5.1
What is the diference between mutually exclusive alternatives and i
5.3
(a) ow many many alter alternat native ives s are are poss possibl ible e !rom !rom !our !our indepe independe ndent nt pro projec jec (b) 'ist all o! the possibilities. (a) lternatives 1* +, (b) 'ist all o! the possibilities. & $% W$&
5.5
What What is is mean meantt by the term term e-ual e-ual servic service? e? -ua -uall serv servic ice e mean means s that that alt alter erna nati tive ves s must must pr provid ovide e serv servic ice e !or !or the the s
5./ compa mpany th that manu manu!a !ac ctur tures ma8n ma8net etic ic memb membrrane ane sw switch itches es is inve inves s cash >ows shown (;1 million units). Which one should be selected on 0nhouse irst 2ost 2ost 0ncome 7alva8e 'i!e i
5.:
2ontract 34 5 16 5 149
4 3.1 5 149
metallur metallur8ica 8icall en8ineer en8ineer is is conside considerin8 rin8 two mater materials ials !or use use in a spa spa selected selected on on the basis basis o! a presen presentt worth worth compari comparison son at at an inter interest est ra not selected above will it become the more economic alternative? alternative?
2 <2 7 'i!e i
$ ; ; ;
% (15#444.44) ; (:#444.44) ; #444.44 ; 5 19
(35#444.44) (/#444.44) 4#444.44 5 19
5.11 =he
2 2 7alva8e i n
; ;
(#5#444.44) ; (1*#444.44) ; *9 54
(3#*1#14.44) 544#444.44 *9 54
5.13 public water utility is tryin8 to decide between two diferent siAes initia initiall cost cost o! ;155#4 ;155#444# 44# wher whereas eas a 344 344mm mm line line will will cost cost ; ;14 14#44 #444. 4. 7 pump pumpin in8 8 cos costt is is exp expec ecte ted d to to be be ;34 ;3444 44 mor more per per year year than than !or !or the the 5 which siAe should should be selected selected on the basis basis o! a present present worth analysi
2 2 i n
54mm line 344mm line ; (155#444.44) ; (14#444.44) ; (3#444.44) 149 149 34 34
5.15 nion# an environmental en8ineerin8 consultin8 "rm# is tryin8 to be use. us e. 0t is cons consid ider erin in8 8 a 8aso 8asoli line nee ele lect ctri ric c hybr hybrid id and and a 8aso 8asoli line ne! !rree all all Holt# olt# whi which ch will will cos costt ;35# ;35#44 444 4 and and have have a ran8 ran8e e o! 64 mil miles es on on the the ele ele 8aso 8asoli line ne en8i en8ine ne EicE EicEs s in. in. ,iss ,issan anGs Gs 'ea! 'ea!## on on the the othe otherr han hand# d# is a pur pure ee its lithiumion battery will have to be rechar8ed. rechar8ed. =he 'ea!Gs relatively ran8e anxiety. =his !act alone alone has caused caused the company company to lean towar towar valu value e o! o! ; ;15 15#4 #444 44 in 5 year years. s. =he =he 'ea 'ea!! cou could ld be leas leased ed !or !or ;36 ;36: : per per m ;154 ;1 544 4 dow down n pay payme ment nt !or !or Iac Iacco coun untt act activ ivat atio ion. n.J J 0! 0! the the cons consul ulti tin8 n8 com com decisi decision# on# which which auto automob mobile ile is is the the better better opti option on on on the basis basis o! o! a pres pres ssume the operatin8 cost will be the same !or both vehicles.
5.11 =he
2 2 7alva8e i n
; ;
(#5#444.44) ; (1*#444.44) ; *9 54
(3#*1#14.44) 544#444.44 *9 54
5.13 public water utility is tryin8 to decide between two diferent siAes initia initiall cost cost o! ;155#4 ;155#444# 44# wher whereas eas a 344 344mm mm line line will will cost cost ; ;14 14#44 #444. 4. 7 pump pumpin in8 8 cos costt is is exp expec ecte ted d to to be be ;34 ;3444 44 mor more per per year year than than !or !or the the 5 which siAe should should be selected selected on the basis basis o! a present present worth analysi
2 2 i n
54mm line 344mm line ; (155#444.44) ; (14#444.44) ; (3#444.44) 149 149 34 34
5.15 nion# an environmental en8ineerin8 consultin8 "rm# is tryin8 to be use. us e. 0t is cons consid ider erin in8 8 a 8aso 8asoli line nee ele lect ctri ric c hybr hybrid id and and a 8aso 8asoli line ne! !rree all all Holt# olt# whi which ch will will cos costt ;35# ;35#44 444 4 and and have have a ran8 ran8e e o! 64 mil miles es on on the the ele ele 8aso 8asoli line ne en8i en8ine ne EicE EicEs s in. in. ,iss ,issan anGs Gs 'ea! 'ea!## on on the the othe otherr han hand# d# is a pur pure ee its lithiumion battery will have to be rechar8ed. rechar8ed. =he 'ea!Gs relatively ran8e anxiety. =his !act alone alone has caused caused the company company to lean towar towar valu value e o! o! ; ;15 15#4 #444 44 in 5 year years. s. =he =he 'ea 'ea!! cou could ld be leas leased ed !or !or ;36 ;36: : per per m ;154 ;1 544 4 dow down n pay payme ment nt !or !or Iac Iacco coun untt act activ ivat atio ion. n.J J 0! 0! the the cons consul ulti tin8 n8 com com decisi decision# on# which which auto automob mobile ile is is the the better better opti option on on on the basis basis o! o! a pres pres ssume the operatin8 cost will be the same !or both vehicles.
2 2 7alva8e i n 5.1/
Holt ; ;
'ea! (35#444.44) ; ; 15#444.44 4./59 *4
(15#444.44) (36:.44) 4./59 *4
n electric switch manu!acturin8 manu!acturin8 company has has to choose choose one o! thre thre cost o! ;64#444# an annual operatin8 operatin8 cost cost o! ;:444# ;:444# and a service li! have an annual operatin8 cost o! ;*444 over its 6year service li!e. operatin8 cost o! ;6444 over its Byear li!e.
2 2 7alva8e i n %ear %ear 4 1 3 6 5 * / B @W
; ;
;
;
(64#444.44) ; (:#444.44) ; 149 (64#444.44) ; (;B#1B1.B) (;/#63B.4) (;3:#B1:.*B) (;*#16/.1) (;3#:4B.B3) (;5#4B4./) (;/#1:/.3B) (;6#1:B.5/) (1/4#:/1.*B) ;
2 (B4#444.44) ; (*#444.44) ; ; 149 6 2 (B4#444.44) ; (;5#656.55) (;6#:5B.*B) (;6#54/.B:) (;6#4:B.4B) (;5B#3**.*4) (;3#3B*.B6) (;3#4/B.:5) (;#/::.46) (1**#*54.*3) ;
(134#444.44) (6#444.44) 1#444.44 149 B (134#444.44) (;3#*3*.3*) (;3#345./:) (;3#445.*) (;#/3.45) (;#6B3.*:) (;#5/.:4) (;#45.*3) (;1#B**.43) (1 (165#/61.*)
5.1:
634444 64444 :5444 149 *
5.1
ccurate ccurate air>ow measurement measurement re-uires re-uires strai8ht unobstructed unobstructed pipe !o downstream downstream o! the measurin8 device. 0n a "eld application# physical physical consider considerin8 in8 installin installin8 8 the the air>ow air>ow probes probes in an an elbow# elbow# Enowin8 Enowin8 that > process control. =his is plan 1# which will be in place !or only 3 years# with the same costs as plan 1 will be available. =his plan will have a estimated at ;5444. @lan involves installation installation o! a recently desi8ne be installe installed d in a drop drop pipe with with the the transmitte transmitterr located located in a waterp waterpro ro ;B3#444# but but because it is accurate accurate and and more durable# it will not hav estimated to be ;1644 per year plus ;544 in year 3 !or replacemen replacemen salva8e value. t an interest rate o! 149 per year# which one should
2 2 dd2 i n
@lan 1 @lan ; (*#444.44) ; (B3#444.44) ; (5#444.44) ; (1#644.44) ; ; ( ( #544.44) 149 149 3 *
5.3 sport sports s mort8a mort8a8e 8e is the the brain brainch child ild o! o! 7tadiu 7tadium m 2apita 2apitall ina inanc ncin8 in8 Fro Fro innovative way to "nance cashstrapped cashstrapped sports pro8rams pro8rams by allowin number o! years !or the ri8ht to buy 8ood seats at !ootball 8ames !or curr curren entt pri price ces. s. 0n 2ali 2ali!o !orn rnia ia## the the locE locEed edi in n pri price ce peri period od is 54 year years. s. s pays !or it now to 8et season season ticEets ticEets !or ;:4 ;:4 each !or 54 years# years# whil increasi increasin8 n8 by ;4 ;4 per year year !or !or 54 years. years. (a) Which Which !an !an made made the bett bett !an $ be willin8 willin8 to pay pay up !ro !ront nt !or !or the mort8a8e mort8a8e to maEe maEe the the two two pla
reason to 8ive extra money to C2' at this point.)
@ @ F i n
an $ an % ; (134#444.44) ; ; (:4.44) ; ; B9 54
(:4.44) (4.44) B9 54
5.5 n assistant to 7tacy 8ave her the @W values !or !our alternatives th vibration control system !or ofshore plat!orm application. =he result alternative(s) should be selected (a) i! the alternatives are exclusive# i169 n @W n @W * @W 1
0
K 3 1*.4B *.:6 3:.1
L 6 31.1 15./B *4.6B
(a) xclusive '2< 1 7elect ' 5./
1 5/.6* *53.: 5/.6* (b) independent @W M 4
=wo processes can be used !or producin8 a polymer that reduces !ric ;/54#444# an operatin8 cost o! ;*4#444 per year# and a salva8e valu cost o! ;1#354#444# an operatin8 cost o! ;5#444 per year# and a ;1 re-uire updatin8 at the end o! year at a cost o! ;:4#444. Which pro analysis at an interest rate o! 19 per year?
2 2 7alva8e i n update
5.:
@roses = @roses W ; (/54#444.44) ; (1#354#444.44) ; (*4#444.44) ; (5#444.44) ; B4#444.44 ; 14#444.44 19 19 6 ; (:4#444.44)
=wo manu!acturers supply
# # # # # "rst cost o! ;#144#444# an operatin8 cost o! ;54#444 the "rst year no salva8e value a!ter its Byear li!e. Which system should be select o! 19 per year?
2 2 7alva8e F i n
5.31
7ystem L 7ystem ' ; (1#*44#444.44) ; (#144#444.44) ; (/4#444.44) ; (54#444.44) ; 644#444.44 ; (3#444.44) 19 19 6 B
wealthy businessman wants to start a permanent !und !or supporti to 8ive e-ual amounts o! money !or each o! the next 5 years# plus on be withdrawn each year !orever# be8innin8 in year *. 0! the !und earn be donated each time? n i
;
O B9 (144#444.44)
22
5.33 ind the capitaliAed cost o! a present cost o! ;344#444# annual costs Cse an interest rate o! 19 per year. @ @eriodic n i
; ; ;
(344#444.44) (35#444.44) (/5#444.44) 5 19
22
5.35 2ompare the alternatives shown on the basis o! their capitaliAed cost < , 2 ; (154#444.44) ; (B44#444.44) ; (54#444.44) ; (1#444.44) 7 ; B#444.44 ; 1#444#444.44 n 5O i 149 149
5.3/ ecause you are thanE!ul !or what you learned in en8ineerin8 econo name o! the pro!essor who tau8ht the course. %ou plan to deposit mo awarded be8innin8 1 years !rom now (which happens to be the exa interest that is accumulated between now and year 1 is to be adde that is earned each year will be awarded as scholarship money. 0! yo year# how much must you donate now i! the !und earns interest at a i n
; ;
(64#444.44) B9 (544#444.44) 11
22
dependent projects? # only one is to be selected# so they are compared a8ainst re# none# one# more than one# or all o! them can be e. ts identi"ed as W# $# %# and &? W W$ $& W%&
$ W% %& $%&
% W& W$% W$%&
me period o! time# and at the same time.
ti8atin8 two production options that have the estimated the basis o! a present worth analysis at 149 per year? %ear
@W
0nhouse 2ontract 0nhouse 4 ; (34.44) 4 1 ;B.1B ;1.44 ;/.66 ;4.:1 3 ;*./* ;4.B3 6 ;*.15 ;4./5 4 5 ;5.5: ;4.*B ; 5.3* ;6.1/ ; 5#35B#:3.5/ ; 6#1*:#B*5.65 7elect 0nhouse production ;34
1
5;
ce vehicle. ll estimates are made. (a) Which should be te o! 19 per year? (b) t what "rst cost !or the material $ %ears
@W
(b) 7elect %
$ % 4 ; (15#444.44) ; 1 (;B#435./1) (;/#1/6./6) 3 (;*#64*.4) 6 (;5#/1:.**) 5 (;5#14*.B6) ; (6*#34B.13) ; (a) 7elect
;
(35#444.44) (;*#54.44) (;5#5B4.3*) (;6#:B.6*) (;6#66B.*3) (;3#:/1.::) (6B#BB6.:4)
4
;:#444 ;15#444
(3#63.6)
1
8radin8 its a8in8 physical !acilities. @lan involves evard that are 5/ and *1 years old# respectively. (=he remodelin8 the lameda station is estimated at ;:5#444 calls !or buyin8 5 acres o! land somewhere between the ctures at the previous sites. =he cost o! land in that area is ould be :444 s-uare !eet with a construction cost o! expected to be ;364#444# and architect !ees will be is adopted# the extra cost !or personnel and e-uipment ticipated to net a positive ;544#444 "ve years in the r the remodeled and new stations to determine which 4
@W
; (6#3/#::6.66) ; 7elect @lan
(3#5B6#:/5.B)
1
;1*#444 ;#5#444
! pipe !or a new water main. 54mm line will have an ince there is more head loss throu8h the 54mm pipe# the 4mm line. 0! the lines are expected to last !or 34 years# s usin8 an interest rate o! 149 per year?
@W
54 mm
54mm line 344mm line ; (1B3#B4./6) ; (14#444.44) 0nstall 54mm line
4
;3#444 ;155#444
co!riendly in ac-uirin8 an automobile !or 8eneral oDce electric hatchbacE. =he hybrid under consideration is F
1
@W
Holt 'ea! ; (5#61:.54) ; 7elect F
(31#B1.51)
4
1
;3#444 ;35#444
diferent assembly methods.
4
7elect
1
;:#444 ;64#444
4
1
;*#444 ;B4#444
robotiAed weldin8 process. Csin8 an interest rate o! 149 s o! a present worth analysis. 7how (a) hand and (b)
(a) hand @Wx
@Wy
7elect
(54#444 *4#444(@R#149#*) 1B4#444(@R#149#3) S /4#444(@R#149#*)) ; (*4/#43/.44) (634#444 64#444(@R#149#*) S :5#444(@R#149#*)) ; (554#5B5.44)
$
4
1
;*4#444 ;54#444
% (b) spreadsheet %ear 4 1 3 6 5 * @W T 149 7elect
; ; ; ; ; ; ; ;
$ (54#444.44) (*4#444.44) (*4#444.44) (64#444.44) (*4#444.44) (*4#444.44) 14#444.44 (*4/#43:.13)
; ; ; ; ; ; ; ;
% (634#444.44) (64#444.44) (64#444.44) (64#444.44) (64#444.44) (64#444.44) 55#444.44 (554#5B5.64)
4
1
;64#444 ;634#444
@lan 1 r a minimum o! 14 diameters upstream and 5 diameters constraints compromise the pipe layout# so the en8ineer is w measurement will be less accurate but 8ood enou8h !or a!ter which a more accurate >ow measurement system rst cost o! ;*#444 with an annual maintenance cost d submersible air>ow probe. =he stainless steel probe can ! enclosure on the handrail. =he "rst cost o! this system is to be replaced !or at least * years. 0ts maintenance cost is o! si8nal processin8 so!tware. ,either system will have a be selected on the basis o! a present worth comparison? %ear 4 1 3 6 5 * @W T 149
@lan 1 ; (*#444.44) ; (5#444.44) ; (5#444.44) ; (31#444.44) ; (5#444.44) ; (5#444.44) ; (5#444.44) ; (*/#314.6:) 7elect @lan 1
; ; ; ; ; ; ; ;
@lan (B3#444.44) (1#644.44) (1#644.44) (3#:44.44) (1#644.44) (1#644.44) (1#644.44) (:4#:/5.*5)
p# a company head-uartered in 2hica8o# 0llinois. 0t is an !ans to si8n up to pay a Imort8a8eJ over a certain several decades with season ticEet prices locEed in at sume C2' !an $ purchases a ;134#444 mort8a8e and !an % buys season ticEets at ;:4 in year 1# with prices er deal i! the interest rate is B9 per year? (b) What should ns exactly e-uivalent economically? (ssume he has no
4
1
;5#444 ;*#444
@lan
4
1
;1#644 ;B3#444
%ear 4 1 3 6 5 * / B : 14 11 1 13 16 15 1* 1/ 1B 1: 4 1 3 6 5 * / B : 34 31 3 33 36 35 3* 3/ 3B 3: 64 61
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
an $ (134#444.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44) (:4.44)
an % ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ;
an $
(:4.44) (314.44) (334.44) (354.44) 4 (3/4.44) (3:4.44) (614.44) (634.44) ;134#444 (654.44) (6/4.44) (6:4.44) (514.44) an % (534.44) (554.44) (5/4.44) (5:4.44) (*14.44) 4 (*34.44) (*54.44) (*/4.44) (*:4.44) (/14.44) (/34.44) (/54.44) (//4.44) (/:4.44) (B14.44) (B34.44) (B54.44) (B/4.44) (B:4.44) (:14.44) (:34.44) (:54.44) (:/4.44) (::4.44) (1#414.44) (1#434.44) (1#454.44) (1#4/4.44) (1#4:4.44)
1
;:4
1
;:4
6 63 66 65 6* 6/ 6B 6: 54 @W T B9
; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (:4.44) ; ; (133#56/./1) ; an % made the better deal
(1#114.44) (1#134.44) (1#154.44) (1#1/4.44) (1#1:4.44) (1#14.44) (1#34.44) (1#54.44) (1#/4.44) (*#33:.5/)
y are comparin8 !or the development o! a remote control in the table use a <NN o! 169 per year. +etermine which and (b) i! the projects are independent. ' * 164.6* 164.6* 46.6*
7elect 0# K# '
ion loss in en8ines. @rocess = will have a "rst cost o! o! ;B4#444 a!ter its year li!e. @rocess W will have a "rst 4#444 salva8e value a!ter its 6year li!e. @rocess W will also cess should be selected on the basis o! a !uture worth
%ear 4 1 3 6 @W T 19 W T 19
@roses = ; (/54#444.44) ; (*4#444.44) ; (/34#444.44) ; (*4#444.44) ; 4#444.44 ; (1#615#51:.61) ; (#/#36/.4) 7elect @rocess =
; ; ; ; ; ; ;
@roses =
@roses W (1#354#444.44) (5#444.44) (115#444.44) (5#444.44) :5#444.44 (1#61#61:.41) (#3*#*34.36)
Gs ospital wishes to replace its current
4
1
;*4#444 ;/54#444
L
4
%ear
@W T 19 W
L ' 4 ; (1#*44#444.44) ; (#144#444.44) 1 ; (/4#444.44) ; (54#444.44) ; (/4#444.44) ; (53#444.44) ' 3 ; (/4#444.44) ; (5*#444.44) 6 ; (1#/4#444.44) ; (5:#444.44) 5 ; (/4#444.44) ; (*#444.44) * ; (/4#444.44) ; (*5#444.44) / ; (/4#444.44) ; (*B#444.44) B ; 334#444.44 ; (/1#444.44) ; (#56B#B43.1:) ; (#3:1#/:*.36) (;*#314#/6.B3) (;5#:1#:::.**) 7elect system '
1
;/4#444 ;1#*44#444
4
1
;54#444
;#144#444
iB9
n8 research directed toward sustainability. =he donor plans e now (i.e.# six donations) so that ;144#444 per year can s interest at a rate o! B9 per year# how much money must 4 ;
1
(B54#/:.44) ;144#444 i19
! ;35#444# and periodic costs every 5 years o! ;/5#444.
;
(*:4#46/./5)
4
1
;344#444 < s usin8 an interest rate o! 149 per year. %ear < , 4 ; (154#444.44) ; 1 ; (54#444.44) ; ; (54#444.44) ; 3 ; (54#444.44) ; 6 ; (54#444.44) ; 5 ; (6#444.44) ;
(B44#444.44) (1#444.44) (1#444.44) (1#444.44) (1#444.44) (1#444.44)
4
1
;54#444
@W T 149 W 22
; (336#5/1.:/) ; (BB#5:.6) ; ; (BB#5:.6) ; 7elect <
;154#444 (1#444.44) (:4#444.44)
y# you plan to start a permanent scholarship !und in the ney now with the stipulation that the scholarships be t time that your dau8hter plans to be8in colle8e). =he to the principal o! the endowment. !ter that# the interest want the amount o! the scholarships to be ;64#444 per rate o! B9 per year? ;
(16#661.63)
iB9
1
;64#444
i149
2ontract ;
16;
16;
16;
16;
16;
3
6
5
5;
5;
5;
5;
4
@W ;5#35B#:3.5/
i19
%
;#444
;:#444
3
;:#444
6
;:#444
5
4
;:#444 @W ; 6*#34B.13
;35#444
i*9
;1*#444
3
;1*#444
6:
;1*#444
54
4
;1*#444 @W ; 6#3/#::6.66
i149
;3#*1#14
344 mm
;3#444
3
;3#444
:
;3#444
34
4
;3#444 @W ; 1B3#B4./6
i4./59
;14#444
'ea! ;15#444
;3#444
3
5:
;3#444
;3#444
*4
4
;3#444 @W ; 5#61:.54
;15#444
i149
;:#444
3
6
;:#444
;64#444
;:#444
5
;:#444
;64#444
*
/
;:#444
;:#444
;64#444
i149
;*#444
3
6
;*#444
;*#444
5
;*#444
*
/
;*#444
;*#444
;B4#444
i149 ;/4#444
;*4#444
3
;*4#444 ;54#444
;/4#444
6
;*4#444
5
;*4#444
*
;*4#444 @W ; *4/#43:.13
i149 ;:5#444
;64#444
3
;64#444
6
;64#444
5
;64#444
*
;64#444 @W ; 554#5B5.64
i149
;5#444
3
;5#444
6
;5#444
5
;5#444
;*#444
*
;5#444 @W ; */#314.6:
i149
;1#644
3
;1#644
6
;1#644
5
;1#644
*
;1#644
;#544 @W ; :4#:/5.*5
iB9
;:4
3
;:4
6:
;:4
54
;:4 @W ; 133#56/./1
iB9
3
6:
54
;314 ;334
;1#54
;1#/4 @W ; *#33:.5/
i19
@roses W ;B4#444
;*4#444 ;/54#444
3
;*4#444
;B4#444
6
4
;*4#444
1
;5#444
W ; #/#36/.4
;1#354#444
i19 ;644#444
;/4#444
3
;/4#444
6
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