Engineering Economic Analysis Canadian Edition

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Engineering Economic AnalysisCanadian Edition

• Chapter 9 Other Analysis Techniques

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Chapter 9. . .

• develops and uses future worth, benefit-cost
  ratio, payback period, and sensitivity analysis
  methods to solve engineering economic problems.
• links the use of the future worth method to the
  present worth and annual worth methods.
• uses spreadsheets to perform sensitivity and
  breakeven analyses.

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Present and Future WorthMethods

• Present Worth (PW)
• What is the present situation of future action?
• Project cash flows are converted to an equivalent
  value (usually) now (see Chapter 5).
• Future Worth (FW)
• What is the future situation of action now?
• Project cash flows are converted to a future
  value (usually at the end of a projects life).

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Future Worth

Find the value of the cash flows at the end of
the 5th year if the rate of interest is 10
compounded annually?
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Economic Criteria

• Projects are judged against an economic
  criterion.

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Economic Criteria Restated Future Worth
Techniques
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Type of Projects

• Independent
• The selection of a project is independent of the
  decision to undertake or not any other project or
  projects.
• Mutually exclusive
• At most one project (including the status quo
  option) can be selected amongst competing
  alternatives.

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• Contingent (dependent)
• The selection of a project is dependent on the
  selection of at least one other project.

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Problem Find FW (i10)

• FW 1,000(F/P,10,7)
• 2,000(F/P,10,6)
• 3,000(F/P,10,5)
• 2,500(F/P,10,4)
• 2,000(F/P,10,3)
• 1,500(F/P,10,2)
• 1,000(F/P,10,1)
• 500(F/P,10,0)
• FW 25,940

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FW and Independent Projects

• Select all projects with non-negative FW.
• if FW 0, accept project
• if FW FW lt 0, reject project
• if FW 0, accept project
• If all projects have a FW lt 0, select the
  status quo option (invest available funds at
  the prevailing (current) interest rate.
• The selection of independent projects is usually
  constrained by a capital budget (limited funds).

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FW and Mutually ExclusiveProjects

• The FW method (as with PW) requires that a common
  period of analysis be used to determine the
  best alternative.
• Incorrect to compare the FW of one-week and
  two-week car rentals without making period of
  analysis adjustments

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Future Worth Analysis

• Future Worth Analysis answers the question
• What will the future situation be if we take a
  particular course of action now?
• FW P(F/P,i,n)
• FW A(F/A,i,n)

Example 9.1
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• When constructing a building, the issue is not
  the dollars out of pocket,but the invested cost
  at start-up.

Example 9-2
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Future and Present Worth Analysis
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• NPW (A)
• -2500 - 900(P/A,10,5) 1800(P/A,10,5)
• 200(P/F,10,5)
• 1,036
• NFW (A)
• -2500(F/P,10,5) - 900(F/A,10,5)
• 1800(F/A,10,5) 200
• 1,668

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• NPW (B)
• -3500 - 700(P/A,10,5) 1900(P/A,10,5)
• 350(P/F,10,5)
• 1,266
• NFW (B)
• -3500(F/P,10,5) - 700(F/A,10,5)
• 1900(F/A,10,5) 350
• 2,039

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• NPW (C)
• -5000 - 1000(P/A,10,5) - 100(P/G,10,5)
• (2100/(0.1-0.15))1-(1.15/1.1)5
• 977
• NFW (C)
• -5000(F/P,10,5) - 1000(F/A,10,5)
• 100(F/G,10,5) (2100/(0.1-0.15))1-
• (1.15/1.1)5(F/P,10,5)
• 1,573

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Useful Lives ? Analysis Period

• Project A has a 3-year life
• Project B has a 4-year life
• Both projects are valid
• because their Net Future
• Worth (NFW) gt 0 (i10)
• Which project is better?

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• Because projects A and B have different lives,
  the FW criterion requires that they beevaluated
  over a common period of analysis (12 years).
• Hence, project A will be repeated 3 times (after
  theinitial investment at t0) and project B
  twice.

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• NFWA (12 years) 2,092.92
• NFWB(12 years) 1,476.55
• Decision Select project A

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Benefit-Cost Ratio

• An alternative is acceptable at a given MARR
  provided
• PW (Benefits) PW (Costs) 0
• FW (Benefits) FW (Costs) 0
• EUAB EUAC 0
• Can be restated as the benefit-cost ratio (B/C)
• B/C PW (Benefits)/PW(Costs) EUAB/EUAC

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Benefit-Cost Ratio Analysis

• If the PW of benefits - PW of costs ³ 0
• The alternative is considered acceptable.
• Restated
• Benefit-cost ratio B/C PW of benefit/PW of cost
  ³ 1.
• Fixed input, maximize B/C.

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Example 9-3
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Economic Criteria Restated Benefit-Cost Method
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B/C and ?B/?C Ratios

• The B/C ratio and other methods such NPW, NFW,
  EUAW, and IRR) lead to the same conclusion as to
  the acceptability of projects
• Better mutually exclusive project (2 projects)
• Best competing alternative (3 projects)

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Benefit-Cost Ratio Analysis

• If the EUAB - EUAC ³ 0
• The alternative is considered acceptable.
• Restated
• Benefit-cost ratio B/C EUAB/EUAC ³ 1
• Neither input or output fixed - use incremental
  B/C.

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Example 9-4
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B/C Ratios and Competing Alternatives

• Moose County has three alternative plans for a
  new road. Benefits and costs are shown below.
  Expected road life is 50 years and MARR 10.

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• Based on the information on the previous slide,
  find
• B/C ratios
• acceptable projects
• the best project

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• Project A
• (B/C) 700 1,500 / 25,000(A/P,10,50)
• 200 / (3,200 / 2,721.5)
• 1.18 gt 1
• Project A is acceptable.

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• Project B
• (B/C) 1,000 1,800 / 35,000 (A/P,10,
• 50) 250
• (3,800 / 3,780.1)
• 1.01 gt 1
• Project B is acceptable.

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• Project C
• (B/C) 1,450 2,400 / 50,000(A/P,10,
• 50) 350
• (6,050 / 5,393)
• 1.12 gt 1
• Project C is acceptable.

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• Incremental B/C Ratios
• Compare A and B
• ?B/?C (3,800 3,200)/(3,780.1 2,721.5)
• 2,850/2,671.5
• 0.57 lt 1
• A is better.

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• Compare A and C
• ?B/?C (6,050 3,200)/(5,393 2,721.5)
• 2,850/2,671.5
• 1.07 gt 1
• C is better. In fact, Project C is best.

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Important Points about Payback Period

• 1. Approximate economic analysis method.
• 2. Prior to payback the effect of timing is
  ignored.
• 3. After payback all economic consequences are
  ignored.
• 4. Will not necessarily produce a recommended
  alternative consistent with equivalent worth and
  rate of return methods.

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Payback Characteristics

• Exclusive focus on liquidity (no concern for
  profitability).
• Liquidity how quickly can the investment (P) be
  recovered from the projects cash flows?
• All other methods of project evaluation (e.g.,
  single sums) focus on profitability (not
  liquidity)
• Usually based on before-tax calculations

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• No time value discounting i.e., the effective
  MARR 0
• A project balance has NO opportunity cost.
• Project Balance P - ?(ORi OCi), i 0, 1 .N

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Project Balance

• A projects balance at any point during the life
  of a project is
• For simple payback a projects un-recovered
  investment (P).
• Discounted payback a projects un-recovered
  investment (P) the annual opportunity cost
  (i.e., interest charges) of the un-recovered
  investment.

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• Generally, net annual revenues (revenues less
  costs) will cause a projects balance to decrease
  over time.
• A project balance is negative until the initial
  investment has been fully recovered.
• Our interest is limited to negative project
  balances.

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The unrecovered investment at any point during
project life
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Liquidity Focus

• Projects A and B have the same five-year recovery
  period (i.e., project balance is zero after five
  years).
• However, they have very different profitability
  profiles (with Project A being more profitable
  than Project B).
• Since this method focuses ONLY on liquidity (how
  fast can I recover my initial investment), you
  would be indifferent between projects A and B.

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Simple Payback(Irregular Cash Flow)

• Recovery period 3 300/(300700) 3.3 years
• Compare 3.3 years to industry threshold to
  determine if project is acceptable.
• If similar investments require, on average, 3
  years to recover, this project would be rejected
  (3.3 years gt standard)

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Payback Period

• The payback period is the period of time required
  for the profit or other benefits of an investment
  to equal the cost of the investment.
• How many years are required to get the money back
  in the following examples?

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Example 9-6
Example 9-7
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Payback Analysis

• What is wrong here?
• Payback and IRR analysis do not agree.
• With alternative A we get ourmoney back in 4
  years but never make a return on the
  investment.
• With alternative B we get ourmoney back in 5
  years and make a return on the investment of
  19.

Example 9-8
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• How should we make a decision?
• Liquidity vs. profitability
• Life of project

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Discounted Payback
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• Recovery period
• 9 years 2410.6/(2410.6227.8)
• 9.91 years
• If the industry average recovery period for this
  type of project is 8 years, this project is not
  acceptable.

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Discounted Payback Project Balance
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Sensitivity and Break-evenAnalysis

• Economic data represent projections of
  expenditures and returns.
• These projections ultimately affect our
  decisions.
• To more fully consider our choice of a decision,
  we should play a what if game to determine the
  amount of change in a data point that might
  change the decision.

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Projected and Actual Cash Flows may Differ

• Technological change
• changes to production costs
• Changes in the size and number of competing firms
• Introduction of new products
• substitutes or complements

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• Changes to key macroeconomic variables
• e.g., inflation, unemployment, economic growth,
  exchange rate
• International events

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Breakeven Analysis
Example 9-9
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Sensitivity Analysis
Example 9-10
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• This problem was solved by copying the original
  NPW setup twice and then solving for the minimum
  and maximum values of the Initial cost of
  alternative B that would not change the decision
  to select B.
• Try and find the sensitivity of the EUAB that
  would not change the decision to select B.
• Remember to first reset the Initial cost of B to
  4,000 or you will have two variables changing
  and not know what is really happening.

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Sensitivity of PW to changes in project parameters
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• The sensitivity of NPW is
• Highest to changes in annual revenues (AOR)
• Smallest to changes in salvage value (SV)