Mechanical Engineering Design Project. MECH 390 Lecture 7

Transcription

1 Mechaical Egieerig Desig Project MECH 390 Lecture 7

2 Aother Example of Costructig a Network Diagram* Activity Duratio Preceded by A 4 B 5 C 4 A D 5 A E 6 A F 4 D,C G 7 F,B H 4 G,E A D 5 Start 4 C 4 E 6 B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 2

3 Example Problem of Fidig the Critical Path* Path Duratio A-E-H 14 A-C-F-G-H 23 A-D-dummy-F-G-H 24 B-G-H 16 A D 5 Start 4 C 4 E 6 B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 3

4 Alterate Method for Determiig Critical Path his approach is more efficiet for larger etworks Use forward sweep to fid earliest start (ES) for each activity Use backward sweep to fid latest start (LS) for each activity Calculate total float (F) for each activity F = LS - ES Critical Path cosists of Activities with F = 0 3/2/2018 Chapter 7-Project Plaig 4

5 Earliest Start* Earliest Start (ES) is the earliest time a activity ca start. It is foud by tracig forward (from tail to head of each activity arrow) from the project Start evet to the tail of the selected activity. Whe several paths are possible, use the logest path as determied by the sum of the activity duratios o that path. For activity F, ES = 9 A D 5 Start 4 C 4 E 6 B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 5

6 Project Duratio* Cotiue util we have ES for all activities that termiate i the project Fiish evet. Whe duratio of each of those activities are added to their respective ES times, the largest of the resultig sums is defied as the Project Duratio. For activity H, ES=20 Project Duratio =20+4=24 A D 5 Start 4 C 4 E 6 B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 6

7 Latest Start* Latest Start (LS) is the latest time a activity ca start ad still have the project completed withi the Project Duratio time. LS is foud by tracig backwards (from head to tail of each activity) from the project Fiish evet to the tail of selected activity. Make sure you reach the tail of the selected activity via the head of that activity. Whe several paths are possible, use the logest path as determied by the sum of the activity duratios o that path. he Project Duratio mius the legth of this logest path is the LS for the selected activity. For activity A, LS=24-24=0 A D 5 Start 4 C 4 E 6 B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 7

8 otal Float otal Float for each activity is the differece betwee the latest start ad the earliest start. F = LS - ES he activities for which F=0 defie the critical path. 3/2/2018 Chapter 7-Project Plaig 8

9 24 Summary of otal Float Calculatios* Activity Duratio ES LS F A B C D E F G Start A 4 D 5 C 4 E 6 H Project Duratio 24 Critical Path cosists of A-D-F-G-H B 5 F 4 G 7 H 4 Fiish 3/2/2018 Chapter 7-Project Plaig 9

10 F 2 F 2 otal Float Calculatios For project show i Fig Activity Duratio Earliest Start Latest Start otal Float B 3 E 3 A B C D E F G H I J K Project Duratio 19 hus, A-B-F-G-H-K is the critical path Start A 3 C 4 Start A 3 C 4 D 1 I 1 B 3 D 1 G 2 H 4 E 3 G 2 J 3 K 5 H 4 J 3 K 5 Fiish Fiish I 1 3/2/2018 Chapter 7-Project Plaig 10

11 3/2/2018 Chapter 7-Project Plaig 11 Example of Critical Path Determiatio A 1 B 2 D 4 H 5 E 6 G 1 L 3 M 4 O 7 F 7 J 2 K 5 I 10 N 6 C 3 Idetify critical path for the diagram Costruct the table for ES ad LS for each activity he oes with F as 0 will form the critical path A,B,D,E,F,G,L,M A 1 B 2 D 4 H 5 E 6 G 1 L 3 M 4 O 7 F 7 J 2 K 5 I 10 N 6 C 3

12 Program Evaluatio ad Review echique Based o Critical Path Method Replaces sigle estimate of activity duratio by a probability distributio Allows estimate of probability of completig project by a specified time 3/2/2018 Chapter 7-Project Plaig 12

13 ypical Beta Distributios for Activity Duratios t o -optimistic estimate; the shortest time withi which this activity ca be completed assumig everythig goes right. his is the left termius of the pdf. t m -the most likely time required to complete the activity. his is the mode of the pdf. t p - pessimistic estimate; the logest time it will take this activity to be completed assumig everythig goes wrog. his is the right termius of the pdf. t o t m t p t o t m t p (a) Skewed-left Beta distributio (b) Skewed-right Beta distributio 3/2/2018 Chapter 7-Project Plaig 13

14 F H PER Procedure Calculate the expected duratio t e (mea) of each activity o, t m, t p, for each activity are show i the diagram t e t 4tm tp Calculate the variace s 2 of each activity 2 s o 6 2 t p t o 6 Start A C B D I E G J K Fiish Use t e to determie the expected project duratio e ad idetify the critical path 3/2/2018 Chapter 7-Project Plaig 14

15 Determiatio of Critical Path for PER Example Calculatio F H Activity Expected ime Variace Earliest Start Latest Start otal Float A B C D E F G H I J K Project Duratio able 7.5 Critical path is C,D,F,G,H,K his is differet from the oe we got with CPM e = for project ad t for activity Start A C B D I E G J K Fiish 3/2/2018 Chapter 7-Project Plaig 15

16 Probability of Completig Project by Specified time s Calculate the variace of the project duratio as the sum of the variaces of the activities o the critical path s ( critical path ) s s s s s s 2 C 2 D 2 F 2 G 2 H 2 K s Use the stadard ormal variable z to fid the probability of completig the project i a specified time s s e z S s s e For s =20 zs From able 5.1 Pr (z < -0.57) = (28.5% chace) s /2/2018 Chapter 7-Project Plaig 16

17 Activities for Space Statio PER Problem Give table ad pert diagram for space statio, fid the probability of completig the space statio i over 60 days Activity A B C D E Costruct shell of module Descriptio Order life support system ad scietific experimetatio package from same supplier Order compoets of cotrol ad avigatioal system Wire module Assemble cotrol ad avigatioal system Start A B C D F E H I G J K Fiish F G H I J K Prelimiary test of life support system Istall life support i module Istall scietific experimetatio package i module Prelimiary test of cotrol ad avigatioal system i module Istall cotrol ad avigatioal system i module Fial testig ad debuggig 3/2/2018 Chapter 7-Project Plaig 17

18 Summary of PER Calculatios for Space Statio Project Activity t e s 2 ES LS F A B C D E F G H I J K Project Duratio Calculate the variace of the project duratio as the sum of the variaces of the activities o the critical path σ t = σ C2 + σ E2 + σ I2 + σ J2 + σ K 2 = ( ) 1/2 = 3.31 Use the stadard ormal variable z to fid the probability of completig the project i a specified time s For s =60 ( )/3.31 = 0.96 From able 5.1 Pr ( S >60) = 1 - Pr (z < 0.96) = = or 17% 3/2/2018 Chapter 7-Project Plaig 18

19 C Aother PER Example Problem* Start A D E B F G H Fiish Activity t e s 2 ES LS F A B C D E F G H Project Duratio /2/2018 Chapter 7-Project Plaig 19

20 Probability of Completig Project by Specified time s * Calculate the variace of the project duratio as the sum of the variaces of the activities o the critical path s s s s s s 2 A 2 D 2 F 2 G 2 H Use the stadard ormal variable z to fid the probability of completig the project i a specified time s For s =30 s z e s From able 5.1 s e z s Pr (z < 1.48) = 1 - Pr (z < -1.48) = = /2/2018 Chapter 7-Project Plaig 20

21 F 2 H 4 Caledarized Versio CPM is good for idetifyig the critical path It does ot display time based relatioship like Gatt chart Caledarizig is doe by chrooligcally umberig the odes Legth of activity proportioal to time All activities (except dummy) are horizotal Horizotal vertical dashed lie to eable coectio Betwee J ad 9 or D ad 4 Dummy activity vertical (betwee 6 ad 8) Nodes from which may activity emerge will be split Nodes 1, 3, ad 4 are split ime omitted o activity but complimeted by a master duratio scale Start 1 Start 1 Start 1 3 A C 2 A 3 C 4 3 B D I F B 3 D 1 E 5 G 4 5 I E 3 G 2 dummy H J J 3 K Fiish K 9 Fiish /2/2018 Chapter 7-Project Plaig 21

22 Closure Purpose of plaig Gatt chart PER ad CPM Calederized chart combies the beefit of CPM ad Gatt Commercial software packages available for these A pla is just a pla Gives a overall tetative estimate of what we thik might happe So it is always good to review oce i a while ad update 3/2/2018 Chapter 7-Project Plaig 22

23 Defiitio of a Egieer A egieer is someoe who ca do for $1 what ay fool ca do for $2. 3/2/2018 Chapter 8-Egieerig Ecoomics 23

24 Fudametal Problem of Egieerig Ecoomics rade offs betwee iitial costs ad dowstream costs You are to decide betwee 2 motors, Ajax ad Baylock here are differece i iitial cost Aual maiteace cost At the ed of 3 years, retrofittig required for baylock motors Ajax is eergy efficiet at 3000/year while baylock requires 3500/year Electricity charge icreases at 5%/year Ajax motors are more reliable ad coveyors will ot have problems so productio is 500/year higher tha baylock motors Additioaly at the ed of five years, ajax motors have a salvage value of 4000, while baylock oe Which motors you will use Four Decisio makig methods 1. Low iitial Cost approach (straight away choose baylock motors because it has the lowest iitial cost 2. Low Life cycle cost approach 3. Average aual rate of retur 4. Payback period 3/2/2018 Chapter 8-Egieerig Ecoomics 24

25 Decisio Rules Lowest iitial cost rule Ajax = 30.00; Blaylock = 20.00; Choose Blaylock sice it has the least first cost otal Life-Cycle Cost Decisio Rule Ajax = 45.08; Blaylock = Choose Ajax sice it has the least total life-cycle cost Ajax Blaylock ($1000) ($1000) Iitial Cost Rebuildig at Ed of 3rd Year Salvage Maiteace (5 years) Productivity Beefit (5 years) Electricity year year year year year otal Costs /2/2018 Chapter 8-Egieerig Ecoomics 25

26 Aual Rate of Retur Decisio Rule Icremetal Ivestmet = Iitial Cost of More Expesive Optio - Iitial Cost of Less Expesive Optio = = Dowstream Beefits = Avoidace of Rebuildig Cost + Icome from Salvage + 5 Years Savigs o Maiteace Costs + Productivity Ehacemet + 5 Years Savigs o Electricity Costs = ( ) ( ) + ( ) + ( ) + ( ) + ( )= Average Aual Beefit = Dowstream Beefits/Project Duratio = 17.26/5 = 3.45 Aual Rate of Retur = [Aual Beefits / Icremetal Ivestmet] 100 = 34.5 %. Choose Ajax uless aother opportuity for ivestig $10,000 provides a greater rate of retur. 3/2/2018 Chapter 8-Egieerig Ecoomics 26

27 PaybackPeriod (time to recover icremetal ivestmet) Beefits i 1st Year = = 2.00 (mait) + (prod) + (elec) otal Beefits i 2 Years = = 4.03 (yr 1) + (mait) + (prod) + (elec) otal Beefits i 3 Years = = 9.05 r 2) + (mait) + (prod) + (elec)+ (rebuild) otal Beefits i 4 Years = = (yr 3) + (mait) + (prod) + (elec) Ajax Blaylock ($1000) ($1000) Iitial Cost Rebuildig at Ed of 3rd Year Salvage Maiteace (5 years) Productivity Beefit (5 years) Electricity year year year year year otal Costs he payback period is 3.5 years. Select Ajax uless aother opportuity to ivest the $10,000 provides a quicker payback. 3/2/2018 Chapter 8-Egieerig Ecoomics 27

28 ime of Moey How much would I have to give you oe year from ow to make that paymet equally attractive as a $100 paymet today? hat premium represets the iterest rate (i) you could ear o the best ivestmet available to you. Compoud Iterest Formula P=preset value of a trasactio F=future value of the same trasactio after years i=iterest rate Preset Formula P=preset value of a trasactio F=future value of the same trasactio i=discout rate =Preset Worth Factor F P 1 i P F i 1 1 i P F FP i,, FP i,, 3/2/2018 Chapter 8-Egieerig Ecoomics 28

29 Uiform Series Preset Worth Factor Maiteace ad productivity improvemet occur at each year ad rebuildig ad salvage costs at oce i five years We ca either add these cost year by year (mait ad prod) or simplify it usig a formula to calculate the overall UP, i, 1 i 1 i 1 i UP, 0. 20, Future/ Aual Ajax Preset Future/ Aual Blaylock Preset Iitial Cost Maiteace UP, 0. 20, otal Preset Of Costs Select Blaylock sice the Net Preset is lower tha for Ajax. Note that a sigle calculatio usig UP gives the same result as five calculatios usig FP. 3/2/2018 Chapter 8-Egieerig Ecoomics 29

30 Preset Calculatio ($1,000)* Use discout rate i=0.20 Future/ Aual Ajax Preset Future/ Aual Blaylock Preset Iitial Cost ,, 1 i FP i Maiteace i 1 st year FP,., Maiteace i 2 d year FP, 0. 20, Maiteace i 3 rd year FP,., UP, i, 1 i 1 i 1 i Maiteace i 4 th year FP, 0. 20, Maiteace i 5 th year FP, 0. 20, otal Preset Of Costs Select Blaylock sice the Net Preset is lower tha for Ajax. 3/2/2018 Chapter 8-Egieerig Ecoomics 30

31 Example A compay is faced with the decisio of selectig either machie A or B, both of which are capable of doig the same job. Machie A costs $1,250 with aual maiteace ad operatig charges of $150 for the first te years ad $180 for the followig te years. Machie B costs $1,500 ad aual operatig ad maiteace expeses are $100 for the 20-year period. Both machies have zero salvage value at the ed of their ecoomic lives. By how much should the maufacturer of machie A icrease or decrease the purchase price of the machie so that it is competitive with machie B at a discout rate of 15 percet? Machie A Machie B 3/2/2018 Chapter 8-Egieerig Ecoomics 31

32 Geometric Series Preset Worth Factor If aual costs are icreasig at a costat aual rate e over the period, the preset value of the etire stream is foud from GP, i, e, 1 i 1 e i e1 i GP,.,., If costs are decreasig at a costat aual rate, e will be egative GP is multiplied by the cost G durig the first year to obtai the preset value of the etire stream. 3/2/2018 Chapter 8-Egieerig Ecoomics 32

33 Preset Calculatio Icludig GP ($1,000) Use discout rate i=0.20,, 1 i FP i Future/ Aual Ajax Preset Future/ Aual Blaylock Preset Iitial Cost Rebuildig at Ed of 3rd year FP,., UP, i, GP, i, e, 1 i 1 i 1 i 1 i 1 e i e1 i Salvage FP, 0. 20, Maiteace UP, 0. 20, Productivity Beefit UP, 0. 20, Electricity GP,.,., otal Preset Of Costs Select Blaylock sice the Net Preset is lower tha for Ajax. 3/2/2018 Chapter 8-Egieerig Ecoomics 33

34 Aualized Cost Aalysis Istead of covertig all costs to their equivalet preset value, we could istead covert all costs to their equivalet aual value. Although the umerical results of the two methods will be differet, the least cost alterative usig the preset value method will also be the least cost alterative usig the aualized cost method. Capital Recovery Factor Sikig Fud Factor Geeralized Sikig Fud Factor m i1 i FU, i, 1 i 1 Geometric Series Sikig Fud Factor 3/2/2018 Chapter 8-Egieerig Ecoomics 34 PU, i, FU, i, 1 i 1 i,, 1 i 1 UP i GU, i, i 1 i i 1 i e i i e

35 Aualized Cost Aalysis Capital Recovery Factor Occur iitially (capital) Sikig Fud Factor Occurs dowstream (recovery) Geeralized Sikig Fud Factor Occurs dowstream (rebuildig where m=3) Geometric Series Sikig Fud Factor Geometrically icreasig trasactio (electricity) Ajax Blaylock Future/ Preset Aual Future/ Preset Aual Iitial Cost PU, 0. 2, Rebuildig at Ed of 3rd year FU,.,, Salvage FU, 0. 2, Maiteace Productivity Beefit Electricity GU,.,., otal Equivalet Aual Costs /2/2018 Chapter 8-Egieerig Ecoomics 35

36 Variatios to Basic Egieerig Ecoomics Problem Uequal lifetimes Effect of taxes No-uiform dowstream trasactios Accoutig for iflatio Dowstream trasactios occurrig other tha at ed of year Log project lifetimes 3/2/2018 Chapter 8-Egieerig Ecoomics 36

37 Example of Uequal Lifetimes Problem Modified Ajax/Blaylock problem (Ajax)=6 (Blaylock)=4 o rebuildig o productivity beefit able shows the regular calculatio of the decisio makig process However if you look at ajax electricity Vs blaylock electricity, Ajax is more expesive evethough it cosumes less power Because it has a loger life his is ufair Alteratively we ca do the process for 4 years But this will be agaist Ajax as well Ajax (=6) Blaylock (=4) ($1000) ($1000) Preset Preset Future/ Aual Future/ Aual Iitial cost Salvage value FP, 0. 20, 6. Maiteace UP, 0. 20, UP, , Electricity GP, 0. 20, , GP, 0. 20, , otal preset value of costs /2/2018 Chapter 8-Egieerig Ecoomics 37

38 hree Approaches to Dealig with Uequal Lifetimes Multiple Lifetimes Aualized Costs PU, i, 1 i 1 i,, 1 i 1 UP i Coversio of Preset s FU, i, i 1 i i 1 i e 3/2/2018 Chapter 8-Egieerig Ecoomics 38 GU, i, i i e

39 Preset Calculatio for Commo Multiple of Lifetimes (=12) Modified Ajax/Blaylock problem (Ajax)=6 (Blaylock)=4 o rebuildig o productivity beefit Multiple Lifetimes Select a aalysis period commo to lifetime of both. I this case, 4 ad 6 years, commo term will be 12 Buy Blayblock at ed of 4 ad 8 years Buy Ajax ad ed of 6 years At 12 year period, Ajax is the better choice Ajax ($1000) Blaylock ($1000) Future/ Aual Preset Future/ Aual Preset Capital Cost (at =0) Capita Cost (at 1 =4) ( FP, 0. 2, ) Capital Cost (at 2 =6) ) ( FP,., Capital Cost (at 3 =8) ) ( FP,., Salvage (at 2 =6) ( FP,., ) Salvage (at 4 =12) ( FP,., Maiteace ) ( UP,., Electricity ) ( GP,.,., ) otal Preset Of Costs /2/2018 Chapter 8-Egieerig Ecoomics 39

40 Aualized Calculatio for Uequal Lifetimes PU, i, 1 i1 i FU, i, i,, 1 i 1 UP i Modified Ajax/Blaylock problem (Ajax)=6 (Blaylock)=4 o rebuildig o productivity beefit Aualized Costs All costs expressed as equivalet aual preset value costs Iverse factors of UP, FP, GP calculated No special treatmet eeded for differece i lifetime Buy Ajax ad ed of 6 years At 12 year period, Ajax is the better choice GU, i, IitialCost ( PU, 0. 2, ) ( PU, 0. 2, ) Salvage ( FU, 0. 2, ) Ajax (=6) Blaylock (=4) ($1000) ($1000) 3/2/2018 Chapter 8-Egieerig Ecoomics 40 i 1 1 Future/ Preset Aual Future/ Preset Aual Maiteace Electricity ( GU, 0. 2, , ) ( GU, 0. 2, 0. 05, ) i 1 i e i i e otal Preset Of Costs

41 Coversio of Preset s* hird approach is to Covert ay Preset for period 1 ito a equivalet Preset based o aother period 2 usig Covert P(Ajax) from 1 =6 to 2 =4 ad compare to P(Blaylock) P ( Ajax) 6 P ( Ajax) 4 PU,0.2,6 UP,0.2, X X Sice P 4 (Ajax) < P 4 (Blaylock), choose Ajax PU, i, 1 i 1 i,, 1 i 1 UP i We ca also do the same for Blayblock for 6 years ad compare as well Future/ Aual 1 PU,i, 1 2 PU,i, 2 otal preset value of costs /2/2018 Chapter 8-Egieerig Ecoomics 41 P P Future/ Aual Ajax (=6) Blaylock (=4) ($1000) ($1000) Preset Preset Iitial cost Salvage value FP, 0. 20, 6. Maiteace UP, 0. 20, 6., UP, Electricity GP, 0. 20, ,., GP, 0. 20,

42 he Effect of axes Corporatio subject to icome taxes ad type of expese have a effect o the tax rate (mortgage Vs.retal) So ecoomic attractio of desig optios may be iflueced Figure shows total icome o the big block ad compaies ca take deductios o the said icome Operatig expeses (payroll, electricity, utility bills etc Depreciatio (idustrial equipmet loosig value over time) here are differet methods of calculatig depreciatio axable icome is total icome the detectios (operatig + depreciatio) otal Icome Operatig Expeses Depreciatio axable Icome axes 3/2/2018 Chapter 8-Egieerig Ecoomics 42

43 MACRS Depreciatio Schedule Depreciatio has two compoets elephoe (15 years) computer (5 years) Modified Accelerated Cost Recovery System % of iitial ivestmet that ca be depreciated usig MARCS show i table Assumed as ivestmets made i the middle of the year, so half year at first ad half year after the depreciatio period is over Depreciatio Period (years) Year he total for each adds up to oe (meas, etire ivestmet is depreciated at the ed of the period, eve though there might be some salvage value remaiig Whe you cosider the differece betwee iitial ivestmet ad salvage value ad divide it over the depreciatio period, this is called the Straight lie approach 3/2/2018 Chapter 8-Egieerig Ecoomics 43

44 Margial ax Rates Oce we kow the depreciatio that we ca get for that year, we have to apply the tax reate to the allowable depreciatio his will determie the tax implicatios of the capital cost of various desig alteratives Margial tax rates show i table axable Icome Margial ax Rates < 50, ,000-75, , , , , ,000-10,000, ,000,000-15,000, ,000,000-18,333, >18,333, /2/2018 Chapter 8-Egieerig Ecoomics 44

45 Icludig Icome ax Effects i Ecoomic Aalysis op half of the table is exactly the same as before where we calculate preset cost % calculated usig MACRS at 5 years assumed compay icome is usd (so 34% tax rate) ax beefit of Depreciatio is egative Maiteace, rebuild ad electricity are operatig expeses so direct apply 34% egative agai (tax beefit) Productio ad salvage cost icur paymet of taxes so hece they are kept positive Cosiderig the taxes, Blayblock is the better alterative (assume 34% tax bracket ad MACRS depreciatio schedule with =5) Ajax Blaylock Fut./A.Val. Pres. Val. Fut,/A.Val. Pres. Val. Iitial Cost Rebuildig at Ed of 3rd year ( FP,0.2, = 0.577) Salvage ( FP,0.2,5 = 0.403) Maiteace ( UP,0.2,5 = 2.99) Productivity Beefit ( UP,0.2,5 = 2.99) Electricity ( GP,0.2,0.05,5 = 3.25) Depreciatio 1st d rd th th th ax Beefits from st year( FP,0.2,1 =0.833) d year ( FP,0.2,2 =0.694) rd year ( FP,0.2,3 =0.579) th year ( FP,0.2,4 =0.482) th year ( FP,0.2,5 =0.402) th year ( FP,0.2,6 =0.335) ax Beefits from Mait.+Rebuild.+Elec ax Burdes from Product otal Preset Of Costs Depreciatio for the Ajax motors is based o eglectig salvage value. Assume o depreciatio allowed for rebuildig Blaylock motors. 3/2/2018 Chapter 8-Egieerig Ecoomics 45

46 Example You recommed spedig $10,000 o equipmet that will icrease sales of your product by $1,000 a year ad reduce aual operatig costs by $800. he equipmet has a 10 year lifetime but ca be depreciated i three years accordig to MACRS. Your compay uses a 10% discout rate ad is i the 25% tax bracket. What is the pretax preset value of this ivestmet? What is the after-tax preset value of this ivestmet? 3/2/2018 Chapter 8-Egieerig Ecoomics 46

47 Example Pretax calculatios show 10 years of additioal icome ad reductios i operatig costs whe discouted at 10% Pretax preset value is 1061 ax o additioal icome (6145*.25) ax loss due to reductio i operatig cost (4916*0.25) Sice happe each year, applied directly to preset cost Depreciatio from MACRS table ad tax beefit from depreciatio hese values coverted to preset value usig FP rule his gives the after tax preset value as 376 UP, i, 1 i 1 i 1 i FP, i, 1 i Future/Aual 3/2/2018 Chapter 8-Egieerig Ecoomics 47 Preset Iitial Cost -10,000 Additioal aual icome UP,0.1,10 = ,000 6,145 Aual savigs i operatig costs UP,0.1,10 = ,916 Pre-tax preset value 1,061 Additioal tax o additioal icome rate = ,536 Lost tax deductio o operatig costs rate = ,229 Depreciatio i year 1 o iitial cost ,330 Depreciatio i year 2 o iitial cost ,450 Depreciatio i year 3 o iitial cost ,480 Depreciatio i year 4 o iitial cost ax beefits of depreciatio i year 1 rate = ax beefits of depreciatio i year 2 rate = ,113 ax beefits of depreciatio i year 3 rate = ax beefits of depreciatio i year 4 rate = Discouted tax beefits of depr. i year 1 FP,0.1,1 = Discouted tax beefits of depr. i year 2 FP,0.1,2 = Discouted tax beefits of depr. i year 3 FP,0.1,3 = Discouted tax beefits of depr. i year 4 FP,0.1,1 = After-ax Preset 376

48 Accoutig for Iflatio Cosider a product whose real cost has just kept pace with iflatio. here are several ways to describe its cost. Regardless of the way that is looked at, a perso has to work 6 hours to get the book, both i 1990 ad 2000 Etity Uits 1990 amout 2000 amout extbook Nomial (curret) dollars $30 $60 Hourly Wage Nomial (curret) dollars $5 $10 extbook Real (costat) 1990 dollars $30 $30 Hourly Wage Real (costat) 1990 dollars $5 $5 extbook Real (costat) 2000 dollars $60 $60 Hourly Wage Real (costat) 2000 dollars $10 $10 3/2/2018 Chapter 8-Egieerig Ecoomics 48

49 Determiig the Real Discout Rate he preset value of a future amout F must be the same, regardless of whether F is expressed i terms of omial dollars or real dollars. But if the aual iflatio rate is f If the Ajax motor salvage value is 4000 at the ed of 5 years, ad F iflatio at 3% F real is 4000/(1+.03) 5 is % appreciatio over 5 years got us P for ajax motors as 4000/(1+.2) 5 is 1610 From this we ca get the i real as (i om f)/(1+f) For i om as 20% ad f as 3% i real will be 16.5% Ad the preset value takig ito accout the iflatio will be real F 1 om f 3/2/2018 Chapter 8-Egieerig Ecoomics 49

50 Example Ivestig $20,000 i ew equipmet will provide beefits of $6,000, $9,000 ad $12,000 at the ed of the first, secod, ad third years respectively. If the real discout rate is 8% ad the iflatio rate is 6%, is this a good ivestmet? Calculate future real value F real Calculate preset value with i real as.08 Alteratively, calculate i om from the equatio i real = (i om f)/(1+f) which ives i om as.145 Ad use the future omial value Both methods give the same aswer for the preset value as 107 Sice this is positive, it is a good ivestmet rasformatio Factors Future Real Preset Ivestmet Beefits i Year 1 FP,ireal,1 = Beefits i Year 2 FP,ireal,2 = Beefits i Year 3 FP,ireal,3 = Preset i real = is.08,, 1 i FP i rasformatio Factors Future Nomial Preset Ivestmet Beefits i Year 1 FP,iom,1 = Beefits i Year 2 FP,iom,2 = Beefits i Year 3 FP,iom,3 = Preset F real F 1 om f 3/2/2018 Chapter 8-Egieerig Ecoomics 50

51 Summary of rasformatio Factors AP,i, GP,i,e, GU,i,e,,i, Factor Name Commets i FP 1 i preset worth factor UP,i, 1 i GP,i,e, FU,i, FU,i,,m 1 i 1 i 1 uiform series preset i 2 i 1 1 i 1 i 1 e i e1 i 1 i i 1 i i i 1 i 1 1 m 1 i 1 e 1 i 1 i e i worth factor arithmetic series preset worth factor geometric series preset worth factor sikig fud factor geeralized sikig fud factor 1 geometric series sikig fud factor he iverse of this is kow as the capital recovery factor 3/2/2018 Chapter 8-Egieerig Ecoomics 51 i e i e m is the year i which the trasactio F occurs; is the period over which the aual paymets U are made.

52 Summary of rasformatio Factors We have ot see Arithmetic series preset worth factor Suppose, the cost of maiteeace of blayblock is 2000 for first year, ad icreases by 200 each year, the AP,i, 1 i i 2 i 1 i 1 he first part 5980, we have already calculated 3/2/2018 Chapter 8-Egieerig Ecoomics 52

53 Summary of rasformatio Factors 3/2/2018 Chapter 8-Egieerig Ecoomics 53

54 Summary of rasformatio Factors 3/2/2018 Chapter 8-Egieerig Ecoomics 54

55 Prelimiary Cost Estimates able 9-50 of Perry s Chemical Egieerig Hadbook, 7th Ed. provides prelimiary capital cost estimates for may types of mechaical equipmet. Capital cost C of a system of size Q is C C ref Q Q ref where C ref, Q ref, ad are give i Perry s. Be careful to distiguish betwee FOB, delivered, ad istalled costs. Also, adjustmets may have to be made to accout for iflatio ad regioal differeces. 3/2/2018 Chapter 8-Egieerig Ecoomics 55

56 Prelimiary Cost Estimates - Example Problem What is the capital cost of a 500 psi, 1000 hp reciprocatig compressor? From Perry s able 9-50, Q ref = 300 hp C ref = $133,000 C = hp $ 133, hp $ 367, 000 3/2/2018 Chapter 8-Egieerig Ecoomics 56

57 Cost Estimate for Machiig Operatio Category Cost ($) Feed 1.48 For desig projects, we eed calculatio of fabricatio costs hey deped o material beig machied, equipmet used, tool, operatio ad rate at which it is performed, desired toleraces, surface fiish, ad labor As example, if we wat to cosider turig a 3.5 dia 19 log shaft o a lathe usig a brazed carbide tool. Shaft is 430 steel Cost is summarized i the table. Ad each cost i itself a detailed calculatio ool chage cost ca be calculated from Rapid raverse 0.11 Load ad uload 0.92 Setup 0.43 ool chage 0.49 ool depreciatio 0.13 ool resharpeig 1.48 Rebrazig 0.16 ip cost 0.10 Grid wheel 0.02 otal $5.33 3/2/2018 Chapter 8-Egieerig Ecoomics 57

58 Costs ad profit After calculatig the direct ad idirect costs, whe you provide the customer, you also eed to take ito accout other factors like ime spet o desig, selectig hardware etc Ma hour * hourly wage * beefits he idirect cost like overheads, utility, telephoe, power, etc I additio, the compay eeds to make profit. It could be a % of total costs Moreover, a ecoomic safety factor to hadle uexpected fluctuatios 3/2/2018 Chapter 8-Egieerig Ecoomics 58