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CE 203 Present Worth Analysis (EEA Chap 5)

CE 203 Present Worth Analysis (EEA Chap 5). Three Techniques for Economic Comparison of Alternatives. Present Worth Analysis (Chapter 5) Annual Cash Flow Analysis (Chapter 6) Rate of Return Analysis (Chapter 7).

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CE 203 Present Worth Analysis (EEA Chap 5)

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  1. CE 203Present Worth Analysis(EEA Chap 5)

  2. Three Techniques for Economic Comparison of Alternatives • Present Worth Analysis (Chapter 5) • Annual Cash Flow Analysis (Chapter 6) • Rate of Return Analysis (Chapter 7)

  3. Present Worth and Economic Criteria for Mutually Exclusive Alternatives 1: For Fixed Input : Maximize present worth of benefits or other outputs 2: For Fixed Output : Minimize present worth of costs or other inputs 3: For Variable Input and Output: Maximize Net Present Worth (NPW) = present worth of benefits minus present worth of costs

  4. Net Present Worth (NPW) NPW = PW of Benefits – PW of Costs= PWB – PWC NPW = P0 + n Fj (P/F, i, n) where Fj = Bj – Cj Fj is + for net benefits, Bj, - for net costs, Cj

  5. Variations in Useful Lives of Alternatives and Analysis Period 1: Useful life (and analysis period) are equal among all alternatives 2: Useful lives of alternatives are not equal 3: Analysis period is infinite, n = 8

  6. Case 1: If useful lives of alternatives and analysis period are all equal… … then choose the alternative with the highest (or least negative) NPW Example:Examine alternatives for railroad/ street intersections in downtown Ames. Assume useful life for all alternatives is 25 years, i = 6%, yearly compounding. 1. Street overpasses at Duff, Kellogg, and Clark 2. Train tunnel through downtown Ames 3. Current (do nothing)

  7. Costs/benefits estimates for various RR/street intersection alternatives for downtown Ames (assume 25-year useful life/analysis period) • Design, construction, loss of business • Maintenance, major refurbishing as noted • Time savings, better safety, increased business • Every 5y

  8. Present Worth evaluations for Costs/Benefits of RR/street intersection alternatives Note: for Alt. #3, $50k@5 y is evaluated as [annualized value]*[series present worth] * means multiply

  9. Net Present Worth of RR/street intersection alternatives (in millions, benefits +, costs -) Note: though “problem” is real, estimates for costs and benefits are largely fabricated!ANALYSIS IS ONLY AS GOOD AS INPUT!!!

  10. Case 2: If useful lives of alternatives are not equal… … then choose an appropriate analysis period: 1) the least common multiple analysis period OR 2) a common analysis period with a terminal (salvage) value

  11. Case 2: If useful lives of alternatives are not equal… Example: Alternatives for railroad/street intersections in downtown Ames as for Case 1, but assume useful life for tunnel is 50 years and useful life for overpasses is 25 years, i = 6%, yearly compounding. … choose (least common multiple) 50-year analysis period and assume overpasses are replaced in 25 years

  12. Costs/benefits estimates for various RR/street intersection alternatives for downtown Ames (assuming 25-year useful life for overpasses, 50-year useful life for tunnel, 50-year analysis)

  13. Present Worth evaluations for Costs/Benefits of RR/street intersection alternatives (Case 2)

  14. Net Present Worth* of RR/street inter-section alternatives(in 106, benefits +, costs -) *For Case 2 (50-year useful life for train tunnel, 25-year useful life for street overpasses)

  15. Variations in Useful Lives of Alternatives and Analysis Period 1: Useful life (and analysis period) are equal among all alternatives 2: Useful lives of alternatives are not equal 3: Analysis period is infinite - calculate an annualized cost equivalent for each alternative - then calculate the capitalized cost

  16. Capitalized Cost is money required now to cover given cash flow foreverCapitalized Cost = A/iwhere A is uniform amount required each period to cover all future cash flow amounts

  17. In-class Example (Capitalized Cost) You have been very successful in your career as a consulting civil engineer and have decided to endow a CE scholarship at ISU. How much would you have to give ISU in order to provide a $5000 dollar scholarship each year indefinitely assuming you were guaranteed 5% interest?

  18. Case 3: Capitalized Cost for infinite analysis period (Present worth for infinite analysis period) Example: Alternatives for railroad/street intersections in downtown Ames as for Case 2 (useful life for tunnel is 50 years and useful life for overpasses is 25 years), i = 6%, yearly compounding, infinite analysis period.

  19. Costs/benefits estimatesfor various RR/street intersection alternatives for downtown Ames (assuming 25-year useful life for overpasses, 50-year useful life for tunnel)

  20. Capitalized Cost for Alternative #1 CC of $20k/yr = $20k/0.06 = $333.33k = $0.333M (-) CC of $10M @ 25 years = $10M [A/F,0.06,25] / 0.06 = $3.038M (-) PW of $750k/y = $750k/0.06 = $12.5M (+) NPW = - 10 - 0.333 - 3.038 + 12.5 =- $0.871M

  21. Capitalized Cost evaluations for RR/street intersection alternatives (Case 3)

  22. Capitalized Costs of RR/street intersection alternatives(in millions; benefits +, costs -) *As an example, the amount of $3.371M covers the $20k/yr maintenance PLUS the capitalized replacement cost at 25 years.

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