Engineering Economics:

Transcription

1 Egieerig Ecoomics: Date:2065/4/15 Recommeded Books: EP Degrama, WG Sulliva ad JA Bostadel NN Borish ad S Kapla Ecoomic aalysis for Egieerig ad Maagerial Decisio makig Gerald J Thuese, WJ Fabrycky Mauals (TU pulchok ad kirah Thapa) Because of resource costats, egieerig must be closely associated with ecoomy It is essetial that egieerig proposals be evaluated i terms of worth ad cost before they are udertake The Bi-Evirometal Natural of Egieerig: Physical eviromet Egieerig Proposal Productio Costructio Ecoomic eviromet Wa t Satisfactio Itroductio: Egieerig: Egieerig is ot a sciece but a applicatio of sciece It is a art composed of skill ad igeuity i adoptig kowledge to the use of humiity Egieerig activities of aalysis ad desig are ot a ed i themselves They are meas for satisfyig huma wats Moder Civilizatio depeds to a large degree upo egieerig Most products ad services used to facilitate work, commuicatio, trasportatio ad atioal defece ad to furish susteace, shelter ad health are directly or idirectly a result of egieerig activities Egieerig is cocer with two itercoected eviromets the physical ad ecoomic Egieers are cofroted with two eviromet, the physical ad ecoomic Their success i alterig the physical eviromet to produce products ad services depeds upo the kowledge of physical laws However, the worth of this products ad services lies i their utility measure i ecoomic term The usual fuctio of egieerig is to maipulate the elemets of oe eviromet, the physical, to create value i secod eviromet, the ecoomy Physical ad Ecoomical Efficecies: Physical effciecies: Output/ Iput = will always he less tha uity or 100% Ecoomys: Ecoomy, the attaimet of a objective at low cost i terms of resource, iput has always bee associated with egieerig Ecoomics deals with the behavior of people idividually ad collectively, particularly as their behavior relates to the satisfactio of their wats 1 Ecoomic efficecy: worth/ cost = ecoomic efficeey ca be exceeded 100% I egieerig activities, ecoomic efficiecies must take precedece over physical efficiecy Thus is because the fuctio

2 of egieerig is to create utility i the ecoomic eviromet by alterig elemets of the physical eviromet Product life cycle: N E E D Coceptua Prelimiary Desig Developmet Detail Desig Productio/ Costructio Product use/ Costructio Desig Acquisitio phase Utilizatio phase I geeral egieers have focus maily o the acquisitio phase of the product life cycle ad have bee evolved i early desig ad aalysis activities aloe Product performace has bee mai objective verses the developmet of a overall system with ecoomic factors i mid However, experiece i recet decades idicates that a properly fuctioig product which is competitive i the market place caot be achieved through efforts applied largely after the product comes ito beig Egieerig Ecoomy: For a egieerig desig to be successful, it must be techically soud ad produce veefits The field of egieerig ecoomy is cocered with the systematic evaluatio of the beefits ad costs of projects ivolvig egieerig desig ad aalysis Thus, egieerig ecoomy requires the applicatio of egieerig desig ad aalysis Priciples to provide goods ad services that satisfy the cosumer at a affordable cost Egieerig ecoomy ivolves the systematic evaluatio of the ecoomic merits of proposed solutios to egieerig problems To be ecoomically acceptable 2 (affordable) solutios to egieerig problems must demostrate a positive balace of log term beefits over log term costs, ad thy must also Promote the well-beig ad survival of the orgaizatio Embody creative ad iovative techology Permit idetificatio ad scrutiy of the estimated outcomes Traslate profitability Priciples of Egieerig Ecoomy: Oce a problem/eed has bee clearly defied, the foudatios of the disciplie ca be discussed i terms of seve priciples 1 Develop the alteratives 2 Focus o the differeces 3 Use of a cosistet viewpoit 4 Use of a commo uit of measure 5 Cosider all relevat criteria 6 Make ucertaity explicit 7 Revisit your decisios Some busiess ad Accoutig Termiology: Value: Value is measure of the worth that a perso ascribes to a good or a service Thus, the value of a object is iheret ot i the object but i regard that a perso has for it Value should ot be cofused with the cost or the price of a object There may be little or o relatio betwee the value a perso ascribes to a article ad the cost of providig it or the price that is asked for it Utility: It is a measure of the power of a good or a service to satisfy huma wats Thus the utility of a object like its value, iheres ot i the object itself but i the regard that a perso has

3 for it Utility ad value are closely related The utility that a object has for a perso is the satisfactio he or she derives from it Cost/Price: The term cost ad price are ofte use together The cost of a product or service is the total of resources, direct ad idirect, required to produce it The price is the value of good or service i the market place I geeral price is equal to cost plus profit Two class of goods are recogized by ecoomist: cosumer goods ad producer goods Cosumer goods are the goods ad services that directly satisfy huma wats Examples are cosumer goods are TV sets, house, shoes, book Producer goods are the goods or services the idirect as part of productio or costructio process Example: bulldozer, machie tools, raw material Iterest: It is retal amout charged by fiacial istitutios for the use of moey Iterest Rate or the rate of capital growth: It is the rate of gai received from a ivestmet Worth: Worth is the equivalet of moey i a commodity(good or service) Date:2065/4/22 Auity: A amout of moey payable to a beeficiary at regular iterval for a prescribed period of time out ofa fid reserved for that purpose - A series of equal paymets occurrig at regular periods of time Figure: Assets: Capital owed by a compay (cash, receivable, equipmet buildig, lad etc) 3 Liability: liabilities are those thigs of moetary values that the compay owes (Short term dept, log debt, payables) Equity: Equity is the worth of what the compay owes to its stock holders ( capital stocks) Fudametal accoutig equatio: Assets = liability + ower s equatig Reveues expeses = profit (or loss) Break Eve poit: 1 I busiess 0peratios, the rate of operatios, outputs or sales at which icome is sufficiet to equal operatig cost 2 The % of capacity operatio of maufacturig plat at which icome will just cover expeses H O J Variable cost L Fixed cost Demad (volume) HL = Fixed Productio cost HK = Fixed cost +variable cost OJ = Icome from sell k

4 Capital: The o-huma igrediets that cotribute to the productio of goods ad services icludig lad, raw, semi fiished materials, tools, buildigs, machiery ad ivetories Cash: The actual rupees comig ito a firm (cash iflow) or paid out by a firm (cash out flow) Compoud iterest: (a) The type of iterest that is periodically added to the amout of ivestmet (or loa) so that subsequet iterest is based o the cumulative amouts (b) The iterest charges uder the coditio that iterest is charged o ay previous iterest eared i ay time period as well as the pricipal Date: 2065/4/23 Decisio Makig: A program of actio udertake as a result of established policy to ifluece the fial decisio Decisio uder certaity: Simple decisio that assume complete iformatio ad the ucertaily coected with the aalysis of the decisios Decisio Uder take: A decisio problem i which the aalyst elects to cosider several possible futures, the probabilities of which ca be estimated Decisio uder Ucertaity: A decisio for which the aalyst elects to cosider several possible futures, the probabilities of which ca ot be estimated Demad: The various quatities per uit of time of a item that a buyer is willig to buy at all alterative price other thigs beig equal 4 Discout Rate: The rate used to calculate the preset value of series of future cash flows Iverse of compoudig Depreciatio: (a) Declie i value of a capitalized cost (b) Loss of value because of obsolescece or due to attritio Ecoomic Goods: Aythig that is useful, trasforable ad ot abudat Ecoomic life: The legth of time a asset will be ecoomically useful Ecoomic efficiecy: The ratio of the value of outputs obtaied from a ecoomic process to the value of iputs ecessary to produce them The higher the value of output per rupees worth of resource iput, the greater the efficiecy of the process Itagibles: (a) Coditios or ecoomic factor s that caot be readily evaluated i quatitative terms as i moey (b) The assets that ca ot be reliably evaluated Iflatio: A coditio is which the price level icreases rapidly Labour: The capacity of huma effort (both mid ad muscle) available for use i producig goods ad services ragig from uskilled, skilled, specialized labor power Opportuity cost: The cost associated with a alterative or foregoe opportuity that a firm or idividual bypasses Payback period: Regardig a ivestmet, the umber of years( or moths) required for the related profit or savig i operatig cost to equal the amout of said ivestmet Simple Iterest : The iterest chages uder the coditio that iterest at ay time is charged oly o the pricipal Study Period: I ecoomic study, the legth of time that is presumed to be covered i the schedule of evets ad appraisal of results Ofte the aticipated life of the project uder

5 cosideratio, but a shorter time may be more appropriate for decisio makig Supply: The various quatities per uit of time of a item that a seller is willig to sell at all alterative prices Time value of moey: The expected iterest rate that capital should or will ear 12 Cash flow: The actual rupees comig ito or out of a firm Cash iflow: Actual rupees comig ito a firm Cash outflow: Actual rupees paid out by a firm = p The use of cash flow (time) diagrams/ tables is strogly recommeded for situatios i which the aalyst eeds to clarify or visualize what is ivolved whe flows of moey occurs at various times The cash flows employs several coditios: 1 The horizotal lie is time scale with progressio of time movig from left to right The period (eg year, quarter, moth) labels ca be applied to itervals of time rather the to poit o the scale 2 The arrows sigify cash flows ad are placed at the ed of the period If a distictio eeds to be made, dowward arrows represet expeses ( egative cash flow or cash outflows) ad upward arrows represets receipts (positive cash flow or cash iflow) 5 3 The Cash flow diagram is depedet o the poit of views For examples the cash flows shows above i the figure are based o the cash flow as see by the leder p = Figure: Borrower s view poit 13 Ecoomic system: Ecoomics system is the istitutioal frame work withi which a society or coutry carries o its ecoomic activities O oe extremity we have private eterprises system which is characterized by private owership of resources as well as goods ad services Private idividuals, busiess eterprises ad associatio of various kids ca egaged i whatever volutary productio ad exchage activities they desire O the other extremity, we have pure socialistic system where there is o private property Resources, goods ad services are owed or cotrolled by the govermet Productio takes place i govermet eterprises ad the govermet specifies the coditio uder which exchage ca offer The private eterprise system is decetralize where as socialistic is highly cetralize Preset day ecoomics are a mixture of socialism ad private eterprises Some part of a ecoomics output will be produce by the profit orieted private sector of the ecoomy Aother part will be produce i a socialist maer by the public sector There are also o profit sectors like hospital, school Date:2065/4/24

6 2 Cost classificatio ad aalysis: I egieerig ecoomics cost classificatio ad aalysis provide vital iformatio Which is subsequetly used for proper plaig, decisio makig ad cotrol of a project 21 Elemet of cost: The elemet of cost are material cost, labour cost, expeses Material cost: These are the costs of raw materials, spare parts, cosumable material, pakig materials Labour cost: Costs of uskilled as well as skilled labour employed i costructio ad productio process fall ito this category Expeses: These iclude costs of special desigs, drawigs or layouts, cost of purchase or hire of tools ad plats (equipmets) for a particular job ad maiteace cost of such tools ad equipmet 22 Classificatio of cost: primary cost ad overhead cost The elemet of cost metio above, ie material cost, labour cost ad expese, costitute the total cost The total is cost is geerally calssified ito prime cost ad overhad cost Prime cost: It is the direct cost that ca be reasoably measure ad allocated to a specific output or work activity Thus it is the aggregate of direct material cost, direct labour cost ad direct expeses Overhead cost: It is idirect cost that caot be reasoably measure ad allocated to specific output or activities Overhead cost is the sum of idirect material cost, idirect labour cost, idirect expeses Compoet of prime cost: a Direct material cost: i Material icludig compoet parts, specially purchased requisitioed for a particular job ordered or processed ii Material processig from oe operatio or process to iii i Idirect material cost ii Idirect labour cost iii 6 Idirect expeses aother Primary packig materials such as cartoo cardboard box etc b Direct labour cost: i Labour egaged i alterig the coditio, coformatio ad compositio of the product ii Ispector, aalyst etc specially required for such productio iii If specially idetified, the wage of forema, chargehads, shopclerks, ways of iteral trasport persoal etc c Direct expeses: i cost of special desig, drawig ad layouts ii Hire of special tools ad equipmet for a particular job iii Maiteace cost of such tools ad equipmet Compoets cost of Overhead cost: Overhead cost may be of 4 types productio overhead, admiistratio overhead, sellig overhead, distributio overhead Here compoet of productio are give:

7 Idirect material cost: Idirect material is the material that ca ot be traced i the fiished product Eg lubricats, cotto, waste, grease, small tools How ever some mior items which eter ito productio ad form pars of its are coveietly treated as idirect material Such as cost of thread i shirt i shirt makig cost Idirect labour cost: Labour cost ot charged directly are idirect labour cost I geeral salary or wage of the followig are treated as idirect wages: forema, supervisor, maiteace labour etc Idirect expeses: a Ret, rates(taxes), isurace i relatio to factory b Depressio, power ad fuel, repair ad maiteace of plat machiery ad buildig c Other sudry expeses like first aid employmet etc Date: 2065/4/27 Q Followig are the data for the productio of a 100 badmito racquets: Labour rate: Rs 40/hr Leather: 50m at Rs 200/metre Gut: 300 m at Rs 50 /meter Graphite: 100kg at Rs 200/kg Total aul factory overhead : Rs Total aual direct labor hours: hrs Total aual direct Labour hours: hrs Labour hours eeded: 200 hrs Show the cost breakdow ad calculate th total cost for per racquet Solutio: 7 Total aual direct Labour hours = hrs Labour hours eeded for 100 racquets = 200 hrs Therefore, Total productio capacity per year = (25000/200)*100 = Nos Cost breakdow for Nos racquet Prime costs: (a) Labour cost: 40* 200/100* = Rs (b) Material cost: i Cost of leather = ((50/100)*200*125000)/100 ii Cost of Gut = (300/100)*50* = Rs iii Cost of Graphite = (100/100)*200) = Rs Therefore, total direct material cost = Rs Therefore Total cost for productio of badmito racquet = Labour cost + material cost = Rs = Rs Overhead cost = Rs Therefore, cost for productio of No of badmito for racquets = prime cost +overhead cost = Rs Rs = Rs Therefore, Maufacturig cost of each racquet = Rs / = Rs 570

8 23 Cost variace aalysis: Whe actual performace are recorded ad compared with the set of stadard some deviatio are observed These deviatios are called variaces Variace may favorable or adverse If Actual cost<stadard cost = favorable Actual cost > stadard cost = adverse Direct materials cost variace: It is differece betwee stadard cost of direct materials specified for output achieved ad actual cost of direct material used Direct wage rate variace: - Actual hours worked at actual rate- Actual hours worked at stadard rate - AH(AR-SR) Direct labour efficiecy variace: - Actual hours worked at stad rate- stadard hours worked at stadard rate - AH*SR-SH*SR - SR(AH-SH) I) Direct material ii) Direct material Price cost uses variace i) Direct material pirce variace = (Actual quatity cossumed X actual rate) (actual quatity cosumed x stadard rate) = AQ(AR-SR) ii) Direct material usage variace: = ( Actual quatity cosumed x st rate) (st quatity specified x stadard rate) = Direct wage variace: This is the variace betwee stadard direct wages specified for the activity achieved ad actual direct wage paid I) Direct wage rate variace ii) Direct labour efficiecy variace c) Variable overhead variace I) Variable overhead Expediture variace Variable overhead expediture variace: = AH * AR AH*AR = AH(AR-SR) Variable overhead efficiecy variace: = AH*SR SH*SR = SR(AH- SH) d) Fixed overhead cost: Actual fixed overhead cost- stadard fixed overhead cost 8 I) Fixed overhead expediture variace ii) Variable overhead efficiecy variace Fixed overhead efficiecy variace

9 Fixed overhead expediture: Actual fixed overhead budgeted fixed overhead = AHx AR AHx SR = AH(AR+SR) Fixed overhead efficiecy variace: AH SR SH x SR = SR(AH-SH) (i) Date:2065/4/29 Q The iformatio give below shows the records of a maufacturig compay comparig the actual data with the data from stadard cost card Stadard Actual Productio (uits) Direct material (kg) Direct material cost(rs) Direct labour cost (Rs) ,425,000 Fixed overhead cost(rs) 13,800,000 7,796,250 Variable overhead cost(rs) 9,200,000 5,197,500 Calculate: a) total material cost variace b) Total wage variace c) Variable overhead variace d) Fixed overhead variace Idicatig the separate compoets of each variace Also idicate favorable or adverse variace a) Total material cost variace: (ii) 9 Direct material price variace = AQ ( AR SR) = 56250(24-25) = = - Rs ( Therefore variace) Diect material uses variace: = SR(AQ-SQ) = 25( ) =Rs ( Therefore adverse variace) Therefore, Total material cost variace = Direct material price variace + Direct material cost variace Hece, Adverse variace = -Rs Rs = Rs (c) Total wage variace: (i) direct wage rate variace = AH(AR-SR) = 67500(10-115) = -Rs (favorable variace) (ii) Direct labour efficiecy variace = (Ah*SR)-(SH)SR) = (AH*SR) ((AP*SH/uit) *SR) = 67500*115-((7500*10,0000/10,000)*115) = = -Rs (favorable variace) Therefore, Total usage variace = (i) +(ii) = -Rs Rs( ) = -Rs Hece the variace is favourable

10 (c ) Variable overhead variace: (i) Variace overhead Expediture variace = AH * AR AH*SR = AH(AR-SR) = 67500( ( /67500) ( /100000)) = 67500( 77-92) = -Rs ( favourable variace) (iii) Variable overhead efficiecy variace: = (AH*SR) (AP*SH/uit*SR) = ( 67500*92)- (7500*100000/10000*92) = -Rs (favaurable variace) Therefore, Variace overhead variace = (i) +(ii) = -Rs (-Rs690000) = -Rs Hece Favourable variace (d) Fixed overhead variace: (i) Fixed overhead expediture variace: = AH( AR-SR) = 67500( / /100000) = 67500( ) = -Rs (favaourable ) (ii) Fixed overhead efficecy variace = (AH* SR) ( AP*SH/uit* SR) = ( *138) ( 7500*100000/10000*138) =-Rs ( favourable) Therefore, Total fixed overhead cost = (i) + (ii) = -Rs (-Rs ) = -Rs (hece favourable variace) 24 Job Costig ad Process costig: [See i maual for theory] 10 Date: 2065/4/31 # Product A is produced after three distict processes The followig iformatio is obtaied from the accouts of a period Items Total Process I II III Direct material Direct wages Direct expeses The productio overhead is Rs1000 ad is 200% of direct wages Productio was 100 kg No opeig or closig stocks prepare process cost accouts assumig o process loss, Solutio: Process cost accout Items Process-I Process-II Process-III Tot i direct material ii direct wages iii direct expeses iv pro Overhead Total cost for each: Process cost for each: Process Now, productio was 100 kg No opeig or closig stocks, Hece, The cost of product A is Rs 5100 ad productio per uit (kg) is = Rs 5100/100Kg = Rs 51 per kg 30 Iterest ad time value of moey:

11 Because of moey ca eared at a certai iterest rate through its ivestmet for a period of time, a rupee received at some future date is ot worth as much as a rupee i had at preset This relatioship betwee iterest ad time leads to the cocept of time value of moey A rupee i had ow is worth more tha a rupee received after year form ow Why? Because havig the rupee ow provides the opportuity for ivestig that rupee years more tha a rupee to be received i years Sice moey has earig power, this opportuity will ear a retur, so that after years the origial rupee + its iterest will be large amout tha the rupee received at that time Year() Amout at Begiig of Year(P) P P(1+i) P(1+i) 2 P(1+i) -2 P(1+i) -1 Compoud amout At ed of year (A) =(P+i) P(1+i) P(1+i) 2 P(1+i) 3 P(l+i) -1 P(1+i) Iterest=Pi/100 i = R/100 Pi P(1+i)i P(1+i) 2 i P(1+i) -2 i P(1+i) -1 i 31 Simple iterest; compoud iterest, iterest tables, iterest charts 1 Simple iterest: I = PTR/100 2 Compoud iterest: Discrete compoudig ad discrete cash flow: a Sigle paymet (sigle cash flow): Compoud amout factor (F/p, i, N ) [i = R/100] F = (Future value) Therefore, A F = P(1+i) I fuctioal form, this is writte as F = P(F/P, i, ) The factor (1+i) is kow as sigle paymet compoud amout factor b Sigle paymet preset worth factor (p/f, i, ) 0 Z P F P = (Preset value) 11 We kow, F = p(1+i) Therefore, P = F/(1+i) = F(1+i) -

12 I fuctioal form, P= F ( p/f, i, ) The factor (1+i) - is kow as sigle paymet preset worth factor ad is desigated as (p/f, i, ) C Equal-paymet, series compoud amout factor (F/, i, ) Cash flow A A A A A Equal aual series ad future amout F = A + A (1+i) 1 +A(1+i) 2 + +A(1+i) -1 (i) F(1+i) = A(1+i)+ A(1+i) 2 + +A(1+i) (ii) From (i) ad (ii) F i = A (1+i) - A F = A{(1+i) -1} = A ( F/A, i%, ) This ca be writte i the fuctioal form as F = A ( F/A, i, ) The factor (1 1 i compoud amout factor is kow as equal paymet series F Date: 2065/5/2 d Equal paymet series sikig fud factor [ A/F, i, ] i A = F (1 1 I geeral form; A = F ( A/F, i, ) i The resultig factor is kow as paymets series (1 1 sikig fud factor ad is desiged [A/F, i, ] e Equal paymet series capital Recovery Factor (A/F, i, ) Figure: i We kow that A = F (i) (1 1 Ad F = P( 1+i) (ii) Puttig the value of F i equatio (i) A = P(1+i) i (1 1 i(1 A = p (1 1 i(1 The resultig factor is kow as equal paymet series (1 1 capital Recovery factor f Equal paymet series Preset worth factor ( P/A, i, ) 12

13 Therefore, A = Rs x 0069 = Rs (1 1 Therefore P = A i(1 (1 1 The resultig factor is kow as equal series preset i(1 worth factor ad is desiged ( P/A, i, ) Hece, the ma has to deposit Rs each year i the savig accout # (2) If a wome deposits Rs 1500 at the ed of each year for 10 cotiuous years, how much moey is accumulated at the ed of 10 years? i = 10% compouded aually # (1) A ma wats to have Rs for the studies of his so after a period of 10 yrs How much does he has to deposit each year i a savig accout that ears 8% per year? Solutio: Rs Solutio: Give, No of year, () = 10 yrs Iterest rate, i = 10% = 01 Auity, A = Rs 1500 F A A A A A A A A A A i = 8% A A A A A A A A A A A=Rs 1500 Give No of years () = 10 yrs (1 We kow that, F = A 1 Iterest rate, i = 8% = 008 i Future worth, F = Rs (1 Auity, A =? Equal paymet series compoud amout factor = 1 i i We kow that, A = F = (1+010) 10-1/ 010 = (1 1 i Sikig Factor = = 008 / (1+ 008) 10-1 = 0069 #(3) How much moey should you deposit, ow i a savig (1 1 accout earig 10% iterest rate compoud rate aually so that you may make eight ed of year withdrawals of Rs 2000 each 13 i = 10%

14 A A A A A A A A P= Rs F i = 10% i = 10% P i = 10% = 8 years A = Rs 2000 P =? (1 1 We kow that, P = A i(1 (1 1 Preset worth factor = or, (p/a, i, ) i(1 = (1+ 010) 8-1/010(1+010) 8 = P = 2000 x = #(4) If a ma wishes to repay a loa of Rs by payig equal amout at the ed of 8 successive years, what is the ed of year paymet? The first paymet is due oe year after receivig the loa, i = 10% Solutio: i = 10% = 010 = 8 yrs P = Rs A =? We kow that i(1 A = P (1 A A A A A A A A 1 = (010(1+010) 8 )/(( 1+010) 8-1) = x = Preset Worth (PW): Preset worth (PW) is the equivalet worth of all cash flows relative to some base poit i time is called preset, ie all cash i flows ad outflows discouted to a base poit at iterest MARR ( miimum Attractive Rate of Retur) Discoutig future amouts to preset, Figure: F 1 F k F 1 2 F 2 F 0 PW = F 0 + F 1 (1+i) F k ( 1+i) -k + F (1+i) - 14 Where, i = effective iterest rate or MARR

15 M = umber of compoudig year r F k = Future cash flow at the ed of period k i = m Date: 2065/5/4 33 Nomial ad effective Iterest rates: The basic aual rate of iterest is kow as omial iterest rate deoted by r The actual or exact rate of iterest eared o the pricipal durig oe year is kow as effective iterest rate deoted by i Relatioship betwee omial iterest ad effective iterest rate is give by : r i m Where M is the o of compoudig period per year = M # Nomial rate of 12% compouded mothly with time iterval of oe year [ M = 12] i r m = M i = = or, 1268% per year # Nomial rate of 18% compouded weekly with the time iterval of oe year [ M = 52] i r m = M i = # Nomial rate 14% compouded mothly with a time iterval of six moths i = = or, 721% per six moths 12 # Nomial rate of 10% compouded weekly with a time iterval of six moths i r m = M i = = or 519 % for 6 moths 52 #Nomial rate of 13% compouded mothly with a time iterval of two years i r m = M i = = or, 2951% per two years Cotiuous Compoudig ad cotiuous compoudig formula: Cotiuous compoudig assumes that cash flows occurs at discrete itervals but the compoudig is cotiuous throughout the iterval (a) Sigle paymet compoud amout factor: For aual compoudig F = P( 1+r) For semi-aual compoudig F = P ( 1 + r/2) 2 For mothly compoudig F = P ( 1+ r/12) 12 I geeral, if there are m compoudig periods per year F = P ( 1+r/m) m

16 Date: 2065/5/13 e r = (1+i) i = e r Cotiuous Compoudig ad cotiuous compoudig formula: Cotiuous compoudig assumes that cash flows occur at discrete itervals but the compoudig is cotiuous throughout the itervals a) Sigle paymet compoud amout factor for aual compoudig F = P(1+r) For semi-aual compoudig F = p(1+1/r) 2 For mothly compoudig F = p(1 + r/12) 12 I geeral, if there are m compoudig periods per year F = p(1+r/m) m Date: 2065/5/13 Whe iterest is assumed to compoud cotiuously The iterest eared is istataeously added to the pricipal at the ed of each ifiitesimal iterest period For cotiuous compoudig, the umber of compoudig periods pre year is cosidered to be ifiite Therefore, F = p* [lim m ( 1+r/m) m ] = p* [lim m { ( 1+r/m) m/r } r ] But, lim m (1+r/m) m/r = e = F = pe r For years the compoud amout factor will be e r Sice e r for cotiuous compoudig correspodig to (1+i) for discrete compoudig 16 b) Sigle paymet preset worth factor ( P/F, r, ) We kow F = pe r Therefore, P = F [ 1/e r ] The resultig factor e -r is the sigle paymet preset worth factor for cotiuous compoudig iterest ad is desigated as (P/F, r, ) c) Equal paymet series compoud amout factor (F/A, r, ): We kow for discrete compoudig F = A[((1+i) -1)/i] ad e r = 1+i i = e r -1 Therefore, F = A [ (e r -1)/e r- ] The resultig factor ( (e r -1)/e r -1) is the equal paymet series compoud amout factor for cotiuous compoudig iterest ad is desigated as [F/A, r, ] d) Equal paymet series sikig fud factor( A/F, r, ) A = F[(e r -1)/e r -1] The resultig factor [(e r -1)/e r -1] is the equal paymet series sikig fud factor for cotiuous compoudig iterest ad is desigated as (A/F, r, ) e) Equal paymet series preset worth factor (P/A, r, ) (1 1 We kow for discrete compoudig P = A i(1 As we have, e r =1+i, i = e r -1 r e 1 For cotiuous compoudig P = A r r ( e 1) e

17 r e 1 The resultig factor r r is the equal paymet series preset ( e 1) e worth factor for cotiuous compoudig ad is desigated as [P/A, r, ] f) Equal paymet series capital recovery factor (A/P, r, ) r r ( e 1) e A = P r e 1 r r ( e 1) e The resultig factor r is the equal paymet series e 1 capital recovery factor for cotiuous compoudig ad desigated as [A/P, r,] 35 Iterest calculatio for uiform gradiet: Some time we have to deal with receipts or expeses that are projected to icrease or decrease by a uiform amout, each period, thus costitutig a arithmetic sequece of cash flows For example, maiteace ad repair expeses o specific equipmet may icrease by a relatively costat amout each period It ca be show i the form of uiform rate give below (-2) (-1) The cash flow diagram give above shows a sequece of ed of period cash flow icreasig by a costat amout G, each period G is kow as uiform gradiet amout It should be oted that the cash flows start from the ed of 2 d period owards All the formule give her are based o this assumptio 17 Ed of year Gradiet series Set of series Equivalet to Gradiet series (-1) 0 0 G 2G 3G (-2)G (-1)G 0 0 G G+G G+G+G G+G +G G+G+G +G Aual series Fidig F whe G is give F = G ( F/A, i, -1) + G(F/A, i, -2)+ +G(F/A, i, 2)+ G(F/A, i, 1) (1 1 (1 1 (1 1 = G + G + + G + i i i 1 (1 1 G i G (1 + (1 + + (1 + (1 ( i) = [ ] i G = [(1 + (1 + + (1 + (1 + 1] i The bracketed term costitute the equal paymet series compoud amout factor for years 0 0 A A A A A G i

18 G (1 1 G preset equivalet value of first year (b) uiform aual equivalet i i i value at the ed of each of the 4 year Fi A whe G is give: G = $ We kow that A = F = 4 (1 1 i = 15% G (1 1 1 G i = 2 i i (1 1 i ( G G i i=15% = 2 i i (1 1 $ $2000 Therefore, A = G is called uipolar gradiet series Po =? i (1 1 $3000 factor ad is desiged G (A/G, i, ) (a) The preset equivalet ca be calculated as Fidig p whe G is give, P 0 = G (p/g, 15%, 4) (1 1 ( i + 1) 1 i As P = = $ i(1 i (1 4 ( ) (1 1 Or, P = G = $ i (1 1 1(1 015 ( ) = $1000*(379) (1 1 = G 2 =$3790 i (1 i(1 (b) The aual equipmet ca be calculated from (1 1 i P = G A = G [A/G, 15%, 4] 2 i (1 1 = G[ ] The term iside bracket is called preset worth coversio factor i ( = $1000 Date: 2065/5/ ( ) 1 = $ 1000 * = $ # Suppose that certai of year cash flow are expected to be $1000 for the secod year, $2000 for the third year ad $3000 for fourth # The cash flow as follows: year ad iterest is 15% per year, it is desiged to fid the (a) Ed of year Cash flow/$ 18

19 Calculate the preset equivalet at i = 15% Solutio: 0 PoT =? 0 PoA =? $5000 $6000 $ i=15% $5000 $5000 $5000 $ # The cash flow as follows: Ed of each year cash flows($) Calculate the preset equivalet at i = 15% Solutio: 0 PoT=? $7000 $6000 $5000 $ i=15% $8000 $8000 $8000 $8000 PoA =? $1000 P OT = P OA + P OG $2000 ( ) $3000 ( i 1 i = A + G P 2 OT = p OA p OG i(1 i (1 (1 1 ( 1 1 i 4 4 ( ) 1 ( ) = -A + G 2 = -$ & i(1 i (1 015( )4 015 ( ) 4 ( ) = -&5000(28550)-$1000(374) =$ $ ( ) 015 = -$ $3790 = -$18065 = -$ PoA =? PoG =? $1000 $1000 $ i=15% ( ) * ( )

20 # (5) The first ivestmet cash for a projects is Rs The et aual reveue from the ed of first years owards are 3,00, 000, 2,50,000, 2,00,000, 1,50,000 ad so o ie decreasig by a amout of Rs 50,000 each year Fid out the FW of this cash flows at the ed of 5 years i = 5% Solutio: 0 Rs Rs Rs Rs25000 Rs Rs Rs Equal to (=) + 5 FW1 =? i=10% A = FW2 =? i=10% i=10% FW3 =? i=10% Give, i = 10%, = 5 yrs, G = Rs 50,000, A = Rs 3,00,000 P = Rs 500,000 Fw T = FW 1 + FW g + FW 3 = -p(1+i ) (1 1 G ( 1 1 G + A i i i i = $5,00000(1+001) ( ) ( ) Rs (6) What is the efficiet iterest rate if the omial rate is 9% per year, a 365 day year is used ad the compoudig period is (a) yearly (b) quarterly (c) daily (d) hourly Solutio: R = 9%, i =? (a) Whe the compoudig period is yearly i = (1+r/m) m + 1 = (1 +009/1) 1 1 = 009 = 9 % (b) Whe compoudig period quarterly i = (1 + r/m ) m -1 = ( /4) 4 1 (c) Whe the compoudig period is daily i = (1+r/m) m -1 = ( /365) (d) whe compoudig period is hourly i = (1+r/m) m -1 = ( 1+009/8760)

21 (7) Solve problem 2,3 ad 4 assumig cotiuous compoudig will ear 10% per year or more o all ivested capital Show whether this is desirable ivestmet by usig the PW method Date: 2065/6/3 Figure: 4 BASIC MEHODOLOGIES OF ENGINEERING ECONOMICS STUDIES: 41 Preset worth ad aual worth method: Preset worth method: It is based o the cocept to equivalet worth of all cash flows relative to some base or begiig poit i time called the preset, ie all cash flows( iflow ad outflows)are discouted to the base poit of MARR PW is a measure as to how much moey will have to be put aside how to provide for future expeditures PW = F 0 (1+i) 0 +F 1 (1+i) -1 +F 2 (1+1) F k (1+i) -k + F (1+i) - Where, i = effective iterest rate or MARR K = idex for each compoudig period F k = Future cash flow = o of compoudig periods The formula is for costat iterest rate If i chages the calculatio has to be doe i steps Higher the iterest rate ad further ito the future a cash flow occurs, lower its preset As log as PW is greater the or equal to zero, the project is ecoomically justified # A ivestmet of $1000 ca be made i a project that will produce a uiform aual reveue of $5310 for five years ad the have a market (salvage) value of $2000 Aual expeses will be $3000 each year The compay is will to accept ay project that 21 PW(10%) = cash iflow cash outflow = Aual reveue + Salvage value ivestmet aual expeses = $5310(p/A,10%, 5) + $2000(p/F, 10%, 5) - $ 10,000 $300(p/A, 10%, 5) 5 ( ) 1 = $ $2000(1+001) -5 -$ ( ) 5 ( ) 1 $ ( ) = $20125+$1245-$ $ = 0, The project is show to be margially accepted Aual worth method: AW of a project is uiform aual series of amouts for a stated study period, which is equivalet to the cash iflows ( receipts or savig) ad or cash outflow (expeses) uder cosideratio I other words AW of a project is its aual equivalet receipts (R) aual equivalet expeses (E), less its aual equivalet capital recovery (CR) amout R,E, CR is computed as MARR Study period is deoted by a which is usually i years As log as AW is greater the or equal to zero the project is ecoomically attractive AW is zero meas aual retur equal to MARR has be eared CR for a project is the equivalet uiform aual cost of capital ivested It is the aual amout that covers (ii) Depreciatio ie loss i the value of assets

22 (iii) Iterest o ivested capital (MARR) called future, to obtaied the future worth If FW 0 the project is CR ca be easily calculated by fidig aual equivalet of iitial feasible If there are several alterative the oe with maximum FW ivestmet ad the subtractig aual equivalet of salvage value is chose CR = I (A/p, i%, ) S (A/F, i%,) FW = F 0 (1+i) +F 1 (1+i) -1 +F 2 (1+1) F k (1+i) --k Where F (1+i) 0 i = iitial ivestmet for a period S = Salvage value at the ed of the study period = project study period Date: 2065/6/10 # A ivestmet of $1000 ca be made i a project that will produce a uiform aual reveue of $5310 for five years ad the have a market (salvage) value of $2000 Aual expeses will be $3000 each year The compay is will to accept ay project that will ear 10% per year or more o all ivested capital Show whether this is desirable ivestmet by usig the PW method Figure: AW(%) = R-E-CR = $ $3000 [ $1000(A/P, 10%, 5) - $2000(A/F,10%, 5) 5 ( ) 010 = $ $ $ $ 5 ( ) 1 5 ( ) $ ( ) 1 = -$5310-$3000-[$2638-$32800] = 0 The project is show to be margially acceptable 42 Future Worth method: I this method all cash iflow ad outflow are compouded forward to a referece poit i the time Iteral rate of retur (IRR) Method: I this method that iterest rate is foud out that equates the equivalet worth of a alterative s Cash iflows ( receipts or savigs) to the equivalet worth of cash outflows (expediture or ivestmets) The iterest rate i % is calculated at which N R 0 k (p/f, i %, k ) = N 0 E k (p/f, i, k) by usig preset worth formulatio For a sigle alterative, IRR is ot positive uless both receipts ad expeses are preset i the cash flow patter ad the sum of receipts exceeds the sum of all cash outflows cash flow patter ad the sum of receipts exceeds the sum of all cash outflows R k = et receipts for k th year E k = et expeses icludig ivestmet for the k th year N = project life Oce i % is calculated it is compared with MARR If i % MARR, the alterative is acceptable, otherwise ot Alterative form N 0 R k (p/f, i %, k) - N 0 E k (P/F, i %, k ) = 0

23 For a alterative with a sigle ivestmet at the preset time (k = 0) followed by a series of +ve cash flows to N, the graph is show The poit at which pw = 0, i % is IRR The value of i % ca also be determied as the iterest rate at which FW = 0 or AW = 0 N 0 R k (F/P, i %, N-K) - N 0 E k (F/P, i %, N-k) = 0 usig FW, R k -E k for 0<K<N agaist urecovered ivestmet ad dashed lie represets opportuity cost of iterest or profit o the begiig of year ivestmet balace IRR is that value of i that ca causes the urecovered ivestmet balace to exactly equal to zero at the ed of study period (N) ad represet the iterval earig of a profit formulatio Aother iterpretatio is that of urecovered ivestmet balace: # Example for IRR method Date: 2065/6/13 10, P (1+i ) 0 P(1+i ) (R1-E1) (R2-E2) (1+i ) (R3-E3) (Rk-Ek) (RN-EN) k N PW = 0 = -$10,000 + ($5310-$3000) (P/A, i %,5) + $2000(P/F, i, 5) Or Pw = 0 = -$ $ 2310 {((1+i ) 5-1)/i (1+i ) 5 } + $200(1+i ) - 5 Now by trail ad error At i = 5%, Pw = -$10000+$2310 {((1+005) 5-1)/005(1+005) 5 }+$2000(1+005) -5 = -$ $2310(43295)+$2000(07835) = +$1568 At i =15%, Pw = -$10000+$2310(33522) + $2000(04972) = -$1262 The figure shows how much of the origial ivestmet to be recovered as a fuctio of time Dowward arrow idicates returs 23

24 PW A $1568 d B e 5% 10% 15% C $1262 Pw = 0 = -$25000+$800(P/A, i %, 5) + $5000(p/F, i %,5) Or PW = 0 = -$ $8000{((1+i ) 5-1)/i (1+i ) 5 }+$5000(1+i ) -5 Lie AB/lie BC = Lie da/lie de 15%5%/$1568-(-1262) = i %5%/$ i % 5% + $1568/($1568+$1262) (15% - 5%) = 5%+ 55% = 105% PW(10%) = -$ $2310(37908) (06209) = 0 IRR = 10% # A piece of ew equipmet has bee purposed by Egieers to icrease the productivity of a certai maual weldig operatio The ivestmet cost is $25000 ad equipmet will have a salvage value of $5000 at the ed of its expected life of five years Icreased productivity attributio to the equipmet will amout to $8000 per year after extra operatig cost have bee subtracted from the value of additioal productio Evaluate the IRR of purpose equipmet Is the ivestmet a good oe? Recall the MARR is 20% per year Cash flow diagram : By trial ad error: 24 i % PW 10% -$25000+$8000(37908)+$5000(06209)= $ % -$25000+$8000(29908)+$5000(04019)= $ % -$25000+$8000(26893)+($ )= -$ By iterpolatio : i % = 20% + [$93430/($ $189710)] (25% - 20%) = 20% + 17% = 217% For exact value of i % i = 21577% ie pw = 0 IRR = 21577% > MARR This ivestmet is a good oe 44 Drawbacks of IRR method: a The IRR method is based o assumptio that recovered fud, if ot cosumed i each time period are reivest at i % rather tha at MARR This is ot always practical

25 b Sometimes it may ot be uiquely defied If the cash flow stream of a project has more tha oe chage i sig, there is a possibility of multiple rates of retur Year cash Pw = 0 = (1+i ) (1+i ) -2 i = 25% ad 400% Both of them are icorrect c IRR method ca be misleadig whe choosig betwee mutually exclusive project that have subsequetially differet outlays Cosider project P ad Q Project Cash flow IRR NPV at i = 12% 0 1 P % 7857 Q % Both projects are good but Q with it higher NPV worth more to the stockholders But for IRR poit of view P looks better Hece IRR criteria is usuitable for rakig project of differet scale Date: 2065/7/20 44 Exteral Rate of Retur method (ERR): The reivestmet assumptio of IRR may ot be valid sometimes for example, if a firm s MARR is 20% per year ad IRR of a project is 40%, it may ot be possible for the firm to reivest et cash proceeds from the project at much more tha 40% ERR method elimiates this drawback to some extet ERR method takes ito accout the exteral iterest rate (E) at which et cash flow geerated by a project over its life ca be reivested outside 25 the firm I geeral all cash outflow are discouted to period 0(preset) at E% per compoudig period while all cash iflow are compouded to period at E% The ERR is the the iterest rate that establishes equivalece betwee the two quatities, ie ERR is the i % at which A project is acceptable whe i % of ERR method is greater the or equal to firm s MARR Advatage: 1 It does ot eed trial ad error to solve i % 2 There is o possibility of multiple rate of retur Example: # A piece of ew equipmet has bee purposed by Egieers to icrease the productivity of a certai maual weldig operatio The ivestmet cost is $25000 ad equipmet will have a salvage value of $5000 at the ed of its expected life of five years Icreased productivity attributio to the equipmet will amout to $8000 per year after extra operatig cost have bee subtracted from the value of additioal productio Evaluate the IRR of purpose equipmet Is the ivestmet a good oe? Recall the MARR is 20% per year Cash flow diagram :

26 $25000 (F/p,i %,5) = $8000(F/A, 20%, 5) + $5000 $25000{(1+i)5} = $8000 {[(1+020)5-1]/020}+$5000 Or, $25000(1+i )5 = $ Or, (1+i)5 = i = 2088%>> MARR (project is ok) Date: 2065/7/22 # Whe E=15% ad MARR is 20% per year determie whether the project whose cash flow diagram appears below is acceptable 1 The amout of moey available for the ivestmet ad the source ad cost of this fud (ie equity fud or borrowed fud) 2 The umber of good projects available for ivestmet ad their purpose (ie whether they sustai preset operatios ad are essetial or expad o preset operatios) 3 The amout of perceived risk associated with ivestmet opportuities available to the firm ad the estimated cost of the projects (short plaig verses log plaig) 4 The type of the orgaizatio ivolved (ie govermet, public utility or competitive idustry) I theory the MARR, which is some times called the Hurdle rate, should be chose to maximize the ecoomic wellbeig of a orgaizatio oe popular approach to establish a MARR ivolves the opportuity cost view poit Here; {$1000+$5000(1+015)-1}(1+i )6 = ($6000-$1000)(F/A,E%, 5) Or, (1+i )6 = $5000[{ (1+015)5-1}/015] Or (1+i )6 = i = 142 < 20 ( so project is ot acceptable) 45 Miimum Attractive Rate of Retur method: (MARR) The miimum attractive rate of retur is usually is a policy issue resolved by top maagemet of a orgaizatio i view of umerous cosideratio This cosideratio are as follows: 47 Payback (Payout) period method: The payback period method maily idicates a project s liquidity rather the its profitability The payback method deals with how fast a ivestmet ca be recovered The payback methods calculate umber of year required for cash iflows to equal cash outflows Simple payback period igores the time vale of moey Some times discouted payback period is calculated which cosiders time value of moey θ k=0 (Rk-Ek)- I 0 ie Simple payback period θ k=0 (Rk-Ek)(p/F, i%, k)-i 0 ie Discouted payback period Drawbacks: 1 The most serious deficiecies of payback period are that it fails to cosider the time value of moey 26

27 2 The Cosequeces of the ivestmet followig the paybackperiod, icludig the magitude ad timig of the cash flows ad the expected life of the ivestmet Date: 2065/7/25 #Calculatio of Simple payback period ad discouted payback period of MARR = 20% Ed of year Net cash flow Pw at i =0% Pw at i =20% For I = 0%, payback period = 4 years (At the ed of 4 th year the balace turs +ve For I = 20% payback perod = 5 years (At the ed of 5 th year the balace turs +ve) Q1 Fid IRR for the followig project Ed of year Net cash flow 0-450, , , , ,200 Solutio: -450, ,200 By usig IRR Method, PW = (p/F, i, 1) (P/F,i, 2) (P/F,i,5) = 0 Or, (1+i ) (1+i ) (1+i ) (1+i ) (1+i ) -5 = 0 Q2 Fid IRR for the give cash flow usig AW method Also show the urecovered ivestmet balace i the tabular form as well as i the graphical form Year Cashflow 0-20, ,000 30,000 30,000 30, AW = R-E-CR = 0 AW = 30, ,000(A/P,i,3) = 0 Or, 30, ,000 [{(1+i ) 3 i }/((1+i ) 3-1)] = 0 27

28 Q3 What do you mea by exteral rate of retur method? Calculate ERR for the followig project of E = 15% per year Year Cashflow , (F/p, i, 5) = 8000(F/A, E%, 5) Or, 25000(1+i ) 5 = 8000 [{(1+015) 5-1}/015]+5000 Or, i = 187% Q4 A ma purchased a buildig 10 year ago for Rs 25,00,000 Its maiteace cost is Rs50,000 per year At the ed of six years he spet Rs150,000 o roof repairs After the ed of 10 years he sold the buildig for Rs Durig the period of owership, he put the buildig o ret for Rs 20,0000 per year paid at the begiig of each year Use PW AW ad FW methods to evaluate this ivestmet whe his MARR is 12% per year Date: 2065/7/27 5 Cost/Beefit aalysis: The objective is to lear how to use the beefit/cost (B/C) ratio method as a criterio for the selectio for the project As the ame implies, the beefit/cost method ivolves the calculatio of a ratio of beefits to costs Whether evaluatig a project i the private sector or i the public sector the time values of moey must be cosidered to accout for the timig of cash flows (or beefits) occurrig after the iceptio of the project Thus B/C ratio is actually a ratio of discouted beefit to discouted costs Ay method for formally evaluatig project i the public sector must be cosider the worthiess of allocatig resources to achieve social goals For over 60 yrs, the B/C ratio method has bee the accepted procedure for makig go/o-go decisios o idepedet projects ad for comparig alterative projects i the public sectors, eve though the other methods ie PW, AW, IRR etc, will lead to idetical recommedatio, assumig all these procedures are properly applied The B/C ratio is defied as the ratio of the equivalet worth of beefits to the equivalet worth of costs The equivalet worth

29 measure applied ca be preset worth, aual worth or future Salvage value 50,000, aual beefit 85000, aual O&M cost worth but customarily Pw or AW is used & I = 15% 51 Covetioal beefit/cost ratio: Covetioal B/C ratio with PW formulatio: B/C = PW(Beefit of proposed project)/pw (cost of proposed project) = PW(B)/PW(C) = PW(B)/{I+PW(O & M)} (i) Where, I = Iitial ivestmet i project O& M = Operatio & maiteace cost B = Beefits of project Covetioal B/C ratio with AW, B/C = AW(Beefit of the proposed project)/aw( Total cost of proposed project) = AW(B)/{CR+AW(O &M)} A project is accepted whe B/C ratio as defied i the above equatio is greater tha or equal to 1 Date: 2065/7/29 52 Modified beefit/cost ratio: The umerator of the modified B/C ratio expresses the equivalet worth of the beefits mius the equivalet worth of the O&M costs ad deomiator icludes oly the iitial ivestmet costs Modified B/C ratio with PW = {PW(B) PW(O&M)}/I (i) Modified B/C ratio with P/W, salvage value icluded, = {PW(B) PW(O&M)}/{I-PW(s)} Modified B/C ratio with AW = {AW(B) AW(O&M)}/CR # Fid both types of B/C ratios usig PW formulatio for a project havig first ivestmet cost Rs , project life 15 yrs, Covetioal B/C ratio formulatio = PW(B)/{I- PW(s)+PW(O&M)} = 85000(p/A,5%,15)/[20, (p/f,15,15)+25000(p/a,15%,15)] Modified B/C ratio with PW formulatio: B/C = PW(B)PW(O&M)/{I PW(s)} 53 Breakdow aalysis: Basic Cocept: C T = C F +C v (x) C v (x) = variable cost per uit of o/p S T = S p (x), S p = sellig price per o/p

30 Cost Break eve poit C T = Total cost Aual tax ad isurace = 1 ½ % of ivestmet MARR = 15% How may hours/yr would the motors have to be operated at full load for load for aual costs to be equal Electricity cost = Rs5/hrs Variable cost C v Fixed costc f Uit of o/p (x) The breakeve pricipal ca be used for the followig parameters: (i) Reveue & aual cost: Solve for aual reveue required to breakdow with aual costs The compare betwee alteratives (ii) Rate of retur: Solve for the rate of retur at which two give alteratives are equally desirable (iii) Salvage value: Solve for future resale that would result i idifferece as to preferece for a alterative (iv) Equipmet life: Solve for the hour of utilizatio per year at which a alteratives are equally desirable Through breakeve aalysis oe ca solve for the value of parameter at which the coclusio is stad off That value is breakeve poit Example: 100 HP Motor A Motor B Purchase cost ,60,000 η 74% 92% Life 10 yrs 10 yrs Maiteace cost 5000/yrs 2500 yrs Motor A: CR cost = ( A/P, 15,10) = [ (015* )/( )] = Operatig cost for power: = (100*0746*5x)/075 = 504x Maiteace cost = 5000/yrs Tax ad isurace cost = 0015 * = 1875 Total Aual cost = x Motor B: CR cost = (A/p, 15, 10) = [(015* )/( )] = OP cost = (100*0746*5x)/092 = 40543x Tax ad isurace cost = *0015 = 2400 Maiteace cost = 2500 Total aual cost = x Now, Accordig to give coditio, Aual cost of Motor A = Aual cost of Motor B x = x x = hrs 30