Internal Rate of Return
0 = Σ CF_t / (1+IRR)^t - Initial Cost
The discount rate that makes NPV exactly zero. IRR tells you the project's implied percentage return.
Variables
Rate where NPV = 0
Cash flow in period t
Example Calculation
Scenario
Invest $1,000 now, receive $600 in year 1 and $600 in year 2.
Given Data
Calculation
Solve: 0 = -1000 + 600/(1+IRR) + 600/(1+IRR)^2. Trial and error or calculator gives IRR ≈ 13.07%
Result
13.07%
Interpretation
The project earns 13.07%. Accept if this exceeds the hurdle rate.
When to Use This Formula
- ✓Quick percentage return comparison
- ✓Supplement to NPV analysis
- ✓Communicating returns to non-finance stakeholders
Common Mistakes
- ✗Relying on IRR alone for mutually exclusive projects
- ✗Ignoring multiple IRR problem with non-conventional cash flows
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Common questions about this formula
They can disagree for mutually exclusive projects or when cash flow patterns differ. Always defer to NPV.
Yes. When cash flows change sign more than once (e.g., initial outflow, then inflows, then another outflow), the IRR equation can have multiple solutions. In these cases, use NPV or MIRR instead.