The Internal Rate of Return (IRR) is the discount rate at which the Net Present Value (NPV) of all future cash flows from an investment equals zero. It represents the annualized effective compounded return of the investment.
Decision rule: - IRR ≥ required rate of return (hurdle rate) → Accept. - IRR < required rate of return → Reject.
Calculation: IRR is generally solved by trial and error or financial calculator. There's no closed-form formula.
Example: Initial investment: −$100,000. Cash flows: +$40,000 at end of years 1–3. - At what discount rate does NPV = 0? (Solve using calculator → IRR ≈ 9.7%) - If required return = 8%, IRR > hurdle rate → Accept.
IRR vs. NPV:
| Issue | NPV | IRR | |---|---|---| | Output | Dollar amount | Percentage rate | | Multiple IRRs | No issue | Can have multiple IRRs with unconventional cash flows | | Scale problem | Correctly handles | Can mislead (small project with high IRR beats large valuable project) | | Preferred for mutually exclusive | Yes | No |
Modified IRR (MIRR): Addresses reinvestment rate assumption — assumes cash flows reinvested at a specified reinvestment rate (often the cost of capital), not at the IRR.
Personal finance IRR: Dollar-weighted return (or money-weighted return) is the IRR of an investor's actual cash flows — accounts for timing of contributions and withdrawals.
> Exam tip: When NPV and IRR conflict, use NPV. IRR assumes reinvestment at the IRR rate — unrealistic for very high IRRs. Know that IRR = discount rate where NPV = 0.