07-Str-B2 · May 2016

Question 3 of 6: Estimating and Bidding — indirect-cost classification and the total-indirect-cost equation

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

Notes on this paper

Paper format: National Exams, May 2016 — 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 answered are marked. All six are worked below so that the paper can be used for revision whichever five a candidate chooses.

Reference texts: Hegazy, T., Computer-Based Construction Project Management (Prentice Hall) — precedence networks with lags, total and free float, project overhead versus general overhead, and the bar-chart/S-curve control method behind Questions 1, 3 and 6; Hendrickson, C. & Au, T., Project Management for Construction (2nd ed., Carnegie Mellon) — Chapters 5 (cost estimation), 10 (scheduling) and 12 (cost control, monitoring and accounting), the source of the earned-value quantities used in Question 6; Halpin, D.W. & Senior, B.A., Construction Management (4th ed., Wiley) — competitive bidding, unbalanced bids, indirect-cost structure and construction safety; Sullivan, W.G., Wicks, E.M. & Koelling, C.P., Engineering Economy (17th ed., Pearson) — Chapters 5 and 6, present-worth analysis and the repeatability assumption for alternatives with unequal lives, used in Question 4; Peurifoy, R.L. & Oberlender, G.D., Estimating Construction Costs (6th ed., McGraw-Hill) — job overhead versus general overhead; Canadian Construction Documents Committee, CCDC 2 — Stipulated Price Contract (2020) and CCDC 23 — A Guide to Calling Bids and Awarding Contracts — bid-call practice, bid security and award criteria for Question 2; Ron Engineering (M.J.B. Enterprises line of cases) as summarised in Goldsmith, I. & Heintzman, T.G., Goldsmith on Canadian Building Contracts (5th ed., Thomson Reuters) — the Contract A/Contract B doctrine that governs a Canadian public bid call; WorkSafeBC, Occupational Health and Safety Regulation (Parts 4, 8, 11, 13, 18, 19 and 20) and the BC Workers Compensation Act, together with CSA Z259 (fall protection), CSA Z94.4 (respirators) and CSA W117.2 (welding safety) — the Canadian rule set behind Question 5.

Question 1 (network). Every activity letter and duration is printed inside its box and reads cleanly. The link routing was traced at high magnification: Start feeds A, D and G; a riser from the right edge of D feeds B; the horizontal link D → E carries the only labelled lag on the sheet, FS 6; a riser from the right edge of G feeds E; G also feeds H, H feeds I, A feeds B, B feeds C, E feeds F; and C, F and I terminate at End. Every unlabelled arrow is an ordinary finish-to-start link with zero lag, which is the only reading consistent with the drawing.

Question 6 (bar chart). Every percentage label falls on a week boundary, so the printed figures are cumulative percent complete at each week end. Planned: A 20/60/100 in weeks 1–3; B 10/80 in weeks 1–2, finishing in week 3; C 20/70 in weeks 3–4, finishing in week 5. Actual: A 10/50/90 in weeks 1–3, its bar closing in week 4; B 70 at week 2, its bar closing in week 3; C 50 at week 3, its bar closing exactly on the week-4 gridline. A bar that closes is read as 100 % complete from that week end onward, which is the standard convention and the only reading that lets part (c) be answered at all.

Question 3: Estimating and Bidding — indirect-cost classification and the total-indirect-cost equation (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 incurred over a project duration of six months.

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
Project duration X		6 months

Find. Each item classified twice — project versus general overhead, and fixed versus variable — then the total indirect cost expressed as $Y=aX+b$ with both parameters explained.

Approach. The two classifications answer different questions and must be kept apart: project versus general overhead asks which cost object bears the cost, while fixed versus variable asks whether the cost grows with project duration. Once the second classification is made, the duration-dependent items divided by the six-month duration give the slope $a$ and the duration-independent items give the intercept $b$.

Apply the project-versus-general test. A cost is project (job) overhead if it is incurred because this particular project exists and can be charged directly to it, even though it cannot be traced to any single work item; it is general (head-office) overhead if it supports the company as a whole and must be recovered across all projects by an allocation. Permits, crane rental, project utilities, mobilisation, the on-site batch plant and site preparation all fail to exist if this project is cancelled, so all six are project overhead. The office secretary is a head-office salary that continues between projects and serves every job the firm runs, so it is general overhead, allocated to this project for the six months it was in progress.
Apply the fixed-versus-variable test. Here the discriminator is whether extending the project by one month adds cost. Permits are bought once for the work regardless of how long it takes; mobilisation is a single move-in event; site preparation is a one-time physical operation; and erecting, commissioning and later dismantling the on-site batch plant is likewise a one-time undertaking. These four are fixed. Crane rental accrues monthly for as long as the crane is on site, the secretary is paid monthly, and utilities are metered monthly, so these three are variable — strictly, time-dependent.
Total the fixed group to obtain the intercept. Summing the duration-independent items: $$ b=4{,}500+8{,}300+12{,}000+3{,}800 $$ $$ \boxed{b = \$28{,}600} $$ This is the indirect cost the project would still incur if it could somehow be executed in zero time.
Total the variable group and convert it to a monthly rate. The three time-dependent items sum to $$ \sum C_{\text{var}}=17{,}000+14{,}000+1{,}200=\$32{,}200 $$ over the six months the project actually ran, so the slope is that total divided by the duration: $$ a=\frac{\sum C_{\text{var}}}{X}=\frac{32{,}200}{6} $$ $$ \boxed{a = \$5{,}366.67\ \text{per month}} $$ Item by item this is $2,833.33/month for the crane, $2,333.33/month for the secretary and $200.00/month for utilities.
Write and check the equation. The total indirect cost as a function of project duration is $$ Y = 5{,}366.67\,X + 28{,}600 $$ Substituting the actual duration $X=6$ months recovers the sum of all seven items, which is the arithmetic check on the whole classification: $$ Y(6)=5{,}366.67\times 6+28{,}600=32{,}200+28{,}600=\$60{,}800 $$ and indeed the seven items sum to $4{,}500+17{,}000+14{,}000+1{,}200+8{,}300+12{,}000+3{,}800=60{,}800$ dollars.
Explain the parameters. $Y$ is the total indirect cost of the project in dollars. $X$ is the project duration in months — the independent variable, and the reason the equation is useful at all. $a$ = $5,366.67 per month is the time-related or marginal indirect cost: it is what one extra month of project duration costs the contractor in overhead alone, and it is the number that belongs in a time–cost trade-off, a delay claim for extended overhead, or a liquidated-damages negotiation. $b$ = $28,600 is the duration-independent indirect cost: the one-time charges that are incurred whatever the schedule, and which therefore cannot be recovered by accelerating. The practical reading is that crashing this project saves $5,366.67 per month saved, and no more — a crash that costs more than that per month is not worth doing on overhead grounds alone.

Final Results — Question 3
Item	Cost	Project or general overhead	Fixed or variable	Contribution
1 — Total cost of permits	$4,500	Project	Fixed	to $b$
2 — Crane rental	$17,000	Project	Variable	$2,833.33/month
3 — Office secretary	$14,000	General	Variable	$2,333.33/month
4 — Cost of project utilities	$1,200	Project	Variable	$200.00/month
5 — Mobilization cost	$8,300	Project	Fixed	to $b$
6 — Batch plant on site	$12,000	Project	Fixed	to $b$
7 — Site preparation for work	$3,800	Project	Fixed	to $b$
Slope $a$ (time-related overhead)	$5,366.67 per month (= $32,200 ÷ 6 months)
Intercept $b$ (one-time overhead)	$28,600
Total indirect cost equation	$Y = 5{,}366.67\,X + 28{,}600$, $X$ in months
Check at $X=6$	$60,800 = sum of the seven listed items

Check — the batch plant is treated as a one-time cost. "Batch plant on site $12,000" is read here as the erection, commissioning and dismantling of a plant the contractor owns, which is a mobilisation-type event and therefore fixed. If the intent were a monthly rental of the plant, the item moves to the variable group and the equation becomes $Y = 7{,}366.67\,X + 16{,}600$, with $a = 44{,}200 \div 6$ and $b = 16{,}600$ dollars; the total at $X=6$ is still $60,800. State whichever reading you adopt — the marks are for the classification logic and the correct construction of $a$ and $b$, not for the reading itself.

Topic. Indirect-cost structure: job overhead versus general overhead, and the linear time–cost model of indirect cost.

Key relations. $Y=aX+b$ with $a=\left(\sum C_{\text{time-dependent}}\right)/X_{\text{actual}}$ and $b=\sum C_{\text{one-time}}$; total bid price $=$ direct cost $+$ project overhead $+$ allocated general overhead $+$ profit; the daily or monthly indirect rate $a$ is the quantity compared against crash cost in a time–cost trade-off.

Why this works. Overhead behaves in two fundamentally different ways, and lumping them together destroys the information a manager needs. Costs tied to an event — buying a permit, moving in, clearing a site — are incurred once and are indifferent to how long the job runs; costs tied to presence on site accrue at a rate for as long as the project is open. Separating them into an intercept and a slope turns a static list of expenses into a model with predictive power: it prices an extra month of duration, which is exactly the number needed to evaluate acceleration, to quantify an extended-overhead claim, and to set liquidated damages that bear some relation to the owner's and contractor's real exposure. The project-versus-general split answers a different question — recoverability. Project overhead can be charged to this contract directly; general overhead has to be recovered through a percentage mark-up spread across the firm's whole workload, which is why under-recovery of head-office overhead is a common cause of contractor insolvency in a downturn.

Common pitfall. The most common error is collapsing the two classifications into one and assuming project overhead is variable while general overhead is fixed. They are independent: the crane is project overhead and variable, the permits are project overhead and fixed, and the head-office secretary here is general overhead and variable with duration. The second error is computing $a$ from the total of all seven items rather than from the time-dependent subset only, which double-counts the fixed costs and destroys the check at $X=6$. The third is quoting $a$ without units; "5,366.67" is meaningless unless it is stated as dollars per month.

Source. Peurifoy & Oberlender, Estimating Construction Costs, Chapter 4 (job overhead and general overhead); Hegazy, Computer-Based Construction Project Management, Chapter 4 (cost estimating and the indirect-cost model); Halpin & Senior, Construction Management, Chapter 11 (project cost structure and mark-up).

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