Module 2 : Comparison of alternatives

Lecture 1 : Comparison of alternatives

The two approaches used for economic comparison of different life span alternatives are as follows;

  1. Comparison of mutually exclusive alternatives over a time period that is equal to least common multiple (LCM) of the individual life spans
  2. Comparison of mutually exclusive alternatives over a study period which is not necessarily equal to the life span of any of the alternatives.

In the first approach the comparison is made over a time period equal to the least common multiple of the life spans of mutually exclusive alternatives. The cash flow of the alternatives i.e. cash flow of the first cycle is repeated and the number of repetitions depends upon the value of least common multiple of life spans between the mutually exclusive alternatives. It may be noted here that the cash flow i.e. all the costs and revenues of the alternatives in the successive cycle will be exactly same as that in the first cycle. For example if there are two alternatives with useful lives of 4 years and 5 years. Then the alternatives will compared over a period of 20 years (least common multiple of life spans) at the given rate of interest per year. Thus the cash flow of the alternative having the life span of 4 years will be repeated 5 times including the first cycle whereas the cash flow of the alternative with life span of 5 years will be repeated 4 times including the first cycle. After that the most economical alternative will be selected. Taking another example, there are two alternatives with life spans of 5 years and 10 years. In this case the alternatives will be compared over a period of 10 years (LCM). Thus the alternative with life span of 5 years will be analyzed for 2 cycles whereas the alternative with 10 year life span will be analyzed for one cycle only at the given rate of interest per year.
In the second approach, a study period is selected over which the economic comparison of mutually exclusive alternatives is carried out. The length of the study period will depend on the overall benefit of the project i.e. it may be shorter or longer (as compared to useful lives of the individual alternatives) depending upon the short-term or long-term benefits as desired for the project. Thus the cash flows of the alternatives occurring during the study period are only considered for the economic comparison. However if any alternative possesses salvage value at the end of its useful life and that occurs after the study period, then its equivalent value must be included in the economic analysis. The values of equivalent present worth of the mutually exclusive alternatives are calculated over the selected study period and the alternative showing maximum positive equivalent present worth or minimum negative equivalent present worth is selected.