8/25/04 Valerie Tardiff and Paul Jensen Operations Research Models and Methods Copyright All rights reserved Costs and Cash Flows

2 Engineering Economic Analysis - Seven Steps 1. Recognize and formulate the problem. 2. Develop feasible alternatives. 3. Develop cash flows for each alternative. 4. Select a criterion (or criteria) for determining the preferred alternative. 5. Analyze and compare alternatives. 6. Select the preferred alternative. 7. Perform monitoring and post-evaluation.

3 Cash Flows A cash flow is a receipt or payment of an amount of money defined by 1) its dollar value and 2) the time of its occurrence Cash flow diagrams represent costs and revenues over time. Cost and Revenue estimation for the future always involve uncertainty.

4 Top-Down Estimate The first step in the determination of the cash flows is the estimation of costs and revenues. The top-down approach takes data from similar projects and modifies them to reflect the current project. Estimate your cost of a college degree: use the cost of your brother’s degree three years ago and adjust it for inflation. Add $5000 for the cost of your participation in extra curricular activities (your brother was a bookworm)

5 Bottom-Up Estimates The bottom-up approach is more detailed, breaking down the project in small manageable units and estimating the cost of the parts first. Bottom-Up: Break down anticipated expenses in categories: tuition and fees, books and supplies, living expenses, transportation and estimate each as accurately as possible.

6 Cost Terminology Variable costs change with the level of output Fixed costs do not change with the level output

7 Cost Terminology (cont’d) Recurring/Nonrecurring Costs: If costs occur every time the organization produces goods or services, they are called recurring. Variable costs are recurring. Direct/Indirect Costs: If costs can be reasonably measured and allocated to specific output, they are called direct. Overhead Costs: all costs of providing goods and services other than direct labor and direct material. Cash/Book Cost: Cost that involves a payment of cash is called a cash cost. Costs reflected in the accounting system only are called book costs.

8 Opportunity Costs Opportunity Cost: Cost of forgoing the chance to earn interest (or profit) on investment funds. Example: Your grandmother owns her home, but lives with your parents. She rents her $185,000-house for $400/month. Good idea or lost opportunity?

9 Sunk Costs Sunk Costs: Past costs that are unrecoverable are not relevant for decision-making purposes. Example: You are shopping for a new car, and, that afternoon, find one you really like for $1000. You leave a $100 deposit and plan to return the next day. That evening, your friend offers to sell you her car for $850. What to do think?

10 Life Cycle Costs

11 Life Cycle Phases The life cycle of a project is separated into two general time periods: the acquisition phase: needs assessments and definition of requirements conceptual design, advanced development, and prototype testing detailed design, production planning, facility and resource acquisition the operation phase: production or construction maintenance and support retirement and disposal

12 Life-Cycle Cost The Life-cycle cost is the sum of all the costs and revenues over the entire life of the structure, or system. All amounts are expressed in dollars and they must be time-equivalent. This time-equivalency is important because a dollar today is worth more than a dollar next year because of the interest (profit) it can earn.

13 Analysis Period The study period for a project is the life- cycle of the product, structure, system, or service studied. However, the accuracy of the cost and revenue estimates decrease with increases in the length of the period, and the effort required to develop cash flows increases with the length of the period. Thus, a shorter time horizon can also be selected.

14 Present Economy Studies When the influence of time on money is not a significant consideration, analyses are referred to as present economy studies Time horizon is one year or less No opportunity for earning interest or profit The criterion for selection is usually Select the alternative that maximizes profit Select the alternative that minimizes cost

15 Material Selection Example After machining, the finished volume of a certain metal part is 0.17 inch 3 Which raw material to choose? BrassAluminum Machining time/piece (min) Cost of material ($/lb) Scrap value ($/lb) 0.24none Cost of operator ($/hr) Density of material (lb/in 3 ) Volume of raw material (in 3 )

16 Labor and Material Costs Labor cost per piece = (time per piece)(labor cost per time) Brass: (0.64 min/piece)($12/hr)(1hr/60 min) = $0.128/pc Aluminum: (0.42 min/piece)($12/hr)(1hr/60 min) = $0.084/pc Material cost per piece = (volume of raw)(lb per volume)(cost per lb)- (leftover vol. of raw)(lb per vol.)(scrap value per lb) Brass: (0.3 in 3 )(0.31 lb/in 3 )($0.96/lb) - (0.13 in 3 )(0.31 lb/in 3 )($0.24/lb) =$0.080/pc Aluminum : (0.45 in 3 )(0.10 lb/in 3 )($0.52/lb) =$0.023/pc

17 Total Cost Brass: $0.128/pc /pc = 0.208/pc Aluminum: $0.084/pc /pc = 0.107/pc Choose aluminum to minimize total cost

18 Make vs. Buy Example A company, not operating at full capacity, is considering making a part currently bought. MakeBuy Direct Material$1.50 Direct Labor$1.35 Overhead - variable$0.90 Overhead - fixed$4.25 Total Unit Cost$8.00$7.50

19 Analysis Utilizing the excess capacity has no opportunity costs since the plant cannot invest unused capacity as easily as it can invest unused cash. Therefore, this product will not change fixed overhead for the plant. So the real cost per unit is: $ $ $0.90 = $3.75 Therefore, it is better to make the product in-house.