FProyectos-05-Evaluación Financiera

8/13/2019 FProyectos-05-Evaluacin Financiera

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Milagro, Abril 2013

Gestin de Proyectos Informticos

Richard Ramrez-Anormaliza [email protected]


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Estudio financieroEstudio financiero

Determina en ltimo trmino suaprobacin o rechazo.


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Herramientas del estudioHerramientas del estudio

financierofinanciero

Anlisis de rentabilidad

Flujo de caja

VAN

TIR

Periodo de recuperacin deinversin


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Project EvaluationProject EvaluationProject EvaluationProject Evaluation

2001 Prentice-Hall , Inc.Fundamentals of Financial Management, 11/e

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


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Project Evaluation:Project Evaluation:

Alternative MethodsAlternative Methods

Project Evaluation:Project Evaluation:

Alternative MethodsAlternative Methods

Payback Period (PBP)

Internal Rate of Return (IRR)

Net Present Value (NPV)

Profitabil ity Index (PI)

Payback Period (PBP)

Internal Rate of Return (IRR)

Net Present Value (NPV)

Profitabil ity Index (PI)


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Independent ProjectIndependent Project

IndependentIndependent -- A project whose

acceptance (or rejection) does notprevent the acceptance of otherprojects under consideration.

For this project, assume that it isindependent of any other potential

projects that Basket Wonders mayundertake.


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

PBPPBP is the period of timerequired for the cumulative

expected cash flows from aninvestment project to equalthe initial cash outflow.

PBPPBP is the period of timerequired for the cumulative

expected cash flows from aninvestment project to equalthe initial cash outflow.

0 1 2 3 4 5

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


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

Payback Solution (#1)Payback Solution (#1)Payback Solution (#1)Payback Solution (#1)

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

0 1 2 3 4 5

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

CumulativeInflows

(a)

(-b) (d)


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Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of lastnegative cumulative cash flow

value.

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of lastnegative cumulative cash flow

value.

Cumulative

Cash Flows

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

0 1 2 3 4 5

-40 K -30 K -18 K -3 K 7 K 14 K


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PBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance Criterion

Yes! The firm will receive back the

initial cash outlay in less than 3.5years. [3.3 Years < 3.5 Year Max.]

Yes! The firm will receive back the

initial cash outlay in less than 3.5years. [3.3 Years < 3.5 Year Max.]

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

Should this project be accepted?


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PBP StrengthsPBP Strengths

and Weaknessesand Weaknesses

PBP StrengthsPBP Strengths

and Weaknessesand WeaknessesStrengthsStrengths::

Easy to use and

understand

Can be used as ameasure of

liquidity Easier to forecast

ST than LT flows

StrengthsStrengths::

Easy to use and

understand

Can be used as ameasure of

liquidity Easier to forecast

ST than LT flows

WeaknessesWeaknesses::

Does not account

for TVM

Does not considercash flows beyond

the PBP Cutoff period is

subjective


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

IRR SolutionIRR SolutionIRR SolutionIRR Solution

$10,000 $12,000

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

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

+ +

++$40,000 =

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


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

$40,000$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) +$15,000(PVIF10%,3) + $10,000(PVIF10%,4) +$ 7,000(PVIF10%,5)

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

$40,000$40,000 = $9,090 + $9,912 + $11,265 +$6,830 + $4,347= $41,444$41,444 [[Rate is too low!!Rate is too low!!]]


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

$40,000$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) +$15,000(PVIF15%,3) + $10,000(PVIF15%,4) +$ 7,000(PVIF15%,5)

$40,000$40,000 = $10,000(.870) + $12,000(.756) +$15,000(.658) + $10,000(.572) +$ 7,000(.497)

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


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.10 $41,444

.05 IRR $40,000 $4,603

.15 $36,841

X $1,444.05 $4,603

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

$1,444X

=


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.10 $41,444

.05 IRR $40,000 $4,603

.15 $36,841

X $1,444.05 $4,603


$1,444X

=


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.10 $41,444

.05 IRR $40,000 $4,603

.15 $36,841

($1,444)(0.05)$4,603


$1,444X

X = X = .0157

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


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IRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance Criterion

No! The firm will receive 11.57% for

each dollar invested in this project ata cost of 13%. [ IRR < Hurdle Rate ]

No! The firm will receive 11.57% for

each dollar invested in this project ata cost of 13%. [ IRR < Hurdle Rate ]

The management of Basket Wondershas determined that the hurdle rate

is 13% for projects of this type.



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IRR StrengthsIRR Strengths


IRR StrengthsIRR Strengths

and Weaknessesand WeaknessesStrengthsStrengths::

Accounts for

TVM

Considers allcash flows

Lesssubjectivity


Accounts for

TVM

Considers allcash flows

Lesssubjectivity


Assumes all cash

flows reinvested atthe IRR

Difficulties with

project rankings andMultiple IRRs


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

NPV is the present value of aninvestment projects net cash

flows minus the projects initialcash outflow.

CF1 CF2 CFn(1+k)1 (1+k)2 (1+k)n+ . . . ++ - ICOICONPV =


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Basket Wonders has determined that theappropriate discount rate (k) for this

project is 13%.

$10,000 $7,000

NPV SolutionNPV SolutionNPV 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 = +


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NPV SolutionNPV SolutionNPV SolutionNPV Solution

NPVNPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) +$15,000(PVIF13%,3) + $10,000(PVIF13%,4) +$ 7,000(PVIF13%,5) - $40,000$40,000

NPVNPV = $10,000(.885) + $12,000(.783) +$15,000(.693) + $10,000(.613) +$ 7,000(.543) - $40,000$40,000

NPVNPV = $8,850 + $9,396 + $10,395 +

$6,130 + $3,801 - $40,000$40,000

= - $1,428$1,428


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NPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance Criterion

No! The NPV is negative. This means

that the project is reducing shareholderwealth. [RejectReject as NPVNPV < 00 ]

No! The NPV is negative. This means

that the project is reducing shareholderwealth. [RejectReject as NPVNPV < 00 ]

The management of Basket Wondershas determined that the required

rate is 13% for projects of this type.



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NPV StrengthsNPV Strengths


NPV StrengthsNPV Strengths



Cash flows

assumed to bereinvested at thehurdle rate.

Accounts for TVM. Considers all

cash flows.


Cash flows

assumed to bereinvested at thehurdle rate.

Accounts for TVM. Considers all

cash flows.


May not include

managerialoptions embeddedin the project. SeeChapter 14.


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Net Present Value Profi leNet Present Value Profi leNet Present Value Profi leNet Present Value Profi le

Discount Rate (%)

0 3 6 9 12 15

IRRNPV@13%

Sum of CFs Plot NPV for eachdiscount rate.

NetPresent

Value

$000s

15

10

5

0

-4


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

PI is the ratio of the present value ofa projects future net cash flows to

the projects initial cash outflow.CF1 CF2 CFn

(1+k)1 (1+k)2 (1+k)n+ . . . ++ ICOICOPI =

PI = 1 + [ NPVNPV / ICOICO ]

>


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PI Acceptance CriterionPI Acceptance CriterionPI Acceptance CriterionPI Acceptance Criterion

No! The PIPI is less than 1.00. This

means that the project is not profitable.[RejectReject as PIPI < 1.001.00 ]

No! The PIPI is less than 1.00. This

means that the project is not profitable.[RejectReject as PIPI < 1.001.00 ]

PIPI = $38,572 / $40,000

= .9643 (Method #1, 13-33)



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PI StrengthsPI Strengths


PI StrengthsPI Strengths



Same as NPV Allows

comparison ofdifferent scale

projects


Same as NPV Allows

comparison ofdifferent scale

projects


Same as NPV Provides only

relative profitability

Potential RankingProblems


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Evaluation SummaryEvaluation Summary

Method Project Comparison Decision

PBP 3.3 3.5 Accept

IRR 11.47% 13% Reject

NPV -$1,424 $0 RejectPI .96 1.00 Reject

Basket Wonders Independent Project


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Other ProjectOther Project

RelationshipsRelationships

Mutually ExclusiveMutually Exclusive -- A projectwhose acceptance precludes the

acceptance of one or morealternative projects.

DependentDependent -- A project whoseacceptance depends on theacceptance of one or more otherprojects.


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Potential ProblemsPotential Problems

Under Mutual ExclusivityUnder Mutual Exclusivity

Potential ProblemsPotential Problems

Under Mutual ExclusivityUnder Mutual Exclusivity

A. Scale of InvestmentA. Scale of Investment

B. CashB. Cash--flow Patternflow Pattern

C. Project LifeC. Project Life

A. Scale of InvestmentA. Scale of Investment

B. CashB. Cash--flow Patternflow Pattern

C. Project LifeC. Project Life

Ranking of project proposals maycreate contradictory results.


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

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

NET CASH FLOWS

Project S Project LEND OF YEAR

0 -$100 -$100,000

1 0 0

2 $400 $156,250


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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% $ 231 3.31

L 25% $29,132 1.29

S 100% $ 231 3.31

L 25% $29,132 1.29


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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 -$1,200 -$1,200

1 1,000 100

2 500 600

3 100 1,080


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D 23% $198 1.17$198 1.17I 17% $198 1.17$198 1.17D 23% $198 1.17$198 1.17I 17% $198 1.17$198 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


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Examine NPV ProfilesExamine NPV ProfilesExamine NPV ProfilesExamine NPV Profiles

Discount Rate (%)

0 5 10 15 20 25-200

0

200

400

600

IRR

NPV@10%

Plot NPV for eachproject at various

discount rates.

N

etPresentVa

lue

($)


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Fishers Rate of IntersectionFishers Rate of IntersectionFishers Rate of IntersectionFishers Rate of Intersection

Discount Rate ($)

0 5 10 15 20 25-200

0

200

400

600

N

etPresentV

alue($)

At k10%, D is best!


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

Let us compare a long li fe (X) projectand a short li fe (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


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X 50% $1,536 2.54

Y 100% $ 818 1.82

X 50% $1,536 2.54

Y 100% $ 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


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Another Way toAnother Way to

Look at ThingsLook at Things

1. Adjust cash f lows to a common terminalyear if project Y will NOTNOT be replaced.

Compound Project Y, Year 1 @10% for 2 years.

Year 0 1 2 3

CF -$1,000 $0 $0 $2,420

Results: IRR* = 34.26% NPV = $818

*Lower IRR from adjusted cash-flow stream. X is still Best.


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Replacing ProjectsReplacing Projects

with Identical Projectswith Identical Projects

2. Use Replacement Chain Approach (Appendix B)when project Y will be replaced.

0 1 2 3

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

--1,000 $2,0001,000 $2,000--1,000 $2,0001,000 $2,000

--$1,000 $1,000 $1,000 $2,000$1,000 $1,000 $1,000 $2,000Results: IRR* = 100% NPV*NPV* = $2,238.17$2,238.17

*Higher NPV, but the same IRR. Y is BestY is Best.


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Capital RationingCapital Rationing

Capital Rationing occurs when aconstraint (or budget ceiling) is placedon the total size of capital expenditures

during a particular period.

Example: Julie Miller must determine whatinvestment opportunit ies to undertake for

Basket Wonders (BW). She is limited to amaximum expenditure of $32,500 only forthis capital budgeting period.


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Available Projects for BWAvailable Projects for BW

Project ICO IRR NPV PI

A $ 500 18% $ 50 1.10

B 5,000 25 6,500 2.30C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67E 12,500 26 500 1.04F 15,000 28 21,000 2.40

G 17,500 19 7,500 1.43H 25,000 15 6,000 1.24


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Choosing by IRRs for BWChoosing by IRRs for BW


C $ 5,000 37% $ 5,500 2.10F 15,000 28 21,000 2.40E 12,500 26 500 1.04B 5,000 25 6,500 2.30

Projects C, F, and E have thethree largest IRRs.

The result ing increase in shareholder wealthis $27,000 with a $32,500 outlay.


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Choosing by NPVs for BWChoosing by NPVs for BW


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

G 17,500 19 7,500 1.43B 5,000 25 6,500 2.30

Projects F and G have thetwo largest NPVs.

The result ing increase in shareholder wealthis $28,500 with a $32,500 outlay.


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Choosing by PIs for BWChoosing by PIs for BW


F $15,000 28% $21,000 2.40B 5,000 25 6,500 2.30

C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67G 17,500 19 7,500 1.43

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

The resulting increase in shareholder wealth is$38,000 with a $32,500 outlay.


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Summary of ComparisonSummary of Comparison

Method Projects Accepted Value Added

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

NPV F and G $28,500IRR C, F, and E $27,000

PIPI generates the greatestgreatest increaseincrease inshareholder wealthshareholder wealth when a limited capital

budget exists for a single period.


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Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*

Two!!Two!! There are as many potentialIRRs as there are sign changes.Two!!Two!! There are as many potentialIRRs as there are sign changes.

Let us assume the following cash flowpattern for a project for Years 0 to 4:

-$100 +$100 +$900 -$1,000How manyHow many potentialpotential IRRs could thisIRRs could this

project have?project have?

* Refer to Appendix A


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NPV ProfileNPV Profile ---- Multiple IRRsMultiple IRRsNPV ProfileNPV Profile ---- Multiple IRRsMultiple IRRs

Discount Rate (%)

0 40 80 120 160 200

NetPresentValue

($000s)

Multiple IRRs atkk = 12.95%12.95% and 191.15%191.15%

75

50

25

0

-100


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Practica 1Practica 1

Una firma de ingenieros consultores quiere decidir entrecomprar o alquilar automviles. Se calcula que losautomvi les de tamao medio costarn $8.300 y tendrn unvalor probable de reventa a los 4 aos de $2.800. El costo

anual de combustible y repuestos se supone de $950 elprimer ao, con incrementos de $50 anuales. De otra partela compaa podra alquilar los mismos automviles a$3.500 anuales pagaderos al comienzo de cada ao. Comoel precio de alquiler incluye algn mantenimiento, secalcula que los costos anuales de operacin ymantenimiento seran $100 menos que si compraran losautos. Si la tasa de retorno mnima para la compaa es18%, qu alternativa debe seleccionar?


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Deber.Deber.-- IndividualIndividual

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