Lecture opportunity

8/10/2019 Lecture opportunity

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ECLT 5930/SEEM 5740: Engineering Economics

201314 Second Term

Master of Science in ECLT & SEEM

Instructors: Dr. Anthony ManCho So

Dr. Man Hong Keith Wong

Department of Systems Engineering & Engineering Management

The Chinese University of Hong Kong

January 16, 2014


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Course Personnel (Updated)

Instructors: Dr. Anthony ManCho SO/Dr. Man Hong Keith WONG Office: ERB 604 Phone: 3943 8477

Office Hours: By appointment Email: [email protected] Website: http://www.se.cuhk.edu.hk/~manchoso

Teaching Assistants:Name Office Phone Email

Ms. Xin LIU ERB 814 3 4438 [email protected]. Chong Man TANG ERB 905 3 4241 [email protected]

Ms. Weijie WU ERB 905 3 4241 [email protected]. Kairen ZHANG ERB 514 3 8319 [email protected]

Office Hours: By appointment

ECLT 5930/SEEM 5740 (201314 Second Term) January 16, 2014 1


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Recap: Engineering Economic Analysis &

Engineering Design Process

1. Problem definition

2. Problem formulation and evaluation

3. Synthesis of possible solutions (alternatives)

4. Analysis, optimization, and evaluation

5. Specification of preferred alternative

6. Communication via performance monitoring



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This Lecture: Analysis of ShortTerm Alternatives

Focus on short term, hence time value of money is negligible

Identify various cost elements in an alternative

Perform economic breakeven analysis and costdriven design optimization



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Identifying Costs

Cost elements differ in their frequency of occurrence, relative magnitude anddegree of impact on the problem at hand

Correctly identifying them is crucial in an engineering economic analysis

Broad Categories Fixed, variable and incremental costs

Direct, indirect and standard costs Cash and book costs

Sunk costs

Opportunity costs

Life-cycle costs



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Fixed, Variable and Incremental Costs

Fixed costs: costs that are unaffected by changes in activity level over a feasiblerange of operations for the capacity available

e.g.: license fees, pipeline installation costs

Variable costs: costs that vary in total with quantity of output or other measuresof activity levels

e.g.: costs of material and labor used in a product or service

Incremental costs: additional cost that results from increasing the output of asystem by one (or more) units

depends on various factors, such as economies of scale, state of the productionsystem, etc.

e.g.: incremental cost of producing a barrel of oil



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Fixed, Variable and Incremental Costs (Contd)

unitsproduced

cost

(a) Fixed cost: cost constant over arange of production

unitsproduced

cost

(b) Variable cost: cost varies withamount of production

Figure 1: Graphs illustrating fixed, variable and incremental costs



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Application: Highway Surfacing

A contractor has to choose from one of two sites on which to set up asphaltmixing plant equipment.

The cost factors relating to the mixing sites are as follows:

Cost Factor Site A Site BAverage hauling distance 6 miles 4.3 milesMonthly rental of site $1,000 $5,000

Cost to set up and remove equipment $15,000 $25,000Hauling expense $1.15/yd3mile $1.15/yd3mileFlagperson not required $96/day



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Application: Highway Surfacing (Contd)

The job requires 50,000 cubic yards of mixed asphalt paving material.

Also, four months (17 weeks of five working days per week) are needed tocomplete the job.

Assume that the cost of return trip is negligible.

Questions: Identify the costs. Which is the better site?



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Application: Highway Surfacing (Contd)

Cost Factor Fixed Variable Site A Site BRent

$4,000 $20,000

Setup/Removal

$15,000 $25,000Flagperson

$0 $8,160

Hauling $345,000 $247,250 Total cost for site A: $364,000

Total cost for site B: $300,410 So site B is better.

Note that the higher fixed costs of site B are being traded off for reduced

variable costs.



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Direct, Indirect and Standard Costs

Direct costs: costs that can be reasonably measured and allocated to a specific

output or work activity

e.g.: material and labor costs directly associated with an economic activity

Indirect costs (aka overheadorburden): costs that are difficult to attribute orallocate to a specific activity

e.g.: costs of common tools, general supplies, equipment maintenance,electricity

typically allocated through a selected formula (e.g., proportional to directlabor hours, direct labor dollars, etc.).

Standard costs: planned costs per unit of output that are established in advanceof actual production or service delivery

developed using anticipated level of production

play an important role in cost control and other management functions, suchas estimating future manufacturing costs, measuring operating performanceby comparing actual vs standard unit cost, etc.



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Remark about the Terminologies

The previously introduced categories are not necessarily mutually exclusive.

Can you think of

a

fixedvariable

cost that is a

directindirect

standard

cost?



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Cash and Book Costs

Cash costs: costs that involve payment of cash and result in cash flow

Noncash or book costs: costs that do not involve cash payments but ratherrepresent the recovery of past expenditures over a fixed period of time

e.g.: depreciation charged for the use of assets such as equipment

In engineering economic analysis, only cash flows or potential cash flows matter e.g.: Depreciation is not a cash flow, but it affects income taxes, which is a

cash flow. More about this later.



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Sunk Costs

Sunk costs: costs that occurred in the past and have no relevance to estimatesof future costs and revenues related to an alternative course of action

e.g.: money spent on a passport, deposit used to secure a flat

Sunk cost is not part of the prospective cash flows and can be disregarded in anengineering economic analysis



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Sunk Costs: Example

John finds a motorcyle he likes and pays $40 as down payment, which will beapplied to the $1,300 purchase price, but will be forfeited if he does not takethe motorcycle.

Over the weekend, he finds another equally desirable motorcyle for a purchaseprice of $1,230.

For the purpose of deciding which motorcycle to buy, the $40 is a sunk cost. It

should not enter into the decision, except that it lowers the remaining cost ofthe first motorcycle.



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Sunk Costs: Another Example

Tom bought a bad second hand mower machine for $100, hoping to spend anadditional $160 on accessories and repair it. Then he would be able to sellit for $500. However, after spending $200, he found that he would still needadditional $250 to finish the repairing.

Question: What is the sunk cost in this case? Hint: Sunk costs are irretrievable consequences of past actions.



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Opportunity Costs

Opportunity costs: costs that are measured in terms of the value of the bestalternative that is not chosen (i.e., foregone)

one of the most important concepts in economics

difficult to define (what is the best alternative?) and is often hidden or

implied Rule of thumb: avoided benefit = cost, avoided cost = benefit Example

A student who could earn $20,000 for working during a year, but choosesinstead to go to school for a year and pay $5,000 in tuition.

His opportunity cost is $20,000 + $5,000 = $25,000.

Question By taking a plane Larry can travel from Hong Kong to Guangzhou in 1 hour.

The same trip takes 5 hours by bus. Airfare is $600 and the bus fare is $200.

If Larry is not travelling, he can work and earn $200 per hour.

What is the opportunity cost for Larry if he travels by bus?



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LifeCycle Costs

Life cycle: roughly, the life cycle of an economic activity consists of two phases:acquisitionandoperation

Acquisition Phase

needs preliminary detailed design;assessment; design; productiondefinition of advanced planning;requirements prototype resource

testing acquisition

Operation Phaseproduction operation; retirement

maintenance and disposaland support

Lifecycle costs: summation of all costs related to an economic activity duringits life span



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Elements of Breakeven Analysis

To perform breakeven analysis, we need to know our sources of revenue andexpenditure.

Typically, these depend ontotal cost,unit selling priceand theactual demand.

These three elements are interrelated: Higher the price, lower the demand

Higher the demand, higher the total cost of production

Hence, we must specify the relationships among them.



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Cost Function

For simplicity, we assume that the total cost (CT) is made up of fixed costs(CF) and variable costs (CV), i.e.,

CT =CF+CV.

Since fixed costs essentially do not vary with the amount of activity, we cantreat CFas a constant.

On the other hand, let us assume that the variable costs dependlinearlyon thedemand, i.e.,

CV =cD,

where D is the demand, and c >0 is the per unit variable cost.



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Cost Function (Contd)

total cost

demand

CT = CF + cD

slope = c

CF

Figure 2: Graph of the total cost function, which is a sum of fixed and variable

costs



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Demand Function

Typically, higher the price, lower the demand.

For simplicity, we assume that unit price (p) and demand (D) arelinearlyrelated,i.e.,

p=a bD,where a, b >0 and0 D a/b(why?).

The coefficient b is related to thedemand elasticity. Generally, the lower the b,the more elastic the demand.

Question: What kind of goods have high (or low) demand elasticity?



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Demand Function (Contd)

price

demand

p=a bD

slope = b

Figure 3: Graph of the demand function



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Total Revenue Function

The total revenue (TR) is simply the product of unit selling price (p) and numberof units sold (D), i.e.,

TR =pD= (a bD)D=aD bD2,

where a, b >0 and0 D a/b. We have expressed total revenue as a function of demand. In particular, we can

find the demand D that maximizes the total revenue:

dTRdD

=a 2bD= 0 D= a2b

.

How to attain the demand D? Just need to set the price right!

p=a b D= a2

.

Question: Is maximizing total revenue the right thing to do?



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CostVolume Relationships

demand

cost/

revenue

max

profit

CT=

CF+

c

D

D

TR = aD bD2

D

CF

Figure 4: Costvolume relationships



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Profit Function

By definition, profit is simply the difference between total revenue and totalcost, i.e.,

profit = total revenue

total cost

= TR CT= (aD bD2) (CF+c D)=

bD2 + (a

c)D

CF,

where a, b, c >0 and 0 D a/b (a negative profit means a loss).

From this identity, we can ask two fundamental economic questions:

Under what conditions would we achieve maximum profit?

Under what conditions would we breakeven?



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Profit Maximization vs Breakeven

To maximize profit, we take the first derivative of the profit function and solved(profit)

dD = 2bD+ (a c) = 0 D = a c

2b .

For this to make sense, we must have a > c to start with.

On the other hand, at a breakeven point, the total revenue equals total cost,i.e.,

aD bD2 =CF+c D bD2 + (c a)D+CF = 0.

Upon solving this quadratic equation, we get

D =(c a)(c a)2 4bCF

2b .

For this to make sense, we must have (c

a)2

4bCF to start with.



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Breakeven Points

demand

cost/

revenue

D2

TR = aD bD2CF

CT=

CF+

c

D

D1

Figure 5: Breakeven points



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Profit Maximization vs Breakeven (Contd)

Note that if the maximum profit is nonnegative, then for any demand D thatfalls in the range D1 D D2, i.e.,

(c

a)(c a)

2

4bCF

2b D (c

a) +(c a)2

4bCF

2b ,

we will be making a profit.


A li i Fi di O i l D d f El i S i h


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Application: Finding Optimal Demand of Electronic Switch

A company produces an electronic timing switch.

Running the production line costs $73,000 per month. Moreover, it costs $83to produce one unit.

The pricedemand relationship is determined as p= $180 0.02D.

Questions:

1. Is there a demand level such that profit occurs?

2. What are the breakeven points? What is the range of profitable demand?


A li i Fi di O i l D d f El i S i h


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In this problem, the fixed cost is $73,000 per month, and the variable cost is

$83 per unit. Hence, the total cost function is given by

CT= $73, 000 + $83D.

Since a c= 180 83>0, our previous result applies. The demand level thatyields the maximum profit is given by

D =a c

2b =

180 832

0.02

= 2, 425 units per month.

The actual profit is given by

profit = total revenue total cost= (aD

b(D)2)

(CF+c

D)

= (180 2, 425 0.02 (2, 425)2) (73, 000 + 83 2, 425)= $44, 612 per month.


A li ti Fi di O ti l D d f El t i S it h


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To find the breakeven points, we need to solve bD2 + (c a)D+CF = 0, or

0.02D2 + (83 180)D+ 73, 000 = 0.

The solutions are

D1

= 97 59.74

0.04 = 932units per month,

D2

= 97 + 59.74

0.04 = 3, 918 units per month.

In particular, the range of profitable demand is

932 D 3, 918.


C t D i D i O ti i ti


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CostDriven Design Optimization

In many engineering problems, there is a tradeoff between cost and performanceof a design.

e.g.: building airplanes, building bridges, writing software

How to optimize the design based on cost considerations?


Cost Driven Design Optimization: An Example


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CostDriven Design Optimization: An Example

The cost of operating a jet can be given by

CO =knv3/2,

where

k is a constant of proportionality,

n is the trip length in miles,

v is velocity in miles per hour.

At 400 miles per hour, the average cost of operation is $300 per mile.

The cost of passengers time (CC) is set at $300,000 per hour.

Question: At what velocity should the trip be planned to minimize the total costCT, which is defined as

CT =CO+CC?


Cost Driven Design Optimization: An Example (Contd)


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CostDriven Design Optimization: An Example (Cont d)

Let us first determinek, the constant of proportionality. From the data, we have

300 =CO

n =k(400)3/2 = k= 0.0375.

Thus, the total cost is given by

CT =CO+CC= 0.0375 nv3/2 + 300, 000 nv

.

To minimize the total cost, we take the first derivative ofCTwith respect to vand solve

dCTdv

=3

2 0.0375 nv1/2 300, 000 n

v2= 0,

i.e.,0.05625 v1/2 300, 000

v2 = 0.

Solving this equation yields v = 490.68 mph.


Application: To Produce or Not to Produce?


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Application: To Produce or Not to Produce?

Department A of a manufacturing plant occupies 100 square meters and produce,among other things, 576 pieces of product X per day.

The average daily production costs for product X are summarized as follows:

Direct labor 1 operator working 4 hours per dayat $22.50 per hour;parttime manager at $30 per day $120.00

Direct material $86.40

Overhead at $0.82 per square meter $82.00Total cost per day $288.40

One can also outsource the production of X to another company at a cost of$0.35 per piece. This results in a total purchase cost of 576 $0.35 = $201.60.

Question: Should the plant shut down the production line for X and purchase it

from the other company?


Whats Next?


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What s Next?

Assignment: Read Chapter 2 of the course textbook.

Next: Costestimation techniques (Chapter 3 of the course textbook)


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