CHAPTER 2 COST CONCEPTS

COST IS IMPORTANT BECAUSE Profit = Revenue – Cost Revenue = (Price)*(Quantity Sold) depends on market conditions, which are often uncontrollable and difficult to predict. Costs = Fixed Costs + Variable Costs(Q) can be estimated easier to control (change engineering methods or materials, hire or layoff workers)

Today’s Topics Cost Estimation Definitions Techniques Cash vs. book Sunk vs. opportunity Fixed, variable, incremental, marginal Recurring, non-recurring Direct, indirect Techniques Maximizing profit when demand and costs are known Minimizing cost “cost-driven design optimization” “Green Engineering”

A process for forecasting present and future costs. COST ESTIMATING A process for forecasting present and future costs. We will learn about Applications Approaches Definitions and Techniques

COST ESTIMATING: APPLICATIONS Help determine whether a new product can be made and distributed at a profit (EG: price = cost + profit) Help set a selling price for quoting, bidding, or evaluating contracts (price > cost) Evaluate how much capital can be justified for process changes or other improvements (are the savings > costs?) Establish benchmarks for productivity improvement programs (which managers or factories need to lower costs?)

COST ESTIMATING: APPROACHES Top-down Approach Bottom-up Approach

TOP-DOWN APPROACH Goal: rough estimate of costs, revenues, and other parameters for current project Uses historical data from similar engineering projects Modifies original data for changes in inflation / deflation, activity level, weight, energy consumption, size, etc… Best use is early in estimating process

BOTTOM-UP APPROACH Goal: more detailed estimate Attempts to break down project into small, manageable units and estimate costs, etc…. Smaller unit costs added together with other types of costs to obtain overall cost estimate Works best when details concerning desired output are well-defined and clear.

Cost Definitions There are many terms used to classify costs… cash costs, book costs, depreciation, sunk costs, opportunity costs, life-cycle costs, recurring costs, fixed costs, variable costs, marginal costs,… For this course, we will need to have a basic understanding of most of these terms.

CASH COST VERSUS BOOK COST Cash cost is a cost that involves payment of cash and results in cash flow; Book cost or noncash cost is a payment that does not involve cash transaction; book costs represent the recovery of past expenditures over a fixed period of time; Depreciation is the most common example of book cost; depreciation is what is charged for the use of assets, such as plant and equipment; depreciation is not a cash flow Usually, only Cash Costs are relevant for economic decision making. The next slide clarifies this further.

SUNK COST AND OPPORTUNITY COST A sunk cost is one that has occurred in the past. It is not related to the present or future costs of alternative business plans, engineering processes, designs, etc. DO NOT CONSIDER SUNK COSTS – SUNK COSTS ARE NOT RELEVANT An opportunity cost is a cost of giving up an opportunity. This kind of cost is sometimes hidden or implied Example – suppose you start your own business Your family gives you $1 million to invest that was previously in a bank savings account. This money is not “free” as the family may be giving up 4%/yr or $40,000/year in interest payments. This is an opportunity cost. Your labor is not “free”. In fact, there is an opportunity cost equal to the salary you are giving up from a “normal job”. ALWAYS CONSIDER OPPORTUNITY COSTS – OPPORTUNITY COSTS ARE RELEVANT

Recurring vs. Non-recurring A recurring cost is repeated at regular times (examples: rent, employee salaries, insurance) A non-recurring cost is anything else. Usually we think of these costs as occurring once. (examples: designing a new product, purchasing durable equipment, settling a law suit, buying another business)

LIFE-CYCLE COST Life-cycle cost is the summation of all costs, both recurring and nonrecurring, related to a product, structure, system, or service during its life span. Life cycle begins with the identification of the economic need or want ( the requirement ) and ends with the retirement and disposal activities.

PHASES OF THE LIFE CYCLE PHASE STEP Acquisition 1. Needs Assessment (buy it) 2. Conceptual design 3. Detailed Design Operation 4. Production/Construction (use it) Operation/Customer Use Retirement 5. Replacement or Disposal (sell it, recycle it, throw it away)

CAPITAL AND INVESTMENT 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;

FIXED, VARIABLE, AND INCREMENTAL COSTS Fixed costs are those unaffected by changes in production/output quantity Q (over some feasible range of Qs). Typical fixed costs include insurance and taxes on facilities, general management and administrative salaries, license fees, and interest costs on borrowed capital. When large changes in usage of resources occur, or when plant expansion or shutdown is involved, fixed costs will be affected.

FIXED, VARIABLE AND INCREMENTAL COSTS Variable costs are those associated with an operation that vary in total with the quantity of output Q 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.

FIXED,VARIABLE AND INCREMENTAL COSTS incremental cost is the additional cost that results from increasing the output of a system by one (or more) units. Incremental Cost = Change in Cost/Change in Units A similar term is marginal cost, usually defined as a derivative of Total Cost, MC =d(TC)/dQ Incremental cost is often associated with “go / no go” decisions that involve a limited change in output or activity level. EXAMPLE the incremental cost of sending 1000kg by ship might be $1.20 / kg. This cost depends on: The type of ship Assuming the ship will also carry some other cargo, but not too much other cargo. The age of the ship and the kind of fuel it uses If the incremental cost of sending 1000kg by railway is $0.80/kg for the same trip, then we might choose to send the cargo by railway.

RECURRING AND NONRECURRING COSTS Recurring costs are repetitive and occur when a firm produces similar goods and services on a continuing basis. Variable costs are recurring costs because they repeat with each unit of output . A fixed cost that is paid on a repeatable basis is also a recurring cost: Office space rental Monthly Insurance payment

RECURRING AND NONRECURRING COSTS Nonrecurring costs are those that are not repetitive, even though the total expenditure may be cumulative over a relatively short period of time; Typically involve developing or establishing a capability or capacity to operate; Examples are purchase cost for real estate upon which a plant will be built, and the construction costs of the plant itself;

DIRECT, INDIRECT AND OVERHEAD COSTS 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, and equipment maintenance ;

DIRECT, INDIRECT AND OVERHEAD COSTS Overhead consists of plant operating costs that are not direct labor or material costs indirect costs, overhead and burden are the same; Prime Cost is a common method of allocating overhead costs among products, services and activities in proportion the sum of direct labor and materials cost ;

STANDARD COSTS Representative costs per unit of output that are established in advance of actual production and service delivery; Standard Cost Element Sources of Data Direct Labor Process routing sheets, + standard times, standard labor rates; Direct Material Material quantities per + unit, standard unit materials cost; Factory Overhead Costs Total factory overhead costs allocated based on prime costs;

SOME STANDARD COST USES Estimating future manufacturing or service delivery costs; Measuring operating performance by comparing actual cost per unit with the standard unit cost; Preparing bids on products or services requested by customers; Establishing the value of work-in-process and finished inventories;

CONSUMER GOODS AND PRODUCER GOODS AND SERVICES Consumer goods and services are those that are directly used by people to satisfy their wants; Producer goods and services are those used in the production of consumer goods and services: machine tools, factory buildings, buses and farm machinery are examples;

Techniques Profit Maximization with linear consumer demand and constant marginal costs Cost-Driven Design Optimization “Green Engineering”

UTILITY AND DEMAND Utility is a measure of the value which consumers of a product or service place on that product or service; Demand is obtained by sorting consumers’ value of product units from high to low. If we assume that consumers will buy when the price is less than the value they receive, then this gives a function relating price to quantity demanded.

PRICE QUANTITY ( OUTPUT )

PRICE We often assume demand is linear. p = a - b Q a QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b PRICE QUANTITY ( OUTPUT ) Total Revenue = p x Q = (a – bQ) x Q QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b PRICE QUANTITY ( OUTPUT ) Total Revenue = p x Q = (a – bQ) x Q =aQ – bQ2 QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b QUANTITY ( OUTPUT ) PRICE MR = dTR / dQ = a –2bQ MR=0  TR is a max Total Revenue = p x Q = (a – bQ) x Q =aQ – bQ2 QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b QUANTITY ( OUTPUT ) PRICE MR = dTR / dQ = a –2bQ = 0 MR=0 Total Revenue = p x Q = (a – bQ) x Q =aQ – bQ2 QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; Q = (a – p) / b QUANTITY ( OUTPUT ) PRICE MR = dTR / dQ = a –2bQ = 0 MR=0 Total Revenue = p x Q TR = Max = (a – bQ) x Q =aQ – bQ2 QUANTITY ( OUTPUT )

PRICE Price equals some constant value minus some multiple of the quantity demanded: p = a - b Q a E > 1 a = Y-axis (quantity) intercept, (price at 0 amount demanded); b = slope of the demand function; E = 1 E < 1 Q = (a – p) / b QUANTITY ( OUTPUT ) PRICE MR = dTR / dQ = a –2bQ = 0 MR=0 Total Revenue = p x Q TR = Max = (a – bQ) x Q =aQ – bQ2 QUANTITY ( OUTPUT )

Profit is maximum where Total Cost by greatest amount Marginal ( Incremental) Cost Profit is maximum where Total Revenue exceeds Total Cost by greatest amount Cost / Revenue Maximum Profit Quantity ( Output ) Demand Marginal Revenue Ct Profit Total Revenue Cost / Revenue Cf Quantity ( Output ) Demand Q’1 Q* Q’2 Q’1 and Q’2 are breakeven points

PROFIT MAXIMIZATION Q* Occurs where total revenue exceeds total cost by the greatest amount; Occurs where marginal cost = marginal revenue; Occurs where dTR/dQ = d TC(Q) /dQ; If TC(Q) = (FC) + (VC) = FC + Cv*Q Q* = [ a - b (Cv) ] / 2

BREAKEVEN POINT Q’1 and Q’2 Occurs where TR = Ct ( aQ - Q2 ) / b = Cf + (Cv ) Q; or - Q2 / b + [ (a / b) - Cv ] Q - Cf = 0 Use the quadratic formula to find the two roots. Recall A X2 + BX + C = 0 implies X = {-B +/- [B2-4AC]}/2A This is easy to do after replacing A=1/b, B=[a/b – cv], and C=–cv with the actual numbers…

COST-DRIVEN DESIGN OPTIMIZATION Must maintain a life-cycle design perspective Ensures engineers consider: Initial investment costs Operation and maintenance expenses Other annual expenses in later years Environmental and other consequences over design life Usually, cost-driven design optimization is focused primarily on the costs to either the customer or the producer.

DESIGN FOR THE ENVIRONMENT (DFE) This green-engineering approach has the following goals: Reduction/Prevention of waste Improved materials selection Reuse and recycling of resources DFE is a kind of cost-driven optimization, where the costs to the environment are considered given additional weight. Emphasizing environment-friendly features is a good marketing strategy, and often has benefits beyond the cost-savings generated for the consumer.

COST-DRIVEN DESIGN OPTIMIZATION PROBLEM TASKS Determine optimal value for certain alternative’s design variable Select the best alternative, each with its own unique value for the design variable

COST-DRIVEN DESIGN OPTIMIZATION PROBLEM COST TYPES Fixed cost(s) Cost(s) that vary directly with the design variable Cost(s) that vary indirectly with the design variable Simplified Format of Cost Model With One Design Variable Cost = aX + (b / X) + k a is a parameter that represents directly varying cost(s) b is a parameter that represents indirectly varying cost(s) k is a parameter that represents the fixed cost(s) X represents the design variable in question (In a particular problem, the parameters a,b and k may actually represent the sum of a group of costs in that category, and the design variable may be raised to some power for either directly or indirectly varying costs.)

GENERAL APPROACH FOR OPTIMIZING A DESIGN WITH RESPECT TO COST Identify primary cost-driving design variable Write an expression for the cost model in terms of the design variable Set first derivative of cost model with respect to continuous design variable equal to 0. (For discrete design variables, compute cost model for each discrete value over selected range). Solve equation in step 3 for optimum value of continuous design variables For continuous design variables, use the second derivative of the cost model with respect to the design variable to determine whether optimum corresponds to global maximum or minimum.

PRESENT ECONOMY STUDIES When alternatives for accomplishing a task are compared for one year or less (I.e., influence of time on money is irrelevant) Rules for Selecting Preferred Alternative Rule 1 – When revenues and other economic benefits are present and vary among alternatives, choose alternative that maximizes overall profitability based on the number of defect-free units of output Rule 2 – When revenues and economic benefits are not present or are constant among alternatives, consider only costs and select alternative that minimizes total cost per defect-free output

PRESENT ECONOMY STUDIES Total Cost in Material Selection In many cases, selection of among materials cannot be based solely on costs of materials. Frequently, change in materials affect design, processing, and shipping costs. Alternative Machine Speeds Machines can frequently be operated at different speeds, resulting in different rates of product output. However, this usually results in different frequencies of machine downtime. Such situations lead to present economy studies to determine preferred operating speed.

Selecting Machine Speeds -- Example 2-13 Facts of the problem (p.55) (figures in US$) Planing lumber increases its worth by $0.10/board-foot. A planing machine can operate at two speeds, called “5000” and “6000”. At speed 5000 Blades need sharpening every 2 hours 1000 board-feet/hour produced (planed) At speed 6000 Blades need sharpening every 1.5 hours 1200 board-feet/hour produced (planed) Sharpening and/or Changing Blades Shut down machine, 15 minutes Cost of sharpening, $10 Blades may be sharpened up to 10 times New blades cost $50 Question: If machine operates all day, which speed is best?

Tricks Use the uptime + downtime to get a cycle time Calculate cycles per work day = 8 hours / cycle time Don’t include or worry about labor cost. Labor costs are identical because workers work 8 hours/day in each case.

Speed: 5000 Cycle Time = 2hrs (uptime) + 0.25 hrs (down time) = 2.25 hrs Cycles per day = 8/2.25 = 3.555 Value added = 3.555 (cycles/day) x 2 hrs uptime/cycle x 1000 board-feet/hour x $0.10 = $711.00 value Cost of sharpening = 3.555 x $10 = $35.50 Cost of Blades = 3.555x$50/10 = $17.18 Profit per day = Value – Costs = $711-$35.50-$17.18 = $657.67

Speed: 6000 Cycle Time = 1.5hrs (uptime) + 0.25 hrs (down time) = 1.75 hrs Cycles per day = 8/1.75 = 4.57 Value added = 4.57 (cycles/day) x 1.5 hrs uptime/cycle x 1200 board-feet/hour x $0.10 = $822.60 value Cost of sharpening = 4.57 x $10 = $45.70 Cost of Blades = 4.57x$50/10 = $22.85 Profit per day = Value – Costs = $822.60-$45.70-$22.85 = $754.05

Compare Speed 5000 Profit $657.67/day Speed 6000 Profit $754.05/day

What we learned: Language - Cost terminology and definitions need a language to better discuss cost concepts Separate relevant from irrelevant costs. Only present and future costs are relevant. Sunk (past) costs are not relevant. saw Applications/Examples maximizing profit with consumer demand model choosing machine speed Final example: textbook error

Example 2-14 6000 board-feet required. Which machine is best? Book calculates costs as $45 for speed 5000 and $50 for speed 6000. Low cost Recommendation: speed 5000.

In 11th edition of your book, they forgot something. Cost estimation technique they are using assumes labor costs are identical  do not need to be calculated. But, speed 6000 is faster (5.83 hours), so requires less labor than speed 5000 (6.75 hours). Can you include labor into the cost calculation? How does the labor cost change the answer? This is a practice problem for you. No need to hand it in – answer given in tutorial.

Hint Wages in the USA range from us$5/hour for unskilled workers to us$10-$25/hr for skilled craftsmen.