Estimating and Bidding: 16-Civ-B8 Management of Construction, May 2016, Q3

Question 3: Estimating and Bidding (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. Seven indirect-cost items totalling $60,800, incurred over a project duration of six months.

Given data — indirect costs incurred on a six-month project
Item	Description	Cost
1	Total cost of permits	$4,500
2	Crane rental	$17,000
3	Office secretary	$14,000
4	Cost of project utilities	$1,200
5	Mobilization cost	$8,300
6	Batch plant on site	$12,000
7	Site preparation for work	$3,800
Total indirect cost		$60,800

Find. A two-way classification of each item — project versus general overhead, and fixed versus variable — and a linear model $Y = aX + b$ of total indirect cost as a function of project duration, with the meaning of a and b explained.

Approach. Classify by attribution first (can the cost be charged to this one project, or does it belong to the company as a whole?), then by behaviour (does the cost accrue with elapsed time, or is it a one-time charge independent of duration?), and finally fit the linear model by making b the sum of the time-independent items and a the time-dependent items divided by the six-month duration.

Separate project overhead from general overhead. Project (job-site or field) overhead is indirect cost that is caused by and traceable to one project but not to any single item of permanent work; general (head-office or company) overhead is the cost of being in business at all, incurred whether or not this particular project exists, and recovered by distributing it across all projects as a percentage of direct cost or revenue. Applying that test: the permits are taken out for this project (item 1); the crane is rented for this site (2); the utilities serve this site (4); mobilization brings plant and personnel to this site (5); the batch plant is erected on this site (6); and the site preparation is done on this site (7). All six are project overhead. The office secretary (item 3) staffs the company office, serving every project and the pursuit of future work, and is therefore general overhead.
Separate fixed from variable indirect cost. In construction estimating the relevant independent variable for indirect cost is time, so “variable” means time-related — the charge continues to accrue for as long as the project runs — while “fixed” means a lump, one-time charge that does not change if the project is extended. Permits (item 1) are paid once at a scheduled fee; mobilization (5) and site preparation (7) are single events at the start; and the batch plant (6) is erected, used and dismantled, its cost set by the installation rather than by the calendar. These four are fixed, and they sum to $$b = 4{,}500 + 8{,}300 + 12{,}000 + 3{,}800 = \$28{,}600$$ The crane is rented by the month (2), the secretary is salaried by the month (3) and the utilities are metered monthly (4); these three are variable and sum to $$\text{variable total} = 17{,}000 + 14{,}000 + 1{,}200 = \$32{,}200$$ and the two groups reconcile to the given total, $b + \text{variable} = 28{,}600 + 32{,}200 = \$60{,}800$.
Convert the variable total into a monthly rate. The variable group accrued over the full six-month duration, so the rate per month is the group total divided by the duration: $$a = \frac{32{,}200}{6}$$ $$\boxed{a = \$5{,}366.67 \text{ per month}}$$
Write the indirect-cost equation. With X the project duration in months and Y the total indirect cost in dollars, $$Y = aX + b$$ $$\boxed{Y = 5{,}366.67\,X + 28{,}600}$$ Checking the model at the observed duration reproduces the data, which is the arithmetic proof that the split is complete and nothing has been double counted: $$Y(6) = 5{,}366.67 \times 6 + 28{,}600 = 32{,}200 + 28{,}600 = \$60{,}800 \;\checkmark$$
Explain the parameters. Y is the total indirect cost of the project in dollars, the amount that must be recovered by the mark-up applied to the direct estimate. X is the independent variable, here the project duration in months; the model is meaningful only over the range in which the same site establishment is maintained. a is the slope, the time-related indirect cost per month — the daily-cost or “standing cost” figure of $5,366.67 per month (about $176 per calendar day) that determines what an extension of time is worth. It is the number quoted when a delay claim is priced, and it is the number that makes acceleration worth paying for. b is the intercept, the time-independent indirect cost of $28,600 that is incurred even for a project of vanishing duration: it is the cost of establishing and removing the site, and it does not shrink if the work is compressed. The practical reading is that extending this project by one month adds $5,367 of indirect cost and no more, while a decision to mobilise at all costs $28,600 before a single month of standing time is counted.

Check: the batch plant (item 6) is treated here as a fixed charge, on the reading that the $12,000 is the cost of erecting and dismantling a plant installed for this job — the natural contrast with item 2, which the paper explicitly calls a rental. If instead the $12,000 is read as a monthly hire of the plant, it moves into the variable group and the model becomes $Y = 7{,}366.67\,X + 16{,}600$, which still reproduces $60,800 at X = 6 but roughly doubles the value of a month of delay. State the reading before pricing any extension of time.

Check: if the equation is wanted for project indirect cost only — that is, with the head-office secretary excluded and recovered instead as a company-wide percentage mark-up — then $a = (17{,}000 + 1{,}200)/6 = \$3{,}033.33$ per month, $b = \$28{,}600$, and $Y(6) = \$46{,}800$.

Final results — classification of the seven indirect-cost items
Item	Description	Cost	Project or general overhead	Fixed or variable
1	Total cost of permits	$4,500	Project	Fixed
2	Crane rental	$17,000	Project	Variable (per month)
3	Office secretary	$14,000	General	Variable (per month)
4	Cost of project utilities	$1,200	Project	Variable (per month)
5	Mobilization cost	$8,300	Project	Fixed
6	Batch plant on site	$12,000	Project	Fixed (see callout)
7	Site preparation for work	$3,800	Project	Fixed
Fixed total, b		$28,600
Variable total (6 months)		$32,200
Slope, a		$5,366.67 per month
Indirect-cost equation		Y = 5,366.67 X + 28,600 (X in months)
Check at X = 6		$60,800 = given total

Topic. Indirect-cost structure of a construction estimate: job overhead versus company overhead, and the time-dependent versus time-independent split that produces the linear indirect-cost model.

Key relations. $Y = aX + b$ with $b=\sum(\text{one-time charges})$ and $a=\sum(\text{time-related charges})/X_{\text{observed}}$; daily standing cost $= a/30.4$; bid price $=$ direct cost $+$ project overhead $+$ general-overhead recovery $+$ profit, with general overhead conventionally recovered as a percentage of direct cost.

Why this works. Indirect costs cannot be attached to a unit of permanent work, so they have to be attached to something else, and the only variable that reliably explains them is elapsed time on site: a crane, a trailer, a superintendent and a power drop all cost the same per month whether the month is productive or not. Splitting the total into a time-rate and a lump therefore captures almost all of the real behaviour with a one-parameter model, and it produces exactly the two numbers a construction manager needs — what a month of delay costs, and what it costs to be on the site at all. The distinction between project and general overhead is a different question, one of attribution rather than behaviour, and it matters because project overhead is estimated and recovered job by job whereas general overhead must be spread across the whole annual volume; a company that wins less work than planned under-recovers its general overhead no matter how well each project is run.

Common pitfall. The first error is to confuse the two classifications and to assume that project overhead is always variable and general overhead always fixed; mobilization is project overhead yet fixed, and the head-office salary is general overhead yet strictly time-related. The second is to compute the slope by dividing the total indirect cost by the duration, which prices the one-time charges as though they recurred every month and grossly inflates the value of a delay claim.

Source. Halpin & Senior, Construction Management, 4th ed., Ch. 5 (estimating: direct, indirect and overhead costs); Hendrickson, Project Management for Construction, 2nd ed., Ch. 5 (cost estimation).

Question 3 of 6: Estimating and Bidding

Question 3: Estimating and Bidding (20 marks)