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

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

3. ISU CCEE 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 Present Worth and Economic Criteria for Mutually Exclusive Alternatives

4. ISU CCEE NPW = PW of Benefits – PW of Costs = PWB – PWC NPW = P 0 + n F j (P/F, i, n) where F j = B j – C j F j is + for net benefits, B j, - for net costs, C j Net Present Worth (NPW)

5. ISU CCEE 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 = Variations in Useful Lives of Alternatives and Analysis Period 8

6. ISU CCEE … then choose the alternative with the highest (or least negative) NPW Example: Examine a lternatives 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) Case 1: If useful lives of alternatives and analysis period are all equal…

7. ISU CCEE Costs/benefits estimates for various RR/street intersection alternatives for downtown Ames (assume 25-year useful life/analysis period) 1.Design, construction, loss of business 2.Maintenance, major refurbishing as noted 3.Time savings, better safety, increased business 4.Every 5y Alternative design Initial Costs 1 Maintenance Costs 2 Annual Benefits 3 #1 (overpasses)$10M$20k/y$0.75M #2 (tunnel)$15M$10k/y$1.0 M #3 (current)$50k$10k/y + $50k @ 5y 4 $0

8. ISU CCEE Present Worth evaluations for Costs/Benefits of RR/street intersection alternatives Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k* [P/A,6%,25] $750k* [P/A,6%,25] #2 (tunnel)$15M$10k* [P/A,6%,25] $1M* [P/A,6%,25] #3 (current)$50k$10k* [P/A,6%,25] + $50k [A/F,6%,5]* [P/A,6%,20] $0 Note: for Alt. #3, $50k@5 y is evaluated as [annualized value]*[series present worth] * means multiply

9. ISU CCEE Net Present Worth of RR/street intersection alternatives (in millions, benefits +, costs -) Alternative design Initial Costs Maintenance Costs Annual BenefitsNPW #1 (overpasses)-$10.00-$0.256+$9.588-$0.67 #2 (tunnel)-$15.00-$0.128+$12.783-$2.34 #3 (current)-$0.05-$0.230$0-$0.28 Note: though “problem” is real, estimates for costs and benefits are largely fabricated! ANALYSIS IS ONLY AS GOOD AS INPUT!!!

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

11. ISU CCEE 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 Case 2: If useful lives of alternatives are not equal…

12. ISU CCEE 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) Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k/yr + $10M @ 25 y $750k #2 (tunnel)$15M$10k/y$1M #3 (current)$50k$10k/y $50k @ 5y $0

13. ISU CCEE Present Worth evaluations for Costs/Benefits of RR/street intersection alternatives (Case 2) Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k[P/A,6%,50] + $10M[P/F,6%,25] $750k* [P/A,6%,50] #2 (tunnel)$15M$10k[P/A,6%,50]$1M* [P/A,6%,50] #3 (current)$50k$10k[P/A,6%,50] + $50k[A/F,6%,5]* [P/A,6%,45] $0

14. ISU CCEE Net Present Worth* of RR/street inter- section alternatives (in 10 6, benefits +, costs -) Alternative design Initial Costs Maintenance Costs Annual BenefitsNPW #1 (overpasses)-$10-$2.645+$11.82-$0.82 #2 (tunnel)-$15-$0.158+$15.76+$.60 #3 (current)-$0.05-$0.295$0-$0.35 *For Case 2 (50-year useful life for train tunnel, 25-year useful life for street overpasses)

15. ISU CCEE 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 Variations in Useful Lives of Alternatives and Analysis Period

16. ISU CCEE Capitalized Cost is money required now to cover given cash flow forever Capitalized Cost = A/i where A is uniform amount required each period to cover all future cash flow amounts

17. ISU CCEE 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. ISU CCEE 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. Case 3: Capitalized Cost for infinite analysis period (Present worth for infinite analysis period)

19. ISU CCEE 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) Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k/yr + $10M @ 25 yrs $750k #2 (tunnel)$15M$10k/yr$1M #3 (current)$50k$10k/yr $50k @ 5yrs $0

20. ISU CCEE Capitalized Cost for Alternative #1 Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k/y + $10M @ 25 y $750k 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. ISU CCEE Capitalized Cost evaluations for RR/street intersection alternatives (Case 3) Alternative design Initial Costs Maintenance Costs Annual Benefits #1 (overpasses)$10M$20k/0.06 + $10M[A/F,0.06,25] 0.06 $750k 0.06 #2 (tunnel)$15M$10k/0.06$1M/0.06 #3 (current)$50k$10k/0.06 + $50k[A/F,0.06,5] 0.06 $0

22. ISU CCEE Capitalized Costs of RR/street intersection alternatives (in millions; benefits +, costs -) Alternative design CC of Initial Costs CC of Maintenance Costs PW of Annual BenefitsNPW #1 (overpasses)-$10-$3.371*+$12.500-$0.87 #2 (tunnel)-$15-$1.028+$16.667+$.64 #3 (current)-$0.05-$0.315$0-$0.37 *As an example, the amount of $3.371M covers the $20k/yr maintenance PLUS the capitalized replacement cost at 25 years.