Rate%20of%20Return%20Analysis:%20Multiple%20Alternatives

1
Chapter 8

• Rate of Return Analysis Multiple Alternatives

2
Recall

• For comparing two alternatives (A and B)
• based on ROR analysis, you need to find
• the ROR for the new cash flow (B-A).
• Year A B B-A (?B-A)
• 0 -100 -200 -100
• 1 200 300 100
• 2 200 300 100
• 3 200 300 100
• Set PW (i) 0
• If ?iB-A lt MARR, Select A.
• If ?iB-A MARR, Select B.

3
Rate of Return Evaluation Using Annual Worth

• To do an AW analysis to calculate ROR, you need
  to set the following equation.
• AW (i) 0
• Both PW and AW techniques give the same answer
  for i.

4
Example

• The incremental cash flows for alternatives M and
  N are below. Determine which should be selected
  using an AW-based rate of return analysis. The
  MARR is 20 per year and alternative N requires
  the larger initial investment.
• Year Incremental cash Flow (N M)
• 0 -25,000
• 1-9 5,000
• 10 8,000

5
Solution

• AW (i) 0
• -25,000(A/P, i,10) 5,000 8000(A/F,i,10) 0
• Using trial and error
• i15.8
• Since i lt MARR, select M.

6
Multiple Alternative Comparison(Mutually
Exclusive)

• 1- Rank alternatives from smallest to the largest
  (initial investment)
• 2- Determine ROR for the first alternative
  (Defender) and the Second alternative
  (Challenger). First develop the cash flow for
  (Challenger Defender).
• 3- Based on the ROR in 2, decide which
  alternative is acceptable (If i MARR,
  challenger is selected. Otherwise, select the
  defender).
• 4- Repeat the procedure until only one
  alternative is left.
• Attention For revenue-generating projects you
  need to consider DN (Do Nothing) alternative as a
  possible choice.

7
Example

• Mountain Pass Canning Company has determined that
  any one of five machines can be used in one phase
  of its canning operation. The costs of the
  machines have a 10-year life. If the minimum
  attractive rate of return is 25 per year,
  determine the one machine that should be selected
  on the basis of a rate of return analysis.
• Machine First Cost, Annual Operating Cost,
• 1 -28,000 -20,000
• 2 -51,000 -12,500
• 3 -32,000 -19,000
• 4 -33,000 -18,000
• 5 -46,000 -14,000
  

8
Solution

• First rank alternative based on increase in First
  Cost (Initial Investment)
• 1? 3? 4? 5?2
• 3 to 1 ( 3 1)
• PW (i)0
• -4000 1000(P/A,i,10)0
• i 21.4 ltMARR
• Select 1 (eliminate 3).
• 1?4?5?2

9
Solution

• 4 to 1 (4-1)
• PW (i)0
• -5000 2000(P/A,i,10)0
• i 38.5 gtMARR
• Select 4 (eliminate 1).
• 4?5?2
• 5 to 4 (5 - 4)
• PW (i)0
• -13000 4000(P/A,i,10)0
• i 28.2 gtMARR
• Select 5 (eliminate 4).
• 5?2

10
Solution

• 5 to 2 ( 25)
• PW (i)0
• -5000 1500(P/A,i,10)0
• i 27.3 gtMARR
• Select 2 (eliminate 5).

11
Recall

• Please pay attention that each alternative should
  have ROR MARR to be considered for evaluation.
• In case of revenue-generating projects, you need
  to consider DN (Do-Nothing) alternative as well.

12
Example

• A metal plating company is considering four
  different methods for
• recovering by-product heavy metals from a
  manufacturing sites
• liquid waste. The investment costs and incomes
  associated with each
• method has been estimated. All methods have a
  10-year life. The
• MARR is 12 per year.
• Method First Cost, Salvage Value, Annual
  Income,
• A -15,000 1,000
  4,000
• B -18,000 2,000
  5,000
• C -25,000 -500
  6,000
• D -35,000 -700
  8,000
• (a) if the methods are independent, because they
  can be implemented at different plants, which
  ones are acceptable?
• (b) If the methods are mutually exclusive,
  determine which one method should be selected,
  using a ROR o evaluation.

13
Solution

• a) Calculate ROR for each project. Any project
  that has RORgt MARR will be selected.
• For A
• PW (i)0
• -15,0001000(P/F,i,10)4000(P/A,i,10)0
• i23.67 gt MARR
• For B
• PW (i)0
• -18,0002000(P/F,i,10)5000(P/A,i,10)0
• i25.12 gt MARR

14
Solution

• For C
• PW (i)0
• -25,000 -500(P/F,i,10)6000(P/A,i,10)0
• i20.09 gt MARR
• For D
• PW (i)0
• -35,000 -700(P/F,i,10) 8000(P/A,i,10)0
• i18.66 gt MARR

15
Solution

• (b)
• Rank the alternatives (increasing initial
  investment)
• Since this is a revenue-generating project, you
  need to consider DN as well.
• DN- A B C- D
• A with DN ( A DN)
• NPW0, i23.67
• Eliminate DN, select A.

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Solution

• B to A ( B A)
• NPW (i) 0
• -3000 1000(P/A,i,10) 1000(P/F,i,10)0
• i31.91gt MARR ? Select B.
• B? C? D
• B to C ( C B)
• NPW (i) 0
• -7000 1000(P/A,i,10) - 2500(P/F,i,10)0
• i 1.75 lt MARR ? Select B.
• B? D

17
Solution

• D to B ( D B)
• NPW (i) 0
• -17000 3000(P/A,i,10) -2700(P/F,i,10)0
• i10.57 lt MARR ? Select B.

18
Example

• Alternative I requires an initial investment of
  20,000 and will yield a rate of return of 25
  per year. Alternative C, which requires a 30,000
  investment, will yield 20 per year. Which of the
  following statements in true bout the rate of
  return in the 10,000 increment?
• (a) It is greater than 20 per year.
• (b) It is exactly 20 per year.
• (c) It is between 20 and 25 per year.
• (d) It is less than 20 per year.

19
Example

• 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 B.
• (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.

20
Example

• The incremental cash flow between two
  alternatives is shown below.
• Year Incremental cash Flow
• 0 -20,000
• 1-10 3,000
• 10 400
• The equation(s) that can be used to correctly
  solve for the incremental rate of return is
  (are)
• (a) 0 -20,000 3000(P/A,?i,10)
• 400(P/F,?i,10)
• (b) 0 -20,000 (A/P, ?i,10) 3000
• 400(A/F,?i,10)
• (c) 0 -20,000 (F/P, ?i,10) 3000(F/A,?i,10)
• 400
• (d) All of the above.