NET PRESENT VALUE ANDNET PRESENT VALUE ANDOTHER INVESTMENTOTHER INVESTMENT

CRITERIACRITERIACHAPTER 9CHAPTER 9

Created by David Moore, PhD

http://www.davidrmoore.com/presentations/www.davidrmoore.com

KEY CONCEPTSKEY CONCEPTS1. Net Present Value (NPV)2. Payback Period3. Internal Rate of Return (IRR)4. Investment criteria (accept/reject decision)5. Mutually Exclusive Projects and Non-conventional cash

�ows

CAPITAL BUDGETINGCAPITAL BUDGETING

PERSONAL CAPITAL BUDGETING EXAMPLESPERSONAL CAPITAL BUDGETING EXAMPLESGraduate School

How expensive is grad school?How long will it take?How much more will I make with a grad degree?What are the opportunity costs of wages while in gradschool?

Repair or Replace CarHow expensive is new car?How much are my expected repair bills going to bewith the old car?How long before the old car is inoperable?

CAPITAL BUDGETING TESLA EXAMPLECAPITAL BUDGETING TESLA EXAMPLE

EXAMPLE: COLLEGE CASH FLOWSEXAMPLE: COLLEGE CASH FLOWSAverage costs to attend a 4 year public university in the U.S. have risen fromabout 27,161 in 1996 to about 39,529 in 2016. As of 2018, the average annual earnings for a high school graduate were

48,000. The average starting annual earnings for a college graduate with abusiness degree were 62,000. For simplicity, let's ignore taxes and justassume these are all after-tax cash �ows. Assume that you complete the degree in 4 years. You work for 45 yearsafter attaining your degree and college salary grows at 3% annually. All cash�ows occur at the end of the period (e.g. no out�ows at t=0).

We will come back to this and use investment criteria to make decision.

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KEY POINTSKEY POINTSAnalysis of potential projects

Fixed AssetNew productEnter new market

Long-term decisionsLarge expendituresDi�cult/impossible to reverseDetermines �rm's strategic direction

DECISION CRITERIADECISION CRITERIA

GOOD DECISION CRITERIAGOOD DECISION CRITERIAAll cash �ows considered?TVM considered?Risk-adjusted?Ability to rank projects?Indicates added value to the �rm?

TOOLSTOOLS1. Net Present Value (NPV)2. Payback Period3. Internal Rate of Return

SAMPLE PROJECTSAMPLE PROJECTYou are looking at a new project and have estimated thefollowing cash �ows, net income and book value data:

Year Cash Flow

0 -165,000

1 63,120

2 70,800

3 91,080Required return = 12%

This project will be the example for all problem exhibits in

this chapter.

NET PRESENT VALUENET PRESENT VALUE

OVERVIEWOVERVIEWHow much value is created from undertaking an investment?

1. Estimate the expected future cash �ows.2. Estimate the required return for projects of this risk

level.3. Find the present value of the cash �ows and subtract the

initial investment to arrive at the Net Present Value.

CALCULATIONCALCULATION

Initial cost is often and is an out�ow.

NPV = ∑t=0

nCFt

(1 + r)t

CF0

DECISION RULEDECISION RULEIf NPV is positive, accept the project

What does a positive NPV mean?Project is expected to add value to the �rmWill increase the wealth of the owners

NPV is a direct measure of how well this project willmeet the goal of increasing shareholder wealth.

NPV FOR SAMPLE PROJECTNPV FOR SAMPLE PROJECT

Year Cash Flow Formula Discounted CF

0 -165,000 =(-165000)/1.12^0 -165,000.00

1 63,120 =(63120)/1.12^1 56,357.14

2 70,800 =(70800)/1.12^2 56,441.33

3 91,080 =(91080)/1.12^3 64,828.94

NPV = 12,627.41

NPV = ∑t=0

nCFt

(1 + r)t

CALCULATORCALCULATORGo to APPS, Finance, 7:npv(Function npv(rate, , )

First parameter = required return entered as apercentageSecond parameter = Cash �ow at time 0 (enter asnegative if out�ow)Third parameter=Cash �ows from time 1 on: enterusing List function

CF0 C − CF1 Ft

LISTS ON CALCULATORLISTS ON CALCULATORHow to make a list?

Enter {Enter Cash �ows separated by,Enter }Hit STOHit L1

⇒

EXCELEXCEL=NPV(rate, )

First parameter = required return entered as a decimalSecond parameter = range of cash �ows beginning withyear 1After computing NPV, subtract the initial investment (

)

C − CF1 Ft

CF0

RATIONALERATIONALENPV = PV in�ows – CostNPV=0 → Project's in�ows are "exactly su�cient torepay the invested capital and provide the required rateof return"NPV = net gain in shareholder wealth

DECISION RULEDECISION RULE

Accept Project if NPV > 0

PROS AND CONSPROS AND CONSPros

Meets all desirable criteriaConsiders all Cash FlowsConsiders Time Value of MoneyAdjusts for riskCan rank mutually exclusive projects

Directly related to �rm valueDominant method; always prevails

Consrelies heavily on correct discount rate

PAYBACK PERIODPAYBACK PERIOD

OVERVIEWOVERVIEWHow long does it take to recover the initial cost of a project?

Computation1. Estimate cash �ows2. Subtract the future cash �ows from the initial cost until

initial investment is recoveredA "break-even" type measure

COMPUTING PAYBACKCOMPUTING PAYBACKYear Cash Flow Cumulative Cash Flows

0 -165,000 -165000

1 63,120 -101,880

2 70,800 -31,080

3 91,080 60,000

Payback = 2 + 31080/91080 2.34 years

Payback = 2 + =2.34 years

Do we accept or reject the project?

3108091080

DECISION RULEDECISION RULE

Accept if the payback period is less than some preset limit

PROS AND CONSPROS AND CONSAdvantages

Easy to understandAdjusts for uncertainty oflater cash �owsBiased towards liquidityGood for small projects(< 10000)

DisadvantagesIgnores the time value ofmoneyRequires an arbitrarycuto� pointIgnores cash �ows beyondthe cuto� dateBiased against long-termprojects, such as researchand development

ASKS THE WRONG QUESTION!

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INTERNAL RATE OF RETURN (IRR)INTERNAL RATE OF RETURN (IRR)

OVERVIEWOVERVIEWMost important alternative to NPVWidely used in practiceIntuitively appealingBased entirely on the estimated cash �owsIndependent of interest rates

DEFINITIONDEFINITIONIRR = discount rate that makes the NPV = 0

Enter NPV = 0, solve for IRR:

NPV = ∑t=0

nCFt

(1 + r)t

COMPUTING IRRCOMPUTING IRRWithout a �nancial calculator or Excel, this becomes atrial-and-error processCalculator

Make list of the cash �ows as for NPVUse IRR(CFO,L1)IRR is found in Finance, option 8

DECISION CRITERIADECISION CRITERIA

Accept the project if the IRR is greater than the required return

EXAMPLEEXAMPLEYear Cash Flow

0 -165,000

1 63,120

2 70,800

3 91,080

=IRR( ) 16.13%

Accept or Reject?

C : CF0 F3

NPV PROFILENPV PROFILE

PROS AND CONSPROS AND CONSAdvantages

Intuitively appealing/Easyto communicate the valueof a projectIf the IRR is high enough,may not need to estimatea required returnConsiders all cash �owsConsiders time value ofmoneyProvides indication of risk

DisadvantagesCan produce multipleanswersCannot rank mutuallyexclusive projectsIgnores cash �ows beyondthe cuto� dateReinvestment assumption�awed

SUMMARY OF DECISIONSSUMMARY OF DECISIONSMethod Criteria Number DecisionNPV NPV 0 12,627.41 AcceptPayback Unknown 2.34 years ???IRR IRR Required Return 16.13% Accept

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NPV VS IRR: ISSUESNPV VS IRR: ISSUES

OVERVIEWOVERVIEWNPV and IRR will generally give the same decisionExceptions

Non-conventional cash �owsCash �ow sign changes more than once

Mutually exclusive projectsInitial investments are substantially di�erentTiming of cash �ows is substantially di�erentWill not reliably rank projects

NON-CONVENTIONAL CASH FLOWSNON-CONVENTIONAL CASH FLOWSCash �ows change sign more than once

Produces more than one IRRWhich one do you use to make your decision?

EXAMPLEEXAMPLESuppose an investment will cost 90,000 initially and will

generate the following cash �ows: Year 1: 132,000Year 2: 100,000Year 3: -150,000

The required return is 15%.

Should we accept or reject the project?

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SUMMARYSUMMARYYear Cash Flow

0 -90,000

1 132,000

2 100000

3 -150000

Investment Criteria

NPV 1,769.54

IRR-1 10.11%

IRR-2 42.66%NPV says Accept IRR-1 says Reject IRR-2 says Accept

NPV PROFILENPV PROFILE

When you cross the x-axis more than once, there will be

more than one return that solves the equation

INDEPENDENT VERSUS MUTUALLYINDEPENDENT VERSUS MUTUALLYEXCLUSIVE PROJECTSEXCLUSIVE PROJECTS

IndependentThe cash �ows of one project are una�ected by theacceptance of the other.

Mutually ExclusiveThe acceptance of one project precludes acceptingthe other.

REINVESTMENT RATE ASSUMPTIONREINVESTMENT RATE ASSUMPTIONIRR assumes reinvestment at IRRNPV assumes reinvestment at the �rm's weightedaverage cost of capital (opportunity cost of capital)

More realistic/better methodNPV should be used to choose between mutuallyexclusive projects

EXAMPLEEXAMPLEWhich project should you accept if the required return is

10% and the you can only �nance one project.Period Project A Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

GRAPH: CROSSOVER RATEGRAPH: CROSSOVER RATE

FINDING CROSSOVER RATEFINDING CROSSOVER RATEPeriod Project A Project B Di�erence

0 -500 -400 -100

1 325 325 0

2 325 200 125

IRR 19.43% 22.17% 11.80%

CROSSOVER RATE GRAPH EXAMPLE 2CROSSOVER RATE GRAPH EXAMPLE 2

CONFLICTS BETWEEN NPV AND IRRCONFLICTS BETWEEN NPV AND IRRNPV directly measures the increase in value to the �rmWhenever there is a con�ict between NPV and anotherdecision rule, always use NPVIRR is unreliable in the following situations:

Non-conventional cash �owsMutually exclusive projects

OTHER CAPITAL BUDGETING TOOLSOTHER CAPITAL BUDGETING TOOLS(we will ignore these, know that they exist)

Modi�ed Internal Rate of Return (MIRR)Average Accounting ReturnDiscounted PaybackPro�tability Index

REAL WORLDREAL WORLD

CAPITAL BUDGETING IMPORTANCECAPITAL BUDGETING IMPORTANCE

WHAT DO MANAGER'S DO?WHAT DO MANAGER'S DO?

WHY IS IRR POPULAR?WHY IS IRR POPULAR?People like rates instead of dollars."Remodeling the clerical wing has a 20% return""At a 10% discount rate, the net present value is 4,000."$

SUMMARYSUMMARYConsider all investment criteria when making decisionsNPV and IRR are the most commonly used primaryinvestment criteriaPayback is a commonly used secondary investmentcriteriaAll provide valuable information

TOOLS SUMMARYTOOLS SUMMARY

NPVNPVNPV= Di�erence between market value (PV of in�ows)and costAccept if No serious �aws

Does require an appropriate discount ratePreferred decision criterion

NPV > 0

PAYBACKPAYBACKPayback = Length of time until initial investment isrecoveredAccept if payback some speci�ed targetDoesn't account for time value of moneyIgnores cash �ows after paybackArbitrary cuto� periodAsks the wrong question

IRRIRRIRR = Discount rate that makes NPV = 0Accept if IRR > required returnSame decision as NPV with conventional cash �owsDoes not require a discount rateUnreliable with:1. Non-conventional cash �ows2. Mutually exclusive projectsMIRR = better alternative (NOT COVERED)

PRACTICEPRACTICE

EXAMPLE 1EXAMPLE 1Consider an investment that costs 100,000 and has a

cash in�ow of 25,000 every year for 5 years. The requiredreturn is 9% and required payback is 4 years.

What is the payback period?What is the NPV?What is the IRR?Should we accept the project?What decision rule should be the primary decisionmethod?When is the IRR rule unreliable?

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SOLUTIONSOLUTION

EXAMPLE 2EXAMPLE 2Benny's is considering adding a new product to its lineup. This product is

expected to generate sales for four years after which time the product will be

discontinued. What is the project's net present value if the �rm wants to earn

a 14 percent rate of return?Year Cash Flow0 -65,0001 16,5002 23,8003 27,1004 23,300

What is the IRR?

What is the payback?

REVISIT COLLEGE DECISIONREVISIT COLLEGE DECISION

CAR LEASE VS BUY EXAMPLECAR LEASE VS BUY EXAMPLE

KEY LEARNING OUTCOMESKEY LEARNING OUTCOMESCalculate: NPV, Payback Period, IRRMake Capital budgeting decision (Decision rule:accept/reject)Pros and cons of NPV, payback, IRRIssues with:

Mutually exclusive projectsUnconventional cash �ows

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