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**Other Analysis Techniques**

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

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**Techniques for Cash Flow Analysis**

Chapter 5 Chapter 6 Chapter 7 Chapter 9 Present Worth Analysis Annual Cash Flow Analysis Rate of Return Analysis Other Techniques: Future Worth Analysis Benefit-Cost Ration Analysis Payback Period Analysis Sensitivity and Breakeven Analysis

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**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.

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**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 < 1. (We can discard F). 3) Arrange the remaining alternatives in ascending order of investment. A B C D E F Cost $4000 $2000 $6000 $1000 $9000 $10000 PWB $7330 $4700 $8730 $1340 $9500 B/C 1.83 2.35 1.46 1.34 1.00 0.95 NPV 3330 2700 1730 340 -500

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**Benefit/Cost Ratio Analysis**

D B A C E F Cost $1000 $2000 $4000 $6000 $9000 $10000 PWB $1340 $4700 $7330 $8730 $9500 B/C 1.34 2.35 1.83 1.46 1.00 0.95 NPV 340 2700 3330 1730 -500 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 < 1. Comparing A to E, again A is best. Finally A is the best project. B-D A-B C - A E-A Incremental Cost $1000 $2000 $5000 Incremental Benefit $3360 $2630 $1400 $1670 Incr.B/Incr. C 3.36 1.32 0.76 0.33

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**Benefit/Cost Ratio Analysis**

PWB F A, B, C, and D are above the 45-degree line; their B/C ratio is > 1. F is below the line: B/C ratio is < 1. We can discard F if we wish. E C A PWB/PWC = 1 Examine each separable increment of investment. B/C < 1 increment is not attractive B/C 1 increment is desirable. B D PWC Begin with D & B: B/C > 1. B “wins”. Next consider A: B/C > 1. A “wins”. C: B/C < 1; discard C. E: B/C < 1; discard E. F was discarded earlier Conclude A is best. Note: Alt. B has the highest B/C ratio B-D A-B C - A E-A Incremental Cost $1000 $2000 $5000 Incremental Benefit $3360 $2630 $1400 $1670 Incr.B/Incr. C 3.36 1.32 0.76 0.33

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**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. It’s “better than nothing.” Use it as a last resort to communicate.

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**Payback Period: Example**

Year Tempo machine Dura -$30,000 -$35,000 1 12,000 1,000 2 9,000 4,000 3 6,000 7,000 4 3,000 10,000 5 13,000 6 16,000 7 19,000 8 22,000 Totals 57,000 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.

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**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.

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**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.

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**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.

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**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, ,000(P/F,8%,n)=100, ,000/(1+i)n= /(1.08)n.

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**Sensitivity and Breakeven Analysis: Example 9-9**

We see the breakeven point between I and II is about 15 years. If n < 15 years, I is cheaper (one-stage). If n > 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.

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**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) = 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 – x 2703,3029 – x – 3029 x x For B to have the largest NPW means that the initial cost of B can be at most 4300. It can be ANY number less than 4300.

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**Sensitivity and Breakeven Analysis: Example 9-10**

NPV NPVC= 3029 NPVA= 2703 NPVB= x X: Initial cost of B 4300 = breakeven

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**Summary Future Worth. Benefit-Cost Ratio Analysis. Payback Period.**

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.

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