Cost Concepts and Design Economics Lecture 2 Cost Analysis NE 364 Engineering Economy

Cost Estimating A term used to describe the process by which the present and future cost consequences of engineering designs are forecast. NE 364 Engineering Economy

Cost estimating used to Provide information used in setting a selling price for quoting, bidding, or evaluating contracts Determine whether a proposed product can be made and distributed at a profit (for simplicity, price = cost + profit) Evaluate how much capital can be justified for process changes or other improvements NE 364 Engineering Economy

Cost Classifications Fixed and Variable Costs Direct and Indirect Costs NE 364 Engineering Economy

Cost Classifications (cont.) Fixed costs are those unaffected by changes in activity level over a feasible range of operations for the capacity or capability available. (e.g. insurance and taxes on facilities, general management and administrative salaries, license fees, and interest costs on borrowed capital). NE 364 Engineering Economy

Cost Classifications (cont.) Variable costs are those associated with an operation that vary in total with the quantity of output or other measures of activity level. Example of variable costs include : costs of material and labor used in a product or service, because they vary in total with the number of output units -- even though costs per unit remain the same. NE 364 Engineering Economy

Cost Classifications (cont.) Direct costs can be reasonably measured and allocated to a specific output or work activity -- labor and material directly allocated with a product, service or construction activity. Indirect costs are difficult to allocate to a specific output or activity -- costs of common tools, general supplies, equipment maintenance and overhead costs. NE 364 Engineering Economy

Cost Terminology Investment Cost or capital investment is the capital (money) required for most activities of the acquisition phase; Working Capital refers to the funds required for current assets needed for start-up and subsequent support of operation activities; Operation and Maintenance Cost includes many of the recurring annual expense items associated with the operation phase of the life cycle; Disposal Cost includes non-recurring costs of shutting down the operation; NE 364 Engineering Economy

Total Cost Calculation Total Cost (TC) = Fixed Costs (CF) + Variable Costs (CV) TC = CF + CV TC = CF + cv * D cost Quantity (D) CF Cv CT NE 364 Engineering Economy

Profit = Total Revenue (TR) – Total Cost (TC) Profit Calculation Profit = Total Revenue (TR) – Total Cost (TC) Scenario1: Constant Price Scenario2: Variable Price NE 364 Engineering Economy

Scenario 1: Constant Price Profit = Total Revenue (TR) – Total Cost (TC) TR = p * D , where p is constant Profit = p * D – TC Break-even point occurs when Profit = 0 TR = TC p * D’ =CF + cv * D’ D’ = CF/ (p – cv) NE 364 Engineering Economy

Breakeven Chart (Scenario 1) TR cost Quantity (D) CF Cv CT BEP (D’) NE 364 Engineering Economy

Scenario 2: Variable Price Profit = Total Revenue (TR) – Total Cost (TC) TR = p * D , where p is variable p = a – b*D Demand (D) Price (p) p = a - b D a is the intercept at the price axis -b is the slope p is the selling price per unit D is the demand NE 364 Engineering Economy

The Total Revenue Function TR Total Revenue = p x D = (a – bD) x D =aD – bD2 QUANTITY ( OUTPUT ) TR = Max D=a/2b NE 364 Engineering Economy

Breakeven Chart (Scenario 2) Cost / Revenue Quantity ( Output ) Demand CT D’1 D’2 D* Profit Total Revenue Maximum Profit (not necessarily at max revenue) D’1 and D’2 are breakeven points NE 364 Engineering Economy

Finding BEP: Scenario 2 NE 364 Engineering Economy

Scenario 2: Profit Maximization D* Occurs where total revenue exceeds total cost by the greatest amount; Occurs at d(profit)/dD=0   NE 364 Engineering Economy

Solved Examples NE 364 Engineering Economy

Example 1: Finding BEP: Scenario 1 A engineering consulting firm measures its output in a standard service hour unit, which is a function of the personnel grade levels in the professional staff. The variable cost is $62 per standard service hour. The charge-out rate (i.e., selling price) is $85.56 per hour. The maximum output of the firm is 160 000 hours per year, and its fixed cost is $2,024,000 per year. For this firm: NE 364 Engineering Economy

Example 1 (cont.) what is the breakeven point in standard service hours and in % of total capacity What is the % reduction in the breakeven point if fixed cost s are reduced by 10%; if variable cost per hour is reduced by 10%; if both costs are reduced by 10%; and if the selling price per unit is increased by 10%? NE 364 Engineering Economy

Example 1: Solution At BEP: Sensitivity Analysis TR=TC p D’ = CF + cvD’ D’ = CF / (p – cv) D’=$2,024,000/($85.56 – $62)=85,908 hours per year D’=85,908/160,000=0.537 (or 53.7% of capacity) Sensitivity Analysis BEP at 10 % reduction in CF: D’= 0.9($2,024,000)/($85.56 – $62)=77,318 hours per year (85,908 – 77,318)/85,908=0.10 (or a reduction of 10% in D’) NE 364 Engineering Economy

Example 1: Solution (cont.) BEP at 10% reduction in cv: D’= ($2,024,000)/($85.56 – 0.9($62))=68,011 hours per year (85,908 – 68,011)/85,908=0.208 (or a reduction of 20.8% in D’) 10 % reduction in both costs D’=$(0.9)(2,024,000)/($85.56 – (0.9)$62)= 61,210 hours per year (85,908 – 61,210)/85,908=0.287 (a reduction of 28.7% in D’) 10% increase in p D’=$2,024,000/((1.1)$85.56 – $62)=63,021 hours per year (85,908-63,021)/85,908=0.266 (26.6% reduction in D’) NE 364 Engineering Economy

Example 1: Solution Summary Change in Factor value (s) Decrease in BEP 10% reduction in CF 10.0% 10% reduction in cv 20.8% 10% reduction in CF and in cv 28.7% 10% increase in p 26.6% NE 364 Engineering Economy

Example 2: Finding BEP: Scenario 2 A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately D= 780-10 p units. (D is the demand or quantity sold per month, and p is the price per dollars.) The fixed cost is $800 per month, and the variable cost is $30 per unit produced. What number of units, D*, should be produced per month and be sold to maximum net profit? What is the maximum profit per month related to the product? Determine D'1 and D'2. NE 364 Engineering Economy

Example 2: Solution Given: D = 780 - 10p (units/month) Fixed Cost (CF) = $800/month Variable Cost per Unit (cv) = $30/unit p= (780 – D )/10 p = 78 – 0.1 * D D* = (78 – 30)/0.2 = 240 units/month NE 364 Engineering Economy

Example 2: Solution (cont.) D* = 240, Profit = 48D - 0.1D2 - 800 Profit = 48(240) - 0.1(240)2 - 800 = $4,960 Maximum Profit = $4,960/month NE 364 Engineering Economy

Example 2: Solution (cont.) 𝐷′ 1,2 = −(78−30)± (78−30) 2 −4(−0.1)(−800) 2(−0.1) D1' = 17.28 or 18 units/month D2' = 462.71 or 462 units/month Profitable range of demand: 18 units/month To 462 units/month NE 364 Engineering Economy

See you next week! NE 364 Engineering Economy