Other Analysis Techniques

1
Other Analysis Techniques

• Future Worth Analysis (FWA)
• Benefit-Cost Ratio Analysis (BCRA)
• Payback Period
• Sensitivity and Breakeven Analysis.

2
Techniques for Cash Flow Analysis

• Present Worth Analysis
• Annual Cash Flow Analysis
• Rate of Return Analysis
• Incremental Analysis
• Other Techniques
• Future Worth Analysis
• Benefit-Cost Ration Analysis
• Payback Period Analysis
• Sensitivity and Breakeven Analysis

• Chapter 5
• Chapter 6
• Chapter 7
• Chapter 8
• Chapter 9

3
Other Analysis Techniques

• Future worth analysis is equivalent to present
  worth analysis
• the best alternative one way is also best the
  other way. There are many situations where we
  want to know what a future situation will be, if
  we take some particular course of action now.
  This is called future worth analysis.
• Since we can write
• PW of cost ? PW of benefit or
• EUAC ? EUAB we can equivalently write
• (PW of benefit)/PW of cost ? 1, or
• EUAB/EUAC ? 1.
• Economic analysis based on these ratios is
  called benefit-cost ratio analysis.
• Payback period is an approximate analysis method.
  For example, if a 1000 investment today
  generates 500 annually in savings, we say its
  payback period is 1000/500 2 years.
• Sensitivity analysis identifies how sensitive
  economic conclusions are to the values of the
  data, and allows making decisions for an entire
  range of the data.  
• Breakeven analysis is closely related to
  sensitivity analysis, and determines conditions
  when two alternatives are equivalent (as well as
  when each is better than the other). It can be
  viewed as a type of sensitivity analysis.

4
Benefit/Cost Ratio Analysis

• Example
• Each of the five mutually exclusive alternatives
  presented below will last for 20 years and has no
  salvage value. MARR 6.
• The steps are the same as in incremental ROR,
  except that the criterion is now ?B/?C, and the
  cutoff is 1 instead of the MARR
• 1) Be sure you identify all alternatives. 
• 2) (Optional) Compute the B/C ratio for each
  alternative. Discard any with a B/C lt 1.
• (We can discard F).
• 3) Arrange the remaining alternatives in
  ascending order of investment.

5
Benefit/Cost Ratio Analysis

• 4) Comparing ?B/?C with 1 for consecutive
  alternatives select the best alternative.
• Thus, for the example, the increments B-D and
  A-B are attractive. We prefer B to D, and we
  prefer A to B. Increment C-A is not attractive,
  as ?B/?C 0.76 lt 1. Comparing A to E, again A is
  best. Finally A is the best project.

6
Benefit/Cost Ratio Analysis
PWB
F

• A, B, C, and D are above the
• 45-degree line their B/C ratio is gt 1.
• F is below the line B/C ratio is lt 1.
• We can discard F if we wish.

E
C
A
PWB/PWC 1
B
Examine each separable increment of
investment. ?B/?C lt 1 ? increment is not
attractive ?B/?C ? 1 ? increment is desirable.
D
PWC
Begin with D B ?B/?C gt 1. B wins. Next
consider A ?B/?C gt 1. A wins. C
?B/?C lt 1 discard C. E
?B/?C lt 1 discard E. F was discarded
earlier Conclude A is best. Note Alt. B has the
highest B/C ratio
7
Payback Period

• Warning
• 1. Payback period is an approximate, rather than
  an exact, analysis calculation. 
• 2. All costs and all profits, or savings of the
  investment prior to payback, are included without
  considering differences in their timing.
• 3. All the economic consequences beyond the
  payback period are completely ignored.
• 4. Payback period may or may not select the same
  alternative as an exact economic analysis method.
• Payback period is used because
• the concept can be readily understood,
• the calculations can be readily made and
  understood by people unfamiliar with the use of
  the time value of money.
• Its better than nothing. Use it as a last
  resort to communicate.

8
Payback Period Example

• A firm is buying production equipment for a new
  plant.
• Two alternative machines are being considered.

PBP analysis would choose Tempo (PBP 4 yrs.)
instead of Dura (PBP 5 yrs.). However, with
IRR analysis we can see that Tempo is not a very
attractive investment. Although, Tempo does
return its investment more quickly than Dura.
9
Payback Period Summary
Lesson from Example liquidity and profitability
can be very different criteria. Final
Conclusions about PBP Analysis This analysis
provides a measure of the speed of the return of
the investment. If a company is short of
working capital, or experiences a rapidly
changing technology, the speed of return can be
important.   PBP analysis should not be
confused with careful economic analysis. PBP
analysis does not always mean the investment is
economically desirable.

• Payback period is an approximate, rather than an
  exact, analysis calculation.
• 2. All costs and all profits, or savings of the
  investment prior to payback, are included without
  considering differences in their timing.
• 3. All the economic consequences beyond the
  payback period are completely ignored.
• 4. Payback period may or may not select the same
  alternative as an exact economic analysis method.
• 5. Payback period is used because the concept
  can be readily understood, the calculations can
  be readily made and understood by people
  unfamiliar with the use of the time value of
  money.
• 6. PBP analysis is better than nothing. Use
  it as a last resort to communicate.

10
Sensitivity and Breakeven Analysis

• Motivating Situation
• garbage model
  garbage
• All engineering economic analysis is based on
  models. If the data the models use is
  inaccurate, the results will not be useful.
• The data often represents projections of future
  consequences, and there may be considerable
  uncertainty about the accuracy of the data.
• An important question is
• To what extent do variations in the data affect
  the decision based on the model.
• Some data may have little or no effect on the
  decision. Other data may have a big effect on
  the decision. A decision is said to be sensitive
  to the estimate when small variations in a
  particular estimate would change the selection of
  the alternative.

11
Sensitivity and Breakeven Analysis

• Hypothetical Example.
• We must make a choice of a replacement machine.
  We must estimate  
• 1) the annual maintenance cost and  
• 2) the salvage value.  
• Perhaps we find that
• our decision is sensitive to changes in the
  annual maintenance estimate
• 2) the decision is insensitive to the
  salvage-value estimate over the full range of its
  possible values.
• This tells us we need to do a very good job with
  1), but having an accurate estimate for 2) is not
  too important.
• The following are examples where sensitivity
  analysis can help.
• Should we install a cable with 400 circuits now,
  or a 200-circuit cable now and another
  200-circuit cable later?
• A 10-cm water main is needed to serve a new area.
  Should the 10-cm main be installed now, or
  should a 15-cm main be installed in order to
  provide an adequate water supply to adjoining
  areas to be developed later?
• A firm needs a 10,000-m2 warehouse now. It
  estimates it will need an extra 10,000-m2 one in
  four years. It could build a 10,000-m2 warehouse
  now and enlarge it later, or it could build a
  20,000-m2 warehouse now.

12
Sensitivity and Breakeven Analysis Example 9-9

• Stage Construction with n as a sensitivity
  parameter.
• We can build a project to full capacity now, or
  construct it in two stages.
• Full-capacity construction in one stage costs
  140,000.
• The first stage construction costs 100,000.
• The second stage construction, n years later,
  costs 120,000.
• Other information
• Either facility will last until 40 years from
  now, regardless of when it is installed,
• and will have zero salvage value then.
• The annual cost of operation and maintenance is
  the same for either alternative.
• The interest rate is 8 a year.
• Our choice between I and II may depend on the
  value of n.
• We shall do a sensitivity analysis for all values
  of n of interest.
• I. Construct full capacity now PWI 140,000
•  
• II. Build in two stages PWII(n)
  100,000120,000(P/F,8,n)100,000120,000/(1i)n
  100000120000/(1.08)n.

13
Sensitivity and Breakeven Analysis Example 9-9

• We see the breakeven point between I and II is
  about 15 years.
• If n lt 15 years, I is cheaper (one-stage).
• If n gt 15 years, II is cheaper (two-stage
  construction).
• The decision on how to construct the project is
  sensitive to the age at which the second stage is
  needed only if the range of estimates includes 15
  years. In this case we need a really accurate
  estimate of n to make a good decision.

14
Sensitivity and Breakeven Analysis Example 9-10

• Example We have 3 mutually exclusive
  alternatives, each with a 20-year life, and no
  salvage value. MARR 6.
• Initial Cost Ann.Benefit
• Alt. A 2,000 410
• Alt. B 4,000 639
• Alt. C 5,000 700
• Based on this data, we found Alt. B was
  preferred.
• Question How sensitive is our choice to the
  estimate of the initial cost of B?
• Alternative A NPWA PW of benefit PW of cost
  410 (P/A,6,20) - 2000 410 (11.470) 2000
  2703
• Alternative B Let x initial cost of B (maybe
  4000), NPWB 639 (P/A,6,20) x 7329 x
• Alternative C NPWC 700 (P/A,6,20) 5000
  3029
• We have NPWB ? NPWA, NPWC ? 7329 x ?
  2703,3029 ?
• ? 7329 x ? 3029 ? 7329 3029 ? x ?
  4300 ? x
• For B to have the largest NPW means that the
  initial cost of B can be at most 4300.

15
Sensitivity and Breakeven Analysis Example 9-10
NPV
NPVC 3029
NPVA 2703
NPVB 7329 - x
X Initial cost of B
4300 breakeven
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Summary

• Future Worth.
• A future worth calculation occurs when the point
  in time at which the comparison between
  alternatives will be made is in the future. The
  best alternative according to future worth should
  also be best according to present worth.
• Benefit-Cost Ratio Analysis.
• We compute a ratio of benefits to costs, using
  either PW or ACF calculations. Graphically, the
  method is similar to PW analysis. Sometimes,
  with neither input nor output fixed, we use
  incremental benefit-cost analysis (?B/?C).
  Benefit-cost ratio analysis is often used in
  government.
• Payback Period.
• The payback period is the period of time needed
  for the profit or other benefits of an investment
  to equal its cost. This method is simple to use
  and understand, but is a poor analysis technique
  for ranking alternatives. It provides a measure
  of the speed of return of the investment, but is
  not an accurate measure of its profitability.
• Sensitivity and Breakeven Analysis.
• We use these techniques to determine how
  sensitive a decision is to estimates of various
  parameters. Breakeven analysis determines
  conditions for which alternatives are equivalent.
  Usually we can visualize the analysis with
  breakeven charts. Sensitivity analysis is an
  examination of a range of values for some
  parameter, to determine their effect on a
  particular decision.