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Copyright © Professor Deok-Joo Lee(Kyunghee University, Korea), Permission required for reproduction or display.
CHAPTER VIII
Rate of Return Analysis:
Multiple Alternatives
Multiple Alternatives
Engineering Economics (KHU, 2011) 1

S ti 8 1
Section 8.1
Why Incremental Analysis?
Why Incremental Analysis?

Why Incremental Analysis Is
Why Incremental Analysis Is
Necessary
• Assume we have two or more mutually
exclusive alternatives
exclusive alternatives
• Objective: Which, if any of the
j , y
alternatives is preferred?
• Prior Chapters: Use the PW or AW
• Prior Chapters: Use the PW or AW
approach
• This chapter: We apply the ROR approach

Si l E l 1
Simple Example 1
A B
Investment 10 100
Return 13 110
ROR 30% 10%
PV
(MARR=5%)
2.28 4.76

Si l E l 2
Simple Example 2

R ki I i t
Ranking Inconsistency
F bl PW d ROR
• For some problems, PW and ROR may
rank the same problems differently. Why?
-> Difference in the amount of (initial)
investment
•Need to analyze whether the incremental
(o e t a) in estment is ot h hile?
(or extra) investment is wotrhwhile?
-> Incremental analysis !
y

Section 8.2/8.3
Sect o 8 /8 3
Incremental ROR Analysis

Incremental cash flow
• Given two or more alternatives
• Given two or more alternatives
• Select the first investment to be the one
i h h l i i
with the lowest time t = 0 investment
amount.
• The next investment is to be the one with
the largest investment at time t = 0 and so
the largest investment at time t 0 and so
on
S i h i i b l
• Summarize the investments in a tabular
format

A B (B-A)
( )
Lowest
First
Next
Highest first
The
Incremental
=
Cost
investment
Cost
investment
Incremental
Cash flows
=

Incremenatal C.F. (Tabular Format)
( )
t Alt A Alt B B A
t Alt. A Alt. B B - A
0 $ $
0 $ $
1 $ $
$ $
2 $ $
… … …
N $ $
Incremenatal cash
fl (B A)
N $ $
flows (B – A)

Is It Worth?
Is It Worth?
• Now the question is….
• Is it worth spending an additional
• Is it worth spending an additional
Investmant to move from investment A to
investment B?
investment B?
• Answer: Compute the ROR (or PW) of the
incremental investment to see!

Incremenatal ROR
t Alt A Alt B B A
t Alt. A Alt. B B - A
0 $ $
0 $ $
1 $ $
$ $
2 $ $
… … …
N $ $
Find the ROR of this
(hypothetic) investment
N $ $
(hypothetic) investment
which is (B – A)

Interpretations of incremental ROR
• The i*i l is the ROR of the additional
• The i incremental is the ROR of the additional
or incremental investment required to
f j h
move from one project to the next most-
costly project.
• If the i*incremental value is > MARR, the
increment is worth it. Go with to higher
investment cash flow.
• Otherwise, stay with lower investment

• Given two mutually exclusive alternatives,
A and B.
A and B.
• The i* (B-A) value also represents the
(B A)
interest rate at which the two alternatives
are economically equivalent (called the
are economically equivalent.(called the
break-even rate)

Before the incremental ROR analysis
Before the incremental ROR analysis
• If Cost-Revenue Problem…
• Calculate the computed i*’s for each
• 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!
• Do not apply the ROR analysis for Cost
• Do not apply the ROR analysis for Cost
Problem!

Independent Projects case
Independent Projects case
• If dealing with independent projects, one
does not have to compute incremental
p
investments among the candidate projects
• Rule: Accept all projects whose ROR>MARR
• Rule: Accept all projects whose ROR>MARR
and stay within any budget limitations

Example
Example
MARR 5%
A B B-A
MARR=5%
year
0 -10 -100
1 13 110
ROR

Example
Example
• Incremental ROR analysis, Mutually Exclusive
• Alternative 1: Initial cost $1,000, Revenue $200/year, 7 Years
• Alternative 2: Initial cost $1 800 Revenue $350/year 7 Years
• Alternative 2: Initial cost $1,800, Revenue $350/year, 7 Years
• No salvage value, MARR = 8%

S ti 8 6
Section 8.6
Incremental ROR Analysis with
Incremental ROR Analysis with
Multiple, Mutually Excusive
Alternatives
Alternatives

Procedure
ocedu e
1. Order the alternatives from smallest to
largest initial investment.
g
2. Compute the cash flows for each
alternative (assume or create equal
alternative (assume or create equal
lives).
3. If the alternatives are revenue-cost
alternatives do the following…

Procedure
ocedu e
4. Compute the i* value for all alternatives
in the considered set.
• If any alternative has an i* < MARR,
drop it from further consideration
drop it from further consideration
• The candidate set will be those
alternatives with computed i* values >
MARR.
• Call this the FEASIBLE set

Procedure
ocedu e
• Calculate i* for the first alternative
• The first alternative is called the
• The first alternative is called the
DEFENDER
• The second (next higher investment
cost) alternative is called the
CHALLENGER
• Compute the incremental cash flow as
• Compute the incremental cash flow as
(Challenger – Defender)

Procedure
ocedu e
5. Compute i*Challenger – Defender
f i* d h
• If i*Challenger – Defender > MARR, drop the
defender and the challenger wins the
current round.
• If i* Challenger – Defender < MARR, drop the
challenger and the defender moves on to
g
the next comparison round

Procedure
ocedu e
• At each round, a winner is determined
• Either be the current Defender or the
• Either be 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

Procedure
ocedu e
6. This process continues until there are
no more challengers remaining.
g g
• The alternative that remains after all
alternatives have been evaluated is the
alternatives have been evaluated is the
final winner.

Example
Example
MARR 7% 10 M t ll l i
Alt. A B C D
MARR=7%, n=10 years, Mutually exclusive
Initial cost 3,000 2,000 5,000 4,000
Annual income 447 259 885 651
ROR

Example
Example

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