Least Common Multiple of Lives Approach

Least Common Multiple of Lives definition

When we have two mutually exclusive projects, it means that the company can only choose one of the two projects. In case both projects have different lives, it is not possible to compare them directly. Instead, we have to make an adjustment first. The least common multiple approach is one such adjustment.

In particular, what we will do is we create a so-called replacement chain. That’s why the approach is also sometimes called the replacement chain method. This means that we repeat the investment of the project with the shortest lifespan a number of times until it matches the lifespan of the project with the longer lifespan.

Least Common Multiple of Lives approach example

Let’s consider an example to make things more clear. Let’s assume we have two projects. The first project has a useful life of 6 years, the second project only has a useful life of only 3 years. Thus, we are dealing with projects with unequal lives.

The solution to the problem is to extend the project with a lifespan of only three years. In particular, after three years we repeat the investment under the second project a second time. That way, both projects have a useful life of 6 years and we can compare the NPVs. The following table implements an example. 

The Excel spreadsheet used to create the example can be downloaded below.