Comparing alternatives with rate of return
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Comparing Alternatives with Rate of Return. Use Incremental Analysis. 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. Rate of Return.

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Presentation Transcript

Topics l.jpg
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


Rate of return l.jpg
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.


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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.


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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


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Example 1:

  • MARR = 13%


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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.


  • Mutually exclusive alternatives l.jpg
    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:


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    Recall Incremental Analysis

    1. Rank the alternatives in increasing order of investment.

    2. Select as the defenderthe 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.



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    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.


    Example 2 incremental analysis l.jpg
    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= -500 (A/P, i, 5) + 125 => ROR = 8% < MARR

      • Decision: Reject Challenger, Project B.


    Example 2 incremental analysis cont d l.jpg
    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= -1500 (A/P, i, 5) + 500 => ROR = 20% > MARR

      • Decision: Accept Challenger, Project C.


    Example 2 incremental analysis cont d14 l.jpg
    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= -1000 (A/P, i, 5) + 260 => ROR = 9% < MARR

      • Decision: Reject Challenger,

      • Keep Defender, Project C


    Example 3 projects with benefits l.jpg
    Example 3: Projects with Benefits

    • Choose one of the three


    Example 3 cont d l.jpg
    Example 3 (cont’d)

    • MARR = 13% (select one and only one)

    • Ranked Projects: C, B, A


    Example 3 incremental analysis l.jpg
    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


    Example 3 incremental analysis cont d l.jpg
    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!!


    Example 3 incremental analysis cont d19 l.jpg
    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


    Example 3 incremental analysis cont d20 l.jpg
    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


    Example 3 incremental analysis cont d21 l.jpg
    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.


    An easier way for different lives l.jpg
    An Easier way for Different Lives

    • Find ROR of A - C

    • NAW(A - C) = NAW(A) - NAW(C) = 0

    • -100(A/P, i, 9) + 20 - [-60(A/P, i, 5) + 18]

    • -100(A/P, i, 9) + 60(A/P, i, 5) + 2 = 0

    • i NAW(A - C)

    • 0% 2889

    • 5% 1789

    • 10% 463

    • 15% -1058

    • 12% -123

    • ROR of A - C is 11.6%. Reject A - C and choose C


    Mutually exclusive alternatives with a do nothing alternative l.jpg
    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


    Example 4 l.jpg
    Example 4 Alternative

    • MARR = 13% (select one or none)


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    Example 4 (cont’d) Alternative

    • 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.


    Conclusion l.jpg
    Conclusion: Alternative

    • 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


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