1.7 Evaluation of projects of unequal lives; The equivalent annual annuity approach and the Replacement chain analysis (Constant scale finite period replication criteria)

When evaluating projects of unequal lives, it can be challenging to directly compare their profitability and determine which one is the most favorable investment. Here are two commonly used methods to evaluate projects of unequal lives:

1. Equivalent Annual Cost (EAC) method: The EAC method aims to make the projects comparable by converting their costs and benefits into equivalent annual amounts. The steps involved in the EAC method are as follows: a. Calculate the net present value (NPV) for each project separately. b. Determine the annuity factor for each project’s life using the discount rate. c. Divide the NPV of each project by its respective annuity factor to obtain the equivalent annual cost. d. Compare the equivalent annual costs of the projects. The project with the lower equivalent annual cost is considered more favorable.
2. Modified Internal Rate of Return (MIRR) method: The MIRR method adjusts the cash flows of the projects to a common project life before comparing their profitability. The steps involved in the MIRR method are as follows: a. Extend the cash flows of the project with the shorter life to match the life of the project with the longer duration. This can be done by assuming the cash flows continue at the same rate as the last period or by using other assumptions. b. Calculate the internal rate of return (IRR) for each extended cash flow stream. c. Compare the IRRs of the projects. The project with the higher MIRR is considered more favorable.