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

3 Discount Factors and the Average Fare

3.1 Revenue forgone by operators due to the free scheme

3.1.1 "No better off and no worse off" reimbursement needs to compensate operators for the revenue forgone, i.e. the revenue that would have been earned by the bus operator from the passenger journey that would have been made if passholders had paid fares rather than travelled for free.

3.1.2 To calculate this, estimates are needed of both the number of journeys that would have been made by passholders if they had to pay the commercial fare, and the commercial fare that would have been paid for "non-generated" concessionary journeys. The greater the commercial fare, the more journeys can be expected to be generated; put another way, a smaller proportion of the journeys would continue to be made, in the absence of the scheme, if the commercial fare is larger rather than smaller.

3.1.3 The "average fare that would be paid by concessionary passholders in the absence of the concession", or more succinctly, "the Average Fare Forgone" (AFF) cannot be directly observed. Instead, it has to be derived from some other measure of the fares charged by an individual operator which is able to reflect changes in fare levels as well as travel patterns. We refer to this as the "reference fare".

3.1.4 The reference fare used by the Scottish Scheme is the "shadow fare", which is recorded for individual concessionary journeys through the Scotland-wide smartcard-based ticketing system. In principle, on boarding the bus each concessionary passenger states his or her destination, from which the driver is able to record the fare that a non-concessionary adult passenger would pay for the same journey made with a cash single ticket. There are various concerns that have been raised regarding the accuracy of this process, but for the present it is assumed that the shadow fare remains the mechanism through which reimbursement calculations are informed about a given operator's fare level.

3.1.5 However, operators offer a variety of tickets, including day returns, multi-journey tickets and period tickets (which allow unlimited use during a given period of validity, e.g. daily, weekly, 4-weekly etc). Generally, the cash single fare will be the most expensive way of purchasing bus travel unless passengers make few and irregular journeys. The majority of journeys made by non-concessionary fare-paying passengers in Scotland currently use these other ticket types rather than buying a cash single fare. It would be expected that in the absence of the concession, passholders would also make some use of discounted tickets as well as paying cash single fares, so that overall the average fare per journey would be less than the average shadow fare. Consequently, a "Discount Factor" needs to be calculated that reflects the extent to which the average fare forgone (that is, the average fare that would be paid by passholders in the absence of the scheme, after taking account of discounted tickets) would be less than the average shadow fare.

3.2 Principles involved in calculating the average fare forgone

3.2.1 The fares paid for individual journeys, or per journey when a period ticket is purchased, obviously vary greatly. The overall average fare per non-concessionary journey paid to a particular operator can, in theory, be calculated by taking the total revenue received and dividing by the total number of journeys made. Alternatively, it could be calculated as a weighted average of the fares paid for each type of ticket, with the weights reflecting the number of journeys made on each ticket type. In order to calculate the average fare forgone by concessionary passholders in the absence of the scheme, we therefore have to estimate the share of journeys that would be made on each of the available ticket types, and the average fare per journey on each ticket type.

3.2.2 The individual passenger will make a choice of ticket type based on a number of factors, but one significant influence is bound to be the relative prices of each of the ticket types that are available. So if a passenger expects to make a given number of bus journeys in a forthcoming period, he or she will tend to choose the combination of ticket types that will enable these journeys to be made at the lowest price. This might involve some combination of single cash fares, day tickets or possibly a week ticket. The relative attractiveness of the period tickets will therefore be determined partly by whether they are more or less expensive compared to alternatives, and in particular compared with making the same journeys by buying cash single tickets. Consequently, the relative price will influence both the share of journeys made on each ticket types, and the average number of journeys made per ticket purchased (and hence the average fare per journey).

3.2.3 The average fare forgone by concessionary passengers cannot be directly observed, but in the past has been inferred from the observed use of different ticket types by equivalent non-concessionary passengers. This was very largely the basis of the recommendations on discount factors made by the ITS team. There are two drawbacks to this method, referred to here as "Method (a)":

  • first, bus operators are generally not able to accurately count the number of journeys made using period tickets[7]. Journey estimates are typically made by applying a "rule of thumb" to the number of tickets sold e.g. 2.5 journeys per day ticket. But as noted, the number of journeys made per ticket will depend upon the relative prices of each, so in addition to relying upon assumptions about the journey numbers, this method cannot be used to distinguish between operators offering very different price structures. This may not be an important consideration with the current National scheme, but could become a significant drawback if there was any move away from a single National reimbursement rate; and
  • second, assumptions are then needed about how the travel patterns of non-concessionary passengers might be different to those of concessionary passengers, taking into account differences in characteristics such as level of employment, car ownership and the journey purpose mix.

3.2.4 An alternative to using data on non-concessionary ticket sales is to use observed data on concessionary journey frequencies ("Method (b)"). This was not practicable until relatively recently when smartcard data started to become available. Smartcard systems make it possible to record complete information about concessionary journeys (including those made by infrequent travellers, as well as very frequent travellers). Method (b) using concessionary smartcard data is now the basis of the method incorporated in the UK Department for Transport (DfT) average fare forgone calculator. With information available about, for example, the number of days in which more than X journeys were made, it is possible to directly infer on how many days a day ticket priced at "X" times the cash fare would be financially advantageous. However, the disadvantage of this method is that assumptions are then required about how the frequencies of observed (free) concessionary journeys would change if the passholders had to pay for their journeys.

3.2.5 The previous work on discount factors by ITS largely used "Method (a)", and the discussion set out here is predominantly also concerned with updating discount factors derived by this method i.e. from observed ticket sales by non-concessionary passengers. However, there are severe limitations to this method in terms of its ability to respond to changing commercial strategies by operators. In contrast, Method (b) demonstrates that differences in commercial strategies (i.e. the relative pricing of cash and different types of period ticket) could have significant implications for the discount factor over time, and for differences between individual operators.

3.3 Data for Method (a) and implications for non-concessionary average fares

3.3.1 Method (a) is very largely dependent upon data provided by bus operators. CPT has been extremely helpful in collating information on ticket sales and revenues in 2011, which has been provided voluntarily by 17 bus operators who between them operate about 85% of the total bus miles in Scotland. The data provided by CPT is summarised in Table 3.1 below.

Table 3.1 Operator data on adult non-concessionary ticket sales in Scotland, 2011
2011 full calender year figures CPT data for 2011 updated by SDG 07-01-2013 Implied values
2011 data supplied to current study, adult non-concessionary passengers Tickets in Circulation Revenue Cost per
Price ratio
Adult singles 67,931,437 £106,583,720 £1.569 1.00
Adult returns 5,530,148 £23,250,545 £4.204 2.68
Ten Journey ticket 204,933 £3,920,100 £19.129 12.19
Day tickets 10,964,361 £39,519,459 £3.604 2.30
Weekly seasons 2,044,755 £26,943,823 £13.177 8.40
4 weekly seasons 563,840 £24,974,052 £44.293 28.23
Annual seasons 1,236 £817,912 £661.741 157.40
Total all ticket types £226,009,611

Source: CPT, as supplied by SDG on 7/1/2013

3.3.2 The supplied data was categorised into seven generic ticket types:

  • the first three are tickets which can only be used by the purchaser for a finite number of journeys, i.e. one journey for a single, two for a return and ten for the ten journey carnet[8]; and
  • the second four are period tickets which can be used for any number of journeys within the period of validity. It is the journeys associated with these tickets about which there is most uncertainty.

3.3.3 The cost per ticket can be calculated from the revenues and ticket sales. The price ratios are the ratio of the price of the ticket compared to an adult cash single fare; it therefore provides an indicator of how many journeys a passenger needs to make in a day, a week or a four-week period to justify purchase of the respective period ticket, as an alternative to buying single tickets.

3.3.4 In order to calculate the overall average fare, assumptions are then necessary about the number of journeys made per ticket sold. It is possible to infer logical lower limits to these assumptions (based on the price ratios) but not higher limits. The assumptions proposed by CPT are shown in Table 3.2.

Table 3.2 CPT Assumptions on journeys, adult non-concessionary passengers
2011 full calender year figures CPT data for 2011 Implied values
2011 data supplied to current study, adult non-concessionary passengers Tickets in Circulation CPT Estimates of Passengers Revenue Cost per ticket Price ratio CPT journeys per ticket
Adult singles 67,931,437 67,931,437 £106,583,720 £1.569 1.00 1.000
Adult returns 5,530,148 11,060,296 £23,250,545 £4.204 2.68 2.000
Ten Journey ticket 204,933 2,049,330 £3,920,100 £19.129 12.19 10.000
Day tickets 10,964,361 30,854,711 £39,519,459 £3.604 2.30 2.814
Weekly seasons 2,044,755 23,685,387 £26,943,823 £13.177 8.40 11.583
4 weekly seasons 563,840 30,013,263 £24,974,052 £44.293 28.23 53.230
Annual seasons 1,236 812,392 £817,912 £661.741 157.40 657.275
Total all ticket types 166,406,817 £226,009,611
Overall average per journey £1.358

3.3.5 Thus overall, the CPT data suggests that for the sample of operators for whom data has been provided, about 180 million journeys were made, for revenues paid of £223 million, giving an overall average fare of £1.358 per journey paid by adult non-concessionary passengers.

3.3.6 There is little hard evidence to support the CPT assumptions about journeys for each of the different ticket types, and no systematic process is available for changing these assumptions when relative ticket prices change. Operators typically will not have accurate counts of the number of journeys made with each type of discount ticket. The most reliable sources for estimating journeys per ticket are the continuous monitoring surveys conducted by some of the English PTEs, which demonstrate (as would be expected) substantial variation in journey rates both between operators and between areas, but there is no equivalent data for Scotland. The journeys per ticket implied by CPT's own data have varied for no obvious reason, and there can be little confidence that the assumptions made by participating operators are either on a consistent basis or are fully representative of Scotland as a whole.

3.3.7 However, it is possible to compare the overall average fare shown in Table 3.2 against an equivalent value calculated from Transport Scotland national data on total bus operator revenues and journeys. This is not directly comparable with the CPT data shown above, but using data supplied by CPT we have been able to allow for the main elements that will be included in the Transport Scotland data but excluded from the CPT data, namely children, students, bus company employees and their families.

3.3.8 The national data implies that the average revenue per adult non-concessionary journey in 2011 is about £1.32, i.e. 2.6% below the value calculated from the CPT assumptions. To match the Transport Scotland data it is necessary to increase the CPT assumptions for journeys per ticket for period tickets by about 5%. The resulting values for adult non-concessionary journeys are summarised in Table 3.3.

Table 3.3 Revised estimates of journeys, adult non-concessionary passengers
2011 full calender year figures CPT data for 2011 Adjusted journeys/ticket to give TS 2011 average fare
2011 data supplied to current study, adult non-concessionary passengers Tickets in Circulation Revenue Adjusted Jneys/ticket Cost per journey Revised journeys Adjusted fare per journey
Adult singles 67,931,437 £106,583,720 1.000 £1.569 67,931,437 £1.57
Adult returns 5,530,148 £23,250,545 2.000 £2.102 11,060,296 £2.102
Ten Journey ticket 204,933 £3,920,100 10.000 £1.913 2,049,330 £1.913
Day tickets 10,964,361 £39,519,459 2.962 £1.217 32,472,328 £1.217
Weekly seasons 2,044,755 £26,943,823 12.191 £1.081 24,927,139 £1.081
4 weekly seasons 563,840 £24,974,052 56.021 £0.791 31,586,766 £0.791
Annual seasons 1,236 £817,912 691.734 £0.957 854,983 £0.957
Total all ticket types £226,009,611 170,882,279
Overall average per journey £1.358 £1.323

3.4 Assumptions about use of tickets by concessionary passholders

3.4.1 In order to use this data to infer the average fare that would be paid by concessionary passengers, it is then necessary to make assumptions about the extent to which concessionary passholders, in the absence of the concession, would mirror the use of discounted tickets by non-concessionary passengers demonstrated in Table 3.3

3.4.2 One issue on which there has been general agreement[9], in the absence of clear evidence, is that concessionary passholders are less likely than non-concessionary passengers to commit to the purchase of four‑weekly or longer period season tickets. The rationale is that a) the majority of passholders are not in full-time employment and b) the primary reason for purchase of these ticket types is to travel to and from work. This is an oversimplification, and there is some evidence of concessionary passholders purchasing four-weekly period tickets prior to free travel in some circumstances[10]. However, we propose that four-weekly tickets continue to be excluded from the discount factor calculations. Including them would potentially significantly lower the average fare forgone and increase the discount factor.

3.4.3 The other ticket type on which a similar issue arises is the weekly ticket. It is probable that the use of weekly tickets by passholders would be substantially less than of other adults, because of the lower proportion of journeys to work. National data assembled by CPT suggests that only 12.5% of the concessionary age group are in employment. CPT therefore initially proposed that the number of weekly tickets which would be purchased by passholders in the absence of the concessionary scheme should be reduced to 12.5% of those made by the non-concessionary fare-paying passengers.

3.4.4 In our view, this reduction is excessive, because it implies that all weekly tickets are only purchased by people in employment, and only used for work journeys. The 12.5% suggested by CPT will therefore be at the bottom end of the range of plausible values and we suggest that a value of 20% should be used in the current calculations. In our view even this higher value is somewhat conservative (i.e. will tend to favour a lower discount factor and hence higher levels of reimbursement) but CPT is likely to have a different view.

3.4.5 Questions could be raised about the relevance of ten-journey carnet tickets to concessionary passholders (using similar arguments about employment). More generally, it is apparent from the relatively expensive pricing of these tickets, which are significantly more expensive per journey than single tickets, that they are targeted at a different market segment to cash singles. On balance, we recommend including them, which would tend to lower the average fare forgone and hence increase the discount factor.

3.5 Concessionary journey length and the average cash fare

3.5.1 The average adult cash single fare that can be calculated from CPT data for adult fare-paying passengers is less than the average adult cash single fare that would be paid by concessionary passengers (as would be measured by the shadow fare, for example). Data provided by CPT for a sample of eight, predominantly large, Scottish bus operators shows that the average concessionary shadow fare is about 19% more than the average (non-concessionary) adult single cash fare paid. Although this may partly reflect possible over-recording of destinations, it is consistent with evidence from a number of sources that the introduction of free travel led to longer journeys by passholders.

3.5.2 It is therefore logical to presume that in the absence of the concession, journey lengths by passholders would reduce, and there is no strong evidence that in the absence of the concession the journey length characteristics of journeys by passholders would not be similar to those of adult non-concessionary passholders. Consequently, it is appropriate to calculate the average fare forgone using the same average fare per journey as implied by the "adjusted" CPT data, as shown in Table 3.3.

3.5.3 However, the discount factor needs to be calculated relative to the reference fare to which it will be applied i.e. the shadow fare, which could be expected to be 19% higher than the average adult cash single fare. So the process to calculate the discount factor involves, first, calculating the average fare forgone (using the non-concessionary average adult cash single fare), and then estimating the discount factor from the average fare forgone relative to the adult cash single fare increased by 19% i.e. £1.867.

3.5.4 This is shown in Table 3.4, which draws on CPT's most recent 2011 data and the various assumptions discussed above.

Table 3.4 Concessionary average fare forgone, (MVA/Minnerva assumptions)
Adult non-concessionary passengers Concessionary passengers
Adult ticket sales Adjusted Jneys/ticket Cost per journey Use of ticket type by passholders? Journeys Revenues using adult cash single fare
Adult cash single fare 67,931,437 1.000 £1.569 100.0% 67,931,437 £106,583,720
Adult returns 5,530,148 2.000 £2.102 100.0% 11,060,296 £23,250,545
Ten Journey ticket 204,933 10.000 £1.913 100.0% 2,049,330 £3,920,100
Day tickets 10,964,361 2.962 £1.217 100.0% 32,472,328 £39,519,459
Weekly seasons 2,044,755 12.191 £1.081 20.0% 4,985,428 £5,388,765
4 weekly seasons 563,840 56.021 £0.791 0.0% - £0
Annual seasons 1,236 691.734 £0.957 0.0% - £0
Total all ticket types 118,498,819 £178,662,589
Average fare £1.508
Discount compared to average concessionary shadow fare of £1.867 19.2%

3.5.5 The "hard data" in the table is the information on ticket sales of non-concessionary adult tickets as provided by CPT. The "adjusted journeys per ticket" are largely based on CPT's assumptions, but modified to more closely reflect the average adult non-concessionary fare implied by Transport Scotland national data. The column labelled "use of ticket type by passholders" reflects the assumptions made about the extent to which concessionary passholders would purchase the same tickets as adult non-concessionary passengers. In the table, identical numbers are assumed for all ticket types except that it is assumed that 20% of the weekly tickets purchases by non-concessionary passengers would be made by concessionary passengers, and none of the 4 weekly or annual tickets. The implied number of journeys and associated revenues can then be calculated.

3.5.6 The average fare that is the result of this calculation is £1.508, which represents a 19.2% discount relative to the equivalent average shadow fare of £1.867. This represents our best estimate of the discount factor, based on CPT's 2011 data on ticket sales and revenues.

3.5.7 As discussed above, this value is based on a "compromise" 20% assumption about the use of weekly tickets by concessionary passholders. The other potential area of contention between ourselves and CPT is the need to adjust CPT journeys per ticket assumptions. In our view, this is a necessary check on what would otherwise be unvalidated assumptions. If the calculations were carried out without this adjustment, then the average fare per journey would be calculated to be £1.532, leading to an estimated discount factor of 18.0%.

3.5.8 Both of these estimated discount factors are significantly larger than the value implicit in the current National Scheme Reimbursement Rate, which is about 7.3%[11].

3.6 Commentary on methods for calculating the average fare forgone

3.6.1 Reliance on assumed journey rates per ticket sold: the fundamental weakness of the method used to calculate discount factors set out above is that it provides no systematic process through which the discount factor can be updated to reflect changes in the relative price of cash and discount tickets over time, or differences in discount factors between bus operators. At a national level, it is probable that relative ticket prices will only change slowly, and values could be updated simply by replicating these calculations on a year-by-year basis. However, it is unlikely that reported data on journeys will properly reflect the journeys made, and at best, updated discount factors will respond to trends in relative ticket prices on an arbitrary and difficult-to-validate basis.

3.6.2 The only systematic method for inferring the consequences of changes in ticket prices draws on observed data on concessionary journey frequencies. This is the basis of the average fare estimates in the Department for Transport Reimbursement Calculator, as widely adopted in England. An equivalent method has been developed for Scotland, although this method also relies upon various assumptions. The greatest benefit from the alternative method would arise from its application to individual bus operators, where variation in discount factors is likely to be greatest. It can be easily demonstrated using this method that the appropriate discount factor will vary substantially from one operator to another. This suggests that on these grounds alone, a single National Reimbursement Rate incorporating a national "average" discount factor is unlikely to satisfy "no better, no worse off" objectives at an individual operator level (as required by EC Regulations).

3.6.3 It is recognised that at present the Scottish Government is committed to retaining a single All-Scotland Reimbursement Rate. Elsewhere in this report we recommend that consideration is given to alternative approaches, in which case the development of discount factor calculations drawing on these principles is likely to provide the most sensible way forward. This could also provide a transparent mechanism for updating the value of overall Discount Factor estimated above on an on-going basis.

3.6.4 Data provision: even if the basis for the journey number assumptions in the data set out above could be more clearly established, the calculations set out above depend entirely on ticket sales and revenue data which has been provided voluntarily by bus operators, collated by CPT. The cooperation of the bus industry in making this information available is gratefully acknowledged. However, given its central role in determining the discount factor, there are possible criticisms of this process in terms of good governance:

  • since it is offered voluntarily, Government has no right of audit, nor a power to compel cooperation;
  • the definition and the specification of the information to be provided is entirely the responsibility of CPT, which, since it represents the best interests of its members, could be argued has a vested interest in the outcomes; and
  • it is not straightforward to fully reconcile the data with other information collected more formally by Government.

3.6.5 Consequently it is recommended that the acquisition of data on commercial ticket sales and revenues is put on a more systematic and formal basis. It should be noted that in England, Regulations provide for local authorities to request operators to supply information on ticket sales and revenues, which can be generated from standard accounting systems and can be readily audited.

3.6.6 The shadow fare: the reference fare specified in the National Scheme is the shadow fare, determined for individual concessionary journeys by reference to the passenger's stated destination. Outside Scotland, other methods are used. The shadow fare mechanism used in Scotland gives rise to a number of issues, including the accuracy with which destinations are reported by passengers and recorded by drivers. In addition, the longer transaction times add to bus journey time, both inconveniencing passengers and increasing operating costs.

3.6.7 The alternative method used by a number of English Travel Concession Authorities is to use the average non-concessionary adult cash fare per journey as the reference fare, in other words to assume that the average cash fare paid by non-concessionary passengers is a reasonable proxy for the average cash fare that concessionary passengers would pay in the absence of the concession. The mechanism for collecting this information is usually through periodic returns submitted by each bus operator summarising the number of adult single (and often return) tickets sold, and the associated revenues. These have the advantage of being readily derived from accounting systems and easily audited.

3.6.8 Were the system to move away from using the shadow fare, it would be important to also change the discount factor so that rather than being calculated relative to the average shadow fare (or an estimate of it), it was calculated relative to the average non-concessionary cash fare, or whatever reference fare was adopted.

3.6.9 It is recommended that Transport Scotland examine other methods of identifying the reference fare as an alternative to the Shadow fare.

3.7 Conclusions with regard to Discount Factors

3.7.1 Discount factors provide a way to convert the shadow fare, representing the adult cash single fare that would have been paid for the concessionary journeys actually carried by an individual operator, into an estimate of the average fare forgone associated with those journeys. Discount factors reflect the likelihood that in the counter‑factual, concessionary passholders would purchase a variety of ticket types, including period tickets, rather than just cash single tickets.

3.7.2 Period tickets allow unlimited travel within specified constraints. The average number of journeys made per ticket purchased, and hence the average price per journey, depends upon the relative prices of the ticket types that are available, and the frequency with which passengers make journeys.

3.7.3 The most common method for taking account of period tickets in calculating the average fare forgone uses actual ticket sales data for non-concessionary passengers ("method (a)"). Although data on actual ticket sales and revenues should (in principle) be readily available and auditable, assumptions are needed about the number of journeys made per ticket, and also about how concessionary ticket purchase would differ from non-concessionary passengers.

3.7.4 The estimates described above of the average all-Scotland Discount Factor are based on the data collated by CPT and their advisors, and largely relies on their assumptions about the number of journeys made per period ticket. This would be a major weakness had it not been possible to confirm the overall plausibility of the CPT assumptions about the journeys made per period ticket sale by checking against Transport Scotland data.

3.7.5 Based on the data provided by CPT shown in Table 3.2, our preferred value for the discount factor is 19.2%; a compromise value which is an average of our preferred value and that obtained by CPT is 18.6%.

3.7.6 In the longer term, the fundamental weakness of method (a) is that it relies on unsubstantiated assumptions about the number of journeys made by commercial passengers for each period ticket purchased. These assumptions are fundamental to the calculation of the discount factor. As relative ticket prices change, there is no systematic method for adjusting these assumptions despite the fact that logically, they are bound to vary.

3.7.7 Method (b), which uses observed frequency of concessionary journeys by passholders, provides an alternative which does not suffer from this fundamental weakness, although it also requires some assumptions for which there is little established evidence base. The possibility of moving to a "method (b)" approach should be kept under review by Transport Scotland, especially if a move away from a single all-Scotland Reimbursement Rate were to be contemplated.