CE 203 Annual Cash Flow Analysis (EEA Chap 6)

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

• 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

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In-class example 6-1

• 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?

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Different approaches to EUAC

• EUAC P(A/P, I, n) - S(A/F, I, n)
• EUAC (P-S)(A/F, I, n) Pi
• EUAC (P-S)(A/P, I, n) Si
• See derivation on p 179-180

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Selection of alternative

• Maximize EUAW EUAB - EUAC
• Choose method based on useful lives
• Useful lives equal for alternatives
• Useful lives not equal for alternatives
• Infinite analysis period

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Case 1 If useful lives of alternatives and
analysis period are all equal

• 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)

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Costs/benefits estimates for various RR/street
intersection alternatives for downtown Ames
(assume 25-year useful life/analysis period)
Alternative Initial Costs1 Periodic Costs2 Annual Benefits3
1 (overpasses) 10M 20k/y 750k
2 (tunnel) 15M 10k/y 1M
3 (current) 50k 10k/y 50k _at_ 5y 0

1. Design, construction, loss of business
2. Maintenance, major refurbishing as noted
3. Time savings, better safety, increased business

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Annual Cash Flow evaluations for Costs/ Benefits
of intersection alternatives
Alternative Initial 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
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Annual Cash Flow for RR/street intersection
alternatives (benefits , costs -)
Alternative Initial Costs Periodic Costs Annual Benefits EUAW
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!!!
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Annual Cash Flow Analysis, if useful lives
of alternatives not equal

• may or may not have to use least common
  multiple analysis period, depending on
  assumptions about replacements for alternatives
  with shorter useful lives

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In-class Example 6-2

• 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.

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Case 2 RR/street intersection problem useful
lives of alternatives 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.
• if overpass replacement is identical to
  original, can use useful life of each for
  comparison.

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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 Costs Periodic Costs Annual Benefits
1 (overpasses) 10M 20k/y 750k
2 (tunnel) 15M 10k/y 1M
3 (current) 50k 10k/y 50k _at_ 5y 0
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Annual Cash Flow evaluations for Costs/ Benefits
of intersection alternatives
Alternative Initial 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
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Annual Cash Flow for RR/street intersection
alternatives (benefits , costs -)
Alternative Initial Costs Periodic Costs Annual Benefits EUAW
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)
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Infinite Analysis Period

• 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

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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 Costs Periodic Costs Annual Benefits
1 (overpasses) 10M 20k/y 750k
2 (tunnel) 15M 10k/y 1M
3 (current) 50k 10k/y 50k _at_ 5y 0
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Annual Cash Flow evaluations for Costs/Benefits
of intersection alternatives
Alternative Initial 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
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Annual Cash Flow for RR/street intersection
alternatives (benefits , costs -)
Alternative Initial Costs Periodic Costs Annual Benefits EUAW
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)