If you’re asking what is internal rate of return (IRR), it is the discount rate that makes the net present value (NPV) of an investment equal to zero. In simpler terms: it’s the annualized rate of return an investment is expected to generate over its life, expressed as a percentage. Businesses use IRR to compare the profitability of different capital projects; generally, the higher the IRR, the more desirable the project.
If a project has an IRR of 15%, it means the investment is expected to generate returns equivalent to earning 15% per year on the money invested.
The Plain-English Definition
Imagine you invest $100 today and receive $121 in two years. What annual return did you earn?
$100 × (1 + r)² = $121
(1 + r)² = 1.21
1 + r = 1.10
r = 10%
That 10% is the IRR – the rate that perfectly discounts the future cash flow back to the original investment amount. You can verify: $121 / (1.10)² = $100 exactly (NPV = 0).
The Mathematical Relationship to NPV
IRR is found by solving this equation for r:
> 0 = CF₀ + CF₁/(1+r)¹ + CF₂/(1+r)² + … + CFₙ/(1+r)ⁿ
There’s no algebraic shortcut – IRR requires iteration. In practice, use Excel’s =IRR() function or a financial calculator.
How to Use IRR for Decision Making
The IRR is compared to the hurdle rate – the minimum acceptable return (usually the company’s cost of capital or WACC):
| Comparison | Decision |
|---|---|
| IRR > Hurdle Rate | ✅ Accept – the project exceeds minimum return requirements |
| IRR < Hurdle Rate | ❌ Reject – the project doesn’t meet the minimum threshold |
| IRR = Hurdle Rate | Neutral – exactly meets the threshold; other factors decide |
Example: A company requires a 10% return on all investments. A project has an IRR of 14%. Accept it – it clears the hurdle.
IRR vs NPV: The Key Differences
| IRR | NPV | |
|---|---|---|
| Output | Percentage (rate of return) | Dollar amount |
| What it answers | “What return does this project generate?” | “How much value does this project create?” |
| Better for comparing projects | When size is equal | Always – accounts for scale |
| Handles unconventional cash flows? | Can give multiple answers | Always one answer |
| Preferred method | Common in practice | Preferred academically |
The reinvestment assumption issue: IRR assumes all interim cash flows are reinvested at the IRR rate – which is often unrealistically high. NPV assumes reinvestment at the discount rate (more conservative and realistic). For this reason, Modified IRR (MIRR) is sometimes preferred.
Limitations of IRR
| Limitation | When It Matters |
|---|---|
| Multiple IRRs | When cash flows change sign more than once |
| Scale blindness | A project with 50% IRR on $1,000 is worth less than 15% on $1,000,000 |
| Reinvestment assumption | Interim cash flows assumed reinvested at IRR (often unrealistic) |
| Mutually exclusive projects | Can rank projects incorrectly when sizes differ |
Quick Reference: IRR in Different Contexts
| Context | Typical IRR Threshold |
|---|---|
| Corporate capital projects | 10%-15% (above WACC) |
| Private equity | 20%-30%+ target |
| Real estate investment | 12%-20% depending on risk |
| Venture capital | 25%-40%+ target |
The Bottom Line
Internal rate of return is the expected annual percentage return on an investment – found by setting NPV to zero and solving for the discount rate. Compare it to your required return (hurdle rate): above it, accept; below it, reject. Use it alongside NPV for the most complete investment analysis, and be aware of its limitations when cash flows are complex or projects differ significantly in size.
