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    CHAPTER 8

    Rate of Return Analysis:Multiple Alternatives

    M cGrawHill

    ENGINEERING ECONOMY SixthEdition

    Blank and

    Tarquin

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    Learning Objectives

    1. Why Incremental Analysis?

    2. Incremental Cash Flows

    3. Interpretation4. Incremental ROR by PW

    5. Incremental ROR by AW

    6. Multiple Alternatives

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    Section 8.1Why Incremental Analysis is

    Necessary

    Assume we have two or moremutually exclusive alternative

    Objective: Which, if any of thealternatives is preferred?

    Prior Chapters: Use the PW or AWapproach

    This chapter: We apply the RORapproach

    Present Worth: Equal service livesmust apply

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    8.1 Ranking Inconsistency

    For some problems, PW and ROR mayrank the same problems differently.Why?

    PW assumes reinvestment at theMARR or discount rate.

    ROR assumes reinvestment at the i*

    or i rate Two different reinvestment rateassumptions apply

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    8.1 Review of Problem Types

    INDEPENDENT AND MUTUALLY EXCLUSIVE ALTERNATIVES

    INDEPENDENT - Selection of onealternative does not effect the selection of others. Example: select all projects with aROR> 20 %

    MUTUALLY EXCLUSIVE - Selection on onealternative precludes the selection of others. Example: select the project with thehighest ROR.

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    8.1 An Example Shows RankingInconsistency Problem

    From Solomon {1956/59} Two Investments A and B Discount rate = 10%

    Each investment requires $100 at t =0 A is a 1-year investment

    B is a 5- year investment

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    8.1 Two Projects; A and B

    A

    $100

    0 1 2 3 45

    $120

    B

    $100

    0 1 2 3 45

    $201.14

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    8.1 Example Problem

    i*A = 0.20 = 20%

    i*B = 0.15 = 15% PW A(10%) = +$9.09

    PB B(10%) = +24.89

    Using ROR, A issuperior to B

    Using PW, B issuperior to A

    InconsistentRankings!

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    8.1 Example Problem - Rankings

    Using ROR Ranking

    A is superior to B (20% > 15%)

    Using a PW(10%) approach B is superior to A ($24.89 > $9.09)

    The two methods do not rank thesame?

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    8.1 Look at A and assumeReinvestment forward to t = 5

    Find F 5 for Alt. A

    $100

    0 1 2 3 45

    $120

    F 5 = ?

    F 5 = 120(F/P,10%,4)=$175.69

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    8.1 ROR of A given reinvestment

    -100 +120(F/P,10%,4)(P/F,i *A, 5) = 0

    Solving for i* A

    (P/F, i* A,5) = 0.569

    i*A/reinvestment @10% = 0.1193

    i*A/ c =10% = 11.93%

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    8.1 Now Compare A to B

    Compare revised A withreinvestment at 10% to B

    i*

    A/c = 10% = 11.93%

    i* B = 15% as before

    ROR Rankings:

    B is superior to A (15% > 11.93%)

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    8.1 Ranking Consistency

    Now, PW(10%) and ROR with thereinvestment imposed on the 1-yearproject rank consistently.

    B is superior to A with both methods

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    8.1 Ranking Inconsistency

    Occurs between ROR and PWbecause

    Both methods have differentreinvestment rate assumptions

    Two different cash flows may notgenerate funds at the same rate

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    Section 8.2ROR for Mutual Exclusive

    Projects Given Two or more alternatives

    Rank the investments based upontheir initial time t = 0 investment

    requirements

    Summarize the investments in atabular format

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    8.2 Tabular Format

    t Alt. A Alt. B B - A

    0 $ $

    1 $ $2 $ $

    N $ $Find the ROR of this investment

    which is(B A)

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    8.2 Example

    Two Investments: A and B

    A costs $30,000 at time t = 0

    B costs $50,000 at time t = 0 MARR = 10%

    Life is 4 years

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    8.2 Example: A and B

    For thisproblem, A issuperior to Bbased on PW

    and on ROR! A is rankedfirst;

    B is rankedsecond

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    8.2 Example: A and B

    Bothalternativeshave a PW > 0and have i*s

    > MARR. Both arefeasiblealternativesinitially.

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    8.2 Form the Difference (B A)

    For mutually exclusive alternatives

    One should focus on the differencesbetween the alternatives

    Differences are illustrated best byforming what is called the incrementalinvestment (B-A)

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    8.2 Incremental Investment

    LowestFirstCost

    investment

    NextHighest first

    Costinvestment

    TheIncrementalinvestment

    A B (B-A)Find theROR of

    thisinvestme

    nt=

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    8.2 Incremental Investment

    B - A

    The incremental Investment

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    8.2 The logic.

    One would go with investment Ainitially because it is the leastexpensive alternative at time t = 0

    And its present worth is > 0.

    So, A is a feasible alternative to start

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    8.2 Explaining the IncrementalInvestment

    Now, is it worth it to the firm toconsider investing (-$50,000 (-$30,000) =

    -$20,000 to get the cash flowsindicated in the (B-A) cash flow series?

    B-A

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    8.2 Explaining.continued

    A B(B-A)

    The investment (B-A) represents the year-

    by-year difference between A and B

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    8.2 Explainingcontinued

    A B (B-A)

    (B-A) is additional investment to move

    from investing in A and moving on to investin B.

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    8.2 The Incremental Investment

    Investing $20,000 at time t = oresults in the following incrementalinvestment

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    8.2 Is it worth it?

    Now the question is.

    Is it worth spending an additional$20,000 to move from investment A toinvestment B?

    Answer: Compute the ROR or PW of the incremental investment to see!

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    8.2 Analysis

    For this problem, NPV(10%) < 0

    and, no ROR could be found!

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    8.2 Analysis

    The incremental investment shows anegative PW and no ROR is found

    Thus, the increment is rejected.

    Moving from A to B is noteconomically worth it

    Stay with A!

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    8.2 Another Example

    Homework Problem 8.21 to illustrate

    Cash Flows are shown on the nextslide

    Two alternatives

    Semiautomatic machine vs.

    Automatic machine

    Assume a 6 year life for ana

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