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Comparing Alternatives with Rate of
Return
Use Incremental Analysis
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Topics
In this section, we• recall the defnition o ROR,
• discuss decision situations or multiple
alternatives, and• discuss the appropriate decision
methodology or each situation
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Rate of Return
• Recall that the ROR o an investment is theinterest rate that makes
• NPW !
•
N"W !• PW #enefts PW $osts
• "W #enefts "W $osts
• %or a single pro&ect, accept i ROR ' ("RR)
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Decisions Involving MultipleProjects
*iven a set o possi+le pro&ects,• any su+set o the pro&ects may +e
selected)
•
only one may +e selected, +ut one must+e chosen)
• only one may +e selected, +ut it is O tochoose none)
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Non-Mutually ExclusiveAlternatives
• -uppose we can select any su+set o thepro&ects)
• -olution (ethodology.
/ $ompute the ROR o each alternative
/ -elect each alternative or which ROR ' ("RR
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Example 1
• ("RR 012
"lternative Investment "nnual
Income
"nnual
$ost
3ie
" 40!!,!!! 45!,!!! 41!,!!! 6# 475,!!! 488,!!! 49!,!!! 5
$ 4:!,!!! 41!,!!! 409,!!! 5
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Mutually Exclusive Alternatives
• -uppose we must select one, only one, +utat least one, alternative)
• -olution (ethodology.
/ =ach increment o investment must yield the("RR)
/ Perorm Incremental "nalysis.
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Recall Incremental Analysis
0) Rank the alternatives in increasing order o
investment)9) -elect as the defender the alternative with
the smallest investment)
1) 3et the challenger +e the alternative withthe ne>t higher investment)
8) "ccept or re&ect the challenger on the +asiso the return on the e>tra investment) <hewinner +ecomes the defender)
5) I the highest level o investment has +eenreached, stop) Otherwise return to step 1)
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Example ! "omparing costalternatives
"lternative Investment Operating $ost
" 45!!! 498!
# 41!!! 47;5
$ 48!!! 45!!
? 495!! 40!!!
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Ran#e$ Alternatives
• ("RR 052
• "lternatives. "ll have fve@year lie and nosalvage
• Ranked "lternatives . Rank +y order o
increasing investment. ?, #, $, ")"lternative Investment Operating $ost
? 495!! 40!!!
# 41!!! 47;5$ 48!!! 45!!
" 45!!! 498!
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Example ! IncrementalAnalysis
• Defender. Pro&ect ?)• Ne>t greater investment A$hallengerB.
Pro&ect #)
• Is the e>tra investment in # over ? &ustifedC
/ Incremental Investment. @45!!
/ Incremental #eneft. 4095
/ N"W @5!! A"DP, i, 5B E 095 F ROR 72 G("RR
/ ?ecision. Re&ect $hallenger, Pro&ect #)
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Example ! IncrementalAnalysis %cont&$'
• Defender. Pro&ect ?)
• Ne>t greater investment A$hallengerB.Pro&ect $)
• Is the e>tra investment in $ over ? &ustifedC/ Incremental Investment. @405!!
/ Incremental #eneft. 45!!
/ N"W @05!! A"DP, i, 5B E 5!! F ROR 9!2 F
("RR/ ?ecision. "ccept $hallenger, Pro&ect $)
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Example ! IncrementalAnalysis %cont&$'
• Defender. Pro&ect $)
• Ne>t greater investment A$hallengerB.Pro&ect ")
• Is the e>tra investment in " over $ &ustifedC/ Incremental Investment. @40!!!
/ Incremental #eneft. 49:!
/ N"W @0!!! A"DP, i, 5B E 9:! F ROR 62 G
("RR/ ?ecision. Re&ect $hallenger,
/ eep Defender, Pro&ect $
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Example ( Projects )it*+ene,ts
Alternative Investment Net Annual
Benefits
Life
A $100,000 $20,000 9
B $85,000 $24,000 5
C $60,000 $18,000 5
• $hoose one o the three
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Example ( %cont&$'
• ("RR 012 Aselect one and only oneB• Ranked Pro&ects. $, #, "
Alternative Investment Net Annual
Benefits
Life
C $60,000 $18,000 5
B $85,000 $24,000 5
A $100,000 $20,000 9
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Example ( IncrementalAnalysis
• Defender. Pro&ect $• $hallenger. Pro&ect #
• Is the e>tra investment in # over $ &ustifedC
/ Incremental Investment. @495,!!!
/ Incremental #eneft. 4:!!!
/ N"W @95 A"DP, i, 5B E : F ROR :)82 G
("RR/ ?ecision. Re&ect $hallenger, eep Pro&ect $
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Example ( IncrementalAnalysis %cont&$'
• Defender. Pro&ect $• $hallenger. Pro&ect "
• Is the e>tra investment in " over $ &ustifedC
/ Incremental Investment. @48!,!!!
/ Incremental #eneft. 49!!!
/ Hseul 3ie. Pro&ect lives are dierentJJ
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Example ( IncrementalAnalysis %cont&$'
• -elect a common study period, say 85years)
"
K
0! 9! 1! 8!
$
0!!,!!!
9!,!!!
07,!!!
:!,!!!
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Example ( IncrementalAnalysis %cont&$'
• $ompute the incremental cash Lows)
• <he cash Lows o "@$ represent a non@simple investment)
"@$ 0! 9! 1! 8!
8!,!!!
9,!!!
:!,!!!
:!,!!!
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Example ( IncrementalAnalysis %cont&$'
• We must veriy graphically Aor withanother methodB that the interest oundcorrespond to a rate o return) 3uckily, it
does) <he rate o return o the incrementalcash Lows is 00):2)
• <hereore re&ect the challenger, pro&ect "and accept $)
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An Easier )ay for Dierent.ives
• %ind ROR o " @ $• N"WA" @ $B N"WA"B @ N"WA$B !• @0!!A"DP, i, 6B E 9! @ M@:!A"DP, i, 5B E 07• @0!!A"DP, i, 6B E :!A"DP, i, 5B E 9 !
• i N"WA" @ $B• !2 9776• 52 0;76• 0!2 8:1
• 052 @0!57• 092 @091• ROR o " @ $ is 00):2) Re&ect " @ $ and choose $
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Mutually Exclusive Alternatives)it* a Do-Not*ing Alternative
• -uppose we can select one alternative orno alternative
• -olution (ethodology.
/ $ompute ROR o each alternative/ Re&ect any alternatives that do not yield the
("RR
/ I only one remains, choose that alternative
/ I more than one remains, do incrementalanalysis to select the +est
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Example /
• ("RR 012 Aselect one or noneB
" lternative Investment Net
Income
3ife ROR 3ife
" 40!!,!!! 49!,!!! 6 01);2 6
# 475,!!! 498,!!! 5 09);2 5
$ 4:!,!!! 407,!!! 5 05)12 5
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Example / %cont&$'
• -ince # does not return 012 it can +e
discarded)
• We most compare " and $, +y computingthe rate o return o the e>tra investment
o " over $)• <he rate o return o " over $ is 00):2)
-ince the return on the e>tra investment isless than 012 Athe ("RRB re&ect the e>tra
investment)• We should choose option $)
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"onclusion
• (easure o merit is the ROR AapercentageB
• %or a single alternative, accept i ROR '("RR
• %or multiple alternatives. "ccept anincrement i the ROR or the increment'("RR