Engineering Economic Analysis Canadian Edition Chapter 2: Engineering Costs and Cost Estimating

Chapter 2 … Defines cost concepts and engineering cost estimating. Explains three types of engineering estimates. Discusses the effect of the learning curve on cost estimates. Covers models for estimating costs and benefits. Presents cash flow diagrams to show costs and benefits.

Engineering Costs Costs: the economic value of the resources used in the production of goods and services. Land, labour, capital, and entrepreneurial skills Initial investment, wages and salaries, material purchases, utilities Profits indicate that scarce economic resources are being used properly. The selling value of the goods and services produced exceeds the cost of the resources used in their production. Losses may reflect a waste of resources.

Classification of Costs Fixed: constant and unchanging Rent on a building is constant regardless of how much space is utilized. Variable: depends on activity level Linear (proportional) or non-linear Amount of raw material used depends on how many units are made. Total cost = Fixed cost + Variable cost Marginal cost: variable cost for the next unit. Average cost: total cost per unit =

Fixed, Variable, and Total Costs (Example 2-1)

Costs Output Total Cost Total Fixed Cost Total Variable Cost Average Fixed Cost Average Variable Cost Average Cost Marginal Cost 1.0 3.0 2.0 2.00 1.00 3.00 3.8 1.8 0.90 1.90 0.8 4.4 2.4 0.67 0.80 1.47 0.6 4.0 4.8 2.8 0.50 0.70 1.20 0.4 5.0 5.2 3.2 0.40 0.64 1.04 6.0 5.8 0.33 0.63 0.97 7.0 6.6 4.6 0.29 0.66 0.94 8.0 7.6 5.6 0.25 0.95 9.0 8.8 6.8 0.22 0.76 0.98 1.2 10.0 10.2 8.2 0.20 0.82 1.02 1.4

Total, Variable, and Fixed Costs

Average and Marginal Costs

Profit and Loss Terms Total revenue = Unit price  units sold Breakeven: total revenue = total costs Just getting by Profit: total revenue > total costs Putting money in the bank Loss: total revenue < total costs Going into debt

Profit and Loss (non-linear cost and revenue) Total cost Total revenue Profit Output Profit Zone

Breakeven (Example 2-2)

Past (Sunk) Costs Sunk cost: money spent due to a past decision. We cannot do anything about these costs. Example: the amount paid to purchase a car two years ago.

Future (Opportunity) Costs Opportunity cost: a benefit that is not realized when a resource is engaged in one activity instead of engaging that same resource in another foregone activity. We make a choice or decision. Example: Buying lunch instead of gas. Examine each cost and determine what type it is (Example 2-3).

Expense Types Recurring expense: anticipated and occurs at regular intervals. Purchasing food, paying rent. Non-recurring expense: one-of-a-kind event that occurs at an irregular interval. Illness, accident, death. Sometimes we attempt to plan for large non-recurring costs by buying insurance. Paying the periodic insurance premium turns this expense into a recurring cost.

Incremental Costs Incremental cost: the difference between the costs of two alternatives (Example 2-4).

Cash versus Book Costs Cash costs: movement of money from one owner to another. Also known as a ‘cash flow’. Payment this month on an auto loan. Book costs: cost of a past transaction that is recorded in a book. Down payment recorded in your cheque book from last year’s automobile purchase.

Life-cycle Costs Life-cycle: all the time from the conception to the death of a product or process. Life-cycle costs: the sum total of all the costs incurred during the life-cycle. Life-cycle costing: designing with an understanding of all the costs associated with a product during its life-cycle.

Phases of Life-cycle Costs Needs assessment and justification Conceptual or preliminary design Detailed design Production or construction Operational use Decline and retirement

Life-cycle Costing In general, the later a product design change is made, the higher the cost. Earlier changes are easier and less costly. Decisions made early in the life-cycle tend to ‘lock-in’ cost that will be incurred. About 70% to 90% of all costs are committed during the design phases. Only 10% to 30% of cumulative life-cycle costs have been spent by the end of the design phase.

Cost Estimating Engineering economic analysis is future based. Future consequences (costs and benefits) of current decisions are analyzed. Requires estimating. Estimated costs and benefits are not known with certainty. The more accurate the estimate, the more reliable the decision.

Types of Estimates Rough: gut level Inaccurate. 30% to +60%. Semi-detailed: based on historical records Reasonably sophisticated and accurate. 15% to +20%. Detailed: based on specifications and cost models Very accurate. 3% to +5%. Difficulties arise when the future is uncertain.

Types of Estimates … One-of-a-kind or first time projects There are few such projects in engineering economic analysis. Example: First NASA mission. Resource constraints Time and human resources. Quality and accuracy of estimates adversely affected. Estimator expertise Experience and knowledge  better quality (and more reliable) estimates.

Estimating Models Model Explanation Per unit Uses a ‘per unit’ factor $/sq ft, Benefits/employee Segmenting Divide problem into items, estimate each and sum Cost indexes Index number based on history Power sizing Scaling previous known costs up or down Triangulation Looking at costs from several perspectives Learning curve Tracking cost improvements Examples Click the Excel® icon to open a spreadsheet of examples.

Learning Curves In general, as the output doubles, the unit production time will be reduced by a fixed percentage or learning curve rate. If the 3rd unit took 200 minutes to produce in a production run with a 90% learning time curve, then the 6th unit will take 200(0.90) = 180 minutes. Estimating time in repetitive tasks: TN = TInitial  Nb where TN = time required for the Nth unit TInitial = time required for the 1st unit N = number of completed units b = learning curve exponent

Learning Curve (Example 2-10) A company has a learning curve rate of 85% and a production run of 20 units. Unit production time is 5.0 minutes when 16 units have been produced. Total production time is 118.8 minutes.

Cash Flow Diagrams Arrows: the usual interpretation is positive for cash inflows (revenues) and negative for cash outflows (expenses). The length of the arrow represents the magnitude ($) of the cash flow. Time dimension: points in time when the positive and negative cash flows occur Discount factor

Categories of Cash Flows First cost ≡ construction, purchase, or installation expense. Operations and maintenance ≡ annual expense. Salvage value ≡ receipt at project termination. Revenues ≡ annual receipts due to sale of products. Overhaul ≡ major capital expenditure occurring during life of asset.

Cash Flow Diagrams … Cash flow diagrams summarize the flow of money over time. They can be represented using a spreadsheet.

Cash Flow: Annuity End of Year Cash Flow $10,000 1 $5,000 2 3 4 5 6 7 $10,000 1 $5,000 2 3 4 5 6 7 8 9 10

Irregular Cash Flow End of Year Cash Flow $10,000 1 $3,000 2 $2,000 3 $10,000 1 $3,000 2 $2,000 3 $1,000 4 $5,000 5 $6,000 6 $2,000 7 8 $3,000 9 $4,000 10 $8,000

Cash Flow: Geometric Series End of Year Cash Flow $10,000 1 $3,000 2 $3,600 3 $4,320 4 $5,184 5 $6,221 6 $7,465 7 $8,958 8 $10,750 9 $12,899 10 $15,479

Suggested Problems 2-3, 2-7, 2-10, 2-11, 2-20, 2-21, 2-23, 2-24, 2-26, 2-27, 2-28, 2-31, 2-32, 2-34, 2-35, 2-36, 2-37