engineering economy (lecture 1)

7/23/2019 Engineering Economy (Lecture 1)

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Definition:

ENGINEERING ECONOMY is a discipline

concerned with the systematic evaluation of the costsand benefits of the proposed business projects andventures. Its objective is to choose which among thealternative course of action will give the maximumbenefit at the least cost.

Engineering Economy, therefore involves theapplication of definite laws of Economics, theories ofinvestment and business practices to engineering

problems involving cost. It also involves the study ofcost features and other financial data and theirapplications in the field of engineering as basis fordecision.


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COST CONCEPTS

DEMAND

is the quantity of a certain commodity that is bought at a certainprice at a given place and time.

SUPPLY is the quantity of a certain commodity that is offered for sale at acertain price at a given place and time.

FIXED COST are costs that do not vary in proportion to the quantity ofoutput.

VARIABLE COST are costs that vary in proportion to quantity of output.

BREAK EVEN POINT is the level of production at which revenue is exactly

equal to total costs


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Elements of Cost:

1) Materials

a) Direct Materials are those which are used in thefinished product itself.

b) Indirect Materials are those materials used inproduction but which do not go into the finishedproduct.

2) Labor

a) Direct Labor is the actual work applied directly tothe manufacture of the product

b) Indirect Labor is the work necessary for theoperation of the factory, but which cannot beidentified with one particular process or productmanufactured.


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3) Overhead Expenses

Expenses which cannot be allocated to directmaterials or direct labir.

PRIME COST = Direct Materials Cost + Direct LaborCost

PRODUCTION COST = Direct Materials Cost + Direct

Labor Cost + Overhead CostOr

PRODUCTION COST = Prime Cost + Overhead Cost


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LAW OF SUPPLY

The supply of the commodity varies directly as theprice of the commodity, though not proportionately

Supply

price


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LAW OF DEMAND

The demand for a commodity varies inversely as the

price of the commodity, though not proportionately

Demand

pric

e


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LAW OF DEMAND AND SUPPLYUnder conditions of perfect competition, the price atwhich any given product will be supplied and purchasedis the price that will result in the supply and the demandbeing equal.

Quantity

pric

e


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The relationship between price and demand can beexpressed as a line

Where a is the intercept on the price (p)axis and b isthe slope.

p = a - bD

price

Demand (D)


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TOTAL REVENUE VOLUME

RELATIONSHIP

Volume (D)

Peak point represents the

Maximum revenueT

OTAL

Rev

enue

D'

Demand that maximizes

Total Revenue

2

)(

bDaDTR

or

DbDaTR

pDTR


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COST - VOLUME RELATIONSHIPTotal Cost

Fixed Cost

Variable CostC

ost

Volume (D)

TFCvcDTC

TFCTVCTC


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COMBINATION OF COST - VOLUME &

REVENUE VOLUME RELATIONSHIP

Volume (D)

Represents the

Maximum ProfitC

o

s

t

R

e

v

en

u

e

D *

Demand that maximizes

Total Profit

or Total Cost

b

vcaD 2

*


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Formulas:

Price:

Total Revenue:

Total Cost :

bDap

2

)(

bDaDTR

or

DbDaTR

pDTR

TFCvcDTC

TFCTVCTC


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Profit:

Demand that maximizes Revenue

Demand that maximizes Profit

(Optimum Profit)

TFCDvcabDP

TFCvcDDbDaP

TFCvcDpDP

TCTRP

)(

)(

)(

2

b

aD 2

b

vca

D 2*


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Break even points: Profit = 0

TFCDvcabD

TFCDvcabDP

TFCvcDDbDaP

TFCvcDpDP

TCTRP

)(0

)(

)(

)(

2

2

)(2

))((4)()( 2'

b

TFCbvcavcaD


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I. COST CONCEPTS

B: Price is not constant

Break even point:

Volume (D)

Revenue

COST

or

Break Even Point

where TR=TC

vcp

TFCD

' vcp

TFCD

'


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Examples:1.A company produces circuit boards to update the

outdated computer equipment. The fixed cost is $42,000per month and the variable cost is $53 per circuit board.

The selling price per unit is p = $150 0.02D. Maximumoutput of the plant is 4000 units per month.

(a) Determine the optimum value for this product.

(b) What is the maximum profit per month?

(c) At what volumes does break-even occur?

(d) What is the companys range of profitable demand?

E l


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Examples

2. A large semiconductor plant has approximately 95% of sales

due to a single circuit design. The plant can therefore beconsidered to produce 3,000,000 printed circuit boards (PCBs)per year. Presently, the plant is operating at 60% of capacity.The selling price of the PCB is p = $19.25 (10- 6 )D, and thevariable cost per PCB is $15.75. At zero output, the plantsannual fixed costs are $1,000,000 and are approximatelyconstant up to the maximum production quantity per year.

a. What is the present expected annual profit or loss (60%capacity)?

b. What the percentageof production capacity that will result inoptimal operation? What is the maximum profit or minimum lossat this optimal volume?

b.Determine at what demand(s) breakeven occurs in the

operation


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Examples:3.A manufacturing company leases for $100,000 per year abuilding that houses its manufacturing facilities. Inaddition, the machinery in the building is being paid for

installments of $20,000 per year. Each unit of productproduced costs $15 in labor and $10 in materials and canbe sold for $40.

a.How many units per year must be sold for the companyto break even?

b. If 10,000 units per year are sold, what is the annualprofit?

c. If the selling price is lowered to $35 per unit, how manyunits must be sold each year for the company to earn aprofit of $60,000 per year?


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4.A company produces and sells a consumer product andthus far has been able to control the volume of the productby varying the selling price. The company is seeking tomaximize its net profit. It has been concluded that therelationship between price and demand, per month, isapproximately where p is the price per unit indollars. The fixed cost is $1,000 per month, and the

variable cost is $20 per unit. Obtain the answermathematically to the following questions:

a. What is demand that will maximize revenue per monthand the maximum revenue

b. What is the optimal number of units that should beproduced and sold per month?

c. What is the maximum profit per month?

d. What are the breakeven sales quantities and the

range of profitable demand (volume)?

D = p500 5 ,


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5. A plant operation has fixed cost of $2,000,000 peryear, and its output capacity is 100,000 electricalappliances per year. The variable cost is $40 perunit, and the product sells for $90 per unit.

a) What is the annual break even volume of thisproduct?

b) Compare annual profit when the plant is operatingat 90% capacity with the plant operation at 100%

capacity. Assume that the first 90% of capacityoutput is sold at $90 per unit and that the remaining10% of production is sold at $70 per unit.


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Examples6. A company has established that the relationshipbetween the sales price for one of its products andthe quantity sold per month is approximately D = 780

10p units. The fixed cost is $800 per month, andthe variable cost is $30 per unit produced. Whatnumber of units should be produced per month andsold to maximize net profit? What is the maximum

profit per month? Determine the range of profitabledemand.


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Examples:7. The annual fixed costs for a plant are P100,000and the variable costs are P140,000 at

70%utilization of available capacity with net

sales of P280,000. What is the break even point

in units of production if the selling price per unit

is P40.


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8. Suppose we know that p=1,000 D/5, where p =

price in dollars and D = annual demand. The totalcost per year can be approximated by $1,000 + 2D2 .

a. Determine the value of D that maximizes profit.

b. Show that in part(a) profit has been maximized

rather than minimized.


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Answer:

(a) p = 1,000 - 0.2DTC = 1,000 + 2D2

Profit = Total Revenue - Total Cost= (1,000 - 0.2D)D - (1,000 + 2D2)= 1,000D - 2.2D2 - 1,000

D* = 227.27 units per year

(b)

Since the second derivative is negative, profit has been maximized atD*.

d

d

Profit

D = 1,000 - 4.4 D = 0*

d

d

2 (Profit)

D = -4.4 < 0

2


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6. The fixed cost for a steam line per meter of pipe is

$450X + $50 per year. The cost for loss of heat fromthe pipe per meter is $4.8/X1/2 per year. Here Xrepresents the thickness of insulation in meters andX is a continuous design variable.

a. What is the optimum thickness of the insulation?b. How do you know that your answer in (a)minimizes total cost per year?


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Answer:

(a) Total Annual Cost (TAC) = Fixed cost + Cost of Heat Loss

= 450X + 50 +

X* = 0.0305 meters(b) for X > 0.

Since the second derivative is positive, X*

= 0.0305 meters is a minimumcost thickness.

(c) The cost of the extra insulation (a directly varying cost) is being traded-off against thevalue of reduction in lost heat (an indirectly varying cost).

3/2X

2.40-450=0=

X

(TAC)

d

d

0.00533=450

2.40

=X3/2

d

d

2 (TAC)

X =

3.6

X > 0

2 5/2

4 80.

X1/ 2


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7. A local defense contractor is considering the

production of fireworks as a way to reducedependence on the military. The variable cost per unitis $40D. The fixed cost that can be allocated to theproduction of fireworks is negligible. The pricechanged per unit will be determined by the equation

p=$180-(5)D, where D represents demand in unitssold per week.

a. What is the optimum number of units the defensecontractor should produce in order to maximize

profit per week?b. What is the profit if the optimum number of units are

produced?


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(a) Total Revenue = p D= (180 5D)D = 180D 5D2

Total Cost = (40D)D = 40D2Total Profit = -5D2 + 180D 40D2

= - 10D + 180 80D = 0;

90D = 180; D* 2 units/week

= -90 < 0 maximum profit

(b) Total Profit = -5(22) + 180(2) 40(22)= -20 + 360 160 = $180 / week

D

(Profit)

d

d

d

d

2 (Profit)

D2


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Seatwork:1. A company has determined that the price and that

monthly demand of one of its products are related bythe equation

The associated fixed costs are $1,125/month, and thevariable costs are $100/unit.

a. What is the optimal number of units to maximize

revenue and the maximum revenue?b. What is the optimal number of units that should beproduced and sold each month to maximize profit?

c. What are the break even points?

)400( pD


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2. A plant operation has fixed cost of $2,000,000 per

year, and its output capacity is 100,000 electricalappliances per year. The variable cost is $40 per unit,and the product sells for $90 per unit.

a) What is the annual break even volume of thisproduct?

b) Compare annual profit when the plant is operatingat 90% capacity with the plant operation at 100%

capacity. Assume that the first 90% of capacity outputis sold at $90 per unit and that the remaining 10% ofproduction is sold at $70 per unit.


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3. A manufacturer is currently selling 1000 decorative lamps

a month to the retailers at a price of P800 per lamp. Itsestimates that for each P50 increase in the price will sell20 fewer lamps each month. The manufacturers costconsists of a fixed overhead of P300,000/ month plusP300 per lamp for labor and materials.

a. Set up the total cost function

b. Set up the demand function

c. Find the Break Even points

d. Find the volume that will maximize profite. What is the maximum profit?

f. What is the volume of sales that will maximize your salesrevenue?


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4. Bragg & Stratton Company manufactures a specializedmotor for chain saws. The company expects to manufactureand sell 30,000 motors in year 2001. It can manufacture an

additional 10,000 motors without adding new machineryand equipment. Its projected total costs for the 30,000 unitsare as follows:Direct Materials $150,000Direct Labor 100,000Manufacturing Overhead:

Variable Portion 100,000Fixed Portion 80,000Selling and Administrative costs:

Variable Portion 180,000Fixed Portion 70,000

The selling price for the motor is $80.a. What is the total manufacturing cost per unit if 300,000motors are produced?b. What is the total manufacturing cost per unit if 40,000motors are produced?c. What is the break even price on the motors?


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FE 1. Total Revenue (TR) = pD = (88.5 0.08D0.75)D

= 88.5D 0.08D1.75

= 88.5 0.08(1.75)D0.75

D0.75 =

D = 1/0.75 = 5,425 units per year

Total Profit (TP) = TR TC

= 88.5D 0.08D1.75 (40,000 + 40D)

= 48.5D 0.08D1.75

= 48.5 0.08(1.75)D0.75 = 0

D0.75 =

D* = 1/0.75 = 2,433 units per year

5)(0.08)(1.7

5.88

D(TR)d

d

5)(0.08)(1.7

5.88

D

(TP)

d

d

5)(0.08)(1.7

5.48

5)(0.08)(1.7

5.48


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(c) FC = [$350,000 - 0.1($350,000)](12) =$3,780,000 per year (10% decrease)

vc = [$0.50 + 0.1 ($0.50)] = $0.55 per unit ofsales (10% increase)

Thus, no change occurred in the originalbreakeven point.

D =$3,780,000

$1 - $0.55 = $8,400,000 per year


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2-20 (a)

(b) Profit(Loss) = Total Revenue - Total Cost

(90% Capacity) = 90,000 ($90) - [$2,000,000 +90,000 ($40)]

= $2,500,000 per year

(100% Capacity) = [90,000($90) + 10,000($70)] -

[$2,000,000 + 100,000($40)]= $2,800,000 per year

D =C

p - c =

$2,000,000

($90 - $40) / unit = 40,000 units per yearF

v


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BREAK EVEN ANALYSIS, TWO ALTERNATIVES

Industry is faced with certain situations where two or more alternatives can beconsidered. When the cost for two alternatives is affected by a common decisionvariable, there may exist a value of the variable for which the two alternatives willincur equal cost. This value is known as the break-even cost. Below this cost, onemethod will be more economical, and above this cost, the other will prove to bebetter economically.

TCATCB

Total Cost

D Volume (D)TCA = TCB


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Examples1. Two manufacturing methods are beingconsidered. Method A has a fixed cost of

P5,000 and a variable cost of P50. Method B

has a fixed cost of P2500 and a variable cost of150. For what production volume would one

prefer (a) Method A, and (b) Method B?


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2. Two companies are engaged in the manufacture of shirts.Company A, using mostly handwork, has a fixed cost monthlyexpense of P45,000 and a variable cost of P15.00 per shirt.Company B has been able to mechanize most of its

operations, and it finds its fixed monthly expenses areP80,000 and the variable cost per shirt is P12.50.

a. How many shirts should be manufactured by eachmonth so that the total cost will be the same for the twocompanies?

b. If each shirt sells for P32.00 to the retailers,determine the monthly gross profit for each company.

engineering economy (lecture 1)

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