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Rate of Return Analysis: Multiple Alternatives

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Rate of Return Analysis: Multiple Alternatives

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    1. Rate of Return Analysis: Multiple Alternatives Chapter 8

    2. 2 Learning Objectives

    3. 3 WHY INCREMENTAL ANALYSIS IS NECESSARY This chapter presents methods where 2 or more alternatives can be evaluated using a rate of return (ROR) comparison based on methods of the previous chapter. The ROR evaluation correctly performed will result in the same selection as the PW, AW and FW analyses, but the computational procedure is considerably different for ROR evaluations.

    4. 4 Assume that a company uses a MARR of 16% per year, has $90,000 available for investment, and that two alternatives (A and B) are being evaluated. Alternative A requires an investment of $50,000 and has an internal rate of return iA* of 35% per year. Alternative B requires $85,000 and has an iB* of 29% per year. Intuitively we may conclude that the better alternative is the one that has the larger return, A in this case. However, this is not necessarily so. While A has the higher projected return, it requires an initial investment that is much less than the total money available ($90,000). What happens to the investment capital that is left over? It is generally assumed that excess funds will be invested at the company’s MARR. Using this assumption, it is possible to determine the consequences of the alternative investments. If alternative A is selected, $50,000 will return 35% per year. The remaining $40,000 will be invested at the MARR of 16% per year. The rate of return on the total capital available, then, will be the weighted average.

    5. 5 A tool and die company in Pittsburgh is considering the purchase of a drill press with fuzzy-logic software to improve accuracy and reduce tool wear. The company has the opportunity to buy a slightly used machine for $15,000 or a new one for $21,000. Because the new machine is a more sophisticated model, its operating cost is expected to be $7000 per year, while the used machine is expected to require $8200 per year. Each machine is expected to have a 25-year life with a 5% salvage value. Tabulate the incremental cash flow.

    6. 6 Solution Incremental cash flow is tabulated in Table 8–2. Using Equation [8.1], the subtraction performed is (new - used) since the new machine has a larger initial cost. The salvage values in year 25 are separated from ordinary cash flow for clarity. When disbursements are the same for a number of consecutive years, it saves time to make a single cash flow listing, as is done for years 1 to 25. This approach cannot be used for spreadsheets (Excel).

    7. 7 Sandersen Meat Processors has asked its lead process engineer to evaluate two different types of conveyors for the bacon curing line. Type A has an initial cost of $70,000 and a life of 8 years. Type B has an initial cost of $95,000 and a life expectancy of 12 years. The annual operating cost (AOC) for type A is expected to be $9000, while the AOC for type B is expected to be $7000. If the salvage values are $5000 and $10,000 for type A and type B, respectively, tabulate the incremental cash flow using their LCM.

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    9. 9 INTERPRETATION OF RATE OF RETURN ON THE EXTRA INVESTMENT The incremental cash flows in year 0 of Tables 8–2 and 8–3 reflect the extra investment or cost required if the alternative with the larger first cost is selected. This is important in an incremental ROR analysis to determine the ROR earned on the extra funds expended for the larger-investment alternative. If the incremental cash flows of the larger investment don’t justify it, we must select the cheaper one. In Example 8.1 the new drill press requires an extra investment of $6000 (Table 8–2). If the new machine is purchased, there will be a “savings” of $1200 per year for 25 years, plus an extra $300 in year 25. The decision to buy the used or new machine can be made on the basis of the profitability of investing the extra $6000 in the new machine. If the equivalent worth of the savings is greater than the equivalent worth of the extra investment at the MARR, the extra investment should be made (i.e., the larger first-cost proposal should be accepted). On the other hand, if the extra investment is not justified by the savings, select the lower-investment proposal. It is important to recognize that the rationale for making the selection decision is the same as if only one alternative were under consideration, that alternative being the one represented by the incremental cash flow series. When viewed in this manner, it is obvious that unless this investment yields a rate of return equal to or greater than the MARR, the extra investment should not be made. As further clarification of this extra-investment rationale, consider the following: The rate of return attainable through the incremental cash flow is an alternative to investing at the MARR. Section 8.1 states that any excess funds not invested in the alternative are assumed to be invested at the MARR. The conclusion: If the rate of return available through the incremental cash flow equals or exceeds the MARR, the alternative associated with the extra investment should be selected.

    10. 10 In 2000, Bell Atlantic and GTE merged to form a giant telecommunications corporation named Verizon Communications. As expected, some equipment incompatibilities had to be rectified, especially for long distance and international wireless and video services. One item had two suppliers - a U.S. firm (A) and an Asian firm (B). Approximately 3000 units of this equipment were needed. Estimates for vendors A and B are given for each unit.

    11. 11 Determine which vendor should be selected if the MARR is 15% per year. These are service alternatives, since all cash flows are costs. Alternatives A and B are correctly ordered with the higher first-cost alternative in column (2). The cash flows for the LCM of 10 years are shown in Table 8–4. The incremental cash flow diagram is shown in Figure 8–1 (next page). There are 3 sign changes in the incremental cash flow series, indicating as many as three roots. There are also three sign changes in the cumulative incremental series that starts negatively at S0 = - $5000 and continues to S10 = +$5000, indicating that more than one positive root may exist. The rate of return equation based on the PW of incremental cash flows is 0 = - 5000 +1900(P/A, i,10) - 11,000(P/F, i, 5) + 2000 (P/F, i, 10) [8.2]

    12. 12 Assume that the reinvestment rate is equal to the resulting i*BA (or i* for a shortened symbol). Solution of Equation [8.2] for the first root finds results for i* between 12 and 15%. By interpolation i* = 12.65%. Since the rate of return of 12.65% on the extra investment is less than the 15% MARR, the lower-cost vendor A is selected. The extra investment of $5000 is not economically justified by the lower annual cost and higher salvage estimates.

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    14. 14 Bank of America uses a MARR of 30% on alternatives for its own business that are considered risky, that is, the response of the public to the service has not been well established by test marketing. Two alternative software systems and the marketing/delivery plans have been jointly developed by software engineers and the marketing department. They are for new online banking and loan services to passenger cruise ships and military vessels at sea internationally. For each system, start-up, annual net income, and salvage value (i.e., sell-out value to another financial corporation) estimates are summarized below. (a) Perform the incremental ROR analysis by computer. (b) Develop the PW vs. i graphs for each alternative and the increment. Which alternative, if either, should be selected.?

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    16. 16 Figure 8–4b (previous slide) provides the opportunity to see why the ROR method can result in selecting the wrong alternative when only i* values are used to select between two alternatives. This is sometimes called the ranking inconsistency problem of the ROR method. The inconsistency occurs when the MARR is set less than the breakeven rate between two revenue alternatives. Since the MARR is established based on conditions of the economy and market, MARR is established external to any particular alternative evaluation. In the previous graph, the breakeven rate is 29.41% and the MARR is 30%. If the MARR were established lower than breakeven, say at 26%, the incremental ROR analysis results in correctly selecting B, because i* = 29.41%, which exceeds 26%. When only the i* values were used, system A would be wrongly chosen, because its i* = 39.31%. This error occurs because the rate of return method assumes reinvestment at the alternative’s ROR value (39.31%), while PW and AW analyses use the MARR as the reinvestment rate. The conclusion: If the ROR method is used to evaluate two or more alternatives, use the incremental cash flows and i* to make the decision between alternatives.

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