# Chapter09 - Chapter 9 Mutually Exclusive Alternatives 9-1...

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135 Chapter 9 Mutually Exclusive Alternatives 9-1 Using an 8-year analysis and a 10% interest rate, determine which alternative should be selected, based on net present worth. Alternative A B First Cost \$5,300 \$10,700 Uniform Annual Benefit 1,800 2,100 Useful life 4 years 8 years Solution NPW = PW(benefits) - PW(costs) Alternative A: NPW = 1,800(P/A, 10%, 8) - 5,300 - 5,300(P/F, 10%, 4) = \$683.10 Alternative B: NPW = 2,100(P/A, 10%, 8) - 10,700 = \$503.50 Select alternative A 9-2 Three purchase plans are available for a new car. Plan A: \$5,000 cash immediately Plan B: \$1,500 down and 36 monthly payments of \$116.25 Plan C: \$1,000 down and 48 monthly payments of \$120.50 If a customer expects to keep the car five years and her minimum attractive rate of return (MARR) is 18% compounded monthly, which payment plan should she choose?

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136 Chapter 9 Mutually Exclusive Alternatives Solution Note that in all cases the car is kept 5 years that is the common analysis period. Therefore PWC is the easiest method. i = 18%/12 = 1½% PWC A = \$5,000 PWC B = 1,500 + 116.25(P/A, 1½%, 36) = \$4,715,59 PWC C = 1,000 + 120.50(P/A, 1½%, 48) = \$5,102.18 Therefore Plan B is best 9-3 Given the following three mutually exclusive alternatives. Alternative A B C Initial Cost \$50 \$30 \$40 Annual Benefits 15 10 12 Useful Life(years) 5 5 5 What alternative is preferable if i = 10%? Solution Using simplest method (NPW): A B C Initial Cost 50.00 30.00 40.00 Annual Benefits 15.00 10.00 12.00 Useful Life(years) 5 5 5 Present Worth Benefits 56.87 37.91 45.49 Present Worth Costs 50.00 30.00 40.00 Net Present Worth = PWB - PWC 6.87 7.91 5.49 Choose C