# Concession Revenue Modelling and Forecasting

Concessions are an important source of revenue for all airports. An airport simulation model should therefore be able to give a good forecast of revenue from different types of concessions -given a small set of assumptions about local future price levels and income development for its international Pax. Since we already have a good forecast model for the expected number of international Pax (and its variation) we will attempt to forecast the airports revenue pr Pax from one type of concession and use both forecasts to estimate the airports revenue from that concession.

The theory behind is simple; the concessionaires sales is a function of product price and the customers (Pax) income level. Some other airport specific variables also enter the equation however they will not be discussed here. As a proxy for change in Pax income we will use the individual countries change in GDP. The price movement is represented by the corresponding movements of a price index.

We assume that changes in the trend for the airports revenue is a function of the changes in the general income level and that the seasonal variance is caused by the seasonal changes in the passenger mix (business/leisure travel).

It is of course impossible to forecast the exact level of revenue, but that is as we shall see where Monte Carlo simulation proves its worth.

The fist step is a time series analysis of the observed revenue pr Pax, decomposing the series in trend and seasonal factors:

The time series fit turns out to be very good explaining more than 90 % of the series variation. At this point however our only interest is the trend movements and its relation to change in prices, income and a few other airport specific variables. We will however here only look at income – the most important of the variable.

Step two, is a time series analysis of income (weighted average of GDP development in countries with majority of Pax) separating trend and seasonal factors. This trend is what we are looking for; we want to use it to explain the trend movements in the revenue.

Step three, is then a regression of the revenue trend on the income trend as shown in the graph below. The revenue trend was estimated assuming a quadratic relation over time and we can see that the fit is good. In fact 98 % of the variance in the revenue trend can be explained by the change in income (+) trend:

Now the model will be as follows – step four:

- We will collect the central banks GDP forecasts (base line scenario) and use this to forecast the most likely change in income trend
- More and more central banks are now producing fan charts giving the possible event space (with probabilities) for their forecasts. We will use this to establish a probability distribution for our income proxy

Below is given an example of a fan chart taken from the Bank of England’s inflation report November 2009. (Bank of England, 2009)^{1}

3. We will then use the relation between historic revenue and income trend to forecast the revenue trend

4. Adding the seasonal variation using the estimated seasonal factors – give us a forecast of the periodic revenue.

For our historic data the result is shown in the graph below:

The calculated revenue series have a very high correlation with the observed revenue series (R=0.95) explaining approximately 90% of the series variation.

Step five, now we can forecast the revenue from concession pr Pax figures for the next periods (month, quarters or years), using Monte Carlo simulation:

- From the income proxy distribution we draw a possible change in yearly income and calculates the new trend
- Using the estimated relation between historic revenue and income trend we forecast the most likely revenue trend and calculate the 95% confidence interval. We then use this to establish a probability distribution for the period’s trend level and draws a value. This value is adjusted with the period’s seasonal factor and becomes our forecasted value for the airports revenue from the concession – for this period.

Running thru this a thousand times we get a distribution as given below:

In the airport EBITDA model this only a small but important part for forecasting future airport revenue. As the models data are updated (monthly) all the time series analysis and regressions are redone dynamically to capture changes in trends and seasonal factors.

The level of monthly revenue from the concession is obviously more complex than can be described with a small set of variable and assumptions. Our model has with high probability specification errors and we may or may not have violated some of the statistical methods assumptions (the model produces output to monitor this). But we feel that we are far better of than having put all our money on a single figure as a forecast. At least we know something about the forecasts uncertainty.

### References

Bank of England. (2009, November). *Inflation Report November 2009 *. Retrieved from http://www.bankofengland.co.uk/publications/inflationreport/ir09nov5.ppt

- The fan chart depicts the probability of various outcomes for GDP growth. It has been conditioned on the assumption that the stock of purchased assets financed by the issuance of central bank reserves reaches £200 billion and remains there throughout the forecast period. To the left of the first vertical dashed line, the distribution reflects the likelihood of revisions to the data over the past; to the right, it reflects uncertainty over the evolution of GDP growth in the future. If economic circumstances identical to today’s were to prevail on 100 occasions, the MPC’s best collective judgement is that the mature estimate of GDP growth would lie within the darkest central band on only 10 of those occasions. The fan chart is constructed so that outturns are also expected to lie within each pair of the lighter green areas on 10 occasions. In any particular quarter of the forecast period, GDP is therefore expected to lie somewhere within the fan on 90 out of 100 occasions. The bands widen as the time horizon is extended, indicating the increasing uncertainty about outcomes. See the box on page 39 of the November 2007
*Inflation Report*for a fuller description of the fan chart and what it represents. The second dashed line is drawn at the two-year point of the projection. [↩]