Estimating for engineers

An engineer's estimate does several jobs at once. Early in a project it tells the owner whether the project is affordable and how much to budget. At tender it is the yardstick against which bids are judged, and the basis for deciding whether to award or retender. During construction it is the reference for pricing changes. Engineers who prepare estimates for owners do not need the full apparatus of a contractor's estimating department, which CON-200 and CON-300 cover in detail, but they do need to know how a contractor builds a price, where the uncertainty lies, and how to express that uncertainty honestly.

Estimate classes

Estimates are classified by the maturity of the design they are based on. The classification published by AACE International, widely used in North America, runs from Class 5, a concept screening estimate made with almost no design, to Class 1, a check estimate or bid made from complete documents. Each class has an expected accuracy range, wide and skewed upward for early estimates, narrowing as the design matures. The ranges are wider than many owners assume: a Class 5 estimate might be 50 % low or 100 % high. Early estimates are wrong more often by being too low than too high, because the unknown scope is mostly additional scope.

Conceptual and parametric estimates

At the concept stage of the Ridgeway project, two years earlier, Kestrel Bay used historical costs from the city's recent road contracts: about CAD 3.5 million per kilometre for full urban reconstruction with storm sewers, plus separate allowances for the culvert, the wall and the roundabout. That Class 4 estimate, about CAD 7 million for construction, was enough to put the project in the capital plan. Parametric estimates of this kind work when the historical projects are similar and the costs are brought to the same date with a construction price index; they fail when the new project has unusual features, such as soft ground, which the historical average hides.

How a contractor builds a unit price

A contractor prices each item from its components. Direct costs are labour, equipment and materials, calculated from the crew, its production rate and the quantity. Subcontract prices are added for work the contractor does not self-perform. Then come indirect costs: the site office, supervision, temporary facilities, small tools, insurance and bonds, often called general conditions or site overhead. Finally the contractor adds home office overhead and profit. In a unit-price bid, all of these are spread over the unit prices, so a unit price for excavation includes a share of the superintendent's wages and the company's profit.

Production rates drive the estimate. The same excavator moves far less soft wet clay than dry sand, and a crew that must stop for traffic every few minutes is slower than one working in a closed road. This is why the engineer's estimate should be built with the site in mind, not just from a price book: the varved clay, the two-stage traffic plan, the narrow working strip along the wall and the in-water work window all reduce production and raise costs.

The Ridgeway engineer's estimate

The Class 1 engineer's estimate for the tender follows the 16 items of the bid form. Quantities come from the takeoff of the final drawings, done by Sofia and checked by Owen. Unit prices come from recent city tenders, adjusted for date and site conditions, and from first-principles pricing of the items with no good history: the box culvert, the cofferdam and the retaining wall. A 5 % allowance covers mobilization, bonds and insurance, which the bid form carries as a separate lump sum.

# Engineer's estimate for the Ridgeway Road East and Kestrel Creek crossing contract,
# then a Monte Carlo range for the contingency
import random
UNITS = "SI"
SI = UNITS == "SI"
CUR = "CAD" if SI else "USD"
# item, unit, quantity, unit price  (unit prices include the contractor's overhead and profit)
if SI:
    items = [("Traffic control and staging", "LS", 1, 420000), ("Asphalt and curb removals", "m2", 9800, 9.0),
             ("Earth excavation", "m3", 14500, 21.0), ("Granular subbase", "m3", 4600, 55.0),
             ("Granular base", "m3", 2300, 72.0), ("Hot-mix asphalt, two lifts", "m2", 11500, 42.0),
             ("Concrete curb and gutter", "m", 3400, 85.0), ("Storm sewer, 300-900 mm", "m", 1150, 680.0),
             ("Catch basins and maintenance holes", "each", 46, 4800.0), ("Precast box culvert 4.5 x 2.4 m", "m", 26, 52000.0),
             ("Cofferdam and creek diversion", "LS", 1, 280000), ("Cantilever retaining wall", "m", 140, 5200.0),
             ("Roundabout at the operations centre", "LS", 1, 820000), ("Bioretention and low impact development", "LS", 1, 410000),
             ("Street lighting", "each", 48, 9800.0), ("Pavement markings and signs", "LS", 1, 110000)]
else:
    items = [("Traffic control and staging", "LS", 1, 330000), ("Asphalt and curb removals", "yd2", 11700, 7.0),
             ("Earth excavation", "yd3", 19000, 15.0), ("Granular subbase", "yd3", 6000, 38.0),
             ("Granular base", "yd3", 3000, 50.0), ("Hot-mix asphalt, two lifts", "yd2", 13750, 30.0),
             ("Concrete curb and gutter", "ft", 11150, 24.0), ("Storm sewer, 12-36 in.", "ft", 3770, 190.0),
             ("Catch basins and manholes", "each", 46, 3900.0), ("Precast box culvert 15 x 8 ft", "ft", 85, 12800.0),
             ("Cofferdam and creek diversion", "LS", 1, 220000), ("Cantilever retaining wall", "ft", 460, 1250.0),
             ("Roundabout at the operations center", "LS", 1, 640000), ("Bioretention and low impact development", "LS", 1, 320000),
             ("Street lighting", "each", 48, 7600.0), ("Pavement markings and signs", "LS", 1, 85000)]
sub = 0.0
for name, unit, q, p in items:
    sub += q * p
    print(f"{name:42s} {q:>8,} {unit:5s} x {p:>10,.2f} = {q*p:>12,.0f}")
mob = 0.05 * sub
print(f"{'Subtotal of unit-price items':42s} {sub:>40,.0f}")
print(f"{'Mobilization, bonds and insurance (5 %)':42s} {mob:>40,.0f}")
est = sub + mob
print(f"{'Engineer estimate (' + CUR + ')':42s} {est:>40,.0f}")
# uncertainty: triangular factors (low, most likely, high) on each item, plus a market factor on the whole bid
rng = {"Earth excavation": (0.90, 1.0, 1.35), "Precast box culvert": (0.95, 1.0, 1.30),
       "Cofferdam": (0.90, 1.0, 1.60), "Storm sewer": (0.92, 1.0, 1.20)}
random.seed(450)
runs = []
for _ in range(5000):
    tot = 0.0
    for name, unit, q, p in items:
        lo, ml, hi = next((v for k, v in rng.items() if name.startswith(k)), (0.93, 1.0, 1.10))
        tot += q * p * random.triangular(lo, hi, ml)
    tot *= 1.05 * random.triangular(0.94, 1.15, 1.0)
    runs.append(tot)
runs.sort()
pc = lambda f: runs[int(f * len(runs)) - 1]
print(f"\nMonte Carlo, 5,000 runs: P10 {pc(0.10):,.0f}  P50 {pc(0.50):,.0f}  P80 {pc(0.80):,.0f}  P90 {pc(0.90):,.0f}")
print(f"Chance the point estimate is not exceeded: {sum(r <= est for r in runs) / len(runs):.0%}")
print(f"Contingency to reach P80: {pc(0.80) - est:,.0f} ({(pc(0.80) - est) / est:.1%} of the estimate)")

Traffic control and staging                       1 LS    x 420,000.00 =      420,000
Asphalt and curb removals                     9,800 m2    x       9.00 =       88,200
Earth excavation                             14,500 m3    x      21.00 =      304,500
Granular subbase                              4,600 m3    x      55.00 =      253,000
Granular base                                 2,300 m3    x      72.00 =      165,600
Hot-mix asphalt, two lifts                   11,500 m2    x      42.00 =      483,000
Concrete curb and gutter                      3,400 m     x      85.00 =      289,000
Storm sewer, 300-900 mm                       1,150 m     x     680.00 =      782,000
Catch basins and maintenance holes               46 each  x   4,800.00 =      220,800
Precast box culvert 4.5 x 2.4 m                  26 m     x  52,000.00 =    1,352,000
Cofferdam and creek diversion                     1 LS    x 280,000.00 =      280,000
Cantilever retaining wall                       140 m     x   5,200.00 =      728,000
Roundabout at the operations centre               1 LS    x 820,000.00 =      820,000
Bioretention and low impact development           1 LS    x 410,000.00 =      410,000
Street lighting                                  48 each  x   9,800.00 =      470,400
Pavement markings and signs                       1 LS    x 110,000.00 =      110,000
Subtotal of unit-price items                                              7,176,500
Mobilization, bonds and insurance (5 %)                                     358,825
Engineer estimate (CAD)                                                   7,535,325

Monte Carlo, 5,000 runs: P10 7,576,061  P50 8,014,816  P80 8,388,262  P90 8,578,997
Chance the point estimate is not exceeded: 8%
Contingency to reach P80: 852,937 (11.3% of the estimate)

The point estimate is CAD 7,535,325. The largest single item is the precast box culvert at CAD 1.35 million, followed by the roundabout, the storm sewer and the retaining wall. The culvert, the cofferdam, the wall and the excavation in soft clay together make up more than a third of the unit-price items, and that is where the uncertainty is concentrated.

Expressing uncertainty: the Monte Carlo range

A single number hides the most important information in an estimate, its uncertainty. Sofia's script assigns each item a triangular distribution: a low, most likely and high factor on its estimated cost. Most items get a narrow range of minus 7 % to plus 10 %. Excavation gets minus 10 % to plus 35 %, because the soft clay may need more subexcavation; the culvert minus 5 % to plus 30 %; the cofferdam minus 10 % to plus 60 %, because its cost depends on water levels during the work window; the storm sewer minus 8 % to plus 20 %. A market factor applied to the whole estimate, from minus 6 % to plus 15 %, represents the bidding climate. The simulation draws 5,000 combinations.

The results are striking. The point estimate of CAD 7.54 million has only about an 8 % chance of not being exceeded. The median is CAD 8.01 million, and the 80th percentile, P80, is CAD 8.39 million. The reason is that every distribution is skewed upward: the most likely value of each item is at the low end of its range, so adding the most likely values gives a total well below the likely total. The contingency needed to reach P80 is CAD 853,000, or 11.3 % of the estimate, which is the figure carried into the capital budget in lesson 1.

Two caveats keep this honest. First, the item ranges are judgements, and the analysis is only as good as the conversations that produced them; the team held a short risk workshop with Dr. Kowalczyk and the city's roads staff to set them. Second, the simulation treats items as independent, apart from the market factor. In reality, if the clay is worse than expected, excavation, the wall and the culvert will all cost more at once. Correlation widens the range, so the P80 above is, if anything, optimistic. More advanced practice models the main risks as events with probabilities and impacts, rather than as ranges on line items.

The estimate at tender

When bids arrive, the engineer's estimate is the benchmark. Bids within about 10 % of a good Class 1 estimate are normal. A low bid far below the estimate prompts a check of the low bidder's understanding of the scope and its unit prices; a cluster of bids well above it suggests either an error in the estimate or a risk that bidders priced and the estimator did not. In lesson 3, Northline's corrected bid of CAD 7.24 million came in 3.9 % below the estimate, and the spread of bids was about 9 %, a healthy result.

The engineer's estimate is usually kept confidential until bids close, because publishing it anchors bidders to it. Some agencies publish a budget range instead. Either way, the estimate and its basis, quantities, prices, sources and assumptions, should be documented well enough that someone else could check it, because it may be needed years later in a claim.

Practical points

• State the class and accuracy range with every estimate.
• Price items with no reliable history from crews, production rates and site conditions.
• Remember that most likely values do not add up to a likely total when ranges are skewed.
• Size contingency from a risk analysis, not a fixed percentage.
• Document the basis of the estimate for use in bid evaluation, changes and claims.