## Internal Rate of Return (IRR)
The IRR considers the time value of money, the initial cash investment, and all cash flows from the investment — but, unlike NPV, it does not use a pre-set desired rate of return.
Instead, IRR is the discount rate that makes the present value of the expected cash inflows equal to the initial cash outflow — i.e., the rate at which NPV = 0.
$$\text{At IRR:}\quad \sum_{t=1}^{n}\frac{C_t}{(1+\text{IRR})^t} = I \quad\Longleftrightarrow\quad \text{NPV} = 0$$
The computed IRR is then compared to a criterion rate — the organisation's desired rate, cut-off rate, or WACC.
### Decision rule
| Condition | Decision |
|---|---|
| IRR ≥ Cut-off rate / WACC | Accept the proposal |
| IRR < Cut-off rate / WACC | Reject the proposal |
### Reinvestment assumption (important)
IRR implicitly assumes interim cash flows are reinvested at the project's own IRR (not at the cost of capital). Consequences:
- Projects with heavy early cash flows are favoured by IRR.
- This assumption is often unrealistic and is the root cause of the conflict between NPV and IRR — addressed by MIRR.
> IRR is usually found by interpolation between two discount rates (one giving positive NPV, one negative). The detailed steps are covered in the Time Value of Money chapter.