2 Learning Objectives Understand various cost concepts
Breakeven charts Understand various cost estimation models Be able
to estimate engineering costs with various models Cash Flow
Diagrams
Slide 3
3 Engineering Costs Fixed costs The costs that do not change
during the time horizon of the study. They may relate to the
constant costs of equipment, utilities, rent, etc. Constant,
independent of the output or activity level. Examples: Property
taxes, insurance Management and administrative salaries License
fees, and interest costs on borrowed capital Rental or lease
Slide 4
A manufacturing plant that assembles television sets has
variable output volume from 200 sets to 350 sets a day. The
building for both manufacturing and warehousing has an area of 80,
000 square feet. It employs about 250 people. It produces all of
the components that go into the assembly. An example for fixed cost
in this plant is -------------------. A) Equipment Cost B) Power
cost C) Labor Cost D) Material Cost 4 Example Equipment cost stays
the same regardless the level of output once the plant has been
designed to produce at a certain level.
Slide 5
5 Engineering Costs Variable costs Costs that vary during the
time horizon of the study. Over the long-term all costs are
variable. Depends on the level of output or activity. Proportional
to the output or activity level. Example: Direct labor cost Direct
materials
Slide 6
A manufacturing plant that assembles television sets has
variable output volume from 200 sets to 350 sets a day. The
building for both manufacturing and warehousing has an area of 80,
000 square feet. It employs about 250 people. It produces all of
the components that go into the assembly. An example for variable
cost in the plant is ---------------. A) Building cost B) Equipment
Cost C) Labor Cost D) Property Taxes 6 Labor cost depends on the
output level Example
Slide 7
7 Relevant Formulae Total Variable Cost = Unit Variable Cost *
Quantity TVC = VC * Q Total Cost = Total Fixed Cost + Total
Variable Cost TC = FC + VC * Q Total Revenue = Unit Selling Price *
Quantity TR = SP * Q where TVC = Total variable cost VC = Variable
cost per unit Q = Production/Selling quantity FC = Total Fixed
costs TR = Total revenue SP = Selling price per unit
Slide 8
Example A company produces a single, high-volume product. One
year its production volume was 780,000 units, its fixed costs were
$3.2 million and its variable costs were $16 per unit. What was the
company's total cost for the year? A) $3,200,000 B) $3,200,016 C)
$12,480,000 D) $15,680,000 8 TVC = 780,000 x 16 = $12,480,000 FC =
$3.2M TC = FC+TVC = $15,680,000
Slide 9
Breakeven Analysis Breakeven point: The level of business
activity at which the total costs to provide the products (goods),
or services are equal to the revenue generated. That is: Total
costs = Total revenue Total costs = Total fixed costs + Total
variable costs Applications of Breakeven analysis: Determining
minimum production quantity Forecast production profit / loss
9
Slide 10
Production Quantity $ Break-even Point Fixed Costs Variable
Costs Total Costs Total Revenue Loss Profit Breakeven Analysis
10
Slide 11
Example 2-1 X # of Customers 15 Fixed Costs = $225 Variable
Costs = 20X Total Costs = $225 + 20X Total Revenue = 35X Loss
Profit $1000 $800 $600 $400 $200 $0 10 5 20 25 11
Slide 12
A manufacturing firms specialty circuit board division has
annual fixed costs of $100,000 and variable costs of $20.00 per
board. If they charge $100 per circuit board, how many circuit
boards must they produce and sell in order to break even? 12
Example To break even, total costs = total revenue, where total
costs = total fixed costs + total variable costs. $100,000 + $20X =
$100X X = $100,000/$80 = 1250 circuit boards.
Slide 13
In breakeven analysis, the profit at the breakeven point is
equal to A) The total cost B) Zero C) The total revenue D) The
variable cost multiplied by the number of items sold 13 Example The
total revenue is equal to the total cost. Therefore
Slide 14
Marginal Costs and Average Costs Marginal Costs Used to decide
whether an additional unit should be made, purchased, or enrolled
in. the variable cost for one more unit of output Capacity
Planning: excess capacity Basis for last-minute pricing Average
Costs: total cost divided by the total number of units produced.
Basis for normal pricing 14
Slide 15
the cost of producing one additional unit. used for making a
decision of whether or not it is economical to produce another unit
of the same item. Example: Taking the fifth person in a taxicab
that can take only four passengers. For the fifth person, a second
cab has to be hired. The cab fare for the second cab is the
marginal cost. 15 Example What is marginal cost? Explain with an
example.
Slide 16
16 Engineering Costs and Cost Estimating Key Question: Where do
the numbers come from that we use in engineering economic analysis?
Cost estimating is necessary in an economic analysis When working
in industry, you may need to consult with professional accountants,
engineers and other specialists to obtain such information
Slide 17
17 Albert plans to charter a bus to take people to see a
wrestling match show in Jacksonville. His wealthy uncle will
reimburse him for his personal time, so his time cost can be
ignored. ItemCost Bus Rental$80 Ticket$12.50 Gas Expense$75
Refreshments$ 7.50 Other Fuel Costs$20 Bus Driver$50 Total
Costs$225.00 Total Costs $20.00 Which of the above are fixed and
which are variable costs? How do we compute Alberts total cost if
he takes n people to Jacksonville? Alberts Charter Bus Venture
(example)
Slide 18
18 Alberts Charter Bus Venture (example) Answer: Total Cost =
$225 + $20 n. Graph of Total Cost Equation: n Total cost
Slide 19
19 marginal cost -The cost to take one more person average cost
- Average cost: the cost per person Avg. Cost = TC/n Avg. Cost =
($225+$20n)/n = $20 + $225/n For n = 30, TC = $885 Avg. Cost =
$885/30 = $29.50
Slide 20
20 Question: Do we have enough information yet to decide how
much money Albert will make on his venture? What else must we know?
Albert needs to know his total revenue Albert knows that similar
ventures in the past have charged $35 per person, so that is what
he decides to charge Total Revenue = 35n (for n people) Total
profit = Total Revenue Total Cost: 35n (225 + 20n) = 15n 225
Question: How many people does Albert need to break even? (not lose
money on his venture)
Slide 21
21 Question: How many people does Albert need to break even?
(not lose money on his venture) Solve 15 n 225 = 0 => n=15 more
than 15, he makes money
Slide 22
22 Alberts Charter Bus Venture (example) Where is the Loss
Region? Where is the Profit Region? Where is the Breakeven
point?
Slide 23
A new machine comes with 100 free service hours over the first
year. Additional time costs $75 per hour. What are the average and
marginal costs per hour for the following quantities? 23 Exercise
2.3 a) 75 hours
Slide 24
A new machine comes with 100 free service hours over the first
year. Additional time costs $75 per hour. What are the average and
marginal costs per hour for the following quantities? 24 Exercise
2.3 b) 125 hours
Slide 25
A new machine comes with 100 free service hours over the first
year. Additional time costs $75 per hour. What are the average and
marginal costs per hour for the following quantities? 25 Exercise
2.3 c) 250 hours
Slide 26
A privately owned summer camp for youngsters has the following
data for a 12-week session: Charge per camper$120 per week Fixed
costs $48,000 per session Variable cost per camper $80 per week
Capacity 200 campers 26 Exercise 2.7 a) Develop the mathematical
relationships for total cost and total revenue.
Slide 27
A privately owned summer camp for youngsters has the following
data for a 12-week session: Charge per camper$120 per week Fixed
costs $48,000 per session Variable cost per camper $80 per week
Capacity 200 campers 27 Exercise 2.7 b) What is the total number of
campers that will allow the camp to just break even? $48,000 = $480
x
Slide 28
A privately owned summer camp for youngsters has the following
data for a 12-week session: Charge per camper$120 per week Fixed
costs $48,000 per session Variable cost per camper $80 per week
Capacity 200 campers 28 Exercise 2.7 c) What is the profit or loss
for the 12-week session if the camp operates at 80% capacity
Slide 29
A privately owned summer camp for youngsters has the following
data for a 12-week session: Charge per camper$120 per week Fixed
costs $48,000 per session Variable cost per camper $80 per week
Capacity 200 campers 29 Exercise 2.7 d) What are marginal and
average costs per camper at 80% capacity? Marginal cost is the
slope of the equation which is equal to $960 Average cost is Total
Cost/x = ($48,000 + $960 * 160)/160 = $1260 x = 160
Slide 30
Costs associated with decisions already made. Money already
spent as a result of a past decision. Cost that has occurred in the
past and has no relevance to estimates of future costs and revenues
related to an alternative Must be ignored because current decisions
can not change the past Sunk Costs 30
Slide 31
A sunk cost is money already spent due to a past decision. As
engineering economists we deal with present and future
opportunities We must be careful not to be influenced by the past
Disregard sunk costs in engineering economic analysis Sunk Costs
31
Slide 32
Example: Suppose that three years ago your parents bought you a
laptop PC for $2000. How likely is it that you can sell it today
for what it cost? Suppose you can sell the laptop today for $400.
Does the $2000 purchase cost have any effect on the selling price
today? The $2000 is a sunk cost. It has no influence on the present
opportunity to sell the laptop for $400. ( stock now costs $20 but
you bought for $80) Sunk Costs 32
Slide 33
All of the following are usually included in an engineering
economic analysis except A) Fixed costs B) Variable costs C) Sunk
costs D) Total revenue 33 Example
Slide 34
Opportunity Costs Using a resource in one activity instead of
another Cost of the foregone opportunity and is hidden or implied
Going for $3000 trip and miss the opportunity of earning $5000 in
summer internship 34
Slide 35
35 Sunk and Opportunity Cost-1 Example 2-3. A distributor has a
case of electric pumps. The pumps are unused, but are three years
old. They are becoming obsolete. Some pricing information is
available as follows. ItemAmountType of Costs Price for case 3
years ago$7,000Sunk cost Storage costs to date$1,000
Slide 36
36 Sunk and Opportunity Cost-2 Example 2-3. (cont.)
ItemAmountType of Costs List price today for a case of new and up
to date pumps $12,000 Can be used to help determine what the lot is
worth today. Amount buyer offered for case 2 years ago $5,000 A
foregone opportunity Case can currently be sold for$3,000 Actual
market value today
Slide 37
Recurring Costs and Non-recurring Costs Recurring Costs:
Repetitive, and occur when a firm produces similar goods and
services on a continuing basis Office space rental Non-recurring
Costs: Not repetitive, even though the total expenditure may be
cumulative over a period of time Typically involves developing or
establishing a capability or capacity to operate Examples are
purchase cost for real estate and the construction costs of the
plant 37
Slide 38
Incremental Costs Incremental Costs: Difference in costs
between two alternatives. Suppose that A and B are mutually
exclusive alternatives. If A has an initial cost of $10,000 while B
has an initial cost of $14,000, the incremental initial cost of (B
- A) is $4,000. 38
Slide 39
Example 2-3 Choosing between Model A & B Cost ItemsModel
AModel B Incremental Cost Purchase Price$10,000$17,500 Installation
Costs$3,500$5,000 Annual Maintenance *$2,500$750 Annual Utility
*$1,200$2,000 Disposal Cost$700$500 $7,500 $1,500 $ -1,750/yr
$800/yr $ -200 39 * Must be multiplied by the number of years of
service.
Slide 40
Cash Costs versus Book Costs Book Costs: Costs that do not
involve money/cash transaction Cost effects from past decisions
that are recorded in the books (accounting books) of a firm Do not
represent cash flows Not included in engineering economic analysis
One exception is for asset depreciation. Depreciation Example:
Depreciation is charged for the use of assets, such as plant and
equipmentThis is used to determine the value of the company and in
computing taxes. 40 You must know this.
Slide 41
Cash Costs versus Book Costs Cash Costs: Costs that involve
money/cash transaction Require the cash transaction of dollars from
one pocket to another. Example: Interest payments, taxes, etc. You
might use Kelley Blue Book to conclude the book value of your car
is $6,000. The book value can be thought of as the book cost. If
you actually sell the car to a friend for $5,500, then the cash
cost to your friend is $5,500. 41 You must know this.
Slide 42
Life-Cycle Costs Life-Cycle Costs: 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 needs or wants (the requirements)
and ends with the retirement and disposal activities. 42 You must
know this.
Slide 43
Phases of Life Cycle 1. Need Assessment 2.Conceptual Design 3.
Detailed Design 4. Production /Construction 5.Operational Use 6.
Decline/ Retirement Requirements Analysis Impact Analysis
Allocation of Resources Production of Goods/ Services Distribution
of Goods/ Services Phase Out Overall Feasibility Study Proof of
Concept Detailed Specifications Building of Supporting Facilities
Maintenance/ Support Disposal Conceptual Design Planning Prototype/
Breadboard Component/ Supplier Selection Quality Control/ Assurance
Retirement Planning Retirement Development/ Testing Production
Planning Operational Planning Detailed Design Planning 43 You must
know this.
Slide 44
Cumulative Life-Cycle Costs Committed and Spent Life-Cycle
Costs Committed Life-Cycle Costs Spent 0% 10% 20% 30% 40% 50% 60%
70% 80% 90% 100% Need Assessment Conceptual Design Detailed Design
Production /Construction Operational /Use Decline/ Retirement 44
You must know this.
Slide 45
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Need Assessment
Conceptual Design Detailed Design Production /Construction
Operational /Use Decline/ Retirement Cost/Ease of Design Changes in
Product Life Cycle Ease of Design Changes Cost of Design Changes 45
You must know this.
Slide 46
Think Pair Share Tech Engineering Inc. makes a consumer product
for which the following cost data are available. Fixed cost/ year =
$120,000 Variable costs/ unit = $15 i. Determine the breakeven
volume if each unit can be sold for $40. ii. If a net profit of
$100,000 is required, determine the number of units that needed to
be sold. 46
Slide 47
Think Pair Share Tech Engineering Inc. makes a consumer product
for which the following cost data are available. Fixed cost/ year =
$120,000 Variable costs/ unit = $15 i. Determine the breakeven
volume if each unit can be sold for $40. 47
Slide 48
Think Pair Share Tech Engineering Inc. makes a consumer product
for which the following cost data are available. Fixed cost/ year =
$120,000 Variable costs/ unit = $15 ii. If a net profit of $100,000
is required, determine the number of units that needed to be sold.
48
Slide 49
49 Cost Estimating and Estimating Models Needs for Cost
Estimating Importance of Cost Estimating Types of Cost Estimating
Rough Estimates -30% to +60% Used for general feasibility
activities Semi-detailed Estimates -15% to +20% Budgeting and
preliminary design decisions Detailed Estimates -3% to +5%
Establishing design details and contracts You must know this.
Slide 50
50 Low High Low Medium High Cost of Estimate Accuracy of
Estimate Trade-off between Accuracy and Cost Figure 2-6. Accuracy
versus cost trade-off in estimation You must know this.
Slide 51
51 Difficulties in Estimation One-of-a-Kind or first-run
projects Estimates Ex: First NASA mission Time and Effort Available
Constraint on time and person-power can make the overall estimating
task more difficult. Estimator Expertise You must know this.
Slide 52
Categories of Cost Estimating Capital Investment (S&H,
Installation, Training) Labor Costs (Direct and Indirect) Material
Costs (Direct & Indirect) Maintenance Costs (Regular &
Overhaul) Property Taxes and Insurance Operating Costs (Rental,
Gas, Electricity) Quality Costs (Scrap, Rework, Inspection)
Overhead Costs (Administration, Sales) Disposal Costs Revenues
Market Values 52 You must know this.
Slide 53
Sources of Cost Estimating Data Accounting records Other
sources within the firm: Engineering, Production, Quality Sales,
Purchasing, Personnel Published information: Statistical Abstract
of US Cost indexes Monthly Labor Review Labor costs Building
Construction Cost Data Other sources outside the firm: Vendor,
Salespeople Research & Development Pilot plant, Test market 53
You must know this.
Slide 54
54 Estimating models Per-Unit Model (Unit Technique) Segmenting
Model Cost Indexes Power-Sizing Model Triangulation Improvement and
the Learning Curve We will look at each of these. You must know
this.
Slide 55
Per-Unit Model (Unit Technique) Construction cost per square
foot (building) Capital cost of power plant per kW of capacity
Revenue / Maintenance Cost per mile (hwy) Utility cost per square
foot of floor space Fuel cost per kWh generated Revenue per
customer served 55 You must know this.
Slide 56
Example 2-4: Cost Estimating using Per-Unit Model Cost
estimation of camping on an island for 24 students over 10 days.
Planned Activities: 2 days of canoeing 3-day hikes 3 days at the
beach Nightly entertainment 56
Slide 57
Cost Data: Van (capacity 15) rental: $50 one way Camp is 50
miles away, van gets 10 miles/gallon, and gas is $1/gallon Each
cabin holds 4 campers, rent is $10/day-cabin Meals are
$10/day-camper Boat transportation is $2/camper (one way)
Insurance/grounds fees/overhead is $1/day-camper Canoe (capacity 3)
rentals are $5/day-canoe Day hikes are $2.50/camper-day Beach
rental is $25/group-(half-day) Nightly entertainment is free
Example 2-4: Cost Estimating using Per-Unit Model 57
Slide 58
Solution: Assumption: 100% participation in all activities
Transportation Costs: Van: $50/van-trip * 2 vans * 2 trips = $200
Gas: $1/gallon * (50 miles / 10 miles/gallon) *2 *2 =20 Boat:
$2/camper-trip * 24 campers * 2 =96 Subtotal$316 Example 2-4: Cost
Estimating using Per-Unit Model` 58
Slide 59
Solution: Living Costs: Meals: $10/day-camper * 24 campers * 10
days = $2400 Cabin rental: $10/day-cabin * (24/4) cabins *10 days
=600 Insurance: $1/day-camper * 24 campers * 10 days = 240
Subtotal$3240 Example 2-4: Cost Estimating using Per-Unit Model`
59
Slide 60
Solution (Continued): Entertainment Costs: Canoe rental:
$5/day-canoe * 2 days * (24/3) canoes = $80 Beach rental:
$25/group-(half-day) * (3*2) half-days =150 Day hike:
$2.50/camper-day* 24 campers * 3 days =180 Nightly entertainment0
Subtotal$410 Total Costs:$3966 Thus, the total cost per student
would be $3966/24 = $165.25 Example 2-4: Cost Estimating using
Per-Unit Model 60
Slide 61
61 Segmenting Model (example) Estimate is decomposed into
individual components Estimates are made at component level
Individual estimates are aggregated back together Consider a
lawnmower A. Chassis B. Drive Train C. Controls D.
Cutting/Collection system
63 Segmenting Model (example) Cost ItemEstimate C.1 Handle
assembly$2.85 C.2 Engine linkage9.55 C.3 Blade linkage5.70 C.4
Speed control linkage20.50 C.5 Drive control assembly7.70 C.6
Cutting height adjuster6.40 Subtotal$52.70 Cost ItemEstimate D.1
Blade assembly$11.80 D.2 Side chute6.05 D.3 Grass bag & adapter
7.75 Subtotal$25.60 C. ControlsD. Cutting/Collection system Total
material cost = $22.85 + $72.70 + $52.70 + $25.60 = $173.85
Slide 64
64 Costs indexes Reflect historical change in cost Cost index
could be individual cost items (labor, material, utilities), or
group of costs (consumer prices, producer prices) Indexes can be
used to update historical costs (Eq. 2-2)
Slide 65
65 Example 2.6 Miriam is interested in estimating the annual
labor and material costs for a new production facility. She was
able to obtain the following labor and material cost data: Labor
cost index value was at 124 ten years ago and is 188 today. Annual
labor costs for a similar facility were $575,500 ten years ago. 188
124 871,800 $575,500
Slide 66
66 Miriam is interested in estimating the annual labor and
material costs for a new production facility. She was able to
obtain the following labor and material cost data: Material cost
index value was at 544 three years ago and is 715 today. Annual
material costs for a similar facility were $2,455,000 three years
ago. Example 2.6 (Continued)
Slide 67
Power-Sizing Model X = Power-sizing exponent
Equipment/FacilityX Blower, centrifugal0.59 Compressor0.32
Crystallizer, vacuum0.37 Dryer, drum0.40 Fan, centrifugal1.17
Equipment/FacilityX Filter, vacuum0.48 Lagoon, aerated1.13
Motor0.69 Reactor0.56 Tank, horizontal0.57 (Eq. 2-3) Example Power
Sizing Exponent Values 67
Slide 68
68 Example 2.7 A. Considering Power-Sizing Index Change Miriam
has been asked to estimate the cost today of a 2500 ft 2 heat
exchange system for the new plant being analyzed. She has the
following data. Her company paid $50.000 for a 1000 ft 2 heat
exchanger 5 years ago. Heat exchangers within this range of
capacity have a power sizing exponent (x) of 0.55
Slide 69
69 B. Considering Cost Index Change Example 2.7 (Continued)
Miriam has been asked to estimate the cost today of a 2500 ft 2
heat exchange system for the new plant being analyzed. She has the
following data. Five years ago the Heat Exchanger Cost Index (HECI)
was 1306; it is 1487 today.
Slide 70
70 Triangulation Techniques Used in Surveying: To map points of
interest by using three fixed points and horizontal angular
distance Application in Economic Analysis: To approach economic
estimate from different perspectives, such as different source of
data, or different quantitative models.
Slide 71
Learning Phenomenon: As the number of repetitions increase,
performance of people becomes faster and more accurate. Learning
curve captures the relationship between task performance and task
repetition. In general, as output doubles the unit production time
will be reduced to some fixed percentage, the learning curve
percentage or learning curve rate Improvement and Learning Curve
71
Slide 72
Let T 1 = Time to perform the 1 st unit T N = Time to perform
the N th unit b = Constant based on learning curve LC% N = Number
of completed units (Eq. 2-4) (Eq. 2-5) Learning Curve 72
Slide 73
73 Example 2.8 Calculate the time required to produce the
hundredth unit of a production run if the first unit took 32.0
minutes to produce and the learning curve rate for production is
80%.
Slide 74
74 Estimate the overall labor cost portion due to a task that
has a learning-curve rate of 85% and reaches a steady state value
of 5.0 minutes per unit after 16 units. Labor and benefits are $22
per hour, and the task requires two skilled workers. The overall
production run is 20 units. Example 2.9
Slide 75
Example 2-9 Cost Estimating using Learning Curve NTNTN 19.60
28.16 37.42 46.94 56.58 66.31 76.08 85.90 95.73 105.59 NTNTN 115.47
125.36 135.26 145.17 155.09 165.00 175.00 185.00 195.00 205.00
Example 2-9: Cost Estimating Using Learning Curve 75
Slide 76
Estimating Benefits-1 Sample Benefits Sales of products
Revenues from bridge tolls & electric power sale Cost reduction
from reduced material or labor costs Less time spent in traffic
jams Reduced risk of flooding 76
Slide 77
Estimating Benefits-2 Cost concepts and cost estimating models
can also be applied to economic benefits Uncertainty in benefit
estimating is typically asymmetric, with a broader limit for
negative outcomes, e.g. -50% to +20% Benefits are more difficult to
estimate than costs 77
Slide 78
Cash Flow Diagrams (CFD) CFD summarize costs & benefits
occur over time CFD illustrates the size, sign, and timing of
individual cash flows Components of CFD A segmented time-based
horizontal line, divided into time units A vertical arrow
representing a cash flow is added at the time it occurs Arrow
pointing down for costs and up for benefits 78
Slide 79
Cash Flow Diagrams (CFD) Example Timing of Cash FlowSize of
Cash Flow At time zero (now)Positive $100 1 time period from
todayNegative $100 2 time periods from todayPositive $100 3 time
periods from todayNegative $150 4 time periods from todayNegative
$150 5 time periods from todayPositive $50 4 0 1 23 5 79
Slide 80
Categories of Cash Flows First cost: expenses to build or to
buy and install Operations and maintenance (O&M): annual
expense, such as electricity, labor, and minor repairs Salvage
value: receipt at project termination for sale or transfer of the
equipment Revenues: annual receipts due to sale of products or
services Overhaul: major capital expenditure that occurs during the
assets life 80
Slide 81
Drawing a Cash Flow Diagram CFD shows when all cash flows occur
In a CFD, the end of period t is the same time as the beginning of
period t+1 Rent, lease, and insurance payments are usually treated
as beginning-of-period cash flows O&M, salvage, revenues, and
overhauls are assumed to be end-of-period cash flows The choice of
time 0 is arbitrary 81
Slide 82
Drawing Cash Flow Diagrams with Spreadsheet Year Capital
CostsO&MOverhaul 0 -$80,000 1 $(12,000) 2 3 $(25,000) 4
$(12,000) 5 6 $ 10,000 $(12,000) 82