Tuesday, June 22, 2010


Projects with Different Lives

The correct way of choosing between mutually exclusive projects with the same lives is to compare their net present values (NPVs), and choose the project with a higher net present value (NPV). The two mutually exclusive projects being compared, however, may have different lives. The use of the net present value (NPV) rule without accounting for the difference in the projects’ lives may fail to indicate correct choice. In analyzing such projects, we should answer the question: what would the firm do after the expiry of the short-lived project if it were acquired instead of the long-lived project?

Annual equivalent value method

Assume we are going to choose one machine from two alternative machines called X and Y. In a choice between machines with different lives, we assume that each machine replaced in the last year of its life. For the purpose of analysis, the replacement chains of the machines can be assumed to extend to the periods of time equal to the least common multiple of the lives of the machines.

The method for handling the choice of the mutually exclusive projects with different lives, as discussed above, can become quite cumbersome if the projects’ lives are very long. The problem fortunately can be handled by a simper method. We can calculate the annual equivalent value (AEV) of cash flows of each project. We shall select the project that has lower annual equivalent cost.

AEV = NPV / Annuity factor

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