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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