Project evalaution techniques
description
Transcript of Project evalaution techniques
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Project Evaluation: Project Evaluation: Alternative MethodsAlternative MethodsProject Evaluation: 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)
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Proposed Project DataProposed Project DataProposed Project DataProposed Project Data
Julie Miller is evaluating a new project for her firm. She has determined that
the after-tax cash flows for the project will be $10,000; $12,000;
$15,000; $10,000; and $7,000, respectively, for each of the Years 1
through 5. The initial cash outlay will be $40,000.
Julie Miller is evaluating a new project for her firm. She has determined that
the after-tax cash flows for the project will be $10,000; $12,000;
$15,000; $10,000; and $7,000, respectively, for each of the Years 1
through 5. The initial cash outlay will be $40,000.
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Independent ProjectIndependent Project
IndependentIndependent -- A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.
For this project, assume that it is independent of any other potential projects that She may undertake.
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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 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 last negative cumulative cash flow
value.
PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years
Note: Take absolute value of last negative cumulative cash flow
value.
CumulativeCash 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 3.5 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?
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PBP Strengths PBP Strengths and Weaknessesand WeaknessesPBP 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
Does not consider cash flows
beyond the PBP
Cutoff period is subjective
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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 =
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$15,000 $10,000 $7,000
IRR SolutionIRR Solution IRR SolutionIRR Solution
$10,000 $12,000
(1+IRR)1 (1+IRR)2
Find the interest rate (IRR) that causes the discounted 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 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 rate
is 13% for projects of this type.
Should this project be accepted?
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IRR Strengths IRR Strengths and Weaknessesand WeaknessesIRR 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
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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 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 =
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Basket Wonders has determined that the appropriate discount rate (k) for this
project is 13%.
$10,000 $7,000
NPV SolutionNPV Solution 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 = +
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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 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?
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NPV Strengths NPV Strengths and Weaknessesand WeaknessesNPV 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.
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Net Present Value ProfileNet Present Value ProfileNet Present Value ProfileNet Present Value Profile
Discount Rate (%)0 3 6 9 12 15
IRRNPV@13%
Sum of CF’s Plot NPV for eachdiscount rate.Three of these points are easy now!
Net
Pre
sen
t V
alu
e
$000s15
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 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:
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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 = $38,572 / $40,000
= .9643 (Method #1, 13-34)
Should this project be accepted?
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PI Strengths PI Strengths and Weaknessesand WeaknessesPI 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
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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 Reject
PI .96 1.00 Reject
Basket Wonders Independent Project
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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.
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Potential Problems Potential Problems Under Mutual ExclusivityUnder Mutual ExclusivityPotential 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.
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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 -$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 1.17
I 17% $198 1.17$198 1.17
D 23% $198 1.17$198 1.17
I 17% $198 1.17$198 1.17
Cash Flow PatternCash Flow PatternCash Flow PatternCash Flow Pattern
Calculate the IRR, NPV@10%, and PI@10%.
Which project is preferred?
Project IRR NPV PI
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Examine NPV ProfilesExamine NPV ProfilesExamine NPV ProfilesExamine NPV Profiles
Discount Rate (%)0 5 10 15 20 25-2
00
0
200
400
600
IRR
NPV@10%
Plot NPV for eachproject at various
discount rates.
Net
Pre
sen
t V
alu
e ($
)
Project IProject I
Project DProject D
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Fisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of Intersection
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!
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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 -$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 to Another Way to Look at ThingsLook at Things
1. Adjust cash flows to a common terminal year 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 Projects Replacing 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 $2,000-1,000 $2,000
-1,000 $2,000-1,000 $2,000
-$1,000 $1,000 $1,000 $2,000-$1,000 $1,000 $1,000 $2,000
Results: 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 a constraint (or budget ceiling) is placed on the total size of capital expenditures
during a particular period.
Example: Julie Miller must determine what investment opportunities to undertake for Basket Wonders (BW). She is limited to a maximum expenditure of $32,500 only for this 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 2.30 C 5,000 37 5,500 2.10 D 7,500 20 5,000 1.67 E 12,500 26 500 1.04 F 15,000 28 21,000 2.40 G 17,500 19 7,500 1.43 H 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 2.10 F 15,000 28 21,000 2.40 E 12,500 26 500 1.04 B 5,000 25 6,500 2.30
Projects C, F, and E have the three largest IRRs.
The resulting increase in shareholder wealth is $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 1.43 B 5,000 25 6,500 2.30
Projects F and G have the two largest NPVs.
The resulting increase in shareholder wealth is $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 2.10 D 7,500 20 5,000 1.67 G 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 $28,500
IRR C, F, and E $27,000
PIPI generates the greatestgreatest increaseincrease in shareholder wealth shareholder wealth when a limited capital
budget exists for a single period.
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Single-Point Estimate Single-Point Estimate and Sensitivity Analysisand Sensitivity AnalysisSingle-Point Estimate Single-Point Estimate and Sensitivity Analysisand Sensitivity Analysis
Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis
Utilize a “base-case” to compare the impact of individual variable changes E.g., Change forecasted sales units to see
impact on the project’s NPV
Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis
Utilize a “base-case” to compare the impact of individual variable changes E.g., Change forecasted sales units to see
impact on the project’s NPV
Sensitivity AnalysisSensitivity Analysis: A type of “what-if” uncertainty analysis in which variables or assumptions are changed from a base case in order to determine their impact on a project’s measured results (such as NPV or IRR).
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Post-Completion AuditPost-Completion Audit
Post-completion Audit
A formal comparison of the actual costs and benefits of a project with original estimates.
Identify any project weaknesses
Develop a possible set of corrective actions
Provide appropriate feedback
Result: Making better future decisions!
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Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*
Two!! Two!! There are as many potential IRRs as there are sign changes.
Two!! Two!! There are as many potential IRRs as there are sign changes.
Let us assume the following cash flow pattern for a project for Years 0 to 4:
-$100 +$100 +$900 -$1,000
How many How many potentialpotential IRRs could this IRRs could this project have?project have?
* Refer to Appendix A
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NPV Profile -- Multiple IRRsNPV Profile -- Multiple IRRsNPV Profile -- Multiple IRRsNPV Profile -- Multiple IRRs
Discount Rate (%)0 40 80 120 160 200
Net
Pre
sen
t V
alu
e($
000s
)
Multiple IRRs atk k = 12.95%12.95% and 191.15%191.15%
75
50
25
0
-100
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NPV Profile -- Multiple IRRsNPV Profile -- Multiple IRRs
Hint: Your calculator will only find ONE IRR – even if there
are multiple IRRs. It will give you the
lowest IRR. In this case, 12.95%.