The Construction Industry

Transcription

1 CHAPTER Costructio Plaig, Equipmet, ad Methods INTRODUCTION Sixth Editio A. J. Clark School of Egieerig Departmet of Civil ad Evirometal Egieerig 1 By Dr. Ibrahim Assakkaf ENCE 420 Costructio Equipmet ad Methods Sprig 2003 Departmet of Civil ad Evirometal Egieerig Uiversity of Marylad, College Park The Costructio Idustry Slide No. 2 The costructio idustry i the U.S. is a $400 billio idustry. Over 1,145,000 cotractors employig over 5 millio people ad utilizig heavy equipmet.

2 The Costructio Idustry Slide No. 3 The idustry is uique i several respects: costructors (cotractors) strive very hard to work themselves out of a job. The faster ad better they perform, the sooer they will be lookig for aother project to build. The products of costructio are usually oe-of-a-kid facilities, idividually desiged ad built. Costructio is iheretly a dagerous occupatio, ivolvig large ad costly costructio equipmet. Costructio Cotract Slide No. 4 A uderstadig of costructio cotracts is essetial for the proper maagemet of a costructio project. Egieer/Architect cotributes a importat service i developig a cotract.

3 Costructio Cotracts Slide No. 5 Costructio cotracts must cotai four legal items to be valid: 1. agreemet (offer ad acceptace) 2. cosideratio 3. capacity 4. legality Costructio Cotracts Slide No. 6 Agreemet: There must be a agreemet betwee the parties ivolved Such a agreemet ivolves offer ad acceptace The siged cotract by the cotractor costitute a OFFER Notificatio by the ower of the wiig proposal costitute ACCEPTANCE

4 Costructio Cotracts Slide No. 7 Cosideratio: I the case of a costructio cotract, if a costructor promises to build a additio to a home without compesatio ad the chages his mid, he geerally caot be forced to build the additio because there was o cosideratio for his or her services. Costructio Cotracts Slide No. 8 Capacity: This meas that both parties must be of sufficiet age to eter ito a cotract ad metally aware of what they are doig

5 Costructio Cotracts Slide No. 9 Legality: For a cotract to be valid, it must be legal. Obviously, a cotract betwee two parties i which oe agrees to commit a illegal act caot be eforced! Costructio Cotracts Slide No. 10 Geeral Types of Costructio Cotracts: Lump-Sum Cotract (LSC) Uit-Price Cotract (UPC) Cost-Plus-Fee Cotract (CPFC)

6 Lump-sum Cotract (LSC) Slide No. 11 I LSC cotract, the ower will pay to the costructor a agreed-upo sum of moey for the completio of a project coformig to a well-defied scope of work. This is the preferred type of cotract for may costructio services because the ower ca obtai the beefits of competitive biddig ad kows what the project will cost before he eters ito a cotract with a costructor. Effective lump-sum cotracts ca oly be obtaied if well-defied scopes of work are prepared i advace, which requires very careful ad complete plaig ad schedulig. Uit-price Cotract (UPC) Slide No. 12 The ower will pay to the costructor a agreed-upo amout of moey for each uit of work completed i a project. The uits of work may be ay items whose quatities ca be determied (e.g. cubic yard of earth, lieal feet of pipe, etc..). Example: Quatity Uit Price ($) Sub-total Pipig $2,250 Seedig 350 (sq. ft) 3 $1,050 Palm Trees $4000 Total $

7 Uit-price Cotract (UPC) Slide No. 13 Paymets are usually made by the ower to the costructor at specified itervals with the amout of each paymet depedig o work actually completed durig the prior period of time. This type of cotract also requires a complete scope of work ad is the preferred type of cotract whe the actual fial quatities are ot kow with certaity beforehad. Uder the terms of this cotract the costructor may ear a profit or icur a loss, depedig o the accuracy of his estimate per uit of work. Cost-plus-fee Cotract (CPFC) Slide No. 14 The ower will reimburse the costructor for all costs specified to costruct the project, icludig all labor costs, material costs, equipmet usage costs, subcotractor costs, ad job supervisio costs. The ower agrees to pay the costructor a additioal fee, which is essetially a maagemet fee, ad to reimburse the costructor for the costs icurred at both his head ad field offices resultig from the executio of the project. Uder this type of cotract the costructor usually takes the least risk, ad therefore has the least icetive to keep costs dow. It is used primarily i situatios where the scope of work caot be well defied ahead of costructio or whe the state of the art for the particular project is ot well kow.

8 Cost-plus-fee Cotract (CPFC) Slide No. 15 To exercise some cotrol ad to give some icetive to the costructor to hold costs dow, there are may variatios to this type of cotract, icludig: cost-plus-a-percetage-of-cost, cost-plus-a-fixed-fee, ad cost-plus-a-slidig-fee all with guarateed maximums or with icetives to hold dow the costs. CPFC cotracts are complicated. Performace Guaratees Slide No. 16 Costructors frequetly are required to furish a performace bod for each project. The bod is a three-party istrumet i which a bodig compay (termed surety) guaratees (or bods) to the ower that the project will be built by the costructor i accordace with the cotract. The cost of a performace bod depeds o the size ad risk of the cotract ad the reputatio ad expertise of the costructor. Good costructors who are costructig typical projects ca obtai performace bods for somethig less tha I % of the project cost.

9 Costructor Specialties Slide No. 17 Costructors or cotractors ted to specialize somewhat i various types of work. There are o clear-cut lies separatig the fields of costructio, they may be divided ito: Residetial Buildig-commercial Idustrial Highway-heavy Airport Specialty work Characteristics of Equipmet- Itesive Operatios The costructor works uder a uique set of productio coditios, which directly affect the selectio of costructio equipmet. A costructio compay carries its factory to each job site. At each site the costructor erects a costructio plat specifically desiged for that project. Slide No. 18 The costructor has little opportuity for fie tuig of his costructio process. Costructio projects are completed too fast, ad lessos leared have limited applicability to future projects because of the oe-of-a-kid ature of each costructio project.

10 Risk Factors i Equipmet- Itesive Work Slide No. 19 There are sigificat risks ivolved i utilizig costructio equipmet o jobs requirig large equipmet-resource ivestmet: Earth ad rock dam costructio ad caal work demad large cocetratios of equipmet. It is usually bid o a uit-price basis ad ca be subject to large variatios betwee estimated ad actual quatities. Highway work, ofte the least profitable of all heavy costructio projects, frequetly requires a equipmet commitmet that is greater tha the gross cotract value. Highway work is usually spread over several miles, makig its cotrol ad maagemet very difficult. Risk Factors i Equipmet- Itesive Work Slide No. 20 Airport costructio requires a large equipmet spread. Pipelie costructio is the most volatile type of equipmet-itesive work. Speed of pipelie work requires costructors to keep curret o job costs ad overrus. All types of costructio share a critical depedece o the climate ad the weather.

11 More Risk Factors i Equipmet- Itesive Work Fiacig Mechaisms Slide No. 21 Govermet-iitiated Costructio Activity Levels Labor Regulatios, Agreemets, ad Safety Fiacig Mechaisms Slide No. 22 Cotract paymet retetio provisios allow owers to retai substatial dollar amouts, which costructors have already eared, for log periods of time. Retaiage shows as a asset o a costructor's books, it caot be utilized for operatio ad growth ad ca cause serious cash flow problems. Most cotractors cosider cash flow to be the critical factor i ay equipmet decisio.

12 Costructio Ecoomics ad the Desiger Slide No. 23 The cost of a project is determied by the requiremets of the cotract documets: Prior to completig the fial desig, the egieer should give careful cosideratio to the method ad equipmet, which may be used to costruct the project Requiremets, which icrease the cost without producig equivalet beefits, should be elimiated The decisios of the egieer should be based o a soud kowledge of the costructio methods ad equipmet to be employed Costructio Ecoomics ad the Desiger Slide No. 24 The budget for a project may be divided ito six or more items: Materials Labor Equipmet Subcotracts Overhead, ad Profit/risk.

13 Costructio Ecoomics ad the Desiger Examples of egieerig practices that icrease cost: Requirig materials that must be trasported over log distaces Excessive testig Not allowig substitutio of equal-quality materials Requirig may oe-of-a-kid items which caot be mass-produced Usig ostadard materials or techiques whe ot required Establishig stadards of quality that are higher tha ecessary. Slide No. 25 Slide No. 26 Costructio Ecoomics ad the Desiger Some ways to to reduce the costs of costructio: 1. Desig cocrete structures with as may duplicate members as practical. 2. Simplify the desig of the structure where possible. 3. Desig for the use of cost-savig equipmet ad methods. 4. Elimiate uecessary special costructio requiremets. 5. Desig to miimize labor-itesive activities. 6. Specify a quality of workmaship that is cosistet with required project quality. 7. Furish adequate subsurface iformatio where possible.

14 Costructio Ecoomics ad the Desiger Slide No Refrai from requirig the costructor to assume the adequacy of desig or the resposibility for iformatio that should be furished by the egieer or architect. 9. Use local materials whe they are satisfactory. 10. Write simple, straightforward specificatios, which clearly state what, is expected. Defie either the results expected or the methods of accomplishig the desired results, but ot both. 11. Whe possible, use stadardized specificatios, which are familiar to the costructors. 12. Hold pre-biddig cofereces with costructors i order to elimiate ucertaities. 13. Use ispectors who have sufficiet judgmet ad experiece to uderstad the project ad to give them the authority to make decisios. Costructio Ecoomics ad the Cotractor (Costructor) Most costructio cotractors work withi a uique market situatio. The job plas ad specificatios, which are supplied by the ower, will dictate the sales coditios ad product, but ot the price. The vast majority of work i the costructio idustry is awarded o a bid basis, through either ope or selective teder procedures. The costructor states his price after estimatig the cost, icludig his overhead, evaluatig the risk, ad addig a desired profit. Usually wiig costructor has bee able to uderbid his competitors because of a more efficiet work pla, lower overhead costs, or a willigess to accept a lower profit, ad icreased risk. Slide No. 28

15 The Time Value of Moey (TVM) Slide No. 29 Moey has a time value Oe dollar today is worth more tha $1 tomorrow Failure to pay the bills results i additioal charge termed The Iterest ( Slide No. 30 Iterest is usually expressed as a percetage of the amout owed. It is due ad payable at the close of each period of time ivolved i the agreed trasactio (usually every moth). Example: If $ 1, is borrowed at 14% iterest, the iterest o the pricipal of $ 1, after oe year is x 1, 000, or $ If the borrower pays back the total amout owed after oe year, she will pay $1, If she does ot pay back ay of the amout owed after oe year, the ormally the iterest owed, but ot paid, is cosidered ow to be additioal pricipal, ad thus the iterest is compouded. After two years she will owe $1, X 1,140.00,or 1,

16 Equivalecy Slide No. 31 The baker ormally does ot care whether you pay him $1, after oe year or $1, after two years. To him, the three values ($1,000, $1,140, ad $1,299.60) are equivalet. $ 1,000 today is equivalet to $1,140 oe year from today, $ 1,000 today is equivalet to $1, two years from today. The three values are ot equal but equivalet. Note: 1.The cocept of equivalece ivolves time ad a specified rate of iterest. The three precedig values are oly equivalet for a iterest rate of 14%, ad the oly at the specified times. 2. Equivalece meas that oe sum or series differs from aother oly by the accumulated iterest at rate i for periods of time. Symbols Slide No. 32 To geeralize the cocept of iterest the followig symbols are used: P = a preset sigle amout of moey F = a future sigle amout of moey, after periods of time i = the rate of iterest per iterest period (usually oe year) = the umber of periods of time (usually years)

17 Fiacial aalysis Slide No. 33 Sigle paymet Uiform series of paymets Discouted preset worth aalysis Rate of retur aalysis Sigle Paymet Aalysis Slide No. 34 To calculate the future value F of a sigle paymet P after periods at a iterest rate i, we make the followig calculatio: At the ed of the first period: F 1 = P + Pi At the ed of the secod period: F 2 = P + Pi + (P + Pi = P(1 + 2 At the ed of the th period: F = P(1 + The future sigle amout of a preset sigle amout is F = P(1 +

18 Sigle Paymet Aalysis Slide No. 35 Note: F is related to P by a factor which depeds oly o i ad. This factor, termed the sigle paymet compoud amout factor (SPCAF), makes F equivalet to P. SPCAF may be expressed i a fuctioal form: F F (1 + =, i, or F = P, i, P P The preset sigle amout of a future sigle amout is = F P or P = F, i, (1 + F P Sigle Paymet Aalysis Slide No. 36 Note: The factor 1/(1+ is called the preset worth compoud amout factor (PWCAF) 1 (1 + ) i = P F, i,

19 Example 1: Sigle Paymet Slide No. 37 A cotractor wishes to set up a revolvig lie of credit at the bak to hadle her cash flow durig the costructio of a project. She believes that she eeds to borrow $12,000 with which to set up the accout, ad that she ca obtai the moey at 1.45% per moth. If she pays back the loa ad accumulated iterest after 8 moths, how much will she have to pay back? F = 12,000( ) 8 = 12,000( )= 13, = $13,465 The amout of iterest will be: $13,465-12,000 = $1,465. Example 2: Sigle Paymet Slide No. 38 A costructio compay wats to set aside eough moey today i a iterest-bearig accout i order to have $ 100,000 five years from ow for the purchase of a replacemet piece of equipmet. If the compay ca receive 8% iterest o its ivestmet, how much should be set aside ow to collect the $100,000 five years from ow? P = 100,000/(I ) 5 =100,000/( ) = $68, = $68,060 To solve this problem you ca also use the tables i Appedix A. P =100,000 (P/F, 8,5) = 100,000( ) $68, = $68,060

20 Uiform Series of Paymets Aalysis Slide No. 39 Ofte paymets or receipts occur at regular itervals, ad such uiform values ca be hadled by the use of additioal fuctios. Aother symbol: A = uiform ed-of-period paymets or receipts cotiuig for a duratio of periods If a uiform amout A is ivested at the ed of each period for periods at a rate of iterest i per period, the the total equivalet amout F at the ed of the periods will be: 1 2 F = A[ ] By multiplyig both sides of above equatio by (1+ ad subtractig from the origial equatio, the followig expressio is obtaied: Fi = A 1 Uiform Series of Paymets Aalysis Slide No. 40 Which ca be rearrage to give F = A 1 The relatioship ca also be expressed i a fuctioal form as F F = A, i, A i [(1+ -1]/i is called the uiform series compoud amout factor (USCAF) It ca also be show that A = F i 1

21 Uiform Series of Paymets Aalysis Slide No. 41 Which ca be expressed i a fuctioal form as A A = F, i, F The relatioship i / [(1+ - 1]is termed as the uiform series sikig fud factor (USSFF) Recall that Hece i ( F = P 1+ 1 P P = A or P = A, i, A Uiform Series of Paymets Aalysis Slide No. 42 The relatioship 1 is called the uiform series preset worth factor i (USPWF) Also i A A = P or A = P, i, 1 P The relatioship (USCRF) i is called the uiform series capital recovery factor 1

22 Cash Flow Diagram for Sigle Paymet Slide No. 43 F P F 1 P or P = F = Cash Flow Diagram for Uiform Series of Paymets F Slide No. 44 A A A A A A A A F A 1 or A = F = i i 1

23 Cash flow diagram for uiform series of paymets Slide No. 45 A A A A A A A A P P A i 1 or A = P i 1 = Example 3 Slide No. 46 A piece of costructio equipmet costs $45,000 to purchase. Fuel, oil, grease, ad mior maiteace are estimated to cost $12.34 for each hour that the equipmet is used. The tires cost $3,200 to replace (estimated to occur every 2,800 hours of use), ad major repairs of $6,000 are expected after 4,200 hours of use. The piece of equipmet is expected to last for 8,400 hours, after which it will have a estimated salvage value of 10% of the purchase price. How much should the ower of the equipmet charge, per hour of use, if he expects to use the piece of equipmet about 1,400 hours per year? Assume a aual iterest rate of 15%.

24 Example 3 (cotiued) Slide No. 47 Cash Flow Diagram 3,200 4, (1,400) 3,200 3,200 3,200 6,000 45,000 Example 3 (cotiued) Slide No. 48 = 8,400/1,400 = 6 years A 1 = - 45,000(A/P,15,6) = - 45,000 ( ) = -11, A 2 = (1,400) = -17, A 3 = - 3,200 (A/F,15,2) = - 3,200 ( ) = -1, A 4 = - 6,000 (P/F,15,3)(A/P,15,6) = - 6,000 ( )( ) = -1, A 5 = +(4, ,200) (A/F,15,6) = A T = the total aual cost = -30, The hourly cost 30,817.99/1,400 = $22.01/hr i A A = P or A = P, i, A = F 1 P 1 P P = A or P = A, i, i A i 1

25 Slide No. 49 Discouted Preset Worth Aalysis Ofte i egieerig ecoomic studies, as well as i geeral fiacial aalyses, a discouted preset worth aalysis is made of each alterative uder cosideratio. It ivolves calculatig the equivalet preset worth or preset value of all the dollar amouts ivolved i the alterative to determie its preset worth. Defiitio: The preset worth is discouted at a predetermied rate of iterest called the miimum attractive rate of retur (MARR or i*). The MARR is usually equal to the curret rate of iterest for borrowed capital plus a additioal rate for such factors as risk, ucertaity, ad cotigecies. MARR = i* =i + i(risk) Example 4 Slide No. 50 The Ace-i-the-Hole Costructio Compay is cosiderig three methods of acquirig compay pickups for use by field egieers. The alteratives are: A. Purchase the pickups for $7,200 each ad sell after 4 years for a estimated $1,200 each. B. Lease the pickups for 4 years for $2,250 per year paid i advace at the begiig of each year. The cotractor pays all operatig ad maiteace costs o the pickups ad the leasig compay retais owership. C. Purchase the pickups o special time paymets with $750 dow ow ad $2,700 per year at the ed of each year for 3 years. Assume the pickups will be sold after 4 years for $1,200 each. If the cotractor's MARR is 15%, which alterative should he choose? Note: All alteratives ivolve equal lives.

26 Example 4 (cotiued) Slide No. 51 To solve, calculate the et preset worth (NPW) of each alterative at 15% ad select the least costly alterative: A 0 1,200 4 NPW A = -7, ,200(P/F),15,4) = -$6,514 7,200 B 0 4 NPW B = -2,250-2,250(P/A),15,3) = -$7,387 2,250 2,250 2,250 2,250 1,200 C 0 4 NPW C = ,700(P/A),15,4)+1,200(P/A),15,4) = -$7, ,700 2,700 2,700 2,700 The least costly alterative is A What to do Whe Alteratives Ivolve Differet Lives Slide No. 52 Approach 1: Trucate (cut off) the loger-lived alterative(s) to equal the shorter lived alterative ad assume a salvage value for the uused portio of the loger lived alteratives. The make the compariso o the basis of equal lives. Approach 2: Assume equal replacemet coditios (costs ad icomes) for each alterative ad compute the discouted preset worth o the basis of the least commo multiple of lives for all alteratives.

27 Example 5 Slide No. 53 A cotractor is cosiderig the purchase of either a ew track-type tractor for $73,570, which has a 6-year life with a estimated et aual icome of $26,000 ad a salvage value of $8,000, or a used track-type tractor for $24,680, with a estimated life of 3 years ad o salvage value ad a estimated et aual icome of $12,000. If the cotractor's MARR is 20%, which tractor, if ay, should she choose? Example 5 (cotiued) Approach 1. (compariso o the basis of equal lives) Slide No. 54 New tractor 8,000 26,000 26,000 26,000 26,000 26,000 26, Assumed Salvage Value 73,750 30,000 Old tractor 12,000 12,000 12, New tractor 26,000 26,000 26, ,680 73,570 NPW ew = -73, ,000(P/A,20,3) + 30,000(P/F,20,3) = -73, ,000( ) + 30,000(0.5787) = -$1,443 NPW old = -24, ,000(P/A,20,3) = -24, ,000( ) = + $597 Coclusio: Old tractor is a better Alterative

28 Example 5 (cotiued) Slide No. 55 Approach 2. (compariso o the basis of equal replacemet coditios) New tractor 0 26,000 26,000 26,000 26,000 26,000 8,000 26, ,570 Old tractor 12,000 12,000 12,000 12,000 12,000 12, ,680 24,680 NPW ew = -73, ,000(P/A,20,6) + 8,000(P/F,20,6) = ,000( ) + 8,000( ) = -$15,570 NPW old = -24, ,000(P/A,20,6) - 24,680(P/F,20,3) = -24, ,000 ( ) - 24,680( ) = +$944 Coclusio: New tractor is a better Alterative Rate of Retur (ROR) Aalysis Slide No. 56 Kowig the aticipated rate of retur of a ivestmet permits decisio maker to have more "perceived" cofidece i its decisio! Defiitio: The rate of retur of a proposed ivestmet is that iterest rate which makes the discouted preset worth of the ivestmet equal to zero. To calculate the rate of retur, simply set up the equatio to be equal to zero ad solve for i.

29 Example 6 Slide No. 57 A cotractor is cosiderig the purchase of either a ew track-type tractor for $73,570, which has a 6-year life with a estimated et aual icome of $26,000, or a used track-type tractor for $24,680, with a estimated life of 3 years ad o salvage value ad a estimated et aual icome of $12,000. If the cotractor's MARR is 20%, which tractor, if ay, should be chose? Example 6 (cotiued) Slide No. 58 Approach 1. (compariso o the basis of equal lives) New tractor 26,000 26,000 26,000 26,000 26,000 26,000 Old tractor ,750 12,000 12,000 12, NPW P = 73, ,000, i,6 = 0 A P 73,570, i,6 = = = A 26,000 i = 26.9% ew ew 6 i ,680 NPW P = 24, ,000, i,3 = 0 A P 24,680, i,3 = = = A 12,000 i = 21.5% old old 3 i 1 3

30 Example 6 (cotiued) Slide No. 59 Iterative Solutio NPW ew P, i,6 = A P = 73, ,000, i,6 = 0 A 73,570 26,000 = = 6 i 1 6 i ew 6 1 ( + = NPW ew P, i,6 = A P = 24, ,000, i,3 = 0 A 24,680 12,000 = = 3 i 1 3 i old 3 1 ( + 3 = Example 6 (cotiued) Iterative Solutio Slide No ( 6 i ew = i NPW ew i NPWold ( 3 i old = i ew = 26.9% i ew = 21.5%

31 Example 6 (cotiued) Slide No. 61 If MARR is 20% The, the ew tractor is selected. Rate of Retur (ROR) Aalysis Slide No. 62 If we assume the salvage value for the ew tractor to be $30,000 after 3 years, the NPW ew will be: NPW old = -24, ,000(P/A,i,3) = 0 i old = 21.5% NPW ew = - 73, ,000(P/A,i,3) + 30,000(P/F,i,3) = 0 i ew = 18.9% Before the decisio ca be reached YOU MUST KNOW YOUR MARR. If MARR = 20% ad 3 year aalysis period, we choose old tractor. If MARR = 30%, we choose either tractor - do othig alterative. If the MARR were 15%, which alterative should we select the?

32 Rate of Retur (ROR) Aalysis Slide No. 63 Both NPW old ad NPW ew exceed the MARR = 15%. But sice the old tractor yields a higher MARR, should it ot be selected? To aswer this questio, determie each alterative's et preset worth at 15%. NPW old = -24, ,000(P/A,15,3) = $2,719 NPW ew = - 73, ,000(P/A,15,3) + 30,000(P/F,15,3) = $5,519 Accordig to the above NPW aalysis, the ew tractor yields a higher value for a MARR of 15%? Should't the alterative with the higher rate of retur would yield the higher NPW regardless of the assumed iterest rate? NO IT SHOULD NOT! The iitial ivestmets i the tractor examples we used are ot the same. Icremetal Rate of Retur (ROR) Aalysis Slide No. 64 Whe we examied the rate of retur of each alterative, we have igored their respective differeces i iitial cash flows. Therefore, we ca obtai misleadig results through such a aalysis. To deal with the problem of uequal iitial ivestmets, a icremetal rate of retur (IROR) aalysis is required. "For alteratives that have a satisfactory rate of retur (ROR), what is the IROR of the differece i the cash flows of the alteratives?" To make this aalysis, first arrage the alteratives i ascedig order of iitial cash flow. The compare alteratives, two by two, alteratively rejectig the alterative with the lower IROR.

33 Icremetal Rate of Retur (ROR) Aalysis Slide No. 65 NPW ew-old = - 48, ,000(P/A,i,6) + 24,680(P/F,i,3) + 8,000(P/F,i,6) = 0 i = 30.9% 24,680 14,000 8, ,890 Icremetal Rate of Retur (ROR) Aalysis Slide No. 66 While the iitial ivestmet of $24,680 for the old tractor will yield a ROR of 21.5%, the icremetal icrease i iitial ivestmet of $48,890 (by purchasig the ew tractor) will yield a IROR of 30.9%. Now that all the rates of retur are kow, a decisio ca be reached which is depedet o the MARR. For a MARR of 20% the ROR of the ew tractor is too low, ad therefore the old tractor is chose. For a MARR of 15% both alteratives exceed it ad we have to examie the IROR. I this case the IROR is higher tha the MARR, so we should choose the ew tractor.