever convention is being used and show the arithmetic; the marks are in the method and the interpolation, not in the convention. Note also that this is a bare square-foot estimate: a real Means estimate would then be adjusted by the city cost index for the location and escalated from the manual’s base date, and would exclude land, site servicing beyond the standard allowance, permits and financing.

Question 6 — results
Quantity	Value
Interpolation fraction between the 2,200 and 2,600 SF columns	0.75
Base cost, Solid Masonry at 2,500 SF	$68.44 per SF
Finished Basement, Add at 2,500 SF	$9.79 per SF
Adjusted rate	$78.23 per SF
Base structure component	$171,093.75
Finished basement component	$24,468.75
Estimated cost of the house	$195,562.50

Topic. Square-foot (order-of-magnitude) estimating from a published cost model, with linear interpolation and additive adjustments.

Key relations. Interpolation $C = C_1 + \dfrac{x-x_1}{x_2-x_1}(C_2-C_1)$; adjusted rate $C_{\text{unit}} = C_{\text{base}} + \sum C_{\text{adj}}$; estimate $= C_{\text{unit}} \times A$. A complete Means estimate then applies the location (city cost) index and time escalation: $C_{\text{local}} = C_{\text{total}} \times \text{CCI}/100 \times (1+e)^{t}$.

Why this works. Square-foot models are conceptual estimates built by regression over completed projects of a defined type and quality. They work because construction cost per unit of floor area is strongly conditioned by a small number of parameters — occupancy, quality, storeys, exterior wall system and total size — and only weakly by the rest of the design. The size effect is real and systematic: fixed elements (one kitchen, one heating plant, one service entry) are spread over more area as the house grows, so the rate declines with size, which is exactly the trend the table shows and the reason interpolation rather than extrapolation is safe. Accuracy of this class of estimate is on the order of ±15 to 20 per cent, adequate for feasibility and budget setting but not for tendering.

Common pitfall. Reading the wrong wall row — the Wood Siding row at 2,500 SF would give $59.21 per SF and understate the estimate by about $23,000; picking the nearest column instead of interpolating; adding the unfinished-basement line when the specification says finished; and interpolating in the wrong direction, which is easy to do because the numbers decrease left to right. Rounding each rate to the cent before multiplying is harmless here but is a habit worth avoiding on larger areas.

Source. RSMeans, Residential Square Foot Costs (square-foot cost models, residential 2-storey section, and the modifications / adjustments tables); Halpin & Senior, Construction Management, 4th ed., Ch. 12 (estimating); Hendrickson, Project Management for Construction, 2nd ed., Ch. 5.

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