Engineering Cost Concepts for the FE Civil Exam

NCEES FE Civil spec: Engineering Economics, B. Cost (e.g., fixed, variable, direct and indirect labor, incremental, average, sunk). FE Reference Handbook: Engineering Economics chapter, nomenclature and definitions.

Cost questions on the FE Civil exam are mostly about vocabulary used correctly: knowing which costs change with output, which can be traced to a product, and which should be ignored. The arithmetic is simple, but the distractors are built around classifying a cost the wrong way.

What the NCEES spec covers

Section B lists fixed, variable, direct and indirect labor, incremental, average and sunk costs. Expect short problems on total and unit cost at a given production level, and conceptual questions on which costs matter for a decision.

Key concepts

Fixed costs do not change with output over the relevant range: rent, insurance, equipment ownership, salaried staff.
Variable costs change in proportion to output: materials, fuel, hourly production labor.
Direct costs can be traced to a specific product or job (the crew placing concrete on this bridge). Indirect costs (overhead) are shared and allocated, such as the estimating department or yard supervision.
Average cost is total cost divided by units. It falls as output rises because fixed cost is spread over more units.
Incremental (marginal) cost is the extra cost of producing additional units. With linear costs it equals the variable cost per unit.
Sunk costs are already spent and cannot be recovered. They are ignored in decisions about the future.
Opportunity cost is the value of the best alternative given up, and it does belong in a decision.

Core formulas

T C = F C + v Q Average cost = \frac{T C}{Q} = \frac{F C}{Q} + v

Incremental cost = \frac{Δ T C}{Δ Q}

Here v is the variable cost per unit and Q is the number of units.

Where it is in the FE Reference Handbook

The Engineering Economics chapter has a nomenclature and definitions list that covers these terms, along with break-even and related entries. Definitions there are brief, so knowing them before the exam saves time.

Worked example

A precast plant has fixed costs of $120,000 per year and variable costs of $45 per panel. Find the total and average cost at 4,000 and at 5,000 panels, and the incremental cost per panel between those levels. Last year the plant spent $30,000 on a feasibility study for a new product line. Should that study cost affect the decision to expand?

T C_{4000} = 120, 000 + 45 (4, 000) = $300, 000 \overset{ˉ}{C} = \frac{300 , 000}{4 , 000} = $75.00

T C_{5000} = 120, 000 + 45 (5, 000) = $345, 000 \overset{ˉ}{C} = \frac{345 , 000}{5 , 000} = $69.00

Incremental = \frac{345 , 000 - 300 , 000}{1 , 000} = $45 per panel

The average cost drops because the fixed cost is spread over more panels, while the incremental cost equals the variable cost. Any price above $45 per panel adds profit on the extra 1,000 panels. The $30,000 study is a sunk cost: it is spent whether or not the plant expands, so it is left out of the decision.

Common mistakes

Including sunk costs in a forward-looking comparison.
Using average cost when the question asks about the cost of extra units.
Calling supervision or office staff a direct cost because it is "labor".
Assuming fixed costs are fixed forever. They are fixed only within a range of output.
Ignoring opportunity cost when an owned asset could be rented out or sold instead.

The cost example works through another set of cost definitions.

Practice Problems

Try these from the free PolyCalc FE Civil problem bank. Each one has a full worked solution.

Which item is a sunk cost when evaluating a future project decision? See the worked solution or practice the Engineering Economics deck
Fixed cost is $30,000, selling price is $80 per unit, and variable cost is $50 per unit. What is the break-even quantity? See the worked solution or practice the Engineering Economics deck
Machine A has fixed costs of $40,000 per year and variable costs of $12 per unit. Machine B has fixed costs of $25,000 per year and $18 per unit. The annual output at which both cost the same is most nearly: See the worked solution or practice the Engineering Economics deck

Related Calculators and Examples

Frequently Asked Questions

What is a sunk cost?

A sunk cost is money already spent that cannot be recovered, such as a completed study or a nonrefundable deposit. It is the same for every future option, so it is ignored in the decision.

What is the difference between incremental cost and average cost?

Average cost is total cost divided by the number of units. Incremental cost is the change in total cost divided by the change in units, which is the cost of producing a few more. With linear costs, incremental cost equals the variable cost per unit.

Is equipment depreciation a fixed or variable cost?

Time-based ownership costs such as straight-line depreciation are usually treated as fixed costs, because they do not change with output. Usage-based wear and fuel are variable.

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