1 capital budgeting techniques how do firms make decisions about whether to invest in costly,...

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Capital Budgeting Techniques

How do firms make decisions about whether to invest in costly, long-lived assets?

How does a firm make a choice between two acceptable investments when only one can be purchased?

How are different capital budgeting techniques related?

Which capital budgeting methods do firms actually use?

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Capital Budgeting

Introduction to Capital Budgeting

Payback Period—traditional and discounted

Net Present Value (NPV)

Internal Rate of Return (IRR)

Modified IRR

Comparison of NPV and IRR

NPV/IRR Ranking Conflicts/Cautions

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Capital Budgeting

Capital Budgeting Basics and Techniquesr—firm’s required rate of return

CF—cash flows generated by an investment Given

Compute

Capital Budgeting—cash flows and riskr—firm’s required rate of return

CF—cash flows generated by an

investment

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Capital Budgeting Basics

Importance of capital budgeting decisionslong-term effect—capital, or long-term funds,

raised by the firms are used to invest in assets that enable the firm to generate revenues several years into the future.

timing of a decision is important—decisions impact the firm for several years.

Generating ideas for capital budgetingemployees, customers, suppliers, and so forthbased on needs and experiences of the firm and

these groups

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Capital Budgeting BasicsProject classifications—replacement decisions versus expansion decisionsreplacement decision—intended to maintain existing

levels of operationsexpansion decision—a decision concerning whether

the firm should expand operations

Project classifications—independent projects versus mutually exclusive projectsindependent project—accepting one independent

project does not affect the acceptance of any other project

mutually exclusive projects—only one project can be purchased

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Capital Budgeting Basics—Capital Budgeting Versus Asset Valuation

Value of an asset = PV of the cash flows the asset is expected to generate during its life:

)(1

CF

r)(1

CF

r)(1

CFValue

Assetn

n2

21

1

r

An asset is an acceptable investment if the cost of the asset is less than its value:

Acceptable if: PV of CFs > Cost

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Capital Budgeting Techniques

Payback period

Net present value

Internal rate of return

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Capital Budgeting TechniquesIllustrative Investment

0 (7,000)1 2,0002 1,0003 5,0004 3,000

r = 15%

tCF

Year Cash Flow,

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Capital Budgeting ExampleCash Flow Time Line

2,000 1,000 5,000 3,000

10 2 3 4

(7,000.00)

15%

1,739.13

756.14

3,287.58

1,715.26

498.11 = 43210 CF ofPV CF ofPV CF ofPV CF ofPV CF

PV = 7,498.11

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Capital Budgeting TechniquesPayback Period

Number of years it takes to recapture

the initial investment. Year Cash Flow Cumulative CF

0 $(7,000) $(7,000)1 2,000 (5,000)2 1,000 (4,000)3 5,000 1,0004 3,000 4,000

} 2<Payback<3

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Year Cash Flow Cumulative CF0 $(7,000) $(7,000)1 2,000 (5,000)2 1,000 (4,000)3 5,000 1,0004 3,000 4,000

} 2<Payback<3

years2.80 $5,000$4,0002

remaining investment $

payback ofyear

in flow cash $

recaptured be to

investment original ofrecovery full

before yearsof #

periodPayback

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Accept the project if Payback, PB < some number of years established by the firm

PB = 2.8 years is acceptable if the firm has established a maximum payback of 4.0 years

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Advantages:SimpleCash flows are usedProvides an indication of the liquidity of a project

Disadvantages:Does not use time value of money conceptsCash flows beyond the payback period are ignored

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Year Cash Flow Cumulative CF0 $(7,000) $(7,000)1 2,000 (5,000)2 1,000 (4,000)3 5,000 1,0004 3,000 4,000

} PB = 2.80 yrs

Year Cash Flow Cumulative CF0 $(7,000) $(7,000)1 2,000 (5,000)2 1,000 (4,000)3 5,000 1,0004 3,000 4,000 5 1,000,000 1,004,000

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Capital BudgetingNet Present Value (NPV)

NPV = present value of future cash flows less the initial investment

An investment is acceptable if NPV > 0

n

0tt

t

r)(1

CF

nn

22

11

0r)(1

CF

r)(1

CF

r)(1

CFCFNPV

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Capital Budgeting—NPV

$498.11

(1.15)

$3,000

(1.15)

$5,000

(1.15)

$1,000

(1.15)

$2,000$7,000NPV

4321

$1,715.26$3,287.58$756.14$1,739.13$7,000

NPV = $498.11 > 0, so the project is acceptable

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10 2 3 4

2,000 1,000 5,000 3,000(7,000.00)

15%

1,739.13

756.14

3,287.58

1,715.26

498.11 = NPV

Capital Budgeting ExampleCash Flow Time Line

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Capital Budgeting—NPV

Advantages:

Cash flows rather than profits are analyzed

Recognizes the time value of money

Acceptance criterion is consistent with the goal of maximizing value

Disadvantage:

Detailed, accurate long-term forecasts are required to evaluate a project’s acceptance

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Solving for NPV

Numerical (equation) solution

Financial Calculator solution

Spreadsheet solution

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Solving for NPVNumerical Solution

$498.11

$1,715.26$3,287.58$756.14$1,739.13$7,000

(1.15)

$3,00

(1.15)

$5,000

(1.15)

$1,000

(1.15)

$2,000$7,000NPV

4321

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Solving for NPVFinancial Calculator Solution

Input the following into the cash flow register:

CF0 = -7,000

CF1 = 2,000

CF2 = 1,000

CF3 = 5,000

CF4 = 3,000

Input I = 15Compute NPV = 498.12

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Capital BudgetingDiscounted Payback Period

Payback period computed using the present values of the future cash flows.

0 $(7,000) $(7,000.00) $(7,000.00)1 2,000 1,739.13 (5,260.87)2 1,000 756.14 (4,504.73)3 5,000 3,287.58 (1,217.14)4 3,000 1,715.26 498.12

} PBdisc= 3.71

CumulativeYear Cash Flow PV of CF @15% PV of CF

A project is acceptable if PBdisc < project’s life

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Capital BudgetingInternal Rate of Return (IRR)

If NPV>0, project’s return > rExample:

Initial investment = $7,000.00

PV of future cash flows = $7,498.12NPV = $498.12 r = 15%

IRR > 15%

If IRR = project’s rate of return

IRR = the rate of return that causes the NPV of the project to equal zero, or where the present value of the future cash flows equals the initial investment.

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n

n

2

2

1

10

IRR)(1

CF

IRR)(1

CF

IRR)(1

CFCF

n

n

2

2

1

10 0

IRR)(1

CF

IRR)(1

CF

IRR)(1

CFCFNPV

A project is acceptable if its IRR > r

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4321 IRR)(1

$3,000

IRR)(1

$5,000

IRR)(1

$1,000

IRR)(1

$2,000$7,000

43210

IRR)(1

3,000

IRR)(1

5,000

IRR)(1

1,000

IRR)(1

2,0007,000NPV

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Internal Rate of Return (IRR)Cash Flow Time Line

10 2 3 4

2,000 1,000 5,000 3,000(7,000)

IRR = ?

0 = NPV

of PVs = 7,000

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Capital Budgeting—IRR

Advantages:Cash flows rather than profits are analyzedRecognizes the time value of moneyAcceptance criterion is consistent with the goal of maximizing value

Disadvantages:Detailed, accurate long-term forecasts are required to evaluate a project’s acceptanceDifficult to solve for IRR without a financial calculator or spreadsheet

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Solving for IRRNumerical Solution

Using the trial-and-error method plug in values for IRR until the left and right side of the following equation become equal.

4321 IRR)(1

$3,000

IRR)(1

$5,000

IRR)(1

$1,000

IRR)(1

$2,000$7,000

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Solving for IRRNumerical Solution

Rate of Return NPV15% 498.12

16 327.4617 162.7218 3.6219 (150.08)} 18<IRR<19

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Solving for IRRFinancial Calculator Solution

Input the following into the cash flow register:

CF0 = -7,000

CF1 = 2,000

CF2 = 1,000

CF3 = 5,000

CF4 = 3,000

Compute IRR = 18.02%

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NPV versus IRR

When NPV > 0, a project is acceptable because the firm will increase its value, which means the firm earns a return greater than its required rate of return (r) if it invests in the project.When IRR > r, a project is acceptable because the firm will earn a return greater than its required rate of return (r) if it invests in the project.When NPV > 0, IRR > r for a project—that is, if a project is acceptable using NPV, it is also acceptable using IRR.

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Accept/Reject Decisions Using NPV, Discounted Payback, and IRR

Technique Evaluation Result Acceptable?NPV NPV > 0IRR IRR > rDiscounted PB PBdisc < project’s life

YESYESYES

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NPV Profile

A graph that shows the NPVs of a project at various required rates of return.Rate of Return NPV

15% 498.1216 327.4617 162.7218 3.6219 (150.08)20 (298.61)21 (442.20)

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NPV Profile

IRR = 18.02%

($2,000)

($1,000)

$0

$1,000

$2,000

$3,000

$4,000

$5,000

5% 10% 15% 20% 25%

NPV

r

NPV > 0

NPV < 0

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Capital Budgeting TechniquesIllustrative Projects A & B

0 (7,000.00)1 2,000.002 1,000.003 5,000.004 3,000.00

r = 15%

Cash Flow,Year Project A

tCF

01 2,000.002 1,000.003 5,000.004 3,000.00

Trad PB = 2.80NPV = 498.12IRR = 18.02%

(8,000.00)6,000.003,000.001,000.00

500.00

Project B

1.67429.22

19.03%

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NPV Profiles for Projects A & B

-2000

-1000

0

1000

2000

3000

4000

5000

5% 10% 15% 20% 25%

NPV

rIRRB = 19.03

IRRA = 18.02

Crossover = 16.15

Project A

Project B

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NPV Profile—Projects A & B

NPVB

429.22318.71210.94105.82

3.26(96.84)(194.55)

NPVB

429.22318.71210.94105.82

3.26(96.84)(194.55)

Rate of Return NPVA

15% 498.1216 327.4617 162.7218 3.6219 (150.08)20 (298.61)21 (442.20)

Rate of Return NPVA

15% 498.1216 327.4617 162.7218 3.6219 (150.08)20 (298.61)21 (442.20)

Rate of Return

15%161718192021

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Capital Budgeting TechniquesIllustrative Projects A & B

0 (7,000) (8,000)1 2,000 6,0002 1,000 3,0003 5,000 1,0004 3,000 500

Cash Flow,Year Project A Project

B

tCF

CFA - CFB1,000(4,000)(2,000)4,0002,500

IRR of (CFA – CFB) Cash Flow Stream = 16.15%At r = 16.15%, NPVA = NPVB = 302.37

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NPV/IRR Ranking Conflicts

Asset A Asset BTraditional PB 2.80 yrs 1.67 yrsDiscounted PB 3.71 yrs 2.78 yrsNPV $498.12 $429.22IRR 18.02% 19.03%

Which asset(s) should be purchased? Asset A, because it has the higher NPV.

Asset ATraditional PB 2.80 yrsDiscounted PB 3.71 yrsNPV $498.12IRR 18.02%

Asset A Asset BTraditional PB 2.80 yrs 1.67 yrsDiscounted PB 3.71 yrs 2.78 yrsNPV $498.12 $429.22IRR 18.02% 19.03%

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NPV/IRR Ranking Conflicts

Ranking conflicts result from:Cash flow timing differencesSize differencesUnequal lives

Reinvestment rate assumptionsNPV—reinvest at the firm’s required rate

of returnIRR—reinvest at the project’s internal

rate of return, IRR

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Multiple IRRs

Conventional cash flow pattern—cash outflow(s) occurs at the beginning of the project’s life, followed by a series of cash inflows.Unconventional cash flow pattern—cash outflow(s) occurs during the life of the project, after cash inflows have been generated.An IRR solution occurs when a cash flow pattern is interrupted; if a cash flow pattern is interrupted more than once, then more than one IRR solution exists.

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Multiple IRRs—Example

Year Cash Flow

0 (15,000)

1 40,150

2 (13,210)

3 (16,495)IRR1 = 22.5%

IRR2 = 92.0%

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Modified Internal Rate of Return (MIRR)

Generally solves the ranking conflict and the multiple IRR problem

nMIRR)+(1

outflows cash ofFV = outflows cash ofPV

n

n

0t

tntn

0tt

t

)MIRR1(

)r1(CIF

)r1(

COF

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MIRR—Example

Year Project A Project B0 (7,000) (8,000)1 2,000 6,0002 1,000 3,0003 5,000 1,0004 3,000 500

Discounted PB 3.71 yrs 2.78 yrsNPV $498.12 $429.22IRR 18.02% 19.03%

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MIRR—ExampleYear Project A Project B

0 (7,000) (8,000)1 2,000 6,0002 1,000 3,0003 5,000 1,0004 3,000 500

)MIRR1(

25.114,13

)MIRR1(

)15.1(000,3)15.1(000,5)15.1(000,1)15.1(000,2000,7

AA

0123

Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRRA

Project B—calculator solution: N = 4, PV = -8,000, PMT = 0, FV = 14,742.75; I/Y = 16.51 = MIRRB

Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRRA

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Capital Budgeting—The Answers

How do firms make decisions about whether to invest in costly, long-lived assets?Firms use decision-making methods that are

based on fundamental valuation concepts

How does a firm make a choice between two acceptable investments when only one can be purchased?The decision should be consistent with the

goal of maximizing the value of the firm

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How are different capital budgeting techniques related?All techniques except traditional payback

period (PB) are based on time value of money

Which capital budgeting methods do firms actually use?Most firms rely heavily on NPV and IRR to

make investment decisions

Capital Budgeting—The Answers

1 capital budgeting techniques how do firms make decisions about whether to invest in costly,...

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