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
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Chapter 9 Mutually Exclusive Alternatives 137 9-4 Consider two investments: (1) Invest $1000 and receive $110 at the end of each month for the next 10 months. (2) Invest $1200 and receive $130 at the end of each month for the next 10 months. If this were your money, and you want to earn at least 12% interest on your money, which investment would you make, if any? What nominal interest rate do you earn on the investment you choose? Solve by present worth analysis. Solution PW Analysis i = 12%/12 = 1% per month Alternative 1: NPW = 110(P/A, 1%, 10) - 1,000 = $41.81 Alternative 2: NPW = 130(P/A, 1%, 10) - 1,200 = $31.23 Choose Alternative 1 Maximum NPW Nominal Interest: NPW = 0 = -1,000 + 110(P/A, i%, 10) (P/A, i%, 10) = 9.1 From tables: i 1.75% Nominal interest = 1.75% x 12 mo. = 21% 9-5 A farmer has just purchased a tractor for which he had to borrow $20,000. The bank has offered the following choice of payment plans determined using an interest rate of 8%. If the farmer's minimum attractive rate of return (MARR) is 15%, which plan should he choose? Plan A: $5,010 per year for 5 years Plan B: $2,956 per year for 4 years plus $15,000 at end of 5 years Plan C: Nothing for 2 years, then $9048 per year for 3 years Solution PWC A = 5,010(P/A, 15%, 5) = $16,794 PWC B = 2,956(P/A, 15%, 4) + 15,000(P/F, 15%, 5) = $15,897. PWC C = 9,048(P/A, 15%, 3)(P/F, 15%, 2) = $15,618 Plan C is lowest cost plan
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138 Chapter 9 Mutually Exclusive Alternatives 9-6 Projects A and B have first costs of $5,000 and $9,000, respectively. Project A has net annual benefits of $2,500 during each year of its 5 year useful life, after which it can be replaced identically.
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This note was uploaded on 09/11/2011 for the course ECON 12 taught by Professor Ablud during the Spring '11 term at West Point.

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

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