# 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?

https://brainmass.com/economics/finance/calculating-ror-incremental-ror-cases-507695

#### 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).

Answer 9.4%

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.

Economics Engineering

1) Consider the following estimates, and use an interest rate of 10% per year. The equivalent annual worth of alternative A is closest to:

A) $-25,130

B) $-37,100

C) $-41,500

D) $-42,900

2) Consider the following estimates, and use an interest rate of 10% per year. The equivalent annual worth of alternative B is closest to:

A) $-25,130

B) $-28,190

C) $-37,080

D) $-39,100

3) With an interest rate of 10% per year and given the following estimates, the annual worth of alternative F is closest to:

A) $32,600

B) $36,100

C) $39,020

D) $43,500

4) Given the following estimates, and with an interest rate of 10% per year, the annual worth of alternative G is closest to:

A) $10,000

B) $30,000

C) $36,000

D) $40,000

5) The first cost of a fairly large flood control dam is expected to be $5 million. The maintenance cost will be $60,000 per year, and a $100,000 outlay will be required every 5 years. If the dam is expected to last forever, its equivalent annual worth at an interest rate of 10% per year is closest to:

A) $-576,380

B) $-591,580

C) $-630,150

D) $-691,460

6) An investment of $50,000 resulted in uniform income of $10,000 per year for 10 years and a single amount of $5000 in year 5. The rate of return on the investment was closest to:

A) 10.6% per year

B) 14.2% per year

C) 16.4 % per year

D) 18.6 % per year

7) Five years ago, an alumnus of a small university donated $50,000 to establish a permanent endowment for scholarships. The first scholarships were awarded 5 years after the money was donated. If the amount awarded each year (i.e., the interest) is $5000, the rate of return earned on the fund is closest to:

A) 7.5% per year

B) 10% per year

C) 11% per year

D) 14% per year

8) When positive net cash flows are generated before the end of a project, and when these cash flows are reinvested at an interest rate that is less than the internal rate of return,

A) The resulting rate of return is equal to the internal rate of return.

B) The resulting rate of return is less than the internal rate of return.

C) The resulting rate of return is equal to the reinvestment rate of return.

D) The resulting rate of return is greater than the internal rate of return.

9) A $10,000 municipal bond due in 10 years pays interest of $400 per year. If an investor purchases the bond now for $9000 and holds it to maturity, the rate of return received by the investor will be closest to:

A) 3.5% per year

B) 4.2% per year

C) 5.3% per year

D) 6.9% per year

10) The difference between revenue and service alternatives is that service alternatives assume revenues are the same for all alternatives.

A) True

B) False

11) The rate of return for alternative X is 18% and for alternative Y is 16%, with Y requiring a larger initial investment. If a company has a minimum attractive rate of return of 16%,

A) The company should select alternative X.

B) The company should select alternative Y.

C) The company should conduct an incremental analysis between X and Y in order to select the correct alternative.

D) The company should select the do-nothing alternative.

12) When conducting a ROR analysis of mutually exclusive projects that have revenue estimates,

A) All the projects must be compared against the do-nothing alternative.

B) More than one project may be selected.

C) The project with the highest ROR should be selected.

D) An incremental investment analysis maybe necessary to identify the best one.

13) Consider the estimates below. If the alternatives are mutually exclusive and the MARR is 15% per year, the one(s) that should be selected is (are):

A) A

B) D

C) E

D) None of them

14) When a B/C analysis is conducted,

A) The benefits and costs must be expressed in terms of their present worth

B) The benefits and costs must be expressed in terms of their annual worth

C) The benefits and costs must be expressed in terms of their future worth

D) The benefits and costs can be expressed in terms of PW, AW, or FW.

15) An alternative has the following cash flows: benefits = $50,000 per year; disbenefits = $27,000 per year; costs = $25,000 per year. The B/C ratio is closest to:

A) 0.92

B) 0.96

C) 1.04

D) 2.00

16) In evaluating three mutually exclusive alternatives by the B/C method, the alternatives were ranked in terms of increasing total equivalent cost (A,B, and C, respectively), and the following results were obtained for the B/C ratios: 1.1, 0.9, and 1.3. On the basis of these results, you should:

A) Select A

B) Select C

C) Select A and C

D) Compare A and C incrementally.

17) The economic service life of an asset is:

A) The longest time that asset will still perform the function that it was originally purchased for.

B) The length of time that will yield the lowest annual worth of costs.

C) The length of time that will yield the lowest present worth of costs.

D) The time required for its market value to reach the originally estimated salvage value.

18) In a replacement study conducted last year, it was determined that the defender should be kept for 3 more years. Now, however, it is clear that some of the estimates that were made for this year and next year were in error. The proper course of action is to:

A) Replace the existing asset now.

B) Replace the existing asset 2 years from now, as was determined last year.

C) Conduct a new replacement study using the new estimates.

D) Conduct a new replacement study using last year's estimates.

19) When all future cash flows are expressed in constant-value dollars, the rate that should be used in the factor equations is the:

A) Market interest rate.

B) Inflation rate.

C) Inflated interest rate.

D) Real interest rate.

20) An assembly line robot arm with a first cost of $25,000 in 1985 had a cost of $29,860 in 1992. If the M&S equipment cost index was 789.6 in 1985 and the robot cost increased exactly in proportion to the index, the value of the index in 1992 was closest to:

A) Less than 800

B) 832.3

C) 914.6

D) More than 925

21) A 50-hp turbine pump was purchased for $2100. If the exponent in the cost capacity equation has a value of 0.76, a 200-hp turbine could be expected to cost about:

A) Less than $5000

B) $5980

C) $6020

D) More than $6100

22) A machine with a 10-year life is to be depreciated by the MACRS method. The machine has a first cost of $30,000 with a $5000 salvage value. Its annual operating cost is $7000 per year. The depreciation charge in year 3 is nearest to:

A) $3600

B) $4320

C) $5860

D) $7120

23) An asset with a first cost of $50,000 is to be depreciated by the straight-line method over a 5-year period. The asset will have annual operating costs of $20,000 and a salvage value of $10,000. According to the straight line method, the book value at the end of year 3 will be closest to:

A) $8000

B) $20,000

C) $24,000

D) $26,000

24) An asset with a first cost of $50,000 is depreciated by the straight line method over a 5-year life. Its annual operating cost is $20,000, and its salvage value is expected to $10,000. The book value at the end of year 5 will be nearest to:

A) $0

B) $8000

C) $10,000

D) $14,000

25) An asset had a first cost of $50,000 an estimated salvage value of $10,000 and was depreciated by the MACRS method. If its book value at the end of year 3 was $21,850 and its market value was $25,850, the amount of depreciation charged against the asset up to that time was closest to:

A) $18,850

B) $21,850

C) $25,850

D) $28,150

26) Calculate the annual worth (years 1 through 10) of the following series of disbursements. Assume that i = 12% per year.

A) $-6817

B) $-5817

C) $-4817

D) $-7817