COMPARING ALTERNATIVES

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CHAPTER 6

• COMPARING ALTERNATIVES

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Objective

• To learn how to properly apply the profitability
  measures described in Chapter 4 to select the
  best alternative out of a set of mutually
  exclusive alternatives (MEA)
• The cash-flow analysis methods (previously
  described) used in this process
• Present Worth ( PW )
• Annual Worth ( AW )
• Future Worth ( FW )
• Internal Rate of Return ( IRR )

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Alternatives

• Organizations have the capability to generate
  potential beneficial projects for potential
  investment
• The alternatives being considered may require
  different amounts of capital investment
• The alternatives may have different useful lives
• The subject of this section will help
• analyze and compare feasible alternatives
• select the preferred alternative

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Feasible Design Alternatives

• Three types of investment categories
• Mutually Exclusive Set
• Independent Project Set
• Contingent
• Mutually exclusive set
• The selection of one alternative excludes the
  consideration of any other alternative
• Once selected, the remaining alternatives are
  excluded
• Independent project set
• Selecting the best possible combination of
  projects from the set that will optimize a given
  criteria
• Subjects to constraints
• Contingent
• The choice of the project is conditional on the
  choice of one or more other projects

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Fundamental Purpose of Capital Investment

• To obtain at least the MARR for every dollar
  invested.
• Basic Rule
• Spend the least amount of capital possible unless
  the extra capital can be justified by the extra
  savings or benefits.
• In other words, any increment of capital spent
  (above the minimum) must be able to pay its own
  way.

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Two Types of Decisions

• 1. Investment Alternatives - each alternative has
  an initial investment producing positive cash
  flows resulting from increased revenues, reduced
  costs, or both.
• "Do nothing" (DN) is usually an implicit
  investment alternative.
• If ?positive cash flows gt ?negative cash flows,
  then IRRgt0.
• If EW(MARR)gt0, investment is profitable, or if
  EW(MARR)lt0, do nothing (DN) is better, where EW
  refers to an equivalent worth method (e.g. PW)
• 2. Cost Alternatives - have all negative cash
  flows except for the salvage value (if
  applicable). These alternatives represent must
  do situations, and DN is not an option
• IRR not defined for cost alternatives. Can you
  explain why?

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Section 6.3 - The Study Period

• Must be appropriate for the decision being made
• Study Period The time interval over which
  service is needed to fulfill a specified function
• Useful Life The period over time during which an
  asset is kept in productive operation
• Case 1 Study period Useful life
• Case 2 Study period ¹ Useful life
• Fundamental Principle Compare MEAs (mutually
  exclusive alternatives) over the same time period

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Section 6.4.1 - (EW) Methods PW, AW, FW (Case 1)

• Procedure for selecting the best MEA using the EW
  method
• 1. Compute the equivalent worth of each
  alternative, using the MARR as the interest rate.
• 2. Investment Alternatives Select the
  alternative having the greatest equivalent worth.
• Note If all equivalent worths are lt 0 for
  investment alternatives, then "do nothing" is the
  best alternative.
• 3. Cost Alternatives Select the alternative
  having the smallest equivalent cost (the one that
  is least negative).
• All three equivalent worth methods (PW, AW, FW)
  will identify the same "best" alternative.

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Study Period Useful Life

• I II III IV
• Investment cost (I) 100,000 152,000
  184,000 220,000
• Net Annual receipts 15,200 31,900
  35,900 41,500
• Salvage value (SV) 10,000
  0 15,000
  20,000
• Useful life 10 10 10 10
• If the MARR is 12, use the PW method to select
  the best alternative
• PW(12) -I A(PA, 12, 10) SV(PF, 12, 10)
• Solution
• PWDN (12) 0, PWI (12) -10,897, PWII (12)
  28.241, PWIII (12) 23,672, PWIV
  (12)20,923
• Select Alternative ___ to maximize PW.

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Cost Alternatives - Example

• Cost Alternatives
• Study Period Useful Life
• A B C
• Initial cost (I) -85,600 -63,200 -71,800
• Annual expenses
• years 1-7 -7,400 -12,100 -10,050
• Use the AW method to choose the best alternative
  (MARR 12)
• AWA -26,155
• AWB -25,947
• AWC -25,781
• Assuming one must be chosen (i.e., DN is not an
  option), select alternative ___ to minimize AW
  costs.

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Rate-of-Return Analysis Multiple Alternatives

• Assume we have two or more mutually exclusive
  Alt.
• Objective Which, if any of the alternatives is
  preferred?
• 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.
• iA 0.20 20, iB 0.15 15, PWA(10)
  9.09, PWB(10) 24.89
• Using ROR Ranking _ is superior to _
• Using a PW(10) approach _ is superior to _
• The two methods do not rank the same?

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Using the IRR Method Another Example

• Why not select the investment opportunity that
  maximizes IRR?
• Consider 2 alternatives A B
• Investment -100 -10,000
• Lump-Sum Receipt 1,000 15,000
• IRR 900 50
• If MARR 20, would you rather have A or B if
  comparable risk is involved?
• If MARR 20, PWA 733 and PWB 2,500

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Is It Worth It?

• Now the question is.
• Is it worth spending an additional 9,900 to move
  from investment A to investment B?
• NEVER simply select the MEA that MAXIMIZES the
  IRR
• Never compare the IRR to anything except the
  MARR.
• We don't maximize rate of return. Look at the
  increment
• Answer Compute the ROR or PW of the incremental
  investment to see!
• IRR A-B PW A-B 0 -9,900 14,000(PF, i',
  1)
• i' A-B 41.4 gt MARR

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Calculations of Incremental Cash Flows for ROR
Analysis

• Given two or more alternatives
• Rank the investments based upon their initial
  time t 0 investment requirements
• Summarize the investments in a tabular format
• Select the first investment to be the one with
  the lowest time t 0 investment amount.
• The next investment is to be the one with the
  larger investment at time t 0

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Example

• Given three MEAs and MARR 15 per year
• 1 2 3
• Investment (FC) -28,000 -16,000
  -23,500
• Net Cash Flow/year 5,500 3,300
  4,800
• Salvage Value 1,500 0
  500
• Useful Life 10 yrs 10 yrs 10 yrs
• Use the Incremental IRR procedure to choose the
  best alternative

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Incremental Investment Analysis Procedure

• 1. Order the feasible alternatives
• 2. Establish a base alternative
• a. Cost alternatives -- The first (LCI)
  alternative is the base
• b. Investment alternatives - If the first (LCI)
  alternative is acceptable, select as base. If
  the first alternative is not acceptable, choose
  the next alternative
• 3. Use iteration to evaluate differences
  (incremental cash flows) between alternatives
  until no more alternatives exist
• a. If incremental cash flow between next
  alternative and current alternative is
  acceptable, choose the next
• b. Repeat, and select as the preferred
  alternative the last one for which the
  incremental cash flow was acceptable

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To Summarize

• 1. Each increment of capital must justify itself
  by producing a sufficient rate of return on that
  increment.
• 2. Compare a higher investment alternative
  against a lower investment alternative only when
  the latter is acceptable.
• 3. Select the alternative that requires the
  largest investment of capital as long as the
  incremental investment is justified by benefits
  that earn at least the MARR. This maximizes
  equivalent worth on total investment at i MARR.

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Case 2 Study Period?Useful Life

• Up until now, study periods and useful lives have
  been the same length
• The study period is frequently taken to be a
  common multiple of the alternatives lives when
  study period ¹ useful life
• Repeatability Assumption (page 244)
• Conditions
• 1. Study period is either indefinitely long or
  equal to a common multiple of the lives of the
  alternative.
• 2. The cash flows associated with an
  alternative's initial life span are
  representative of what will happen in succeeding
  life spans.

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Example

• Cost Alternatives Study Period gt Useful Life
  MARR 15. A B
• Investment cost 14,000 65,000
• Annual costs 14,000 9,000
• Useful life 5 20
• SV (MKT value) 8,000 13,000
• If the study period 20 years, which alternative
  is preferred?

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Different Lives

• Comparison must be made over equal time periods
• Compare over the least common multiple, LCM, for
  their lives
• Remember if the lives of the alternatives are
  not equal, one must create or force a study
  period where the life is the same for all of the
  alternatives

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AW for Unequal Lives

• Consider the AW over the useful life of
  Alternative A
• AWA -14,000(AP, 15, 5)- 14,000 8,000(AF,
  15, 5) -16,990
• Life 1 AW 1-5 -16,990
• Life 2 AW 6-10 -14,000(AP, 15, 5)- 14,000
  8,000(AF, 15, 5) -16,990
• Life 3 AW 11-15 -16,990
• Life 4 AW 16-20 -16,990
• AWB -65,000(AP,15,20) 9000
  13,000(AF,15,20) -19,259.6
• Shortcut If the study period equals a common
  multiple of the alternatives' lives, simply
  compare AW computed over the respective useful
  lives (assuming repeatability is valid). In this
  case, Alt. A is preferred.

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PW Approach

• LCM 20 years MARR 15
• Because Repeatability Assumption applies then
• Identical replacement of Alternative A at EOY of
  5,10, 15
• No replacement for Alternative B
• Draw CFD
• PW(15)A -14,000 -6,000(P/F,15,5) -
  6,000(P/F,10,10) - 6,000 (P/F,10,15) -
  14,000(P/A,15,20) -106,834
• PW(15)B -65,000 13,000(P/F,15,20) -
  9,000(P/A,15,20) -120,539
• Therefore, alternative A is preferred

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Example 6-8
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Example 6-8

• LCM 12 years MARR 10 Study Period 12 years
• If Repeatability assumption applies then
• Identical replacement of Alternative A at EOY of
  4 and 8. Last 2 years reinvestment at MARR
• Identical replacement of Alternative B at EOY of
  6.
• Draw CFD
• PW(10)A -3,500 -3,500(P/F,10,4)
  -3,500(P/F,10,8) 1,255(P/A,10,12) 1,028
• PW(10)B -5,000 -5,000(P/F,10,6)
  1,480(P/A,10,12) 2,262
• Therefore, alternative B is preferred

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Problem?

• What if the study period is not a common multiple
  of the alternatives' lives or repeatability is
  not applicable?
• A finite and identical study period is used for
  all alternatives
• This planning horizon, combined with appropriate
  adjustments to the estimated cash flows, puts the
  alternatives on a common and comparable basis
• Used when repeatability assumption is not
  applicable
• Frequently used in engineering practice

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Use the Cotermination Assumption

• Procedure The cash flows of the alternatives
  need to be adjusted to terminate at the end of
  the study period.
• Cost alternatives Assuming repeatability, repeat
  part of the useful life of the original
  alternative, and then use an estimated MV to
  truncate it at the end of the study period
• Without repeatability, we must purchase/lease the
  service/asset for the remaining years.
• Investment alternatives Assume all cash flows
  will be reinvested at the MARR to the end of the
  study period (i.e., calculate FW at end of useful
  life and move this to the end of the study period
  using the MARR).

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Study Period lt Useful Life

• When the study period is explicitly stated to be
  shorter than the useful life, use the
  cotermination assumption
• Procedure The cash flows of the alternatives
  need to be adjusted to terminate at the end of
  the study period.
• Truncate the alternative at the end of the study
  period using an estimated Market Value.

Alt-1 N 5 yrs
Alt-2 N 7 yrs
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Example of Cotermination

• Suppose the study period had been stated to be 20
  years. Which boiler would you recommend? Boil
  er A Boiler B
• Investment cost 50,000 120,000
• Useful life 20 yrs. 40 yrs.
• SV_at_end of useful life 10,000 20,000
• Annual costs 9,000 6,000
• Useful life of A 20 years study period
• Useful life of B 40 years gt study period
• Assume MV B _at_ EOY 20 50,000
• The MARR is 10 per year.

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Solution

• AWA (10) -14,700, AWB (10) -19,225
• Select _
• What would the market value of Boiler B _at_ EOY 20
  have to be in order to select Boiler B instead of
  A?
• Set AWA AWB
• -14,700 -6,000 - 120,000(AP, 10, 20) -
  X(AF,10, 20)
• X 308,571 therefore, MVB gt 308,571 to favor B
• Such a value is very unlikely because X is more
  than the initial cost of Boiler B.

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Problem Revisited with Cotermination

• If the study period 10 years and the estimated
  market value for alternate B 25,000 _at_ EOY 10,
  which alternative is preferred?

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Comparing Alternatives Using the Capitalized
Worth Method

• Capitalized Worth (CW) method -- Determining the
  present worth of all revenues and / or expenses
  over an infinite length of time
• Capitalized cost -- Determining the present worth
  of expenses only over an infinite length of time
• Capitalized worth or capitalized cost is a
  convenient basis for comparing mutually exclusive
  alternatives when a period of needed services is
  indefinitely long and the repeatability
  assumption is applicable

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Capitalized Cost

• CAPITALIZED COST- the present worth of a project
  which lasts forever.
• Government Projects
• Roads, Dams, Bridges, project that possess
  perpetual life
• Infinite analysis period
• Start with the closed form for the P/A factor
• Next, let N approach infinity