You may select one of two mutually exclusive alternatives. Doing nothing is allowed. (Note: Engineering economists often use the term “mutually exclusive alternatives” to emphasize that selecting one alternative precludes selecting any other.) The alternatives are as follows: Any money not invested

Question

You may select one of two mutually exclusive alternatives. Doing nothing is allowed. (Note: Engineering economists often use the term “mutually exclusive alternatives” to emphasize that selecting one alternative precludes selecting any other.) The alternatives are as follows:

Alt. 2	Alt. 1	Year
− $2000	− $1000	0
+ 2800	+ 1500	1

Any money not invested here may be invested elsewhere at the MARR of 6%. If you can choose at most one alternative one time, using the internal rate of return (IRR) analysis method, which one would you select?

Accepted Answer

For Alternative 1, if $1000 increases to $1500 in a year, then the rate of return must be 50% (= 500/1000). For Alternative 2, if $2000 increases to $2800 in a year, then the rate of return must be 40% (= 800/2000). Both rates are very attractive, so both alternatives are clearly better than doing nothing and investing elsewhere at 6%. To decide which is better—incremental analysis is needed.

Alt. 2	Alt. 1	Year
− $2000	− $1000	0
+ 2800	+ 1500	1

One can see that if $1000 increases to $1300 in one year, the interest rate must be 30%, which is far higher than the 6% MARR. The additional $1000 investment to obtain Alt. 2 is superior to investing the $1000 elsewhere at 6%. The interest rate can also be easily calculated using a future worth equation.

[latex]FW=0=-1000(1+i)+1300[/latex]

[latex]1+i=1300/1000[/latex]

[latex]i=30\%[/latex]

To understand an intuitively appealing—but incorrect—approach to Example 7–11, consider the rate of return for each alternative. The interest rates for Alternatives 1 and 2 were 50% and 40%. The higher rate of return of Alt. 1 is attractive, but Alt. 1 is not the correct solution. This analysis only compares each alternative with doing nothing rather than with the other alternative.

Figure 7–5 shows why comparing the alternatives with nothing is not enough. Those rates of 50% and 40% are very attractive, but it is not correct to choose the alternative with the highest rate. It is also not correct to choose the largest project with a good rate of return. The alternatives must be directly compared with incremental analysis.

On the graph we can see that Alternative 1 has a rate of return of 50%, Alternative 2 has a rate of 40%, and the increment Alternative 2-1 has a rate of 30%. All of these rates are high compared with a MARR of 6%. The incremental rate determines that Alternative 2 is better.

These results are consistent with a present worth analysis. At 6% Alternative 2 clearly has a higher PW. The exact values are $415 for Alternative 1 and $642 for Alternative 2.

Question 7.11: You may select one of two mutually exclusive alternatives. D...

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