Capital BudgetingCapital Budgeting

Rules for Sensible Rules for Sensible Investment Decisions!!Investment Decisions!!

Cost vs. BenefitsCost vs. Benefits

• Investment typically has two Investment typically has two components:components:– Outflow of cash (cost)Outflow of cash (cost)– Inflow of cash (benefits)Inflow of cash (benefits)

• TVM requires all cash flows to be TVM requires all cash flows to be compared at the same point in timecompared at the same point in time– Most convenient is time 0Most convenient is time 0

Recall Forbes ExampleRecall Forbes Example

• Tax savings: $500,000 foreverTax savings: $500,000 forever• Campaign Costs: $40 millionCampaign Costs: $40 million• r = 10%r = 10%

• PV of Benefits: .5 mill / .10 = $5 PV of Benefits: .5 mill / .10 = $5 millionmillion

• Cost: $40 millionCost: $40 million• Benefit - Cost = 5- 40 = -$35 millionBenefit - Cost = 5- 40 = -$35 million

Forbes example...Forbes example...

• Obviously this is a lousy investmentObviously this is a lousy investment

• What you just used in analyzing this What you just used in analyzing this ‘investment’ proposal is NPV rule!‘investment’ proposal is NPV rule!

• It turns out the NPV rule is the most It turns out the NPV rule is the most sensible rule to use for evaluating sensible rule to use for evaluating projectsprojects

Examples of Capital Examples of Capital Budgeting ProjectsBudgeting Projects

• To open a corner latte standTo open a corner latte stand• To replace replace a 486 computer used To replace replace a 486 computer used

in business with a Pentium computerin business with a Pentium computer• To decide between a coal-fired and a To decide between a coal-fired and a

nuclear fuel power plant costing $1 nuclear fuel power plant costing $1 billionbillion

• To add 5 stories to an existing office To add 5 stories to an existing office towertower

• To shut down an aging factory making To shut down an aging factory making ball bearingsball bearings

Evaluating InvestmentsEvaluating Investments

• There are many ways to evaluate There are many ways to evaluate investmentsinvestments

• Among all the investment rules we Among all the investment rules we will consider, NPV rule is the will consider, NPV rule is the onlyonly rule that rule that alwaysalways gives correct gives correct answer in all situations!!answer in all situations!!

• Other rules may or may not give an Other rules may or may not give an answer consistent with NPV ruleanswer consistent with NPV rule

Net Present ValueNet Present Value

• NPV = PV of Benefits - PV of CostsNPV = PV of Benefits - PV of Costs

• AcceptAccept project if NPV > 0 project if NPV > 0• RejectReject project if NPV < 0 project if NPV < 0

Another ExampleAnother Example......

0 1 2

Initial outlay($1,100)

Revenues $1,000Expenses 500

Cash flow $500

Revenues $2,000Expenses 1,000

Cash flow $1,000

– $1,100.00

+454.54

+826.45

+$180.99

1$500 x 1.10

1$1,000 x 1.10

2

NPV

NPV FormulaNPV Formula

• ‘‘r’ has many names:r’ has many names:– ‘‘r’ is called the discount rate orr’ is called the discount rate or– ‘‘r’ is called the required return orr’ is called the required return or– ‘‘r’ is called the cost of capitalr’ is called the cost of capital

Computing NPV on Computing NPV on calculatorcalculator

• Use the CFUse the CFjj key key– First entry is at time 0First entry is at time 0– Subsequent entries are time 1, 2, 3, ... and so Subsequent entries are time 1, 2, 3, ... and so

onon– make sure the cash flows have the proper signsmake sure the cash flows have the proper signs

• Enter ‘r’ as the I/YREnter ‘r’ as the I/YR• Use the Use the keys keys

That’s it!!That’s it!!

NPV

Another Example..Another Example..

Time Cash Flow

0 -$718

1 $250

2 $575

3 $100

r = 12%4

NPV = $ _______

Accept / Reject Project ?

• The cash flows areThe cash flows are

YearYear Cash Cash

flowflow

00 -$252-$252

11 1431 1431

22 -3035-3035

33 2850 2850

44 -1000-1000

r = 10%r = 10%

NPV = _______NPV = _______

Accept / Reject ??Accept / Reject ??

Another Example...Another Example...

Example continued...Example continued...• This was an example of This was an example of

unconventionalunconventional cash flows cash flows

• ConventionalConventional Cash Flows: Only one Cash Flows: Only one change in sign (from + to - or vice change in sign (from + to - or vice versa)versa)e.g. e.g. -- ++ ++ ++ ++

• UnconventionalUnconventional Cash Flows: More Cash Flows: More than one change in signthan one change in signe.g.e.g. -- ++ ++ -- ++ --

Importance of NPVImportance of NPV• NPV is the dollar value added to the NPV is the dollar value added to the

enterpriseenterprise– it’s the amount by which the enterprise is it’s the amount by which the enterprise is

richer!richer!

• For public companies, NPV is the For public companies, NPV is the increase in total market value of equityincrease in total market value of equity

• Managers should Managers should notnot take negative NPV take negative NPV projects since it reduces the firm valueprojects since it reduces the firm value

Other RulesOther Rules

• Alternative rules of evaluating Alternative rules of evaluating investments are:investments are:

– Internal Rate of Return (IRR)Internal Rate of Return (IRR)– PaybackPayback– Discounted PaybackDiscounted Payback– Profitability IndexProfitability Index– Accounting Rate of ReturnAccounting Rate of Return

IRR RuleIRR Rule• IRR: the IRR: the discount ratediscount rate that makes NPV = that makes NPV =

00

• Rule: Rule: AcceptAccept if IRR > required returnif IRR > required return RejectReject if IRR < required returnif IRR < required return

01 1 1 10

1 22

33

CFCF

IRR

CF

IRR

CF

IRR

CF

IRRn

n( ) ( )....

( )

IRR and Required ReturnIRR and Required Return

• Required return also called the Required return also called the ‘Hurdle Rate’‘Hurdle Rate’

• Required return is the Required return is the costcost of of investment fundsinvestment funds– i.e. what it costs to borrow money or i.e. what it costs to borrow money or

raise equity capital for investmentsraise equity capital for investments– it is the same cost of capital ‘r’ used in it is the same cost of capital ‘r’ used in

NPV calculationsNPV calculations

IRR on CalculatorIRR on Calculator

• Enter the cash flows as beforeEnter the cash flows as before

• Use the Use the keyskeys

• That’s it!That’s it!

• Without financial calculator, IRR is Without financial calculator, IRR is computed by trial and errorcomputed by trial and error

IRR/YR

IRR ExampleIRR Example

Year Cash flowYear Cash flow

00 -200-200

11 5050 22 100100 33 150150

5050 100 100 150150

0 = -200 + + +0 = -200 + + + (1+IRR)(1+IRR)11 (1+IRR) (1+IRR)2 2 (1+IRR)(1+IRR)33

IRR = ______%IRR = ______%

Hurdle rate = 9%

Accept / reject?

Another ExampleAnother Example

• What is the IRR?What is the IRR? Ans: _____Ans: _____• What is the NPV if r = 16%What is the NPV if r = 16% Ans: _____Ans: _____• Do IRR and NPV give the same answer?Do IRR and NPV give the same answer?

0 2 3 4 5 61

-256 +31 +128 +194 +61 +55 +108

Year Cash flow

0 – $275 1 100 2 100 3 100 4 100

Net Present Value ProfileNet Present Value Profile

Discount rate2% 6% 10% 14% 18%

120

100

80

60

40

20

Net present value

0

– 20

– 40

22%

IRR

NPV>0

NPV < 0

IRR and Unconventional Cash IRR and Unconventional Cash FlowsFlows

The cash flows are

Year Cash flow

0 -$252

11431

2 -3035

32850

4 -1000

IRR = ?

Example continued....Example continued....

• What’s the IRR?What’s the IRR?

at 25.00%:at 25.00%: NPV = _______NPV = _______

at 33.33%:at 33.33%: NPV = _______NPV = _______

at 42.86%:at 42.86%: NPV = _______NPV = _______

at 66.66%:at 66.66%: NPV = _______NPV = _______

• Two questions:Two questions:– 1.1. What’s going on here?What’s going on here?– 2.2. How many IRRs can How many IRRs can

there be?there be?

NPV Profile - Multiple IRR ProblemNPV Profile - Multiple IRR Problem

$0.06

$0.04

$0.02

$0.00

($0.02)

NPV

($0.04)

($0.06)

($0.08)

0.2 0.28 0.36 0.44 0.52 0.6 0.68

IRR = 25%

IRR = 33.3% IRR =

42.8%

IRR = 66.6%

Discount rate

Problem 1 with IRR Problem 1 with IRR RuleRule

• IRR Rule does not always give a clear IRR Rule does not always give a clear answer with answer with unconventionalunconventional cash flows cash flows

• In the above example, there are In the above example, there are multiple IRRsmultiple IRRs

• The accept/reject decision in the The accept/reject decision in the example depends on required rate of example depends on required rate of returnreturn

Another Problem with Another Problem with IRRIRR

Year

0 1 2 3 4

Project A: – $350 50 100 150 200

Project B: – $250 125 100 75 50

If the projects are mutually exclusive (i.e. can take one or the other, but not both), which project to take?

Example Continued...Example Continued...

Project A Project B

IRR 12.9% 17.8%

NPV @ 5% $82.44 $65.67

NPV @ 14% -$9.53 $16.82

Decision with mutually Decision with mutually exclusive projectsexclusive projects

IRR Rule does not always give a correct answer with mutually exclusive projects

In the above example, it seems we would

prefer Project ________ (higher IRR)

Mutually Exclusive… Mutually Exclusive… (contd.)(contd.)

• But always take the project with But always take the project with higher NPV!!higher NPV!!

• If r = 5%, then accept project AIf r = 5%, then accept project A

• If r = 14%, then accept project BIf r = 14%, then accept project B

IRR, NPV, and Mutually Exclusive IRR, NPV, and Mutually Exclusive ProjectsProjects

Discount rate %2% 6% 10% 16% 20%

60

40

20

0

– 20

– 40

Net present value $

– 60

– 80

– 100

24%

IRR A < IRR B

0

140

120

100

80

160

NPV B >NPV A

NPV A >NPV B

Project A

Project B

Crossover rate

Cross-over RateCross-over Rate

• the discount rate that makes NPV of the discount rate that makes NPV of two projects equaltwo projects equal

• the interest rate at which you are the interest rate at which you are indifferentindifferent between two mutually between two mutually exclusive projects exclusive projects

Finding Crossover RateFinding Crossover Rate• Take difference between cash Take difference between cash

flows of two projects and find IRR flows of two projects and find IRR (of these incremental cash flows)(of these incremental cash flows)

Year

0 1 2 3 4

Project A: – $350 150 120 150 200

Project B: – $250 125 100 75 165

Difference: –$100 25 20 75 35

IRR (difference) = _______ %

Another exampleAnother example

• Find the crossover rate of these two projectsFind the crossover rate of these two projects• Answer: _________Answer: _________

IRR - CriticismsIRR - Criticisms

• Not a measure of dollar value addedNot a measure of dollar value added• Does not consider the scale of the Does not consider the scale of the

projectproject• Interim cash flows are assumed to be Interim cash flows are assumed to be

reinvested at the IRR which is reinvested at the IRR which is unrealisticunrealistic

• Does not give correct answer whenDoes not give correct answer when– you have mutually exclusive projectyou have mutually exclusive project– unconventional cash flowsunconventional cash flows

Payback RulePayback Rule

• Measure of the length of time until Measure of the length of time until the sum of future cash flows equals the sum of future cash flows equals the initial investmentthe initial investment– Time it takes to get you money backTime it takes to get you money back

• AcceptAccept: if payback period is : if payback period is lessless than some pre-specified benchmarkthan some pre-specified benchmark

Payback ExamplePayback Example

The cash flows are

Year Proj. A Proj. B

0 -$100 -$100

1 90 15

2 15 90

3 10 10

4 10 20

Payback = 2 yrs

Problem with PaybackProblem with Payback

Year Proj. A Proj. B

0 -$100 -$100

1 90 15

2 15 90

3 10 100

4 10 2000

Payback rule ignores these cash flows

Although both projects have the same payback, Proj. B is clearly superior

Payback Rule - CriticismsPayback Rule - Criticisms

• It does not take into account time It does not take into account time value of money (i.e. no discounting of value of money (i.e. no discounting of cash flows)cash flows)

• Payback rule ignores all the cash flows Payback rule ignores all the cash flows that occur after the payback periodthat occur after the payback period

• Required payback benchmark is Required payback benchmark is arbitraryarbitrary

Discounted PaybackDiscounted Payback

• Length of time until Length of time until present valuepresent value of of future cash flows equals the intial future cash flows equals the intial investmentinvestment– avoids the time value criticism of simple avoids the time value criticism of simple

payback rulepayback rule

• Accept if discounted payback less than Accept if discounted payback less than pre-specified benchmarkpre-specified benchmark

• Does not avoid other criticisms of Does not avoid other criticisms of payback rulepayback rule

Disc. Payback ExampleDisc. Payback Example The cash flows are

Year Proj. A PV (r=10%)

0 -$100 -$100

1 90 81.82

2 15 12.40

3 10 7.51

4 10 6.83

discountedpayback= 3 years

Discounted Payback - Discounted Payback - criticismcriticism

• Incorporates time value in decision in Incorporates time value in decision in contrast with simple payback,contrast with simple payback,

• It still ignores all cash flows occuring after It still ignores all cash flows occuring after the required payback periodthe required payback period

• Benchmark is still arbitraryBenchmark is still arbitrary

BUT

Profitability IndexProfitability Index

• Ratio of PV of benefits to PV of costsRatio of PV of benefits to PV of costs– ““Bang for the buck”Bang for the buck”

• Rule: Rule: AcceptAccept Project if Project if PI > 1PI > 1RejectReject project if project if PI < 1PI < 1

P. I. ExampleP. I. Example

• P. I. = ______P. I. = ______ =________=________200200

• InterpretationInterpretation: NPV of $0.204 is : NPV of $0.204 is added for each $1 of investiment.added for each $1 of investiment.

Year 0 1 2 3CashFlow -200 50 100 150

r = 10%

Problems with P. I.Problems with P. I.

• As with IRR, it does not consider the As with IRR, it does not consider the scalescale of the project. of the project. – Not a measure of Not a measure of totaltotal $ value added to $ value added to

firmfirm

• With mutually exclusive projects, P. With mutually exclusive projects, P. I. can give wrong rankingsI. can give wrong rankings

Another ExampleAnother Example

• Although Proj. A has higher P. I., Although Proj. A has higher P. I., Proj. B should be accepted because Proj. B should be accepted because NPV is higherNPV is higher

Project A Project B

Cost (t=0) -$100 -$200

NPV $50 $80

P. I. 1.5 1.4

Average Accounting Average Accounting ReturnReturn

• Measure of avg. accounting profit Measure of avg. accounting profit divided by avg. accounting value of divided by avg. accounting value of investment:investment:

A. A. R. = A. A. R. = avg. net incomeavg. net incomeavg. book value of invest.avg. book value of invest.

• AcceptAccept if ifAAR > benchmark returnAAR > benchmark returnRejectReject if if AAR < benchmark returnAAR < benchmark return

A. A. R. ExampleA. A. R. ExampleAverage net income:

Year

1 2 3

Sales $440 $240 $160

Costs 220 120 80

Gross profit 220 120 80

Depreciation 80 80 80

Earnings before taxes140 40 0

Taxes (25%) 35 10 0

Net income $105 $30 $0

Average net income = (105 + 30 + 0)/3 = $45

Example continuedExample continuedAverage book value:

Initial investment = $240

Average investment = ($240 + 160 + 80 + 0)/4 = $120

(or) = $240/2 = $120

Average accounting return (AAR):

Average net income $45

AAR = = = 37.5% Average book value $120

Problems with AARProblems with AAR

• Does not use cash flowsDoes not use cash flows

• Ignores timing of incomeIgnores timing of income

• Pre-specified benchmark is arbitraryPre-specified benchmark is arbitrary

SummarySummary

• Of all the rules considered, NPV Of all the rules considered, NPV consistently gives the correct consistently gives the correct answersanswers

• Other rules may or may not give the Other rules may or may not give the same answer as NPVsame answer as NPV

• Decisions based on NPV rule are Decisions based on NPV rule are alwaysalways correct! correct!

SummarySummary• Why study other rules?Why study other rules?• Corporations often use more than one Corporations often use more than one

rulerule• However, most corporations have However, most corporations have

adopted the NPV ruleadopted the NPV rule• In practice, IRR is the strongest In practice, IRR is the strongest

challenge to the NPV rulechallenge to the NPV rule• managers seem to prefer talking about managers seem to prefer talking about

investment ‘returns’ rather than NPV investment ‘returns’ rather than NPV

Major remaining issuesMajor remaining issues

• So far we have ignored from where So far we have ignored from where we got the cash flows and ‘r’:we got the cash flows and ‘r’:

• How do you compute the correct How do you compute the correct cash flows to use in NPV?cash flows to use in NPV?– accounting income vs. relevant cash accounting income vs. relevant cash

flowsflows

• How do you determine the correct How do you determine the correct

cost of capital ‘r’?cost of capital ‘r’?– risk and returnrisk and return