Chapter 8x
Transcript of Chapter 8x
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CHAPTER 8
Rate of Return Analysis:Multiple Alternatives
M cGrawHill
ENGINEERING ECONOMY SixthEdition
Blank and
Tarquin
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Learning Objectives
1. Why Incremental Analysis?
2. Incremental Cash Flows
3. Interpretation4. Incremental ROR by PW
5. Incremental ROR by AW
6. Multiple Alternatives
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Section 8.1Why Incremental Analysis is
Necessary
Assume we have two or moremutually exclusive alternative
Objective: Which, if any of thealternatives is preferred?
Prior Chapters: Use the PW or AWapproach
This chapter: We apply the RORapproach
Present Worth: Equal service livesmust apply
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8.1 Ranking Inconsistency
For some problems, PW and ROR mayrank the same problems differently.Why?
PW assumes reinvestment at theMARR or discount rate.
ROR assumes reinvestment at the i*
or i rate Two different reinvestment rateassumptions apply
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8.1 Review of Problem Types
INDEPENDENT AND MUTUALLY EXCLUSIVE ALTERNATIVES
INDEPENDENT - Selection of onealternative does not effect the selection of others. Example: select all projects with aROR> 20 %
MUTUALLY EXCLUSIVE - Selection on onealternative precludes the selection of others. Example: select the project with thehighest ROR.
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8.1 An Example Shows RankingInconsistency Problem
From Solomon {1956/59} Two Investments A and B Discount rate = 10%
Each investment requires $100 at t =0 A is a 1-year investment
B is a 5- year investment
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8.1 Two Projects; A and B
A
$100
0 1 2 3 45
$120
B
$100
0 1 2 3 45
$201.14
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8.1 Example Problem
i*A = 0.20 = 20%
i*B = 0.15 = 15% PW A(10%) = +$9.09
PB B(10%) = +24.89
Using ROR, A issuperior to B
Using PW, B issuperior to A
InconsistentRankings!
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8.1 Example Problem - Rankings
Using ROR Ranking
A is superior to B (20% > 15%)
Using a PW(10%) approach B is superior to A ($24.89 > $9.09)
The two methods do not rank thesame?
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8.1 Look at A and assumeReinvestment forward to t = 5
Find F 5 for Alt. A
$100
0 1 2 3 45
$120
F 5 = ?
F 5 = 120(F/P,10%,4)=$175.69
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8.1 ROR of A given reinvestment
-100 +120(F/P,10%,4)(P/F,i *A, 5) = 0
Solving for i* A
(P/F, i* A,5) = 0.569
i*A/reinvestment @10% = 0.1193
i*A/ c =10% = 11.93%
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8.1 Now Compare A to B
Compare revised A withreinvestment at 10% to B
i*
A/c = 10% = 11.93%
i* B = 15% as before
ROR Rankings:
B is superior to A (15% > 11.93%)
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8.1 Ranking Consistency
Now, PW(10%) and ROR with thereinvestment imposed on the 1-yearproject rank consistently.
B is superior to A with both methods
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8.1 Ranking Inconsistency
Occurs between ROR and PWbecause
Both methods have differentreinvestment rate assumptions
Two different cash flows may notgenerate funds at the same rate
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Section 8.2ROR for Mutual Exclusive
Projects Given Two or more alternatives
Rank the investments based upontheir initial time t = 0 investment
requirements
Summarize the investments in atabular format
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8.2 Tabular Format
t Alt. A Alt. B B - A
0 $ $
1 $ $2 $ $
N $ $Find the ROR of this investment
which is(B A)
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8.2 Example
Two Investments: A and B
A costs $30,000 at time t = 0
B costs $50,000 at time t = 0 MARR = 10%
Life is 4 years
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8.2 Example: A and B
For thisproblem, A issuperior to Bbased on PW
and on ROR! A is rankedfirst;
B is rankedsecond
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8.2 Example: A and B
Bothalternativeshave a PW > 0and have i*s
> MARR. Both arefeasiblealternativesinitially.
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8.2 Form the Difference (B A)
For mutually exclusive alternatives
One should focus on the differencesbetween the alternatives
Differences are illustrated best byforming what is called the incrementalinvestment (B-A)
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8.2 Incremental Investment
LowestFirstCost
investment
NextHighest first
Costinvestment
TheIncrementalinvestment
A B (B-A)Find theROR of
thisinvestme
nt=
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8.2 Incremental Investment
B - A
The incremental Investment
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8.2 The logic.
One would go with investment Ainitially because it is the leastexpensive alternative at time t = 0
And its present worth is > 0.
So, A is a feasible alternative to start
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8.2 Explaining the IncrementalInvestment
Now, is it worth it to the firm toconsider investing (-$50,000 (-$30,000) =
-$20,000 to get the cash flowsindicated in the (B-A) cash flow series?
B-A
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8.2 Explaining.continued
A B(B-A)
The investment (B-A) represents the year-
by-year difference between A and B
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8.2 Explainingcontinued
A B (B-A)
(B-A) is additional investment to move
from investing in A and moving on to investin B.
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8.2 The Incremental Investment
Investing $20,000 at time t = oresults in the following incrementalinvestment
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8.2 Is it worth it?
Now the question is.
Is it worth spending an additional$20,000 to move from investment A toinvestment B?
Answer: Compute the ROR or PW of the incremental investment to see!
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8.2 Analysis
For this problem, NPV(10%) < 0
and, no ROR could be found!
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8.2 Analysis
The incremental investment shows anegative PW and no ROR is found
Thus, the increment is rejected.
Moving from A to B is noteconomically worth it
Stay with A!
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8.2 Another Example
Homework Problem 8.21 to illustrate
Cash Flows are shown on the nextslide
Two alternatives
Semiautomatic machine vs.
Automatic machine
Assume a 6 year life for analysis
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8.2 Example (Problem 8.21)
Year SemiAutoA
AutoB
(B-A)
0 -$40,000 -$90,000 -$50,000
1 -100,000 -85,000 15,000
2 -100,000 -85,000 15,000
3 -135,000 -85,000 50,000
4 -100,000 -85,000 15,000
5 -100,000 -85,000 15,000
6 -95,000 -74,000 21,000
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8.2 Analysis
Computed PW@ 18% showsthat B has the
lowest PW costand would bepreferred to A
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8.2 Incremental Cash Flow(B-A)
-$50,000
15,000
15,000
50,000
15,000
15,000
21,000
0
1
2
3
4
5
6
Question? Is it worth spending anadditional $50,000 in theautomatic machine inorder to receive theincremental savingsshown to the left?
Compute the ROR of theincremental Cash Flow
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8.2 Incremental ROR = 35.95%
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8.2 NPV Plot of A and B
A is equivalent to B @ IncrementalROR rate of 35.95%
NPV PLOT-INC. C.F.
-800000.00
-700000.00
-600000.00
-500000.00
-400000.00
-300000.00
-200000.00
-100000.00
0.00
0 . 0 0
0 . 1 0
0 . 2 0
0 . 3 0
0 . 4 0
0 . 5 0
0 . 6 0
0 . 7 0
0 . 8 0
0 . 9 0
1 . 0 0
1 . 1 0
1 . 2 0
1 . 3 0
1 . 4 0
1 . 5 0
1 . 6 0
1 . 7 0
1 . 8 0
1 . 9 0
2 . 0 0
Disc. Rate s
N P V ( i % )
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8.2 i* (B-A) = 35.95%
The incremental i* (B-A) is greater than
the firms discount rate of 18%
Since i* (B-A) > MARR, accept theincrement and go with Alternative B.
Same results as PW(18%) shows
B is clearly the winner
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Section 8.3 Interpretations of ROR
The i* incremental is the ROR of the
additional or incremental investment
required to move from one project tothe next most costly project
If the i* incremental value is < MARR the
increment is not worth it. Go with tolower investment cash flow
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8.3 Multiple Alternatives
If Cost-Revenue Problem
Calculate the computed i*s for eachalternative in the set
Discard those alternatives whose i*value is less than the MARR theywould lose anyway!
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8.3 Independent Projects
If dealing with independent projects,one does not compute incrementalinvestments among the candidate
projects Rule: Accept all projects whose ROR >MARR and stay within any budget
limitations
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8.3 The i* (B-A) value
Given two mutually exclusivealternatives, A and B.
The i* (B-A) value also representsthe interest rate at which the twoalternatives are economicallyequivalent.
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CHAPTER 8
Section 8.4ROR Using PW:
Incremental andBreakeven
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8.4 PW Approach Mutually ExclusiveCase
Given multiple alternatives
If unequal lives either establish
a common project life or, Apply the LCM of life approachfound in chapter 5
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8.4 PW Approach Mutually ExclusiveCase
Order (rank) the alternatives bytheir initial time t = 0 investmentcost
Start with the smallerinvestment alternative refer to
it a A The next highest investmentcost is called B
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8.4 PW Approach Mutually ExclusiveCase
Compute the incremental cash flow(B-A)
Given the MARR find the PW of (B-A)investment
If PW( MARR ) of (B-A) is >0; accept theincrement go with the higherinvestment cost alternative. Else, reject the increment and go withthe lower investment cost option
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8.4 ROR Case Unique i* (B-A)
Compose the incremental Cash Flow
Examine that cash flow for sighchanges and apply the Norstrom test(from Chapter 7)
If a unique i* (B-A) is indicated solvefor it and compare it to the MARR
If i* (B-A) > MARR, accept the incrementelse reject
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8.4 Setup A vs. B PW(15%) showsthat A has the
lowest PW Costand should win!
Note: No ROR forA (all negativesigns) and Bs
cannot bedetermined!
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8.4 PW analysis
We could stop because the PW(15%)has signaled that A is the winner!
Lowest PW cost
Proceed with a ROR analysis BUT.
ROR must be performed on the
incremental investment
8 4 I t l C h Fl Fig
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8.4 Incremental Cash Flow Fig.8-2
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8.4 Inc. Cash Flow Results
Inc. PV(18%)and is
negative.Thus, reject
theincrement
and go withA!
i* (B-A) is lessthan theMARR of
18%.Reject
incrementand go with
A!
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8.4 So-called Breakeven ROR
Recall, the incremental i* (B-A) is theinterest rate at which the twoalternatives are economically
equivalent. This special interest rate is called:
Breakeven Interest Rate
Fisherian Intersection Rate
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8.4 Breakeven Rate Illustrated
For Example 8.3 the NPV Plot is:NPV PLOT-INC. C.F.
-50000.00
-45000.00
-40000.00
-35000.00
-30000.00
-25000.00
-20000.00
-15000.00
-10000.00
-5000.00
0.00
0 . 0 0 0 . 1 0 0 . 2 0 0 . 3 0 0 . 4 0 0 . 5 0 0 . 6 0 0 . 7 0 0 . 8 0 0 . 9 0 1 . 0 0 1 . 1 0 1 . 2 0 1 . 3 0 1 . 4 0 1 . 5 0 1 . 6 0 1 . 7 0 1 . 8 0 1 . 9 0 2 . 0 0
Disc. Rate s
N P V ( i % )
i*(B-A) rate;Alternativesare identical at this rate.
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8.4 Conclusions i* (B-A) = 12.65%
For MARR < 12.65% extra investmentis justified. Go with B
For MARR > 12.65%, the extrainvestment is not justified: Go with A
If MARR = 12.65%, both options areeconomically equivalent.
Recall: MARR = 18%
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CHAPTER 8
Section 8.5ROR Evaluation Using
Annual Worth
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8.5 ROR Using AW
ROR approach requires comparisonover an equal-service life
When the lives are equal or unequalset up the AW relationship for the cashflows of each alternative
Then solve 0 = AW B AW A for the i*value
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8.5 ROR Using Annual Worth
See Example 8.5
Manual approach
It is best to avoid this approach andstay with either the PW or ROR overthe total life of the project or the LCMlife
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Section 8.6
Incremental RORAnalysis of Multiple,
Mutually ExclusiveAlternatives
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8.6 Criteria
Select the one alternative that:
Requires the largest investment
And indicates that the extrainvestment over another acceptablealternative is justified
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8.6 Ranking Rules - Ordering
1. Order the alternatives fromsmallest to largest initial investment
2. Compute the cash flows for eachalternative (assume or create equallives)
3. If the alternatives are revenue-costalternatives do the following
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8.6 Revenue-Cost Problems
4. Compute the i* value for allalternatives in the considered set.
If any alternative has an i* < MARRdrop it from further consideration
The candidate set will be thosealternatives with computed i* values >MARR. Call this the FEASIBLE set
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8.6 Revenue-Cost - Approach
Calculate i* for the first alternative
The first alternative is called theDEFENDER
The second (next higher investmentcost) alternative is called theCHALLENGER
Compute the incremental cash flow as
(Challenger Defender)
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8.6 Revenue-Cost
4. Compute i* Challenger Defender
If i* Challenger Defender > MARR drop the
defender and the challenger wins thecurrent round.
5. If i* Challenger Defender < MARR, drop thechallenger and the defender moves onto the next comparison round
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8.6 Revenue-Cost
6. This process continues until thereare no more challengers remaining.
The alternative that remains after allalternatives have been evaluated isthe final winner.
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8.6 Potential Problems
See Example 8.6 for the potentialproblems that can occur using RoR
Pitfalls often exist when one uses theROR approach for the analysis of alternatives
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8.6 Cost Problems
Remember Cost problems do not have computed
RoRs since there are more costamounts that revenue amounts(salvage values may exist)
Thus there are no feasible i*s foreach alternative
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8.6 Cost Problems - Rules
Rank the alternatives according totheir investment requirements (low tohigh)
For the first round compare:
Challenger Defender Cash Flow
Compute i*
Challenger Defender
If i* Challenger Defender > MARR,Challenger wins; else Defender wins
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8.6 Cost Problems
The current winner now becomes thedefender for the next round.
Compare the current defender to thenext challenger and compute i* Challenger Defender
The winner becomes the currentchampion and moves to the next roundas the defender
Repeat until all alternatives havebeen compared.
Section 8.7
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Section 8.7Spreadsheet Applications
Use the E-solve software for PW-AW,and ROR Analysis
Study and evaluate example 8.8
Create your own spreadsheet fromscratch and employ the built infinancial functions.
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Chapter 8 Summary
PW and AW methods are preferredmethods for evaluating alternatives
ROR can be used but care must betaken
If ROR, must perform an incrementalanalysis
Two at a time (paired comparison) isrequired
ENGINEERING ECONOMY Sixth
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End of Chapter 8 SlideSet
Mc
GrawHill
ENGINEERING ECONOMY Edition
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