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Net Present Value
and OtherInvestment Criteria
Chapter 9
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9.2 Key Concepts and Skills
• Be able to compute payback and discounted payback and understand their shortcomings
• Understand accounting rates of return and
their shortcomings• Be able to compute the internal rate of return
and understand its strengths and weaknesses
• Be able to compute the net present value andunderstand why it is the best decision criterion
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9.3 Chapter Outline
• Net resent !alue• "he ayback #ule
• "he $iscounted ayback
• "he %verage %ccounting #eturn• "he &nternal #ate of #eturn
• "he rofitability &nde'
• "he ractice of (apital Budgeting
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9.) Good Decision Criteria
• *e need to ask ourselves the following+uestions when evaluating decision criteria
, $oes the decision rule ad-ust for the time value of
money
, $oes the decision rule ad-ust for risk
, $oes the decision rule provide information on
whether we are creating value for the firm
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9./ Project Eample In!ormation
• 0ou are looking at a new pro-ect and you haveestimated the following cash flows1 , 0ear 1 ( 4 567/8
, 0ear 61 ( 4 73862 N& 4 63872
, 0ear 21 ( 4 :8; N& 4 383
, 0ear 31 ( 4 968; N& 4 2986
, %verage Book !alue 4 :28
• 0our re+uired return for assets of this risk is62
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9.7 Net Present Value
• "he difference between the market value of a pro-ect and its cost
• =ow much value is created from undertaking
an investment , "he first step is to estimate the e'pected future
cash flows.
, "he second step is to estimate the re+uired return
for pro-ects of this risk level.
, "he third step is to find the present value of the
cash flows and subtract the initial investment.
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9.: NPV " Decision #ule
• If the NPV is positive, accept the project • % positive N! means that the pro-ect is
e'pected to add value to the firm and will
therefore increase the wealth of the owners.• >ince our goal is to increase owner wealth8
N! is a direct measure of how well this
pro-ect will meet our goal.
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9.; Computin$ NPV !or the Project
• Using the formulas1 , N! 4 [email protected] :8;[email protected] 968;?
@6.62A3 , 67/8 4 62872:.)2
•Using the calculator1 , ( 4 567/8 (6 4 73862 6 4 6 (2 4
:8; 2 4 6 (3 4 968; 3 4 6 N! & 4
62 (" N! 4 62872:.)2
• Do we accept or reject the project?
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9.9 Decision Criteria %est & NPV
• $oes the N! rule account for the time valueof money
• $oes the N! rule account for the risk of the
cash flows• $oes the N! rule provide an indication about
the increase in value
• >hould we consider the N! rule for our primary decision criteria
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9.6 Calculatin$ NPVs 'ith a Spreadsheet
• >preadsheets are an e'cellent way to compute N!s8 especially when you have to compute
the cash flows as well.
• Using the N! function , "he first component is the re+uired return enteredas a decimal
, "he second component is the range of cash flows
beginning with year 1
, >ubtract the initial investment after computing the
N!
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9.66 Pay(ack Period
• =ow long does it take to get the initial cost back in a nominal sense
• (omputation
, Cstimate the cash flows , >ubtract the future cash flows from the initial cost
until the initial investment has been recovered
• $ecision #ule , Accept if the payback period
is less than some preset limit
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9.62 Computin$ Pay(ack )or %he Project
• %ssume we will accept the pro-ect if it pays back within two years.
, 0ear 61 67/8 , 73862 4 668;; still to
recover
, 0ear 21 668;; , :8; 4 368; still to recover
, 0ear 31 368; , 968; 4 578 project pays
back in year 3
• Do we accept or reject the project?
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9.63 Decision Criteria %est & Pay(ack
• $oes the payback rule account for the timevalue of money
• $oes the payback rule account for the risk of
the cash flows• $oes the payback rule provide an indication
about the increase in value
• >hould we consider the payback rule for our primary decision criteria
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9.6) *dvanta$es and Disadvanta$es o! Pay(ack
• %dvantages
, Casy to understand
, %d-usts for uncertainty
of later cash flows
, Biased towards li+uidity
• $isadvantages
, &gnores the time value of
money
, #e+uires an arbitrary
cutoff point , &gnores cash flows
beyond the cutoff date
, Biased against long5term
pro-ects8 such asresearch and
development8 and new
pro-ects
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9.6/ Discounted Pay(ack Period
• (ompute the present value of each cash flowand then determine how long it takes to
payback on a discounted basis
•(ompare to a specified re+uired period
• $ecision #ule 5 Accept the project if it pays
back on a discounted basis within the
specified time
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9.67 Computin$ Discounted Pay(ack !or the Project
• %ssume we will accept the pro-ect if it pays back on a discounted basis in 2 years.
• (ompute the ! for each cash flow and
determine the payback period usingdiscounted cash flows
, 0ear 61 67/8 , 73862?6.626 4 6;87)3
, 0ear 21 6;87)3 , :8;?6.622 4 /2822
, 0ear 31 /2822 , 968;?6.623 4 562872: pro-ect
pays back in year 3
• Do we accept or reject the project?
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9.6: Decision Criteria %est " Discounted Pay(ack
• $oes the discounted payback rule account forthe time value of money
• $oes the discounted payback rule account for
the risk of the cash flows• $oes the discounted payback rule provide an
indication about the increase in value
• >hould we consider the discounted paybackrule for our primary decision criteria
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9.6; *dvanta$es and Disadvanta$es o! Discounted Pay(ack
• %dvantages
, &ncludes time value of
money
, Casy to understand
, $oes not accept negativeestimated N!
investments
, Biased towards li+uidity
• $isadvantages
, Day re-ect positive N!
investments
, #e+uires an arbitrary
cutoff point , &gnores cash flows
beyond the cutoff point
, Biased against long5term
pro-ects8 such as #E$and new products
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9.69 *vera$e *ccountin$ #eturn
• "here are many different definitions foraverage accounting return
• "he one used in the book is1 , %verage net income ? average book value
, Note that the average book value depends on howthe asset is depreciated.
• Need to have a target cutoff rate
• $ecision #ule1 Accept the project if the AAis !reater than a preset rate"
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9.2 Computin$ **# )or %he Project
• %ssume we re+uire an average accountingreturn of 2/<
• %verage Net &ncome1
, @63872 383 2986A ? 3 4 6/83)• %%# 4 6/83) ? :28 4 .263 4 26.3<
• Do we accept or reject the project?
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9.26 Decision Criteria %est & **#
• $oes the %%# rule account for the time valueof money
• $oes the %%# rule account for the risk of the
cash flows• $oes the %%# rule provide an indication
about the increase in value
• >hould we consider the %%# rule for our primary decision criteria
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9.22 *dvanta$es and Disadvanta$es o! **#
• %dvantages
, Casy to calculate
, Needed information will
usually be available
• $isadvantages
, Not a true rate of return
time value of money is
ignored
, Uses an arbitrary
benchmark cutoff rate
, Based on accounting net
income and book values8
not cash flows and
market values
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9.23 Internal #ate o! #eturn
• "his is the most important alternative to N!• &t is often used in practice and is intuitively
appealing
• &t is based entirely on the estimated cash flowsand is independent of interest rates found
elsewhere
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9.2) I## " De!inition and Decision #ule
• $efinition1 # is the return that makes the N! 4
• $ecision #ule1 Accept the project if the I
is !reater than the re#uired return
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9.2/ Computin$ I## )or %he Project
• &f you do not have a financial calculator8 thenthis becomes a trial and error process
• (alculator
, Cnter the cash flows as you did with N! , ress # and then ("
, # 4 67.63< F 62< re+uired return
• Do we accept or reject the project?
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9.27 NPV Pro!ile )or %he Project
# 4 67.63<
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9.2: Decision Criteria %est & I##
• $oes the # rule account for the time valueof money
• $oes the # rule account for the risk of the
cash flows• $oes the # rule provide an indication about
the increase in value
• >hould we consider the # rule for our primary decision criteria
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9.29 Summary o! Decisions )or %he Project
Summary
Net resent !alue Accept
ayback eriod eject
$iscounted ayback eriod eject
%verage %ccounting #eturn eject
&nternal #ate of #eturn Accept
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9.3 Calculatin$ I##s +ith * Spreadsheet
• 0ou start with the cash flows the same as youdid for the N!
• 0ou use the # function
, 0ou first enter your range of cash flows8 beginningwith the initial cash flow
, 0ou can enter a guess8 but it is not necessary
, "he default format is a whole percent , you will
normally want to increase the decimal places to atleast two
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9.36 NPV Vs, I##
• N! and # will generally give us the samedecision
• C'ceptions
, Non5conventional cash flows , cash flow signschange more than once
, Dutually e'clusive pro-ects
• &nitial investments are substantially different
• "iming of cash flows is substantially different
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9.32 I## and Non&conventional Cash )lo's
•*hen the cash flows change sign more thanonce8 there is more than one #
• *hen you solve for # you are solving for
the root of an e+uation and when you cross the
'5a'is more than once8 there will be more than
one return that solves the e+uation
• &f you have more than one #8 which one do
you use to make your decision
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9.33 *nother Eample " Non&conventional Cash )lo's
•>uppose an investment will cost I98initially and will generate the following cash
flows1
, 0ear 61 6328
, 0ear 21 68
, 0ear 31 56/8
• "he re+uired return is 6/hould we accept or re-ect the pro-ect
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9.3) NPV Pro!ile
# 4 6.66< and )2.77<
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9.3/ Summary o! Decision #ules
•"he N! is positive at a re+uired return of6/
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9.37 I## and -utually Eclusive Projects
•Dutually e'clusive pro-ects , &f you choose one8 you canHt choose the other
, C'ample1 0ou can choose to attend graduate
school ne't year at either =arvard or >tanford8 but
not both
• &ntuitively you would use the following
decision rules1
, N! , choose the pro-ect with the higher N!
, # , choose the pro-ect with the higher #
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9.3: Eample +ith -utually Eclusive Projects
eriod ro-ect % ro-ect B
5/ 5)
6 32/ 32/
2 32/ 2
# 69.)3< 22.6:<
N! 7)./ 7.:)
"he re+uired returnfor both pro-ects is
6
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9.3; NPV Pro!iles
# for % 4 69.)3<
# for B 4 22.6:<
(rossover oint 4 66.;<
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9.39 Con!licts .et'een NPV and I##
• N! directly measures the increase in value tothe firm
• *henever there is a conflict between N! and
another decision rule8 you should always use
N!
• # is unreliable in the following situations
, Non5conventional cash flows
, Dutually e'clusive pro-ects
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9.) Pro!ita(ility Inde
•Deasures the benefit per unit cost8 based onthe time value of money
• % profitability inde' of 6.6 implies that for
every I6 of investment8 we create an
additional I.6 in value
• "his measure can be very useful in situations
where we have limited capital
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9.)6 *dvanta$es and Disadvanta$es o! Pro!ita(ility Inde
• %dvantages
, (losely related to N!8
generally leading to
identical decisions
, Casy to understand and
communicate
, Day be useful when
available investment
funds are limited
• $isadvantages
, Day lead to incorrect
decisions in comparisons
of mutually e'clusive
investments
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9.)2 Capital .ud$etin$ In Practice
•*e should consider several investment criteriawhen making decisions
• N! and # are the most commonly used
primary investment criteria
• ayback is a commonly used secondary
investment criteria
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9.)3 Summary " Discounted Cash )lo' Criteria
• Net present value
, $ifference between market value and cost , "ake the pro-ect if the N! is positive , =as no serious problems , referred decision criterion
• &nternal rate of return
, $iscount rate that makes N! 4 , "ake the pro-ect if the # is greater than re+uired return , >ame decision as N! with conventional cash flows , # is unreliable with non5conventional cash flows or mutually
e'clusive pro-ects• rofitability &nde'
, Benefit5cost ratio , "ake investment if & F 6 , (annot be used to rank mutually e'clusive pro-ects , Day be use to rank pro-ects in the presence of capital rationing
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9.)) Summary " Pay(ack Criteria
• ayback period
, Kength of time until initial investment is recovered
, "ake the pro-ect if it pays back in some specified period
, $oesnHt account for time value of money and there is an
arbitrary cutoff period• $iscounted payback period
, Kength of time until initial investment is recovered on a
discounted basis
, "ake the pro-ect if it pays back in some specified period , "here is an arbitrary cutoff period
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9.)/ Summary " *ccountin$ Criterion
• %verage %ccounting #eturn
, Deasure of accounting profit relative to book
value
, >imilar to return on assets measure
, "ake the investment if the %%# e'ceeds some
specified return level
, >erious problems and should not be used
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9.)7 /uick /ui0
• (onsider an investment that costs I68 and has acash inflow of I2/8 every year for / years. "here+uired return is 9< and re+uired payback is )years.
, *hat is the payback period
, *hat is the discounted payback period
, *hat is the N!
, *hat is the #
, >hould we accept the pro-ect• *hat decision rule should be the primary decision
method
• *hen is the # rule unreliable