Capital Budgeting Tools

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Net Present Value and Other Net Present Value and Other

Investment CriteriaInvestment Criteria



11

Key Concepts and SkillsKey Concepts and Skills

Be able to compute payback and discountedBe able to compute payback and discountedpayback and understand their shortcomingspayback and understand their shortcomings

Understand accounting rates of return and their Understand accounting rates of return and their

shortcomingsshortcomings Be able to compute the internal rate of return andBe able to compute the internal rate of return and

understand its strengths and weaknessesunderstand its strengths and weaknesses

Be able to compute the net present value andBe able to compute the net present value and

understand why it is the best decision criterionunderstand why it is the best decision criterion



22

Chapter OutlineChapter Outline

Net Present ValueNet Present Value

The Payback RuleThe Payback Rule

The Discounted PaybackThe Discounted Payback The Average Accounting ReturnThe Average Accounting Return

The Internal Rate of ReturnThe Internal Rate of Return

The Profitability IndexThe Profitability Index The Practice of Capital BudgetingThe Practice of Capital Budgeting



33

Good Decision CriteriaGood Decision Criteria

We need to ask ourselves the followingWe need to ask ourselves the followingquestions when evaluating capitalquestions when evaluating capital

budgeting decision rulesbudgeting decision rules Does the decision rule adjust for the timeDoes the decision rule adjust for the time

value of money?value of money?

Does the decision rule adjust for risk?Does the decision rule adjust for risk?

Does the decision rule provide information onDoes the decision rule provide information onwhether we are creating value for the firm?whether we are creating value for the firm?



44

Project Example InformationProject Example Information

You are looking at a new project and you haveYou are looking at a new project and you haveestimated the following cash flows:estimated the following cash flows:

Year 0:Year 0: CF =CF = --165,000165,000

Year 1:Year 1: CF = 63,120; NI = 13,620CF = 63,120; NI = 13,620



Average Book Value = 72,000 Average Book Value = 72,000

Your required return for assets of this risk isYour required return for assets of this risk is12%.12%.



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Net Present ValueNet Present Value

The difference between the market value of aThe difference between the market value of aproject and its costproject and its cost

How much value is created from undertaking anHow much value is created from undertaking an

investment?investment? The first step is to estimate the expected future cashThe first step is to estimate the expected future cash

flows.flows.

The second step is to estimate the required return for The second step is to estimate the required return for projects of this risk level.projects of this risk level.

The third step is to find the present value of the cashThe third step is to find the present value of the cashflows and subtract the initial investment.flows and subtract the initial investment.



66

NPVNPV ± ± Decision RuleDecision Rule

If the NPV is positive, accept the project If the NPV is positive, accept the project

A positive NPV means that the project is A positive NPV means that the project isexpected to add value to the firm and willexpected to add value to the firm and will

therefore increase the wealth of the owners.therefore increase the wealth of the owners.

Since our goal is to increase owner wealth, NPVSince our goal is to increase owner wealth, NPVis a direct measure of how well this project willis a direct measure of how well this project will

meet our goal.meet our goal.



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Computing NPV for the ProjectComputing NPV for the Project

Using the formulas:Using the formulas:

NPV = 63,120/(1.12) + 70,800/(1.12)NPV = 63,120/(1.12) + 70,800/(1.12)22 ++91,080/(1.12)91,080/(1.12)33 ± ± 165,000 = 12,627.42165,000 = 12,627.42

Using the calculator:Using the calculator: CFCF00 == --165,000; C01 = 63,120; F01 = 1; C02 =165,000; C01 = 63,120; F01 = 1; C02 =

70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12;70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12;CPT NPV = 12,627.41CPT NPV = 12,627.41

Do we accept or reject the project? Do we accept or reject the project?



88

Decision Criteria TestDecision Criteria Test -- NPVNPV

Does the NPV rule account for the time value of Does the NPV rule account for the time value of money?money?

Does the NPV rule account for the risk of theDoes the NPV rule account for the risk of the

cash flows?cash flows?

Does the NPV rule provide an indication aboutDoes the NPV rule provide an indication aboutthe increase in value?the increase in value?

Should we consider the NPV rule for our primaryShould we consider the NPV rule for our primarydecision rule?decision rule?



99

Calculating NPVs with aCalculating NPVs with a

SpreadsheetSpreadsheet Spreadsheets are an excellent way to computeSpreadsheets are an excellent way to compute

NPVs, especially when you have to computeNPVs, especially when you have to computethe cash flows as well.the cash flows as well.

Using the NPV functionUsing the NPV function The first component is the required return enteredThe first component is the required return entered

as a decimalas a decimal

The second component is the range of cash flowsThe second component is the range of cash flows

beginning with year 1beginning with year 1 Subtract the initial investment after computing theSubtract the initial investment after computing the

NPVNPV



1010

Payback PeriodPayback Period

How long does it take to get the initial cost backHow long does it take to get the initial cost backin a nominal sense?in a nominal sense?

ComputationComputation

Estimate the cash flowsEstimate the cash flows

Subtract the future cash flows from the initial cost untilSubtract the future cash flows from the initial cost untilthe initial investment has been recoveredthe initial investment has been recovered

Decision RuleDecision Rule ± ± Accept if the payback period Accept if the payback period

is less than some preset limit is less than some preset limit



1111

Computing Payback for theComputing Payback for the

ProjectProject Assume we will accept the project if it pays back Assume we will accept the project if it pays back

within two years.within two years.

Year 1: 165,000Year 1: 165,000 ± ± 63,120 = 101,880 still to recover 63,120 = 101,880 still to recover

Year 2: 101,880Year 2: 101,880 ± ± 70,800 = 31,080 still to recover 70,800 = 31,080 still to recover

Year 3: 31,080Year 3: 31,080 ± ± 91,080 =91,080 = --60,00060,000 project pays back project pays back

in year 3in year 3




1212

Decision Criteria TestDecision Criteria Test -- PaybackPayback

Does the payback rule account for the timeDoes the payback rule account for the timevalue of money?value of money?

Does the payback rule account for the risk of theDoes the payback rule account for the risk of the


Does the payback rule provide an indicationDoes the payback rule provide an indicationabout the increase in value?about the increase in value?

Should we consider the payback rule for our Should we consider the payback rule for our primary decision rule?primary decision rule?



1313

Advantages and Disadvantages Advantages and Disadvantagesof Paybackof Payback

Advantages Advantages

Easy to understandEasy to understand

Adjusts for uncertainty Adjusts for uncertainty

of later cash flowsof later cash flows Biased toward liquidityBiased toward liquidity

DisadvantagesDisadvantages Ignores the time valueIgnores the time value

of moneyof money

Requires an arbitraryRequires an arbitrarycutoff pointcutoff point

Ignores cash flowsIgnores cash flowsbeyond the cutoff datebeyond the cutoff date

Biased against longBiased against long--term projects, such asterm projects, such asresearch andresearch anddevelopment, and newdevelopment, and newprojectsprojects



1414

Discounted Payback PeriodDiscounted Payback Period

Compute the present value of each cash flowCompute the present value of each cash flowand then determine how long it takes to payand then determine how long it takes to payback on a discounted basisback on a discounted basis

Compare to a specified required periodCompare to a specified required period

Decision RuleDecision Rule -- Accept the project if it pays Accept the project if it pays

back on a discounted basis within theback on a discounted basis within the

specified timespecified time



1515

Computing Discounted Payback for Computing Discounted Payback for the Projectthe Project

Assume we will accept the project if it pays back on a Assume we will accept the project if it pays back on adiscounted basis in 2 years.discounted basis in 2 years.

Compute the PV for each cash flow and determine theCompute the PV for each cash flow and determine thepayback period using discounted cash flowspayback period using discounted cash flows Year 1: 165,000Year 1: 165,000 ± ± 63,120/1.1263,120/1.1211 = 108,643= 108,643

Year 2: 108,643 Year 2: 108,643 ± ± 70,800/1.1270,800/1.1222 = 52,202= 52,202

Year 3: 52,202 Year 3: 52,202 ± ± 91,080/1.1291,080/1.1233 == --12,627 project pays back in12,627 project pays back inyear 3year 3




1616

Decision Criteria TestDecision Criteria Test ± ± DiscountedDiscounted

PaybackPayback Does the discounted payback rule account for the timeDoes the discounted payback rule account for the time

value of money?value of money?

Does the discounted payback rule account for the riskDoes the discounted payback rule account for the risk

of the cash flows?of the cash flows?

Does the discounted payback rule provide an indicationDoes the discounted payback rule provide an indicationabout the increase in value?about the increase in value?

Should we consider the discounted payback rule for Should we consider the discounted payback rule for

our primary decision rule?our primary decision rule?



1717

Advantages and Disadvantages of Advantages and Disadvantages of Discounted PaybackDiscounted Payback


Includes time value of Includes time value of moneymoney

Easy to understandEasy to understand Does not acceptDoes not accept

negative estimatednegative estimatedNPV investmentsNPV investments

when all future cashwhen all future cashflows are positiveflows are positive

Biased towardsBiased towardsliquidityliquidity

DisadvantagesDisadvantages

May reject positiveMay reject positiveNPV investmentsNPV investments

Requires an arbitraryRequires an arbitrarycutoff pointcutoff point

Ignores cash flowsIgnores cash flowsbeyond the cutoff pointbeyond the cutoff point

Biased against longBiased against long--term projects, such asterm projects, such asR&D and newR&D and newproductsproducts



1818

Average Accounting Return Average Accounting Return

There are many different definitions for averageThere are many different definitions for averageaccounting returnaccounting return

The one used in the book is:The one used in the book is:

Average net income / average book value Average net income / average book value

Note that the average book value depends on howNote that the average book value depends on howthe asset is depreciated.the asset is depreciated.

Need to have a target cutoff rateNeed to have a target cutoff rate

Decision Rule:Decision Rule: Accept the project if the AAR Accept the project if the AAR

is greater than a preset rate.is greater than a preset rate.



1919

Computing AAR for the ProjectComputing AAR for the Project

Assume we require an average accounting Assume we require an average accountingreturn of 25%return of 25%

Average Net Income: Average Net Income: (13,620 + 3,300 + 29,100) / 3 = 15,340(13,620 + 3,300 + 29,100) / 3 = 15,340

AAR = 15,340 / 72,000 = .213 = 21.3% AAR = 15,340 / 72,000 = .213 = 21.3%

Do we accept or reject the project?




2020

Decision Criteria TestDecision Criteria Test -- AAR AAR

Does the AAR rule account for the time value of Does the AAR rule account for the time value of money?money?

Does the AAR rule account for the risk of theDoes the AAR rule account for the risk of the


Does the AAR rule provide an indication aboutDoes the AAR rule provide an indication aboutthe increase in value?the increase in value?

Should we consider the AAR rule for our primaryShould we consider the AAR rule for our primarydecision rule?decision rule?



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Advantages and Disadvantages Advantages and Disadvantages

of AARof AAR Advantages Advantages

Easy to calculateEasy to calculate

Needed informationNeeded information

will usually bewill usually beavailableavailable


Not a true rate of Not a true rate of return; time value of return; time value of

money is ignoredmoney is ignored Uses an arbitraryUses an arbitrary

benchmark cutoff ratebenchmark cutoff rate

Based on accountingBased on accounting

net income and booknet income and bookvalues, not cash flowsvalues, not cash flowsand market valuesand market values



2222

Internal Rate of ReturnInternal Rate of Return

This is the most important alternative toThis is the most important alternative toNPVNPV

It is often used in practice and is intuitivelyIt is often used in practice and is intuitivelyappealingappealing

It is based entirely on the estimated cashIt is based entirely on the estimated cashflows and is independent of interest ratesflows and is independent of interest ratesfound elsewherefound elsewhere



2323

IRRIRR ± ± Definition and DecisionDefinition and Decision

RuleRule Definition: IRR is the return that makes theDefinition: IRR is the return that makes the

NPV = 0NPV = 0

Decision Rule:Decision Rule: Accept the project if the I RR Accept the project if the I RR is greater than the required returnis greater than the required return



2424

Computing IRR for the ProjectComputing IRR for the Project

If you do not have a financial calculator , then thisIf you do not have a financial calculator , then thisbecomes a trial and error processbecomes a trial and error process

Calculator Calculator

Enter the cash flows as you did with NPVEnter the cash flows as you did with NPV

Press IRR and then CPTPress IRR and then CPT

IRR = 16.13% > 12% required returnIRR = 16.13% > 12% required return





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NPV Profile for the ProjectNPV Profile for the Project

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Discount Rate

N P V

IRR = 16.13%



2626

Decision Criteria TestDecision Criteria Test -- IRRIRR

Does the IRR rule account for the time value of Does the IRR rule account for the time value of money?money?

Does the IRR rule account for the risk of theDoes the IRR rule account for the risk of the


Does the IRR rule provide an indication aboutDoes the IRR rule provide an indication aboutthe increase in value?the increase in value?

Should we consider the IRR rule for our primaryShould we consider the IRR rule for our primarydecision criteria?decision criteria?



2727

Advantages of IRR Advantages of IRR

Knowing a return is intuitively appealingKnowing a return is intuitively appealing

It is a simple way to communicate the value of aIt is a simple way to communicate the value of aproject to someone who doesn¶t know all theproject to someone who doesn¶t know all the

estimation detailsestimation details

If the IRR is high enough, you may not need toIf the IRR is high enough, you may not need toestimate a required return, which is often aestimate a required return, which is often adifficult taskdifficult task



2828

Summary of Decisions for theSummary of Decisions for the

ProjectProjectSummarySummary

Net Present ValueNet Present Value Accept Accept

Payback PeriodPayback Period R eject R eject

Discounted Payback PeriodDiscounted Payback Period R eject R eject

Average Accounting Return Average Accounting Return R eject R eject

Internal Rate of ReturnInternal Rate of Return Accept Accept



2929

Calculating IRRs With ACalculating IRRs With A

SpreadsheetSpreadsheet You start with the cash flows the same as youYou start with the cash flows the same as you

did for the NPVdid for the NPV

You use the IRR functionYou use the IRR function

You first enter your range of cash flows, beginningYou first enter your range of cash flows, beginningwith the initial cash flowwith the initial cash flow

You can enter a guess, but it is not necessaryYou can enter a guess, but it is not necessary

The default format is a whole percentThe default format is a whole percent ± ± you willyou willnormally want to increase the decimal places to atnormally want to increase the decimal places to atleast twoleast two



3030

NPV vs. IRRNPV vs. IRR

NPV and IRR will generally give us theNPV and IRR will generally give us thesame decisionsame decision

ExceptionsExceptions NonNon--conventional cash flowsconventional cash flows ± ± cash flowcash flow

signs change more than oncesigns change more than once

Mutually exclusive projectsMutually exclusive projects

�� Initial investments are substantially differentInitial investments are substantially different

�� Timing of cash flows is substantially differentTiming of cash flows is substantially different



3131

IRR and NonIRR and Non--conventional Cashconventional Cash

FlowsFlows When the cash flows change sign more thanWhen the cash flows change sign more than

once, there is more than one IRRonce, there is more than one IRR

When you solve for IRR you are solving for theWhen you solve for IRR you are solving for theroot of an equation and when you cross the xroot of an equation and when you cross the x--axis more than once, there will be more thanaxis more than once, there will be more thanone return that solves the equationone return that solves the equation

If you have more than one IRR, which one doIf you have more than one IRR, which one doyou use to make your decision?you use to make your decision?



3232

Another Example Another Example ± ± NonNon--conventional Cash Flowsconventional Cash Flows

Suppose an investment will cost $90,000Suppose an investment will cost $90,000initially and will generate the following cashinitially and will generate the following cashflows:flows:

Year 1: 132,000Year 1: 132,000

Year 2: 100,000Year 2: 100,000

Year 3:Year 3: --150,000150,000

The required return is 15%.The required return is 15%. Should we accept or reject the project?Should we accept or reject the project?



3333

NPV ProfileNPV Profile

($10,000.00)

($8,000.00)

($6,000.00)

($4,000.00)

($2,000.00)

$0.00

$2,000.00

$4,000.00

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55

Discount Rate

N P V

IRR = 10.11% and 42.66%



3434

Summary of Decision RulesSummary of Decision Rules

The NPV is positive at a required return of The NPV is positive at a required return of 15%, so you should15%, so you should Accept Accept

If you use the financial calculator , youIf you use the financial calculator , youwould get an IRR of 10.11% which wouldwould get an IRR of 10.11% which wouldtell you totell you to R eject R eject

You need to recognize that there are nonYou need to recognize that there are non--conventional cash flows and look at theconventional cash flows and look at theNPV profileNPV profile



3535

IRR and Mutually ExclusiveIRR and Mutually Exclusive

ProjectsProjects Mutually exclusive projectsMutually exclusive projects

If you choose one, you can¶t choose the other If you choose one, you can¶t choose the other

Example: You can choose to attend graduate school at either Example: You can choose to attend graduate school at either

Harvard or Stanford, but not bothHarvard or Stanford, but not both Intuitively you would use the following decision rules:Intuitively you would use the following decision rules:

NPVNPV ± ± choose the project with the higher NPVchoose the project with the higher NPV

IRRIRR ± ± choose the project with the higher IRRchoose the project with the higher IRR



3636

Example With Mutually ExclusiveExample With Mutually ExclusiveProjectsProjects

PeriodPeriod ProjectProject A A

ProjectProjectBB

00 --500500 --400400

11 325325 325325

22 325325 200200

IRRIRR 19.43%19.43% 22.17%22.17%

NPVNPV 64.0564.05 60.7460.74

The r equir ed r eturn

for both projects is

10%.

Which project

should you acce pt

and why?



3737

NPV ProfilesNPV Profiles

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00

$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

N P V A

B

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%



3838

Conflicts Between NPV and IRRConflicts Between NPV and IRR

NPV directly measures the increase in value toNPV directly measures the increase in value tothe firmthe firm

Whenever there is a conflict between NPV andWhenever there is a conflict between NPV and

another decision rule, you shouldanother decision rule, you should alwaysalways useuseNPVNPV

IRR is unreliable in the following situationsIRR is unreliable in the following situations

NonNon--conventional cash flowsconventional cash flows

Mutually exclusive projectsMutually exclusive projects



3939

Profitability IndexProfitability Index

Measures the benefit per unit cost, basedMeasures the benefit per unit cost, basedon the time value of moneyon the time value of money

A profitability index of 1.1 implies that for A profitability index of 1.1 implies that for every $1 of investment, we create anevery $1 of investment, we create anadditional $0.10 in valueadditional $0.10 in value

This measure can be very useful inThis measure can be very useful insituations in which we have limited capitalsituations in which we have limited capital



4040

Advantages and Disadvantages Advantages and Disadvantagesof Profitability Indexof Profitability Index


Closely related toClosely related toNPV, generallyNPV, generally

leading to identicalleading to identicaldecisionsdecisions

Easy to understandEasy to understandand communicateand communicate

May be useful whenMay be useful whenavailable investmentavailable investmentfunds are limitedfunds are limited


May lead to incorrectMay lead to incorrectdecisions indecisions in

comparisons of comparisons of mutually exclusivemutually exclusiveinvestmentsinvestments



4141

Capital Budgeting In PracticeCapital Budgeting In Practice

We should consider several investmentWe should consider several investmentcriteria when making decisionscriteria when making decisions

NPV and IRR are the most commonlyNPV and IRR are the most commonlyused primary investment criteriaused primary investment criteria

Payback is a commonly used secondaryPayback is a commonly used secondaryinvestment criteriainvestment criteria



4242

SummarySummary ± ± Discounted Cash FlowDiscounted Cash FlowCriteriaCriteria Net present valueNet present value

Difference between market value and costDifference between market value and cost Take the project if the NPV is positiveTake the project if the NPV is positive Has no serious problemsHas no serious problems Preferred decision criterionPreferred decision criterion

Internal rate of returnInternal rate of return

Discount rate that makes NPV = 0Discount rate that makes NPV = 0 Take the project if the IRR is greater than the required returnTake the project if the IRR is greater than the required return Same decision as NPV with conventional cash flowsSame decision as NPV with conventional cash flows IRR is unreliable with nonIRR is unreliable with non--conventional cash flows or mutuallyconventional cash flows or mutually

exclusive projectsexclusive projects

Profitability IndexProfitability Index

BenefitBenefit--cost ratiocost ratio Take investment if PI > 1Take investment if PI > 1

Cannot be used to rank mutually exclusive projectsCannot be used to rank mutually exclusive projects May be used to rank projects in the presence of capital rationingMay be used to rank projects in the presence of capital rationing



4343

SummarySummary ± ± Payback CriteriaPayback Criteria Payback periodPayback period

Length of time until initial investment is recoveredLength of time until initial investment is recovered

Take the project if it pays back within some specified periodTake the project if it pays back within some specified period

Doesn¶t account for time value of money and there is anDoesn¶t account for time value of money and there is an

arbitrary cutoff periodarbitrary cutoff period Discounted payback periodDiscounted payback period

Length of time until initial investment is recovered on aLength of time until initial investment is recovered on adiscounted basisdiscounted basis

Take the project if it pays back in some specified periodTake the project if it pays back in some specified period

There is an arbitrary cutoff periodThere is an arbitrary cutoff period



4444

SummarySummary ± ± Accounting Accounting

CriterionCriterion Average Accounting Return Average Accounting Return

Measure of accounting profit relative to bookMeasure of accounting profit relative to bookvaluevalue

Similar to return on assets measureSimilar to return on assets measure

Take the investment if the AAR exceeds someTake the investment if the AAR exceeds somespecified return levelspecified return level

Serious problems and should not be usedSerious problems and should not be used



4545

Quick QuizQuick Quiz Consider an investment that costs $100,000 and has aConsider an investment that costs $100,000 and has a

cash inflow of $25,000 every year for 5 years. Thecash inflow of $25,000 every year for 5 years. Therequired return is 9% and required payback is 4 years.required return is 9% and required payback is 4 years.

What is the payback period?What is the payback period?

What is the discounted payback period?What is the discounted payback period?

What is the NPV?What is the NPV?

What is the IRR?What is the IRR?

Should we accept the project?Should we accept the project?

What decision rule should be the primary decisionWhat decision rule should be the primary decision

method?method? When is the IRR rule unreliable?When is the IRR rule unreliable?



4646

End of Chapter End of Chapter



4747

Comprehensive ProblemComprehensive Problem

An investment project has the following cash An investment project has the following cashflows: CF0 =flows: CF0 = --1,000,000; C01 1,000,000; C01 ± ± C08 = 200,000C08 = 200,000eacheach

If the required rate of return is1

2%,

whatIf the required rate of return is1

2%,

whatdecision should be made using NPV?decision should be made using NPV?

How would the IRR decision rule be used for How would the IRR decision rule be used for this project, and what decision would bethis project, and what decision would be

reached?reached? How are the above two decisions related?How are the above two decisions related?

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Capital Budgeting Tools