Summary / Key takeaways
– IRR (internal rate of return) is the discount rate that makes the net present value (NPV) of a series of cash flows equal to zero. It is expressed as an annualized percentage return.
– IRR helps compare projects or investments with different cash‑flow timing: higher IRR generally indicates a more attractive investment, all else equal.
– Use IRR as a decision check against a hurdle rate (commonly the company’s WACC). For mutually exclusive projects, use NPV to resolve conflicts.
– Common practical tools: Excel’s IRR, XIRR (irregular dates), and MIRR (addresses reinvestment-rate assumption).
– Limitations: multiple IRRs for non‑conventional cash flows, implicit reinvestment assumptions, scale and timing biases, and sensitivity to cash‑flow estimates.
Source: Investopedia — “Internal Rate of Return (IRR)”
1. What IRR means (plain language)
– IRR is the annualized rate at which the present value of an investment’s expected inflows equals its initial outflow. In other words, it is the rate of return that makes the project’s NPV = 0.
– It is not an absolute dollar profit; it’s a percentage that reflects the time value of money for the projected cash flows.
2. The IRR formula (conceptual)
NPV = sum_{t=1 to T} (C_t / (1 + IRR)^t) − C_0
Set NPV = 0 and solve for IRR, where:
– C_0 = initial investment (usually a negative cash flow),
– C_t = net cash inflow at period t,
– T = total periods.
Because IRR appears in the denominator of each term, it generally cannot be solved algebraically and requires iteration.
3. How to calculate IRR — methods
A. Manual (trial and error / numerical root‑finding)
– Choose a discount rate guess, compute NPV.
– Adjust the rate upward if NPV > 0, downward if NPV hurdle rate; reject if IRR required rate of return.
– Mutually exclusive projects: Use NPV at the appropriate discount rate to choose the best project.
– Non‑conventional cash flows or multiple IRRs: do not rely on IRR alone; use NPV and MIRR.
12. Final checklist before acting on IRR
– Verify cash‑flow signs and timing.
– Confirm whether cash flows are periodic or irregular.
– Compute IRR and NPV at the appropriate discount rate.
– Consider MIRR if reinvestment assumptions matter.
– Perform sensitivity analysis.
– Make the decision in the context of strategy, capital constraints, and alternative uses of funds.
Further reading / source
– Investopedia — Internal Rate of Return (IRR)
Editor’s note: The following topics are reserved for upcoming updates and will be expanded with detailed examples and datasets.