copyright oxford university press 2009 chapter 8 choosing the best alternative

Copyright Oxford University Press 2009

Chapter 8Choosing the Best Alternative


• Incremental Analysis• Graphical Technique in Solving problems

with Mutually Exclusive Alternatives• Using Spreadsheets in Incremental

Analysis

Chapter Outline


• Define Incremental Analysis• Apply Graphical Technique in solving

Problems with Mutually Exclusive Alternatives

• Use Spreadsheets in Incremental Analysis

Learning Objectives


• Only one alternative may be implemented

• All alternatives serve the same purpose

• Objective of incremental analysis is to select the best of these mutually exclusive alternatives

Mutually Exclusive Alternatives


Incremental Analysis

• Could be applied to rate of return (IRR), present worth (PW), equivalent uniform annual cost (EUAC), or equivalent uniform annual worth (EUAW) approaches.

• [Higher-cost alternative] = [Lower-cost alternative] + [Increment between them]

• The “defender” is the best alternative identified so far in the process, and “challenger” is the next higher-cost alternative to be evaluated.

• For a set of N mutually exclusive alternatives, (N - 1) “challenger/defender” comparisons must be made from [N(N-1)/2] possibilities.


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PW

Example 8-1 Incremental Analysisusing Graphical Comparison

High Low IncrementCost $13,400 $10,310 $3090Capacity 150 100 50Benefit $4000/year $3300/year $700/yearLife 5 years 5 years 5 years

IRRLowIRRHigh

IRRIncrement


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PW

IRRY

IRRIncrement

Example 8-2 Incremental Analysis using Graphical Comparison

Machine X Machine YInitial Cost $200 $700Uniform Annual Benefit $95 $120End-of-Useful-Life Salvage Value $50 $150Useful Life, in Years 6 12



A B CInitial Cost $2000 $4000 $5000Uniform Annual Benefit 410 639 700

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NPW

If MARR ≥ 9.6%,Choose Alt. A

If 9.6% ≥ MARR≥2%,Choose Alt. B

If 2% ≥ MARR ≥ 0%,Choose Alt. C

IRRB-A=9.6%

IRRC-B=2%IRRC-B= 2%


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EUAC


Brass Stainless TitaniumCost $100,000 $175,000 $300,000Life 4 10 25

If 6.3% ≥ MARR ≥ 0%,Choose Titinium

If 15.3% ≥ MARR≥ 6.3%,Choose Stainless

If MARR ≥ 15.3%,Choose Brass

IRRStainless - Brass=15.3%

IRRTitanium - Stainless= 6.3%


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EUAW

Example 8-5 Incremental Analysis(with Do-Nothing option)

Machine X Machine Y Machine ZInitial Cost $200 $700 $425Uniform Annual Benefit 65 110 100Useful Life, in years 6 12 8

If MARR≥23%,Choose “Do-Nothing”

If 23%≥MARR≥11%,Choose X

If 11%≥MARR≥3.5%,Choose Z

If 2%≥MARR≥0%,Choose Y

IRRZ-X=11%IRRY-Z=3.5%

IRRX=23%


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EUAW

Example 8-5 Incremental Analysis(without Do-Nothing option)

Machine X Machine Y Machine ZInitial Cost $200 $700 $425Uniform Annual Benefit 65 110 100Useful Life, in years 6 12 8

If MARR≥11%,Choose X

If 11%≥MARR≥3.5%,Choose Z

If 2%≥MARR≥0%,Choose Y

IRRZ-X=11%IRRY-Z=3.5%

IRRX=23%


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NPW


A B C D EInitial Cost $4000 $2000 $6000 $1000 $9000Uniform Annual Benefit 639 410 761 117 785

If MARR≥20%, Choose Do-Nothing

If 20%≥MARR≥11%,Choose B

If 11%≥MARR≥2%,Choose A

If 2%≥MARR≥0%,Choose C

IRRA-B=11%

IRRC-A=2%

IRRB=20%


Example 8-7 Incremental Analysis using Pair-wise Comparisons

A B C D EInitial Cost $4000 $2000 $6000 $1000 $9000Uniform Annual Benefit 639 410 761 117 785

1. Rearrange the alternatives in order of increasing costD B A C E

Initial Cost $1000 $2000 $4000 $6000 $9000Uniform Annual Benefit 117 410 639 761 785

2. Calculate IRR of the least expensive alternative to see if it is better than “Do Nothing” at MARR of 10%

PWD = 0 = -$1000 + $117 (P/A, IRRD, 20)

IRRD = 9.94% < 10%

“Do Nothing” is preferred, and is still the “Defender.”



3. Calculate IRR of the next alternative, B, to see if it is better than “Do Nothing” at MARR of 10%

PWB = 0 = -$2000 + $410 (P/A, IRRB, 20)

IRRB = 19.96% > 10%

“Alternative B” is preferred, and is the new “Defender.”

4. Compare Defender B with the next alternative, A. This comparison must be made incrementally.

PWA-B = 0 = -($4000-$2000)+(639-410)(P/A, IRRA-

B,20)

IRRA-B = 9.63% < 10%

“Alternative B” is preferred, and is still the “Defender.”



6. Compare Defender B with the next alternative, E. This comparison must be made incrementally.

PWE-B = 0 = -($9000-$2000)+(785-410)(P/A, IRRE-

B,20)

IRRE-B = 0.67% < 10%

“Alternative B” is preferred, and is the final selection.

5. Compare Defender B with the next alternative, C. This comparison must be made incrementally.

PWC-B = 0 = -($6000-$2000)+(761-410)(P/A, IRRC-

B,20)

IRRC-B = 6.08% < 10%

“Alternative B” is preferred and is still the “Defender.”


1. Identify all alternatives.2. Construct an NPW or EUAW graph showing all

alternatives on the same axes. 3. Examine the line of maximum values and

determine which alternative create it, and over what range.

4. Determine the changeover point.5. Create a choice table to summarize the

information.

Elements in Comparing Mutually Exclusive Alternatives


• All analysis methods provide consistent solutions.• Rate of Return Analysis

• Easier to explain• Most frequently used• More difficult to calculate (without spreadsheet) • Does not require a Minimum Attractive Rate of

Return in calculation• Present Worth or Annual Cash Flow Analysis

• Require a known Minimum Attractive Rate of Return in calculation

• Easier to calculate (without spreadsheet)

Choosing an Analysis Method

copyright oxford university press 2009 chapter 8 choosing the best alternative

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