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# Calculating ROR and incremental ROR in the given cases

Solutions are provided for the problems given below.

1. Consider the following data for three alternatives A, B and C
Year A B C (A-B) (A-C) (C-B)
0 -3200 -1600 -2400 -1600 -800 -800
1 800 380 700 420 100 320
2 800 380 700 420 100 320
3 800 380 700 420 100 320
4 800 380 700 420 100 320
6 800 380 700 420 100 320
7 800 380 700 420 100 320
ROR 16% 15% 22% 18% -3% 35%

MARR = 10 %. The recommended alternative is A, B or C.
Correct option is C.

8-3
Consider three alternatives A, B and "do-nothing."
Year A B
0 -\$100 -\$150
1 30 43
2 30 43
3 30 43
4 30 43
5 30 43

3. Problem 8-3: What is the incremental ROR for (B-A).
4. Problem 8-3: If MARR = 6%, which alternative should be selected?
5. Problem 8-3: If MARR = 8%, which alternative should be selected?
6. Problem 8-3: If MARR = 10 %, which alternative should be selected?
7. Problem 8-3: If MARR = 16%, which alternative should be selected?

8-14
The following three mutually exclusive alternatives have no salvage value after 5 years:
A B C
First Cots \$200 \$300 \$600
Uniform annual benefit 59.7 77.1 165.2
Computed rate of return 15% 9% 11.7%

8. Problem 8-14: The Incremental ROR for (B-A) is?
9. Problem 8-14: What is the value of the Incremental ROR for (C-B)?
10. Problem 8-14: For what range of values of MARR is Alt C the preferred alternative?

8-15
Consider four mutually exclusive alternatives, each having an 8-year useful life:
A B C D
First Cost \$1000 \$800 \$600 \$500
Uniform annual benefit 122 120 97 122
Salvage value 750 500 500 0
If the minimum attractive rate of return is 8%,

11. Problem 8-15: The Rate of Return of A is?
12. Problem 8-15: The incremental ROR of ( C-D ) is?
13. Problem 8-15: The recommended alternative is?

5-83
Six mutually exclusive alternatives, A-F, are being examined. For an 8% interest rate, which alternative should be selected? Each alternative has a 6-year useful life.
Initial Cost Uniform annual benefit
A \$20 \$6.00
B 35 9.25
C 55 13.38
D 60 13.78
E 80 24.32
F 100 24.32

14. Problem 5-83: The rate of return for alternative A is?
15. Problem 5-83: The rate of return for alternative B is?
16. Problem 5-83: The rate of return for alternative C is?
17. Problem 5-83: The rate of return for alternative D is?
18. Problem 5-83: The rate of return for alternative E is?
19. Problems 5-83: The rate of return for alternative F is?
20. Problems 5-83: The incremental rate of return for the increment B-A is?
21. Problems 5-83: The incremental rate of return for the increment C-B is?
22. Problems 5-83: The incremental rate of return for the increment D-B is?
23. Problems 5-83: The incremental rate of return for the increment E-B is?
24. Problems 5-83: The incremental rate of return for the increment E-D is?
25. Problems 5-83: The incremental rate of return for the increment F-D is?
26. Problems 5-83: The incremental rate of return for the increment E-C is?
27. Problems 5-83: incremental rate of return for the increment E-A is?
28. Problems 5-83: The incremental rate of return for the increment D-A is?
29. Problems 5-83: The incremental rate of return for the increment F-B is?
30. Problems 5-83: The incremental rate of return for the increment C-A is?
31. Problems 5-83: The incremental rate of return for the increment F-A is?
32. Problems 5-83: The incremental rate of return for the increment F-C is?
33. Problems 5-83: The first incremental analysis should be?
34. Problems 5-83: The second incremental analysis should be?
35. Problems 5-83: The third incremental analysis should be?
36. Problems 5-83: The fourth incremental analysis should be?
37. Problems 5-83: The fifth and last incremental analysis should be?
38. Problems 5-83: The selected alternative should be?

#### Solution Preview

Please refer attached files for complete solutions.

1. Consider the attached data for the three alternatives A, B and C.
MARR = 10 %. The recommended alternative is A, B or C.
Correct option is C.

3. Problem 8-3: What is the incremental ROR for (B-A).

4. Problem 8-3: If MARR = 6%, which alternative should be selected?

Project B as incremental ROR is higher than 6%

5. Problem 8-3: If MARR = 8%, which alternative should be selected?

Project B as incremental ROR is higher than 8%

6. Problem 8-3: If MARR = 10 %, which alternative should be selected? (Points : 1)

Project A as incremental ROR is less than 10%

7. Problem 8-3: If MARR = 16%, which alternative should be selected? (Points : 1)

ROR is less than 16% in each case. So, none of the given projects can be selected
Correct option is C i.e. Neither

8. Problem 8-14: The Incremental ROR for (B-A) is most nearly:
- negative
- 1.3%
- 2.9%
...

#### Solution Summary

ROR Technique plays an important role in financial decision making. Solutions to given problems depict the methodology to calculate ROR and incremental ROR. Solutions are derived with the help of suitable functions in MS Excel.

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