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Chapter 5Present-Worth Analysis
Loan versus Project Cash Flows
Initial Project Screening Methods
Present-Worth Analysis
Methods to Compare Mutually !clusive Alternatives
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Chapter Opening Story –Federal Express"ature o# Project$
%uip &'(''' courierswith Power Pads
Save )' seconds perpic*up stopInvestment cost$ +),'million
!pected savings$ + 'million per year
Federal Express
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Ultimate Questions
Is it worth investing +),' million to save + 'million per year( say over )' years.
/ow long does it ta*e to recover the initialinvestment.
What *ind o# interest rate should 0e used inevaluating 0usiness investment opportunities.
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Bank Loan vs. Invest ent
Pro!ect
Bank Customer
Loan
Interest + Repayment
Company ProjectInvestment
Return
Bank Loan ( loan cash flow )
Investment Project ( project cash flow )
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Initial Pro!ect "creening#ethod
Payback #ethod screens pro!ects on the basis o$ho% long it takes $or net receipts to e&ual invest ent
spending. Principle :
ow fast can I recover my initial investment!
"etho# :Base# on cumulative cash flow (or accountin$ profit)
%creenin$ &ui#eline :If the pay'ack perio# is less than or e ual to some specifie# pay'ack perio# the project woul# 'e consi#ere# for furtheranalysis*eakness :,oes not consi#er the time value of money
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E'a ple 5.( Conventional PaybackPeriod %ith "alvage )alue
N Cash Flow Cum. Flow
012345
6
-$105,000+$20,000$35,000$45,000$50,000$50,000$45,000
$35,000
-$85,000-$50,000
-$5,000$45,000$95,000
$140,000
$175,000
Pay'ack perio# shoul# occurs somewhere 'etween N - . an# N - /*
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0122 222
032 222
2
32 222
122 222
132 222
2 1 . / 4 3 56ears ( n )
/*. yearsPay'ack perio#
783 222
713 2227.3 222
7/3 222743 222 743 222
7/3 222
2
1 . / 4 3 56ears
9 n n u a l c a s h
f l o w
C u m u l a t
i v e c a s h
f l o w
( 7 )
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E'a ple 5.* +iscounted Payback PeriodCalculation
# o#ify the proce#ure an# consi#er time value of money such as the cost of money(interest) use# to support the project*
Period Cash Flow Cost o# Funds1),234
CumulativeCash Flow
' -+5,(''' ' -+5,('''
) ),(''' -+5,('''1'6),3 7 -+) (8,' -5 (8,'
,(''' -+5 (8,'1'6),3 7 -) (&)9 -8'():9
9 9,(''' -+8'():91'6),3 7 -)'(, & -&,(:58
& &,(''' -+&,(:581'6),3 7-:(5,9 -8(,&'
, &,(''' -+8(,&'1'6),3 7 -)()9) 9:(9 ;
: 9,(''' +9:(9 ;1'6),3 7 ,(&&; 8:(885
* Cost of funds = (Unrecovered beginning balance) X (interest
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Present Worth
Analysis
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,et Present Worth ,PW
#easure Principle : Compute the e uivalent net surplus at n - 2 fora $iven interest rate of i*
,ecision Rule : 9ccept the project if the net surplus is positive*
. / 4 32 1
Inflow
utflow
2
P ( i)inflow
P ( i)outflow
;et surplus
P ( i) < 2
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Present Worth A ounts at )aryingInterest 4ates
i 123 PW1i 3 i 123 PW1i 3
' +9 (,'' ' -+9(&)8(8&9 -,(; && 9(9'; & -5( ;:: );():; : -)'(,9;
5 ),( ;: 5 -) (::)' ))(:8' 9' -)&(:89) 5( 8' 9 -):(,5')& ,('88 9& -)5(9:'): ('8: 9: - '())'
)86&,4 ' 95 - )(8&,)5 -8,) &' - 9(9'
@Break even interest rate
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0/2
0.2
012
2
12
.2
/2
42
2 3 12 13 .2 .3 /2 /3 42
P W ( i ) ( $ h o u s a ! " s )
i # %&& (')
7/33/ 1>*43?
Break even interest rate(or rate of return)
9ccept Reject
Present Worth Pro le
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$75,000
' ) 9
+ &(&''+ 8(9&'
+,,(8:'
Investment pool
/ow much would you have i# theInvestment is made.
+ &(&''1F >P (),2( 3 7 +9 ( :;+ 8(9&'1F >P (),2()3 7 +9)(&&)+,,(8:'1 F >P (),2('3 7 +,,(8:'NFW of the project $119,470
/ow much would you have i# theinvestment was not made.
+8,('''1 F >P (),2(93 7 +))&('::
What is the net gain #rom theinvestment.
+));(&8' - +))&(':: 7 +,(&'&
Project
? e t u r n
t o i n v e s t m
e n t p o o l
N 7 9a!i! o* P s ! Wo h
PW(15%) = $5, ! (P"#,15%, ) = $ ,55
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Pro!ect Balance ConceptBank loan
N N 00 11 22 33i!!i!
ala!
/! s
Pa m !
P oala!
07>3 222
07>3 222
07>3 222
0711 .32
+7.4 422
0751 832
0751 832
07A .>8
+7.> /42
074/ >88
074/ >88
075 358
+733 >52
+73 424
;et future worth (13?)
PW(15') # $5,404 ( P F , 15', 3) # $3,553
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Pro!ect Balance +iagra52 222
42 222
.2 222
2
0.2 222
042 222
052 222
082 222
0122 222
01.2 2222 1 . /
07>3 2220751 832
074/ >88
73 424
a ( n )
erminal project 'alance
(net future worth or project surplus)
,iscounte# pay'ack perio#
P , o 1 . 4 a l a ! . ( $ )
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Co paring #utuallyE'clusive Alternatives
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Co paring #utually E'clusivePro!ects "utually DEclusive Projects
hen alternatives are mutually eEclusive any one if the alternatives will fulfill thesame nee# an# the selection of one alternative implies that the others will 'eeEclu#e#* DEample of 'uyin$ versus leasin$ car*
9lternative vs* Project hen we use terms alternative an# project interchan$ea'ly to mean #ecisionoption*
,o0;othin$ 9lternative hen consi#erin$ an investment we are in one of two situations: Dither the project
is aime# at replacin$ an eEistin$ asset or system or it is a new attempt*
If a process or system alrea#y in place to accomplish our 'usiness o'jectives isa#e uate then we must #etermine which if any new proposals are economicalreplacement* If none are feasi'le then we #o nothin$*
If the eEistin$ system has faile# then the choice amon$ propose# alternatives isman#atory (i*e* #o nothin$ is not an option)*
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Revenue Projectsare projects that $enerate revenues that #epen# onthe choice of alternative that we want to select thealternative with the lar$est net $ains
%ervice Projectsare projects that $enerate revenues that #o not#epen# on the choice of project 'ut must pro#uce
the same amount of output (revenue) with lower pro#uction cost*
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9nalysis Perio#is h im s a! o whi h h o!omi ** s o* a! i! s m ! will alua ".
h s u" (a!al sis) io", som im s all " h planning horizon , is hs l " im io" o whi h u uall lusi al !a i s a
om a ".
Fa o s i!*lu ! h " isio! a : h ;ui " s i io", h us *ulli* o* h sho li " al !a i , h us *ul li " o* h lo! li "al !a i , om a! oli a!" so o!.
Co!si" %!al sis io" o & ;ui " < i P io".
=! o! !i ! hoi o* a!al sis is h io" o* h us *ul li* o* hi! s m ! o .
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Co paring #utuallyE'clusive Pro!ects
F Case 1Case 1 :: Project lives lon$er than theProject lives lon$er than theanalysis perio#analysis perio# (DEample 3*5)(DEample 3*5)
F Case .Case . : Project lives shorter than the: Project lives shorter than theanalysis perio#analysis perio# (DEample 3*>)(DEample 3*>)
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E'a ple 5.6 - Co parison o$ une&ual-livedservice pro!ects %hen the re&uired service
period is shorter than the individual pro!ectli$e
Required er!ice "eriod # %ears
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"W&15'() # *$+ 4,000"W&15'(- # *$+ ,000
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2)
Come up with replacement projects thatmatch or eEcee# the re uire# service perio#*
Compute the P for each project over the
re uire# service perio# *
Case 2Case 2 :: ro!e"t li#es shorterro!e"t li#es shorterthan thethan the analysisanalysisperiodperiod $Example %&)($Example %&)(
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E'a ple 5.7 - Co parison $or "ervicePro!ects %ith 2ne&ual Lives %hen the
re&uired service period is longer than theindividual pro!ect li$e
?e%uired ServicePeriod 7 , years
Model A
Model @
+),('''
+) (,''
+&(''' +&(,'' +,('''+,(,''
+)(,''
+,(''' +,(,'' +:('''
+ ('''
& ,
,
'
'
)9
) 9&
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"W&15'(- # *$+5.9 9
"W&15'() # *$++,17+