Why Projects Sometimes Have More Than One IRR?

Imagine you are planting a tree. You spend money initially to buy the sapling and prepare the ground; that’s an initial investment, a cash outflow. As the tree grows, it might provide shade, beauty, or even fruit over many years; those are cash inflows. For most projects, the cash flow pattern is similar: you invest money upfront, then you receive returns for a period. We use a metric called the Internal Rate of Return, or IRR, to understand the profitability of such projects. Think of IRR as the effective interest rate your project is earning. It’s the rate that, if you used it to discount all those future cash inflows back to today and compared them to your initial investment, the net result would be exactly zero. In simpler terms, it’s the break-even return rate for your project.

Typically, we expect to find a single, clear IRR for a project. If the IRR is high, it signals a potentially attractive investment. If it’s low, it might be less appealing. However, things can get a bit more complicated, and sometimes, a project’s cash flow stream can lead to the possibility of having more than one IRR, or even no IRR at all.

The reason for this unusual situation lies in the pattern of the project’s cash flows, specifically when we encounter what are called non-conventional cash flows. Conventional cash flows are straightforward: an initial outflow followed by a series of inflows. Think back to our tree example. Non-conventional cash flows, on the other hand, involve more complex patterns. They are characterized by cash flow signs changing more than once.

Let’s consider a slightly different project. Imagine a mining operation. Initially, you invest heavily in setting up the mine, an outflow. Then, for several years, you extract valuable minerals and generate income, inflows. But after many years, you might be legally obligated to restore the land, which requires another significant cash outflow. So, the cash flow stream could look like this: outflow, then inflows, and finally, another outflow. This pattern, with multiple changes in the direction of cash flow, is the key to understanding multiple IRRs.

To visualize this, imagine plotting the Net Present Value, or NPV, of a project at different discount rates. For conventional projects, as the discount rate increases, the NPV usually decreases in a smooth curve, crossing the zero NPV line only once. That single point where the NPV is zero is the unique IRR. However, with non-conventional cash flows, the NPV curve can become more wavy. It might cross the zero NPV line not just once, but multiple times. Each point where the NPV curve intersects the zero line represents a different IRR.

Think of it like a rollercoaster track. For a conventional project, the track goes downhill from left to right, crossing the ground level once. For a project with multiple IRRs, the track might go up and down several times, crossing the ground level at multiple points. These crossings represent different discount rates where the project’s NPV becomes zero, hence, multiple IRRs.

Why does this happen mathematically? The IRR is essentially solving a polynomial equation. The degree of the polynomial is related to the life of the project. When you have non-conventional cash flows, this polynomial equation can have multiple positive roots. Each positive root corresponds to a potential IRR.

The existence of multiple IRRs can make investment decisions confusing when relying solely on the IRR metric. Which IRR should you choose? In such scenarios, it becomes crucial to understand the underlying NPV profile and potentially rely more on the Net Present Value method for decision-making, as NPV typically provides a clearer and more consistent picture of project profitability, especially when dealing with non-conventional cash flows. While IRR can be a useful tool, understanding its limitations, particularly when cash flows are not straightforward, is essential for making sound financial decisions. Projects with non-conventional cash flows remind us that financial analysis sometimes requires us to look beyond a single metric and understand the broader dynamics of project profitability across different scenarios.