The Ministry of Finance in Chile uses a spreadsheet model to quantify the fiscal implications of the revenue guarantees and revenue-sharing arrangements (and, when they were in force, the exchange-rate guarantees). The spreadsheet has three main parts. The first is a model of the guarantee-related provisions of the concession contracts. The second is a stochastic model of traffic revenue (that is, a model that allows traffic revenue to evolve with a random as well as a predictable element). Together, the first two parts generate estimates of the probability distributions of the government's future payments and receipts. The third part of the spreadsheet values the guarantees and revenue-sharing arrangements.
The first part of the model essentially translates the clauses of a concession contract concerned with revenue guarantees and revenue sharing into formulas in a spreadsheet. The essence of the revenue guarantees is simple: if actual traffic revenue exceeds the guaranteed level, the government pays nothing; otherwise it pays the difference between actual and guaranteed traffic revenue. The guarantee can thus be modeled by using 'if-then' or maximum functions. Some of the revenue-sharing (or more accurately profit-sharing provisions) are more complicated. The model simplifies aspects of the contracts. For example, in some concessions, the government's payments under the revenue guarantee depend on the number of traffic accidents, and this dependency is ignored in the model.
The second part of the spreadsheet is a model of traffic revenue for each of the roads and airports with revenue guarantees. Over the years, different approaches have been tried. Some have analyzed revenue as the product of traffic and tariffs for various types of vehicle (cars, motorcycles, light trucks, and so on) and allowed different types of traffic to respond differently to changes in the economy. Some have analyzed traffic revenue as a function of gross domestic product and the price of petrol and have used stochastic models of evolution of these underlying variables.
The approach now used is simpler: it projects traffic revenue directly. For each concession in operation, the projection starts with actual revenue last year. Estimates of expected growth may come from traffic forecasts, if they are recent and still considered useful, or from forecasts of GDP and an estimate of the income elasticity of traffic revenue. Randomness is incorporated by assuming that traffic revenue evolves as a kind of random walk, namely a geometric random walk with drift (growth). The geometric aspect of the random walk means that rates of growth and volatility of revenue are assumed to be proportional to current revenue. The expected growth rate can change from year to year, as well as differing from concession to concession. The rate of volatility is assumed to be the same for all years and all roads-although it would be easy to change this assumption if there was evidence of differences. The main source of the estimate of volatility is historical variation in revenue on roads that have been open for a few years. A rough estimate of the correlations among the revenues on different roads is also incorporated in the model. Chile's concessions have been operating for many years, and there were public toll roads before there were concessions, so historical data are plentiful. Of course, the future won't be the same as the past, and the estimates of volatility, correlations, and growth rates are very rough.
For roads that have not yet been opened to traffic, initial revenue is treated as a random variable. The random variable is assumed to have a lognormal distribution, which means that initial revenue cannot be negative (something that would be possible if it were normally distributed). To account for optimism, the mean of the random variable is allowed to be lower than forecast of revenue prepared when the concession was developed. Estimates of optimism and of the standard deviation of initial revenue can also be informed by historical experience in Chile, as well as international research, such as Skamris and Flyvbjerg (1997) and Standard & Poor's (2003).
The two parts of the spreadsheet model just described estimate the frequency distribution of payments by and to the government in each future year of each concession. They generate the graphs in Figure 2. In some cases, the frequency distributions can be estimated analytically (that is, with a formula that can be entered in a cell of a spreadsheet). But most estimates are derived from Monte Carlo simulation.
The third part of the spreadsheet estimates of the value of the government's right to receive possible revenue-sharing payments and its obligation to make possible guarantee payments. This part generates the values of revenue guarantees shown in Table 4. A simple way to estimate these values would be to compute the sum of expected payments discounted at an estimate of the risk-free borrowing rate. Given the uncertainty inherent in estimates of future rates of growth and volatility, this simple approach would not be unreasonable. But it would tend to undervalue guarantees and overvalue revenue-sharing arrangements and make the concessions seem less costly and risky to the government than they really are. The reason is that revenue guarantees are more likely to be triggered when the economy is doing poorly and revenue-sharing payments when it is doing well. Rights and obligations that have these characteristics should have values that differ from the sum of expected payments discounted at the risk-free rate. In particular, rights to payments that are usually received when the economy is doing badly are worth more than rights to payments that are usually received when it is doing well. This, at any rate, is the idea underlying standard models of the price of risk.
The spreadsheet model uses the capital-asset pricing model to price the risk of revenue guarantees and revenue-sharing arrangements. In particular, it uses a rough estimate of a parameter closely related to the CAPM beta of security valuation. That parameter is used to generate projections of risk-adjusted revenue. Those projections then generate estimates of risk-adjusted expected payments, or certainty equivalents. The certainty equivalents are then discounted at the risk-free rate to get present values.