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134 CHAPTER 5 Comparison Methods Part 2

From the interest factor tables, or by trial and error with a spreadsheet, (P/4,14%,8) = 4.6388 (P/A,IS%,8) = 4.4873

By interpolation or further trial and error, i*= 14.5%

The slicer alone is thus economically justified and is better than the "do nothing" alternative.

We now consider the system with the slicer and loader. Its IRR is 12.5%, which may be seen by solving for /* in

(P/4,12%,8) = 4.9676 (P/4,13%,8) = 4.7987 /*= 12.5%

The IRR of the meat slicer and automatic loader is about 12.5%, which on the surface appears to meet the 12% .AIARR requirement. But, on the incremental investment, Alonster Aleats would be earning only 7%. This may be seen by looking at the IRR on the extra, or incremental, € 1 8 000 spent on the loader.

-(68 000 - 50 000) + (14 000 - 11 000)(P/A,i*,8) = 0

This is less than the ALARR; therefore, Alonster Aleats should not buy the automated loader.

When the IRR was calculated for the system including the loader, the surplus return on investment earned by the slicer alone essentially subsidized the loader. The slicer investment made enough of a return so that, even when it was coupled with the money-losing loader, the whole machine still seemed to be a good buy. In fact, the extra €18 000 would be better spent on some other project at the MARR or higher. The relation between the potential projects is shown in Figure SAM

Figure 5.4 Monster Meats

 1 Loader HRR as 7% >r IRR = 12.5% Slicer H R R = 14.5% and Slicer ->

The fundamental principle illustrated by the two examples is that, to use the IRR to compare two or more mutually exclusive alternatives properly, we cannot make the decision on the basis of the IRRs of individual alternatives alone; we must take the IRRs of the incremental investments into consideration. In order to properly assess the worthiness of the incremental investments, it is necessary to have a systematic way to conduct pair-wise comparisons of projects. Note that before undertaking a systematic analysis of mutually exclusive alternatives with the IRR method, you should ensure that the alternatives have equal lives. If they do not have equal lives, then the methods of Section 4.4.4 (study period or repeated lives methods) must be applied first to set up comparable cash flows.

The first step in the process of comparing several mutually exclusive alternatives using the IRR is to order the alternatives from the smallest first cost to the largest first cost. Since one alternative must be chosen, accept the alternative with the smallest first cost (which may be the "do nothing" alternative with SO first cost) as the current best alternative regardless of its IRR exceeding the ALARR. This means that the current best alternative may have an IRR less than the ALARR. Even if that's the case, a proper analysis of the IRRs of the incremental investments will lead us to the coirect best overall alternative. For this reason, we don't have to check the IRR of any of the individual alternatives.

The second step of the analysis consists of looking at the incremental investments of alternatives that have a higher first cost than the current best alternative. Assume that there are ;/ projects and they are ranked from 1 (the current best) to n, in increasing order of first costs. The current best is "challenged" by the project ranked second. One of two things occurs:

1. The incremental investment to implement the challenger does not have an IRR at least equal to the ALARR. In this case, the challenger is excluded from further consideration and the current best is challenged by the project ranked third.

2. The incremental investment to implement the challenger has an IRR at least as high as the ALARR. In this case, the challenger replaces the current best. It then is challenged by the alternative ranked third.

The process then continues with the next alternative challenging the current best until all alternatives have been compared. The current best alternative remaining at the end of the process is then selected as the best overall alternative. Figure 5.5 summarizes the incremental investment analysis for the mutually exclusive projects.

EXAMPLE 5.6 (REPRISE OF EXAMPLE 4.4)

Fly-by-Xight .Aircraft must purchase a new lathe. It is considering one of four new lathes, each of which has a life of 10 years with no scrap value. Given a AIARR of 15%, which alternative should be chosen?

 Lathe 1 2 3 4 First cost \$100 000 SI50 000 S200 000 S255 000 Annual savings 25 000 34 000 46 000 55 000

The alternatives have already been ordered from lathe 1, which has the smallest first cost, to lathe 4, which has the greatest first cost. Since one lathe must be purchased, accept lathe 1 as the current best alternative. Calculating the IRR for lathe 1, although not necessary, is shown as follows:

An approximate IRR is obtained by trial and error with a spreadsheet, i* =21.4%

The current best alternative is then challenged by the first challenger, lathe 2, which has the next-highest first cost. The IRR of the incremental investment from lathe 1 to lathe 2 is calculated as follows:

(150 000 - 100 000) - (34 000 - 25 QQQ)(P/A,i*,D) = 0

[150 000 - 34 000(PA4,/*,10)] - [100 000 - 25 000(PA4,/*,10)] = 0

(P/A,i*,lO) = 50 000/9000 = 5.556 An approximate IRR is obtained by trial and error.

Since the IRR of the incremental investment falls below the ALARR, lathe 2 fails the challenge to become the current best alternative. The reader can verify that lathe 2 alone has an IRR of approximately 18.7%. Even so, lathe 2 is not considered a viable alternative. In other words, the incremental investment of \$50 000 could be put to better use elsewhere. Lathe 1 remains the current best and the next challenger is lathe 3.

As before, the incremental IRR is the interest rate at which the present worth of lathe 3 less the present worth of lathe 1 is 0:

[200 000 - 46 QQQ(P/A,i ,10)] - [100 000 - 25 000(PA4,/*,10)] = 0

(P/A,i*,10) = 100 000/21 000 = 4.762 An approximate IRR is obtained by trial and error.

The IRR on the incremental investment exceeds the ALARR, and therefore lathe 3 is preferred to lathe 1. Lathe 3 now becomes the current best. The new challenger is lathe 4. The IRR on the incremental investment is

[255 000 - 55 000(PA4,/*,10)] - [200 000 - 46 000(P/4,/*,10)] = 0

The additional investment from lathe 3 to lathe 4 is not justified. The reader can verify that the IRR of lathe 4 alone is about 17%. Once again, we have a challenger with an IRR greater than the ALARR, but it fails as a challenger because the incremental investment from the current best does not have an IRR at least equal to the ALARR. The current best remains lathe 3. There are no more challengers, and so the best overall alternative is lathe 3 .•

In the next section, the issue of multiple IRRs is discussed, and methods for identifying and eliminating them are given. Note that the process described in Figure 5.5 requires that

Figure 5.5 Flowchart for Comparing Mutually Exclusive Alternatives

Rank mutually exclusive projects from 1 to n, in increasing order of first cost.

Current best = Smallest first cost

Challenge =