Chapter 13Chapter 13

Capital Budgeting Capital Budgeting TechniquesTechniques

Capital Budgeting Capital Budgeting TechniquesTechniques

© Pearson Education Limited 2004Fundamentals of Financial Management, 12/e

Created by: Gregory A. Kuhlemeyer, Ph.D.Carroll College, Waukesha, WI

Proposed Project DataProposed Project DataProposed Project DataProposed Project Data

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be Tk10,000; Tk12,000; Tk15,000; Tk10,000; and Tk7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be Tk40,000.

• For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake.

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

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be Tk10,000; Tk12,000; Tk15,000; Tk10,000; and Tk7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be Tk40,000.

• For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake.

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

1. Project Evaluation: 1. Project Evaluation: Alternative MethodsAlternative Methods

1. Project Evaluation: 1. Project Evaluation: Alternative MethodsAlternative Methods

– Payback Period (PBP)– Internal Rate of Return (IRR)– Net Present Value (NPV)– Profitability Index (PI)

– Payback Period (PBP)– Internal Rate of Return (IRR)– Net Present Value (NPV)– Profitability Index (PI)

Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)

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

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

0 1 2 3 4 5

-40 K 10 K 12 K 15 K 10 K 7 K10 K 22 K 37 K 47 K 54 K

Cumulative Inflows

PBPPBP = a + ( b - c ) / d = 3 + (40 - 37) / 10

= 3 + (3) / 10

= 3.3 Years3.3 Years

PBPPBP = a + ( b - c ) / d = 3 + (40 - 37) / 10

= 3 + (3) / 10

= 3.3 Years3.3 Years

(a)

(c)-b(d)

a – minimum whole year for recovery

b – initial cash outflow

c – maximum amount not crossing b

d – portion of payment necessary for payback

a – minimum whole year for recovery

b – initial cash outflow

c – maximum amount not crossing b

d – portion of payment necessary for payback

PBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance Criterion

Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]

Yes! The firm will receive back the initial cash outlay in less than 3.5 years. [3.3 Years < 3.5 Year Max.]

The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.

Should this project be accepted?

If maximum PBP is set for 3 years?

No! The firm will receive back the initial cash outlay in more than 3 years. [3.3 Years > 3 Year Max.]

If maximum PBP is set for 3 years?

No! The firm will receive back the initial cash outlay in more than 3 years. [3.3 Years > 3 Year Max.]

PBP Strengths PBP Strengths and Weaknessesand Weaknesses

PBP Strengths PBP Strengths and Weaknessesand Weaknesses

StrengthsStrengths::– Easy to use and understand

– Can be used as a

measure of liquidity– Easier to forecast

ST than LT flows

StrengthsStrengths::– Easy to use and understand

– Can be used as a

measure of liquidity– Easier to forecast

ST than LT flows

WeaknessesWeaknesses::– Does not account for TVM (time value of money)

– Does not consider cash flows beyond the PBP

– Cutoff period is subjective

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

IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash

outflow.

CF1 CF2 CFn

(1+IRR)1 (1+IRR)2 (1+IRR)n+ . . . +

+ICO = +

Tk15,000 Tk10,000 Tk7,000Tk10,000 Tk12,000

(1+IRR)1 (1+IRR)2+Tk40,000 =

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

Find the interest rate (IRR) that causes the discounted cash flows to equal Tk40,000.

IRR Solution (Try 10% and 15%)IRR Solution (Try 10% and 15%)IRR Solution (Try 10% and 15%)IRR Solution (Try 10% and 15%)

Tk40,000Tk40,000 = Tk10,000(PVIF10%,1) + Tk12,000(PVIF10%,2) +Tk15,000(PVIF10%,3) + Tk10,000(PVIF10%,4) + Tk 7,000(PVIF10%,5)

Tk40,000Tk40,000 = Tk10,000(.909) + Tk12,000(.826) + Tk15,000(.751) + Tk10,000(.683) + Tk 7,000(.621)

Tk40,000Tk40,000 = Tk9,090 + Tk9,912 + Tk11,265 + Tk6,830 + Tk4,347

=Tk 41,444Tk 41,444 [[Rate is too low!!Rate is too low!!]]

Tk40,000Tk40,000 = Tk10,000(PVIF15%,1) + Tk12,000(PVIF15%,2) + Tk15,000(PVIF15%,3) + Tk10,000(PVIF15%,4) + Tk 7,000(PVIF15%,5)

Tk40,000Tk40,000 = Tk10,000(.870) + Tk12,000(.756) + Tk15,000(.658) + Tk10,000(.572) + Tk 7,000(.497)

Tk40,000Tk40,000 = Tk8,700 + Tk9,072 + Tk9,870 + Tk5,720 + Tk3,479 = Tk 36,841Tk 36,841 [[Rate is too high!!Rate is too high!!]]

.10 Tk41,444

.05 IRR Tk40,000 Tk4,603

.15 Tk36,841

X Tk1,444

IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)

Tk1,444X

=.05 Tk4,603

.10 Tk41,444

.05 IRR Tk40,000 Tk4,603

.15 Tk36,841

X Tk1,444

IRR Solution IRR Solution (Interpolate [Trial and Error])(Interpolate [Trial and Error])

IRR Solution IRR Solution (Interpolate [Trial and Error])(Interpolate [Trial and Error])

Tk1,444X

=.05 Tk4,603

.10 Tk41,444

.05 IRR Tk40,000 Tk4,603

.15 Tk36,841

(Tk1,444)(0.05)

IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)

Tk1,444X

X = X = .0157

IRR = .10 + .0157 = .1157 or 11.57%

Tk4,603

IRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance Criterion

No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%.

[ IRR < Hurdle Rate ]

No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%.

[ IRR < Hurdle Rate ]

The management of Basket Wonders has determined that the Hurdle (cutoff) rate is 13% for projects of this type.

Should this project be accepted?

IRR Strengths IRR Strengths and Weaknessesand Weaknesses

IRR Strengths IRR Strengths and Weaknessesand Weaknesses

StrengthsStrengths: : – Accounts for

TVM– Considers all

cash flows– Less

subjectivity

StrengthsStrengths: : – Accounts for

TVM– Considers all

cash flows– Less

subjectivity

WeaknessesWeaknesses: : – Assumes all cash

flows reinvested at the IRR– Difficulties with project rankings and Multiple IRRs

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

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

initial cash outflow.

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

+ . . . ++ - ICOICONPV =

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

13%.

Tk10,000 Tk7,000

NPV SolutionNPV Solution NPV SolutionNPV Solution

Tk10,000 Tk12,000 Tk15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - Tk40,000Tk40,000(1.13)4 (1.13)5

NPVNPV = +

NPV SolutionNPV SolutionNPV SolutionNPV Solution

NPVNPV = Tk10,000(PVIF13%,1) + Tk12,000(PVIF13%,2) + Tk15,000(PVIF13%,3) + Tk10,000(PVIF13%,4) + Tk 7,000(PVIF13%,5) - Tk40,000Tk40,000

NPVNPV = Tk10,000(.885) + Tk12,000(.783) + Tk15,000(.693) + Tk10,000(.613) + Tk 7,000(.543) - Tk40,000Tk40,000

NPVNPV = Tk8,850 + Tk9,396 + Tk10,395 + Tk6,130 + Tk3,801 - Tk40,000Tk40,000

= - Tk1,428Tk1,428

NPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance Criterion

No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject Reject

as NPVNPV < 00 ]

No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject Reject

as NPVNPV < 00 ]

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

type.

Should this project be accepted?

NPV Strengths NPV Strengths and Weaknessesand Weaknesses

NPV Strengths NPV Strengths and Weaknessesand Weaknesses

StrengthsStrengths::– Cash flows

assumed to be reinvested at the hurdle rate.

– Accounts for TVM.– Considers all

cash flows.

StrengthsStrengths::– Cash flows

assumed to be reinvested at the hurdle rate.

– Accounts for TVM.– Considers all

cash flows.

WeaknessesWeaknesses::– May not include managerial options embedded in the project. See Chapter 14.

Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)

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

outflow.

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

+ . . . ++ ICOICOPI =

PI = 1 + [ NPVNPV / ICOICO ]

<< OR >>

Method #2:

Method #1:

PI Acceptance CriterionPI Acceptance Criterion PI Acceptance CriterionPI Acceptance Criterion

No! The PIPI is less than 1.00. This means that the project is not profitable. [Reject Reject as PIPI <

1.001.00 ]

No! The PIPI is less than 1.00. This means that the project is not profitable. [Reject Reject as PIPI <

1.001.00 ]

PIPI = Tk38,572 / Tk40,000= .9643 (Method #1, 13-34)

Should this project be accepted?

PI Strengths PI Strengths and Weaknessesand Weaknesses

PI Strengths PI Strengths and Weaknessesand Weaknesses

StrengthsStrengths::– Same as NPV– Allows comparison of different scale projects

StrengthsStrengths::– Same as NPV– Allows comparison of different scale projects

WeaknessesWeaknesses::– Same as NPV– Provides only relative profitability– Potential Ranking

Problems

Evaluation SummaryEvaluation Summary

Method Project Comparison Decision

PBP 3.3 3.5 Accept

IRR 11.47% 13% Reject

NPV -$1,424 $0 Reject

PI .96 1.00 Reject

Basket Wonders Independent Project

Other Project Other Project RelationshipsRelationships

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

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

Potential Problems Potential Problems Under Mutual ExclusivityUnder Mutual Exclusivity

Potential Problems Potential 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 may create contradictory results.

A. Scale DifferencesA. Scale DifferencesA. Scale DifferencesA. Scale Differences

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

NET CASH FLOWSProject S Project LEND OF YEAR

0 -Tk100 -Tk100,000

1 0 0

2 Tk400 Tk156,250

Scale DifferencesScale DifferencesScale DifferencesScale Differences

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

Which project is preferred? Why? Project IRR NPV PI

S 100% Tk 231 3.31

L 25% Tk29,132 1.29

S 100% Tk 231 3.31

L 25% Tk29,132 1.29

B. Cash Flow PatternB. Cash Flow PatternB. Cash Flow PatternB. Cash Flow Pattern

Let us compare a decreasing cash-flow (D) project and an increasing cash-flow (I) project.

NET CASH FLOWSProject D Project IEND OF YEAR

0 -Tk1,200 -Tk1,200 1 1,000 100

2 500 600

3 100 1,080

D 23% Tk198 1.17Tk198 1.17

I 17% Tk198 1.17Tk198 1.17

D 23% Tk198 1.17Tk198 1.17

I 17% Tk198 1.17Tk198 1.17

Cash Flow PatternCash Flow PatternCash Flow PatternCash Flow Pattern

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

Which project is preferred?

Project IRR NPV PI

Examine NPV ProfilesExamine NPV ProfilesExamine 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 (T

k)

Project IProject I

Project DProject D

Fisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of Intersection

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

00

0

200

400

600

Net

Pre

sen

t V

alu

e (T

k)

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!

C. Project Life DifferencesC. Project Life DifferencesC. Project Life DifferencesC. Project Life Differences

Let us compare a long life (X) project and a short life (Y) project.

NET CASH FLOWSProject X Project YEND OF YEAR

0 -Tk1,000 -Tk1,000 1 0 2,000

2 0 0

3 3,375 0

X 50% Tk1,536 2.54

Y 100% Tk 818 1.82

X 50% Tk1,536 2.54

Y 100% Tk 818 1.82

Project Life DifferencesProject Life DifferencesProject Life DifferencesProject Life Differences

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

Which project is preferred? Why?

Project IRR NPV PI