# Copyright Oxford University Press 2009 Chapter 8 Choosing the Best Alternative.

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Copyright Oxford University Press 2009 Chapter 8 Choosing the Best Alternative

Copyright Oxford University Press 2009 Incremental Analysis Graphical Technique in Solving problems with Mutually Exclusive Alternatives Using Spreadsheets in Incremental Analysis Chapter Outline

Copyright Oxford University Press 2009 Define Incremental Analysis Apply Graphical Technique in solving Problems with Mutually Exclusive Alternatives Use Spreadsheets in Incremental Analysis Learning Objectives

Copyright Oxford University Press 2009 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

Copyright Oxford University Press 2009 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.

Copyright Oxford University Press 2009 Example 8-1 Incremental Analysis using Graphical Comparison HighLowIncrement Cost\$13,400\$10,310\$3090 Capacity15010050 Benefit\$4000/year\$3300/year\$700/year Life5 years IRR Low IRR High IRR Increment

Copyright Oxford University Press 2009 IRR Y IRR Increment Example 8-2 Incremental Analysis using Graphical Comparison Machine XMachine Y Initial Cost\$200\$700 Uniform Annual Benefit\$95\$120 End-of-Useful-Life Salvage Value\$50\$150 Useful Life, in Years612

Copyright Oxford University Press 2009 Example 8-3 Incremental Analysis using Graphical Comparison ABC Initial Cost\$2000\$4000\$5000 Uniform Annual Benefit410639700 If MARR ≥ 9.6%, Choose Alt. A If 9.6% ≥ MARR≥2%, Choose Alt. B If 2% ≥ MARR ≥ 0%, Choose Alt. C IRR B-A =9.6% IRR C-B =2%

Copyright Oxford University Press 2009 Example 8-4 Incremental Analysis using Graphical Comparison BrassStainlessTitanium Cost\$100,000\$175,000\$300,000 Life41025 If 6.3% ≥ MARR ≥ 0%, Choose Titinium If 15.3% ≥ MARR≥ 6.3%, Choose Stainless If MARR ≥ 15.3%, Choose Brass IRR Stainless - Brass =15.3% IRR Titanium - Stainless = 6.3%

Copyright Oxford University Press 2009 Example 8-5 Incremental Analysis (with Do-Nothing option) Machine XMachine YMachine Z Initial Cost\$200\$700\$425 Uniform Annual Benefit65110100 Useful Life, in years6128 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 IRR Z-X =11% IRR Y-Z =3.5% IRR X =23%

Copyright Oxford University Press 2009 Example 8-5 Incremental Analysis (without Do-Nothing option) Machine XMachine YMachine Z Initial Cost\$200\$700\$425 Uniform Annual Benefit65110100 Useful Life, in years6128 If MARR≥11%, Choose X If 11%≥MARR≥3.5%, Choose Z If 2%≥MARR≥0%, Choose Y IRR Z-X =11% IRR Y-Z =3.5% IRR X =23%

Copyright Oxford University Press 2009 Example 8-6 Incremental Analysis using Graphical Comparison ABCDE Initial Cost\$4000\$2000\$6000\$1000\$9000 Uniform Annual Benefit639410761117785 If MARR≥20%, Choose Do-Nothing If 20%≥ MARR≥11%, Choose B If 11%≥MARR≥2%, Choose A If 2%≥MARR≥0%, Choose C IRR A-B =11% IRR C-A =2% IRR B =20%

Copyright Oxford University Press 2009 Example 8-7 Incremental Analysis using Pair-wise Comparisons ABCDE Initial Cost\$4000\$2000\$6000\$1000\$9000 Uniform Annual Benefit639410761117785 1.Rearrange the alternatives in order of increasing cost DBACE Initial Cost\$1000\$2000\$4000\$6000\$9000 Uniform Annual Benefit117410639761785 2.Calculate IRR of the least expensive alternative to see if it is better than “Do Nothing” at MARR of 10% PW D = 0 = -\$1000 + \$117 (P/A, IRR D, 20) IRR D = 9.94% < 10% “Do Nothing” is preferred, and is still the “Defender.”

Copyright Oxford University Press 2009 Example 8-7 Incremental Analysis using Pair-wise Comparisons 3.Calculate IRR of the next alternative, B, to see if it is better than “Do Nothing” at MARR of 10% PW B = 0 = -\$2000 + \$410 (P/A, IRR B, 20) IRR B = 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. PW A-B = 0 = -(\$4000-\$2000)+(639-410)(P/A, IRR A-B,20) IRR A-B = 9.63% < 10% “Alternative B” is preferred, and is still the “Defender.”

Copyright Oxford University Press 2009 Example 8-7 Incremental Analysis using Pair-wise Comparisons 6.Compare Defender B with the next alternative, E. This comparison must be made incrementally. PW E-B = 0 = -(\$9000-\$2000)+(785-410)(P/A, IRR E-B,20) IRR E-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. PW C-B = 0 = -(\$6000-\$2000)+(761-410)(P/A, IRR C-B,20) IRR C-B = 6.08% < 10% “Alternative B” is preferred and is still the “Defender.”

Copyright Oxford University Press 2009 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

Copyright Oxford University Press 2009 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