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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
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
($1,444)(0.05)$4,603
IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)
$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.
Should this project be accepted?
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IRR StrengthsIRR Strengths
and Weaknessesand Weaknesses
IRR StrengthsIRR Strengths
and Weaknessesand WeaknessesStrengthsStrengths::
Accounts for
TVM
Considers allcash flows
Lesssubjectivity
StrengthsStrengths::
Accounts for
TVM
Considers allcash flows
Lesssubjectivity
WeaknessesWeaknesses::
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.
Should this project be accepted?
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NPV StrengthsNPV Strengths
and Weaknessesand Weaknesses
NPV StrengthsNPV Strengths
and Weaknessesand Weaknesses
StrengthsStrengths::
Cash flows
assumed to bereinvested at thehurdle rate.
Accounts for TVM. Considers all
cash flows.
StrengthsStrengths::
Cash flows
assumed to bereinvested at thehurdle rate.
Accounts for TVM. Considers all
cash flows.
WeaknessesWeaknesses::
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)
Should this project be accepted?
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PI StrengthsPI Strengths
and Weaknessesand Weaknesses
PI StrengthsPI Strengths
and Weaknessesand Weaknesses
StrengthsStrengths::
Same as NPV Allows
comparison ofdifferent scale
projects
StrengthsStrengths::
Same as NPV Allows
comparison ofdifferent scale
projects
WeaknessesWeaknesses::
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
Project ICO IRR NPV PI
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
Project ICO IRR NPV PI
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
Project ICO IRR NPV PI
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