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Costs Engineering and Cost Estimating Costs: Fixed and Variable Direct and Indirect Marginal and Average Sunk and Opportunity Recurring and Non-Recurring Incremental Cash and Book Life-Cycle Cost Indices Estimating Benefits Cash Flow Diagrams 1 Engineering Costs and Cost Estimating Fixed Costs: are constant and unchanging regardless of the level of the activity over a feasible range of operations for the capacity or capability available. Variable costs: operating costs that vary in total with the quantity of output or other measures of activity level. Direct Costs: cost that can be reasonably measured and allocated to a specific output or work activity. Indirect/Overhead Cost: cost that it is difficult to attribute or allocate to a specific output or work activity. 2 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 to obtain such information 3 Engineering Costs and Cost Estimating Example 2-1. Albert s Charter Bus Venture 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 Total Costs Cost $80 $75 $20 $50 $225.00 Item Cost Ticket Refreshments $ $12.50 7.50 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? 4 Albert s Charter Bus Venture (example) Answer: Total Cost = $225 + $20 n. Graph of Total Cost Equation: Total cost n 5 Albert s Charter Bus Venture (example) marginal cost -The cost to take one more person (marginal tax) Marginal and Average Costs $300.00 average cost - Average cost: the cost per person Avg. Cost = TC/n Avg. Cost = ($225+$20n)/n For n = 30, TC = $885 Avg. Cost = $885/30 = $29.50 Total cost cannot be calculated from an average cost value Cost $250.00 $200.00 Average $150.00 $100.00 $50.00 $0.00 1 3 5 7 9 11 13 15 17 19 21 23 Number of People Marginal Trip Ticket For n =35, TC 35*($29.50) = $ 1,032.50 6 Suppose Albert s ticket cost drops to $10 per person if he brings 20 or more people. What is the total cost Albert s Charter Bus Venture (example) Question: Do we have enough information yet to decide how much 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 Albert's Charter Bus Venture money Albert will make on his venture? What else must we know? Total Revenue = 35n (for n people) $1,000.00 Total profit = Total Revenue Total Cost: Total Cost $800.00 $600.00 $400.00 $200.00 $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 Cost Revenue Profit 35n (225 + 20n) = 15n 225 Question: How many people does Albert need to break even? (not lose money on his venture) Solve 15 n 225 = 0 => n=15 7 Albert s Charter Bus Venture (example) Where is the Loss Region? Where is the Profit Region? Where is the Breakeven point? Can you make this chart in Excel? Albert's Charter Bus Venture $1,000.00 $800.00 $600.00 Total Cost $400.00 $200.00 $0.00 0 ($200.00) ($400.00) Number of People 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Cost Revenue Profit 8 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 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 costs now $20 you bought for $80) 9 Opportunity Cost An opportunity cost is the benefit that is foregone by engaging a business resource in a chosen activity instead of engaging that same resource in the foregone activity. Example: Suppose your wealthy uncle gives you $75,000 when you graduate from high school. It is enough to put you through college (5 years at $15,000 per year). It is also enough for you to open a business making web pages for small companies instead of going to college. You estimate you would make $20,000 per year with this business. If you decide to go to college you give up the opportunity to make $20,000 per year Your opportunity cost is $20,000 Your total cost per year is $35,000 10 Sunk and Opportunity Cost 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 Price for case 3 years ago Storage costs to date List price today for a case of new and up to date pumps Amount buyer offered for case 2 years ago Case can currently be sold for Amount $7,000 $1,000 $12,000 Type of Costs Sunk cost Sunk cost Can be used to help determine what the lot is worth today. A foregone opportunity Actual market value today 11 $5,000 $3,000 Recurring and Non-Recurring Costs Recurring costs are those expenses that are known, anticipated, and occur regular at intervals. These costs can be modeled as cash flows. Non-recurring costs are one-of-a-kind and occur at irregular intervals. They are difficult to plan for or anticipate. Example. You decide to landscape a lot of ground and then care for it. Which are recurring and which are non-recurring costs you incur? Remove existing trees, vegetation Have land graded with bulldozer Have yard planted with grass Plant shrubs, trees Mow grass Fertilize grass, shrubs Water grass, shrubs 12 Incremental Cost Incremental Cost is the additional cost that results from: Increasing the output of a system by one (or more) units Selecting one alternative over another Example 2-4. Philip can choose between model A or model B. The following information is available. Cost Items Purchase price Installation cost Annual maintenance cost Annual utility expense Disposal cost after useful life Model A $10,000 $3,500 $2,500 $1,200 $700 Model B $17,500 $5,000 $750 $2,000 $500 Incremental Cost of B $7,500 $1,500 $-1,750/yr $800/yr $-200 13 Can we conclude that model B is more expensive than model A? Cash Costs vs. Book Costs Cash costs require the cash transaction of dollars from one pocket to another . Book costs are 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 (used for tax purposes). Example: You might use Edmond s Used Car Guide to 14 conclude the book value of your car is $6,000. The book Life-Cycle Costs Life-cycle costs are the summation of all costs, both recurring and nonrecurring, related to a product, structure, system, or service during its life span Products go through a life cycle, just like people Assessment & Justification Phase Conceptual or Preliminary Design Phase Detailed Design Phase Production or Construction Phase Operational Use Phase Decline and Retirement Phase 15 Life-Cycle Costs % Total L.C. Cost Life Cycle Cost Chart 120.00% 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% N ee L.C. costs committed L.C. costs spent D ce ef pt . .D D et sg ai n. le d D sg P n. ro du ct io O n pn l. U se D ec lin e C on ds Project Phase 16 Life-Cycle Costs Comments: The later design changes are made in the life-cycle, the higher the costs. Decisions made early in the life-cycle tend to lock in costs incurred later in the life cycle: Nearly 70 to 90% of all costs are set during the design phases, while only 10 to 30% of the cumulative life-cycle costs have been spent. Question. When is the best time to consider all life-cycle effects, and make design changes? Bottom Line. Engineers should consider all life-cycle costs when designing products and the systems that produce them. 17 Cost Indices The U.S. federal government publishes cost index data through the Department of Commerce Bureau of Statistics. The Statistical Abstract of the United States publishes cost indexes for labor, construction, and materials. The best-known example is the consumer price index (CPI), a measure of inflation. The measure is scaled, so it is only the relative values of any two measures that are meaningful. For example, in 1920, the measure was about 20; in 1997 it was about 160. The conclusion is that one would have to spend 160/20, or 8 times as much in 1997 as in 1920 for the same consumables. Cost indices work in the same way as price indices. Cost indices are dimensionless. 18 Cost Indices 19 Estimating Benefits For the most part, we can use exactly the same approach to estimate benefits as to estimate costs: Fixed and variable benefits Recurring and non-recurring benefits Incremental benefits Life-cycle benefits Rough, semi-detailed, and detailed benefit estimates Difficulties in estimation Segmentation and index models Major differences between benefit and cost estimation: Costs are more likely to be underestimated Benefits are most likely to be overestimated Benefits tend to occur further in the future than costs 20 Example Two summer Camps have the following data for a 12-week session: Camp A Charge per camper Fixed costs Variable cost per camper Capacity $120 per week $48,000 per session $80 per week 200 campers Camp B Charge per camper Fixed costs Variable cost per camper Capacity $100 per week $60,600 per session $50 per week 150 campers a. Develop the mathematical relationships for total cost and total revenue for camp A b. What is the total number of campers that will allow camp B to break even? c. What is the profit or loss for the 12-week session if camp A operates at 80% capacity? d. Determine the breakeven number of campers for the two camps to have equal total costs for a 12-week session. 21 Cash Flow Diagrams Cash flow diagrams (CFD) summarize the costs and benefits of projects A CFD illustrates the size, sign, and timing of individual cash flows Periods may be months, quarters, years, etc. Example: Time Period 0 (today) 1 2 3 4 5 Size of Cash Flow Receive $100 (positive CF) Pay $100 (negative CF) Positive CF of $100 Negative CF of $150 Negative CF of $150 Positive CF of $50 COMMENTS: The end of one period is the beginning of the next one Arrows point up for revenues or benefits, down for costs One person s payment (cash outflow w. neg. sign) is another person s receipt (cash inflow w. pos. sign) It is essential to use only one perspective in any CFD Today Tomorrow 100 100 50 0 1 100 2 3 4 5 150 150 22

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