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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: 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.
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?
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: 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: 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 20- year life and no salvage value, and a MARR of 6%. 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?