Se 307-Chapter 5 Present Worth Analysis

8/18/2019 Se 307-Chapter 5 Present Worth Analysis

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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+

Se 307-Chapter 5 Present Worth Analysis

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