Chapter 2: Cost Concepts and Design Economics Cost categories 1) Fixed costs (costs unaffected by changes in a specific range of operating conditions). 2) Variable costs (costs that vary with the quantity of output). 3) Incremental cost (additional cost resulting from increasing the output by one or more units). Raw materials Direct labor wages Supplies Property taxes Utilities (electricity bill) Administrative salaries Sales commission Rent Shipping charges Example: highway paving A new highway is to be paved and the contractor has two locations to set up their asphalt mixing equipment. The job requires 50,000 yd3 of asphaltic material and the project duration is estimated to be 4 months (17 weeks of 5 working days). Which option is better?  Site B is better. Assume the contractor is paid $12/yd3 asphalt delivered to the site and assume the cost of material is $1.5/yd3 . At what point does he breakeven and begin to make a profit? Break-even means: Total revenue = Total expenses $90,750 + [$2.75 × 3 X] + [$1.5 × X] = $12 X X = 40,333 yd3 Other categories of cost - Direct costs (directly measured and allocated to a specific outcome or work activity). - Indirect costs (overhead or burden): difficult to allocate to a specific output or work activity. A specific formula can be used (proportions). - Standard costs (established ahead of production or service delivery: anticipated labor and material costs + overhead cost per unit). Cost terminology Cash cost: involves payment of cash and results in cash flow. Book cost: does not involve a cash transaction and is normally reflected as a noncash cost. Sunk cost: payment occurred in the past with no relevance to future cost and revenue estimates (not a part of future cash flows and is typically disregarded in engineering economy problems). Opportunity costs: monetary advantage foregone due to limited resources or the cost of the best rejected opportunity. Life-cycle cost: summation of all costs related to a product, a system, a structure, or a service during its lifespan. General price-demand relationship Where: 𝑝𝑝 = 𝑎𝑎 − 𝑏𝑏 × 𝐷𝐷 𝑝𝑝 = price 𝐷𝐷 = demand 𝑎𝑎 and b = constants that depend on the product or service. 0 < 𝐷𝐷 < 𝑎𝑎/b 𝑎𝑎 > 0; b > 0 Total revenue and breakeven point Total revenue (TR) from selling a product or a service is: 𝑇𝑇𝑇𝑇 = 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 × 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑 = 𝑝𝑝 × 𝐷𝐷 Total costs (𝐶𝐶𝑇𝑇) = Fixed costs (𝐶𝐶𝐹𝐹 ) + Variable costs (𝐶𝐶𝑉𝑉 ) Assuming a linear relationship between variable costs and demand, 𝐶𝐶𝑉𝑉 = 𝑐𝑐𝑐𝑐 × 𝐷𝐷, where 𝑐𝑐𝑣𝑣 is the variable cost per unit demand. 𝐶𝐶𝑇𝑇 = 𝐶𝐶𝐹𝐹 + 𝑐𝑐𝑉𝑉 × 𝐷𝐷  Scenario 1: demand is a function of price.  Scenario 2: demand and price are independent from each other. Profit – scenario 1 Profit = Total revenue – Total costs 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑎𝑎𝑎𝑎 − 𝑏𝑏𝐷𝐷2 − (𝐶𝐶𝐹𝐹 + 𝑐𝑐𝑉𝑉 𝐷𝐷) 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = −𝑏𝑏𝐷𝐷2 + 𝑎𝑎 − 𝑐𝑐𝑉𝑉 𝐷𝐷 − 𝐶𝐶𝐹𝐹 To maximize profit, 𝑑𝑑(𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃) = 𝑎𝑎 − 𝑐𝑐𝑣𝑣 − 2𝑏𝑏𝑏𝑏 = 0 𝑑𝑑𝑑𝑑 Optimal 𝐷𝐷  𝐷𝐷* = 𝑎𝑎−𝑐𝑐𝑣𝑣 2𝑏𝑏 Two breakeven points (profit = 0) are found by: Total revenue = Total cost 𝐷𝐷′ = −(𝑎𝑎 − 𝑐𝑐𝑣𝑣 ) ± 𝑎𝑎 − 𝑐𝑐𝑣𝑣 2 − 4(−𝑏𝑏)(−𝐶𝐶𝐹𝐹 ) 2(−𝑏𝑏) Profit – scenario 2 Price per unit (𝑝𝑝) and demand (𝐷𝐷) are independent from each other. Profit = Total revenue – Total costs 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 = 𝑝𝑝 𝐷𝐷 − (𝐶𝐶𝐹𝐹 + 𝑐𝑐𝑉𝑉 𝐷𝐷) Only one breakeven point. No optimal demand. Example A company produces an electronic timing switch that is used in consumer and commercial products. The fixed cost (𝐶𝐶𝐹𝐹 ) is $73,000 per month, and the variable cost (𝑐𝑐𝑣𝑣 ) is $83 per unit. The selling price per unit is 𝑝𝑝 = $180 − 0.02(𝐷𝐷). 1) Determine the optimal volume for this product and confirm that a profit occurs (instead of a loss) at this demand. 2) Find the volumes at which breakeven occurs; that is, what is the range of profitable demand. (1) D∗ = 𝑎𝑎−𝑐𝑐𝑣𝑣 2𝑏𝑏 = $180−$83 2∗0.02 = 2,425 𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢𝑢 𝑝𝑝𝑝𝑝𝑝𝑝 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚ℎ (𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝). Or write down the equation of profit, derive, and equate to zero. 𝑃𝑃 = 180 𝐷𝐷 − 0.02 𝐷𝐷 2 − 73,000 + 83 𝐷𝐷 = −0.02 𝐷𝐷2 + 97 𝐷𝐷 − 73,000 For a profit to occur, the 2nd derivative should be negative (-0.04). Also, substitute the optimal demand (𝐷𝐷∗ ) in the profit equation: Profit= [$180 × 2,425 – 0.02 × 2,4252] – [$73,000 + $83 × 2,425] = $44,612 (+ve profit). (2) 𝑎𝑎 = 180 𝑏𝑏 = 0.02 D′ = −(180 − 83) ± 𝐷𝐷’1 = 932 units and 𝐷𝐷’2 = 3,918 units. 𝑐𝑐𝑣𝑣 = 83 𝐶𝐶𝐹𝐹 = 73000 180 − 83 2 − 4(−0.02)(−73,000) 2(−0.02) Example An engineering consulting firm measures its output in a standard service hour unit. The variable cost (𝑐𝑐𝑣𝑣 ) is $62 per standard service hour and the charge-out rate [i.e., selling price (𝑝𝑝)] is $85.56 per hour. The maximum output of the firm is 160,000 hours per year, and its fixed cost (𝐶𝐶𝐹𝐹 ) is $2,024,000 per year. What is the breakeven point in standard service hours and in percentage of total capacity? Total revenue = Total costs 𝐷𝐷’ × $85.56/ℎ = $2,024,000 + $62 × 𝐷𝐷’ 𝐷𝐷’ = 85,908 ℎ. 85,908 % 𝑜𝑜𝑜𝑜 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 = × 100% = 54% 160,000 Present economy studies Duration < one year  time influence on money is ignored (present economy). Comparing multiple alternatives: (1) For variable known revenue and benefits, select the alternative with maximum profit. (2) For constant or unknown revenue and benefits, select the alternative with minimum total cost per defect-free product or service. Example The demand for a certain part is 100,000 units. The part is produced on a high-speed turret lathe, using screw-machine steel costing $0.30 per pound. A study was conducted to determine whether it might be cheaper to use brass screw stock, costing $1.40 per pound. Because the weight of steel required per piece was 0.0353 pounds and that of brass was 0.0384 pounds, the material cost per piece was $0.0106 for steel and $0.0538 for brass. However, when the manufacturing engineering department was consulted, it was found that, although 57.1 defect-free parts per hour were being produced by using steel, the output would be 102.9 defect-free parts per hour if brass were used. Assuming the machine attendant is paid $15.00 per hour, and the variable (i.e., traceable) overhead costs for the turret lathe are estimated to be $10.00 per hour. Which material should be used for this part? Unknown or constant revenue (demand is constant)  compare the cost per defect-free unit  Select brass Example Two machines with approximately the same capital investment are being considered for the production of a part. The important differences between the machines are their production capacities (production rate × available production hours) and their reject rates (percentage of parts produced that cannot be sold). Consider the following table: The material cost is $6.00 per part, and all defect-free parts produced can be sold for $12 each (rejected parts have negligible scrap value.) For either machine, the operator cost is $15.00 per hour and the variable overhead rate for traceable costs is $5.00 per hour. Assume that the daily demand for this part is large enough that all defect-free parts can be sold. Which machine should be selected?

Chapter 2 Cost Concepts and Design Economics

Related Documents

Recommended Documents

Description

Related Documents

Free up your schedule!

Take 5 seconds to unlock