1. Break Even Analysis

7/23/2019 1. Break Even Analysis

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BREAK EVENANALYSIS

Topic 1

Engr. Tafalla

November 30 !01"



Definition:

ENGINEERING ECONOMY is a discipline

concerned with the systematic evaluation of the costsand enefits of the proposed usiness pro!ects andventures" Its o!ective is to choose which amon# thealternative course of action will #ive the ma$imumenefit at the least cost"

En#ineerin# Economy% therefore involves theapplication of definite laws of Economics% theories ofinvestment and usiness practices to en#ineerin#prolems involvin# cost" It also involves the study ofcost features and other financial data and theirapplications in the field of en#ineerin# as asis fordecision"



COST CONCEPTS

DEMAND – is the &uantity of a certain commodity that is ou#ht at a certainprice at a #iven place and time"

SUPPLY ' is the &uantity of a certain commodity that is offered for sale at acertain price at a #iven place and time"

FIXED COST ' are costs that do not vary in proportion to the &uantity ofoutput"

VARIABLE COST ' are costs that vary in proportion to &uantity of output"

BREAK EVEN POINT ' is the level of production at which revenue is e$actly

e&ual to total costs



Elements of Cost:

()Materials

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

) Indirect Materials are those materials used inproduction ut which do not #o into the finishedproduct"

*) +aor

a) Direct +aor is the actual wor, applied directly tothe manufacture of the product

) Indirect +aor is the wor, necessary for theoperation of the factory% ut which cannot eidentified with one particular process or productmanufactured"



-) Overhead E$penses

E$penses which cannot e allocated to directmaterials or direct lair"

.RIME CO/0 1 Direct Materials Cost 2 Direct +aorCost

.ROD3C0ION CO/0 1 Direct Materials Cost 2 Direct

+aor Cost 2 Overhead CostOr

.ROD3C0ION CO/0 1 .rime Cost 2 Overhead Cost



LAW OF SUPPLY 0he supply of the commodity varies directly as theprice of the commodity% thou#h not proportionately

/upply

pr ice



LAW OF DEMAND

0he demand for a commodity varies inversely as the

price of the commodity% thou#h not proportionately

Demand

pr ic

e



LAW OF DEMAND AND SUPPLY 3nder conditions of perfect competition% the price atwhich any #iven product will e supplied and purchasedis the price that will result in the supply and the demandein# e&ual"

4uantity

pr ic

e



0he relationship etween price and demand can ee$pressed as a line

5here a is the intercept on the price 6p)a$is and –b isthe slope"

p = a - bD

pr ice

Demand 6D)



TOTAL REVENUE – VOLUME

RELATIONSHIP

7olume 6D)

Peak point – represents te

Ma!i"#" re$en#e0

O0 8+

Rev

enue

D%

De"an& tat "a!i"i'es

Tota( Re$en#e

2

)(

bDaDTR

or

DbDaTR

pDTR

−=

−=

=



COST - VOLUME RELATIONSHIP

TFC vcDTC

TFC TVC TC

+=

+=0otal Cost

9i$ed Cost

7ariale CostC

ost

7olume 6D)



COM)INATION O* COST - VOLUME +

REVENUE VOLUME RELATIONSHIP

b

vca D 2

* −=

Vo(#"e ,D

Represents te

Ma!i"#" Pro.itC

o

s

t

R

e

$

en

#

e

D /

De"an& tat "a!i"i'es

Tota( Pro.it

or Tota( Cost



9ormulas:

.rice:

0otal Revenue:

0otal Cost :

bDa p −=

2

)(

bDaDTR

or

DbDaTR

pDTR

−=

−=

=

TFC vcDTC

TFC TVC TC

+=

+=



.rofit:

Demand that ma$imies Revenue

Demand that ma$imies .rofit

6Optimum .rofit)

TFC DvcabD P

TFC vcD DbDa P

TFC vcD pD P

TC TR P

−−+−=

−−−=

+−=

−=

)(

)(

)(

2

b

a D 2=

b

vca

D 2

* −=



;rea, even points: .rofit 1 <

TFC DvcabD

TFC DvcabD P

TFC vcD DbDa P

TFC vcD pD P

TC TR P

−−+−=

−−+−=

−−−=

+−=

−=

)(0

)(

)(

)(

2

2

)(2

))((4)()( 2

'

b

TFC bvcavca D

−

−−−−±−−=



I" CO/0 CONCE.0/

;: .rice is not constant

;rea, even point:

+ o s s

. R O 9 I 0

7olume 6D)

Revenue

CO/0

or

)reak E$en Point

0ere TR=TC

vc p

TFC D

−=

' vc p

TFC D

−=

'



E$amples:(" 8 company produces circuit oards to update the

outdated computer e&uipment" 0he fi$ed cost is =>*%<<<per month and the variale cost is =?- per circuit oard"

0he sellin# price per unit is p 1 =(?< ' <"<*D" Ma$imumoutput of the plant is ><<< units per month"

6a) Determine the optimum value for this product"

6) 5hat is the ma$imum profit per month@

6c) 8t what volumes does rea,Aeven occur@

6d) 5hat is the companyBs ran#e of profitale demand@



E$amples*" 8 lar#e semiconductor plant has appro$imately ? of sales

due to a sin#le circuit desi#n" 0he plant can therefore econsidered to produce -%<<<%<<< printed circuit oards 6.C;s)per year" .resently% the plant is operatin# at < of capacity"0he sellin# price of the .C; is p 1 =("*? ' 6(<A E )D% and the

variale cost per .C; is =(?"F?" 8t ero output% the plantsannual fi$ed costs are =(%<<<%<<< and are appro$imatelyconstant up to the ma$imum production &uantity per year"

a" 5hat is the present e$pected annual profit or loss 6<capacity)@

" 5hat the percentage of production capacity that will result inoptimal operation@ 5hat is the ma$imum profit or minimum lossat this optimal volume@

"Determine at what demand6s) rea,even occurs in theoperation



E$amples:12 8 manufacturin# company leases for =(<<%<<< per year auildin# that houses its manufacturin# facilities" Inaddition% the machinery in the uildin# is ein# paid for

installments of =*<%<<< per year" Each unit of productproduced costs =(? in laor and =(< in materials and cane sold for =><"

a"ow many units per year must e sold for the companyto rea, even@

" If (<%<<< units per year are sold% what is the annualprofit@

c" If the sellin# price is lowered to =-? per unit% how manyunits must e sold each year for the company to earn aprofit of =<%<<< per year@



>"8 company produces and sells a consumer product and thusfar has een ale to control the volume of the product yvaryin# the sellin# price" 0he company is see,in# to ma$imie

its net proHt" It has een concluded that the relationshipetween price and demand% per month% is appro$imately

where p is the price per unit in dollars" 0he H$ed cost is=(%<<< per month% and the variale cost is =*< per unit"

Otain the answer mathematically to the followin# &uestions:a" 5hat is demand that will ma$imie revenue per monthand the ma$imum revenue

" 5hat is the optimal numer of units that should e

produced and sold per month@c" 5hat is the ma$imum proHt per month@

d" 5hat are the rea,even sales &uantities and the ran#eof proHtale demand 6volume)@

D = p500 5 ,−



?" 8 plant operation has fi$ed cost of =*%<<<%<<< peryear% and its output capacity is (<<%<<< electricalappliances per year" 0he variale cost is =>< per unit%and the product sells for =< per unit"

a) 5hat is the annual rea, even volume of thisproduct@

) Compare annual profit when the plant is operatin# at< capacity with the plant operation at (<<

capacity" 8ssume that the first < of capacity outputis sold at =< per unit and that the remainin# (< ofproduction is sold at =F< per unit"



E$amples" 8 company has estalished that the relationship

etween the sales price for one of its products andthe &uantity sold per month is appro$imately D 1 F< ' (<p units" 0he fi$ed cost is =<< per month% andthe variale cost is =-< per unit produced" 5hatnumer of units should e produced per month andsold to ma$imie net profit@ 5hat is the ma$imum

profit per month@ Determine the ran#e of profitaledemand"



E$amples:F" Te ann#a( .i!e& 3osts .or a p(ant are P4556555

an& te $ariab(e 3osts are P4756555 at

859#ti(i'ation o. a$ai(ab(e 3apa3it: 0it net sa(es

o. P;<565552 at is te break e$en point in #nits

o. pro&#3tion i. te se((in> pri3e per #nit is P752



" /uppose we ,now that p1(%<<< ' DJ?% where p 1

price in dollars and D 1 annual demand" 0he totalcost per year can e appro$imated y =(%<<< 2 *D* "

a"Determine the value of D that ma$imies profit"

"/how that in part6a) profit has een ma$imied ratherthan minimied"



Ans0er?

,a p 1 (%<<< A <"*D0C 1 (%<<< 2 *D*

.rofit 1 0otal Revenue A 0otal Cost 1 6(%<<< A <"*D)D A 6(%<<< 2 *D*)1 (%<<<D A *"*D* A (%<<<

DK 1 **F"*F units per year

,b

/ince the second derivative is ne#ative% profit has een ma$imied atDK"

d

d

Profit

D = 1,000 - 4.4 D = 0*

d

d

2 (Profit)

D = - 4.4 < 0

2



" 0he fi$ed cost for a steam line per meter of pipe is

=>?<L 2 =?< per year" 0he cost for loss of heat fromthe pipe per meter is =>"JL(J* per year" ere Lrepresents the thic,ness of insulation in meters andL is a continuous desi#n variale"

a" 5hat is the optimum thic,ness of the insulation@" ow do you ,now that your answer in 6a)minimies total cost per year@



Ans0er?

,a 0otal 8nnual Cost 608C) 1 9i$ed cost 2 Cost of eat +oss

1 >?<L 2 ?< 2

LK 1 <"<-<? meters,b for L <"

/ince the second derivative is positive% L K 1 <"<-<? meters is a minimum cost thic,ness"

,3 0he cost of the e$tra insulation 6a directly varyin# cost) is ein# tradedAoff a#ainst thevalue of reduction in lost heat 6an indirectly varyin# 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



F" 8 local defense contractor is considerin# the

production of firewor,s as a way to reducedependence on the military" 0he variale cost per unitis =><D" 0he fi$ed cost that can e allocated to theproduction of firewor,s is ne#li#ile" 0he pricechan#ed per unit will e determined y the e&uationp1=(<A6?)D% where D represents demand in unitssold per wee,"

a"5hat is the optimum numer of units the defensecontractor should produce in order to ma$imie profit

per wee,@"5hat is the profit if the optimum numer of units are

produced@



,a 0otal Revenue 1 p D1 6(< ' ?D)D 1 (<D ' ?D*

0otal Cost 1 6><D)D 1 ><D*

0otal .rofit 1 A?D* 2 (<D ' ><D*

1 A (<D 2 (< ' <D 1 <

<D 1 (< DK * unitsJwee,

1 A< < ∴ ma$imum profit

6) 0otal .rofit 1 A?6**) 2 (<6*) ' ><6**) 1 A*< 2 -< ' (< 1 =(< J wee,

D

(Profit)

d

d

d

d

2(Profit)

D2



/eatwor,:(" 8 company has determined that the price and that

monthly demand of one of its products are related ythe e&uation

0he associated fi$ed costs are =(%(*?Jmonth% and thevariale costs are =(<<Junit"

a" 5hat is the optimal numer of units to ma$imie

revenue and the ma$imum revenue@" 5hat is the optimal numer of units that should eproduced and sold each month to ma$imie profit@

c" 5hat are the rea, even points@

)400( p D −=



*" 8 plant operation has fi$ed cost of =*%<<<%<<< peryear% and its output capacity is (<<%<<< electricalappliances per year" 0he variale cost is =>< per unit%and the product sells for =< per unit"

a) 5hat is the annual rea, even volume of thisproduct@

) Compare annual profit when the plant is operatin#at < capacity with the plant operation at (<<

capacity" 8ssume that the first < of capacity outputis sold at =< per unit and that the remainin# (< ofproduction is sold at =F< per unit"



-" 8 manufacturer is currently sellin# (<<< decorative lamps

a month to the retailers at a price of .<< per lamp" Itsestimates that for each .?< increase in the price will sell*< fewer lamps each month" 0he manufacturerBs costconsists of a fi$ed overhead of .-<<%<<<J month plus.-<< per lamp for laor and materials"

a"/et up the total cost function

"/et up the demand function

c" 9ind the ;rea, Even points

d"9ind the volume that will ma$imie profite"5hat is the ma$imum profit@

f" 5hat is the volume of sales that will ma$imie your salesrevenue@



>" ;ra## P /tratton Company manufactures a specialiedmotor for chain saws" 0he company e$pects to manufactureand sell -<%<<< motors in year *<<(" It can manufacture an

additional (<%<<< motors without addin# new machineryand e&uipment" Its pro!ected total costs for the -<%<<< unitsare as follows:Direct Materials =(?<%<<<Direct +aor (<<%<<<Manufacturin# Overhead:

7ariale .ortion (<<%<<<9i$ed .ortion <%<<<

/ellin# and 8dministrative costs:7ariale .ortion (<%<<<9i$ed .ortion F<%<<<

0he sellin# price for the motor is =<"a" 5hat is the total manufacturin# cost per unit if -<<%<<<motors are produced@" 5hat is the total manufacturin# cost per unit if ><%<<<motors are produced@c" 5hat is the rea, even price on the motors@



5)(0.08)(1.

5.88

D(T!)d

d

5)(0.08)(1.

5.88

D

(TP)

d

d

5)(0.08)(1.

5.48

5)(0.08)(1.

5.48



,3 9C 1 Q=-?<%<<< A <"(6=-?<%<<<)6(*) 1

=-%F<%<<< per year 6(< decrease)

vc 1 Q=<"?< 2 <"( 6=<"?<) 1 =<"?? per unit ofsales 6(< increase)

0hus% no chan#e occurred in the ori#inalrea,even point"

′D ="3,80,000

"1 - "0.55 = "8,400,000 #$r %$&r



;-;5 ,a

,b .rofit6+oss) 1 0otal Revenue A 0otal Cost

6< Capacity) 1 <%<<< 6=<) A Q=*%<<<%<<< 2<%<<< 6=><)

1 =*%?<<%<<< per year

6(<< Capacity) 1 Q<%<<<6=<) 2 (<%<<<6=F<) A

Q=*%<<<%<<< 2 (<<%<<<6=><) 1 =*%<<%<<< per year

′D =C

# - ' =

"2,000,000

("0 - "40) / it = 40,000 it+ #$r %$&r



)REA@ – EVEN ANALSIS6 TO ALTERNATIVES

In&#str: is .a3e& 0it 3ertain sit#ations 0ere t0o or "ore a(ternati$es 3an be3onsi&ere&2 en te 3ost .or t0o a(ternati$es is a..e3te& b: a 3o""on &e3ision$ariab(e6 tere "a: e!ist a $a(#e o. te $ariab(e .or 0i3 te t0o a(ternati$es 0i((in3#r eB#a( 3ost2 Tis $a(#e is kno0n as te break-e$en 3ost2 )e(o0 tis 3ost6 one"eto& 0i(( be "ore e3ono"i3a(6 an& abo$e tis 3ost6 te oter 0i(( pro$e to bebetter e3ono"i3a((:2

0C8

0C; 0otal Cost

DB 7olume 6D) 0C8 1 0C;



E$amples42 T0o "an#.a3t#rin> "eto&s are bein>

3onsi&ere&2 Meto& A as a .i!e& 3ost o.

P6555 an& a $ariab(e 3ost o. P52 Meto& )

as a .i!e& 3ost o. P;55 an& a $ariab(e 3ost o.452 *or 0at pro&#3tion $o(#"e 0o#(& one

pre.er ,a Meto& A6 an& ,b Meto& )



;2 T0o 3o"panies are en>a>e& in te "an#.a3t#re o. sirts2Co"pan: A6 #sin> "ost(: an&0ork6 as a .i!e& 3ost "ont(:e!pense o. P76555 an& a $ariab(e 3ost o. P4255 per sirt2Co"pan: ) as been ab(e to "e3ani'e "ost o. its

operations6 an& it .in&s its .i!e& "ont(: e!penses areP<56555 an& te $ariab(e 3ost per sirt is P4;252

a2 Ho0 "an: sirts so#(& be "an#.a3t#re& b: ea3"ont so tat te tota( 3ost 0i(( be te sa"e .or te t0o3o"panies

b2 I. ea3 sirt se((s .or P1;255 to te retai(ers6&eter"ine te "ont(: >ross pro.it .or ea3 3o"pan:2

1. Break Even Analysis

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