CHAPTER 2CHAPTER 2

COST CONCEPTSCOST CONCEPTS

COST IS IMPORTANT BECAUSECOST IS IMPORTANT BECAUSE

Profit = Revenue – CostProfit = Revenue – Cost

Revenue = (Price)*(Quantity Sold)Revenue = (Price)*(Quantity Sold)depends on market conditions, which are often depends on market conditions, which are often

uncontrollable and difficult to predict. uncontrollable and difficult to predict.

Costs = Fixed Costs + Variable Costs(Q)Costs = Fixed Costs + Variable Costs(Q)can be estimatedcan be estimatedeasier to control (change engineering methods or easier to control (change engineering methods or

materials, hire or layoff workers)materials, hire or layoff workers)

Today’s TopicsToday’s Topics

• Cost EstimationCost Estimation• DefinitionsDefinitions

– Cash vs. bookCash vs. book– Sunk vs. opportunitySunk vs. opportunity– Fixed, variable, incremental, marginalFixed, variable, incremental, marginal– Recurring, non-recurringRecurring, non-recurring– Direct, indirectDirect, indirect

• TechniquesTechniques– Maximizing profit when demand and costs are knownMaximizing profit when demand and costs are known– Minimizing cost “cost-driven design optimization”Minimizing cost “cost-driven design optimization”– ““Green Engineering”Green Engineering”

COST ESTIMATINGCOST ESTIMATING

A process for forecastingA process for forecasting

present and future costs.present and future costs.

We will learn aboutWe will learn about

• ApplicationsApplications

• ApproachesApproaches

• Definitions and TechniquesDefinitions and Techniques

COST ESTIMATING: COST ESTIMATING: APPLICATIONSAPPLICATIONS

• Help determine whether a new product can be Help determine whether a new product can be made and distributed at a profit (EG: price = made and distributed at a profit (EG: price = cost + profit)cost + profit)

• Help set a selling price for quoting, bidding, or Help set a selling price for quoting, bidding, or evaluating contracts (price > cost)evaluating contracts (price > cost)

• Evaluate how much capital can be justified for Evaluate how much capital can be justified for process changes or other improvements (are process changes or other improvements (are the savings > costs?) the savings > costs?)

• Establish benchmarks for productivity Establish benchmarks for productivity improvement programs (which managers or improvement programs (which managers or factories need to lower costs?)factories need to lower costs?)

COST ESTIMATING: COST ESTIMATING: APPROACHESAPPROACHES

• Top-down ApproachTop-down Approach

• Bottom-up ApproachBottom-up Approach

TOP-DOWN APPROACH TOP-DOWN APPROACH

Goal: rough estimate of costs, revenues, Goal: rough estimate of costs, revenues, and other parameters for current projectand other parameters for current project

• Uses historical data from similar Uses historical data from similar engineering projects engineering projects

• Modifies original data for changes in Modifies original data for changes in inflation / deflation, activity level, weight, inflation / deflation, activity level, weight, energy consumption, size, etc…energy consumption, size, etc…

• Best use is early in estimating processBest use is early in estimating process

BOTTOM-UP APPROACHBOTTOM-UP APPROACHGoal: more detailed estimateGoal: more detailed estimate• Attempts to break down project into small, Attempts to break down project into small,

manageable units and estimate costs, manageable units and estimate costs, etc….etc….

• Smaller unit costs added together with Smaller unit costs added together with other types of costs to obtain overall cost other types of costs to obtain overall cost estimateestimate

• Works best when details concerning Works best when details concerning desired output are well-defined and clear.desired output are well-defined and clear.

Cost DefinitionsCost Definitions

There are many terms used to classify There are many terms used to classify costs…costs…

cash costs, book costs, depreciation, sunk cash costs, book costs, depreciation, sunk costs, opportunity costs, life-cycle costs, costs, opportunity costs, life-cycle costs, recurring costs, fixed costs, variable recurring costs, fixed costs, variable costs, marginal costs,…costs, marginal costs,…

For this course, we will need to have a basic For this course, we will need to have a basic understanding of most of these terms.understanding of most of these terms.

CASH COST VERSUS BOOK COSTCASH COST VERSUS BOOK COSTCASH COST VERSUS BOOK COSTCASH COST VERSUS BOOK COST

• Cash costCash cost is a cost that involves payment of cash is a cost that involves payment of cash and results in cash flow;and results in cash flow;

• Book costBook cost or noncash cost is a payment that does or noncash cost is a payment that does not involve cash transaction; book costs not involve cash transaction; book costs represent the recovery of past expenditures over represent the recovery of past expenditures over a fixed period of time;a fixed period of time;

• DepreciatioDepreciation is the most common example of n is the most common example of book cost; depreciation is what is charged for the book cost; depreciation is what is charged for the use of assets, such as plant and equipment; use of assets, such as plant and equipment; depreciation is not a cash flowdepreciation is not a cash flow

• Usually, only Cash Costs are relevant for Usually, only Cash Costs are relevant for economic decision making. The next slide economic decision making. The next slide clarifies this further.clarifies this further.

• Cash costCash cost is a cost that involves payment of cash is a cost that involves payment of cash and results in cash flow;and results in cash flow;

• Book costBook cost or noncash cost is a payment that does or noncash cost is a payment that does not involve cash transaction; book costs not involve cash transaction; book costs represent the recovery of past expenditures over represent the recovery of past expenditures over a fixed period of time;a fixed period of time;

• DepreciatioDepreciation is the most common example of n is the most common example of book cost; depreciation is what is charged for the book cost; depreciation is what is charged for the use of assets, such as plant and equipment; use of assets, such as plant and equipment; depreciation is not a cash flowdepreciation is not a cash flow

• Usually, only Cash Costs are relevant for Usually, only Cash Costs are relevant for economic decision making. The next slide economic decision making. The next slide clarifies this further.clarifies this further.

SUNK COST AND OPPORTUNITY SUNK COST AND OPPORTUNITY COSTCOST

SUNK COST AND OPPORTUNITY SUNK COST AND OPPORTUNITY COSTCOST

• A A sunk costsunk cost is one that has occurred in the is one that has occurred in the pastpast..• It is It is notnot related to the present or future costs of alternative business related to the present or future costs of alternative business

plans, engineering processes, designs, etc.plans, engineering processes, designs, etc.

DO NOT CONSIDER SUNK COSTS – DO NOT CONSIDER SUNK COSTS – SUNK COSTS ARE NOT RELEVANTSUNK COSTS ARE NOT RELEVANT

• An An opportunity costopportunity cost is a cost of giving up an opportunity. This kind of is a cost of giving up an opportunity. This kind of cost is sometimes hidden or implied cost is sometimes hidden or implied

• Example – suppose you start your own businessExample – suppose you start your own business– Your family gives you $1 million to invest that was previously in a 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 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 be giving up 4%/yr or $40,000/year in interest payments. This is an opportunity cost.opportunity cost.

– Your labor is not “free”. In fact, there is an opportunity cost equal Your labor is not “free”. In fact, there is an opportunity cost equal to the salary you are giving up from a “normal job”. to the salary you are giving up from a “normal job”.

ALWAYS CONSIDER OPPORTUNITY COSTS – ALWAYS CONSIDER OPPORTUNITY COSTS –

OPPORTUNITY COSTS ARE RELEVANTOPPORTUNITY COSTS ARE RELEVANT

• A A sunk costsunk cost is one that has occurred in the is one that has occurred in the pastpast..• It is It is notnot related to the present or future costs of alternative business related to the present or future costs of alternative business

plans, engineering processes, designs, etc.plans, engineering processes, designs, etc.

DO NOT CONSIDER SUNK COSTS – DO NOT CONSIDER SUNK COSTS – SUNK COSTS ARE NOT RELEVANTSUNK COSTS ARE NOT RELEVANT

• An An opportunity costopportunity cost is a cost of giving up an opportunity. This kind of is a cost of giving up an opportunity. This kind of cost is sometimes hidden or implied cost is sometimes hidden or implied

• Example – suppose you start your own businessExample – suppose you start your own business– Your family gives you $1 million to invest that was previously in a 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 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 be giving up 4%/yr or $40,000/year in interest payments. This is an opportunity cost.opportunity cost.

– Your labor is not “free”. In fact, there is an opportunity cost equal Your labor is not “free”. In fact, there is an opportunity cost equal to the salary you are giving up from a “normal job”. to the salary you are giving up from a “normal job”.

ALWAYS CONSIDER OPPORTUNITY COSTS – ALWAYS CONSIDER OPPORTUNITY COSTS –

OPPORTUNITY COSTS ARE RELEVANTOPPORTUNITY COSTS ARE RELEVANT

Recurring vs. Non-recurringRecurring vs. Non-recurring

A A recurring costrecurring cost is repeated at regular times is repeated at regular times (examples: rent, employee salaries, (examples: rent, employee salaries, insurance)insurance)

A A non-recurring cost non-recurring cost is anything else. is anything else. Usually we think of these costs as Usually we think of these costs as occurring once. (examples: designing a occurring once. (examples: designing a new product, purchasing durable new product, purchasing durable equipment, settling a law suit, buying equipment, settling a law suit, buying another business)another business)

LIFE-CYCLE COSTLIFE-CYCLE COSTLIFE-CYCLE COSTLIFE-CYCLE COST

Life-cycle cost is the summation of all Life-cycle cost is the summation of all costs, both recurring and costs, both recurring and nonrecurring, related to a product, nonrecurring, related to a product, structure, system, or service during its structure, system, or service during its life span.life span.

Life cycle begins with the identification Life cycle begins with the identification of the economic need or want ( the of the economic need or want ( the requirement ) and ends with the requirement ) and ends with the retirement and disposal activities.retirement and disposal activities.

Life-cycle cost is the summation of all Life-cycle cost is the summation of all costs, both recurring and costs, both recurring and nonrecurring, related to a product, nonrecurring, related to a product, structure, system, or service during its structure, system, or service during its life span.life span.

Life cycle begins with the identification Life cycle begins with the identification of the economic need or want ( the of the economic need or want ( the requirement ) and ends with the requirement ) and ends with the retirement and disposal activities.retirement and disposal activities.

PHASES OF THE LIFE CYCLEPHASES OF THE LIFE CYCLEPHASES OF THE LIFE CYCLEPHASES OF THE LIFE CYCLE

PHASEPHASE STEPSTEPAcquisitionAcquisition 1. Needs Assessment 1. Needs Assessment(buy it) 2. Conceptual design(buy it) 2. Conceptual design 3. Detailed Design3. Detailed Design

OperationOperation 4. Production/Construction 4. Production/Construction(use it) Operation/Customer Use(use it) Operation/Customer Use

Retirement 5. Replacement or Disposal Retirement 5. Replacement or Disposal (sell it, recycle it, throw it away)(sell it, recycle it, throw it away)

PHASEPHASE STEPSTEPAcquisitionAcquisition 1. Needs Assessment 1. Needs Assessment(buy it) 2. Conceptual design(buy it) 2. Conceptual design 3. Detailed Design3. Detailed Design

OperationOperation 4. Production/Construction 4. Production/Construction(use it) Operation/Customer Use(use it) Operation/Customer Use

Retirement 5. Replacement or Disposal Retirement 5. Replacement or Disposal (sell it, recycle it, throw it away)(sell it, recycle it, throw it away)

CAPITAL AND INVESTMENTCAPITAL AND INVESTMENTCAPITAL AND INVESTMENTCAPITAL AND INVESTMENT

• Investment CostInvestment Cost or capital investment is the or capital investment is the capital (money) required for most activities of the capital (money) required for most activities of the acquisition phase;acquisition phase;

• Working CapitalWorking Capital refers to the funds required for refers to the funds required for current assets needed for start-up and current assets needed for start-up and subsequent support of operation activities;subsequent support of operation activities;

• Operation and Maintenance CostOperation and Maintenance Cost includes many includes many of the recurring annual expense items associated of the recurring annual expense items associated with the operation phase of the life cycle;with the operation phase of the life cycle;

• Disposal CostDisposal Cost includes non-recurring costs of includes non-recurring costs of shutting down the operation;shutting down the operation;

• Investment CostInvestment Cost or capital investment is the or capital investment is the capital (money) required for most activities of the capital (money) required for most activities of the acquisition phase;acquisition phase;

• Working CapitalWorking Capital refers to the funds required for refers to the funds required for current assets needed for start-up and current assets needed for start-up and subsequent support of operation activities;subsequent support of operation activities;

• Operation and Maintenance CostOperation and Maintenance Cost includes many includes many of the recurring annual expense items associated of the recurring annual expense items associated with the operation phase of the life cycle;with the operation phase of the life cycle;

• Disposal CostDisposal Cost includes non-recurring costs of includes non-recurring costs of shutting down the operation;shutting down the operation;

FIXED, VARIABLE, AND INCREMENTAL COSTS

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 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

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.

• 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

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.

• 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 COSTSRECURRING AND NONRECURRING COSTSRECURRING AND NONRECURRING COSTSRECURRING AND NONRECURRING COSTS

• Recurring costsRecurring costs are repetitive and occur are repetitive and occur when a firm produces similar goods and when a firm produces similar goods and services on a continuing basis.services on a continuing basis.

• Variable costs are recurring costs because Variable costs are recurring costs because they repeat with each unit of output .they repeat with each unit of output .

• A fixed cost that is paid on a repeatable A fixed cost that is paid on a repeatable basis is also a recurring cost:basis is also a recurring cost:

– Office space rentalOffice space rental

– Monthly Insurance paymentMonthly Insurance payment

• Recurring costsRecurring costs are repetitive and occur are repetitive and occur when a firm produces similar goods and when a firm produces similar goods and services on a continuing basis.services on a continuing basis.

• Variable costs are recurring costs because Variable costs are recurring costs because they repeat with each unit of output .they repeat with each unit of output .

• A fixed cost that is paid on a repeatable A fixed cost that is paid on a repeatable basis is also a recurring cost:basis is also a recurring cost:

– Office space rentalOffice space rental

– Monthly Insurance paymentMonthly Insurance payment

RECURRING AND NONRECURRING COSTSRECURRING AND NONRECURRING COSTSRECURRING AND NONRECURRING COSTSRECURRING AND NONRECURRING COSTS

• Nonrecurring costs are those that are not Nonrecurring costs are those that are not repetitive, even though the total repetitive, even though the total expenditure may be cumulative over a expenditure may be cumulative over a relatively short period of time;relatively short period of time;

• Typically involve developing or Typically involve developing or establishing a capability or capacity to establishing a capability or capacity to operate;operate;

• Examples are purchase cost for real estate Examples are purchase cost for real estate upon which a plant will be built, and the upon which a plant will be built, and the construction costs of the plant itself;construction costs of the plant itself;

• Nonrecurring costs are those that are not Nonrecurring costs are those that are not repetitive, even though the total repetitive, even though the total expenditure may be cumulative over a expenditure may be cumulative over a relatively short period of time;relatively short period of time;

• Typically involve developing or Typically involve developing or establishing a capability or capacity to establishing a capability or capacity to operate;operate;

• Examples are purchase cost for real estate Examples are purchase cost for real estate upon which a plant will be built, and the upon which a plant will be built, and the construction costs of the plant itself;construction costs of the plant itself;

DIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTS

• Direct costsDirect costs can be reasonably measured can be reasonably measured and allocated to a specific output or work and allocated to a specific output or work activity -- labor and material directly activity -- labor and material directly allocated with a product, service or allocated with a product, service or construction activity;construction activity;

• Indirect costsIndirect costs are difficult to allocate to a are difficult to allocate to a specific output or activity -- costs of specific output or activity -- costs of common tools, general supplies, and common tools, general supplies, and equipment maintenance ;equipment maintenance ;

• Direct costsDirect costs can be reasonably measured can be reasonably measured and allocated to a specific output or work and allocated to a specific output or work activity -- labor and material directly activity -- labor and material directly allocated with a product, service or allocated with a product, service or construction activity;construction activity;

• Indirect costsIndirect costs are difficult to allocate to a are difficult to allocate to a specific output or activity -- costs of specific output or activity -- costs of common tools, general supplies, and common tools, general supplies, and equipment maintenance ;equipment maintenance ;

• OverheadOverhead consists of plant operating costs consists of plant operating costs that are not direct labor or material coststhat are not direct labor or material costs– indirect costs, overhead and burden are the indirect costs, overhead and burden are the

same;same;

• Prime CostPrime Cost is a common method of is a common method of allocating overhead costs among allocating overhead costs among products, services and activities in products, services and activities in proportion the sum of direct labor and proportion the sum of direct labor and materials cost ;materials cost ;

• OverheadOverhead consists of plant operating costs consists of plant operating costs that are not direct labor or material coststhat are not direct labor or material costs– indirect costs, overhead and burden are the indirect costs, overhead and burden are the

same;same;

• Prime CostPrime Cost is a common method of is a common method of allocating overhead costs among allocating overhead costs among products, services and activities in products, services and activities in proportion the sum of direct labor and proportion the sum of direct labor and materials cost ;materials cost ;

DIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTSDIRECT, INDIRECT AND OVERHEAD COSTS

STANDARD COSTSSTANDARD COSTSSTANDARD COSTSSTANDARD COSTS• Representative costs per unit of output that Representative costs per unit of output that

are established in advance of actual are established in advance of actual production and service delivery;production and service delivery;

Standard Cost ElementStandard Cost Element Sources of DataSources of Data

Direct LaborDirect Labor Process routing sheets, +Process routing sheets, +standard times, standard standard times, standard labor rates;labor rates;

Direct MaterialDirect Material Material quantities per Material quantities per + + unit, standard unit unit, standard unit

materials cost;materials cost;

Factory Overhead CostsFactory Overhead Costs Total factory overhead Total factory overhead costs allocated based costs allocated based

on on prime costs;prime costs;

• Representative costs per unit of output that Representative costs per unit of output that are established in advance of actual are established in advance of actual production and service delivery;production and service delivery;

Standard Cost ElementStandard Cost Element Sources of DataSources of Data

Direct LaborDirect Labor Process routing sheets, +Process routing sheets, +standard times, standard standard times, standard labor rates;labor rates;

Direct MaterialDirect Material Material quantities per Material quantities per + + unit, standard unit unit, standard unit

materials cost;materials cost;

Factory Overhead CostsFactory Overhead Costs Total factory overhead Total factory overhead costs allocated based costs allocated based

on on prime costs;prime costs;

SOME STANDARD COST USESSOME STANDARD COST USESSOME STANDARD COST USESSOME STANDARD COST USES• Estimating future manufacturing or service Estimating future manufacturing or service

delivery costs;delivery costs;

• Measuring operating performance by Measuring operating performance by comparing actual cost per unit with the comparing actual cost per unit with the standard unit cost;standard unit cost;

• Preparing bids on products or services Preparing bids on products or services requested by customers;requested by customers;

• Establishing the value of work-in-process Establishing the value of work-in-process and finished inventories;and finished inventories;

• Estimating future manufacturing or service Estimating future manufacturing or service delivery costs;delivery costs;

• Measuring operating performance by Measuring operating performance by comparing actual cost per unit with the comparing actual cost per unit with the standard unit cost;standard unit cost;

• Preparing bids on products or services Preparing bids on products or services requested by customers;requested by customers;

• Establishing the value of work-in-process Establishing the value of work-in-process and finished inventories;and finished inventories;

CONSUMER GOODS AND PRODUCER CONSUMER GOODS AND PRODUCER GOODS AND SERVICESGOODS AND SERVICES

CONSUMER GOODS AND PRODUCER CONSUMER GOODS AND PRODUCER GOODS AND SERVICESGOODS AND SERVICES

• Consumer goods and servicesConsumer goods and services are those are those that are directly used by people to satisfy that are directly used by people to satisfy their wants;their wants;

• Producer goods and servicesProducer goods and services are those are those used in the production of consumer goods used in the production of consumer goods and services: machine tools, factory and services: machine tools, factory buildings, buses and farm machinery are buildings, buses and farm machinery are examples;examples;

• Consumer goods and servicesConsumer goods and services are those are those that are directly used by people to satisfy that are directly used by people to satisfy their wants;their wants;

• Producer goods and servicesProducer goods and services are those are those used in the production of consumer goods used in the production of consumer goods and services: machine tools, factory and services: machine tools, factory buildings, buses and farm machinery are buildings, buses and farm machinery are examples;examples;

TechniquesTechniques

1.1. Profit Maximization with linear Profit Maximization with linear consumer demand and constant consumer demand and constant marginal costsmarginal costs

2.2. Cost-Driven Design OptimizationCost-Driven Design Optimization

3.3. ““Green Engineering”Green Engineering”

UTILITY AND DEMANDUTILITY AND DEMANDUTILITY AND DEMANDUTILITY AND DEMAND

• UtilityUtility is a measure of the value which is a measure of the value which consumers of a product or service place on consumers of a product or service place on that product or service;that product or service;

• DemandDemand is obtained by sorting consumers’ is obtained by sorting consumers’ value of product units from high to low. If value of product units from high to low. If we assume that consumers will buy when we assume that consumers will buy when the price is less than the value they receive, the price is less than the value they receive, then this gives a function relating price to then this gives a function relating price to quantity demanded.quantity demanded.

• UtilityUtility is a measure of the value which is a measure of the value which consumers of a product or service place on consumers of a product or service place on that product or service;that product or service;

• DemandDemand is obtained by sorting consumers’ is obtained by sorting consumers’ value of product units from high to low. If value of product units from high to low. If we assume that consumers will buy when we assume that consumers will buy when the price is less than the value they receive, the price is less than the value they receive, then this gives a function relating price to then this gives a function relating price to quantity demanded.quantity demanded.

PRICE

QUANTITY ( OUTPUT )

PRICE

QUANTITY ( OUTPUT )

We often assume demand is linear.

p = a - b Qa

PRICE

QUANTITY ( OUTPUT )

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;

PRICE

QUANTITY ( OUTPUT )

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 )

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

Total Revenue = p x Q= (a – bQ) x Q

QUANTITY ( OUTPUT )

PRICE

QUANTITY ( OUTPUT )

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

Total Revenue = p x Q= (a – bQ) x Q=aQ – bQ2

QUANTITY ( OUTPUT )

PRICE

QUANTITY ( OUTPUT )

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

Total Revenue = p x Q= (a – bQ) x Q=aQ – bQ2

QUANTITY ( OUTPUT )

MR = dTR / dQ = a –2bQMR=0 TR is a max

PRICE

QUANTITY ( OUTPUT )

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

Total Revenue = p x Q= (a – bQ) x Q=aQ – bQ2

QUANTITY ( OUTPUT )

MR = dTR / dQ = a –2bQ = 0MR=0

PRICE

QUANTITY ( OUTPUT )

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

Total Revenue = p x Q= (a – bQ) x Q=aQ – bQ2

QUANTITY ( OUTPUT )

MR = dTR / dQ = a –2bQ = 0MR=0

TR = Max

PRICE

QUANTITY ( OUTPUT )

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

Total Revenue = p x Q= (a – bQ) x Q=aQ – bQ2

QUANTITY ( OUTPUT )

MR = dTR / dQ = a –2bQ = 0MR=0

TR = Max

E > 1

E = 1

E < 1

Co

st /

Rev

enu

e

Quantity ( Output )Demand

Marginal ( Incremental) Cost

Co

st /

Rev

enu

e

Quantity ( Output )Demand

Cf

Ct

Q’1 Q’2Q*

Profit Total Revenue

MaximumProfit

Profit is maximum where Total Revenue exceeds

Total Cost by greatest amount

Q’1 and Q’2 are breakeven points

MarginalRevenue

PROFIT MAXIMIZATIONPROFIT MAXIMIZATIONQ*Q*

• Occurs where total revenue exceeds Occurs where total revenue exceeds total cost by the greatest amount;total cost by the greatest amount;

• Occurs where marginal cost = Occurs where marginal cost = marginal revenue;marginal revenue;

• Occurs where Occurs where ddTR/TR/ddQ = Q = d d TC(Q)TC(Q) / /ddQ;Q;

If TC(Q) = (FC) + (VC) = FC + If TC(Q) = (FC) + (VC) = FC + CCvv*Q*Q

• Q* = [ a - b (Q* = [ a - b (CCvv) ] / 2) ] / 2

BREAKEVEN POINTBREAKEVEN POINTQ’Q’11 and Q’ and Q’22

• Occurs where TR = COccurs where TR = Ctt

( aQ - Q( aQ - Q22 ) / b = C ) / b = Cff + (C + (Cvv ) Q; or ) Q; or

- Q- Q22 / b + [ (a / b) - / b + [ (a / b) - CCvv ] Q - ] Q - CCf f = 0= 0

Use the quadratic formula to find the two Use the quadratic formula to find the two roots. Recall A Xroots. Recall A X22 + BX + C = 0 implies + BX + C = 0 implies

X = {-B +/- X = {-B +/- [B[B22-4AC]}/2A-4AC]}/2AThis is easy to do after replacing A=1/b, B=[a/b – cThis is easy to do after replacing A=1/b, B=[a/b – cvv], and ], and

C=–cC=–cvv with the actual numbers… with the actual numbers…

COST-DRIVEN DESIGN OPTIMIZATIONCOST-DRIVEN DESIGN OPTIMIZATION

Must maintain a life-cycle design perspectiveMust maintain a life-cycle design perspectiveEnsures engineers consider:Ensures engineers consider:• Initial investment costsInitial investment costs• Operation and maintenance expensesOperation and maintenance expenses• Other annual expenses in later yearsOther annual expenses in later years• Environmental and other consequences over design Environmental and other consequences over design

lifelifeUsually, cost-driven design optimization is focused Usually, cost-driven design optimization is focused

primarily on the costs to either the customer or the primarily on the costs to either the customer or the producer.producer.

DESIGN FOR THE ENVIRONMENTDESIGN FOR THE ENVIRONMENT(DFE)(DFE)

This This green-engineering approach has the following approach has the following goals:goals:

• Reduction/Prevention of wasteReduction/Prevention of waste• Improved materials selectionImproved materials selection• Reuse and recycling of resourcesReuse and recycling of resourcesDFE is a kind of cost-driven optimization, where the DFE is a kind of cost-driven optimization, where the

costs to the environment are considered given costs to the environment are considered given additional weight.additional weight.

Emphasizing environment-friendly features is a good Emphasizing environment-friendly features is a good marketing strategy, and often has benefits beyond the marketing strategy, and often has benefits beyond the cost-savings generated for the consumer.cost-savings generated for the consumer.

COST-DRIVEN DESIGN OPTIMIZATION COST-DRIVEN DESIGN OPTIMIZATION PROBLEM TASKSPROBLEM TASKS

1.1. Determine optimal value Determine optimal value for certain alternative’s for certain alternative’s design variabledesign variable

2.2. Select the best alternative, Select the best alternative, each with its own unique each with its own unique value for the design value for the design variablevariable

COST-DRIVEN DESIGN OPTIMIZATION COST-DRIVEN DESIGN OPTIMIZATION PROBLEM COST TYPESPROBLEM COST TYPES

1.1. Fixed cost(s)Fixed cost(s)

2.2. Cost(s) that vary Cost(s) that vary directlydirectly with the design variable with the design variable

3.3. Cost(s) that vary Cost(s) that vary indirectlyindirectly with the design variable with the design variable

Simplified Format of Cost Model With One Design VariableSimplified Format of Cost Model With One Design Variable

Cost = Cost = aaX + (X + (bb / / XX) + ) + kkaa is a parameter that represents directly varying cost(s) is a parameter that represents directly varying cost(s)

bb is a parameter that represents indirectly varying cost(s) is a parameter that represents indirectly varying cost(s)

kk is a parameter that represents the fixed cost(s) is a parameter that represents the fixed cost(s)

XX represents the design variable in question represents the design variable in question

(In a particular problem, the parameters (In a particular problem, the parameters a,ba,b and and kk may actually represent may actually represent the sum of a group of costs in that category, and the design variable 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 may be raised to some power for either directly or indirectly varying costs.) costs.)

GENERAL APPROACH FOR OPTIMIZING GENERAL APPROACH FOR OPTIMIZING A DESIGN WITH RESPECT TO COSTA DESIGN WITH RESPECT TO COST

1.1. Identify primary cost-driving design variableIdentify primary cost-driving design variable2.2. Write an expression for the cost model in terms Write an expression for the cost model in terms

of the design variableof the design variable3.3. Set first derivative of cost model with respect to Set first derivative of cost model with respect to

continuous design variable equal to 0. (For continuous design variable equal to 0. (For discrete design variables, compute cost model discrete design variables, compute cost model for each discrete value over selected range).for each discrete value over selected range).

4.4. Solve equation in step 3 for optimum value of Solve equation in step 3 for optimum value of continuous design variablescontinuous design variables

5.5. For continuous design variables, use the second For continuous design variables, use the second derivative of the cost model with respect to the derivative of the cost model with respect to the design variable to determine whether optimum design variable to determine whether optimum corresponds to global maximum or minimum.corresponds to global maximum or minimum.

PRESENT ECONOMY STUDIESPRESENT ECONOMY STUDIESWhen alternatives for accomplishing a task are When alternatives for accomplishing a task are

compared for one year or less (I.e., influence of compared for one year or less (I.e., influence of time on money is irrelevant)time on money is irrelevant)

Rules for Selecting Preferred AlternativeRules for Selecting Preferred AlternativeRule 1Rule 1 – When revenues and other economic – When revenues and other economic

benefits are present and vary among alternatives, benefits are present and vary among alternatives, choose alternative that maximizes overall choose alternative that maximizes overall profitability based on the number of defect-free profitability based on the number of defect-free units of outputunits of output

Rule 2Rule 2 – When revenues and economic benefits are – When revenues and economic benefits are not present or are constant among alternatives, not present or are constant among alternatives, consider only costs and select alternative that consider only costs and select alternative that minimizes total cost per defect-free outputminimizes total cost per defect-free output

PRESENT ECONOMY STUDIESPRESENT ECONOMY STUDIESTotal Cost in Material SelectionTotal Cost in Material Selection

In many cases, selection of among materials In many cases, selection of among materials cannot be based solely on costs of materials. cannot be based solely on costs of materials. Frequently, change in materials affect design, Frequently, change in materials affect design, processing, and shipping costs.processing, and shipping costs.

Alternative Machine SpeedsAlternative Machine SpeedsMachines can frequently be operated at different Machines can frequently be operated at different speeds, resulting in different rates of product speeds, resulting in different rates of product output. However, this usually results in different output. However, this usually results in different frequencies of machine downtime. Such frequencies of machine downtime. Such situations lead to present economy studies to situations lead to present economy studies to determine preferred operating speed.determine preferred operating speed.

Selecting Machine Speeds -- Selecting Machine Speeds -- Example 2-13Example 2-13

Facts of the problem (p.55) (figures in US$)Facts of the problem (p.55) (figures in US$)• Planing lumber increases its worth by $0.10/board-foot. A Planing lumber increases its worth by $0.10/board-foot. A

planing machine can operate at two speeds, called “5000” planing machine can operate at two speeds, called “5000” and “6000”.and “6000”.

• At speed 5000At speed 5000– Blades need sharpening every 2 hoursBlades need sharpening every 2 hours

– 1000 board-feet/hour produced (planed)1000 board-feet/hour produced (planed)

• At speed 6000At speed 6000– Blades need sharpening every 1.5 hoursBlades need sharpening every 1.5 hours

– 1200 board-feet/hour produced (planed)1200 board-feet/hour produced (planed)

• Sharpening and/or Changing BladesSharpening and/or Changing Blades– Shut down machine, 15 minutesShut down machine, 15 minutes– Cost of sharpening, $10Cost of sharpening, $10

– Blades may be sharpened up to 10 timesBlades may be sharpened up to 10 times

– New blades cost $50New blades cost $50

Question: If machine operates all day, which speed is best?Question: If machine operates all day, which speed is best?

TricksTricks

• Use the uptime + downtime to get a Use the uptime + downtime to get a cycle timecycle time

• Calculate cycles per work dayCalculate cycles per work day= 8 hours / cycle time= 8 hours / cycle time• Don’t include or worry about labor Don’t include or worry about labor

cost. Labor costs are identical cost. Labor costs are identical because workers work 8 hours/day in because workers work 8 hours/day in each case.each case.

Speed: 5000Speed: 5000

Cycle Time = 2hrs (uptime) + 0.25 hrs (down Cycle Time = 2hrs (uptime) + 0.25 hrs (down time) = 2.25 hrstime) = 2.25 hrs

Cycles per day = 8/2.25 = 3.555Cycles per day = 8/2.25 = 3.555Value added = 3.555 (cycles/day) xValue added = 3.555 (cycles/day) x2 hrs uptime/cycle x 1000 board-feet/hour x 2 hrs uptime/cycle x 1000 board-feet/hour x

$0.10 = $711.00 value$0.10 = $711.00 valueCost of sharpening = 3.555 x $10 = $35.50Cost of sharpening = 3.555 x $10 = $35.50Cost of Blades = 3.555x$50/10 = $17.18Cost of Blades = 3.555x$50/10 = $17.18Profit per day = Value – Costs = $711-$35.50-Profit per day = Value – Costs = $711-$35.50-

$17.18 = $657.67$17.18 = $657.67

Speed: 6000Speed: 6000

Cycle Time = 1.5hrs (uptime) + 0.25 hrs (down Cycle Time = 1.5hrs (uptime) + 0.25 hrs (down time) = 1.75 hrstime) = 1.75 hrs

Cycles per day = 8/1.75 = 4.57Cycles per day = 8/1.75 = 4.57Value added = 4.57 (cycles/day) xValue added = 4.57 (cycles/day) x1.5 hrs uptime/cycle x 1200 board-feet/hour x 1.5 hrs uptime/cycle x 1200 board-feet/hour x

$0.10 = $822.60 value$0.10 = $822.60 valueCost of sharpening = 4.57 x $10 = $45.70Cost of sharpening = 4.57 x $10 = $45.70Cost of Blades = 4.57x$50/10 = $22.85Cost of Blades = 4.57x$50/10 = $22.85Profit per day = Value – Costs = $822.60-Profit per day = Value – Costs = $822.60-

$45.70-$22.85 = $754.05$45.70-$22.85 = $754.05

CompareCompare

Speed 5000Speed 5000

Profit $657.67/dayProfit $657.67/day

Speed 6000Speed 6000

Profit $754.05/dayProfit $754.05/day

What we learned:What we learned:

• Language - Cost terminology and definitionsLanguage - Cost terminology and definitions– need a language to better discuss cost conceptsneed a language to better discuss cost concepts

• Separate relevant from irrelevant costs. Only Separate relevant from irrelevant costs. Only present and future costs are relevant. Sunk present and future costs are relevant. Sunk (past) costs are not relevant.(past) costs are not relevant.

• saw Applications/Examplessaw Applications/Examples– maximizing profit with consumer demand modelmaximizing profit with consumer demand model– choosing machine speedchoosing machine speed

• Final example: textbook errorFinal example: textbook error

Example 2-14Example 2-14

6000 board-feet required. 6000 board-feet required.

Which machine is best? Which machine is best?

Book calculates costs as $45 for speed Book calculates costs as $45 for speed 5000 and $50 for speed 6000. 5000 and $50 for speed 6000.

Low cost Recommendation: speed Low cost Recommendation: speed 5000.5000.

In 11In 11thth edition of your book, edition of your book, they forgot something. they forgot something.

Cost estimation technique they are using Cost estimation technique they are using assumes labor costs are identical assumes labor costs are identical do not do not need to be calculated. need to be calculated.

But, speed 6000 is faster (5.83 hours), so But, speed 6000 is faster (5.83 hours), so requires less labor than speed 5000 (6.75 requires less labor than speed 5000 (6.75 hours). hours).

Can you include labor into the cost calculation?Can you include labor into the cost calculation?How does the labor cost change the answer?How does the labor cost change the answer?This is a practice problem for you. No need to This is a practice problem for you. No need to

hand it in – answer given in tutorial.hand it in – answer given in tutorial.

HintHint

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