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TAG Unit 3.5.3: Transport User Benefit Calculation
April 2004
 Unit 3.5.3 (Adobe Acrobat - 202kb)
1. Introduction
2. Transport User Benefits
3. Implementing the 'Sugden' Approach
4. Impacts on Transport Providers
5. Impacts on Indirect Tax Revenue
6. Annualisation Factors
7. Further Information
8. References
9. Document Provenance
1. Introduction
1.1.1 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
2.1.1
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.
2.1.2
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.
2.1.3
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).
2.1.4
'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.
2.1.5
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:
where Pi 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.
Figure 1 Simple change in
Consumer Surplus
2.1.6
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:
Figure 2 Complex change in
Consumer Surplus
2.1.7
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.
2.1.8
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).
2.1.9
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 P0 or P1 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.
2.1.10
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.
2.1.11
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-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.
2.1.12
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.
2.1.13
These sorts of policy-relevant questions can be
answered by a carefully-designed 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.
2.1.14
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.
2.1.15
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).
2.1.16
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:
2.1.17
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.
2.1.18
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, 1977.
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
3.1.1
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.
3.1.2
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).
3.1.3
To accommodate these distinctions, the following
discussion will present separate results for work and non-work
trips.
3.1.4
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, Piij 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.
3.1.5
User benefits.
In Sugden's paper, user benefits are given by the term
3.1.6
The terms (S1 - S0) are
the increase in consumer surplus, calculated for transport appraisal
using the rule of half:
where Tiij is the number of trips from
i to j.
3.1.7
The term (N1 - N0) 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, (N1 - N0)
becomes:
3.1.8
The general definitions of perceived costs
are
(The ij subscripts have been omitted from these equations,
for simplicity.).
3.1.9
For public transport trips, the terms Fi
and Ni should always be zero. For private transport
trips (cars and goods vehicles), the terms Mi may
be zero, unless tolls or parking charges apply.
3.1.10
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 (Mi, Fi and Ni)
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 Vi 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.
3.1.11
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.
3.1.12
The composition of each component in perceived
costs is as follows (the subscript ij is used here to highlight
that the costs are required for individual i to j movements):
Miij
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.
Fiij
should be based on fuel consumed and the cost of fuel:
Fiij = KFLiij,
where KF is the cost per litre of fuel, and
Liij is the number of litres consumed
between i and j. The preferred method of calculating
Liij 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:
where Jiij is the journey time between
i and j, Diij 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 Diij
/ Jiij, 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.
3.1.13
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.
3.1.14
Thus, the disaggregated work
trip user benefits are given by the following:
4. Impacts
on Transport Providers
4.1.1
Revenues are given by the following equation:
for both work and non-work trips. In this calculation, fares
and charges Miij should include all
appropriate duties and VAT. Although fares and some other
charges (on-street 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.
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.
4.1.3
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.
4.1.4 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
5.1.1
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.
5.1.2
The changes in indirect tax revenue are a little
more complicated:
6. Annualisation
factors
6.1.1
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.
6.1.2
Different annualisations may be required to
represent vehicle flows, modal shifts to public transport
and congestion relief. This need arises since in urban 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 |
8. 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).
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 020 7944 6176
Fax 020 7944 2198
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