Chapter 8
Investment Criteria
• nderstand accountin" rates o# return and their pro!lems
• nderstand the internal rate o# return and its stren"ths and $eaknesses
 
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• &he Pro#ita!ility Inde)
 
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,ood ecision Criteria
• .e need to ask ourselves the #ollo$in" /uestions $hen evaluatin" decision criteria
 0 oes the decision rule ad1ust #or the time value o# money
 0 oes the decision rule ad1ust #or risk
 
8-3
Pro1ect 4)ample In#ormation • 5ou are lookin" at a ne$ pro1ect and
you have estimated the #ollo$in" cash #lo$s6  0 5ear 76 C 9 -:;3<777
 0 5ear :6 C 9 ;%<:27= NI 9 :%<;27
 0 5ear 26 C 9 >7<877= NI 9 %<%77
 0 5ear %6 C 9 ?:<787= NI 9 2?<:77
 0 (vera"e *ook Value 9 >2<777
 
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value o# a pro1ect and its cost
• Bo$ much value is created #rom undertakin" an investment  0 &he #irst step is to estimate the e)pected
#uture cash #lo$sA
 0 &he second step is to estimate the re/uired return #or pro1ects o# this risk levelA
 
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• If the NPV is positive, accept the project 
 
• sin" the #ormulas6
 0 NPV 9 ;%<:27D:A:2E F >7<877D:A:2E2 F ?:<787D:A:2E% 0 :;3<777 9 G:2<;2>A+:
• sin" the calculator6
 0 C7 9 -:;3<777= C7: 9 ;%<:27= 7: 9 := C72
9 >7<877= 72 9 := C7% 9 ?:<787= 7% 9 := NPV= I 9 :2= CP& NPV 9 :2<;2>A+:
• Do we accept or reject the project? 
 
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ecision Criteria &est - NPV
• oes the NPV rule account #or the time value o# money
• oes the NPV rule account #or the risk o# the cash #lo$s
• oes the NPV rule provide an indication a!out the increase in value
 
Calculatin" NPVs $ith a Spreadsheet
• Spreadsheets are an e)cellent $ay to compute NPVs< especially $hen you have to compute the cash #lo$s as $ellA
• sin" the NPV #unction  0 &he #irst component is the re/uired return
entered as a decimal
 0 &he second component is the ran"e o# cash #lo$s beginning with year 1
 
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Pay!ack Period
• Bo$ lon" does it take to "et the initial cost !ack in a nominal sense
• Computation  0 4stimate the cash #lo$s
 0 Su!tract the #uture cash #lo$s #rom the initial cost until the initial investment has !een recovered
• ecision 'ule 0 Accept if the payback
 period is less than some preset limit 
 
Computin" Pay!ack or the Pro1ect
•  (ssume $e $ill accept the pro1ect i# it pays !ack $ithin t$o yearsA  0 5ear :6 :;3<777 0 ;%<:27 9 :7:<887 still to recover 
 0 5ear 26 :7:<887 0 >7<877 9 %:<787 still to recover 
 0 5ear %6 %:<787 0 ?:<787 9 -;7<777 project pays back
during year 3
 0 Pay!ack 9 2 years F %:<787?:<787 9 2A%+ years
• Do we accept or reject the project? 
 
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ecision Criteria &est - Pay!ack
• oes the pay!ack rule account #or the time value o# money
• oes the pay!ack rule account #or the risk o# the cash #lo$s
• oes the pay!ack rule provide an indication a!out the increase in value
 
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 0  (d1usts #or uncertainty o# later cash #lo$s
 0 *iased to$ards li/uidity
money
 0 I"nores cash #lo$s !eyond the cuto## date
 
 (vera"e (ccountin" 'eturn
• &here are many di##erent de#initions #or avera"e accountin" return
• &he one used in the !ook is6  0 (vera"e net income avera"e !ook value
 0 Note that the avera"e !ook value depends on ho$ the asset is depreciatedA
• Need to have a tar"et cuto## rate
 
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•  (ssume $e re/uire an avera"e accountin" return o# 23@
•  (vera"e Net Income6 DG:%<;27 F %<%77 F 2?<:77E % 9 G:3<%+7
•  ((' 9 G:3<%+7 >2<777 9 A2:% 9 2:A%@
• Do we accept or reject the project? 
 
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• oes the ((' rule account #or the time value o# money
• oes the ((' rule account #or the risk o# the cash #lo$s
• oes the ((' rule provide an indication a!out the increase in value
 
 0 Needed in#ormation $ill usually !e availa!le
• isadvanta"es  0 Not a true rate o#
return= time value o# money is i"nored
 0 ses an ar!itrary !enchmark cuto## rate
 
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• &his is the most important alternative to NPV
• It is o#ten used in practice and is intuitively appealin"
 
I'' 0 e#inition and ecision 'ule
• e#inition6 I'' is the return that makes the NPV 9 7
• ecision 'ule6 Accept the project if the
IRR is reater than the re"#ired ret#rn
 
Computin" I'' or the Pro1ect
• I# you do not have a #inancial calculator< then this !ecomes a trial-and-error process
• Calculator  4nter the cash #lo$s as you did $ith NPV
Press I'' and then CP&
I'' 9 :;A:%@ H :2@ re/uired return
• Do we accept or reject the project? 
 
IRR = 16.13%
ecision Criteria &est - I''
• oes the I'' rule account #or the time value o# money
• oes the I'' rule account #or the risk o# the cash #lo$s
• oes the I'' rule provide an indication a!out the increase in value
 
• Kno$in" a return is intuitively appealin"
 
Summary
 
Calculatin" I''s .ith a Spreadsheet
• 5ou start $ith the cash #lo$s the same as you did #or the NPV
• 5ou use the I'' #unction
 0 5ou #irst enter your ran"e o# cash #lo$s< !e"innin" $ith the initial cash #lo$
 0 5ou can enter a "uess< !ut it is not necessary
 
• NPV and I'' $ill "enerally "ive us the same decision
• 4)ceptions
 0 Nonconventional cash #lo$s 0 cash #lo$ si"ns chan"e more than once
 0 Jutually e)clusive pro1ects • Initial investments are su!stantially di##erent
• &imin" o# cash #lo$s is su!stantially di##erent
 
I'' and Nonconventional Cash lo$s
• .hen the cash #lo$s chan"e si"ns more than once< there is more than one I''
 
 (nother 4)ample 0 Nonconventional Cash lo$s
• Suppose an investment $ill cost G?7<777 initially and $ill "enerate the #ollo$in" cash #lo$s6
 0 5ear :6 G:%2<777
 0 5ear 26 G:77<777
 0 5ear %6 -G:37<777
• &he re/uired return is :3@A
• Should $e accept or re1ect the pro1ect
 
 
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Summary o# ecision 'ules
• &he NPV is positive at a re/uired return o# :3@< so you should Accept 
• I# you use the #inancial calculator< you $ould "et an I'' o# :7A::@ $hich $ould tell you to Reject 
 
I'' and Jutually 4)clusive Pro1ects
• Jutually e)clusive pro1ects  0 I# you choose one< you cant choose the other 
 0 4)ample6 5ou can choose to attend "raduate school ne)t year at either Barvard or Stan#ord< !ut not !oth
• Intuitively< you $ould use the #ollo$in" decision rules6  0 NPV 0 choose the pro1ect $ith the hi"her NPV
 
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Period Pro1ect  (
.hich pro1ect should you accept and $hy
 
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I'' #or * 9 22A:>@
Crossover Point 9 ::A8@
8-%3
Con#licts *et$een NPV and I'' • NPV directly measures the increase in
value to the #irm
• .henever there is a con#lict !et$een NPV and another decision rule< you should always use NPV
• I'' is unrelia!le in the #ollo$in" situations
 0 Non-conventional cash #lo$s
 0 Jutually e)clusive pro1ects
Jodi#ied Internal 'ate o# 'eturn DJI''E
• Compute I'' o# modi#ied cash #lo$s • Controls #or some pro!lems $ith I'' • iscountin" (pproach 0 iscount #uture
out#lo$s to present and add to C7
• 'einvestment (pproach - Compound all Cs e)cept the #irst one #or$ard to end
• Com!ination (pproach 0 iscount out#lo$s to present= compound in#lo$s to end
 
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• Pro1ect cash #lo$s6
• &ime 76 -G377 today= &ime :6 F G:<777= &ime 26 -G:77
• se com!ined method and ''' 9 ::@
• PV Dout#lo$sE 9 -G377 F -G:77D:A::E2 9 - G38:A:;
• V Din#lo$E 9 G:<777 ) :A:: 9 G:<::7
 
Pro#ita!ility Inde)
• Jeasures the !ene#it per unit cost< !ased on the time value o# money
 
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•  (dvanta"es  0 Closely related to
NPV< "enerally leadin" to identical decisions
 0 4asy to understand and communicate
 0 Jay !e use#ul $hen availa!le investment #unds are limited
• isadvanta"es  0 Jay lead to incorrect
decisions in comparisons o# mutually e)clusive investments
 
• .e should consider several investment criteria $hen makin" decisions
• NPV and I'' are the most commonly used primary investment criteria
• Pay!ack is a commonly used secondary investment criteria
 
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Luick Lui • Consider an investment that costs G:77<777 and
has a cash in#lo$ o# G23<777 every year #or 3 yearsA &he re/uired return is ?@ and the re/uired pay!ack is + yearsA
 0 .hat is the pay!ack period
 0 .hat is the NPV
 0 .hat is the I''
 0 Should $e accept the pro1ect
• .hat should !e the primary decision method
• .hen is the I'' rule unrelia!le
 
8-+2
Comprehensive Pro!lem
•  (n investment pro1ect has the #ollo$in" cash #lo$s6 C7 9 -:<777<777= C7: 0 C78 9 277<777 each
• I# the re/uired rate o# return is :2@< $hat decision should !e made usin" NPV
• Bo$ $ould the I'' decision rule !e used #or this pro1ect< and $hat decision $ould !e reached
• Bo$ are the a!ove t$o decisions related