COST CONCEPTS AND
DESIGN ECONOMICS
Chapter # 2
Objectives
Objectives of Chapter 2 are:
Describe some of the basic cost
c ost terminology and concepts encountered
in the book
Illustrate how they should be used in engineering economic analysis and
decision making
Following topics are discussed:
Fixed, variable and incremental costs
Recurring and nonrecurring costs
Direct, indirect and overhead costs
Standard costs
Cash cost versus book cost
Sunk and opportunity costs
Life cycle and life cycle costs
General economic environment
Relationship between price and demand, total revenue function
Break even point(s), maximizing profits, present economy studies
s tudies
Objectives
Objectives of Chapter 2 are:
Describe some of the basic cost
c ost terminology and concepts encountered
in the book
Illustrate how they should be used in engineering economic analysis and
decision making
Following topics are discussed:
Fixed, variable and incremental costs
Recurring and nonrecurring costs
Direct, indirect and overhead costs
Standard costs
Cash cost versus book cost
Sunk and opportunity costs
Life cycle and life cycle costs
General economic environment
Relationship between price and demand, total revenue function
Break even point(s), maximizing profits, present economy studies
s tudies
Introduction
Need balancing between technical and economical
feasibility
Engineering economy should be used to attain
acceptable
acceptab
le balance
Chapter # 2 integrates cost concepts, principles of
engineering economy and design considerat
consideration
ion
Cost Estimating
The process by which the present and future cost consequences of engineering
designs are forecast
Most prospective characteristics
Projects – relatively unique
Based on past outcomes and adjust the data
Involve personnel from several sectors
Purposes
Provide information used in setting a selling price for quoting, bidding, or
evaluating contracts
Determine whether a proposed product can be made and distributed at a profit (for
simplicity, price=cost + profit)
Evaluate how much capital can be
be justified for process changes or other
improvements
Establish benchmarks for productivity improvement programs
Cost Estimating – Approaches
Top-down Approach
Uses historical data for current projects - costs, revenues, and
other parameters
Modifies original data for changes in inflation/deflation, activity
level, weight, energy consumption, size, etc...
Works well at earlier stages of the estimation
Bottom-up Approach
More detailed method of cost estimating
Break down a project into small, manageable units and estimate
costs and economic consequences
Works best when details concerning desired output are
defined and clarified
Origins of Engineering Economy
Fixed, Variable & Incremental Costs
Fixed Cost
Variable Costs
Those unaffected by changes in activity level over a
feasible range of operations for the capacity or capability
available
Those associated with an operation that vary in total with
the quantity of output or other measures of activity level
Incremental Costs or Incremental Revenue
The additional cost or revenue that results from increasing
the output of a system by one (or more) units
Example 2-1
In connection with surfacing a new highway, a contractor has a choice of two sites on which
to set up the asphalt-mixing plant equipment. The contractor estimates that it will cost $1.15
per cubic yard per mile (yd/mile) to haul the asphalt-paving material from the mixing plant to
the job location. Factors relating to the two mixing sites are as follows (production costs at
each site are the same):
Cost Factor
Site A
Site B
Average hauling distance
6 miles
4.3 miles
Monthly rental of site
$1,000
$5,000
Cost to set up and remove equipment
$15,000
$25,000
Hauling expense
Flag person
$1.15/yd3-mile $1.15/yd3-mile
Not required
$96/day
The job requires 50,000 cubic yards of mixed-asphalt-paving material. It is estimated that
four months (17 weeks of five working days per week) will be required for the job. Compare
the two sites in terms of their fixed, variable, and total costs. Assume that the cost of the
return trip is negligible. Which is the better site? For the selected site, how many cubic
yards of paving material does the contractor have to deliver before starting to make a profit
if paid $8.05 per cubic yard delivered to the job location?
Example 2-1
Select a site among A & B (tables) ?
Requires 50,000 yd3 at job location
1.15/yd3-mile for asphalt mixing plant
production costs at each site are the same
4 month ( 17 weeks x 5 days)
Break even with paid $8.05 / yd 3 ?
Cost Factor
Site A
Site B
Average hauling distance
6 miles
4.3 miles
Monthly rental of site
$1,000
$5,000
Cost to set up and remove equipment
$15,000
$25,000
Hauling expense
$1.15/yd3 - mile
$1.15/yd3 - mile
Flag person
Not required
$96/day
Example 2-1
Cost
Fixed
Rent
X
= $ 4,000
= $ 20,000
Setup/removal
X
= 15,000
= 25,000
Flag person
X
=0
Hauling
Variable
X
Site A
6(50,000) ($1.15)
Total:
Site B
= 45,000
5(17)($96) = 8,160
4.3(50,000)($1.15) = 247,250
$ 364,000
Select B : larger fixed cost + smaller variable cost
Profit (break even)
4.3 ($1.15) = $4.945/ yd 3
Total Cost = Total Revenue
fixed + variable = Revenue
$53,160 + $4.945 X = $8.05 x $4.945
X = 17,121 yd 3 delivered
= $300,410
Example 2-2
Problem : Cost for trips
4 students
400 miles driving x 2 ways
Cost list (table)
Cost Element
Gasoline
Oil and lubrication
Tires
Depreciation
Insurance and taxes
Repairs
Garage
Total
Cost per mile
$0.120 *
0.021 *
0.027 *
0.150
0.024
0.030 *
0.012
$0.384
Example 2-2
Solution 1 (Car owner)
Solution 2 (Other students)
Cost/mile = $ 0.384 (annual average 15,000 miles)
0.384 x 800 mile = $ 102.4 x 3
Cost/mile = $ 0.198 (Gasoline, Oil and lubrication, Tires, Repairs)
0.198 x 800 mile = $ 158.40 = $ 52.80 x 3
Solution 3 (considering additional miles)
15,000 x $0.384
18,000 x $ ?
$810 / 3,000
0.27 x 800 mile
= $5760
= $6570 (given cost service)
= $0.270
= $216.00 = $72.00 x 3
Recurring and Nonrecurring Costs
Recurring costs
repetitive and occur when a firm produces similar goods
and services on a continuing basis
variable costs – recurring
fixed cost paid on a repeatable basis - recurring
•
ex: office rental
Nonrecurring costs
not repetitive, even though the total expenditure may be
cumulative over a relatively short period of time
ex: purchase cost for real estate, construction costs
Direct, Indirect and Standard Costs
Direct costs
reasonably measured and allocated to a specific output or work activity
labor and material directly allocated with a product, service or construction
activity
ex: material cost for a pair of scissors
Indirect costs
difficult to allocate to a specific output or activity
costs allocated through a selected formula (such as, proportional to direct
labor hours, direct labor cost, direct material cost, or others)
•
ex: costs of common tools, general supplies, and equipment maintenance
indirect costs = overhead = burden
•
ex: electricity, general repairs, property taxes, supervision
•
administrative selling expenses – added to direct cost
•
allocate overheads costs among product/services/activates
Direct, Indirect and Standard Costs
Standard Costs
representative costs/unit established in advance
developed from anticipated direct labor hours, materials,
overhead categories with their established costs per unit
Important role in cost control and other management
some typical uses are the following:
•
•
•
•
estimating future manufacturing costs
measuring operating performance by comparing actual cost
per unit with the standard unit cost
preparing bids on products or services requested by
customers
establishing the value of work in process and finished
inventories
Standard Costs
Standard Cost Element
Sources of Data for Standard Costs
Direct Labor
Process Routing sheets, standard times,
standard labor rates
+
Direct Material
Material quantities per unit, standard unit
material costs
+
Factory Overheads
= Standard cost (per unit)
Total factory overhead costs allocated
based on prime costs (direct labor plus
direct material costs)
Cash Cost versus Book Cost
Cash cost
a cost that involves payment in cash and results in cash flow
future transaction (potential) incurred for the alternatives
Book cost
costs that do not involve cash payment but rather represent the
recovery of past expenditures over a fixed period of time such as
depreciation
depreciation
•
•
is not a cash flow
only affects income taxes, cash flow
EE needs to consider only cash flows or potential cash flows
Sunk Cost
Sunk cost
one that has occurred in the past
has no relevance to estimates of future costs and revenues related to an
alternative course of action
nonrefundable cash outlays
ex
motorcycle 1 - $40 (down payment) + $1260 = $1300
motorcycle 2 - $40 (down payment) + $1230 = $1270
emotionally difficult to do
Example 2-3
Original Purchasing Price - $50,000
Current Book value - $ 20,000
Current Market price - $5,000
Sunk Cost
•
•
View 1 - $50,000 : sunk cost for replacement
View 2 - $15,000 : difference between real value and book value
Opportunity Cost
Opportunity cost
the cost of the best rejected (i.e., foregone) opportunity
Incurred because of the limited resources
Ex: Student
for working - $20,000
for going to school - $5,000 (expenses)
opportunity cost - $25,000 ($5,000 cash outlay and
$20,000 for income foregone)
Example 2-4
Purchasing - $50,000
Book value - $ 20,000
Market price - $5,000
By keeping the equipment, the firm is giving up the
opportunity to obtain $5,000 from its disposal
$5,000 immediate selling price is really the
investment cost of not replacing the equipment and
is based on the opportunity cost concept
Life – Cycle Cost
Summation of all costs
both recurring and nonrecurring
related to a product, structure, system, or service during its life
span
Life cycle
begins with the identification of the economic need or want
ends with the retirement and disposal activities
functional or economic basis (shorter than functional)
ex: old boiler may be able to produce the steam required, but not
economically enough for the intended use
Figure 2-1 Phases of the Life Cycle and Their
Relative Cost
Figure 2-2 Costs of Design Changes Are
Significant
Life – Cycle Cost
Investment cost
Working capital
funds required for current assets for start up & operational activities
materials in inventory for delivery
spare parts, tools, personnel for maintenance
cash for employee salaries, other expenses
Operation & Maintenance cost
capital required in acquisition phase
a single or a series of expenditure
capital investment
recurring annual expense items
people, machine, materials, energy & information
Disposal cost
nonrecurring cost
be offset by remaining market value
Example 2-5
Consider the situation where equipment and related support for a new
computer aided design / computer-aided manufacturing work station are being
acquired for the engineering department that you work in. The applicable cost
elements and estimated expenditures are as follows:
Cost Element
Install a leased telephone line for communication
Lease CAD/CAM software (includes installation & debugging)
Purchase hardware (CAD/CAM workstation)
Cost
$1,100/month
500/month
20,000
Purchase 9600-baud modem
2,500
Purchase a high-speed printer
1,500
Purchase four-color plotter
Shipping costs
Initial training (in house) to gain proficiency with CAD/CAM software
What is the investment of this CAD/CAM software?
10,000
500
The General Economy
Environment
Consumer / Producer Goods and Services
Consumer goods/services
products or services, directly used by people
ex: food, clothing, homes, cars, TV sets, opera,
haircuts, and medical services etc
Producers must be aware of the changing wants of the
people
Producer goods/services
products or services to produce consumer goods and
services or other producer goods
ex: machine tools, factory buildings, buses, etc
Measures of Economic Worth
Goods/services are produced and desired because
directly or indirectly they have UTILITY.
Utility
measure of the value which consumers of a product or
service place on that product or service
power to satisfy human wants and needs
commonly measured in terms of value, expressed in
some medium of exchange as the price
Necessities, Luxuries, and Price Demand
Necessities and luxuries – Two types of goods and services
These terms are relative
one person considers Goods/Services a necessity, another
considers it a luxury
Price - equals some constant value minus some multiple of
the quantity demanded
p = a – bD for 0 ≤ D ≤ a/b, and a>0, b>o
D = (a – p) / b (b≠0)
Lower price - Large demand
(2-1)
(2-2)
p
p = a – bD
:
e
c
i
r
P
Units of Demand : D
Price-Demand Relationship for Luxuries &
Necessities
Extent to which price changes
influence demand varies according
to the elasticity of demand
Demand is elastic when a decrease
in selling price results in
considerable increase in sales
If a change in selling price produces
little or no effect on demand, the
demand is said to be inelastic
Competition
Competition exists in general economic situations
Perfect competition
Monopoly
product is supplied by a large number of vendors
no restriction on additional suppliers
complete freedom on the part of both buyer and seller
may never occur in actual practice.
opposite from perfect competition
products/service is only available from a single supplier
prevent the entry of all others
perfect monopolies rarely occur in practice
Oligopoly
when there are so few suppliers of a product or service that action by one
will almost inevitably result in similar action by the other
Total Revenue Function
Total Revenue
TR = price × demand = p(D)
TR = (a – bD) D = aD – bD2 for 0 ≤ D ≤ a/b, and a>0, b>0
Maximum revenue
For MR, dTR/dD = a –2bD = 0
D’ = a / 2b
MR
= aD–bD2
= a(a/2b) – b(a/2b) 2
= a2/2b - a2/4b
= a2/4b
(2-5)
(2-6)
(2-3)
(2-4)
Cost, Volume, and Breakeven Point
Relationships
CT = CF + CV
CV = c v . D
Scenario 1: p = a - b D , Larger Volume – lower price
Profit is maximized where total revenue exceeds total cost by
greatest amount
Cost, Volume, and Breakeven Point
Relationships
Max Profit
D* occurs where Profit (total revenue - total costs) is maximized
PR = (aD-bD2) - (CF+CvD)
= -bD2+(a-Cv)D - CF
(2-9)
(a - cv) > 0; that is price per unit that will result in no demand
has to be greater than variable cost per unit
Total revenue (TR) must exceed total cost CT for the period
involved
dPR/dD = a – cv – 2bD = 0
D* = [ a - Cv ]/2b
(2-10)
Cost, Volume, and Breakeven Point
Relationships
Max Profit
D* occurs where Profit (total revenue - total costs) is
maximized
PR = (aD-bD2) - (CF+CvD) = -bD2+(a-Cv)D - CF (2-9)
dPR/dD=0
D* = [ a - Cv ]/2b
(2-10)
Breakeven points (D’1, D’2) occur when
TR = CT or Profit = 0
-bD2 +(a-Cv)D - CF = 0
D’
= [-(a - Cv) +/- {(a-Cv)2 - 4(-b)(-CF)}1/2 ]/2(-b)
Example 2 – 6
A company producing electronic timing switch.
Per month: Cf = $73; 000 and Cv = $83
Moreover, p = $180 – 0.02(D)
Determine:
(a)
(b)
Optimal volume and confirm that a profit occurs at
this demand
Volume at which breakeven occurs
Example 2 – 6
A company produces an electronic timing switch that is used in consumer
and commercial products made by several other manufacturing firms. The
fixed cost (Cf) is $73,000 per month, and the variable cost (cv) is $83 per
unit. The selling price per unit is p - $180 - 0.02(D), based on Equation (21). For this situation:
a) Determine the optimal volume for this product and confirm that
a profit occurs (instead of a loss) at this demand, and
b) Find the volumes at which breakeven occurs; that is, what is
the domain of profitable demand?
Example 2-6
Example 2-6
Cost, Volume, and Breakeven Point
Relationships
Example 2-7
Example 2-7
Example 2-7
Thus, the breakeven
point is more sensitive
to a reduction in
variable cost per hour
than to the same
percentage reduction
in the fixed cost
Furthermore, notice
that the breakeven
point in this example
is highly sensitive to
the selling price per
unit, p.
Present Economy Studies
Present Economy Study
One year or less period
Rule 1
When the influence of time on money is not significant consideration, cost
analysis
When revenues and other economic benefits are present and vary among
alternatives, choose the alternative that maximizes overall profitability
based on the number of defect-free units of a product or service produced
Rule 2
When revenues and other economic benefits are not present or are constant
among all alternatives, consider only the costs and select the alternative that
minimizes total cost per defect-free unit of product or service output
Present Economy Studies
Total Cost in Material Selection
Material selection cannot be based solely on costs of materials.
Change in materials frequently affect design, processing, and
shipping costs.
Alternative Machine Speeds
Machine speeds result in different rates of product output and
frequencies of machine downtime.
Such situations lead to present economy studies
Present Economy Studies
Make vs. Purchase (Outsourcing) Studies
Short run production, one year or less
Choose “Make” rather than “Purchase” at a price lower than
production costs if:
•
•
Decision, based on
•
•
Costs (direct, indirect, overhead) are incurred regardless of whether
the item is purchased
Incremental production cost is less than purchase price
incremental costs
opportunity costs of resources
For long run, capital investments in additional manufacturing plant
may be feasible alternatives
Example : Total Cost in Material Selection
A good example of this situation is illustrated by a part for which annual
demand is 100,000 units. The part is produced on a high-speed turret
lathe, using 1112 screw-machine steel costing $0.30 per pound. A
study was conducted to determine whether it might be cheaper to use
brass screw stock, costing $1.40 per pound. Because the weight of
steel required per piece was 0.0353 pounds and that of brass was
0.0384 pounds, the material cost per piece was $0.0106 for steel and
$0.0538 for brass. However, when the manufacturing engineering
department was consulted, it was found that, although 57.1 defect-free
parts per hour were being produced by using steel, the output would
be 102.9 defect- free parts per hour if brass were used. Which material
should be used for this part?
Example : Solution
The machine attendant was paid $7.50 per hour, and the variable (i.e.,
traceable) overhead costs for the turret lathe were estimated to be $10.00 per
hour. Thus, the total-cost comparison for the two materials is as follows:
1112 Steel
Material
Labor
Overhead
Total cost per piece
Brass
$0.30 x 0.0353
= $0.0106
$1.40 x 0.0384
$7.50/57.1
= 0.1313
$7.50/102.9
= 0.0729
$10.00/57.1
= 0.1751
$10.00/102.9
= 0.0972
$0.4484
= $0.0538
$0.2968
Saving per piece by use of brass = $0.3179 - $0.2239 = $0.0931
Because a large number of parts are made each year, the saving of $93.10
per thousand was a substantial amount. It is also clear that costs other than
the cost of material are of basic importance in the economy study
Example
Later history of same product illustrates that shipping costs also must often be
considered in selecting between materials. It was found desirable to supply domestic /
foreign assembly plants of company by using air freight for shipping. This led to a
study of the possible use of a heat-treated Al alloy. This material cost $0.85/pound
and the cost of a heat treating each part, at an outside plant, was $0.018. Production
studies indicated that Al alloy could be machined at the same speeds as brass stock.
Specific gravities of brass and Al alloy are 8.7 and 2.75 respectively.
Brass (lb)
Aluminum Alloy (lb)
Raw Material
0.0384
(0.0384)(2.75/8.8) = 0.01213
Finished Part
0.0150
(0.0150)(2.75/8.8) = 0.00474
Consequently, comparative costs, including shipping at $3.00/lb of finished part is:
Brass (lb)
Aluminum Alloy (lb)
Material
$1.40 x 0.0384 = $0.0538
$0.85 x 0.01213 = $0.0103
Labor
$7.50 / 102.90 = $0.0729
$7.50 / 102.90 = $0.0729
Heat treatment
Overhead
Shipping
-
= $0.0180
$10 / 102.90 = $0.0972
$10 / 102.90 = $0.0972
$3.00 x 0.0150 = $0.0450
$3.00 x 0.00474 = $0.0142
Example : Alternative Machine Speeds
A simple example of alternative machine speeds involves the
planing of lumber. Lumber put through the planer increases in
value by $0.10 per board foot. When the planer is operated at a
cutting speed of 5,000 feet per minute, the blades have to be
sharpened after 2 hours of operation, and the lumber can be
planed at the rate of 1,000 board-feet per hour. When the
machine is operated at 6,000 feet per minute, the blades have to
be sharpened after 1-1/2 hours of operation, and the rate of
planing is 1,200 board-feet per hour. Each time the blades are
changed, the machine has to be shut down for 15 minutes. The
blades, unsharpened, cost $50 per set and can be sharpened 10
times before having to be discarded. Sharpening costs $10 per
occurrence. The crew that operates the planer changes and
resets the blades. At what speed should the planer be operated?
Example : Solution
Because the labor cost for the crew would be the same for either
speed of operation and because there was no discernible
difference in wear upon the planer, these factors did not have to
be included in the study.
In problems of this type, the operating time plus the delay time
due to the necessity for tool changes constitute a cycle time that
determines the output from the machine . The time required for a
complete cycle determines the number of cycles that can be
accomplished in a period of available time (e.g., one day), and a
certain portion of each complete cycle is productive. The actual
productive time will be the product of the productive time per
cycle and the number of cycles per day
Example : Solution
At 5,000 feet per minute
Cycle time = 2 hours + 0.25 hour = 2.25 hours
Cycles per day = 8 ÷ 2.25 = 3.555
Value added by planing = 3.555 x 2 x 1,000 x $0.10 =
Cost of resharpening blades = 3.555 x $10 = $35.55
Cost of blades = 3.555 x $50/10 = 17.78
Total cost
Net increase in value (profit) per day
At 6,000 feet per minute
Cycle time = 1.5 hours + 0.25 hour = 1.75 hours
Cycles per day = 8 ÷ 1.75 = 4.57
Value added by planing = 4.57 x 1.5 x 1,200 x $0.10 =
Cost of resharpening blades = 4.57 x $10 = $45.70
Cost of blades = 4.57 x $50/10 = 22.85
Total cost
Net increase in value (profit) per day
(cycles/day)(hours/cycle)(board feet/hour)(dollar value/board-foot) = dollars/day
$711.00
-53.33
$657.67
$822.00
-68.55
$754.05
Example 2-8 : Make vs Purchase Studies
A manufacturing plant consists of three departments: A, B, and C. Department A
occupies 100 square meters in one corner of the plant. Product X is one of
several products being produced in Department A. The daily production of
Product X is 576 pieces. The cost accounting records show the following average
daily production costs for Product X:
Direct labor
(1 operator working 4 hours per day at $22.50/hr,
$120.00
including fringe benefits, plus a part-time foreman
at $30 per day)
86.40
Direct material
Overhead
(at $0.82 per square meter of floor area)
Total cost per day =
82.00
$288.40
The department foreman has recently learned about an outside company that sells
Product X at $0.35 per piece. Accordingly, the foreman figured a cost per day of
$0.35(576) = $201.60, resulting in a daily savings of $288.40-$201.60 = $86.80.
Therefore, a proposal was submitted to the plant manager for shutting down the
production line of Product X and buying it from the outside company
Example 2-8
However, after examining each component separately, the plant manager decided not
to accept the foreman's proposal based on the unit cost of Product X:
1. Direct labor: Because the foreman was supervising the manufacture of other
products in Department A in addition to Product X, the only possible savings
in labor would occur if the operator working 4 hours per day on Product X
were not reassigned after this line is shut down. That is, a maximum savings
of $90.00 per day would result
2.
Materials: The maximum savings on direct material will be $86.40. However,
this figure could be lower if some of the material for Product X is obtained
from scrap of another product
3.
Overhead: Because other products are made in Department A, no reduction
in total floor space requirements will probably occur. Therefore, no reduction
in overhead costs will result from discontinuing Product X. It has been
estimated that there will be daily savings in the variable overhead costs
traceable to Product X of about $3.00 due to a reduction in power costs and in
insurance premiums
