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Chapter 2 Engineering Costs Chapter 2 Engineering Costs

Chapter 2 Engineering Costs - PowerPoint Presentation

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Chapter 2 Engineering Costs - PPT Presentation

and Cost Estimating 1 2 Learning Objectives Understand various cost concepts Breakeven charts Understand various cost estimation models Be able to estimate engineering costs with various models ID: 815227

costs cost 000 total cost costs total 000 unit variable time estimating cash labor camper production day today fixed

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Slide1

Chapter 2Engineering Costs and Cost Estimating

1

Slide2

2Learning ObjectivesUnderstand various cost conceptsBreakeven chartsUnderstand various cost estimation models

Be able to estimate engineering costs with various models

Cash Flow Diagrams

Slide3

3Engineering CostsFixed costsThe 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

Slide4

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 -------------------.

Equipment Cost

Power cost

Labor Cost

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.

Slide5

5Engineering CostsVariable costsCosts 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

Slide6

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

Slide7

7Relevant FormulaeTotal Variable Cost = Unit Variable Cost * QuantityTVC = VC * QTotal Cost = Total Fixed Cost + Total Variable CostTC = 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

Slide8

ExampleA 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

Slide9

Breakeven AnalysisBreakeven 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

Slide10

Production Quantity$Break-even Point

Fixed Costs

Variable Costs

Total Costs

Total Revenue

Loss

Profit

Breakeven Analysis

10

Slide11

Example 2-1 X# of Customers15

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

Slide12

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?

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.

Slide13

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…

Slide14

Marginal Costs and Average CostsMarginal CostsUsed to decide whether an additional unit should be made, purchased, or enrolled in.the variable cost for one more unit of outputCapacity 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

Slide15

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.

Slide16

16Engineering Costs and Cost EstimatingKey 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

Slide17

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.

Item Cost Item Cost

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 Albert’s

total cost

if he takes

n

people to Jacksonville?

Albert’s Charter Bus Venture (example)

Slide18

18Albert’s Charter Bus Venture (example)Answer: Total Cost = $225 + $20 n.  Graph of Total Cost Equation:  

n

Total cost

Slide19

19marginal 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

Slide20

20Question: 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)

Slide21

21Question: 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

Slide22

22Albert’s Charter Bus Venture (example)Where is the Loss Region?Where is the Profit Region? Where is the Breakeven point

?

Slide23

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

Slide24

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

Slide25

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

Slide26

A privately owned summer camp for youngsters has the following data for a 12-week session:Charge per camper $120 per weekFixed costs $48,000 per session Variable cost per camper $80 per weekCapacity 200 campers26

Exercise

2.7

a) Develop the mathematical relationships for total cost and total revenue.

Slide27

A privately owned summer camp for youngsters has the following data for a 12-week session:Charge per camper $120 per weekFixed costs $48,000 per session Variable cost per camper $80 per weekCapacity 200 campers27

Exercise

2.7

b) What is the total number of campers that will allow the camp to just break even?

$48,000 = $480 x

Slide28

A privately owned summer camp for youngsters has the following data for a 12-week session:Charge per camper $120 per weekFixed costs $48,000 per session Variable cost per camper $80 per weekCapacity 200 campers28

Exercise

2.7

c) What is the profit or loss for the 12-week session if the camp operates at 80% capacity

Slide29

A privately owned summer camp for youngsters has the following data for a 12-week session:Charge per camper $120 per weekFixed costs $48,000 per session Variable cost per camper $80 per weekCapacity 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

Slide30

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 alternativeMust be ignored because current decisions can not change the past

Sunk Costs

30

Slide31

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

Slide32

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

Slide33

All of the following are usually included in an engineering economic analysis exceptA) Fixed costs 

B) Variable costs 

C) Sunk costs 

D) Total revenue 

33

Example

Slide34

Opportunity CostsUsing a resource in one activity instead of anotherCost of the foregone opportunity and is hidden or impliedGoing for $3000 trip and miss the opportunity of earning $5000 in summer internship

34

Slide35

35Sunk 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

Sunk cost

Storage costs to date $1,000

Slide36

36Sunk 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

Slide37

Recurring Costs and Non-recurring CostsRecurring Costs: Repetitive, and occur when a firm produces similar goods and services on a continuing basisOffice space rentalNon-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

Slide38

Incremental CostsIncremental 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

Slide39

Example 2-3 Choosing between Model A & BCost Items

Model A

Model 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.

Slide40

Cash Costs versus Book CostsBook Costs: Costs that do not involve money/cash transactionCost 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.

Slide41

Cash Costs versus Book CostsCash Costs: Costs that involve money/cash transactionRequire 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.

Slide42

Life-Cycle CostsLife-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.

Slide43

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.

Slide44

Cumulative Life-Cycle CostsCommitted 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.

Slide45

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.

Slide46

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

Slide47

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

Slide48

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

Slide49

49Cost Estimating and Estimating ModelsNeeds for Cost EstimatingImportance 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.

Slide50

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.

Slide51

51Difficulties in EstimationOne-of-a-Kind or first-run projects EstimatesEx: First NASA missionTime and Effort Available

Constraint on time and person-power can make the overall estimating task more difficult.

Estimator Expertise

You must know this.

Slide52

Categories of Cost EstimatingCapital 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.

Slide53

Sources of Cost Estimating DataAccounting recordsOther 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.

Slide54

54Estimating modelsPer-Unit Model (Unit Technique)Segmenting ModelCost Indexes

Power-Sizing Model

Triangulation

Improvement and the Learning Curve

We will look at each of these.

You must know this.

Slide55

Per-Unit Model (Unit Technique)Per-Unit Model (Unit Technique)Construction cost per square foot (building)Capital cost of power plant per kW of capacityRevenue / 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.

Slide56

Example 2-4: Cost Estimating using Per-Unit ModelCost 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

Slide57

Cost Data:Van (capacity 15) rental: $50 one wayCamp 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

Slide58

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

Slide59

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

Slide60

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

Example 2-4:

Cost Estimating using Per-Unit Model

60

Slide61

61Segmenting Model (example)Estimate is decomposed into individual componentsEstimates are made at component levelIndividual estimates are aggregated back together

Consider a lawnmower

A. Chassis

B. Drive Train

C. Controls

D. Cutting/Collection system

Slide62

62Segmenting Model (example)

Cost Item

Estimate

A.1 Deck

$7.00

A.2 Wheels

10.00

A.3 Axles

5.85

Subtotal

$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

A. Chassis

B. Drive Train

Slide63

63Segmenting Model (example)

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

Cost Item

Estimate

D.1 Blade assembly

$11.80

D.2 Side chute

6.05

D.3 Grass bag & adapter

7.75

Subtotal

$25.60

C. Controls

D. Cutting/Collection system

Total material cost = $22.85 + $72.70 + $52.70 + $25.60 = $173.85

Slide64

64Costs indexesReflect historical change in costCost 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)

Slide65

65Example 2.6Miriam 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

Slide66

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)

Slide67

Power-Sizing Model

X = Power-sizing exponent

Equipment/Facility

X

Blower, centrifugal

0.59

Compressor

0.32

Crystallizer, vacuum

0.37

Dryer, drum

0.40

Fan, centrifugal

1.17

Equipment/Facility

X

Filter, vacuum

0.48

Lagoon, aerated

1.13

Motor

0.69

Reactor

0.56

Tank, horizontal

0.57

(Eq. 2-3)

Example Power Sizing Exponent Values

67

Slide68

68Example 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

Slide69

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.

Slide70

70TriangulationTechniques 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.

Slide71

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

Slide72

Let T1 = Time to perform the 1st 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

Slide73

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%.

Slide74

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

Slide75

Example 2-9 Cost Estimating using Learning Curve

N

T

N

1

9.60

2

8.16

3

7.42

4

6.94

5

6.58

6

6.31

7

6.08

8

5.90

9

5.73

10

5.59

N

T

N

11

5.47

12

5.36

13

5.26

14

5.17

15

5.09

16

5.00

17

5.00

18

5.00

19

5.00

20

5.00

Example 2-9:

Cost Estimating Using Learning Curve

75

Slide76

Estimating Benefits-1Sample Benefits Sales of productsRevenues 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

Slide77

Estimating Benefits-2Cost concepts and cost estimating models can also be applied to economic benefitsUncertainty 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

Slide78

Cash Flow Diagrams (CFD)CFD summarize costs & benefits occur over timeCFD illustrates the size, sign, and timing of individual cash flowsComponents of CFDA 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

Slide79

Cash Flow Diagrams (CFD)ExampleTiming of Cash Flow

Size of Cash Flow

At time zero (now)

Positive $100

1 time period from today

Negative $100

2 time periods from today

Positive $100

3 time periods from today

Negative $150

4 time periods from today

Negative $150

5 time periods from today

Positive $50

4

0

1

2

3

5

79

Slide80

Categories of Cash FlowsFirst cost: expenses to build or to buy and installOperations and maintenance (O&M): annual expense, such as electricity, labor, and minor repairsSalvage 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

Slide81

Drawing a Cash Flow DiagramCFD shows when all cash flows occurIn 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

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Drawing Cash Flow Diagrams with SpreadsheetYear

Capital Costs

O&M

Overhaul

0

-$80,000

1

$(12,000)

2

$(12,000)

3

$(12,000)

$(25,000)

4

$(12,000)

5

$(12,000)

6

$ 10,000

$(12,000)

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End of Chapter 2