Engineering Economics
Engineering Costs
and Cost Estimating
William Loendorf, P.E.
1
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, training,
material handling, fixtures and tooling,
data management, technical support, as
well as general support costs (overhead).
Engineering Costs
Classifications of costs
– Fixed - constant, unchanging
• Rent is constant (single, married, children)
• Typically includes building leases, insurance,
salaries, heating, and lighting costs.
– Variable - depend on activity level
• Food depends on the number of occupants
• Typically vary with the level of production.
– Marginal - variable cost for the next unit
• Depends on the next unit (adult, child, baby)
– Average - total cost/number of units
• Rent+ food+…+n/number of units
Engineering Costs
• For example, in a production environment a
fixed cost, such as costs for factory floorspace
and equipment, remains the same even though
the production quantity, number of employees,
or level of work-in-process are varying.
• Labor costs are classified as a variable cost
because they depend on the number of
employees in the factory.
• Thus fixed costs are level or constant regardless
of output or activity, and variable costs are
changing and related to the level of output or
activity.
Fixed, Variable and Total Costs
Example 1
• An entrepreneur named DK was considering the
money making potential of chartering a bus to
take people from his hometown to an event in a
larger city.
• DK planned to provide transportation, tickets to
the event, and refreshments on the bus for those
who signed up.
• He gathered data and categorized these
expenses as either fixed or variable:
Fixed, Variable and Total Costs
Example 1
Fixed Costs
Variable Costs
Bus Rental $ 80.00 Event Tickets $ 12.50
Gas Expense $ 75.00 Refreshments $
7.50
Other Fuels $ 20.00
Bus Driver $ 50.00
Total FC
$ 225.00 Total VC
$ 20.00
Fixed cost
$ 225.00
$ 225.00
$ 225.00
$ 225.00
$ 225.00
Variable cost
$
$ 100.00
$ 200.00
$ 300.00
$ 400.00
$800.00
Total cost
$ 225.00
$ 325.00
$ 425.00
$ 525.00
$ 625.00
Cost ($)
People
0
5
10
15
20
Total costs
$600.00
Total cost
$400.00
Fixed cost
$200.00
$0
5
10
Volume
15 20
Profit and Loss Terms
• In terms of costs and revenues there are
three possible profit and loss points for a
business activity.
• Breakeven: total revenue = total costs
– Just getting along
• Profit region: total revenue > total costs
– Putting money in the bank
• Loss region: total revenue < total costs
– Going into debt
Profit and Loss
Breakeven Charts
•
•
•
•
Example 2
DK developed an overall total cost equation for his
business expenses.
Now DK wants to evaluate the potential to make money
from this chartered bus trip.
Total Cost = Total Fixed Cost + Total Variable Cost
= $225 + ($20)(the number of people on the trip)
Let x = number of people on the trip
Thus,
Total Cost = 225 + 20x
• Using this relationship, DK can calculate the total cost for
any number of people - up to the capacity of the bus.
Breakeven Charts
• What he lacks is a revenue equation to offset his costs.
• DK's total revenue from this trip can be expressed as:
Total Revenue =
= (Charter ticket price)(number of people on the trip)
= (ticket price)(x)
• Profit or loss can now be calculated as:
Total Profit =
= [Total Revenue] - [Total Costs]
= [ticket price]x – [225 + 20x]
If he charged a charter ticket price of $35, then
= [35x] - [225 + 20x]
= 15x - 225
Breakeven Charts
Example 2
People
0
5
10
15
20
25
30
35
40
Variable Costs
Event Tickets
$
12.50
Refreshments $
7.50
Total VC
$
$
$
$
$
$
$
$
$
$
Fixed cost
225.00
225.00
225.00
225.00
225.00
225.00
225.00
225.00
225.00
Ticket price
$
35.00
20.00
Variable cost
$
$
100.00
$
200.00
$
300.00
$
400.00
$
500.00
$
600.00
$
700.00
$
800.00
$
$
$
$
$
$
$
$
$
Total cost
225.00
325.00
425.00
525.00
625.00
725.00
825.00
925.00
1,025.00
Revenue
$
$
175.00
$
350.00
$
525.00
$
700.00
$
875.00
$ 1,050.00
$ 1,225.00
$ 1,400.00
Profit
Region
$ (225.00)
Loss
$ (150.00)
Loss
$ (75.00)
Loss
$
Breakeven
$
75.00
Profit
$ 150.00
Profit
$ 225.00
Profit
$ 300.00
Profit
$ 375.00
Profit
Profit-loss breakeven chart
$1,500.00
Cost ($)
Fixed Costs
Bus Rental
$ 80.00
Gas Expense $ 75.00
Other Fuels
$ 20.00
Bus Driver
$ 50.00
Total FC
$ 225.00
Total cost
$1,000.00
Fixed cost
$500.00
Revenue
$0
5 10 15 20 25 30 35 40
Volume
Past (Sunk) Costs and
Future (Opportunity) Costs
• Sunk cost - money spent due to a past
decision. We cannot do anything about
these costs.
– Purchase price paid for a car two years ago.
• Opportunity cost - a benefit that is
foregone by engaging a resource in a
chosen activity instead of engaging that
same resource in some other activity. We
make a choice or decision.
– Buying lunch instead of gas.
Which amount is the value at present?
Example 3
• A distributor of electric pumps must decide what
to do with a "lot" of old electric pumps that was
purchased 3 years ago.
• Soon after the distributor purchased the lot,
technology advances were made.
• These advances made the old pumps less
desirable to customers.
• The pumps are becoming more obsolescent as
they sit in inventory.
• The pricing manager has the following
information.
Which amount is the value at present?
Example 3
Price when purchased
Storage costs
List price when purchased
Current list price of new pumps
Amount offered for pumps 2 years ago
Current price that the pumps could be sold for
$ 7,000.00 Sunk cost
Past decisions
$ 1,000.00 Sunk cost
Past decisions
$ 9,500.00 Old list
Past decisions
$ 12,000.00 New list dif erent features Past decisions
$ 5,000.00 Foregone opportunity Past decisions
$ 3,000.00 Market value
Present opportunity
Expense Types
• Recurring costs – known, anticipated
and occurs at regular intervals.
– Purchasing food, paying rent.
• Non-recurring costs - one-of-a-kind
event that occurs at an irregular interval.
– Emergency maintenance expenses.
Sometimes we attempt to plan for large non-recurring costs
by buying insurance. Paying the periodic insurance
premium turns this expense into a recurring cost.
Incremental Costs
• An incremental cost is the difference between the
costs of two alternatives.
Example 4
• Choose between alternative models A and B. What
incremental costs occur with model B?
Costs
Model
Cost Items
Purchase price
Installation costs
Annual maintenance costs
Annual utility expenses
Disposal costs after useful life
A
$ 10,000.00
$ 3,500.00
$ 2,500.00
$ 1,200.00
$ 700.00
B
$ 17,500.00
$ 5,000.00
$ 750.00
$ 2,000.00
$ 500.00
Incremental
$ 7,500.00
$ 1,500.00
$(1,750.00)
$ 800.00
$ (200.00)
Cash Costs vs. Book Costs
• Cash costs - movement of money from
one owner to another - also known as a
cash flow.
– Payment this month on an auto loan.
• Book cost - cost of a past transaction
that is recorded in an accounting book.
– Down payment recorded in your
checkbook from last years automobile
purchase.
Life-cycle Costs
• Life-cycle - all the time from the initial
conception of an idea to the death of a
product (process).
• Life-cycle costs - sum total of all the
costs incurred during the life cycle.
• Life-cycle costing - designing a
product with an understanding of all the
costs associated with a product during
it’s life-cycle.
Product Life-cycle
Cumulative Life-cycle Costs
Committed and Dollars Spent
Life-cycle Design Change Costs
and Ease of Change
Cost Estimating
• Economic analysis is future based.
• Costs and benefits in the future require
estimating.
• Estimated costs are not known with
certainty.
• The more accurate the estimate, the
more reliable the decision.
• Estimating is the foundation of
economic analysis.
Types of Estimates
•
There are three general types of
estimates:
1. Rough – order of magnitude, used for
high level planning, inaccurate, range
from -30% to +60% of actual values.
2. Semi-detailed - based on historical
records, reasonably sophisticated and
accurate, -15% to +20% of actual values.
3. Detailed - based on detailed
specifications and cost models, very
accurate, within -3% to +5% of actual.
Accuracy vs. Cost Tradeoff in
Estimating
Estimating Models
Model
Explanation
Per Unit
Uses a “per unit” factor.
$/sq ft, Benefits/employee
Segmenting
Divide problem into items,
estimate each & sum.
Cost Indexes
Index number based on historical
changes in cost.
Scaling previous known costs up
or down (economies of scale).
Power Sizing
Triangulation
Looking at costs from several
perspectives.
Learning
Curve
Tracking cost improvements.
Examples
US CPI
Estimating Benefits
• So far we have focused on cost terms and cost
estimating.
• However, engineering economists must often
also estimate benefits.
• Example benefits include sales of products,
revenues from bridge tolls and electric power
sales, cost reductions from reduced material or
labor costs, reduced time spent in traffic jams,
and reduced risk of flooding.
• These benefits are the reasons that many
engineering projects are undertaken.
• The cost concepts and cost estimating models
can also be applied to economic benefits.
Cash Flow Diagrams
• The costs and benefits of engineering projects occur
over time and are summarized on a Cash Flow Diagram
(CFD).
• Specifically, a CFD illustrates the size, sign, and timing
of individual cash flows. In this way the CFD is the basis
for engineering economic analysis.
• A Cash Flow Diagram is created by first drawing a
segmented time-based horizontal line, divided into
appropriate time units.
• The time units on the CFD can be years, months,
quarters or any other consistent time unit.
• Then at each time when there is a cash flow, a vertical
arrow is added - pointing down for costs and up for
revenues or benefits.
• These cash flows are drawn to relative scale.
Cash Flow Diagrams
Cash Flow Diagrams
• Summarizes the flow of money over time
• Can be represented using a spreadsheet
Year
0
1
2
3
4
5
6
Capital costs
$ (80,000.00)
$ 10,000.00
O&M
Overhaul
$ (12,000.00)
$ (12,000.00)
$ (12,000.00)
$ (12,000.00)
$ (12,000.00)
$ (12,000.00)
Total
$ (80,000.00)
$ (12,000.00)
$ (12,000.00)
$ (25,000.00) $ (37,000.00)
$ (12,000.00)
$ (12,000.00)
$ (2,000.00)
Cash flow
Cash flow
$20,000.00
$$(20,000.00)
$(40,000.00)
$(60,000.00)
$(80,000.00)
$(100,000.00)
0
1
2
3
4
5
6
Overhaul
O&M
Capital costs
Ye ar
Summary
• This chapter introduced the cost concepts: fixed and
variable, marginal and average, sunk, opportunity,
recurring and nonrecurring, incremental, cash and
book, and lifecycle.
• Fixed costs are constant and unchanging as
volumes change, while variable costs change as
output changes.
• Fixed and variable costs are used to find the
breakeven value between costs and revenues, as
well as the regions of net profit and loss.
• A marginal cost is for one more unit, while the
average cost is the total cost divided by the number
of units.