Measuring the inadequacy of IRR in PFI schemes using profitability index and AIRR

The internal rate of return (IRR) is widely used in Private Finance Initiative (PFI) schemes in the UK for measuring performance. However, it is well-known that the IRR may be a misleading indicator of economic profitability. Treasury Guidance (2004) recognises that the IRR should not be used and net present value (NPV) should be calculated instead, unless the cash flow pattern is even. The distortion generated by the IRR can be quantified by the notion of scheduling effect, introduced in Cuthbert and Cuthbert (2012). We combine this notion with the notion of average IRR (AIRR), introduced in Magni (2010, 2013) and show that a positive scheduling effect arises if the AIRR, relative to a flat payment stream, exceeds the project's IRR. The scheduling component can be measured in two separate ways, in terms of specific AIRRs, one of which enables the scheduling component to be decomposed into relative capital and relative rate components. We also highlight the role of average capital, whose quotation in the market, in association with IRRs or AIRRs, would deepen the economic analysis of the project.