ISU CCEE CE 203 Annual Cash Flow Analysis (EEA Chap 6)

ISU CCEE Compare alternatives based on equivalent annual cash flow Convert amounts to – Equivalent Uniform Annual Cost (EUAC)* – Equivalent Uniform Annual Benefit (EUAB) Calculate Present Value (C5) and then annualize (often the best approach) EUAB/EUAC = P(A/P, i, n) * Also known as the capital recovery cost Annual Cash Flow Analysis

ISU CCEE a) What is the EUAC for a $25,000 car that is expected to last for 10 years assuming an interest rate of 6%? b) What is the EUAC for the same $25,000 car (6%, 10-year life) if it has a salvage value of $5000? In-class example 6-1

ISU CCEE Different approaches to EUAC l EUAC = P(A/P, I, n) - S(A/F, I, n) l EUAC = (P-S)(A/F, I, n) + Pi l EUAC = (P-S)(A/P, I, n) + Si See derivation on p

ISU CCEE Maximize EUAW = EUAB - EUAC Choose method based on useful lives – Useful lives equal for alternatives – Useful lives not equal for alternatives – Infinite analysis period Selection of alternative

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

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 Alternative Initial Costs 1 Periodic Costs 2 Annual Benefits 3 #1 (overpasses)$10M$20k/y$750k #2 (tunnel)$15M$10k/y$1M #3 (current)$50k$10k/y 5y $0

ISU CCEE Annual Cash Flow evaluations for Costs/ Benefits of intersection alternatives AlternativeInitial Costs Periodic Costs Annual Benefits #1 (overpasses)-$10M [A/P,6%,25]-$20k+$750k #2 (tunnel)-$15M [A/P,6%,25]-$10k+$1M #3 (current)-$50k [A/P,6%,25]-$10k -$50k [A/F,6%,5] $0

ISU CCEE Annual Cash Flow for RR/street intersection alternatives (benefits +, costs -) Alternative Initial Costs Periodic Costs Annual BenefitsEUAW #1 (overpasses)-$782k-$20k+$750k-$52k #2 (tunnel)-$1,173k-$10k+$1000k-$183k #3 (current)-$3.9k-$18.9k$0-$22.8k As before, “problem” is real, but estimates for costs and benefits are largely fabricated! ANALYSIS IS ONLY AS GOOD AS INPUT!!!

ISU CCEE … may or may not have to use least common multiple analysis period, depending on assumptions about “replacements” for alternatives with shorter useful lives … Annual Cash Flow Analysis, if useful lives of alternatives not equal…

ISU CCEE Given Alternative A with a useful life of 12 years and Alternative B with a useful life of 6 years. Alternative B has an initial cost of $5,000 and a salvage value of $1,000. Calculate the EUAC for Alternative B considering a single life and 12-year analysis period (i.e., two lives back to back). APR = 7%. In-class Example 6-2

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. … if overpass replacement is identical to original, can use useful life of each for comparison. Case 2: RR/street intersection problem useful lives of alternatives not equal…

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 Initial CostsPeriodic Costs Annual Benefits #1 (overpasses)$10M$20k/y$750k #2 (tunnel)$15M$10k/y$1M #3 (current)$50k$10k/y 5y $0

ISU CCEE Annual Cash Flow evaluations for Costs/ Benefits of intersection alternatives AlternativeInitial Costs Periodic Costs Annual Benefits #1 (overpasses)-$10M [A/P,6%,25] -$20k+$750k #2 (tunnel)-$15M [A/P,6%,50] -$10k+$1M #3 (current)-$50k [A/P,6%,50] -$10k + -$50k [A/F,6%,5] $0

ISU CCEE Annual Cash Flow for RR/street intersection alternatives (benefits +, costs -)* Alternative Initial Costs Periodic Costs Annual BenefitsEUAW #1 (overpasses)-$782k-$20k+$750k-$52k #2 (tunnel)-$951k-$10k+$1000k+$39k #3 (current)-$3.9k-$18.9k?$0-$22.8k *For Case 2 (50-year useful life for train tunnel, 25-year useful life for street overpasses)

ISU CCEE Calculate an annualized cost equivalent for each alternative. In general… – Annualize periodic costs/benefits as before – Use A = P * i to convert present costs for alternatives with infinite lives to annualized values Infinite Analysis Period

ISU CCEE Costs/benefits estimates for various RR/street intersection alternatives assuming 25-year useful life for overpasses, infinite useful life for tunnel, infinite analysis period… Costs/benefits estimates for various RR/street intersection alternatives assuming 25-year useful life for overpasses, infinite useful life for tunnel, infinite analysis period… Alternative Initial CostsPeriodic Costs Annual Benefits #1 (overpasses)$10M$20k/y$750k #2 (tunnel)$15M$10k/y$1M #3 (current)$50k$10k/y 5y $0

ISU CCEE Annual Cash Flow evaluations for Costs/Benefits of intersection alternatives AlternativeInitial Costs Periodic Costs Annual Benefits #1 (overpasses)-$10M [A/P,6%,25] -$20k+$750k #2 (tunnel)-$15M * 6%-$10k+$1M #3 (current)-$50k [A/P,6%, 25 ] -$10k + -$50k [A/F,6%,5] $0

ISU CCEE Annual Cash Flow for RR/street intersection alternatives (benefits +, costs -)* Alternative Initial Costs Periodic Costs Annual BenefitsEUAW #1 (overpasses)-$782k-$20k+$750k-$52k #2 (tunnel)-$900k-$10k+$1000k+$90k #3 (current)-$3.9k-$18.9k$0-$22.8k *For Case 3 (infinite useful life for tunnel, 25-year useful life for street overpasses)