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
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Slide1
Chapter 2Engineering Costs and Cost Estimating
1
Slide22Learning ObjectivesUnderstand various cost conceptsBreakeven chartsUnderstand various cost estimation models
Be able to estimate engineering costs with various models
Cash Flow Diagrams
Slide33Engineering 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
Slide4A 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.
Slide55Engineering 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
Slide6A 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
Slide77Relevant 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
Slide8ExampleA 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 =
$15,680,000
Slide9Breakeven AnalysisBreakeven point: The level of business activity at which the total costs to provide the products (goods), or services are equal to the revenue generated. That is:Total costs = Total revenue
Total costs = Total fixed costs + Total variable costs
Applications of Breakeven analysis:
Determining minimum production quantity
Forecast production profit / loss
9
Slide10Production Quantity$Break-even Point
Fixed Costs
Variable Costs
Total Costs
Total Revenue
Loss
Profit
Breakeven Analysis
10
Slide11Example 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
Slide12A 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.
Slide13In 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…
Slide14Marginal 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
Slide15the 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.
Slide1616Engineering 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
Slide1717 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)
Slide1818Albert’s Charter Bus Venture (example)Answer: Total Cost = $225 + $20 n. Graph of Total Cost Equation:
n
Total cost
Slide1919marginal 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
Slide2020Question: 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)
Slide2121Question: 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
Slide2222Albert’s Charter Bus Venture (example)Where is the Loss Region?Where is the Profit Region? Where is the Breakeven point
?
Slide23A 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
Slide24A 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
Slide25A 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
Slide26A 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.
Slide27A 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
Slide28A 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
Slide29A 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
Slide30Costs 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
Slide31A 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
Slide32Example: 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
Slide33All 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
Slide34Opportunity 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
Slide3535Sunk 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
Slide3636Sunk 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
Slide37Recurring 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
Slide38Incremental 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
Slide39Example 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.
Slide40Cash 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.
Slide41Cash 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.
Slide42Life-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.
Slide43Phases 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.
Slide44Cumulative 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.
Slide450%
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.
Slide46Think – 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
Slide47Think – 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
Slide48Think – 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
Slide4949Cost 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.
Slide5050
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.
Slide5151Difficulties 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.
Slide52Categories 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.
Slide53Sources 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.
Slide5454Estimating 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.
Slide55Per-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.
Slide56Example 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
Slide57Cost 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
Slide58Solution: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
Slide59Solution: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
Slide60Solution (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
Slide6161Segmenting 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
Slide6262Segmenting 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
Slide6363Segmenting 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
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)
Slide6565Example 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
Slide6666
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)
Slide67Power-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
Slide6868Example 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
Slide6969
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.
Slide7070TriangulationTechniques 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.
Slide71Learning 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
Slide72Let 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
Slide7373
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%.
Slide7474
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
Slide75Example 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
Slide76Estimating 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
Slide77Estimating 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
Slide78Cash 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
Slide79Cash 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
Slide80Categories 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
Slide81Drawing 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
81
Slide82Drawing 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)
82
Slide83End of Chapter 2