engineering economics
amrjaghoob
Chapter2.pptxChapter 2 Engineering Costs and Cost Estimating
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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
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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
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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
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Example
Equipment cost stays the same regardless the level of output once the plant has been designed to produce at a certain level.
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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
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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
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Labor cost depends on the output level
Example
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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
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
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TVC = 780,000 x 16 = $12,480,000
FC = $3.2M
TC = FC+TVC = $15,680,000
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
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Production Quantity
$
Break-even Point
Fixed Costs
Variable Costs
Total Costs
Total Revenue
Loss
Profit
Breakeven Analysis
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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
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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?
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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.
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
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Example
The total revenue is equal to the total cost. Therefore…
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
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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.
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Example
What is marginal cost? Explain with an example.
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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
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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)
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Albert’s Charter Bus Venture (example)
Answer: Total Cost = $225 + $20 n.
Graph of Total Cost Equation:
n
Total cost
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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
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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)
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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
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Albert’s Charter Bus Venture (example)
Where is the Loss Region?
Where is the Profit Region?
Where is the Breakeven point?
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?
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Exercise 2.3
a) 75 hours
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?
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Exercise 2.3
b) 125 hours
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?
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Exercise 2.3
c) 250 hours
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
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Exercise 2.7
a) Develop the mathematical relationships for total cost and total revenue.
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
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Exercise 2.7
b) What is the total number of campers that will allow the camp to just break even?
$48,000 = $480 x
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
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Exercise 2.7
c) What is the profit or loss for the 12-week session if the camp operates at 80% capacity
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
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Exercise 2.15
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
at x = 160
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
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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
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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
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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
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Example
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
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Sunk and Opportunity Cost-1
Example 2-2. 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
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Sunk and Opportunity Cost-2
Example 2-2. (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
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
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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.
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Example 2-3 Choosing between Model A & B
| Cost 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
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* Must be multiplied by the number of years of service.
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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.
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You must know this.
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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.
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You must know this.
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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.
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You must know this.
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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 |
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You must know this.
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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
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You must know this.
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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
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You must know this.
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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.
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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.
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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.
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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.
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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.
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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.
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
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You must know this.
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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
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You must know this.
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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.
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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
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You must know this.
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Example A: 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
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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 A: Cost Estimating using Per-Unit Model
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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 A: Cost Estimating using Per-Unit Model`
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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 A: Cost Estimating using Per-Unit Model`
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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 A: Cost Estimating using Per-Unit Model
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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
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Segmenting Model (example 2-5)
| 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
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Segmenting Model (example 2-5)
| 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
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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)
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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
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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)
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
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Example 2.7
A. Considering Power-Sizing Index Change
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
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B. Considering Cost Index Change
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.
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
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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
(Eq. 2-4)
(Eq. 2-5)
Learning Curve
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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%.
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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 B
Example 2-9 Cost Estimating using
Learning Curve
| N | TN |
| 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 | TN |
| 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 B:
Cost Estimating Using Learning Curve
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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
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Cash Flow Diagrams (CFD) Example
| Timing 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
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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
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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
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Drawing Cash Flow Diagrams with Spreadsheet
| Year | 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
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Marginal and Average Costs
$0.00
$50.00
$100.00
$150.00
$200.00
$250.00
$300.00
1357911131517192123
Number of People
Cost
Average
Marginal
Trip Ticket
Chart6
| 245 | 20 | 35 |
| 132.5 | 20 | 35 |
| 95 | 20 | 35 |
| 76.25 | 20 | 35 |
| 65 | 20 | 35 |
| 57.5 | 20 | 35 |
| 52.1428571429 | 20 | 35 |
| 48.125 | 20 | 35 |
| 45 | 20 | 35 |
| 42.5 | 20 | 35 |
| 40.4545454545 | 20 | 35 |
| 38.75 | 20 | 35 |
| 37.3076923077 | 20 | 35 |
| 36.0714285714 | 20 | 35 |
| 35 | 20 | 35 |
| 34.0625 | 20 | 35 |
| 33.2352941176 | 20 | 35 |
| 32.5 | 20 | 35 |
| 31.8421052632 | 20 | 35 |
| 31.25 | 20 | 35 |
| 30.7142857143 | 20 | 35 |
| 30.2272727273 | 20 | 35 |
| 29.7826086957 | 20 | 35 |
Alber's Charter Bus
| Albert's Charter Bus Venture | ||||
| Fixed Costs | Variable Costs | |||
| Bus Rental | $80 | Ticket | $12.50 | |
| Gas Expense | $75 | Refreshments | $7.50 | |
| Other Fuel Costs | $20 | |||
| Bus Driver | $50 | |||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |
| Ticket Price | $35 | |||
| Number of people | Cost | Revenue | Profit | Avr. Cost |
| 0 | ||||
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 | ||||
| 7 | ||||
| 8 | ||||
| 9 | ||||
| 10 | ||||
| 11 | ||||
| 12 | ||||
| 13 | ||||
| 14 | ||||
| 15 | ||||
| 16 | ||||
| 17 | ||||
| 18 | ||||
| 19 | ||||
| 20 | ||||
| 21 | ||||
| 22 | ||||
| 23 |
Albert's Charter Bus (solution)
| Albert's Charter Bus Venture | ||||||
| Fixed Costs | Variable Costs | |||||
| Bus Rental | $80 | Ticket | $12.50 | |||
| Gas Expense | $75 | Refreshments | $7.50 | |||
| Other Fuel Costs | $20 | |||||
| Bus Driver | $50 | |||||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |||
| Trip Ticket Price | $35 | |||||
| Number of people | Cost | Revenue | Profit | Avr. Cost | Marg. Cost | Trip Ticket Price |
| 0 | $225.00 | $0 | ($225.00) | $20.00 | $35 | |
| 1 | $245.00 | $35 | ($210.00) | $245.00 | $20.00 | $35 |
| 2 | $265.00 | $70 | ($195.00) | $132.50 | $20.00 | $35 |
| 3 | $285.00 | $105 | ($180.00) | $95.00 | $20.00 | $35 |
| 4 | $305.00 | $140 | ($165.00) | $76.25 | $20.00 | $35 |
| 5 | $325.00 | $175 | ($150.00) | $65.00 | $20.00 | $35 |
| 6 | $345.00 | $210 | ($135.00) | $57.50 | $20.00 | $35 |
| 7 | $365.00 | $245 | ($120.00) | $52.14 | $20.00 | $35 |
| 8 | $385.00 | $280 | ($105.00) | $48.13 | $20.00 | $35 |
| 9 | $405.00 | $315 | ($90.00) | $45.00 | $20.00 | $35 |
| 10 | $425.00 | $350 | ($75.00) | $42.50 | $20.00 | $35 |
| 11 | $445.00 | $385 | ($60.00) | $40.45 | $20.00 | $35 |
| 12 | $465.00 | $420 | ($45.00) | $38.75 | $20.00 | $35 |
| 13 | $485.00 | $455 | ($30.00) | $37.31 | $20.00 | $35 |
| 14 | $505.00 | $490 | ($15.00) | $36.07 | $20.00 | $35 |
| 15 | $525.00 | $525 | $0.00 | $35.00 | $20.00 | $35 |
| 16 | $545.00 | $560 | $15.00 | $34.06 | $20.00 | $35 |
| 17 | $565.00 | $595 | $30.00 | $33.24 | $20.00 | $35 |
| 18 | $585.00 | $630 | $45.00 | $32.50 | $20.00 | $35 |
| 19 | $605.00 | $665 | $60.00 | $31.84 | $20.00 | $35 |
| 20 | $625.00 | $700 | $75.00 | $31.25 | $20.00 | $35 |
| 21 | $645.00 | $735 | $90.00 | $30.71 | $20.00 | $35 |
| 22 | $665.00 | $770 | $105.00 | $30.23 | $20.00 | $35 |
| 23 | $685.00 | $805 | $120.00 | $29.78 | $20.00 | $35 |
Albert's Charter Bus (solution)
Chart5
| 0 | 0 |
| 1 | 35 |
| 2 | 70 |
| 3 | 105 |
| 4 | 140 |
| 5 | 175 |
| 6 | 210 |
| 7 | 245 |
| 8 | 280 |
| 9 | 315 |
| 10 | 350 |
| 11 | 385 |
| 12 | 420 |
| 13 | 455 |
| 14 | 490 |
| 15 | 525 |
| 16 | 560 |
| 17 | 595 |
| 18 | 630 |
| 19 | 665 |
| 20 | 700 |
| 21 | 735 |
| 22 | 770 |
| 23 | 805 |
2
3
4
Chart6
| 245 | 20 | 35 |
| 132.5 | 20 | 35 |
| 95 | 20 | 35 |
| 76.25 | 20 | 35 |
| 65 | 20 | 35 |
| 57.5 | 20 | 35 |
| 52.1428571429 | 20 | 35 |
| 48.125 | 20 | 35 |
| 45 | 20 | 35 |
| 42.5 | 20 | 35 |
| 40.4545454545 | 20 | 35 |
| 38.75 | 20 | 35 |
| 37.3076923077 | 20 | 35 |
| 36.0714285714 | 20 | 35 |
| 35 | 20 | 35 |
| 34.0625 | 20 | 35 |
| 33.2352941176 | 20 | 35 |
| 32.5 | 20 | 35 |
| 31.8421052632 | 20 | 35 |
| 31.25 | 20 | 35 |
| 30.7142857143 | 20 | 35 |
| 30.2272727273 | 20 | 35 |
| 29.7826086957 | 20 | 35 |
Alber's Charter Bus
| Albert's Charter Bus Venture | ||||
| Fixed Costs | Variable Costs | |||
| Bus Rental | $80 | Ticket | $12.50 | |
| Gas Expense | $75 | Refreshments | $7.50 | |
| Other Fuel Costs | $20 | |||
| Bus Driver | $50 | |||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |
| Ticket Price | $35 | |||
| Number of people | Cost | Revenue | Profit | Avr. Cost |
| 0 | ||||
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 | ||||
| 7 | ||||
| 8 | ||||
| 9 | ||||
| 10 | ||||
| 11 | ||||
| 12 | ||||
| 13 | ||||
| 14 | ||||
| 15 | ||||
| 16 | ||||
| 17 | ||||
| 18 | ||||
| 19 | ||||
| 20 | ||||
| 21 | ||||
| 22 | ||||
| 23 |
Albert's Charter Bus (solution)
| Albert's Charter Bus Venture | ||||||
| Fixed Costs | Variable Costs | |||||
| Bus Rental | $80 | Ticket | $12.50 | |||
| Gas Expense | $75 | Refreshments | $7.50 | |||
| Other Fuel Costs | $20 | |||||
| Bus Driver | $50 | |||||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |||
| Trip Ticket Price | $35 | |||||
| Number of people | Cost | Revenue | Profit | Avr. Cost | Marg. Cost | Trip Ticket Price |
| 0 | $225.00 | $0 | ($225.00) | $20.00 | $35 | |
| 1 | $245.00 | $35 | ($210.00) | $245.00 | $20.00 | $35 |
| 2 | $265.00 | $70 | ($195.00) | $132.50 | $20.00 | $35 |
| 3 | $285.00 | $105 | ($180.00) | $95.00 | $20.00 | $35 |
| 4 | $305.00 | $140 | ($165.00) | $76.25 | $20.00 | $35 |
| 5 | $325.00 | $175 | ($150.00) | $65.00 | $20.00 | $35 |
| 6 | $345.00 | $210 | ($135.00) | $57.50 | $20.00 | $35 |
| 7 | $365.00 | $245 | ($120.00) | $52.14 | $20.00 | $35 |
| 8 | $385.00 | $280 | ($105.00) | $48.13 | $20.00 | $35 |
| 9 | $405.00 | $315 | ($90.00) | $45.00 | $20.00 | $35 |
| 10 | $425.00 | $350 | ($75.00) | $42.50 | $20.00 | $35 |
| 11 | $445.00 | $385 | ($60.00) | $40.45 | $20.00 | $35 |
| 12 | $465.00 | $420 | ($45.00) | $38.75 | $20.00 | $35 |
| 13 | $485.00 | $455 | ($30.00) | $37.31 | $20.00 | $35 |
| 14 | $505.00 | $490 | ($15.00) | $36.07 | $20.00 | $35 |
| 15 | $525.00 | $525 | $0.00 | $35.00 | $20.00 | $35 |
| 16 | $545.00 | $560 | $15.00 | $34.06 | $20.00 | $35 |
| 17 | $565.00 | $595 | $30.00 | $33.24 | $20.00 | $35 |
| 18 | $585.00 | $630 | $45.00 | $32.50 | $20.00 | $35 |
| 19 | $605.00 | $665 | $60.00 | $31.84 | $20.00 | $35 |
| 20 | $625.00 | $700 | $75.00 | $31.25 | $20.00 | $35 |
| 21 | $645.00 | $735 | $90.00 | $30.71 | $20.00 | $35 |
| 22 | $665.00 | $770 | $105.00 | $30.23 | $20.00 | $35 |
| 23 | $685.00 | $805 | $120.00 | $29.78 | $20.00 | $35 |
Albert's Charter Bus (solution)
Chart5
| 0 | 0 |
| 1 | 35 |
| 2 | 70 |
| 3 | 105 |
| 4 | 140 |
| 5 | 175 |
| 6 | 210 |
| 7 | 245 |
| 8 | 280 |
| 9 | 315 |
| 10 | 350 |
| 11 | 385 |
| 12 | 420 |
| 13 | 455 |
| 14 | 490 |
| 15 | 525 |
| 16 | 560 |
| 17 | 595 |
| 18 | 630 |
| 19 | 665 |
| 20 | 700 |
| 21 | 735 |
| 22 | 770 |
| 23 | 805 |
2
3
4
Albert's Charter Bus Venture
($400.00)
($200.00)
$0.00
$200.00
$400.00
$600.00
$800.00
$1,000.00
01234567891011121314151617181920212223
Number of People
Total Cost
Cost
Revenue
Profit
Chart7
| 0 | 0 | -225 |
| 1 | 35 | -210 |
| 2 | 70 | -195 |
| 3 | 105 | -180 |
| 4 | 140 | -165 |
| 5 | 175 | -150 |
| 6 | 210 | -135 |
| 7 | 245 | -120 |
| 8 | 280 | -105 |
| 9 | 315 | -90 |
| 10 | 350 | -75 |
| 11 | 385 | -60 |
| 12 | 420 | -45 |
| 13 | 455 | -30 |
| 14 | 490 | -15 |
| 15 | 525 | 0 |
| 16 | 560 | 15 |
| 17 | 595 | 30 |
| 18 | 630 | 45 |
| 19 | 665 | 60 |
| 20 | 700 | 75 |
| 21 | 735 | 90 |
| 22 | 770 | 105 |
| 23 | 805 | 120 |
Alber's Charter Bus
| Albert's Charter Bus Venture | ||||
| Fixed Costs | Variable Costs | |||
| Bus Rental | $80 | Ticket | $12.50 | |
| Gas Expense | $75 | Refreshments | $7.50 | |
| Other Fuel Costs | $20 | |||
| Bus Driver | $50 | |||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |
| Ticket Price | $35 | |||
| Number of people | Cost | Revenue | Profit | Avr. Cost |
| 0 | ||||
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 | ||||
| 7 | ||||
| 8 | ||||
| 9 | ||||
| 10 | ||||
| 11 | ||||
| 12 | ||||
| 13 | ||||
| 14 | ||||
| 15 | ||||
| 16 | ||||
| 17 | ||||
| 18 | ||||
| 19 | ||||
| 20 | ||||
| 21 | ||||
| 22 | ||||
| 23 |
Albert's Charter Bus (solution)
| Albert's Charter Bus Venture | ||||||
| Fixed Costs | Variable Costs | |||||
| Bus Rental | $80 | Ticket | $12.50 | |||
| Gas Expense | $75 | Refreshments | $7.50 | |||
| Other Fuel Costs | $20 | |||||
| Bus Driver | $50 | |||||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |||
| Trip Ticket Price | $35 | |||||
| Number of people | Cost | Revenue | Profit | Avr. Cost | Marg. Cost | Trip Ticket Price |
| 0 | $225.00 | $0 | ($225.00) | $20.00 | $35 | |
| 1 | $245.00 | $35 | ($210.00) | $245.00 | $20.00 | $35 |
| 2 | $265.00 | $70 | ($195.00) | $132.50 | $20.00 | $35 |
| 3 | $285.00 | $105 | ($180.00) | $95.00 | $20.00 | $35 |
| 4 | $305.00 | $140 | ($165.00) | $76.25 | $20.00 | $35 |
| 5 | $325.00 | $175 | ($150.00) | $65.00 | $20.00 | $35 |
| 6 | $345.00 | $210 | ($135.00) | $57.50 | $20.00 | $35 |
| 7 | $365.00 | $245 | ($120.00) | $52.14 | $20.00 | $35 |
| 8 | $385.00 | $280 | ($105.00) | $48.13 | $20.00 | $35 |
| 9 | $405.00 | $315 | ($90.00) | $45.00 | $20.00 | $35 |
| 10 | $425.00 | $350 | ($75.00) | $42.50 | $20.00 | $35 |
| 11 | $445.00 | $385 | ($60.00) | $40.45 | $20.00 | $35 |
| 12 | $465.00 | $420 | ($45.00) | $38.75 | $20.00 | $35 |
| 13 | $485.00 | $455 | ($30.00) | $37.31 | $20.00 | $35 |
| 14 | $505.00 | $490 | ($15.00) | $36.07 | $20.00 | $35 |
| 15 | $525.00 | $525 | $0.00 | $35.00 | $20.00 | $35 |
| 16 | $545.00 | $560 | $15.00 | $34.06 | $20.00 | $35 |
| 17 | $565.00 | $595 | $30.00 | $33.24 | $20.00 | $35 |
| 18 | $585.00 | $630 | $45.00 | $32.50 | $20.00 | $35 |
| 19 | $605.00 | $665 | $60.00 | $31.84 | $20.00 | $35 |
| 20 | $625.00 | $700 | $75.00 | $31.25 | $20.00 | $35 |
| 21 | $645.00 | $735 | $90.00 | $30.71 | $20.00 | $35 |
| 22 | $665.00 | $770 | $105.00 | $30.23 | $20.00 | $35 |
| 23 | $685.00 | $805 | $120.00 | $29.78 | $20.00 | $35 |
Albert's Charter Bus (solution)
2
3
4
Chart7
| 0 | 0 | -225 |
| 1 | 35 | -210 |
| 2 | 70 | -195 |
| 3 | 105 | -180 |
| 4 | 140 | -165 |
| 5 | 175 | -150 |
| 6 | 210 | -135 |
| 7 | 245 | -120 |
| 8 | 280 | -105 |
| 9 | 315 | -90 |
| 10 | 350 | -75 |
| 11 | 385 | -60 |
| 12 | 420 | -45 |
| 13 | 455 | -30 |
| 14 | 490 | -15 |
| 15 | 525 | 0 |
| 16 | 560 | 15 |
| 17 | 595 | 30 |
| 18 | 630 | 45 |
| 19 | 665 | 60 |
| 20 | 700 | 75 |
| 21 | 735 | 90 |
| 22 | 770 | 105 |
| 23 | 805 | 120 |
Alber's Charter Bus
| Albert's Charter Bus Venture | ||||
| Fixed Costs | Variable Costs | |||
| Bus Rental | $80 | Ticket | $12.50 | |
| Gas Expense | $75 | Refreshments | $7.50 | |
| Other Fuel Costs | $20 | |||
| Bus Driver | $50 | |||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |
| Ticket Price | $35 | |||
| Number of people | Cost | Revenue | Profit | Avr. Cost |
| 0 | ||||
| 1 | ||||
| 2 | ||||
| 3 | ||||
| 4 | ||||
| 5 | ||||
| 6 | ||||
| 7 | ||||
| 8 | ||||
| 9 | ||||
| 10 | ||||
| 11 | ||||
| 12 | ||||
| 13 | ||||
| 14 | ||||
| 15 | ||||
| 16 | ||||
| 17 | ||||
| 18 | ||||
| 19 | ||||
| 20 | ||||
| 21 | ||||
| 22 | ||||
| 23 |
Albert's Charter Bus (solution)
| Albert's Charter Bus Venture | ||||||
| Fixed Costs | Variable Costs | |||||
| Bus Rental | $80 | Ticket | $12.50 | |||
| Gas Expense | $75 | Refreshments | $7.50 | |||
| Other Fuel Costs | $20 | |||||
| Bus Driver | $50 | |||||
| Total Fixed Cost | $225 | Total Variable Cost | $20.00 | |||
| Trip Ticket Price | $35 | |||||
| Number of people | Cost | Revenue | Profit | Avr. Cost | Marg. Cost | Trip Ticket Price |
| 0 | $225.00 | $0 | ($225.00) | $20.00 | $35 | |
| 1 | $245.00 | $35 | ($210.00) | $245.00 | $20.00 | $35 |
| 2 | $265.00 | $70 | ($195.00) | $132.50 | $20.00 | $35 |
| 3 | $285.00 | $105 | ($180.00) | $95.00 | $20.00 | $35 |
| 4 | $305.00 | $140 | ($165.00) | $76.25 | $20.00 | $35 |
| 5 | $325.00 | $175 | ($150.00) | $65.00 | $20.00 | $35 |
| 6 | $345.00 | $210 | ($135.00) | $57.50 | $20.00 | $35 |
| 7 | $365.00 | $245 | ($120.00) | $52.14 | $20.00 | $35 |
| 8 | $385.00 | $280 | ($105.00) | $48.13 | $20.00 | $35 |
| 9 | $405.00 | $315 | ($90.00) | $45.00 | $20.00 | $35 |
| 10 | $425.00 | $350 | ($75.00) | $42.50 | $20.00 | $35 |
| 11 | $445.00 | $385 | ($60.00) | $40.45 | $20.00 | $35 |
| 12 | $465.00 | $420 | ($45.00) | $38.75 | $20.00 | $35 |
| 13 | $485.00 | $455 | ($30.00) | $37.31 | $20.00 | $35 |
| 14 | $505.00 | $490 | ($15.00) | $36.07 | $20.00 | $35 |
| 15 | $525.00 | $525 | $0.00 | $35.00 | $20.00 | $35 |
| 16 | $545.00 | $560 | $15.00 | $34.06 | $20.00 | $35 |
| 17 | $565.00 | $595 | $30.00 | $33.24 | $20.00 | $35 |
| 18 | $585.00 | $630 | $45.00 | $32.50 | $20.00 | $35 |
| 19 | $605.00 | $665 | $60.00 | $31.84 | $20.00 | $35 |
| 20 | $625.00 | $700 | $75.00 | $31.25 | $20.00 | $35 |
| 21 | $645.00 | $735 | $90.00 | $30.71 | $20.00 | $35 |
| 22 | $665.00 | $770 | $105.00 | $30.23 | $20.00 | $35 |
| 23 | $685.00 | $805 | $120.00 | $29.78 | $20.00 | $35 |
Albert's Charter Bus (solution)
2
3
4
B
A
B
A
Index
Index
Cost
Cost
yrs
now
yrsNow
Index
Index
CostLaborCostLabor
10
10
=
÷
÷
ø
ö
ç
ç
è
æ
=
___
___
_______
33nowNowyrsyrsIndexMaterialCostMaterialCostIndex
$2,455,000
=
715
544
æö
ç÷
èø
$3,227,000
=
()()XAABBSizeCapacityCostCostSizeCapacity
800,82$
1000
2500
000,50$
ft1000
ft2500
CostCost
55.0
55.0
2
2
ft1000ft2500
22
55nowNowyrsyrsIndexCostCostIndex
$82,800
14871306
$94,300
b
1N
NTT
loglnlog2ln2LCLCb
1001(100)bTT
ln%ln2b
b
N
NTT
1
ln(0.8)ln2
0.3219
0.3219(32.0)(100)7.27
0.5)16(T)16(TT
2345.0
1
b
116
2345.0
2ln
)85.0ln(
2ln
%ln
b
6.9)16/(0.5T
2345.0
1
2345.0b
1N
N)6.9(NTT
2345.0b
1N
N)6.9(NTT
0.00
2.00
4.00
6.00
8.00
10.00
12.00
135791113151719
N
TN
Chart2
| 9.6 |
| 8.1598034741 |
| 7.4196991963 |
| 6.93566591 |
| 6.5820740972 |
| 6.3065924249 |
| 6.0826908283 |
| 5.8951740404 |
| 5.7345766838 |
| 5.594628238 |
| 5.4709739686 |
| 5.3604744561 |
| 5.2607966736 |
| 5.1701626826 |
| 5.0871885301 |
| 5 |
| 5 |
| 5 |
| 5 |
| 5 |
Sheet1
| N | TN | log(N) | log(Tn) | ln(N) | ln(Tn) |
| 1 | 9.60 | 0.0000 | 0.9823 | 0 | 2.2617630985 |
| 2 | 8.16 | 0.3010 | 0.9117 | 0.6931471806 | 2.0992200846 |
| 3 | 7.42 | 0.4771 | 0.8704 | 1.0986122887 | 2.0041385168 |
| 4 | 6.94 | 0.6021 | 0.8411 | 1.3862943611 | 1.9366770708 |
| 5 | 6.58 | 0.6990 | 0.8184 | 1.6094379124 | 1.884349908 |
| 6 | 6.31 | 0.7782 | 0.7998 | 1.7917594692 | 1.8415955029 |
| 7 | 6.08 | 0.8451 | 0.7841 | 1.9459101491 | 1.8054471685 |
| 8 | 5.90 | 0.9031 | 0.7705 | 2.0794415417 | 1.7741340569 |
| 9 | 5.73 | 0.9542 | 0.7585 | 2.1972245773 | 1.7465139351 |
| 10 | 5.59 | 1.0000 | 0.7478 | 2.302585093 | 1.7218068942 |
| 11 | 5.47 | 1.0414 | 0.7381 | 2.3978952728 | 1.699456657 |
| 12 | 5.36 | 1.0792 | 0.7292 | 2.4849066498 | 1.6790524891 |
| 13 | 5.26 | 1.1139 | 0.7211 | 2.5649493575 | 1.6602824741 |
| 14 | 5.17 | 1.1461 | 0.7135 | 2.6390573296 | 1.6429041547 |
| 15 | 5.09 | 1.1761 | 0.7065 | 2.7080502011 | 1.6267253263 |
| 16 | 5.00 | 1.2041 | 0.6990 | 2.7725887222 | 1.6094379124 |
| 17 | 5.00 | 1.2304 | 0.6990 | 2.8332133441 | 1.6094379124 |
| 18 | 5.00 | 1.2553 | 0.6990 | 2.8903717579 | 1.6094379124 |
| 19 | 5.00 | 1.2788 | 0.6990 | 2.9444389792 | 1.6094379124 |
| 20 | 5.00 | 1.3010 | 0.6990 | 2.9957322736 | 1.6094379124 |
Sheet1
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
| 0 |
Sheet2
Sheet3
-200
-150
-100
-50
0
50
100
150
012345
Series2
Chart1
| 0 |
| 1 |
| 2 |
| 3 |
| 4 |
| 5 |
Sheet1
| Timing of Cash Flow | Size of Cash Flow | ||
| At time zero (now) | Positive $100 | 0 | 100 |
| 1 time period from today | Negative $100 | 1 | -100 |
| 2 time periods from today | Positive $100 | 2 | 100 |
| 3 time periods from today | Negative $150 | 3 | -150 |
| 4 time periods from today | Negative $150 | 4 | -150 |
| 5 time periods from today | Positive $50 | 5 | 50 |
Sheet1
Sheet2
Sheet3
$(90,000)
$(80,000)
$(70,000)
$(60,000)
$(50,000)
$(40,000)
$(30,000)
$(20,000)
$(10,000)
$-
$10,000
$20,000
0123456
Year
Cash Flows
Capital CostsO&MOverhaul
Chart2
| 0 | 0 | 0 |
| 1 | 1 | 1 |
| 2 | 2 | 2 |
| 3 | 3 | 3 |
| 4 | 4 | 4 |
| 5 | 5 | 5 |
| 6 | 6 | 6 |
Sheet1
| Year | 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) |
Sheet1
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
| 0 | 0 | 0 |
