1. Cost Concepts & Design Economics

Summer 2015

07/01/2015

Session 1

Objective

The objectives of today’s class are: to illustrate the concept of engineers

cost-driven optimization to analyze short-term alternatives when

the time value of money is not a factor

Cost Categorization

Fixed cost: unaffected by changes in activity level

Variable cost: vary in total with the quantity of output (or similar measure of activity)

Incremental cost: additional cost resulting from increasing output of a system by one (or more) units

Other Categories

Direct: can be measured and allocated to a specific work activity – cost of materials

Indirect: difficult to attribute or allocate to a specific output or work activity (also overhead or burden) – equipment maintenance

Standard cost: cost per unit of output, established in advance of production or service delivery – future manufacturing costs

Cost Terminology Cash cost: a cost that involves a

payment of cash Book cost: a cost that does not involve a

cash transaction but is reflected in the accounting system

Sunk cost: a cost that has occurred in the past and has no relevance to estimates of future costs and revenues related to an alternative course of action

Pop Quiz

A. $5,000B. $20,000C. $50,000D. $15,000

A. B. C. D.

25% 25%25%25%

An equipment originally costs $50,000, but it is registered in the company’s account as worth $20,000 due to depreciation. It has a market value of only $5,000. What is the sunk cost of this equipment?

Common Cost Terms

Opportunity cost the monetary advantage foregone

due to limited resources the cost of the best rejected

opportunity Life-cycle cost

the summation of all costs related to a product, structure, system, or service during its life span

Pop Quiz

A. $5,000B. $20,000C. $50,000D. $15,000

A. B. C. D.

25% 25%25%25%

An equipment originally costs $50,000, but it is registered in the company’s account as worth $20,000 due to depreciation. It has a market value of only $5,000. What is the opportunity cost of this equipment?

Phases of the Life Cycle & Their Relative Cost

Price-Demand Relationship

The demand for a product or service is directly related to its price according to p=a-bD where p is price, D is demand, and a and b are constants that depend on the particular product or service.

Revenue = f(price, demand)

Total revenue is the product of the selling price per unit, p, and the number of units sold, D

Solving, the optimal demand is

Maximize Revenue

02 bDadD

dTR

b

aD

2ˆ

Maximize Profit

Profit is revenue minus cost, so

for

Differentiating, we can find the value of D that maximizes profit,

b

caD v

2*

0,0 and 0 bab

aD

Fv CDcabD )(Profit 2

Acme Manufacturing is a major player in the lawn sprinkler business Their high-end sprinkler is used commercially,

and is quite popular with golf course greens keepers

In producing these sprinklers Acme’s fixed cost is $55,000 per month with a variable cost of $15.50 per unit

The selling price for these high-end sprinklers is described by the equation

What is the optimal volume of sprinklers? Does Acme make a profit at that volume?

What is the range of profitable demand?

Example

)( FC

)( vc

Dp 02.050.87$

Breakeven

Breakeven is found when total revenue = total cost

Solving, we find the demand at which this occurs

)(2

))((4)()( 2

b

CbcacaD Fvv

Engineers’ Cost Considerations

Engineers must consider costs in the design of products, processes and services

“Cost-driven design optimization” is critical in today’s competitive business environment

In our brief examination we examine discrete and continuous problems that consider a single primary cost driver

Tasks in Cost-Driven Optimization

1. Determine the optimal value for a certain alternative’s design variable.

2. Select the best alternative, each with its own unique value for the design variable.

Cost models are developed around the design variable, X

4-Step Design Optimization Process

1. Identify the design variable that is the primary cost driver

2. Express the cost model in terms of the design variable

3. For continuous cost functions, differentiate to find the optimal value For discrete functions, calculate cost over a

range of values of the design variable

4. Solve the equation in step 3 for a continuous function For discrete, the optimum value has the

minimum cost value found in step 3

Simplified Cost Function

where,

a is a parameter that represents the directly varying cost(s),

b is a parameter that represents the indirectly varying cost(s),

k is a parameter that represents the fixed cost(s), and

X represents the design variable in question

kX

baXCost

Example: Demand is a Function of Price

A company produces an electronic timing switch that is used in consumer and commercial products The fixed cost is $73,000 per month, and

the variable cost is $83 per unit The selling price per unit is Determine the optimal volume for this

product and confirm that a profit occurs (instead of a loss) at this demand

Find the volumes at which breakeven occurs, i.e., what is the range of profitable demand?

)( FC

)( vc

Dp 02.0180$

Solution

Two pumps capable of delivering 100 hp to an agricultural application are being evaluated in a present economy study. The selected pump will only be utilized for one year, and it will have no market value at the end of the year. Pertinent data are summarized as follows:

If electric power costs $0.10 per kWh and the pump will be operated 4,000 hours per year, which pump should be chosen?Hint: 1 hp = 0.746 kW

Investing in Electrical Efficiency

ABC Pump XYZ Pump

Purchase price $2,900 $6,200Annual maintenance $170 $510Efficiency 80% 90%