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Chapter 2 Engineering Costs and Cost Estimating 1 Learning Objectives Understand various cost concepts Breakeven charts Understand various cost estimation models Be able to estimate engineering costs with various models Cash Flow Diagrams 2 Engineering Costs Fixed costs The costs that do not change during the time horizon of the study. They may relate to the constant costs of equipment, utilities, rent, etc. Constant, independent of the output or activity level. Examples: Property taxes, insurance Management and administrative salaries License fees, and interest costs on borrowed capital Rental or lease 3 Example A manufacturing plant that assembles television sets has variable output volume from 200 sets to 350 sets a day. The building for both manufacturing and warehousing has an area of 80, 000 square feet. It employs about 250 people. It produces all of the components that go into the assembly. An example for fixed cost in this plant is -------------------. A) Equipment Cost Equipment cost stays the same B) Power cost regardless the level of output once C) Labor Cost the plant has been designed to produce at a certain level. D) Material Cost 4 Engineering Costs Variable costs Costs that vary during the time horizon of the study. Over the long-term all costs are variable. Depends on the level of output or activity. Proportional to the output or activity level. Example: Direct labor cost Direct materials 5 Example A manufacturing plant that assembles television sets has variable output volume from 200 sets to 350 sets a day. The building for both manufacturing and warehousing has an area of 80, 000 square feet. It employs about 250 people. It produces all of the components that go into the assembly. An example for variable cost in the plant is ---------------. A) Building cost B) Equipment Cost Labor cost depends on the output level C) Labor Cost D) Property Taxes 6 Relevant Formulae Total Variable Cost = Unit Variable Cost * Quantity TVC = VC * Q Total Cost = Total Fixed Cost + Total Variable Cost TC = FC + VC * Q Total Revenue = Unit Selling Price * Quantity TR = SP * Q where TVC = Total variable cost VC = Variable cost per unit Q = Production/Selling quantity FC = Total Fixed costs TR = Total revenue SP = Selling price per unit 7 Example A company produces a single, high-volume product. One year its production volume was 780,000 units, its fixed costs were $3.2 million and its variable costs were $16 per unit. What was the company's total cost for the year? A) $3,200,000 TVC = 780,000 x 16 = $12,480,000 B) $3,200,016 FC = $3.2M C) $12,480,000 D) $15,680,000 TC = FC+TVC = $15,680,000 8 Breakeven Analysis Breakeven point: The level of business activity at which the total costs to provide the products (goods), or services are equal to the revenue generated. That is: Total costs = Total revenue Total costs = Total fixed costs + Total variable costs •Applications of Breakeven analysis: – Determining minimum production quantity – Forecast production profit / loss 9 Breakeven Analysis Total Revenue $ Profit Total Costs Variable Costs Fixed Costs Loss Break-even Point Production Quantity 10 Example 2-1 Total Revenue = 35X $1000 $800 Total Costs = $225 + 20X $600 Variable Costs = 20X Profit $400 $200 $0 Fixed Costs = $225 Loss 5 10 15 20 25 X # of Customers 11 Example A manufacturing firm’s specialty circuit board division has annual fixed costs of $100,000 and variable costs of $20.00 per board. If they charge $100 per circuit board, how many circuit boards must they produce and sell in order to break even? To break even, total costs = total revenue, where total costs = total fixed costs + total variable costs. $100,000 + $20X = $100X X = $100,000/$80 = 1250 circuit boards. 12 Example In breakeven analysis, the profit at the breakeven point is equal to A) The total cost B) Zero The total revenue is equal to the total cost. Therefore… C) The total revenue D) The variable cost multiplied by the number of items sold 13 Marginal Costs and Average Costs Marginal Costs Used to decide whether an additional unit should be made, purchased, or enrolled in. the variable cost for one more unit of output Capacity Planning: excess capacity Basis for last-minute pricing Average Costs: total cost divided by the total number of units produced. Basis for normal pricing 14 Example What is marginal cost? Explain with an example. the cost of producing one additional unit. used for making a decision of whether or not it is economical to produce another unit of the same item. Example: Taking the fifth person in a taxicab that can take only four passengers. For the fifth person, a second cab has to be hired. The cab fare for the second cab is the marginal cost. 15 Engineering Costs and Cost Estimating Key Question: Where do the numbers come from that we use in engineering economic analysis? • Cost estimating is necessary in an economic analysis • When working in industry, you may need to consult with professional accountants, engineers and other specialists to obtain such information 16 Albert’s Charter Bus Venture (example) Albert plans to charter a bus to take people to see a wrestling match show in Jacksonville. His wealthy uncle will reimburse him for his personal time, so his time cost can be ignored. Item Bus Rental Gas Expense Other Fuel Costs Bus Driver Cost $80 $75 $20 $50 Total Costs $225.00 Item Ticket Refreshments Total Costs Cost $12.50 $ 7.50 $20.00 • Which of the above are fixed and which are variable costs? • How do we compute Albert’s total cost if he takes n people to Jacksonville? 17 Albert’s Charter Bus Venture (example) Answer: Total Cost = $225 + $20 n. Graph of Total Cost Equation: Total cost n 18 marginal cost -The cost to take one more person Marginal and Average Costs average cost $300.00 - Average cost: the cost per person Avg.$250.00 Cost = TC/n Cost Avg.$200.00 Cost = ($225+$20n)/n = $20 + $225/n Average Marginal $150.00 For n = 30, TC = $885 $100.00 Trip Ticket Marginal and Average Costs Avg. Cost = $885/30 = $29.50 $300.00 $50.00 $250.00 1 3 5 7 9 11 Cost $200.00 $0.00 Average $150.00 13 19 17 15 Marginal 23 21 Trip Ticket $100.00 Number of People $50.00 $0.00 1 3 5 7 9 11 13 15 17 19 21 23 Number of People 19 Question: Do we have enough information yet to decide how much money Albert will make on his venture? What else must we know? Albert needs to know his total revenue Albert knows that similar ventures in the past have charged $35 per person, so that is what he decides to charge Total Revenue = 35n (for n people) Total profit = Total Revenue – Total Cost: 35n – (225 + 20n) = 15n – 225 Question: How many people does Albert need to break even? (not lose money on his venture) 20 Albert's Charter Bus Venture Question: $1,000.00 How many people does Albert need to break even? (not lose money on his venture) $800.00 Solve$600.00 15 n – 225 = 0 => n=15 Total Cost more$400.00 than 15, he makes money Cost Revenue $200.00 Profit $0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ($200.00) ($400.00) Number of People 21 Albert’s Charter Bus Venture (example) Where is the Loss Region? Where is the Profit Region? Where is the Breakeven point? Albert's Charter Bus Venture $1,000.00 $800.00 Total Cost $600.00 Cost $400.00 Revenue $200.00 Profit $0.00 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ($200.00) ($400.00) Number of People 22 Exercise 2.3 A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities? a) 75 hours 23 Exercise 2.3 A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities? b) 125 hours 24 Exercise 2.3 A new machine comes with 100 free service hours over the first year. Additional time costs $75 per hour. What are the average and marginal costs per hour for the following quantities? c) 250 hours 25 Exercise 2.7 A privately owned summer camp for youngsters has the following data for a 12-week session: Charge per camper $120 per week Fixed costs $48,000 per session Variable cost per camper $80 per week Capacity 200 campers a) Develop the mathematical relationships for total cost and total revenue. 26 Exercise 2.7 A privately owned summer camp for youngsters has the following data for a 12-week session: Charge per camper $120 per week Fixed costs $48,000 per session Variable cost per camper $80 per week Capacity 200 campers b) What is the total number of campers that will allow the camp to just break even? $48,000 = $480 x 27 Exercise 2.7 A privately owned summer camp for youngsters has the following data for a 12-week session: Charge per camper $120 per week Fixed costs $48,000 per session Variable cost per camper $80 per week Capacity 200 campers c) What is the profit or loss for the 12-week session if the camp operates at 80% capacity 28 Exercise 2.7 A privately owned summer camp for youngsters has the following data for a 12-week session: Charge per camper $120 per week Fixed costs $48,000 per session Variable cost per camper $80 per week Capacity 200 campers d) What are marginal and average costs per camper at 80% capacity? x = 160 Marginal cost is the slope of the equation which is equal to $960 Average cost is Total Cost/x = ($48,000 + $960 * 160)/160 = $1260 29 Sunk Costs Costs associated with decisions already made. Money already spent as a result of a past decision. Cost that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative Must be ignored because current decisions can not change the past 30 Sunk Costs A sunk cost is money already spent due to a past decision. As engineering economists we deal with present and future opportunities We must be careful not to be influenced by the past Disregard sunk costs in engineering economic analysis 31 Sunk Costs Example: Suppose that three years ago your parents bought you a laptop PC for $2000. How likely is it that you can sell it today for what it cost? Suppose you can sell the laptop today for $400. Does the $2000 purchase cost have any effect on the selling price today? The $2000 is a sunk cost. It has no influence on the present opportunity to sell the laptop for $400. ( stock now costs $20 but you bought for $80) 32 Example All of the following are usually included in an engineering economic analysis except A) Fixed costs B) Variable costs C) Sunk costs D) Total revenue 33 Opportunity Costs Using a resource in one activity instead of another Cost of the foregone opportunity and is hidden or implied Going for $3000 trip and miss the opportunity of earning $5000 in summer internship 34 Sunk and Opportunity Cost-1 Example 2-3. A distributor has a case of electric pumps. The pumps are unused, but are three years old. They are becoming obsolete. Some pricing information is available as follows. Item Amount Type of Costs Price for case 3 years ago $7,000 Sunk cost Storage costs to date $1,000 Sunk cost 35 Sunk and Opportunity Cost-2 Example 2-3. (cont.) Item Amount Type of Costs List price today for a case of new and up to date pumps $12,000 Can be used to help determine what the lot is worth today. Amount buyer offered for case 2 years ago $5,000 A foregone opportunity Case can currently be sold for $3,000 Actual market value today 36 Recurring Costs and Non-recurring Costs Recurring Costs: Repetitive, and occur when a firm produces similar goods and services on a continuing basis Office space rental Non-recurring Costs: Not repetitive, even though the total expenditure may be cumulative over a period of time Typically involves developing or establishing a capability or capacity to operate Examples are purchase cost for real estate and the construction costs of the plant 37 Incremental Costs Incremental Costs: Difference in costs between two alternatives. Suppose that A and B are mutually exclusive alternatives. If A has an initial cost of $10,000 while B has an initial cost of $14,000, the incremental initial cost of (B - A) is $4,000. 38 Example 2-3 Choosing between Model A & B Cost Items Model A Model B Incremental Cost Purchase Price $10,000 $17,500 $7,500 Installation Costs $3,500 Annual Maintenance * $2,500 Annual Utility * $1,200 $2,000 $700 $500 Disposal Cost $5,000 $1,500 $750 $ -1,750/yr $800/yr $ -200 * Must be multiplied by the number of years of service. 39 You must know this. Cash Costs versus Book Costs Book Costs: Costs that do not involve money/cash transaction Cost effects from past decisions that are recorded in the books (accounting books) of a firm Do not represent cash flows Not included in engineering economic analysis One exception is for asset depreciation. Depreciation Example: Depreciation is charged for the use of assets, such as plant and equipment—This is used to determine the value of the company and in computing taxes. 40 You must know this. Cash Costs versus Book Costs Cash Costs: Costs that involve money/cash transaction Require the cash transaction of dollars from “one pocket to another”. Example: Interest payments, taxes, etc. You might use Kelley Blue Book to conclude the book value of your car is $6,000. The book value can be thought of as the book cost. If you actually sell the car to a friend for $5,500, then the cash cost to your friend is $5,500. 41 You must know this. Life-Cycle Costs Life-Cycle Costs: Summation of all costs, both recurring and nonrecurring, related to a product, structure, system, or service during its life span. Life cycle begins with the identification of the economic needs or wants (the requirements) and ends with the retirement and disposal activities. 42 You must know this. Phases of Life Cycle 1. Need Assessment 2.Conceptual Design 3. Detailed Design 4. Production /Construction 5.Operational Use 6. Decline/ Retirement Requirements Analysis Impact Analysis Allocation of Resources Production of Goods/ Services Distribution of Goods/ Services Phase Out Overall Feasibility Study Proof of Concept Detailed Specifications Building of Supporting Facilities Maintenance/ Support Disposal Conceptual Design Planning Prototype/ Breadboard Component/ Supplier Selection Quality Control/ Assurance Retirement Planning Retirement Development/ Testing Production Planning Operational Planning Detailed Design Planning 43 You must know this. Cumulative Life-Cycle Costs Committed and Spent 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Life-Cycle Costs Committed Life-Cycle Costs Spent Need Assessment Conceptual Design Detailed Design Production Operational /Construction /Use Decline/ Retirement 44 You must know this. Cost/Ease of Design Changes in Product Life Cycle 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Ease of Design Changes Cost of Design Changes Need Assessment Conceptual Design Detailed Design Production Operational /Construction /Use Decline/ Retirement 45 Think – Pair – Share Tech Engineering Inc. makes a consumer product for which the following cost data are available. Fixed cost/ year = $120,000 Variable costs/ unit = $15 i. Determine the breakeven volume if each unit can be sold for $40. ii. If a net profit of $100,000 is required, determine the number of units that needed to be sold. 46 Think – Pair – Share Tech Engineering Inc. makes a consumer product for which the following cost data are available. Fixed cost/ year = $120,000 Variable costs/ unit = $15 i. Determine the breakeven volume if each unit can be sold for $40. 47 Think – Pair – Share Tech Engineering Inc. makes a consumer product for which the following cost data are available. Fixed cost/ year = $120,000 Variable costs/ unit = $15 ii. If a net profit of $100,000 is required, determine the number of units that needed to be sold. 48 You must know this. Cost Estimating and Estimating Models Needs for Cost Estimating Importance of Cost Estimating Types of Cost Estimating Rough Estimates -30% to +60% Used for general feasibility activities Semi-detailed Estimates -15% to +20% Budgeting and preliminary design decisions Detailed Estimates -3% to +5% Establishing design details and contracts 49 You must know this. Trade-off between Accuracy and Cost Cost of Estimate High Low Low Medium High Accuracy of Estimate Figure 2-6. Accuracy versus cost trade-off in estimation 50 You must know this. Difficulties in Estimation One-of-a-Kind or first-run projects Estimates Ex: First NASA mission Time and Effort Available Constraint on time and person-power can make the overall estimating task more difficult. Estimator Expertise 51 You must know this. Categories of Cost Estimating Capital Investment (S&H, Installation, Training) Labor Costs (Direct and Indirect) Material Costs (Direct & Indirect) Maintenance Costs (Regular & Overhaul) Property Taxes and Insurance Operating Costs (Rental, Gas, Electricity) Quality Costs (Scrap, Rework, Inspection) Overhead Costs (Administration, Sales) Disposal Costs Revenues Market Values 52 You must know this. Sources of Cost Estimating Data Accounting records Other sources within the firm: Engineering, Production, Quality Sales, Purchasing, Personnel Published information: Statistical Abstract of US – Cost indexes Monthly Labor Review – Labor costs Building Construction Cost Data Other sources outside the firm: Vendor, Salespeople Research & Development Pilot plant, Test market 53 You must know this. Estimating models Per-Unit Model (Unit Technique) Segmenting Model Cost Indexes Power-Sizing Model Triangulation Improvement and the Learning Curve We will look at each of these. 54 You must know this. Per-Unit Model (Unit Technique) Per-Unit Model (Unit Technique) Construction cost per square foot (building) Capital cost of power plant per kW of capacity Revenue / Maintenance Cost per mile (hwy) Utility cost per square foot of floor space Fuel cost per kWh generated Revenue per customer served 55 Example 2-4: Cost Estimating using Per-Unit Model Cost estimation of camping on an island for 24 students over 10 days. Planned Activities: 2 days of canoeing 3-day hikes 3 days at the beach Nightly entertainment 56 Example 2-4: Cost Estimating using Per-Unit Model Cost Data: • Van (capacity 15) rental: $50 one way • Camp is 50 miles away, van gets 10 miles/gallon, and gas is $1/gallon • Each cabin holds 4 campers, rent is $10/day-cabin • Meals are $10/day-camper • Boat transportation is $2/camper (one way) • Insurance/grounds fees/overhead is $1/day-camper • Canoe (capacity 3) rentals are $5/day-canoe • Day hikes are $2.50/camper-day • Beach rental is $25/group-(half-day) • Nightly entertainment is free 57 Example 2-4: Cost Estimating using Per-Unit Model` Solution: • Assumption: 100% participation in all activities • Transportation Costs: – Van: $50/van-trip * 2 vans * 2 trips = $200 – Gas: $1/gallon * (50 miles / 10 miles/gallon) *2 *2 = 20 – Boat: $2/camper-trip * 24 campers * 2 = 96 – Subtotal $316 58 Example 2-4: Cost Estimating using Per-Unit Model` Solution: • Living Costs: – Meals: $10/day-camper * 24 campers * 10 days = $2400 – Cabin rental: $10/day-cabin * (24/4) cabins *10 days =600 – Insurance: $1/day-camper * 24 campers * 10 days = 240 – Subtotal $3240 59 Example 2-4: Cost Estimating using Per-Unit Model Solution (Continued): • Entertainment Costs: – Canoe rental: $5/day-canoe * 2 days * (24/3) canoes = $80 – Beach rental: $25/group-(half-day) * (3*2) half-days = 150 – Day hike: $2.50/camper-day* 24 campers * 3 days = 180 – Nightly entertainment 0 – Subtotal $410 • Total Costs: $3966 Thus, the total cost per student would be $3966/24 = $165.25 60 Segmenting Model (example) Estimate is decomposed into individual components Estimates are made at component level Individual estimates are aggregated back together Consider a lawnmower A. Chassis B. Drive Train C. Controls D. Cutting/Collection system 61 Segmenting Model (example) A. Chassis Cost Item A.1 Deck A.2 Wheels A.3 Axles Subtotal B. Drive Train Estimate $7.00 10.00 5.85 $22.85 Cost Item Estimate B.1 Engine $38.50 B.2 Starter assembly 6.90 B.3 Transmission 4.45 B.4 Drive disc assembly 10.00 B.5 Clutch linkage 6.15 B.6 Belt assemblies 8.70 Subtotal $72.70 62 Segmenting Model (example) C. Controls Cost Item Estimate C.1 Handle assembly $2.85 C.2 Engine linkage 9.55 C.3 Blade linkage 5.70 C.4 Speed control linkage 20.50 C.5 Drive control assembly 7.70 C.6 Cutting height adjuster 6.40 Subtotal $52.70 D. Cutting/Collection system Cost Item D.1 Blade assembly D.2 Side chute D.3 Grass bag & adapter Subtotal Estimate $11.80 6.05 7.75 $25.60 Total material cost = $22.85 + $72.70 + $52.70 + $25.60 = $173.85 63 Costs indexes Reflect historical change in cost Cost index could be individual cost items (labor, material, utilities), or group of costs (consumer prices, producer prices) Indexes can be used to update historical costs Cost A Index A Cost B Index B (Eq. 2-2) 64 Example 2.6 Miriam is interested in estimating the annual labor and material costs for a new production facility. She was able to obtain the following labor and material cost data: • Labor cost index value was at 124 ten years ago and is 188 today. • Annual labor costs for a similar facility were $575,500 ten years ago. Labor Cost Now Indexnow Labor Cost10 yrs Index 10 yrs _______ $575,500 188 ___ ___ 124 871,800 65 Example 2.6 (Continued) Miriam is interested in estimating the annual labor and material costs for a new production facility. She was able to obtain the following labor and material cost data: • Material cost index value was at 544 three years ago and is 715 today. • Annual material costs for a similar facility were $2,455,000 three years ago. Indexnow Material Cost Now Material Cost3 yrs Index 3 yrs 715 $2, 455, 000 $3, 227, 000 544 66 Power-Sizing Model Size(Capacity ) A Cost A Cost B Size ( Capacity ) B X (Eq. 2-3) X = Power-sizing exponent Example Power Sizing Exponent Values Equipment/Facility X Equipment/Facility X Blower, centrifugal Compressor Crystallizer, vacuum Dryer, drum Fan, centrifugal 0.59 0.32 0.37 0.40 1.17 Filter, vacuum Lagoon, aerated Motor Reactor Tank, horizontal 0.48 1.13 0.69 0.56 0.57 67 Example 2.7 Miriam has been asked to estimate the cost today of a 2500 ft2 heat exchange system for the new plant being analyzed. She has the following data. • Her company paid $50.000 for a 1000 ft2 heat exchanger 5 years ago. • Heat exchangers within this range of capacity have a power sizing exponent (x) of 0.55 A. Considering Power-Sizing Index Change 2500 ft Cost1000 ft 2 2 1000 ft 2 Cost 2500 ft 2 2500 $50,000 1000 0.55 0.55 $82,800 68 Example 2.7 (Continued) Miriam has been asked to estimate the cost today of a 2500 ft2 heat exchange system for the new plant being analyzed. She has the following data. • Five years ago the Heat Exchanger Cost Index (HECI) was 1306; it is 1487 today. B. Considering Cost Index Change Indexnow Cost Now Cost5 yrs Index 5 yrs 1487 $94,300 $82,800 1306 69 Triangulation Techniques Used in Surveying: To map points of interest by using three fixed points and horizontal angular distance Application in Economic Analysis: To approach economic estimate from different perspectives, such as different source of data, or different quantitative models. 70 Improvement and Learning Curve Learning Phenomenon: As the number of repetitions increase, performance of people becomes faster and more accurate. Learning curve captures the relationship between task performance and task repetition. In general, as output doubles the unit production time will be reduced to some fixed percentage, the learning curve percentage or learning curve rate 71 Learning Curve Let T1 = Time to perform the 1st unit TN = Time to perform the Nth unit b = Constant based on learning curve LC% N = Number of completed units TN T1 Nb (Eq. 2-4) log LC ln LC b log 2 ln 2 (Eq. 2-5) 72 Example 2.8 Calculate the time required to produce the hundredth unit of a production run if the first unit took 32.0 minutes to produce and the learning curve rate for production is 80%. ln % ln(0.8) b 0.3219 ln 2 ln 2 TN T1 N b T100 T1 (100) (32.0)(100) 0.3219 7.27 b 73 Example 2.9 Estimate the overall labor cost portion due to a task that has a learning-curve rate of 85% and reaches a steady state value of 5.0 minutes per unit after 16 units. • Labor and benefits are $22 per hour, and the task requires two skilled workers. • The overall production run is 20 units. ln % ln(0.85) b 0.2345 ln 2 ln 2 T16 T1 (16)b T1 (16)0.2345 5.0 T1 5.0 /(16) 0.2345 9 .6 TN T1 Nb (9.6) N0.2345 74 Example 2-9: Cost Estimating Using Learning Curve 8.16 7.42 6.94 6.58 6.31 6.08 5.90 5.73 5.59 12 13 14 15 16 17 18 19 20 5.36 5.26 5.17 5.09 5.00 5.00 5.00 5.00 5.00 8.00 TN N 1 2 3 4 5 6 7 8 9 10 TNExample T1 Nb 2-9 (9Cost .6) N0.2345 TNEstimating N Tusing 12.00 N 9.60 11 Curve 5.47 Learning 10.00 6.00 4.00 2.00 0.00 1 3 5 7 9 11 13 15 17 19 N 75 Estimating Benefits-1 Sample Benefits Sales of products Revenues from bridge tolls & electric power sale Cost reduction from reduced material or labor costs Less time spent in traffic jams Reduced risk of flooding 76 Estimating Benefits-2 Cost concepts and cost estimating models can also be applied to economic benefits Uncertainty in benefit estimating is typically asymmetric, with a broader limit for negative outcomes, e.g. -50% to +20% Benefits are more difficult to estimate than costs 77 Cash Flow Diagrams (CFD) CFD summarize costs & benefits occur over time CFD illustrates the size, sign, and timing of individual cash flows Components of CFD A segmented time-based horizontal line, divided into time units A vertical arrow representing a cash flow is added at the time it occurs Arrow pointing down for costs and up for benefits 78 Cash Flow Diagrams (CFD) Example 150 100 Timing of Cash Flow At time zero (now) 1 time period from today 2 time periods from today 3 time periods from today 4 time periods from today 5 time periods from today 0 Size of Cash Flow 50 Positive $100 0 0 Negative $100 -50 -100 Positive $100 -150 Negative $150 -200 Negative $150 Positive $50 1 2 3 4 1 2 3 4 5 Series2 5 79 Categories of Cash Flows First cost: expenses to build or to buy and install Operations and maintenance (O&M): annual expense, such as electricity, labor, and minor repairs Salvage value: receipt at project termination for sale or transfer of the equipment Revenues: annual receipts due to sale of products or services Overhaul: major capital expenditure that occurs during the asset’s life 80 Drawing a Cash Flow Diagram CFD shows when all cash flows occur In a CFD, the end of period t is the same time as the beginning of period t+1 Rent, lease, and insurance payments are usually treated as beginning-of-period cash flows O&M, salvage, revenues, and overhauls are assumed to be end-of-period cash flows The choice of time 0 is arbitrary 81 Drawing Cash Flow Diagrams with Spreadsheet 0 -$80,000 0 O&M 1 $(12,000) 2 $(12,000) 3 $(12,000) 4 $(12,000) 5 $(12,000) 6 $ 10,000 $(12,000) Overhaul $(25,000) Cash Flows Year Capital Costs 1 2 3 4 5 6 $20,000 $10,000 $$(10,000) $(20,000) $(30,000) $(40,000) $(50,000) $(60,000) $(70,000) $(80,000) $(90,000) Year Capital Costs O&M Overhaul 82 End of Chapter 2