2.1 The IRR is defined mathematically as the discount rate which, when applied to discount a series of cash outflows followed by cash inflows, returns a net present value (NPV) of zero. The most intuitive way of understanding the meaning of the IRR is to think of it as the equivalent constant interest rate at which a given series of cash outflows must be invested in order for the investor to earn a given series of cash inflows as income. It is in this sense a measure of the underlying return the private sector expects to achieve by investing in the project.
2.2 Thus in the table below Investment A, of 1,000, produces cash flows of 1,350 over the next 5 years. The IRR of this investment is 12.08%, i.e. as shown in the NPV column when each of the cash flows is discounted at 12.08% per annum the NPV of all of them is zero.
End | Investment A |
| Investment B |
NPV @ |
0 | -1,000 | -1,000 | -1,000 | -1,000 |
Total | 350 | 0 | 350 | 0 |
2.3 IRR calculations are highly sensitive to the timing of cash flows: as can be seen by comparing Investments A and B in the above table. Both are investments of 1,000 which each produce a net cash flow of 1,350 over 5 years, but different IRRs (9.94% in the case of Investment B) because of the different timings of these cash flows.
2.4 The IRR calculation is most properly applied in situations where a project produces negative cash flow (outflows) in the beginning, followed by positive cash flow (inflows) in later years. This is typical of most PFI projects, where large construction costs are incurred by the Contractor early on, followed by cash inflows in the form of surpluses from operations. In cases where positive and negative cash flows alternate with each other, the IRR will not be uniquely determinate and is unlikely to be the appropriate measure.
2.5 The Authority should be aware that IRRs are generally not a reliable alternative to NPV-based calculations for the measurement of the value of an investment. For example, two projects with the same IRR but different concession periods (e.g. 15 and 25 years) will have very different NPVs at all discount rates except the IRR. The widespread use of IRRs in PFI projects reflects the generally even pattern of year-on-year operational cash flows in such projects. However, if a project has an uneven cash flow profile, the Authority should exercise great caution in using an IRR as the basis of valuing investment in the project.