Transport User Benefit Calculation

Transcription

1 TAG Unit April 2004 Department for Transport Transport Analysis Guidance (TAG) This Unit is part of a family which can be accessed at

2 Contents 1 Introduction 1 2 Transport user benefits 1 3 Implementing the Sugden Approach 5 4 Impacts on Transport Providers 8 5 Impacts on indirect tax revenue 9 6 Annualisation factors 9 7 Further Information 10 8 References 10 9 Document Provenance 10 This Unit is part of a family which can be accessed at

3 1 Introduction TAG Unit This TAG Unit provides background material on a number of aspects of transport economic efficiency analyses. It covers the following topics: the calculation of transport user benefits; implementing the method of benefit calculation recommended by Sugden; impacts on transport providers; and annualisation factors. 2 Transport user benefits The calculation of transport user benefits is based on the conventional consumer surplus theory. This section discusses the use of consumer surplus theory for the assessment of user benefits and disbenefits and the following section covers the disaggregation of user benefits by mode and by the components of perceived cost. The theoretical analysis outlined below has been incorporated in the Department s standard software package TUBA The transport system exists in order to facilitate a range of activities in the economy and in society at large. Those who use the transport system do so because the inconvenience of having to travel from one location to another is outweighed by the opportunities and potential benefits which arise at the destination. This perhaps gives an exaggerated impression of individuals freedom of choice, since in the short term, having decided to live at A and work at B, the individual then has relatively little choice but to travel from A to B each workday, at least until he or she is able to change his or her long term plan and commitments. Similar arguments could be put for other individual decisions, and for decisions made by businesses and other organisations. Nevertheless, in the longer term, and for the purposes of appraisal, use of the transport system is assumed to be the result of a balanced consideration of pros and cons by each individual decision-maker, subject to all the various constraints which exist Changes in the transport system give rise to changes in the perceived cost of personal travel and freight movement from certain points of origin to certain destinations. This perceived cost is a broadly defined measure of the inconvenience to the user of moving between two points, and includes changes in money costs (such as fares, tolls and expenditure on car fuel). The items to be included when estimating changes in perceived cost for a particular journey are: changes in travel time; changes in user charges, including fares, tariffs and tolls; and changes in vehicle operating costs met by the user (i.e. for private transport) Consumer surplus is defined as the benefit which a consumer enjoys, in excess of the costs which he or she perceives. For example, if a journey would be undertaken by a traveller provided it takes no more than 20 minutes, but not if it takes more than 20 minutes, then the total value of the journey is equivalent to the cost to that traveller of 20 minutes of travel time. If actual travel time for the journey is only 15 minutes, then the traveller enjoys a surplus of 5 minutes. If a new proposal reduces travel time further, to 12 minutes, then the increase in consumer surplus from the proposal is 3 minutes Across all travellers, the change in consumer surplus is the difference between the change in the total benefit enjoyed and the change in the costs perceived. In the simplest case, where time or money costs change, but demand stays the same, the total change in consumer surplus shown in Figure 1 equals: Page 1

4 change in cost * number of travellers = (P 0 -P 1 )*T TAG Unit where P i is the perceived cost of travel (note that the superscript i is used to denote the scenario - 0 for do minimum, 1 for do something), and T is the number of travellers. Unit Cost per Trip P 0 Inelastic demand curve Supply 0 Supply 1 P 1 T Volume of Trips Figure 1 Simple change in Consumer Surplus Where, as is more usual, demand changes in response to the increase or decrease in costs, there is an additional impact on new or lost travellers. With relatively small changes in costs, the convention is to attribute half of the change in costs to the trips lost or gained. The total change in consumer surplus, shown in Figure 2 then becomes: (change in cost * do-minimum demand) = (P 0 -P 1 )T 0 +½(P 0 -P 1 )(T 1 -T 0 ) = ½ (T 0 +T 1 )(P 0 -P 1 ) + (half change in costs * change in demand) Page 2

5 Unit Cost per Trip P 0 Elastic demand curve Supply 0 Supply 1 P 1 Figure 2 Complex change in Consumer Surplus T 0 T 1 Volume of Trips This convention is known as the rule of half, and assumes implicitly that there is a linear relationship between the cost of travel and demand. If this is not the case, and the demand curve is convex to the origin, then the rule of half will tend to overstate the benefits: with very small changes in cost, the inaccuracy is not significant In general, the true situation is highly complex compared with the above. The main substitutes and complements for travel from A to B are travel from A to other destinations, by other modes, using other routes and so on. Notwithstanding this, provided that consistency can be achieved between the pattern of travel demand and the outturn costs - and this is key for the evaluation - the rule of a half formula can be extended to cover network appraisal with many modes and origin/destination pairs. A useful source which discusses the principles and assumptions is Jones (1977) There is a significant caveat to the application of the rule of half formula. Under certain circumstances, the perceived cost of a particular trip (either P 0 or P 1 in the equations and diagrams above) is not defined. This can occur when a mode is either newly-introduced in the do-something case, or when a mode exists in the do-minimum case but is actually removed within the strategy or plan. Typical examples of each are: the introduction of an LRT, in an urban context, or the closure of a rural rail service Faced with the introduction of an entirely new mode (so that perceived cost is in effect infinity for that mode in the do-minimum scenario) the Rule of a Half formula fails. This is discussed in more depth in Alternatives to the rule of a half in matrix-based appraisal. Proceedings of European Transport Conference (Nellthorp and Hyman, 2001) and further advice is available in the TUBA Guidance Special treatment of unperceived costs. Special treatment within the appraisal is required to consider unperceived costs. These are costs that fall on the individual making the journey, but do not influence travel decisions. Non- Page 3

6 working car drivers are assumed not to perceive non-fuel elements of cost, such as tyres, maintenance and depreciation. Changes in non-work car travel can lead to changes in these costs. These net changes must be calculated and added to the results obtained by application of the rule of half formula Disaggregating user benefits. The question naturally arises: who benefits from the option? Will the beneficiaries be rail travellers or car travellers? What share of the benefits accrue to freight traffic and what share to personal travel? Will the gainers be rural or urban dwellers? How will the option affect those in deprived areas relative to those in more affluent districts? At the individual household level, what will be the impact of the option on lower income as against higher income households? What impact will there be on car owners? And non-car owners? These are strictly questions which relate to the distribution and equity supporting analysis but need to be considered in principle here, given that they lie at the heart of the user benefit analysis These sorts of policy-relevant questions can be answered by a carefullydesigned appraisal, but in order to be able to do so, the appraisal needs to feature: a forecasting model which is capable of separating out its forecasts according to these different categories of user and different types of use of the transport system; and a user benefit analysis which preserves these categories and presents its results with an explicit breakdown of the benefits (and costs) by group A clear implication of this is that if there is a particular group within the population whose welfare is of particular policy importance, then both the forecasting model and the user benefit analysis need to be designed from the start to identify the impacts on this group. The Appraisal Process (TAG Unit 2.5) sets out the level of detail likely to be required in the breakdown of benefits, and indicates some extensions which may be desirable to address issues of distribution and equity within the Supporting Analysis There are particular problems in attempting to draw conclusions such as rail users benefit by x million. The difficulty can be seen by considering a corridor served by train and coach services as well as a road (or roads) open to private car drivers. Suppose an option is proposed which is forecast to lead to a substantial increase in use of the rail service and some increase in coach ridership, combined with some reduction in peak hour private car traffic on the road. Rail users in the do-minimum case are clearly different from rail users in the do-something case, so which group is to be considered? Transport models are typically unable to identify individual users behaviour in each case - they can only provide the net effect of complex movements between modes. Thus, it is impossible to say how many travellers switched from road to rail, how many from rail to bus and so on. The dilemma for cost/benefit analysis is that:... while the overall benefit calculation is independent of the details by which individuals change between the before and after situation, the attribution of benefits to particular groups of changers is not. (Common Appraisal Framework, Appendix E, E1.4) In order to address these problems, the approach advocated by Sugden (Section 11 of Sugden, 1999) should be adopted for multi-modal studies. This approach relates the breakdown of benefits by mode of transport to the mode where the benefit occurs (that, is, the source of the benefits), and not to particular groups of travellers. The formula for attributing benefits to modes as the source of those benefits is the rule of a half formula, applied at the modal level, e.g. for mode m: Page 4

7 m m m m 1 Change in consumer surplus RoH m T T P P 2 i j Note that the benefits are given by the initial and final perceived costs on the mode, whatever the cause of the cost change. For example, if an improvement on rail creates decongestion benefits on road, these benefits are attributed to the road mode by the above formulation There is a caveat to this approach. When demand curves shift (for example, because generalised cost has changed on competing or complementary modes simultaneously) there is (theoretically) no unique attribution of benefits by source. In order to carry out a calculation, an assumption is needed that there is symmetry of substitution between alternatives. The appropriateness of this assumption and the implications for benefit estimation are discussed in depth in Jones, In line with his conclusion, and the approaches adopted by the Common Appraisal Framework and Sugden, for practical purposes, when attributing benefits to modes of transport, the appropriate formula remains the rule of a half as expressed in the equation given above. 3 Implementing the Sugden Approach The extent to which the appraisal is disaggregated by mode, purpose, vehicle type, time period, vehicle availability or other category will be for analysts to decide. Whatever choice is made, the following calculations are applicable to the trip matrix for each category It is, however, important to distinguish between work and non-work trips, for two reasons: for non-working trips, some costs are assumed to be unperceived - this requires special treatment; and different (overall) indirect taxation rates apply to work and non-work trips, because VAT is levied only on final consumption (and thus only applicable to non-work trips), whereas duties are levied on all purchases (thus applying to work and non-work trips alike) To accommodate these distinctions, the following discussion will present separate results for work and non-work trips Terms and definitions. This discussion will adopt the same basic notation as is used in Sugden s paper, including the use of the superscript i to denote the scenario - 0 for do minimum, 1 for do something. However, Sugden s notation must be extended by the use of additional subscripts to denote values for specific zone to zone movements. Thus, P i will be used to denote perceived costs for trips from i to j. Terms will be defined as they are introduced, but the following list provides a summary of all the terms used in this paper. S i consumer surplus for travellers between i and j ; P i perceived cost of trip between i and j; F i N i fuel cost of highway trips between i and j, including indirect taxes; non-fuel vehicle operating costs (such as tyres, maintenance, depreciation) of highway trips between i and j, including indirect taxes (note that, for non-work highway trips, N i is assumed to be unperceived); Page 5

8 M i fares, tolls and other charges including parking, for trips between i and j; (Note that, for work trips, values of F i, N i and M i should exclude VAT but include all other indirect taxes.) V i perceived time cost of trips between i and j (note that V i = J i * K T ); J i journey time between i and j; D i distance between i and j; L i fuel consumed between i and j; T i number of trips between i and j; K T K F t t F t F t N t N t M t M value of time; cost of fuel; average rate of indirect tax on final consumption; rate of indirect tax on fuel as a final consumption good; rate of indirect tax on fuel as an intermediate good; rate of indirect tax on non-fuel vehicle operating costs as final consumption goods; rate of indirect tax on non-fuel vehicle operating costs as intermediate goods; rate of indirect tax on fares, tolls and other charges as final consumption goods; rate of indirect tax on fares, tolls and other charges as intermediate goods. (Note that the taxation rates relating to costs as intermediate goods are applicable to work trip costs, while the rates for costs as final consumption goods are applicable to non-work trip costs.) User benefits. In Sugden s paper, user benefits are given by the term (S 1 S 0 ) (1+t) for work trips, and (S 1 S 0 ) - (N 1 N 0 ) for non-work trips The terms (S 1 S 0 ) are the increase in consumer surplus, calculated for transport appraisal using the rule of half: (S 1 S 0 ) = ½ (T1 + T 0 )(P 0 P 1 ) where T i is the number of trips from i to j The term (N 1 N 0 ) is the change in users expenditure on unperceived money costs (those making non-work car trips are assumed not to perceive vehicle operating costs other than fuel - there may be other examples of unperceived money costs). For a matrix based appraisal, (N 1 N 0 ) becomes: Page 6

9 (N 1 - N o ) = T1 N 1 - T 0 N The general definitions of perceived costs are P i = M i + F i + N i + V i for work trips, and P i = M i + F i + V i for non-work trips (The subscripts have been omitted from these equations, for simplicity.) For public transport trips, the terms F i and N i should always be zero. For private transport trips (cars and goods vehicles), the terms M i may be zero, unless tolls or parking charges apply It is important to note that all of the components of perceived costs must reflect the costs perceived by the traveller. This means that money costs (M i, F i and N i ) must include the appropriate indirect taxes. Thus, for non-work trips, the components should be full market prices, inclusive of duties and VAT, where appropriate. For work trips (including goods vehicle trips), the components should exclude VAT but include all other indirect taxes. Thus, for example, the value of a litre of fuel should be the pump price for non-work trips, but should exclude VAT for work trips. Time costs V i should be based on the gross wage rate for work trips, and on individuals willingness to pay for time savings without adjustment for indirect taxation for non-work trips However, for computational purposes, it may be convenient to multiply work trip perceived cost (or its components) by (1+t) before carrying out the calculation of consumer surplus, rather than afterwards The composition of each component in perceived costs is as follows (the subscript is used here to highlight that the costs are required for individual i to j movements): M i F i fares and charges will often not be directly related to distance travelled. For example, tolls may be restricted to selected links in the network, and may be entry point based, rather than distance based. Bus and train fares may vary by route, and do not apply to the access stages of journeys. should be based on fuel consumed and the cost of fuel: F i = K F L i, where K F is the cost per litre of fuel, and L i ji is the number of litres consumed between i and j. The preferred method of calculating L i ji is by application of the formula included in Values of Time and Operating Costs (TAG Unit 3.5.6) (parameters adjusted) on a link by link basis, since this allows variations in speed during the journey to be taken into account. This is not possible within a matrix based appraisal package. An acceptable approximation is: L i = (a + b(d i / J i ) + c(d i / J i ) 2 ) D i where J i is the journey time between i and j, D i is the distance between i and j, and a, b and c are the relevant parameters from Values of Time and Operating Costs (TAG Unit 3.5.6). (This is an approximation because it uses the term D i / J i, the average speed for the journey, rather than separate speed values for each link). Alternative fuel consumption models may also be used, subject to comparison with the standard model. Page 7

10 N i Non-fuel vehicle operating costs, should be based on application of the formula: N i = a D i + b J i where a and b are the parameters given in Values of Time and Operating Costs (TAG Unit 3.5.6). V i Time costs, will be based on journey time and the appropriate value of time: V i = K T J i where K T is the value of time Disaggregating user benefits. The calculations outlined above will produce the overall user benefit. This must be disaggregated into the following components: time; vehicle operating costs; and user charges. This should be done by disaggregating perceived cost and applying the above procedures to each component separately Thus, the disaggregated work trip user benefits are given by the following: user charges: ½ (1 + t) vehicle operating costs: ½ (1 + t) travel time: ½ (1 + t) and for non-work trips: (T1 + T 0 )(M 0 M 1 ) ( T1 + T 0 )(F 0 + N 0 F 1 N 1 ) ( T1 + T 0 )(V 0 V 1 ) user charges: ½ ( T1 + T 0 )( M 0 M 1 ) vehicle operating costs: ½ ( T1 + T 0 )(F 0 F 1 ) T1 N 1 T 0 N 0 travel time: ½ ( T1 + T 0 )( V 0 V 1 ). 4 Impacts on Transport Providers Revenues are given by the following equation: (M 1 M 0 ) = T1 M 1 T 0 M 0 for both work and non-work trips. Although fares and some other charges (onstreet parking for example) do not attract VAT, these revenues must be converted to the market price unit of account by uprating by a factor of (1+t) where t is equal to the average rate of indirect taxation on final consumption. Where revenues do include VAT, this must be removed and the resulting value (in factor cost unit of account) should be uprated by (1+t). Together, these adjustments make consistent the treatment of transport provider revenues with other values in the appraisal, including operating and construction costs. Page 8

11 4.1.2 Formulations for public transport operating costs are less well established than for private vehicles (cars and goods vehicles) and may differ from study to study. However, it is important that these elements of the appraisal are tackled - entering zeros will certainly give rise to misleading results Where possible, advice should be taken from the appropriate operators. However, care will need to be taken to ensure that costs exclude any elements of investment costs and subsidies, since these are dealt with separately. Costs should also exclude VAT which is recoverable by the operator, but should include duties and other indirect taxes (fuel duty rebates should be treated as subsidy). All costs incurred by operators should be multiplied by (1+t) to convert them to the market prices unit of account In the absence of better advice, operating costs for buses may be determined using the PSV operating cost models specified in Values of Time and Operating Costs (TAG Unit 3.5.6), applied as for other road vehicles - see paragraph 3.12 above. 5 Impacts on indirect tax revenue The impacts on indirect tax revenue are not part of the Transport Economic Efficiency analysis but are part of the Public Accounts analysis. They are included here because the calculations are closely related to those carried out for the TEE analysis The changes in indirect tax revenue are a little more complicated: work trips: (F 1 - F 0 ) t F (1 + t)/(1 + t F ) + (M 1 - M 0 ) t M (1 + t)/(1 + t M ) + (N 1 - N 0 ) t N (1 + t)/(1 + t N ) non-work trips: (F 1 - F 0 ) (t F - t)/(1 + t F ) + (M 1 - M 0 ) (t M - t)/(1 + t M ) where + (N 1 - N 0 ) (t N - t)/(1 + t N ) (F 1 - F o ) = (M 1 - M o ) = (N 1 - N o ) = T1 F 1 - T 0 F 0 T1 M 1 - T 0 M 0 T1 N 1 - T 0 N 0 6 Annualisation factors For the purpose of applying the output from the model in the appraisal of an intervention, it is important to develop techniques for the expansion of the data from the modelling periods so that it represents a full year. A number of separate annualisation factors may need to be developed to represent each of the modelled periods, and these factors may need to consider the relative use of different modes at different times of the day, days of the week and months of the year Different annualisations may be required to represent vehicle flows, modal shifts to public transport and congestion relief. This need arises since in urban Page 9

12 transport systems, where there is significant congestion the propensity to transfer modes and generate congestion relief benefits increases more than proportionately with the level of demand. In the case of an inter-urban study, where congestion may be less of a issue single annualisation factors may be appropriate for flows, modal shifts and congestion relief. 7 Further Information The following documents provide information that follows on directly from the key topics covered in this TAG Unit. For information on: See: TAG Unit number: Breaking down the benefits of transport options to specific groups of society. The Appraisal Process TAG Unit 2.5 Cost Benefit Analysis Costs Benefit Analysis TAG Unit Public Accounts Transport Economic Efficiency The Public Accounts Sub- Objective The Transport Economic Efficiency Sub-Objective TAG Unit TAG Unit References Jones (1977) Urban Transport Appraisal published by Macmillan London Nellthorp J and G Hyman (2001) Alternatives to the rule of a half in matrix-based appraisal. Proceedings of European Transport Conference. ITEA (Mar 2001) Transport Users Benefit Appraisal User Manual, TUBA User Guidance with accompanying TUBA software The MVA Consultancy, Oscar Faber TPA and ITS, Leeds (1994). Common Appraisal Framework for Urban Transport Projects. Report to Birmingham City Council and the Department of Transport Sugden (1999) Review of cost/benefit analysis of transport projects 9 Document Provenance This Transport Analysis Guidance (TAG) Unit is based on part of Appendix F of Guidance on the Methodology for Multi-Modal Studies Volume 2 (DETR, 2000), updated to take account of the amendments set out in GOMMMS Errata (DETR, 2000). Technical queries and comments on this TAG Unit should be referred to: Integrated Transport Economics and Appraisal (ITEA) Division Department for Transport Zone 3/08 Great Minster House 76 Marsham Street London SW1P 4DR itea@dft.gsi.gov.uk Tel Fax Page 10