Developed By:
Dr. Don Smith, P.E.
Department of Industrial
Engineering
Texas A&M University
College Station, Texas
Executive Summary Version
Chapter 8
Rate of Return
Analysis:
Multiple Alternatives
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LEARNING OBJECTIVES
Work with mutually exclusive alternatives based upon
ROR analysis
1.
2.
3.
4.
5.
6.
7.
Why Incremental Analysis?
Incremental Cash Flows
Interpretation
Incremental ROR by PW
Incremental ROR by AW
Multiple alternatives
Spreadsheets
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Sct 8.1 Why Incremental Analysis is N
Necessary
 Assume we have two or more mutually
exclusive alternative
 Objective: Which, if any of the alternatives is
preferred?
 Prior Chapters: Use the PW or AW approach
 This chapter: We apply the ROR approach
 Present Worth: Equal service lives must apply
When using the ROR method to select from among
alternatives one must always use the incremental cash flow
approach.
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Ranking Inconsistency
 For some problems, PW and ROR may
rank the same problems differently. Why?
 PW assumes reinvestment at the MARR
or discount rate.
 ROR assumes reinvestment at the i* or
i’ rate
 Two different reinvestment rate
assumptions apply
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Review of Problem Types
•
INDEPENDENT
AND MUTUALLY
EXCLUSIVE ALTERNATIVES


INDEPENDENT - Selection of one alternative
does not effect the selection of others. Example:
select all projects with a ROR> 20%
MUTUALLY EXCLUSIVE - Selection on one
alternative precludes the selection of others.
Example: select the project with the highest
ROR.
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Sct 8.2 ROR for Mutual Exclusive
Projects
 Given Two or more alternatives
 Rank the investments based upon their
initial time t = 0 investment requirements
 Rank from low to high
 Summarize the investments in a tabular
format
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Tabular Format
t
0
Alt. A
Lowest
$
Alt. B
Highest
$
1
$
$
2
$
$
…
N
B-A
Find
… the ROR of…this
investment which is
(B – A) $
$
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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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Example: A and B
• For this
problem, A is
superior to B
based on PW
and on ROR!
•A is ranked
first
•B is ranked
second
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Form the Difference (B – A)
 For mutually exclusive alternatives…
 One should focus on the differences
between the alternatives
“Differences” are illustrated best by
forming what is called the incremental
investment (B-A)
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Incremental Investment
A
Lowest
First
Cost
investment
B
Next
Highest first
Cost
investment
(B-A)
The
Incremental
investment
Find the
ROR of this
investment
=
The investment (B-A) measures the difference between investment B and investment A
The decision maker will go with A at first. If the extra investment in moving from A to B is “worth it”, then
the decision maker will go with B. If the extra investment is not “worth it” then B is rejected and one would
stay with A
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Example for Two Alternatives A and B
• Computed PW
@ 18% shows
that B has the
lowest PW cost
and would be
preferred to A
Note:
No ROR exists…these are pure cost
type problems
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Focus on the Incremental Cash Flow
(B-A)
15,000
 Question? Is it worth spending
an additional $50,000 in the
automatic machine in order to
receive the incremental savings
shown to the left?
2
15,000
 Compute the ROR of the
incremental cash flows
3
50,000
4
15,000
0
1
-$50,000
5
15,000
6
21,000
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The incremental cash flows
have a mixture of (+) and (-)
signs
 As such, an i* value may indeed
exist
8-13
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Incremental ROR = 35.95%
Using the Excel IRR
function, we observe
that the i* value for the
incremental investment
is 35.95%.
This exceeds the firm's
MARR, so the higher
cost alternative is worth
the incremental
investment
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NPV Plot of A and B
• A is equivalent to B at incremental ROR
rate of 35.95%
NPV PLOT-INC. C.F.
0.
00
0.
10
0.
20
0.
30
0.
40
0.
50
0.
60
0.
70
0.
80
0.
90
1.
00
1.
10
1.
20
1.
30
1.
40
1.
50
1.
60
1.
70
1.
80
1.
90
2.
00
0.00
-100000.00
-200000.00
NPV(i%)
-300000.00
-400000.00
-500000.00
Note: The two PW plots
intersect at 35.95%
-600000.00
-700000.00
-800000.00
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Disc. Rates
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i* (B-A) = 35.95%
 The incremental i*(B-A) is greater than
the firm’s discount rate of 18%
 Since i*(B-A) > MARR, accept the
increment and go with Alternative B
 This is the same decision if PW at 18%
is found
 B is clearly the winner!
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Sct 8.3 Interpretation of Rate of return
on the Extra Investment
 The i*incremental is the ROR of the
additional or incremental investment
required to move from one project to the
next most costly project
 If the i*incremental value is < MARR the
increment is not worth it. Go with the
lower investment cash flow
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Multiple Alternatives
 If Cost-Revenue Problem…
Calculate the computed i*’s for each
alternative in the set
Discard those alternatives whose i* value is
less than the MARR – they would lose anyway!
 Remember:
 If the calculated rate of return earned on an
incremental investment is ≥MARR, the
alternative associated with the higher
investment is preferred
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Independent Projects
 If dealing with independent projects,
one does not compute incremental
investments among the candidate projects
 Rule:
Accept all projects whose calculated
ROR > MARR and stay within any
budget limitations
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Observation About the i* (B-A) value
 Given two mutually exclusive
alternatives, A and B.
 The i*
value also represents the
interest rate at which the two
alternatives are economically
equivalent.
(B-A)
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Sct 8.4 Rate of Return Evaluation Using
PW: Incremental and Breakeven
The PW approach based on the
development in Chapter 5 for ME (mutually
exclusive) alternatives is:
 Given multiple alternatives
 If unequal lives, either
 Apply the LCM of life approach
 Or, establish a common project life
(study period)
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PW Approach for ME Alternatives
 Order (rank) the alternatives by their initial
investment cost at time t = 0
 The smaller investment alternative is “A”.
The next highest investment cost is called “B”
 Compute the incremental investment (B-A)
and cash flows
 Calculate the PW at i% of the incremental
cash flows. Usually i% = MARR
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PW Approach – Mutually Exclusive Case
Decision Rule:
If PW(MARR) of (B-A) is > 0;
accept the increment –
go with the higher investment cost
alternative.
Else,
reject the increment and go with the lower
investment cost option
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ROR Case for Unique i*(B-A)
For ME alternatives, using the incremental ROR approach, the
steps are:
 Determine incremental cash flows
 Examine the cash flows for sign changes and apply
the cumulative cash flow (CCF) or Norstrom’s
test from Chapter 7
 If a unique i*(B-A) is indicated, solve for it and
compare it to MARR
 If i*(B-A) > MARR, accept the increment, else reject
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Incremental ROR: Example 8.3
 10 year project (merger)
 New equipment is required
 Two vendors (A and B)
 MARR = 15%
 Which vendor should be selected?
 Cost /Service Problem
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Setup: B vs. A
Note: Cannot determine
the i* for A or B since
there are no + cash flows
involved.
PW at 15% of A is less than the PW at
15% of B. Based upon computed PW,
A is the least costly alternative.
Select A!
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Conclusion to PW Analysis; Moving
to ROR Analysis
 We could stop now, because the PW at
15% has signaled that A is the winner!
 Lowest PW cost
 To proceed with a ROR analysis, the
incremental ROR must be determined on
the incremental investment (B-A)
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Incremental Cash Flow
•Focus on (B-A) cash flow series
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Incr. Cash Flow Results
i*
The PW at 15% of
incremental cash
flow is negative.
Result: Reject the
increment…reject B
in favor of A
is less
than the
MARR of
18%.
Reject
increment and
go with A!
(B-A)
Consistent Decision!
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The Breakeven ROR
 The incremental i*(B-A) is the interest
rate at which the two alternatives are
economically equivalent.
This special interest rate is called:
 Breakeven Interest Rate or,
 Fisherian Intersection Rate
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Breakeven Rate Illustrated
• For Example 8.3 the NPV Plot is:
NPV PLOT-INC. C.F.
0.
00
0.
10
0.
20
0.
30
0.
40
0.
50
0.
60
0.
70
0.
80
0.
90
1.
00
1.
10
1.
20
1.
30
1.
40
1.
50
1.
60
1.
70
1.
80
1.
90
2.
00
0.00
-5000.00
-10000.00
NPV(i%)
-15000.00
-20000.00
-25000.00
-30000.00
i*(B-A) rate; Alternatives
are identical at this rate.
-35000.00
-40000.00
-45000.00
-50000.00
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Disc. Rates
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Conclusions i*(B-A) = 12.65%
Given: The MARR = 15%
 For MARR < 12.65% extra investment
is justified. Go with B
 For MARR > 12.65%, the extra
investment is not justified: Go with A
 If MARR = 12.65%, both options are
economically equivalent.
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Sct 8.5 Rate of return Evaluation
Using AW
 ROR approach requires comparison over
an equal-service life
 When the lives are equal or unequal set
up the AW relationship for the cash flows
of each alternative
 Then solve 0 = AWB – AWA for the i*
value
 See Example 8.5
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Sct 8.6 Incremental ROR Analysis of
Multiple Mutually Exclusive Alternatives
 Given N mutually exclusive alternatives
 Using the incremental ROR method
 Select the one alternative that
 Requires the largest investment, and at the
same time
 Indicates that the extra investment over
another acceptable investment is justified
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Ranking Rules - Ordering
1. Order the alternatives from smallest to
largest initial investment
2. Compute the cash flows for each
alternative (assume or create equal lives)
3. If the alternatives are revenue-cost
alternatives do the following…
•Next slide
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Revenue-Cost Alternatives
4.
Compute the i* value for all
alternatives in the considered set.
 If any alternative has an i* < MARR
drop it from further consideration
 The candidate set will be those
alternatives with computed i* values >
MARR.
 Call this the FEASIBLE set
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Revenue-Cost Alternatives– Approach continued
 Calculate i* for the first alternative
 The first alternative is called the
DEFENDER
 The second (next higher investment
cost) alternative is called the
CHALLENGER
 Compute the incremental cash flow as
(Challenger – Defender)
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Revenue-Cost Approach - continued
4. Compute i*Challenger – Defender
 If i*Challenger – Defender > MARR drop the
defender and the challenger wins the
current round.
5. If i* Challenger – Defender < MARR, drop the
challenger and the defender moves on to
the next comparison round
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Revenue-Cost - continued
 At each round, a winner is determined
 Either the current Defender or the
current Challenger
 The winner of a given round moves to
the next round and becomes the current
DEFENDER and is compared to the next
challenger
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Revenue-Cost - continued
6. This process continues until there are
no more challengers remaining.
 The alternative that remains after all
alternatives have been evaluated is the
final winner.
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Costs Only (Service) Problems –
ROR Approach
Remember
 Cost problems do not have computed
RoR’s since there are more cost amounts
that revenue amounts (salvage values
may exist)
 Thus there are no feasible i*’s for each
alternative
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Costs Only Problems - Rules
 Rank the alternatives according to their
investment requirements (low to high)
 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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Costs Only Problems -continued
 The current winner now becomes the defender
for the next round.
 Compare the current defender to the next
challenger and compute i* Challenger – Defender
 The winner becomes the current champion and
moves to the next round as the defender
 Repeat until all alternatives have been
compared.
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Sct 8.7 Spreadsheet Application
PW, AW, and ROR Analysis all in one
 Use the E-solve software for a PW, AW
or ROR Analysis
 Study and evaluate Example 8.8
 Create your own spreadsheet from
scratch and employ the built in
financial functions.
 Formatting is most important
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Chapter Summary
 PW and AW methods are preferred
methods for evaluating alternatives
 ROR can be used, but care must be
taken
 If ROR, must perform an incremental
analysis
 Two at a time (paired comparison of
alternatives) is required
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Chapter 8
End of Slide Set
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