Equivalent Annual Annuity (EAA): Comparing Projects with Unequal Lifespans

When evaluating mutually exclusive projects with different lifespans, a simple Net Present Value (NPV) comparison can be misleading. Projects lasting longer might appear more attractive simply because they generate cash flows over a longer period. The Equivalent Annual Annuity (EAA) method provides a solution by converting the NPV of each project into an equivalent annual cash flow, allowing for a fair comparison regardless of the projects’ durations.

What is EAA?

The Equivalent Annual Annuity (EAA) is the constant annual cash flow that a project would need to generate to have the same present value as the project’s actual, potentially uneven, cash flows. It effectively represents the average annual return a project is expected to provide, considering the time value of money.

How to Calculate EAA:

The EAA is calculated using the following steps:

1. Calculate the Net Present Value (NPV) for each project. This involves discounting all future cash flows back to their present value using the appropriate discount rate (cost of capital). The formula for NPV is:
   NPV = Σ [Cash Flow_t / (1 + r)^t] – Initial Investment
   where:
   • Cash Flow_t is the cash flow in year t
   • r is the discount rate
   • t is the year
2. Calculate the EAA using the following formula:
   EAA = NPV / [1 – (1 + r)^-n] / r
   where:
   • NPV is the Net Present Value calculated in step 1
   • r is the discount rate
   • n is the lifespan of the project in years

   The term “[1 – (1 + r)^-n] / r” is the Present Value Annuity Factor (PVAF). You can either calculate it directly or use a PVAF table.

Decision Rule:

When comparing projects using EAA, the project with the higher EAA is generally considered the more desirable investment. This is because it provides a higher equivalent annual return, considering the time value of money and the project’s lifespan.

Advantages of Using EAA:

• Fair Comparison of Projects with Unequal Lifespans: This is the primary benefit. EAA allows for a direct comparison of projects, regardless of how long they last.
• Intuitive Interpretation: EAA provides an easily understandable “average annual return” figure.
• Accounts for the Time Value of Money: Like NPV, EAA incorporates the discount rate, reflecting the opportunity cost of capital.

Limitations of Using EAA:

• Assumes Project Replication: EAA implicitly assumes that the projects can be replicated indefinitely. This might not be realistic in all situations (e.g., a one-time opportunity).
• Sensitivity to Discount Rate: The EAA result is heavily influenced by the discount rate used. An inaccurate discount rate can lead to a flawed decision.
• Does Not Consider Real Options: EAA does not account for flexibility or real options that might be embedded in a project (e.g., the option to abandon, expand, or defer).

Conclusion:

The EAA method is a valuable tool for comparing mutually exclusive projects with unequal lifespans. It allows for a more accurate and fair evaluation than a simple NPV comparison. However, it’s crucial to understand the underlying assumptions and limitations of the method and to consider other relevant factors before making an investment decision.