Capital budgeting techniques

Capital Capital Budgeting Budgeting TechniquesTechniques

CAPITAL BUDGETINGCAPITAL BUDGETING

The process of identifying, The process of identifying, analyzing and selecting analyzing and selecting investment projects whose investment projects whose returns (cash flows) are returns (cash flows) are expected to extend beyond one expected to extend beyond one year. year.

Capital Budgeting Capital Budgeting TechniquesTechniques

Project Evaluation and SelectionProject Evaluation and Selection Potential DifficultiesPotential Difficulties Capital RationingCapital Rationing Project MonitoringProject Monitoring Post-Completion AuditPost-Completion Audit

1.1. New product or Expansion New product or Expansion

2.2. Replacement Replacement

3.3. Research and DevelopmentResearch and Development

4.4. ExplorationExploration

5.5. Other purposes ( Advertisement, Other purposes ( Advertisement, safety or pollution related )safety or pollution related )

Key Motives for Making Key Motives for Making Capital ExpendituresCapital Expenditures

Key Motives for Making Key Motives for Making Capital ExpendituresCapital Expenditures

Project Evaluation: Project Evaluation: Alternative MethodsAlternative Methods

Payback Period (PBP)Payback Period (PBP) Internal Rate of Return Internal Rate of Return (IRR)(IRR)

Net Present Value (NPV)Net Present Value (NPV) Profitability Index (PI)Profitability Index (PI)

Project RelationshipsProject Relationships

Mutually ExclusiveMutually Exclusive -- A -- A project whose acceptance project whose acceptance precludes the acceptance of precludes the acceptance of one or more alternative one or more alternative projects. projects.

• IndependentIndependent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.

• DependentDependent -- A project whose acceptance depends on the acceptance of one or more other projects.

Payback Period (PBP)Payback Period (PBP)

PBP PBP is the period of time is the period of time required for the cumulative required for the cumulative expected cash flows from an expected cash flows from an investment project to equal the investment project to equal the initial cash outflow.initial cash outflow.

PBP PBP is the period of time is the period of time required for the cumulative required for the cumulative expected cash flows from an expected cash flows from an investment project to equal the investment project to equal the initial cash outflow.initial cash outflow.

Proposed Project DataProposed Project Data

Julie Miller is evaluating a new project Julie Miller is evaluating a new project for her firm for her firm Basket Wonders (BW)Basket Wonders (BW). . She has determined that the after-tax She has determined that the after-tax cash flows for the project will be cash flows for the project will be $10,000, $12,000, $15,000, $10,000, $10,000, $12,000, $15,000, $10,000, and $7,000 and $7,000 respectively for each of respectively for each of the the Years 1 through 5Years 1 through 5. The initial . The initial cash outlay will be cash outlay will be $40,000$40,000..

(c)10 K 22 K 37 K 47 K 54 K

Payback Solution Payback Solution

PBPPBP = = aa + ( + ( bb - - c c ) / ) / dd= = 33 + ( + (4040 - - 3737) / ) / 1010 = = 33 + +

((33) / ) / 1010 = = 3.3 3.3 YearsYears

PBPPBP = = aa + ( + ( bb - - c c ) / ) / dd= = 33 + ( + (4040 - - 3737) / ) / 1010 = = 33 + +

((33) / ) / 1010 = = 3.3 3.3 YearsYears

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K

CumulativeInflows

(a)

(-b) (d)

PBP Acceptance CriterionPBP Acceptance Criterion

The management of The management of Basket Basket Wonders Wonders has set a maximum PBP has set a maximum PBP

of of 3.5 Years 3.5 Years for projects of this for projects of this type.type.

Should this project be accepted?Should this project be accepted?

Yes! Yes! The firm will receive back the The firm will receive back the initial cash outlay in less than 3.5 initial cash outlay in less than 3.5

Years. [Years. [3.3 Years 3.3 Years < < 3.5 Year Max3.5 Year Max..]]

PBP Strengths and PBP Strengths and WeaknessesWeaknesses

StrengthsStrengths:: Easy to use and Easy to use and

understandunderstand Can be used as a Can be used as a

measure of measure of liquidityliquidity

Weaknesses:•Does not account for TVM•Does not consider cash flows beyond the PBP• Cutoff period is subjective

Net Present Value Net Present Value (NPV)(NPV)

NPV NPV is the present value of an is the present value of an investment project’s net cash investment project’s net cash

flows minus the project’s initial flows minus the project’s initial cash outflow.cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ - ICOICONPV =

Decision Criteria

If NPV > 0, accept the project If NPV < 0, reject the project If NPV = 0, technically

indifferent

Basket Wonders Basket Wonders has determined that has determined that the appropriate discount rate (k) for the appropriate discount rate (k) for

this project is 13%.this project is 13%.

$10,000 $7,000

NPV SolutionNPV Solution

$10,000 $12,000 $15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - $40,000$40,000(1.13)4 (1.13)5

NPVNPV = +

NPV SolutionNPV Solution

NPVNPV = = $10,000$10,000(PVIF(PVIF13%13%,,11) + ) + $12,000$12,000(PVIF(PVIF13%13%,,22) + ) + $15,000$15,000(PVIF(PVIF13%13%,,33) ) + + $10,000$10,000(PVIF(PVIF13%13%,,44) + ) +

$ 7,000$ 7,000(PVIF(PVIF13%13%,,55) - ) - $40,000$40,000

NPVNPV = = $10,000$10,000(.885) + (.885) + $12,000$12,000(.783) + (.783) + $15,000$15,000(.693) + (.693) + $10,000$10,000(.613) +(.613) +

$ 7,000$ 7,000(.543) - (.543) -

$40,000$40,000

NPVNPV = = $8,850 + $9,396 + $10,395 + $8,850 + $9,396 + $10,395 + $6,130 + $3,801 - $6,130 + $3,801 - $40,000$40,000

==- $1,428- $1,428

NPV Acceptance NPV Acceptance CriterionCriterion

No! No! The The NPVNPV is is negativenegative. This . This means that the project is reducing means that the project is reducing

shareholder wealth. [shareholder wealth. [Reject Reject as as NPVNPV < < 00 ] ]

No! No! The The NPVNPV is is negativenegative. This . This means that the project is reducing means that the project is reducing

shareholder wealth. [shareholder wealth. [Reject Reject as as NPVNPV < < 00 ] ]

The management of The management of Basket Basket Wonders Wonders has determined that the has determined that the required rate is 13% for projects required rate is 13% for projects

of this type.of this type.


NPV Strengths and WeaknessesNPV Strengths and Weaknesses

StrengthsStrengths:: Cash flows Cash flows

assumed to be assumed to be reinvested at the reinvested at the

hurdle rate.hurdle rate. Accounts for TVM.Accounts for TVM. Considers all Considers all

cash flows.cash flows.

StrengthsStrengths:: Cash flows Cash flows

assumed to be assumed to be reinvested at the reinvested at the

hurdle rate.hurdle rate. Accounts for TVM.Accounts for TVM. Considers all Considers all

cash flows.cash flows.

WeaknessesWeaknesses:: May not include May not include

managerial managerial options options embedded embedded

in the in the project. project.

Profitability Index (PI)Profitability Index (PI)

PI is the ratio of the present value of PI is the ratio of the present value of a project’s future net cash flows to a project’s future net cash flows to the project’s initial cash outflow.the project’s initial cash outflow.

CF1 CF2 CFn (1+k)1 (1+k)2 (1+k)n

+ . . . ++ ICOICOPI =

PI = 1 + [ NPVNPV / ICOICO ]

<< OR >>

PI Acceptance CriterionPI Acceptance Criterion

No! No! The The PIPI is is less than 1.00less than 1.00. This. This means that the project is not means that the project is not

profitable. [profitable. [Reject Reject as as PIPI < < 1.001.00 ] ]

No! No! The The PIPI is is less than 1.00less than 1.00. This. This means that the project is not means that the project is not

profitable. [profitable. [Reject Reject as as PIPI < < 1.001.00 ] ]

PIPI = $38,572 / $40,000= $38,572 / $40,000

= .9643= .9643


PI Strengths and WeaknessesPI Strengths and Weaknesses

StrengthsStrengths:: Same as NPVSame as NPV Allows Allows comparison of comparison of different scale different scale projectsprojects

StrengthsStrengths:: Same as NPVSame as NPV Allows Allows comparison of comparison of different scale different scale projectsprojects

WeaknessesWeaknesses:: Same as NPVSame as NPV Provides only relative Provides only relative

profitabilityprofitability Potential Ranking Potential Ranking

ProblemsProblems

Internal Rate of Return Internal Rate of Return (IRR)(IRR)

IRR is the discount rate that equates IRR is the discount rate that equates the present value of the future net the present value of the future net

cash flows from an investment cash flows from an investment project with the project’s initial cash project with the project’s initial cash

outflow.outflow.

CF1 CF2 CFn (1+IRR)1 (1+IRR)2 (1+IRR)n

+ . . . ++ICO =

$15,000 $10,000 $7,000

IRR SolutionIRR Solution

$10,000 $12,000

(1+IRR)1 (1+IRR)2

Find the interest rate (Find the interest rate (IRRIRR) that causes the ) that causes the discounted cash flows to equal discounted cash flows to equal $40,000$40,000..

+ +

++$40,000 =

(1+IRR)3 (1+IRR)4 (1+IRR)5

IRR Solution (Try 10%)IRR Solution (Try 10%)

$40,000$40,000 = = $10,000(PVIF$10,000(PVIF10%10%,,11) + ) + $12,000(PVIF$12,000(PVIF10%10%,,22) )

+ $15,000(PVIF+ $15,000(PVIF10%10%,,33) + ) + $10,000(PVIF$10,000(PVIF10%10%,,44) + ) +

$ 7,000(PVIF$ 7,000(PVIF10%10%,,55) )

$40,000$40,000 = = $10,000(.909) + $12,000(.826) $10,000(.909) + $12,000(.826) + + $15,000(.751) + $15,000(.751) + $10,000(.683) + $10,000(.683) + $ $ 7,000(.621)7,000(.621)

$40,000$40,000 = = $9,090 + $9,912 + $11,265 + $9,090 + $9,912 + $11,265 + $6,830 + $4,347$6,830 + $4,347 = = $41,444$41,444

[[Rate is too low!!Rate is too low!!]]

IRR Solution (Try 15%)IRR Solution (Try 15%)

$40,000$40,000 = = $10,000(PVIF$10,000(PVIF15%15%,,11) + ) + $12,000(PVIF$12,000(PVIF15%15%,,22) + ) + $15,000(PVIF$15,000(PVIF15%15%,,33) + $10,000(PVIF) + $10,000(PVIF15%15%,,44) + ) +

$7,000(PVIF$7,000(PVIF15%15%,,55) )

$40,000$40,000 = = $10,000(.870) + $12,000(.756) + $10,000(.870) + $12,000(.756) + $15,000(.658) + $15,000(.658) +

$10,000(.572) + $ 7,000(.497)$10,000(.572) + $ 7,000(.497)

$40,000$40,000 = = $8,700 + $9,072 + $9,870 + $8,700 + $9,072 + $9,870 + $5,720 + $3,479$5,720 + $3,479 = = $36,841$36,841 [[Rate Rate is too high!!is too high!!]]

IRR Solution (Interpolate)IRR Solution (Interpolate)

IRRIRR = .10 + = .10 + .0157.0157 = = .1157 .1157 or or 11.57%11.57%

Decision Criteria

If IRR > cost of capital, accept the project

If IRR < cost of capital, reject the project

If IRR = cost of capital, technically indifferent

IRR Acceptance IRR Acceptance CriterionCriterion

No! No! The firm will receive The firm will receive 11.57%11.57% for each dollar invested in this for each dollar invested in this

project at a cost of project at a cost of 13%13%. [ . [ IRRIRR < < Hurdle Rate Hurdle Rate ]]

No! No! The firm will receive The firm will receive 11.57%11.57% for each dollar invested in this for each dollar invested in this

project at a cost of project at a cost of 13%13%. [ . [ IRRIRR < < Hurdle Rate Hurdle Rate ]]

The management of The management of Basket Basket Wonders Wonders has determined that the has determined that the hurdle rate hurdle rate is is 13% 13% for projects of for projects of

this type.this type.


IRR Strengths and WeaknessesIRR Strengths and Weaknesses

StrengthsStrengths: : Accounts for Accounts for

TVMTVM Considers all Considers all

cash cash flowsflows Less Less

SubjectivitySubjectivity

StrengthsStrengths: : Accounts for Accounts for

TVMTVM Considers all Considers all

cash cash flowsflows Less Less

SubjectivitySubjectivity

WeaknessesWeaknesses: : Assumes all cash Assumes all cash

flows reinvested at flows reinvested at the IRRthe IRR

Difficulties with Difficulties with project rankings project rankings

and and Multiple IRRsMultiple IRRs

Evaluation SummaryEvaluation Summary

Basket Wonders Independent Project

9-30

Which Approach is Which Approach is Better?Better?

On a purely theoretical basis, NPV is the On a purely theoretical basis, NPV is the better approach because:better approach because: NPV assumes that intermediate cash flows are NPV assumes that intermediate cash flows are

reinvested at the cost of capital whereas IRR reinvested at the cost of capital whereas IRR assumes they are reinvested at the IRR,assumes they are reinvested at the IRR,

Certain mathematical properties may cause a Certain mathematical properties may cause a project with non-conventional cash flows to have project with non-conventional cash flows to have more than one real IRR. more than one real IRR.

Despite its theoretical superiority, however, Despite its theoretical superiority, however, financial managers prefer to use the IRR financial managers prefer to use the IRR because of the preference for rates of because of the preference for rates of return.return.

Potential Ranking Problems Potential Ranking Problems Under Mutual ExclusivityUnder Mutual Exclusivity

A. Scale of InvestmentA. Scale of Investment

B. Cash-flow PatternB. Cash-flow Pattern

C. Project LifeC. Project Life

A. Scale of InvestmentA. Scale of Investment

B. Cash-flow PatternB. Cash-flow Pattern

C. Project LifeC. Project Life

Ranking of project proposals Ranking of project proposals may may create create contradictory results.contradictory results.

A. Scale DifferencesA. Scale Differences

Compare a small (S) and a large (L) Compare a small (S) and a large (L) project.project.

NET CASH FLOWSProject S Project LEND OF YEAR

0 -$100 -$100,000

1 0 0

2 $400 $156,250

S S .50 Yrs 100% .50 Yrs 100% $231 $231 3.31 3.31

L 1.28 Yrs 25%L 1.28 Yrs 25% $29,132 $29,132 1.291.29 S S .50 Yrs 100% .50 Yrs 100% $231 $231 3.31 3.31

L 1.28 Yrs 25%L 1.28 Yrs 25% $29,132 $29,132 1.291.29

Scale DifferencesScale Differences

Calculate the PBP, IRR, NPV@10%, Calculate the PBP, IRR, NPV@10%, and PI@10%.and PI@10%.

Which project is preferred? Why?Which project is preferred? Why?ProjectProject PBPPBP IRRIRR NPVNPV PIPI

B. Cash Flow PatternB. Cash Flow Pattern

Let us compare a Let us compare a decreasingdecreasing cash-flow (D) cash-flow (D) project and an project and an increasingincreasing cash-flow (I) project. cash-flow (I) project.

NET CASH FLOWSProject D Project IEND OF YEAR

0 -$1,200 -$1,200 1 1,000 100

2 500 600

3 100 1,080

DD 23%23% $198 1.17 $198 1.17

II 17% 17% $198 1.17 $198 1.17 DD 23%23% $198 1.17 $198 1.17

II 17% 17% $198 1.17 $198 1.17

Cash Flow PatternCash Flow Pattern

Calculate the IRR, NPV@10%, and Calculate the IRR, NPV@10%, and PI@10%.PI@10%.

Which project is preferred? Which project is preferred?

ProjectProject IRRIRR NPVNPV PIPI

Examine NPV ProfilesExamine NPV Profiles

Discount Rate (%)0 5 10 15 20 25-2

00

0

200

400

600

IRR

NPV@10%

Plot NPV for eachproject at various

discount rates.

Net

Pre

sen

t V

alu

e ($

)

Fisher’s Rate of Fisher’s Rate of IntersectionIntersection

Discount Rate ($)0 5 10 15 20 25-2

00

0

200

400

600

Net

Pre

sen

t V

alu

e ($

)

At k<10%, I is best!At k<10%, I is best! Fisher’s Fisher’s RateRate of ofIntersectionIntersection

At k>10%, D is best!At k>10%, D is best!

Let us compare a Let us compare a longlong life (X) life (X) project and a project and a shortshort life (Y) project. life (Y) project.

NET CASH FLOWSProject X Project YEND OF YEAR

0 -$1,000 -$1,000 1 0 2,000

2 0 0

3 3,375 0

C. Project Life DifferencesC. Project Life Differences

Project Life DifferencesProject Life Differences

X 50% X 50% $1,536 2.54$1,536 2.54

YY 100% 100% $ 818 1.82$ 818 1.82 X 50% X 50% $1,536 2.54$1,536 2.54

YY 100% 100% $ 818 1.82$ 818 1.82

Calculate the PBP, IRR, NPV@10%, Calculate the PBP, IRR, NPV@10%, and PI@10%.and PI@10%.

Which project is preferred? Why?Which project is preferred? Why?

ProjectProject IRRIRR NPVNPV PIPI

Capital RationingCapital Rationing

Capital Rationing Capital Rationing occurs when a occurs when a constraint (or budget ceiling) is constraint (or budget ceiling) is

placed on the total size of capital placed on the total size of capital expenditures during a particular expenditures during a particular

period.period.ExampleExample

Julie Miller must determine what Julie Miller must determine what investment opportunities to investment opportunities to

undertake for undertake for Basket Wonders Basket Wonders (BW)(BW). She is limited to a . She is limited to a maximum maximum

expenditure of $32,500 expenditure of $32,500 onlyonly for for 199X.199X.

Available Projects for BWAvailable Projects for BW

Project ICO IRR NPV PIProject ICO IRR NPV PI A $ 500 18%A $ 500 18% $ 50 1.10 $ 50 1.10

BB 5,000 5,000 25 25 6,500 2.30 6,500 2.30

C C 5,000 5,000 37 37 5,500 2.10 5,500 2.10 DD 7,5007,500 20 20 5,000 1.67 5,000 1.67 EE 12,50012,500

26 26 500 1.04 500 1.04

FF 15,000 15,000 28 28 21,000 2.40 21,000 2.40

GG 17,50017,500 19 19 7,500 7,500 1.43 1.43 HH 25,00025,000 15 15 6,000 1.246,000 1.24

Choosing by IRRs for BWChoosing by IRRs for BW

Project ICO IRR NPV PIProject ICO IRR NPV PI C $ 5,000C $ 5,000 37%37% $ 5,500 2.10 $ 5,500 2.10 FF 15,000 15,000 2828 21,000 2.40 21,000 2.40 EE 12,500 12,500 2626 500 1.04 500 1.04 BB 5,000 5,000 2525 6,500 2.3 6,500 2.3

Projects C, F, and E have the three Projects C, F, and E have the three largest largest IRRsIRRs..

The resulting The resulting increaseincrease inin shareholder wealth shareholder wealth is is $27,000$27,000 with a with a $32,500 outlay$32,500 outlay..

Choosing by NPVs for Choosing by NPVs for BWBW

Project ICO IRR NPV Project ICO IRR NPV PIPI

F $15,000 F $15,000 28% 28% $21,000$21,000 2.40 2.40

G 17,500G 17,500 19 19 7,5007,500 1.43 1.43

B 5,000B 5,000 25 25 6,500 2.30 6,500 2.30

Projects F and G have the two Projects F and G have the two largest largest NPVsNPVs..

The resulting The resulting increase increase inin shareholder shareholder wealthwealth is is $28,500$28,500 with a with a $32,500 outlay$32,500 outlay..

Choosing by PIs for BWChoosing by PIs for BW

Project ICO IRR NPV PIProject ICO IRR NPV PI FF $15,000 $15,000 28% 28% $21,000$21,000 2.402.40

BB 5,000 5,000 25 25 6,500 6,500 2.302.30 C C 5,000 5,000 37 37 5,500 5,500

2.102.10 DD 7,500 7,500 20 20 5,0005,000 1.671.67 GG 17,500 17,500 19 19 7,500 7,500 1.431.43

Projects F, B, C and D have the four Projects F, B, C and D have the four largest PIslargest PIs..

The resulting The resulting increaseincrease inin shareholder wealth shareholder wealth is is $38,000$38,000 with a with a $32,500 outlay$32,500 outlay..

Summary of ComparisonSummary of Comparison

MethodMethod Projects AcceptedProjects Accepted Value Value AddedAdded

PIPI F, B, C, and D $38,000 F, B, C, and D $38,000

NPVNPV F and G $28,500 F and G $28,500

IRRIRR C, F and E $27,000C, F and E $27,000

PIPI generates the generates the greatestgreatest increaseincrease in in shareholder wealth shareholder wealth when a limited when a limited

capital budget exists for a capital budget exists for a single periodsingle period..

Post-Completion AuditPost-Completion Audit

Post-completion AuditPost-completion Audit

A formal comparison of the actual costs A formal comparison of the actual costs and benefits of a project with original and benefits of a project with original

estimates.estimates. Identify any project weaknessesIdentify any project weaknesses

Develop a possible set of corrective Develop a possible set of corrective actionsactions

Provide appropriate feedbackProvide appropriate feedback

Result: Result: Making better future decisions!Making better future decisions!

Technology

Capital budgeting techniques