Engineering Economic Analysis

28 ENGINEERINGCOSTSAND COST ESTIMATING

This chapter defines fundamental cost concepts. These include fixed and variable costs,

marginal and average costs, sunk and opportunity costs, recurring and nonrecurring costs,

incremental cash costs, book costs, and life-cycle costs. We then describe the various types

of estimates and difficulties sometimes encountered. The models that are described include

unit factor, segmenting, cost indexes";power sizing, triangulation, and learning curves. The

chapter discusses estimating benefits, developing cash flow diagrams, and drawing these

diagrams with spreadsheets.

Understanding engineering costs is fundamental to the engineering economic analysis

process, and therefore this chapter addresses an important question: Where do the numbers

come from?

ENGINEERING COSTS

Evaluating a set of feasible alternatives requires that many costs be analyzed. Examples

include costs for initial investment, new construction, facility modification, general labor,

parts and materials, inspection and quality, contractor and subcontractor labor, training,

computer hardware and software, material handling, fixtures and tooling, data management,

and technical support, as well as general support costs (overhead). In this section we describe

several concepts for classifying and understanding these costs.

Fixed, Variable, Marginal, and Average Costs

Fixed costs are constant or unchanging regardless of the level of output or activity. In

contrast, variable costs depend on the level of output or activity. A marginal cost is the

variable cost for one more unit, while the average cost is the total cost divided by the

number of units.

For example, in a production environment fixed costs, such as those for factory floor

space and equipment, remain the same even though production quantity, number of em-

ployees, and level of work-in-process may vary.Labor costs are classified as avariablecost

because they depend on the number of employees in the factory. Thusfixedcosts are level

or constant re~ardless of output or activity, andvariablecosts are changing and related to

the level of output or activity.

As another example, many universities charge full-time students a fixed cost for 12 to

18 hours and a cost per credit hour for each credit hour over 18. Thus for full-time students

who are taking an overload (> 18 hours), there is a variable cost that depends on the level

of activity.

This example can also be used to distinguish betweenmarginalandaveragecosts. A

marginal cost is the cost of one more unit. This will depend on how many credit hours the

student is taking. If currently enrolled for 12 to 17 hours, adding one more is free. The

marginal cost of an a~ditional credit hour is $0. However, if the student is taking 18 or more.

hours, then the marginal cost equals the variable cost of one more hour.

To illustrate average costs, the fixed and variable costs need to be specified. Suppose

the cost of 12 to 18 hours is $1800 per term and overload credits are $ 120/hour.If a student

takes 12 hours, theaveragecost is $1800/12 =$150 per credit hour. If the student were

to take 18 hours, theaverage cost decreases to $1800/18 = $100 per credit hour. If the

student takes 21 hours, theaveragecost is $102.86 per credit hour [$1800 + (3 x $120) /21].

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