Internal Rate of Return (IRR)

Executive Summary

The Internal Rate of Return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. It is the annualized rate of return where NPV equals zero.

Key Takeaways
  • break-even rate: IRR is the discount rate that makes the Net Present Value (NPV) of cash flows equal to zero.
  • investment ranking: Projects with higher IRRs are generally accepted if they exceed the required hurdle rate.
  • iterative math: IRR cannot be solved analytically and requires numerical methods like Newton-Raphson.
Formula
∑ [ CF_t / (1 + IRR)^t ] = 0

Internal Rate of Return (IRR) Formula

Variable Glossary
SymbolMeaning & Description
IRRInternal Rate of Return (solved discount rate r)
CF_tCash flow amount at period t
Step-by-Step Worked Example
1. Mapped Variables
Cash Flows Ledger
-10000, 3000, 4200, 6000
2. Equation Substitution
Equation with standard inputs
NPV(IRR) = 0 (solved iteratively)
3. Calculation Steps
Step 1: Check cash flow signs

Ensure there is at least one negative outlay and one positive inflow.

Step 2: Apply numerical search (Newton-Raphson)

The solver starts at 10% guess, adjusting rate iteratively until NPV converges to 0.

Step 3: Output IRR solved rate

Solved IRR = 13.54%

Final Resolved Internal Rate of Return (IRR)13.54%
Live Simulation

IRR Calculator Sandbox

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Common Mistakes to Avoid

Multiple IRRs: For cash flows that alternate between positive and negative values multiple times, the equation can yield multiple mathematical solutions, making simple interpretation difficult.

Frequently Asked Questions
Interactive Tool

IRR Calculator

Calculate the Internal Rate of Return (IRR) for capital budgeting projects.

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