1. Comparing Alternatives with Rate of Return
Use Incremental Analysis

2. Topics In this section, we recall the definition of ROR,
discuss decision situations for multiple alternatives, and
discuss the appropriate decision methodology for each situation

3. Rate of Return
Recall that the ROR of an investment is the interest rate that makes
NPW = 0
NAW = 0
PW Benefits = PW Costs
AW Benefits = AW Costs
For a single project, accept if ROR ≥ MARR.

4. Decisions Involving Multiple Projects
Given a set of possible projects,
any subset of the projects may be selected.
only one may be selected, but one must be chosen.
only one may be selected, but it is OK to choose none.

5. Non-Mutually Exclusive Alternatives
Suppose we can select any subset of the projects.
Solution Methodology:
Compute the ROR of each alternative
Select each alternative for which ROR ≥ MARR

6. Example 1:
MARR = 13%

7. Analysis
ROR of A = 13.7%
ROR of B = 12.7%
ROR of C = 15.3%
Both A and C have ROR larger than our MARR. Therefore, select both A and C.

8. Mutually Exclusive Alternatives
Suppose we must select one, only one, but at least one, alternative.
Solution Methodology:
Each increment of investment must yield the MARR.
Perform Incremental Analysis:

9. Recall Incremental Analysis
1. Rank the alternatives in increasing order of investment.
2. Select as the defender the alternative with the smallest investment.
3. Let the challenger be the alternative with the next higher investment.
4. Accept or reject the challenger on the basis of the return on the extra investment. The winner becomes the defender.
5. If the highest level of investment has been reached, stop. Otherwise return to step 3.

10. Example 2: Comparing cost alternatives

11. Ranked Alternatives MARR = 15%
Alternatives: All have five-year life and no salvage
Ranked Alternatives : Rank by order of increasing investment: D, B, C, A.

12. Example 2: Incremental Analysis
Defender: Project D.
Next greater investment (Challenger): Project B.
Is the extra investment in B over D justified?
Incremental Investment: -$500
Incremental Benefit: $125
NAW= (A/P, i, 5) => ROR = 8% < MARR
Decision: Reject Challenger, Project B.

13. Example 2: Incremental Analysis (cont’d)
Defender: Project D.
Next greater investment (Challenger): Project C.
Is the extra investment in C over D justified?
Incremental Investment: $1500
Incremental Benefit: $500
NAW= (A/P, i, 5) => ROR = 20% > MARR
Decision: Accept Challenger, Project C.

14. Example 2: Incremental Analysis (cont’d)
Defender: Project C.
Next greater investment (Challenger): Project A.
Is the extra investment in A over C justified?
Incremental Investment: -$1000
Incremental Benefit: $260
NAW= (A/P, i, 5) => ROR = 9% < MARR
Decision: Reject Challenger,
Keep Defender, Project C

15. Example 3: Projects with Benefits
Choose one of the three

16. Example 3 (cont’d) MARR = 13% (select one and only one)
Ranked Projects: C, B, A

17. Example 3: Incremental Analysis
Defender: Project C
Challenger: Project B
Is the extra investment in B over C justified?
Incremental Investment: $25,000
Incremental Benefit: $6000
NAW= -25 (A/P, i, 5) + 6 => ROR = 6.4% < MARR
Decision: Reject Challenger, Keep Project C

18. Example 3: Incremental Analysis (cont’d)
Defender: Project C
Challenger: Project A
Is the extra investment in A over C justified?
Incremental Investment: $40,000
Incremental Benefit: $2000
Useful Life: Project lives are different!!

19. Example 3: Incremental Analysis (cont’d)
Select a common study period, say 45 years.
20,000 A 10 20 30 40
100,000 …
18,000 C
60,000

20. Example 3: Incremental Analysis (cont’d)
Compute the incremental cash flows.
The cash flows of A-C represent a non-simple investment.
60,000
2,000
A-C 10 20 30 40
40,000
60,000

21. Example 3: Incremental Analysis (cont’d)
We must verify graphically (or with another method) that the interest found correspond to a rate of return. Luckily, it does. The rate of return of the incremental cash flows is 11.6%.
Therefore reject the challenger, project A and accept C.

22. An Easier way for Different Lives
Find ROR of A - C
NAW(A - C) = NAW(A) - NAW(C) = 0
-100(A/P, i, 9) [-60(A/P, i, 5) + 18]
-100(A/P, i, 9) + 60(A/P, i, 5) + 2 = 0
i NAW(A - C) 0% 5%
10%
15%
12%
ROR of A - C is 11.6%. Reject A - C and choose C

23. Mutually Exclusive Alternatives with a Do-Nothing Alternative
Suppose we can select one alternative or no alternative
Solution Methodology:
Compute ROR of each alternative
Reject any alternatives that do not yield the MARR
If only one remains, choose that alternative
If more than one remains, do incremental analysis to select the best

24. Example 4
MARR = 13% (select one or none)

25. Example 4 (cont’d) Since B does not return 13% it can be discarded.
We most compare A and C, by computing the rate of return of the extra investment of A over C.
The rate of return of A over C is 11.6%. Since the return on the extra investment is less than 13% (the MARR) reject the extra investment.
We should choose option C.

26. Conclusion: Measure of merit is the ROR (a percentage)
For a single alternative, accept if ROR ≥ MARR
For multiple alternatives: Accept an increment if the ROR for the increment≥ MARR