Chapter 8 - Incremental
Rate of Return Analysis
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EGR 403 Capital Allocation Theory
Dr. Phillip R. Rosenkrantz
Industrial & Manufacturing Engineering Department
Cal Poly Pomona
EGR 403 - The Big Picture
• Framework: Accounting & Breakeven Analysis
• “Time-value of money” concepts - Ch. 3, 4
• Analysis methods
–
–
–
–
Ch. 5 - Present Worth
Ch. 6 - Annual Worth
Ch. 7,7A,8 - Rate of Return (incremental analysis)
Ch. 9 - Benefit Cost Ratio & other techniques
• Refining the analysis
– Ch. 10, 11 - Depreciation & Taxes
– Ch. 12 - Replacement Analysis
EGR 403 - Cal Poly Pomona - SA11
2
Incremental Analysis
• Required for examining three or more
alternatives.
• Defined as the examination of differences
between alternatives to determine if the
increased costs are justified by the increased
benefits.
High cost alt. - Low cost alt. = Difference between alt.
EGR 403 - Cal Poly Pomona - SA11
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Elements of Rate of Return Analysis
• Identify all acceptable alternatives that fulfill
similar system outcomes.
• Arrange the alternatives in ascending order of
investment.
• Compute the rate of return for each alternative.
Discard alternatives where ROR < MARR.
• Make a pair-wise analysis of the contender and
present selection. For investment:
– If DROR  MARR select the contender.
– If DROR MARR keep the present selection.
EGR 403 - Cal Poly Pomona - SA11
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Incremental Rate of Return Analysis
Example 8 - 7
•PWB = A (P/A, 6%, 20) = A (11.47)
•MARR = 6% (given)
•All projects are initially acceptable because IRR  MARR
Cost
EUAB (A)
PWB
IRR
P/A
A
4000
639
7330
15%
6.26
B
2000
410
4700
20%
4.88
C
6000
761
8730
11%
7.88
EGR 403 - Cal Poly Pomona - SA11
D
1000
117
1340
10%
8.55
E
9000
785
9000
6%
11.47
5
Incremental Analysis
1. Rank from lowest cost to highest cost
2. Start with two lowest cost alternatives
3. Compare increments using MARR criteria
4. Repeat until a “winner” is determined
Cost
EUAB (A)
Increment
incr. Cost
incr. UAB
incr. ROR
Keep
P/A
D
1000
117
B
2000
410
A
4000
639
C
6000
761
E
9000
785
B-D
1000
293
29%
B
3.413
A-B
2000
229
10%
A
8.73
C-A
2000
122
2%
A
16.393
E-A
5000
146
< 0%
A
34.236
EGR 403 - Cal Poly Pomona - SA11
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Graphical Solutions
PWB vs. PWC at MARR
Above the 45 degree line projects are acceptable (NPW>0)
Benefit-cost Graph
MARR 6.00 %
Alternatives
30
Present Worth of Benefit
POSITIVE NPW
25
0.06
20
15
0
0
$26.42
$26.42
10
5
NEGATIVE NPW
0
0
5
10
15
20
25
30
Present Worth of Cost
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Graphical Solution
• Projects B, A, C and E shown.
• Incremental analysis looks at adjacent points on the BenefitCost Graph
EGR 403 - Cal Poly Pomona - SA11
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Graphical Incremental Analysis
If line between two alternatives is > 45 degrees, accept higher
cost alternative. Alternative A wins.
EGR 403 - Cal Poly Pomona - SA11
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Graphical Incremental Analysis
• Graphical solution has a logical connection to NPW
•Incremental analysis seeks out the alternative with highest
NPW. Alternative A maximizes NPW.
EGR 403 - Cal Poly Pomona - SA11
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Choosing an Analysis Method
Method
MARR
Computations*
Explanation
PW
Required for
calculation
Required for
calculation
Less
Depends
Less
Depends
For comparison
More
Depends
AW
ROR
*Not an issue when using a spreadsheet.
Do what the Organization requires. Occasionally augment with
alternate methods where the method adds beneficial information.
EGR 403 - Cal Poly Pomona - SA11
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