Mastering Capital Investment Decisions: Equivalent Annual Cost Analysis

Introduction to Capital Investment Decisions with Varying Economic Lives

When it comes to capital investment decisions, the process can become complex when dealing with projects that have different economic lives. The Net Present Value (NPV) method has been a staple for evaluating the profitability of a project, but it may not always provide an accurate comparison when projects differ in duration.

Why NPV Alone May Be Misleading

While NPV is a useful tool, it operates under the assumption that all projects under consideration have the same economic life. This isn't always the case in the real world, where the length of projects can vary significantly. Relying solely on NPV could lead to a misleading decision-making process.

The Alternative: Equivalent Annual Cost (EAC) Method

To address this issue, the Equivalent Annual Cost (EAC) method is employed. This technique allows for a fair comparison by converting NPV into an annualized figure. Here's how it works:

1. Calculate the NPV or the present value (PV) of the project's cash flows.
2. Divide the NPV by the annuity factor to determine the EAC or equivalent annual annuity.

Example Illustration:

Consider two machines, A and B, with different cash flows and economic lives. Machine A has a three-year life, while Machine B's life extends to five years.

• Machine A has a cash flow of 15 units at year 0.
• Machine B has cash flows of 10 units at year 0, followed by 6 units in years 1 and 2.

Using a discount rate of 6%, we calculate the PVs and then divide each by their respective annuity factors to find the EAC:

• Machine A: PV is 28.37, which divided by the annuity factor for three years at 6% results in an EAC of 10.61.
• Machine B: PV is 20, which divided by the annuity factor for five years at 6% results in an EAC of 11.45.

Decision Making Based on EAC

In this scenario, Machine A is the preferred option since it has a lower EAC. This decision contrasts with a decision made by looking at PV alone, where Machine B would seem more attractive due to its lower PV.

Case Study: Project Analysis

Let's compare two projects, A and B, with different cash flows and required rates of return:

• Project A: Initial investment of 15 units with subsequent cash flows.
• Project B: Initial investment of 20 units with different cash flows.

At a required rate of return of 9%, Project A has a higher NPV. However, when we calculate the equivalent annual annuity, we find that Project B, with an annual annuity of 1.10, is more favorable than Project A's 0.87.

The Bottom Line

When faced with projects of varying economic lives, comparing NPVs to choose the one with the highest value is insufficient. Instead, calculating the EAC or equivalent annual cash flow provides a more accurate assessment, enabling better decision-making.

Key Takeaways:

• The EAC method equates projects with different lifespans for a fair comparison.
• Decisions based on EAC can differ from those based on NPV alone.
• Utilizing EAC helps in selecting the most cost-effective project over its economic life.

If you have any questions or need further clarification, please feel free to reach out via group discussion forums or email.

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