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1 MER 439 Design of Thermal Fluid Systems Engineering Economics 3. Comparing Alternatives Professor Wilk Winter 2007

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2 Choosing Between Alternatives 5 Methods (that we will cover) (1)Present Worth Method (2) Annual Cost Method (3) Capitalized Cost Method (4)Benefit Cost Ratio Method (5)Rate of Return

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3 1. Present Worth Method (Equal Lives) Calculate the PW of each alternative: we would like to: Maximize PW (benefits) Minimize PW (costs) Maximize Net PW (i.e. PW of benefits-PW of costs)

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4 Present Worth Example Example 1: Three ideas to reduce labor costs are proposed A - Continue with current method B – Make Equipment to reduce labor costs C - Purchase New Equipment Use i = 10% and n = 10 yrs

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5 Unequal Lives PW method requires that the lives of all of the options are equal. If the alternatives have different lives, assume costs are repeated. Repeat until Lowest Common Multiple of the unequal lives. Example 2: Two excavating machines are available: Which one should be selected based on an interest rate of 18% per year?

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6 2. Annual Cost Method Alternatives that have unequal lives are more easily compared using the annual cost method. Assumes each alternative will be replaced by an identical twin at the end of its life. (infinite renewal) Example 3: Which of the following alternatives is superior over a 30 year period if i = 6%?

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7 Annual Cost Method A A = 1800(A/P, 6%, 30) + 5 = $136 A B = 450(A/P, 6%, 10) + 20 = $81 Alternative B is better because its annual cost is lower than that of Alternative A. ANALYZE EACH AT ITS OWN RESPECTIVE LIFE

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8 3. Capitalized Cost Method The present worth of a project with an infinite life is called the capitalized or life cycle cost. It is the amount of money required at time zero to perpetually support the project on the earned interest only. CC = Initial Cost + Annual Costs/i =PW of an alternative that will last “forever”

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9 Capitalized Cost Example 4 What is the capitalized cost of a public works project that will cost $25,000,000 now and will require $2,000,000 in maintenance annually. i=12%. Solution: CC = 25 + 2/0.12 =$41.67 million

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10 Capitalized Cost Example 5 A city plans a pipeline to transport water from a distant watershed to the city. The pipeline will cost $8 million and have an expected life of 60 years. The city anticipates it will cost $120,000/yr to keep it up and running and that they will need to keep the water line in service indefinitely. Compute the capitalized cost assuming 6% interest.

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11 4. Benefit Cost Ratio Method B = Benefits = Cash Inflows C = Costs = Cash Outflows Want B-C > 0 or B/C > 1 Can use either P or A to evaluate Benefits and Costs

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12 Benefit Cost Ratio Method Example 6 A company is trying to decide between two alternatives to reduce costs. Both devices cost $1000 and have useful lives of 5 years and no salvage value. Device A is expected to result in $300 /yr. savings. Device B is expected to save $400 in the first year, but will decline $50 annually, making the 2 nd year savings $350, 3 rd yr. savings $300, etc. For i=6%, which device should be purchased.

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13 Benefit Cost Ratio Method Example 7 Two machines are being considered for purchase. Assuming 10% interest, which machine should be bought? X Y Initial cost$200 $700 Uniform annual benefit 95120 End of life salvage value 50 150 Useful life (yrs) 6 12

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14 5. Rate of Return Method It is often useful to calculate the rate of return on an investment. Solve for the interest rate that equates the worth of cash inflows to that of cash outflows ==> Result is IRR = Internal Rate of Return (i at which the benefits are equivalent to the costs) Set up Net P or Net A = 0 and solve for i.

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15 Rate of Return Ways to set up: P(benefits)/P(costs) = 1 P(benefits) = P(costs) P(benefits)-P(costs) = 0 Net P = 0 A(benefits) – A(costs) = 0 Etc. Solve for i

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16 Rate of Return Example 8 a) If you pay me $15,000 now and I promise to pay you back in 10 end of year payments of $1,250 what is your rate of return?

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17 Rate of Return Example Okay here’s another deal: b) If you pay me $15,000 now and I promise to pay you back in 10 end of year payments of $2,800 what is your rate of return?

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