Internal Rate of Return (IRR)
Find the discount rate that makes NPV equal to zero.
Compare investment returns regardless of project size.
The Formula
The IRR is the interest rate at which the present value of all future cash flows equals the initial investment. If the IRR exceeds your required return, the project is worth pursuing.
Variables
| Symbol | Meaning |
|---|---|
| IRR | Internal Rate of Return (percentage) |
| CF_t | Cash flow in period t |
| C₀ | Initial investment |
| t | Time period |
Note: IRR cannot be solved algebraically. It requires iteration (trial and error) or a financial calculator.
Example 1
Invest $5,000, receive $2,000/year for 3 years. Estimate the IRR.
Try r = 10%: NPV = 2000/1.1 + 2000/1.21 + 2000/1.331 - 5000 = -27 (slightly negative)
Try r = 9.7%: NPV ≈ 0
IRR ≈ 9.7%
Example 2
Invest $20,000, returns: Year 1 = $8,000, Year 2 = $10,000, Year 3 = $12,000
Try r = 15%: NPV = 6957 + 7561 + 7890 - 20000 = +2,408
Try r = 25%: NPV = 6400 + 6400 + 6144 - 20000 = -1,056
IRR is between 15% and 25%
IRR ≈ 21.2% (by interpolation or calculator)
When to Use It
Use the IRR when:
- Comparing projects of different sizes on an equal basis
- Determining if a project meets the minimum required return
- Ranking investment alternatives
- Communicating returns to stakeholders in a simple percentage