Our numbers were obtained directly from cash flow data and projections, in contrast to indirect estimates based on the cost of private versus public funds, for instance. Thus, the IRRs we report can be used to evaluate whether the advantages or disadvantages of PPPs compensated for the higher or lower cost of funds when compared with public provision.

Our estimates for the rates of return have a large dispersion, implying a large variance in the results of PPP projects. This explains the pressure for contract renegotiation and underlies the fiscal risks discussed earlier in this paper. The large variance in actual returns indicates that infrastructure investment is intrinsically risky, independent of whether the project is financed by the public purse or as a PPP.

# <u>4.2 Methodology</u>

One of the challenges we faced when calculating the IRRs was the switch from traditional Chilean accounting standards to IFRS standards that took place in the mid-2000s. This meant that the income statements could not be used directly, because several of its components are marked to market under IFRS. This change also implied that fluctuations in interest rates can affect the operational results, which would bias our IRR estimates. For this reason and taking advantage of the fact that PPPs are Single Purpose Vehicles (SPVs), we used cash inflows and outflows –which are not marked to market-- to determine the profitability of projects. These cash flows are somewhat erratic in individual years, with inflows and outflows that are large in magnitude and whose nature is sometimes unspecified. Over longer periods however, this problem tends to cancel out and should not have a large impact on our estimates. Also, some items were excluded for reasons we explain below.

To estimate the IRR of a given PPP, we began by constructing a cash-flow series for years with information on cash flows. We classified inflows and outflows reported in the SPV’s financial statements into three categories: operations, investment, and financing. Next, we used this information to determine net investment cash flows and net operational cash flow, excluding interest payments for the latter. The difference between these flows, the net cash flows, was used to estimate the realized (ex post, actual) IRR. The details may be found in the Appendix, as well as the judgement calls we made and how they varied with whether the SPV chose the direct or indirect method to present cash flows.<sup>58</sup> We considered all highway and airport PPPs with at least 5 complete operational years up to 2019 (see the Appendix for a detailed definition), resulting in a sample of 50 projects, where 31 are highways and 19 are airports. For the 14 (out of 50) concessions that had concluded by 2019, the last year for which we have data, we obtained the IRR directly. For the remaining 36 concessions, we used regression-based simulations to forecast future net cash flows and then calculate the IRR. The regression we used estimates a linear relation between annual cash flows (normalized by MOP ́s estimate of total investment reported in the bidding documents) and year of operation. The regression also includes concession and calendar year fixed effects.

Our estimates show that cash flows increase with the year of operation, albeit at a decreasing rate (see Figure 2). We used these estimates together with the regression residuals to simulate 1000 cash-flow series for every ongoing concession and calculated the IRR for every simulated series. The estimated IRR is the median of the 1,000 IRRs obtained this way. In the case of PVR contracts we used an auxiliary regression model to determine the concession length for a given

> 58 These methods differ in how they record operative cash flows: the direct method reports cash inflows and outflows from operating activities, while the indirect method adjusts the period’s net income by adding changes in short-term assets and liabilities to determine the implied cash flow.

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