ROR Analysis of multiple alternativesROR Analysis of multiple alternatives

Chapter 8

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ROR Incremental Analysis• The complete procedure by hand or computer for an

incremental ROR analysis for two alternatives is as follows:

• 1. Order the alternatives by initial investment or cost, starting with the smaller one, called A. The one with the larger initial investment is in the column labeled B.

• 2. Develop the cash flow and incremental cash flow series using the LCM of years, assuming reinvestment in alternatives.

• 3. Draw an incremental cash flow diagram , if needed.

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ROR Incremental Analysis• 4. Count the number of sign changes in the

incremental cash flow series to determine if multiple rates of return may be present. If necessary, use Norstrom's criterion on the cumulative incremental cash flow series to determine if a single positive root exists.

• 5. Set up the PW equation for the incremental cash flows, and determine Δi*B-A using trial and error by hand or spreadsheet functions.

• 6. Select the economically better alternative as follows:

• If Δi*B-A < MARR, select alternative A.• If Δi*B-A >= MARR, the extra investment is justified;

select alternative B.3

ROR Incremental Analysis (EX 8.3)

• 1. Alternatives A and B are correctly ordered with the higher first-cost alternative in coJumn (2).

• 2. The cash flows for the LCM of 10 years are tabulated in TabJe 8-4.• 3. The incremental cash flow diagram is shown in Figure 8-l.• 4. There are three 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, which starts negatively at So = $- 5000 and continues to SI0 = $+5000, indicating that more than one positive root may exist.

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ROR Incremental Analysis (EX 8.3)

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ROR Incremental Analysis (EX 8.3)

• Assume that the reinvestment rate is equal to the resulting Δi*B-A (or Δi* for a shortened symbol). Solution of Equation [8.2] for the first root Discovered results in Δi*: between 12 and 15%. By interpolation Δi* = 12.65%.

• 6. 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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Breakeven Example (Ex 8.4)

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Ex 8.4

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Ex 8.4

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Ex 8.4 (plot)

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Ex 8.4 (plot)

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Example 8.7