[1]Set A 1. a) Engineer Engineering ing Economy Economy is the analysi analysis s and evaluati evaluation on of the factors factors that will will aect the economic success success of engineering projects to the end that a recommendation recommendation can e made which will insure the est use of capital. ) !nelastic demand occurs when a decrease in the selling price produces a less than proportionate increase in sales. c) An interest rate is the rate at which interest is paid y a orrower for the use of money that they orrow from a lender lender.. Speci"cally# the interest rate $!%m) is a percent of principal $!) paid at some rate $m). &or e'ample# a small company orrows capital from a an( to uy new assets for their usiness# and in return the lender receives interest at a predetermined interest rate for deferring the use of funds and instead lending it to the orrower. !nterest rates are normally e'pressed as a percentage percentage of of the principal principal for for a period of one year d) ompound interest is the sum of the capital plus the total amount of interest accumulated in previous periods. periods. *hus compound interest means means interest on top of interest. interest. A an( account# for e'ample# may have its interest compounded every year+ in this case# an account with ,1--- initial principal and -/ interest per year would have a alance of ,1-- at the end of the "rst year# ,100- at the end of the second year# and so on. e) iscount on a negotiale paper is the dierence dierence etween the present worth$ the amount received received for the paper in cash) and the worth of the paper at some time in the future $the face value of the paper or principal). iscount is interest paid in advance. E'ample is that when you orrowed ,2--- from a an( and agreed to pay the loan at the end of 3 months and the an( discounted the loan and gave you ,0--- in cash. ,resent ,resent worth 4 the worth of money or commodity at present time. 5oney may worth higher or lower depending on the economic staility of nation. *he amount of commodities or services changes due to the supply and demand.
Set 6
1. a) ,erfect ,erfect competition competition occurs occurs in a situation where a commodity commodity or service is supplied supplied y a numer of vendors and there is nothing to prevent additional additional vendors entering the mar(et. 5onopoly is the opposite of perfect competition. A perfect monopoly e'ists when a uni7ue product or service is availale from a single vendor and that vendor can prevent the entry of all others into the mar(et. 8ligopoly e'ists when there are so few suppliers of a product or service that action y one will almost inevitaly result in similar action y others. ) *he law of supply and demand may e stated as follows+ 9nder conditions of perfect competition the price at which a given product will e supplied and purchased is the price that will result in the supply and demand eing e7ual. c) 8rdinary annuity is one where the payments are made at the end of each period. d) the capitali:ed cost of any property is the sum of the "rst cost and the present worth of all costs of replacement# operation and maintenance for a long time or forever. e) Amorti:ation is any method of repaying a det# the principal and interest included# included# usually y a series of e7ual payments at e7ual interval of time. E'ample + ,ensioner
[] SE* A+ ,rolem ;. hat is the depreciation change during the 0 th year and the oo( value at the end of the 0 th year. a. 6y Sin(ing &und 5ethod# at ?/. @ = yea years rs l, l,1 1##---o, o,10 10-# -#---- n0 n0 . &ind ind 0 0 and and 0 d $ol)%&%A#i/#@) ,10#;02.2 0s$&%A#i/#n),B0#B01 0s$&%A#i/#n),B0#B01 $epreciation $epreciation charge charge during the 0th year) 0 o40 ,=2#;23 $oo( value at the end of the 0 th year) . 6y declining alance method (14$l%o)C$1%@) 14$1#---%10-#---)C1 14$1#---%10-#---)C1%=-.3B%=-.3B0$o$14()C$n41))($-.3B-)$10----)$14-. 0$o$14()C$n41))( $-.3B-)$10----)$14-.3B-)C041 3B-)C041 ,10023 0o$14()Cn10-#---$14-.3B-)C0;0;?3 0. 5r Domualdo ought a ond having a face value of ,1--- for ,3=-. *he ond rate was 10/ nominal and interest payments were made to him semiannually semiannually for a total of = years.
At the end of the seventh year# he sold the ond to a friend at a price that resulted a yield of 1B/ nominal on his investment. >hat was the selling price
,DA*!A@ *F!GH!GI *88@S+ 1. ,5! $,lus# 5inus# !nteresting) A crystalli:ation of the open4minded attitude used delierately. *he treatment of ideas # suggestions# and proposals. !nstead of just deciding whether or not you li(e an idea# this thin(ing operation leads you to "nd the good points $,,lus)# the ad points$55inus) and the interesting points $! !nteresting) aout an idea. *he natural reaction to an idea is to li(e or disli(e it# to approve or disapproveJ and then stop further evaluation. 9sing ,5! leads to a delierate operation of going eyond natural emotional reaction to an idea# to enlarge the view of a situation. ,rinciples+ A. ,5! is important ecause without it you may reject a valuale idea that seems ad at "rst sight. 6. >ithout a ,5! you are very unli(ely to see the disadvantages of an idea that you li(e very much. . ,5! can show that ideas are not just good or ad ut can also e interesting if they lead to other ideas. . >ithout ,5! major judgements are ased not on the value of the ideas itself ut on your emotions at that time. E. >ith a ,5! # you decide whether or not you li(e the idea after you have e'plored it instead of efore. ,ractice e'amples+ 1. All the seats should e ta(en out of uses . >indows should e made of transparent plastic instead of glass. . K S + onse7uence and Se7uel KS is a crystalli:ation of the process of loo(ing ahead to see the conse7uences of some action# plan# decision# rule# invention etc. KS goes eyond A&# what may happen after the decision has een made. !mmediate conse7uences as well as short4term $ 142 years)# medium4term $242 years) and long term conse7uences $over 2 years). *he intention is to enlarge the view eyond immediate eect of that action. An action may seem worthwhile if the immediate eect is good. 6ut if one ma(es a delierate eort to loo( at longer term conse7uences# the action may not e worthwhile at all and vice versa.
,rinciples+ A. 8ther people may e ale to see the conse7uences of your action more easily than you can yourself. 6. !t is important to (now whether the conse7uences are reversile or not. . *he immediate conse7uences may e good and long4term conse7uences ad or the other way around. . ithout a sense of purpose# all actions are either reactions to a situation or matters of hait or imitation. ,rinciples+ A. !f you (now e'actly what your ojectives are# it is easier to achieve them. 6. !n the same situation dierent people may have dierent ojectives. . 8n the way to a "nal ojective# there may e a chain of smaller ojectives# each one following from the previous one.
. 8jectives should e near enough# real enough and possile enough for a person to really try to reach them E. *here may e many ojectives# ut some are more important than others. ,ractice e'amples+ 1. AI8 of politician vs. usiness e'ecutive . AI8 of school principal ;. !n respect to food# AI8 of homema(er# coo( in restaurant# food manufacturer# farmer# government.
[] SE* A + e"nition 1.E,DE!A*!8G 4is the decrease in the value of physical property with the passage of time. a) ,urpose of epreciation 1. *o provide for the recovery of capital which has een invested in physical property. . *o enale the cost of depreciation to e charged to the cost of producing products or services that result from the use of the property. ) *ypes of epreciation 1. Gormal epreciation a. physical L is due to the lessening of the physical aility of a property to produce results. !tMs common causes are wear and deterioration. . functional L is due to the lessening in the demand for the function which the property was designed to render. !tMs common causes are inade7uacy# changes in styles# population center shift# saturation of mar(ets# or more eNcient machines are produced. . epreciation due to changes in price levels L is almost impossile to predict and therefore is not considered in economy studies ;. epletion L refers to the decrease in the value of a property due to t he gradual e'traction of its contents. c) De7uirements of a depreciation method 1. !t should e simple. . !t should recover capital ;. *he oo( value will e reasonaly close to the mar(et value at any time 0. *he method should e accepted y the 6ureau of !nternal Devenue. d) *he Straight line method 4*his method assumes that the loss in value is directly proportional to the age of the property. d $o L l)%@ n n$o4l)%@ n o4n e. Sin(ing fund 4*his method assumes that a sin(ing fund is estalished in which funds will accumulate for replacement. *he total depreciation that has ta(en place up to any given time is assumed to e e7ual to the accumulated amount in the sin(ing fund at that time. d $o L l)%$&%A# i/#@) n d$&%A# i/# n)
n o4n f. eclining alance !n this method# sometimes called the constant percentage method or the 5atheson &ormula# it is assumed that the annual cost of depreciation is a "'ed percentage of the salvage value at the eginning of the year. *he ratio of the depreciation in any year to the oo( value at the eginning of that year is constant throughout the life of the property and is designated y ( the rate of depreciation. *his method does not apply# if the salvage value is :ero# ecause ( will e e7ual to one and d1 will e e7ual to o. dndepreciation during the nth year dn$o$14()Cn41)( n o$14()Cn o $l%o)Cn%@ l o$14()C@ ( 14$n%o)C1%n 14$l%o)C@ . A,!*A@ a) E7uity apital or ownership funds are those supplied and used y the owners of an enterprise in the e'pectation that a pro"t will e earned. ) 6orrowed funds or capital are those supplied y others on which a "'ed rate of interest must e paid and the det must e repaid at a speci"ed time. c. 6ond &inancing A ond is a certi"cate of indetedness of a corporation usually for a period not less than ten years and guaranteed y a mortgage on a certain assets of the corporation or its susidiaries. 6onds are issued when there is need for more capital such as for e'pansion of the plant or the services rendered y the corporation. *he face or par value of a ond is the amount stated on the ond. >hen the face value has een repaid# the ond is said to have een retired or redeemed. *he ond rate is the interest rate 7uoted on the ond. d. *he orporation L is a distinct legal entity# separate from the individuals who own it# and which can engage in almost any type of usiness transaction in which a real person could occupy himself or herself. Advantages+ 1. !t enjoys perpetual life without regard to any change in the person of its owners# the stoc(holders. . *he stoc(holders of the corporation are not liale for the dets of the corporation. ;. !t is relatively easier to otain large amounts of money for e'pansion# due to its perpetual life. 0. *he ownership in the corporation is readily transferred. 2. Authority is easily delegated y the hiring of managers. isadvantages 1. *he activities of a corporation is limited to those stated in its charter. . !t is relatively complicated in formation and administration. ;. *here is a greater degree of governmental control as compared to other types of usiness organi:ations. [] SE* 6 + e"nition 1.
a) 5ar(et Oalue of a property4 is the amount which a willing uyer will pay to a willing seller for the property where each has e7ual advantage and is under no compulsion to uy or sell. ) &air value is the value which is usually determined y a disinterested third party in order to estalish a price that is fair to oth seller and uyer. c) oo( value sometimes called depreciated oo( value is the worth of a property as shown in the accounting records of an enterprise. d)Salvage value or resale value is the price that can e otained from the sale of the property after it has een used. e. Scrap Oalue is the amount the property would sell for if disposed o as jun(. . a) !ndividual ownership or sole proprietorship is the simplest form of usiness organi:ation# wherein person uses his or her own capital to estalish a usiness and is the sole owner. Advantages of the individual ownership+ 1. !t is easy to organi:e . *he owner has full control of the enterprise. ;. *he owner is entitled to whatever ene"ts and pro"ts that accrue from the usiness. 0. !t is easy to dissolve. isadvantages of the !ndividual 8wnership 1. *he amount of e7uity capital which can e accumulated is limited. . *he organi:ation ceases upon the death of the owner ;. !t is diNcult to otain orrowed capital# owing to the uncertainty of the life of the organi:ation. 0. *he liaility of the owner for his dets is unlimited. ,artnership L is an association of two or more persons for the purpose of engaging in a usiness for pro"t. Advantages+ 1. 5ore capital may e otained y the partners pooling their resources together. . !t is ound y few legal re7uirements as to its accounts# procedures# ta' forms and other items of operation. ;. issolution of the partnership may ta(e place at any time y mere agreement of the partners. 0. !t provides an easy method wherey two or more persons of diering talents may enter into usiness# each carrying those urdens that he can est handle. isadvantages+ 1. *he amount of capital that can e accumulated is de"nitely limited. . *he life of the partnership is determined y the life of the individual partners. >hen any partner dies# the partnership automatically ends. ;. *here are many serious disagreement among the individual partners. 0. Each partner is liale for the dets of t he partnership. ) Stoc( ownership is the practice of companies in giving their sta memers shares !n their company as part of the salary. !t also means owning a stoc( in a company investment. c) ommon stoc( represents ordinary ownership without special guarantees of return. ommon stoc(holders have certain legal rights# among which are the following+ 1. Oote at stoc(holdersM meeting.
. Elect directors and delegates to them power to conduct the aairs of the usiness. ;. Sell or dissolve the corporation 0. 5a(e and amend the y laws of the corporation 2. Suject to government approval# amend or change the character or capital structure. B. ,articipate in the pro"ts. =. !nspect the oo(s of the corporation. d) ,referred Stoc( ,referred stoc(holders are guaranteed a de"nite dividend on their stoc(s. !n case the corporation is dissolved# the assets must e used to satisfy the claims of the preferred stoc(holders efore those of the holders of the common stoc(. ,referred stoc(holders usually have the right to vote in meetings ut not always. e. 6ond &inancing A ond is a certi"cate of indetedness of a corporation usually for a period not less than ten years and guaranteed y a mortgage on a certain assets of the corporation or its susidiaries. 6onds are issued when there is need for more capital such as for e'pansion of the plant or the services rendered y the corporation. *he face or par value of a ond is the amount stated on the ond. >hen the face value has een repaid# the ond is said to have een retired or redeemed. *he ond rate is the interest rate 7uoted on the ond. f) eclining alance !n this method# sometimes called the constant percentage method or the 5atheson &ormula# it is assumed that the annual cost of depreciation is a "'ed percentage of the salvage value at the eginning of the year. *he ratio of the depreciation in any year to the oo( value at the eginning of that year is constant throughout the life of the property and is designated y ( the rate of depreciation. *his method does not apply# if the salvage value is :ero# ecause ( will e e7ual to one and d1 will e e7ual to o. dndepreciation during the nth year dn$o$14()Cn41)( n o$14()Cn o $l%o)Cn%@ l o$14()C@ ( 14$n%o)C1%n 14$l%o)C@ g) sum of the yearMs digits $S<) @et dn depreciation charge during the nth year dn $depreciation factor)$total depreciation) dn $reverse digit$o4l)%$Sum of digits) &or e'ample# for a property whose life is 2 years.
[]SE* 6+ ,rolem ;. o ,1--#---
@ 2 years l ,1-#--n; a) 6y doule declining method dn $%@)$o)$14%@) Cn41 $%2)$1--#---)$14%2)C ,10#0-n o$14%@)Cn 1--#---$14%2)C; ,1#B-) 6y Sum of the yearMs digits $S<) o L l 3-#--
2
0. A ond issue of ,--#--- in 1- year onds# in ,1#--- units# paying 1B/ nominal interest in semiannual payments# must e retired y the use of a sin(ing fund that earns 1/ compounded semiannually. >hat is the total semiannual e'pense Solution+ & --#--- r 1B/% ?/ i1/% Bn1-$)A $,--#---)%$&%A#B/#-),--#---%;B.=?2B,2#0;= !&r$,--#---)$-.-?),1B#-- *otal Semiannual e'pense ,2#0;= Q ,1B#--- ,1#0;= ,DA*!A@ *F!GH!GI *88@S 1. A&$onsider All &actors) Delated to action# decisions# planning# judgment# and conclusions. elierate operation directing attention from the ovious factors to loo(ing around for all the factors. Also factors aecting oneself# others and society in general. A& diers from ,5! in that ,5! is a reaction to an idea whereas A& is an e'ploration of a situation efore coming up with an idea. ,rinciples+ A. A& is useful efore choosing# deciding or planning. 6. !t is etter to consider all the factors "rst and then pic( out the ones that matter most. .
E. !f you do a A& on someone elseMs thin(ing you may e ale to tell the person what has een left out. ,ractice e'amples+ 1. A young couple is undecided whether to get married at once or wait. >hat factors should they e considering . *he sugar industry is demanding protection from foreign imports which are coming into the country at a lower price and ta(ing over the mar(et# what factors should the government consider in this matter. . AI84 Aims# Ioals# 8jectives &ocus on ,urpose + Aim is the general direction. Ioal is an ultimate destination. 8jective is a recogni:ale point of achievement along the way. >ithout a sense of purpose# all actions are either reactions to a situation or matters of hait or imitation. ,rinciples+ A. !f you (now e'actly what your ojectives are# it is easier to achieve them. 6. !n the same situation dierent people may have dierent ojectives. . 8n the way to a "nal ojective# there may e a chain of smaller ojectives# each one following from the previous one. . 8jectives should e near enough# real enough and possile enough for a person to really try to reach them E. *here may e many ojectives# ut some are more important than others. ,ractice e'amples+ 1. AI8 of politician vs. usiness e'ecutive . AI8 of school principal ;. !n respect to food# AI8 of homema(er# coo( in restaurant# food manufacturer# farmer# government.
;. E!S!8GS 6ring together in particular &!, and A, and also the other tools in a more general way. A&# AI8# &!,# KS# A, and also the ,5!. *his helps to increase (nowledge of the situation so that the decision either ma(es itself# or is at least easier to ma(e ecause the alternatives are more numerous and the conse7uences etter de"ned. *he "nal considerations are the personal values of the decision ma(er. ,rinciples+ A.
E. !n ma(ing a decision# you should consider all factors$A&)# loo( at the conse7uences $KS)# e very clear aout ojectives $AI-)# and assess the priorities$&!,). And "ll all the possile alternatives$A,). >hen you have done this# a decision may e much easier. ,ractice E'amples+ 1. Fow do people decide to spend their money . A young woman has two oys# one of them is 7uite and hardwor(ing. *he other is the etter loo(ing and more fun ut rather unreliale. 6oth want to marry her. She has to decide. [;] Set A46+ SET A a
SCIENCE, a term derived from @atin word Rscientia# is a systemati:ed ody of (nowledge ased on facts and events of life arranged according to order. !t is a system of gaining (nowledge ased on a scienti"c method which has the following steps+ uniased oservations# formulation of hypothesis# gathering of data# systematic e'perimentation# analysis of data and conclusion. !t aims to give etter understanding of current phenomena and a etter aility to infer future events. !t e'presses general truths and principles to e'plain how things wor(.
ENGINEERING is an applied science. !t aims to solve prolems to improve the status 7uo. !t can also e de"ned as the optimal conversion of the natural resources to products that will ma(e for optimum and safe utili:ations of humans. !t solves prolems not just y e'plaining ut y actually designing and manufacturing products# engines and devices which will last for a long time and under a speci"cation of safety.
c
PRESENT ECONOMY PROBLEMS There are many cases in engineering economy stuies !here interest is not a "actor, these stuies are "re#uent$y ca$$e %resent economy %ro&$ems' Such stuies usua$$y in(o$(e the se$ection &et!een a$ternati(e esigns, materia$s, or methos'
RATE O) RET*RN +ROR MET-O. The rate o" return on the ca%ita$ in(este is gi(en &y the "ormu$a,
Rateof return
=
net annual profit capital invested
Rate o" return is a measure o" e/ecti(eness o" an in(estment o" ca%ita$' It is a 0nancia$ e1ciency' 2hen this metho is use, it is necessary to ecie !hether the com%ute rate o" return is su1cient to 3usti"y the in(estment' The a(antage o" this metho is that it is easi$y unerstoo &y management an in(estors' The a%%$ications o" the rate o" return metho is contro$$e &y the "o$$o!ing conitions' A sing$e in(estment o" ca%ita$ at the &eginning o" the 0rst
year o" the %ro3ect $i"e an ientica$ re(enue an cost ata "or each year' The ca%ita$ in(este is the tota$ amount o" ca%ita$ in(estment re#uire to 0nance the %ro3ect, !hether e#uity or &orro!e' e
PRESENT 2ORT- +P2 MET-O.
This %attern "or economy stuies is &ase on the conce%t o" %resent !orth' I" the %resent !orth' I" the %resent !orth o" the net cash 4o!s is e#ua$ to, or greater than, 5ero, the %ro3ect is 3usti0e economica$$y' The %resent !orth metho is 4e6i&$e an can &e use "or any ty%e o" economy stuy' It is use e6tensi(e$y in ma7ing economy stuies in the %u&$ic !or7s 0e$, !here $ong8$i(e structures are in(o$(e' SET B f
SCIENCE, a term derived from @atin word Rscientia# is a systemati:ed ody of (nowledge ased on facts and events of life arranged according to order. !t is a system of gaining (nowledge ased on a scienti"c method which has the following steps+ uniased oservations# formulation of hypothesis# gathering of data# systematic e'perimentation# analysis of data and conclusion. !t aims to give etter understanding of current phenomena and a etter aility to infer future events. !t e'presses general truths and principles to e'plain how things wor(.
g
ENGINEERING is an applied science. !t aims to solve prolems to improve the status 7uo. !t can also e de"ned as the optimal conversion of the natural resources to products that will ma(e for optimum and safe utili:ations of humans. !t solves prolems not just y e'plaining ut y actually designing and manufacturing products# engines and devices which will last for a long time and under a speci"cation of safety.
h
ANN*AL 2ORT-. !n this method# interest on the original investment $sometimes called minimum re7uired pro"t) is included as the cost. !f the e'cess of annual cash inTows over annual cash out Tows is not less than :ero the proposed investment is justi"ed L is valid. *his method is covered y the same limitations as the rate of return pattern a single initial investment of capital and uniform revenue and cost throughout the life of investment.
i
)*T*RE 2ORT-' *he future worth method for economy studies is e'actly comparale to the present worth method e'cept that all cash inTows and outTows are compounded forward to a reference point in time called the future. !f the future worth of the net cash Tows is e7ual to# or greater than# :ero# the project is justi"ed economically.
j
PAYBAC9 PERIO.' *he payac( period is commonly de"ned as the length of time re7uired to recover the "rst cost of an investment from the net cash Tow produced y that investment for an interest rate of :ero !nvestment L salvage value ,ayout period $years) Get annual cash Tow
h.) E8G85!S is the social science that deals with the production# distriution# and consumption of goods and services and with the theory and management of economies or economic systems. !t is also the theories# principles# and models that deal with how the mar(et process wor(s. !t attempts to e'plain how wealth is created and distriuted in communities# how people allocate resources that are scarce and have many alternative uses# and other such matters that arise in dealing with human wants and their satisfaction.
[0] SE* A4e"nition 1. a)apitali:ed 5ethod *he capitali:ed cost method is a variation of the present worth cost pattern. *his method is used for alternatives having long lives. *o use the method# determine the capitali:ed cost of all the alternatives and choose that one with the least capitali:ed cost. ) Annual cost method *o apply this method# the annual cost of the alternatives including interest on investment is determined. *he alternative with the least annual cost is chosen. *his pattern# li(e the rate of return on additional investment pattern# applies only to alternatives which has a uniform cost data for each year and a single investment of capital at the eginning of the "rst year of the project life. c) E7uivalent 9niform Annual ost 5ethod !n this method# all cash Tows$irregular or uniform) must e converted to an e7uivalent uniform annual cost# that is# a year4end amount which is the same each year. *he alternative with the least e7uivalent uniform annual cost is preferred. >hen the E9A method is used# the e7uivalent uniform annual cost of the alternatives must e calculated for one life cycle only. *his method is Te'ile and can e used for any type of alternative selection prolems. *he method is a modi"cation of the annual cost pattern. d. Oariale cost Oariale costs are those costs which vary with output or any change in the activities of an enterprise. 9nli(e "'ed costs# which remain constant regardless of output# variale costs are a direct function of production volume# rising whenever production e'pands and falling whenever it contracts. E'amples of common variale costs include raw materials# pac(aging# and laor directly involved in a companyUs manufacturing process. &or e'ample# a "rm pays for raw materials. >hen activity is decreased# less raw material is used# and so the spending for raw materials falls. >hen activity is increased# more raw material is used and spending therefore rises. Gote that the changes in e'penses happen with little or no need for managerial intervention. *hese costs are variale costs. e) 5arginal cost 5arginal cost is the additional cost of producing one more unit of a product. *hat is# it is the cost of producing one more unit of a good. !f producing additional vehicles re7uires# for e'ample# uilding a new factory# the marginal cost of those extra vehicles includes the cost of the new factory.
f) !ncrement cost !ncrement costs are those that arise as the result of a change in operations or policy. A very simple e'ample would e a factory ma(ing widgets where it ta(es one employee an hour to ma(e a widget. As a simple "gure# the incremental cost of a widget would e the wages for the employee for an hour plus the cost of the materials needed to produce a widget. g) Sun( ost Sun( ost represents money which has een spent or capital which has een invested and which cannot e recovered due to certain reasons. &or e'ample# if a "rm sin(s V1 million on an enterprise software installation# that cost is Wsun(W ecause it was a one4 time thing and cannot e recovered once e'pended. SE* A4,rolem A company is considering two types of e7uipment for its manufacturing plant. ,ertinent data are as follows+ *ype A *ype 6 &irst cost ,--#--,;--#--Annual 8perating cost ,;#--0#--Annual laor cost ,2-#--;#--!nsurance and property ta'es ;/ ;/ -.-;$&irst cost) -.-;$&irst ost) ,B#--,3#--,ayroll ta'es 0/ 0/ -.-0$Annual laor cost) ,#--,1#?Estimated life 1- yrs 1- yrs !f the minimum re7uired rate of return is 12/# which e7uipment should e selected 1 a.) 6y D8D on additional investment method *ype A Annual osts+ epreciation &irst ost%$&%A#12/#1-) --#---%-.;-;= ,3#?28peration ,;#--@aor ,2-#--,ayroll ta'es -.-0$Annual laor cost) 2----$-.-0) #-- *a'es K !nsurance -.-;$&irst cost) $,--#---)$-.-;) ,B#-- *otal Annual ost ,33#?2 *ype 6 Annual osts+ epreciation &irst ost%$&%A#12/#1-) ;--#---%-.;-;= ,10#==B 8peration ,0#--@aor ,;#--,ayroll ta'es -.-0$Annual laor cost) ;---$-.-0) ,1#?-
*a'es K !nsurance -.-;$&irst cost) $,;--#---)$-.-;) ,3#-- *otal Annual ost ,?1# -2B Annual Savings ,33#?2- L ,?1#-2B ,1?#=30 Additional !nvestment ,;--#--- L ,--#--- ,1--#--Date of Deturn on Additional !nvestment ,1?#=30$1--)%,1--#--- 1?.=3 X 12/ *ype 6 should e selected.
.) ,resent >orth ost 5ethod *ype A Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,3-#--,>a &irst cost Q Annual cost$,%A# 12/#1-) ,--#--- Q $3-#---)$2.-1??) ,B21#B3
*ype 6 Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,BB#?,> &irst ost Q Annual cost $,%A# 12/# 1-) ;--#--- Q $BB#?-)$2.-1??) ,B;#B0B Since ,> Y ,>a for the same period of time# type 6 should e selected. . Iiven+ 11#--- units%year ,1;%unit E7uipment cost+, 1-#--8ther e7uipment+ ,#--@aor cost+ ,2%unit 5aterial cost+ ,0%unit *a'es and insurance + ;/ 8verhead cost+ -/ 8perating and maintenance+ ,3#--apital cost+ 1B/ Solution+ Annual revenue 11#--- units%yr $,1;%unit)
Annual revenue ,10;#--Annual cost+ 8ther e7uipment+ ,#--@aor cost+ ,2%unit$11#---units%yr) ,22#--5aterial cost+ ,0%unit$11#---units%yr) ,00#-- *a'es and insurance + -.-;$e7uipment cost) -.-;$1-#---),;#B-8verhead cost+ -.$laor cost) -.$22#---) ,11#--8perating and maintenance+ ,3#--apital cost+ -.1B$e7uipment cost)-.1B$1-#---),13-epreciation e7uipment cost% $&%A# 1B/#2) ,1=#2-Annual cost ,1B1#;-Annual Devenue L Annual ost 4,1?#;- *herefore# this opportunity should not e acceptedZ [0] SE* 6+ e"nition a. Date of Deturn on additional investment method *he formula for the rate of return on additional investment is# Date of return on additional investment annual net savings%additional investment !f the rate of return on additional investment is satisfactory# then# the alternative re7uiring a igger investment is more economical and should e chosen. . Annual ost 5ethod *o apply this method# determine the annual cost of each alternative including the interest on capital%investment. hoose the alternative which has a least annual cost. *his pattern# li(e the rate of return on additional investment pattern is applicale only to alternatives which has a uniform cost data for each year and a single investment of capital at the eginning of the "rst year of the project life. c. apitali:ed 5ethod *he capitali:ed cost method is a variation of the present worth cost pattern. *his method is used for alternatives having long lives. *o use the method# determine the capitali:ed cost of all the alternatives and choose that one with the least capitali:ed cost. d. ,ayac($,ayout) ,eriod 5ethod *o use this method# the payac( period of each alternative is computed. *he alternative with the shortest payac( period is adopted. *his method is seldom used. e. &i'ed costs &i'ed costs are those costs which remain constant# whether or not a given change in operations or policy is adopted. 9nli(e variale costs# "'ed costs are not :ero when production is :ero. Iood e'amples of "'ed costs would e insurance# rent# periodic load payments# interest paid# "'ed permanent employee salaries. *otal "'ed costs remain unchanged as volume increases# while "'ed costs per unit decline. &or e'ample# if a icycle
usiness had total "'ed costs of V1#--- and only produced one i(e# then the full V1#--- in "'ed costs must e applied to that i(e. 8n the other hand# if the same usiness produced 1- i(es# then the "'ed costs per unit decline to V1--. f. Oariale osts Oariale costs are those costs which vary with output or any change in the activities of an enterprise. 9nli(e "'ed costs# which remain constant regardless of output# variale costs are a direct function of production volume# rising whenever production e'pands and falling whenever it contracts. E'amples of common variale costs include raw materials# pac(aging# and laor directly involved in a companyUs manufacturing process. &or e'ample# a "rm pays for raw materials. >hen activity is decreased# less raw material is used# and so the spending for raw materials falls. >hen activity is increased# more raw material is used and spending therefore rises. Gote that the changes in e'penses happen with little or no need for managerial intervention. *hese costs are variale costs. g. 5arginal costs 5arginal cost is the additional cost of producing one more unit of a product. *hat is# it is the cost of producing one more unit of a good. !f producing additional vehicles re7uires# for e'ample# uilding a new factory# the marginal cost of those extra vehicles includes the cost of the new factory.
[0 ]SE* 64,rolem A company is considering two types of e7uipment for its manufacturing plant. ,ertinent data are as follows+ *ype A *ype 6 &irst cost ,--#--,;--#--Annual 8perating cost ,;#--0#--Annual laor cost ,2-#--;#--!nsurance and property ta'es ;/ ;/ -.-;$&irst cost) -.-;$&irst ost) ,B#--,3#--,ayroll ta'es 0/ 0/ -.-0$Annual laor cost) ,#--,1#?Estimated life 1- yrs 1- yrs !f the minimum re7uired rate of return is 12/# which e7uipment should e selected 1. a. ) 6y e7uivalent 9niform Annual ost 5ethod *ype A Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,3-#--E9Aa &irst cost $A%,#12/#1-) Q Annual cost $--#---)$-.133;) Q 3-#--- ,13#?B-
*ype 6 Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,BB#?E9A &irst cost $A%,#12/#1-) Q Annual cost ,;--#---$-.133;) Q BB#?- ,1B#-=Since E9A Y E9Aa# type 6 is more economical. 1..) ,resent >orth ost 5ethod *ype A Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,3-#--,>a &irst cost Q Annual cost$,%A# 12/#1-) ,--#--- Q $3-#---)$2.-1??) ,B21#B3
*ype 6 Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q ,ayroll ta'esQ !nsurance and property ta'es Annual osts$e'cluding depreciation) Annual operating cost Q Annual laor cost Q -.-0$Annual laor cost) Q -.-;$&irst cost) ,BB#?,> &irst ost Q Annual cost $,%A# 12/# 1-) ;--#--- Q $BB#?-)$2.-1??) ,B;#B0B Since ,> Y ,>a for the same period of time# type 6 should e selected. . Iiven+ 11#--- units%year ,1;%unit E7uipment cost+, 1-#--8ther e7uipment+ ,#--@aor cost+ ,2%unit 5aterial cost+ ,0%unit *a'es and insurance + ;/ 8verhead cost+ -/ 8perating and maintenance+ ,3#--apital cost+ 1B/ Solution+ Annual revenue 11#--- units%yr $,1;%unit) Annual revenue ,10;#--Annual cost+
8ther e7uipment+ ,#--@aor cost+ ,2%unit$11#---units%yr) ,22#--5aterial cost+ ,0%unit$11#---units%yr) ,00#-- *a'es and insurance + -.-;$e7uipment cost) -.-;$1-#---),;#B-8verhead cost+ -.$laor cost) -.$22#---) ,11#--8perating and maintenance+ ,3#--apital cost+ -.1B$e7uipment cost)-.1B$1-#---),13-epreciation e7uipment cost% $&%A# 1B/#2) ,1=#2-Annual cost ,1B1#;-Annual Devenue L Annual ost 4,1?#;- *herefore# this opportunity should not e acceptedZ [2] SE* A
. *wo electric motors are eing considered to power an industrial hoist. Each is capale of providing 1-- hp. ,ertinent data for each motor are as follows+ 5otor A !nvestment ,2#--Electrical eNciency ?0/ 5aintenance per year 0-@ife# years 15otor 6 !nvestment ,;#--Electrical eNciency ??/ 5aintenance per year B-@ife# years 15oney is worth -/. !f the e'pected usage of the hoist is =-- hours per year# what would e the cost of electrical power have to e efore 5otor A is favored over motor 6 Solution+ @et ' cost of electrical power for oth motors to e e7ually economical 5otor A Annual osts+ epreciation $!nvestment)%$&%A# -/# 1-) ,3B; ,ower $1--)$-.=0B)$=--)$')%-.?0 B#1B=' maintenance 0-!nterest on capital !nvestment$-.-) 2#-- *otal annual cost ,B#;B; Q B#1B=' 5otor 6
Annual osts+ epreciation $!nvestment)%$&%A# -/# 1-) ,,1#; ,ower $1--)$-.=0B)$=--)$')%-.?? 2B#;01' maintenance B-!nterest on capital !nvestment$-.-) B#0- *otal annual cost ,?; Q 23;01' ,B;B; Q ,B1B=' ?; Q 23;01' ,-.BB10 per (wh 5otor A will e more economical for electrical power cost less than ,-.BB10 per (wh. ;. 5otor reuild+ !nvestment 2-#--5aintenance 12#--@ife 2 years Gew motor !nvestment 12-#--5aintenance 1#--@ife 1Deuild epreciation $2-#---)%$&%A# 1B/#2) ,=#=5aintenance ,12#--!nterest on investment $2-#---)$-.1B) ,?#-- *otal + ;-#=Gew motor+ epreciation $12-#---)%$&%A# 1B/#1-) ,=#-;2 5aintenance ,1#--!nterest on !nvestment $12-#---)$-.1B) ,0#-- *otal+ ,0;#-;2 *hus# reuild the old motor. 0. &irst cost -#---#--!nterest B / Annual operation and maintenance cost ,11#---#--Annual income%ene"t B#---#--@ife B- years a) 6y E9A 5ethod
Annual ene"t B#---#--E9A -#---#---$A%,#B/#B-) Q 11#---#--E9A 0#B1?#--6% $ene"t)%$E9A) 1.-B X 1 *herefore# this is o(Z .) 6y ,resent >orth 5ethod ,>ene"t B#---#--- $,%A# B/# B-) ,>ene"t 0- '1-C2 ,>cost -#---#--- Q 11#---#---$,%A# B/#B-) ,>cost ;#3=?'1-C2 6% $,>ene"t)%$,>cost) 1.-B X 1.therefore # this is o(Z
[2] SE* 6
1. a) Dental or lease possiilities 4!t is possile to rent identical or comparale asset or property# thus freeing capital for other and more pro"tale use. 6) ,hysical impairment *he e'isting asset is completely or partially worn out and will no longer function satisfactorily without e'tensive repairs. c. !nade7uacy *he e'isting asset does not have suNcient capacity to meet the present demands that is placed on it. d. 6rea(4even analysis !n engineering economy# many situations are encountered where the cost of two or more alternatives may e aected y a common variale. 6rea(4even point is the value of the variale for which the costs for the alternatives will e e7ual. 1 f1$') and f$') >here+ 1 certain speci"ed total cost applicale to alternative 1 . certain speci"ed total cost applicale to alternative . a common independent variale aecting alternative 1 and .
*he rea( even point is where 1 and are e7ual # f1$')f$') which may e solved for '# the rea( even point. 6rea(4even chart is a graphical representation of rea(4even analysis. *he rea( L even point is the 7uantity of production at which the income is e7ual to total cost. !t is the intersection of the income line and the total cost line on the rea( even chart. >hen two alternatives are to e compared# the rea(4even point is the intersection of the total cost line for each alternative on the rea( even chart. [2] Set 6+
. 8ld 5otor $Deuild) &irst cost B-#--@ife B years Annual operation and maintenance 10#--Gew 5otor &irst cost 1=-#--@ife 11 years Annual operation and maintenance 11#--5oney worth 12/ Solution+ 6y D8D on additional investment 8ld 5otor epreciation $&irst cost)%$&%A#12/# B) ,B#?20 Annual operation and maintenance 10#-- *otal + ,-#?20 Gew 5otor epreciation $&irst cost)%$&%A#12/#11) B#3? Annual operation and maintenance 11#-- *otal+ ,1=#3? Annual Savings 8ld L Gew -#?20 L 1=3? #?= Additional annual investment 1=-#--- L B-#--- 11-#--D8D on additional investment $#?=%11-#---) ' 1-- .B1/ Y 12/ *herefore# the old motor should e reuilt.
;. A local factory assemling calculators produces 0-- units per month and sells them at ,1#?-- each. ividends are ?/ on the ?#--- shares with a par value of ,2- each. *he "'ed operating cost per month is ,2#---. 8ther costs are ,1#--per unit. etermine the rea(4even point. !f only -- units were produced per month# determine the pro"t or loss. Solution + !ncome + 1.?-- per unit &i'ed costs ,2#--- per month Oariale costs ,1#--- per unit ividend ?/ per year ,ar value 2- each shares ?--@et ' numer of calculators per month to rea( even !ncome 1#?--' *otal cost ,2#--- Q ,1#---' *o rea( even# !ncome *otal cost 1#?--' 2#--- Q 1#---' ;1.2 or ; units ividend $par value)$dividend percent)$share)%1months $2-)$-.-?)$?---)%1 ,1;#;;; per month &or -- units+ !ncome *otal cost Q ividend Q,ro"t %loss ,1#?--$--) ,2#--- Q $1#---)$--) Q 1;#;;; Q ,ro"t%loss ,ro"t ,11#BB= per month 0. &irst cost -#---#--!nterest B / Annual operation and maintenance cost ,11#---#--Annual income%ene"t B#---#--@ife B- years
a) 6y E9A 5ethod Annual ene"t B#---#--E9A -#---#---$A%,#B/#B-) Q 11#---#--E9A 0#B1?#--6% $ene"t)%$E9A) 1.-B X 1 *herefore# this is o(Z .) 6y ,resent >orth 5ethod ,>ene"t B#---#--- $,%A# B/# B-) ,>ene"t 0- '1-C2 ,>cost -#---#--- Q 11#---#---$,%A# B/#B-) ,>cost ;#3=?'1-C2 6% $,>ene"t)%$,>cost) 1.-B X 1.therefore # this is o(Z
