# Scotland-wide Older and Disabled Persons Concessionary Bus Scheme - Further Reimbursement Research

### 6 Reimbursement Calculations

**6.1** **Summary of key findings on reimbursement inputs**

6.1.1 The preceding Chapters have considered the main elements that in combination determine "no better off/no worse off" reimbursement for bus operators.

6.1.2 Very broadly, our conclusions on the reimbursement parameters that should be used for calculation of 2013-14 reimbursement of operators are as follows:

- Discount factor: appropriate values are between 18.0% and 19.25% (prior to any "degeneration", and as used to estimate the average fare forgone from the shadow fare), on the basis of the non-concessionary ticket sales and revenues reported by CPT for 2011. The gap between the two values reflects different assumptions by ourselves and CPT, but the difference is not great. A potential compromise value calculated from the average of these two figures is 18.60%;
- Elasticity parameters: a wide range of values could be used, depending upon views about data reliability, willingness to make assumptions about comparability of source and application, and estimating assumptions. A potential compromise value would be represented by the average of the two principal candidates, representing our best estimate of the long-run All-Scotland value, and CPT's.
- Choice of price index for Reimbursement Factor calculation: it is necessary to allow for price inflation in calculating the impact of changes in fare levels on the demand for journeys by passholders in the absence of the concession. We propose an index based on the General Retail Price Index, but with additional element that reflects the impact of changes in the price of petrol on passholder car/bus mode choice decisions. We have proposed that a combined index in which the Petrol and oil component of the RPI is given a 22% weight, against 78% for the general RPI.
- Additional cost rate: reimbursement for additional costs should be calculated as the product of estimated generated concessionary journeys and an additional cost rate per generated concessionary passenger; we propose that the cost rate is based on the value estimated by ITS in the 2009 study for Transport Scotland, but with the rate increased from £0.344 per generated passenger to £0.428 per generated passenger, in 2009-10 prices. CPT believe that an additional increase is justified to £0.459 per generated passenger in 2009-10 prices, on the grounds that concessionary trip lengths have continued to increase from 2006-7. We do not believe there is clear evidence that this is so. A potential compromise value representing the average of these two would give a value of £0.443 per generated passenger in 2009-10 prices.

**6.2** **Projected All-Scotland values for illustrations**

6.2.1 In order to illustrate the reimbursement implications of any given set of reimbursement parameters, we have used projections of likely out-turn concessionary journey numbers for Scotland in 2012-13 and average shadow fare values as currently forecast by Transport Scotland. In order to illustrate the reimbursement calculations going forward, we have assumed no change in concessionary journeys from 2012-13, and that the adult cash single fare will increase by 5% in current prices per year. These assumptions are intended purely for illustrative purposes and have no other status.

6.2.2 With regard to price levels, outturn figures are available for the various RPI and CPI components up to and including September 2012. It has been assumed that the annual change in prices reported at September will continue at the same rate for the remaining six months of the year, to the end of March 2013. For 2013-14 and 2014-15, it has been assumed that all indices will change by 2.5% per year.

6.2.3 The data, and these various assumptions and projections are summarised for 2012-13, 2013-14 and 2014-15, in Table 6.1.

6.2.4 For 2012-13, we have shown the reimbursement that would be paid under the current National Rate, if no Reimbursement cap applied, and also the Reimbursement cap itself. The Reimbursement Cap for 2013-14 and 2014-15 has not yet been determined.

**6.3** **The Reimbursement Calculation process**

6.3.1 The calculation of reimbursement is illustrated in Table 6.2, which works through the reimbursement implications of a single set of reimbursement parameters, in this case the MVA/Minnerva Preferred parameter values.

6.3.2 The initial parts of the table set out the key inputs. The significant steps in the calculation produce:

- the average fare forgone in current prices, necessary to work out the revenue forgone;
- the Reimbursement Factor, which determines how many of the observed concessionary journeys are regarded as non-generated (i.e. would have been made even if there was no concession), and generated;
- the reimbursement for revenue forgone; and
- the reimbursement for additional costs.

6.3.3 The total reimbursement calculated for projected 2012-13 concessionary journeys and shadow fares on the basis of this scenario is £171.5 million.

6.3.4 If these calculations were to be applied in the form of a standard All-Scotland National Reimbursement Rate, the rate that would be used is 57.3%. This is calculated by relating the total reimbursement (£171.5m) to the total value of concessionary journeys as measured by the average shadow fare. In this case the average shadow fare is £2.041, so that the total value of concessionary journeys is 146.568m*2.041 = £299.15m. So the overall Reimbursement Rate is 171.5/299.15 = 57.3%.

6.3.5 The calculated value of Reimbursement can be compared to the actual amount of Reimbursement paid under the current scheme, or the Reimbursement Cap if this would be smaller.

6.3.6 The reimbursement parameters defined in the Current Scheme are shown for comparison. The current Reimbursement Factor is 61.5%, which compares with the value of 58.4% calculated from the combination of the current Shadow Fare, and the preferred Discount Factor and elasticity parameters. The "current scheme" Discount Factor is 4.5% (post-degeneration), which contrasts with the 11.2% implied by the combination of selected Discount Factor and Reimbursement factor. The additional cost element of reimbursement illustration is calculated as a proportion of the value of the scheme; at 11.2% this is somewhat larger than the (broad) 10% that is nominally incorporated in the current National rate.

6.3.7 However, these comparisons can easily be misleading, because of the way in which the components of the current scheme are defined. A more useful comparison is between the current National rate (67.5%), and the calculated National rate from the Reimbursement Scenario (the 57.3%). But the current national Rate is not a correct guide to actual levels of reimbursement, because of the application of reimbursement caps. As was shown in Table 6.1, the projected reimbursement spend in 2012-13 would have been over £200 million if a cap on Reimbursement of £187 million had not applied. The effective National Reimbursement Rate as applied in 2012-13, because of the Reimbursement cap, is actually 62.8%.

**6.4** **Illustrations of alternative Reimbursement Scenarios (2012-13)**

6.4.1 There are different possible combinations of reimbursement parameters, which collectively imply a wide range of levels of reimbursement. Table 6.3 focusses on the main alternatives that have emerged from the study process which are as follows:

- the MVA/Minnerva preferred values, based on the most recent data and having considered all of the issues and arguments raised by CPT;
- those proposed by CPT
^{[28]}; and - values proposed by MVA/Minnerva which represent a compromise position.

6.4.2 These three sets of reimbursement parameters are indicative of the uncertainties surrounding reimbursement levels and represent a plausible range of values from within which Transport Scotland could choose with confidence.

6.4.3 It can be seen that collectively, these various choices of reimbursement parameter imply net Reimbursement Rates (relative to the Shadow Fare) of between 57.3% (Minnerva/MVA preferred parameters), and 61.0% (CPT values based on medium/log run elasticities). The compromise values of parameters lead to a Net Rate between these two of 59.2%. CPT's analysis of shorter-run elasticities, for example of change in demand to 2005-6, would give larger Net Reimbursement Rates (for example 62.3% on the above data), but these are less relevant because of their short-run nature, and also the fact that they will exclude behavioural response from the introduction of the National concession.

6.4.4 In our view, the lower values within this range are the most robust and best reflect the available evidence. However, there are various underlying uncertainties that cannot be readily quantified, which are likely to imply that the confidence intervals associated with the Net Reimbursement Rate are larger than the range of values quoted above would suggest.

6.4.5 We also recognise that in making decisions on reimbursement arrangements, a number of factors need to be taken into account that cannot be reduced to evidence-based analysis. In particular, consideration needs to be given to the practical impact of large scale changes in the amount of concessionary travel reimbursement, as well as budgetary restraints.

6.4.6 It is also worth emphasising that nearly all combinations of reimbursement parameters that we have established imply that 2012-13 levels of reimbursement payment should be less than those actually made (as constrained by the current Reimbursement cap), and significantly less than the payments that would be made under the current 67% Reimbursement Rate, if no cap was applied. In our view there is a very strong argument that the reimbursement arrangements of the current National scheme are over-generous and should be reduced.

**6.5** **Potential Reimbursement Levels in 2013-14 and 2014-15**

6.5.1 Forecasts of both reimbursement quantities and updated Net Reimbursement Rates with the various alternative reimbursement parameters are summarised in Table 6.4 below. These draw on the forecasting assumptions set out in Table 6.1 of the volume of concessionary journeys, the change in fare levels, and the likely change in price levels. It should be emphasised that these are for illustrative purposes and have no particular status.

6.5.2 For simplicity and without giving them any particular status, we have assumed for the purpose of illustration that in 2013-14:

- concessionary journeys stay at the expected level of the 2012-13 outturn that is 146.358m older and disabled concessionary journeys. Journeys declined by 2.5% between 2011-12 and the expected 2012-13 outturn, so this assumption assumes that this trend decline is halted;
- it is assumed that all price indices increase by 2.5% relative to 2013-14, which is very similar to the increase from 2011-12 to 2012-13; and
- the shadow fare increase by 5%, which is somewhat less than the 7.5% (nominal) increase observed between 2011-12 and 2012-13.

6.5.3 The reimbursement consequences of these assumptions are shown in Table 6.4, using the same combinations of reimbursement options as was illustrated in Table 6.3.

6.5.4 The change from 2012-13 to 2013-14 does not affect the relativities between the reimbursement options, but does impact on the different components of the calculation. Using the Minnerva/MVA preferred reimbursement parameters for illustration, we see that relative to 2012-13, the 2013-14 calculation:

- gives a higher overall quantity of reimbursement (increasing from £171.5m, to £178.4m); this is largely a result of the higher fare and average cost rate;
- the net Reimbursement Rate reduces slightly from 57.3% to 56.8%, reflecting the assumed increase in fares above the rate of inflation; and
- the latter impact is also evident in the reduced Reimbursement Factor ("Generation Factor" G), which reduces from 58.4% to 57.9%.

6.5.5 If the Reimbursement Rate did not change between the two years (as is the case with the current National Rate), the impact of a 5% increase in fares in current price terms is to increase overall reimbursement by 5%, even if this was substantially more than the rate of inflation. In the counterfactual, the journeys not generated by the concession would fall if fares increased in real terms. By using an elasticity-based model, this can be reflected in the Reimbursement Factor, which would reduce. Reimbursement still increases with above inflation fares, both in current price and real price terms, but to a lesser extent than it would with a fixed Reimbursement Rate.

6.5.6 With the forecast assumptions for 2013-14 as set out above, the Net Reimbursement Rate with the Compromise parameter values is 58.6%, with total reimbursement of £184.2 million.

6.5.7 Similar calculations for illustrative 2014-15 forecasts are shown below in Table 6.5. These use the same assumptions of no growth in journeys, 5% growth in adult cash single fares per annum, and 2.5% increase in prices per annum, as for 2013-14. The forecast growth in adult cash single fares relative to the forecast change in price levels leads to a Net Reimbursement Rate of 56.2% with our Preferred reimbursement parameters, and a Rate of 58.1% with the compromise parameters. If concessionary journeys remained at the predicted 2012-13 level, the resulting level of concessionary reimbursement payment would be £185.5m with our preferred reimbursement parameters, and £191.6m with the compromise amounts.