Internal Rate of Return (IRR) in a nutshell

 

Hi all,

 

We all know that this is a place to learn from unprecedented models, methods & techniques.

Today, let’s explore IRR. We all know it is a discount rate where NPV is 0. How it is derived is through these 2 formulas

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So how do we assess IRR based on cash flows? The process is straightforward. For this purpose, we have selected three different cash‑flow patterns across three projects:

Incremental cash flows

Even cash flows

Uneven cash flows

We often hear discussions about the timing and nature of cash flows, and that is precisely what we are going to examine here.

Project A contains incremental cash flows, with annual percentage increases of 100%, 50%, 33%, 25%, 20%, 17%, 14%, and 13%.

Project B consists of even cash flows, resulting in a natural annual percentage change of 0%.

Project C exhibits uneven cash flows, with annual percentage changes of –300%, –30%, –243%, –200%, 0%, 20%, –125%, and –950%.

The annual growth rate of cash flows appears irrelevant. But IRR is highly sensitive to the timing and pattern of those cash flows. In all three projects, the WACC is 15%, the total undiscounted cash inflows equal CU 35, and the average annual cash flow is CU 5.

Even when projects have identical total cash inflows, identical average inflows, and identical discount rates, their IRR and NPV can differ substantially due to the timing and volatility of cash flows. Evenly distributed inflows maximise both IRR and NPV because value is realised early and consistently. Back‑loaded inflows inflate IRR mathematically but reduce NPV due to discounting. Highly uneven inflows depress both IRR and NPV because volatility and late timing destroy present value. This confirms that IRR rankings are unreliable when cash‑flow timing differs, and NPV remains the superior decision metric.