Chapter 2
Engineering Costs
and Cost Estimating
1
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
2
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
3
Example
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
Equipment cost stays the same
B) Power cost
regardless the level of output once
C) Labor Cost
the plant has been designed to
produce at a certain level.
D) Material Cost
4
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
5
Example
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
Labor cost depends on the output level
C) Labor Cost
D) Property Taxes
6
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
7
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
TVC = 780,000 x 16 = $12,480,000
B) $3,200,016
FC = $3.2M
C) $12,480,000
D) $15,680,000
TC = FC+TVC = $15,680,000
8
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
Breakeven Analysis
Total Revenue
$
Profit
Total Costs
Variable Costs
Fixed Costs
Loss
Break-even Point
Production Quantity
10
Example 2-1
Total Revenue
= 35X
$1000
$800
Total Costs
= $225 + 20X
$600
Variable Costs
= 20X
Profit
$400
$200
$0
Fixed Costs
= $225
Loss
5
10
15
20
25
X
# of Customers
11
Example
A manufacturing firm’s 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?
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.
12
Example
In breakeven analysis, the profit at the breakeven point is
equal to
A) The total cost
B) Zero
The total revenue is equal to the total cost.
Therefore…
C) The total revenue
D) The variable cost multiplied by the number of items
sold
13
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
Example
What is marginal cost? Explain with an
example.
 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
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
16
Albert’s Charter Bus Venture (example)
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.
Item
Bus Rental
Gas Expense
Other Fuel Costs
Bus Driver
Cost
$80
$75
$20
$50
Total Costs
$225.00
Item
Ticket
Refreshments
Total Costs
Cost
$12.50
$ 7.50
$20.00
• Which of the above are fixed and which are variable costs?
• How do we compute Albert’s total cost if he takes n people to Jacksonville?
17
Albert’s Charter Bus Venture (example)
 Answer: Total Cost = $225 + $20 n.
Graph of Total Cost Equation:
Total cost
n
18
marginal cost
-The cost to take one more person
Marginal and Average Costs
average cost
$300.00
- Average
cost: the cost per person
Avg.$250.00
Cost = TC/n
Cost
Avg.$200.00
Cost = ($225+$20n)/n
= $20 + $225/n
Average
Marginal
$150.00
 For
n = 30, TC = $885
$100.00
Trip Ticket
Marginal and Average Costs
Avg. Cost = $885/30 = $29.50
$300.00
$50.00
$250.00
1
3
5
7
9
11
Cost
$200.00
$0.00
Average
$150.00
13
19
17
15
Marginal
23
21
Trip Ticket
$100.00
Number of People
$50.00
$0.00
1
3
5
7
9
11
13
15
17
19
21
23
Number of People
19
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)
20
Albert's Charter Bus Venture
Question:
$1,000.00
How
many people does Albert need to break even?
(not lose money on his venture)
$800.00
Solve$600.00
15 n – 225 = 0 => n=15
Total Cost
more$400.00
than 15, he makes money
Cost
Revenue
$200.00
Profit
$0.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
($200.00)
($400.00)
Number of People
21
Albert’s Charter Bus Venture (example)
Where is the Loss Region?
Where is the Profit Region?
Where is the Breakeven point?
Albert's Charter Bus Venture
$1,000.00
$800.00
Total Cost
$600.00
Cost
$400.00
Revenue
$200.00
Profit
$0.00
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
($200.00)
($400.00)
Number of People
22
Exercise 2.3
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?
a) 75 hours
23
Exercise 2.3
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?
b) 125 hours
24
Exercise 2.3
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?
c) 250 hours
25
Exercise 2.7
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
a) Develop the mathematical relationships for total cost and total revenue.
26
Exercise 2.7
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
b) What is the total number of campers that will allow the camp to
just break even?
$48,000 = $480 x
27
Exercise 2.7
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
c) What is the profit or loss for the 12-week session if the camp
operates at 80% capacity
28
Exercise 2.7
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
d) What are marginal and average costs per camper at
80% capacity?
x = 160
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
29
Sunk Costs
 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
30
Sunk Costs
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
31
Sunk Costs
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)
32
Example
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
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
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.
Item
Amount
Type of Costs
Price for case 3 years ago
$7,000
Sunk cost
Storage costs to date
$1,000
Sunk cost
35
Sunk and Opportunity Cost-2
Example 2-3. (cont.)
Item
Amount
Type 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
36
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
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
Example 2-3
Choosing between Model A & B
Cost Items
Model A Model B
Incremental
Cost
Purchase Price
$10,000 $17,500
$7,500
Installation Costs
$3,500
Annual Maintenance *
$2,500
Annual Utility *
$1,200
$2,000
$700
$500
Disposal Cost
$5,000
$1,500
$750 $ -1,750/yr
$800/yr
$ -200
* Must be multiplied by the number of years of service.
39
You must know this.
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 equipment—This is used to determine the value of the
company and in computing taxes.
40
You must know this.
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.
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.
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.
Cumulative Life-Cycle Costs
Committed and Spent
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Life-Cycle Costs Committed
Life-Cycle Costs Spent
Need
Assessment
Conceptual
Design
Detailed
Design
Production Operational
/Construction
/Use
Decline/
Retirement
44
You must know this.
Cost/Ease of Design Changes in
Product Life Cycle
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0%
Ease of Design Changes
Cost of Design Changes
Need
Assessment
Conceptual
Design
Detailed
Design
Production Operational
/Construction
/Use
Decline/
Retirement
45
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
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
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
You must know this.
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
49
You must know this.
Trade-off between Accuracy and Cost
Cost of Estimate
High
Low
Low
Medium
High
Accuracy of Estimate
Figure 2-6. Accuracy versus cost trade-off in estimation
50
You must know this.
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
51
You must know this.
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.
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.
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.
54
You must know this.
Per-Unit Model (Unit Technique)
 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
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
Example 2-4:
Cost Estimating using Per-Unit Model
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
57
Example 2-4:
Cost Estimating using Per-Unit Model`
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
58
Example 2-4:
Cost Estimating using Per-Unit Model`
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
59
Example 2-4:
Cost Estimating using Per-Unit Model
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 entertainment
0
– Subtotal
$410
• Total Costs:
$3966
Thus, the total cost per student would be
$3966/24 = $165.25
60
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
61
Segmenting Model (example)
A. Chassis
Cost Item
A.1 Deck
A.2 Wheels
A.3 Axles
Subtotal
B. Drive Train
Estimate
$7.00
10.00
5.85
$22.85
Cost Item
Estimate
B.1 Engine
$38.50
B.2 Starter assembly
6.90
B.3 Transmission
4.45
B.4 Drive disc assembly
10.00
B.5 Clutch linkage
6.15
B.6 Belt assemblies
8.70
Subtotal
$72.70
62
Segmenting Model (example)
C. Controls
Cost Item
Estimate
C.1 Handle assembly
$2.85
C.2 Engine linkage
9.55
C.3 Blade linkage
5.70
C.4 Speed control linkage
20.50
C.5 Drive control assembly
7.70
C.6 Cutting height adjuster
6.40
Subtotal
$52.70
D. Cutting/Collection system
Cost Item
D.1 Blade assembly
D.2 Side chute
D.3 Grass bag &
adapter
Subtotal
Estimate
$11.80
6.05
7.75
$25.60
Total material cost = $22.85 + $72.70 + $52.70 + $25.60 = $173.85
63
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
Cost A Index A

Cost B Index B
(Eq. 2-2)
64
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.
Labor Cost Now
 Indexnow 

 Labor Cost10 yrs 
 Index

10
yrs


 _______
$575,500




188 
___

 
___ 
124
871,800
65
Example 2.6 (Continued)
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.
 Indexnow 
Material Cost Now  Material Cost3 yrs 
 Index 
3 yrs 

 715 
 $2, 455, 000 
  $3, 227, 000
 544 
66
Power-Sizing Model
 Size(Capacity ) A 
Cost A  Cost B 

Size
(
Capacity
)

B 
X
(Eq. 2-3)
X = Power-sizing exponent
Example Power Sizing Exponent Values
Equipment/Facility
X
Equipment/Facility
X
Blower, centrifugal
Compressor
Crystallizer, vacuum
Dryer, drum
Fan, centrifugal
0.59
0.32
0.37
0.40
1.17
Filter, vacuum
Lagoon, aerated
Motor
Reactor
Tank, horizontal
0.48
1.13
0.69
0.56
0.57
67
Example 2.7
Miriam has been asked to estimate the cost today of a 2500 ft2
heat exchange system for the new plant being analyzed. She
has the following data.
• Her company paid $50.000 for a 1000 ft2 heat exchanger 5
years ago.
• Heat exchangers within this range of capacity have a
power sizing exponent (x) of 0.55
A. Considering Power-Sizing Index Change
 2500 ft
 Cost1000 ft 2 
2
1000
ft

2
Cost 2500 ft 2
 2500 
 $50,000

 1000 



0.55
0.55
 $82,800
68
Example 2.7 (Continued)
Miriam has been asked to estimate the cost today of a 2500 ft2
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.
B. Considering Cost Index Change
 Indexnow 
Cost Now  Cost5 yrs 
 Index 
5 yrs 

 1487   $94,300
 $82,800 

1306


69
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.
70
Improvement and Learning Curve
 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
71
Learning Curve
Let T1 = Time to perform the 1st unit
TN = Time to perform the Nth unit
b = Constant based on learning curve LC%
N = Number of completed units
TN  T1  Nb
(Eq. 2-4)
log LC ln LC
b

log 2
ln 2
(Eq. 2-5)
72
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%.
ln % ln(0.8)
b
 0.3219

ln 2
ln 2
TN  T1  N
b
T100  T1  (100)  (32.0)(100) 0.3219  7.27
b
73
Example 2.9
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.
ln % ln(0.85)
b

 0.2345
ln 2
ln 2
T16  T1  (16)b  T1  (16)0.2345  5.0
T1  5.0 /(16)
0.2345
 9 .6
TN  T1  Nb  (9.6)  N0.2345
74
Example 2-9:
Cost Estimating Using Learning Curve
8.16
7.42
6.94
6.58
6.31
6.08
5.90
5.73
5.59
12
13
14
15
16
17
18
19
20
5.36
5.26
5.17
5.09
5.00
5.00
5.00
5.00
5.00
8.00
TN
N
1
2
3
4
5
6
7
8
9
10
TNExample
 T1  Nb 2-9
 (9Cost
.6)  N0.2345
TNEstimating
N
Tusing
12.00
N
9.60
11 Curve
5.47
Learning
10.00
6.00
4.00
2.00
0.00
1
3
5
7
9
11
13
15
17
19
N
75
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
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
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
Cash Flow Diagrams (CFD)
Example
150
100
Timing of Cash Flow
At time zero (now)
1 time period from today
2 time periods from today
3 time periods from today
4 time periods from today
5 time periods from today
0
Size of Cash Flow
50
Positive $100
0
0
Negative $100
-50
-100
Positive $100
-150
Negative $150
-200
Negative $150
Positive $50
1
2
3
4
1
2
3
4
5
Series2
5
79
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 asset’s life
80
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
Drawing Cash Flow Diagrams
with Spreadsheet
0
-$80,000
0
O&M
1
$(12,000)
2
$(12,000)
3
$(12,000)
4
$(12,000)
5
$(12,000)
6
$ 10,000 $(12,000)
Overhaul
$(25,000)
Cash Flows
Year
Capital
Costs
1
2
3
4
5
6
$20,000
$10,000
$$(10,000)
$(20,000)
$(30,000)
$(40,000)
$(50,000)
$(60,000)
$(70,000)
$(80,000)
$(90,000)
Year
Capital Costs
O&M
Overhaul
82
End of Chapter 2