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ISE 211
Engineering Economy
Other Analysis
Techniques
Chapter 9
Choosing an Analysis Method
 At this point, we have examined in detail the three major economic analysis
techniques: PWA, ACFA, and RORA.
 A practical question is, “which method should be used?”
 Unless MARR is given, neither PWA nor ACFA can be done
 PWA and ACFA often requires far less computations than RORA
 In some situations, RORA is easier to explain to people unfamiliar with
economic analysis. At other times, ACFA may be easier to explain
 Business enterprises generally adopt one, or at most two analysis
techniques for broad categories of problems.
Other Techniques
 In this chapter, the following four techniques will be
considered:
 Future Worth Analysis
 Benefit-Cost Ratio Analysis
 Payback Period
 Sensitivity and Breakeven Analysis
Other Techniques (cont’d)
 Future worth analysis is very much like present worth analysis, dealing with
then (future worth) rather than with now (present worth) situations.
 Benefit-Cost Ratio Analysis is a type of analysis that is based on one of the
following ratios: PW(B) / PW( C) = 1.0 or EUAB/EUAC = 1.0
 Payback period is an approximate analysis technique, generally defined as the
time required for cumulative benefits to equal cumulative costs.
 Sensitivity describes the relative magnitude of a particular variation in one or
more elements of a problem that is sufficient to change a particular decision.
 Breakeven analysis determines the conditions where two alternatives are
equivalent (a form of sensitivity analysis)
Future Worth Analysis: Example 1
An engineer is considering the purchase of a copy
machine for her consulting company office. The copy
machine will cost $2000 and have a resale value of $400
at the end of its 5-year life. Having the machine in the
office will reduce the copy costs by $1000 a year. Copy
machine maintenance will be $500 for the first year and
will increase by $100 each year. If the interest rate is 6%,
should the machine be purchased?
Example 2
Consider four mutually exclusive alternatives:
Initial Cost
Uniform annual benefit
A
$750
188
B
$500
139
C
$150
45
D
$900
238
Each alternative has a five year useful life and no
salvage value. The MARR is 10%. Which alternative
should be selected, based on FWA?
Benefit-Cost Ratio Analysis
 At a given MARR, we could consider an alternative acceptable provided that:
PW(B) – PW(C )  0, or EUAB – EUAC  0.
 These could also be stated as a ratio of benefits to costs as follows:
 Benefit-Cost Ratio, B/C = PW(B)/PW(C ) or

B/C = EUAB/EUAC
 Where a ratio greater than 1.0 indicates an acceptable project.
 When multiple mutually exclusive alternatives are considered, the analysis is
performed using an Incremental Approach.
 Important: Salvage value is considered to be reduction in cost, rather than
increases in benefits.
Benefit-Cost Ratio Analysis
Example 1
A transportation agency is considering a highway project
that will cost $1,500,000. The annual benefits are
expected to be $99,000 per year over a twenty year
analysis period. Reusable material will be valued at
$300,000 at the end of the useful life. If the discount rate
(i.e., government borrowing rate) is 8% per annum,
determine whether or not the project should be
undertaken using:
a) PWA
b) B/C Analysis
Example 2
Two machines are being considered for purchase.
Assuming 10% interest, which machine should be bought?
Initial Cost
Uniform annual benefit
End of useful life salvage value
Useful life (years)
X
$200
95
50
6
Y
$700
120
150
12
B/C Analysis for Multiple Alternatives
1) Be sure all the alternatives are identified
2) (Optional) Compute the B/C ratio for each alternative – discard alternatives
with B/C < 1.0.
3) Arrange the remaining alternatives in ascending order of investment.
4) Make a two-alternative B/C analysis for the first two alternatives.
5) Take the preferred alternative from step 4, and the next alternative from the
list created in step 4 --- proceed with another two-alternative analysis.
6) Continue until all alternatives have been examined and the best of the
multiple alternatives has been identified.
Example 1
Consider four mutually exclusive alternatives:
Cost
Uniform annual benefit
A
$750
188
B
$500
139
C
$150
45
D
$900
238
Each alternative has a five-year useful life and no
salvage value. The MARR is 10%. Which
alternative should be selected, based on B/C ratio
analysis?
Payback Period
 Payback period is the period of time required for the profit or other benefits
from an investment to equal the investment.
 Example: This investment will pay for itself in 12 months.
 It should be emphasized that this method is an approximate economic
analysis measure – because the timing of receipts and payments is not
considered, and all consequences beyond the payback period are completely
ignored.
 Nevertheless, due to the fact that the method is so easy to understand and
execute, this method is used more than any other comparison method.
 Being an approximate calculation, payback period may or may not select the
correct alternative!!
Example 1
A piece of new equipment has been proposed by the ISE
Department to increase the productivity of a certain manual
welding operation. The initial investment is $25,000, and the
equipment will have a salvage value of $5,000 at the end of its
expected life of 5 years. Increased productivity
attributable to the equipment will amount to $8,000 per year after
extra operating costs have been subtracted from the value of the
additional production. In view of a minimum acceptable
payback period of 5 years, is this alternative attractive?
Example 2
Consider four mutually exclusive alternatives:
Cost
Uniform annual benefit
A
$750
188
B
$500
139
C
$150
45
D
$900
238
Each alternative has a five-year useful life and no
salvage. The MARR is 10%. What are the payback
periods of the various investments? Which alternative
should be selected?
Sensitivity and Breakeven Analysis
Sensitivity analysis considers the extent to which critical parameters can
deviate from an original estimates before a preference is reversed, either from
acceptance to rejection or between competing to rejection.
As a result, the decision maker gets a better feel for the situation, i.e., how
sensitive it is to estimate for the various parameters.
Breakeven analysis is a special form of sensitivity analysis which is performed
to locate conditions where the alternatives are equivalent.
Sensitivity analysis can be performed with NPW, NFW, ECFA, or RORA.
Example 1
A business investor plans to invest $2,000 on a molding
machine that makes Vulcan-like ears. The machine’s
manufacturer, assured the investor that he would make a
profit of about $400 (A) a year at Star Trek conventions
for the next ten (n) years or so. The investor projects that
the interest rate (i) will be 10%. Suppose that A, i, and n
can vary between +50% and –50% of their anticipated
values. Use Present Worth analysis to reach conclusions
about the desirability of pursuing this investment.
Example 3
Consider the following three mutually exclusive alternatives, each with a 20year life and no salvage value, and a MARR of 6%.
Initial Cost
Uniform annual benefit (in year k)
A
$2,000
410
B
$4,000
639
C
$5,000
700
In the previous chapter, we found that alternative B is the preferred
alternative. Here we would like to know how sensitive the
decision is to our estimate of the initial cost of B. If B is preferred
at an initial cost of $4,000, it will continue to be preferred at any
smaller initial cost. But how much higher than $4,000 can the
initial cost be and still have B the preferred alternative?
Homework # 09 (Chapter # 9)
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