A B C D E F G H I J K L
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Concessionary Travel for Older and Disabled People: Guidance on
6 Reimbursing Bus Operators
7 Reimbursement Calculator
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9 Version 2.2 Issued: 16 February 2011
Note Paragraph reference in
10 Reference Introduction DfT guidance
This spreadsheet tool is designed to assist Travel Concession Authorities (TCAs) and operators in calculating reimbursement due from
concessionary fares schemes. It should be used in conjunction with the appropriate written DfT guidance, the latest version of which can be
11 found on the DfT website.
The written guidance, and this calculator, set out DfT preferred methodology for calculating reimbursement based on the best available
evidence. TCAs may use the methodology of their choice in calculating reimbursement for bus operators, subject to consistency with the
12 objective that operators are left no better and no worse off. It is vital that users refer to the guidance when using this calculator.
Hyperlinks are provided throughout this model to assist in its use. Clicking on the relevant note number to the left of the various rows in the
analysis worksheets will bring you back to this instructions sheet and the relevant detailed note. Clicking on the note reference on this sheet
will take you back to the relevant section of the analysis sheet. To the right of the notes on this page are paragraph references to the DfT
13 written guidance. Buttons are also provided to help navigation between different sections.
This tool is subdivided into 6 separate worksheets. The Start Page, the Average Fares (AF) Model, the Reimbursement Factor (RF) Model, the
Additional Costs (AC) Model, the Marginal Capacity Cost Model (MCC) and the Results Page. The steps within each of these worksheets are
described below. Additional hidden worksheets contain the detailed calculations underpinning the calculations for Average Fares and the
Reimbursement Factor. All Additional Costs calculations are done in the model sheets. A worked example for MCC costs is provided in 'MCC
example' and the 'PTE' and 'Non-PTE' sheets show the derivation of the Single Demand Curve . Hidden sheets can be unhidden by going to
Format\Sheet\Unhide. All worksheets are protected except for the cells where data need to be entered to prevent overwriting formulae
by mistake. A worksheet can be unprotected by going into Tools\Protection\Unprotect Sheet. Annex D of the guidance includes some
14 worked examples based on this Calculator.
15 Calculator cells are colour-coded as follows:
16 Key User input
17 Calculation or DfT assumption that cannot be overwritten
18 Output (Intermediate/Final)
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20 Instructions for use
21 Start Page (Step 1)
22 1 Choose the suitable area type (PTE or Non PTE). 6.11-6.16
23 2 Choose the suitable period/year for which reimbursement is being calculated.
24 3 Enter the number of observed concessionary journeys in the relevant period/year. 4.1-4.2
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26 Average Fare Calculator (Step 2)
Choose the appropriate method with which to calculate the average fare forgone in Cell [C10]. The choices available are presented by
buttons. Clicking on the 'Discount Factor Method' button directs users to Cell [B16] to use the discount factor calculator. Clicking on the
"Basket of Fares Method" button directs users to Cell [B33] to use the basket of fares template. Clicking on the "Enter Average Fare Forgone
directly" button directs users to Cell [C10] where the average fare forgone can be entered directly. Please refer to the guidance for
27 4 application guidelines. 5.5-5.13
28 5 The Discount Factor Method 5.14-5.34
This method consists in calculating a discount factor to adjust the full commercial adult cash fare so as to reflect the fact that in the absence
of free-fare schemes, individuals would buy cash fares as well as discounted tickets. The discount factor is based on the prevailing ticket
price structure of an operator and the trip distribution of concessionary travellers at zero fare suitably abated to allow for degeneration.
There are two options. (1) Clicking on the "Use templates to calculate average ticket prices" will take users to Cell [B55] where the template
can be used to estimate the cash fare. Clicking on the "Calculate daily ticket price" button takes users to Cell [B69] which contains the
appropriate template. Clicking on the "Calculate weekly ticket price" button takes users to Cell [B83] where the appropriate template is
available. Clicking on the "Done" button after entering appropriate values will redirect users to the next step and associated Average Fare
Foregone in [C10]. (2) Clicking on the "Enter average ticket prices directly" will take users to Cell [C21] where average fares for cash fares,
29 daily and weekly tickets can be entered.
30 6 Enter the average cash fare for the calculation period. 5.27-5.30
31 7 Enter the average daily fare for the calculation period. 5.27-5.30
Enter the average weekly fare or the calculation period. If there are no weekly tickets available, click on button 'No weekly tickets' and the
32 8 Calculator will automatically input an extremely high average weekly ticket price so that no trips are allocated to that ticket type. 5.27-5.30
33 9 Discount factor before degeneration: This is the discount factor at zero fares. D20
34 10 FINAL discount factor after degeneration: This is the discount factor at full fares. D20
35 11 Discounted average fare (forgone): this is the average cash fare discounted by the discount factor. 5.31
This table shows the final allocation of ticket types. If the proportion of daily or period ticket to cash fare ticket sales is higher for
36 12 concessionary passengers than current fare paying passengers, the discount method may not be appropriate. 5.10
37 13 Basket of Fares Method 5.35-5.44
This method allows to estimate the effective discount rate by calculating a weighted average fare per journey from assumed usage of
38 different commercial ticket types.
A B C D E F G H I J K L
Type of Ticket: Enter all the ticket types that would have been purchased by concessionary passholders in the absence of the scheme.
39 14 Operators or survey evidence will be helpful in deciding which tickets to include. 5.38
Price £: Enter the commercial price of each type of ticket that would have been purchased by concessionary passholders in the absence of
40 15 the scheme. 5.38
Assumed journeys per ticket purchased: Enter assumed number of journeys typically made by holders of each ticket type. Although this is
reasonably obvious for single and return tickets, it requires some judgements to be made on the use of pass-type tickets. Again hard
41 16 evidence from operators or surveys will be helpful in deciding what assumptions to make here. 5.39-5.40
Implied Revenue per journey £: This is the ticket price for each ticket type divided by the number of journeys typically made by
42 17 concessionary passholders. 5.42
% of total journeys with this ticket type: Assumed proportion of total journeys that are made by eligible concessionaires in the absence of
43 18 the scheme using each type of ticket. These must add up to 100 per cent. 5.41
Weighted Revenue per Ticket: This is the implied revenue per journey multiplied by the percentage share of journeys made with each ticket
44 19 type. 5.42-5.43
45 20 Weighted Average Fare: This is the average fare forgone calculated under the basket of fares method.
Average Fare Forgone: This cell displays the average fare forgone to be used in the calculation of the appropriate reimbursement factor
46 21 based on the chosen method of calculation.
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48 22a Reimbursement Factor Calculator (Step 3)
Reimbursement Factor Calculator: The reimbursement factor is the proportion of total concessionary journeys made at zero fare that are
estimated to be made if the concessionaires were to pay full fare. The reimbursement rate is calculated based on the appropriate demand
49 curve and the change in the average fare foregone calculated in the AF Worksheet. 6.4-6.10
In this section users can opt for one of three methods to input a change in nominal fares in the Model using the appropriate buttons. In all
cases, from 2010/11 onwards, it is the operator-specific nominal fare change that is used except in the case of new operators. Option (1)
The change in operator-specific nominal fares between 2005/06 and the year of calculation is used. Option (2) The change in TCA-wide
nominal fares between 2005/06 and 2010/11 is used. From 2010/11, the change in operator specific fares is used. Option (3) In the absence
of appropriate data, a national bus index and the CPI index can be used between 2005/06 and 20010/11 and then the change in operator-
specific fares from 2010/11. For new operators, the change in TCA wide nominal average fare between 2005/6 and current reimbursement
50 22b period can be entered. 6.17-6.32, D.27-D.28
51 23 Area Type: Displays the relevant area type (PTE or Non-PTE) that was chosen in the Start Page. 6.17-6.32, D.27-D.28
52 24 Year: Displays the relevant period for which reimbursement is being calculated as chosen in the Start Page. 6.17-6.32, D.27-D.28
Current Average Fare: Displays the average fare forgone for the period for which reimbursement is being calculated in the Average Fare
53 25 Calculator. 6.17-6.32, D.27-D.28
Reimbursement Factor: Generates the reimbursement factor from the single demand curve for the area type and average fare forgone
54 26 based on the changes in local fares (PTE or non-PTE) 6.17-6.32, D.27-D.28
Percentage change in the operator specific nominal fares between 2005/06 and the period for which reimbursement is being calculated:
55 27 This is estimated from comparable operator fare data, and is a nominal change. It is entered as a percentage. 6.17-6.32, D.27-D.28
TCA-wide change in nominal average fares. Two data items need to be entered: the change in TCA-wide nominal fares from 2005/06 to
2010/11 and from 2010/11 to the reimbursement period (for reimbursement periods beyond 2010/11) the change in the operator-specific
56 28 nominal fares. 6.17-6.32, D.27-D.28
Enter TCA-wide change in nominal fare between 2005/06 and 2010/11. This is the percentage change in the TCA average fare between
2005/06 and 2010/11 in nominal terms. It is entered as a percentage.
57 29 6.17-6.32, D.27-D.28
Enter operator specific change in nominal fare between 2010/11 and current reimbursement period (if reimbursement is calculated in latter
years). This is the percentage change in the operator specific fare for comparable operator fare data, and is a nominal change. It is entered
58 30 as a percentage. 6.17-6.32, D.27-D.28
Option (3) National Bus Fare Index: This is the average change in fares by broad area derived from the DfT’s bus fare index, but using general
estimates for 2005/06 and 2010/11 for which comparable data is not available. The Calculator already holds this data, so there is no need to
59 31 enter data apart operator-specific data from 2010/11 onwards. 6.17-6.32, D.27-D.28
Percentage change in operator specific nominal fare between 2010/11 and current reimbursement period. This is the percentage change in
60 32 the operator specific fare for comparable operator fare data, and is a nominal change. It is entered as a percentage. 6.17-6.32, D.27-D.28
61 33 New operator: This is the section for operators who are new or who have had significant changes in services since 2010/11. 6.17-6.32, D.27-D.28
Enter TCA wide change in nominal fare between 2005/06 and current reimbursement period: This is the percentage change in the TCA
62 34 average fare between 2010/11 and current reimbursement period in nominal terms. It is entered as a percentage. 6.17-6.32, D.27-D.28
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64 35 Additional Costs Calculator (Step 4)
Additional costs are split into up to 4 distinct elements. These are scheme administration costs, marginal operating costs, marginal capacity
65 costs and Peak Vehicle Requirement (PVR). 7.1-7.5, 7.6
66 36 Reimbursement Period: Displays the reimbursement period chosen in the Start Page
67 37 Administration costs are those costs to the operator from the scheme such as publicity, timetables etc.
68 38 Enter Administration Costs: Enter locally determined administration costs 7.7-7.9
Marginal Operating Costs: These are the additional costs to the operator for carrying one additional passenger assuming a fixed service level
and include fuel, tyres and oil, maintenance etc. The calculator automatically uprates unit marginal operating costs for inflation (using the
69 39 GDP Deflator) for the relevant reimbursement period. 7.10-7.11
Fixed Element (£): This is the fixed component of the marginal operating costs per additional concessionary passenger. This is equal to 4.2 p
70 40 in 2009/10 prices 7.13-7.14
Journey Length: The marginal operating cost can also be varied by journey length. You can either use the default national average journey
length (NTS) of 3.9 miles, or choose a journey length that is locally derived. If there is evidence to suggest that the local journey length is
significantly different from this default, choose "Use Local Value" in the drop down menu in Cell [C9] to enter a locally derived journey
71 41 length in Cell [D10]. 7.13-7.14
72 42 Variable Element (£): This calculates the variable element of the marginal operating cost with the chosen average journey length. 7.13-7.14
73 43 Total Marginal Operating Costs: Displays total marginal operating costs uprated to the year of calculation. 7.13-7.14
Marginal Capacity Costs Button: Click on this button to get to MCC Model. Marginal Additional Capacity Costs are the costs to the operator
of carrying additional passengers and allowing the additional capacity of the bus to increase by using the existing fleet of buses more
74 44 intensively to provide increased frequency. The calculator automatically uprates unit marginal operating costs for inflation (using the GDP 7.19-7.51, D.42-D.63
A B C D E F G H I J K L
Peak Vehicle Requirement Costs: These are the costs associated with the requirement to run additional vehicles in the peak period due to
generated concessionary travel. Where the operator supplies information for a claim for additional peak vehicle costs, the appropriate level
75 45 of PVR costs should be calculated off model. 7.52-7.67
76 46 Enter total Peak Vehicle Requirement Costs 7.52-7.67
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78 Marginal Capacity Costs Model (Step 5) 7.19-7.51, D.42-D.63
This Calculator can be used to estimate MCCs for a whole network (use the first line only) or for all the routes within a network separately
(use multiple lines). To activate calculation for a particular line, select 'Yes' in dropdown menu. 7.22 There is a presumption that marginal
capacity costs could potentially apply to all routes within a network. However, it is not expected that there will be positive marginal capacity
costs on every route. It is important that when using the Calculator on a route by route basis the data can be audited and that the Calculator
is used for all routes and a not a selected sample that could bias any results. It is also important that where local values are used they must
be consistent with. So for example: if the local route length is longer, the trip length is likely to be longer, the average speed higher and
79 47 the average fare higher. Please refer to Guidance Para 7.24-7.25. 7.19-7.51, D.42-D.63
80 48 Enter Route/Network description. 7.19-7.51, D.42-D.63
81 49 The generation factor estimated in the RF model. 7.19-7.51, D.42-D.63
82 50 The total concessionary trips on a route/network. 7.19-7.51, D.42-D.63
Mohring Power: This is the relationship between demand and bus service level. This is set at 0.6 as a network average and applied to all
83 51 routes. 7.19-7.51, D.42-D.63
The unit cost per bus hour is a network average (set at £13.30 per veh/hour) and applied to all routes. The amount is adjusted for inflation
84 52 to the year of calculation. 7.19-7.51, D.42-D.63
The unit cost per bus mile (set at £0.61 per bus mile) is a network average and applied to all routes. The amount is adjusted for inflation to
85 53 the year of calculation. 7.19-7.51, D.42-D.63
Speed (miles per hour): This is the average bus speed (including turns) for the route/network. The default value is a national average of 8.79
miles/hour for PTE areas and 10.03 miles for Non-PTE areas (first line). If there is evidence to suggest that bus speed for your local area is
significantly different from these averages, choose "Use Local Value" from the drop down menu in the second line and enter local value in
second line. The Comparison of Urban Bus Systems (CUBS) website (follow link: http://cubs.reseaulutions.com/towninformation-
86 54 overview.php) contains average bus speed data by area type. 7.19-7.51, D.42-D.63
Mean Vehicle Occupancy: The default average is 10 passengers per bus mile. If there is evidence to suggest that the mean vehicle occupancy
for the local area under consideration is different, choose "Use Local Value" in the drop down menu and enter local average in the second
87 55 line. 7.19-7.51, D.42-D.63
Mean trip length: The default average is 3.1 miles in PTEs and 3.6 miles in NPTEs. If there is evidence to suggest that the mean vehicle
occupancy for the local area under consideration is different, choose "Use Local Value" in the drop down menu and enter local average in
88 56 the second line. 7.19-7.51, D.42-D.63
Mean route length: The default average is 6.2 miles in PTEs and 7.1 miles in NPTEs. If there is evidence to suggest that the mean vehicle
occupancy for the local area under consideration is different, choose "Use Local Value" in the drop down menu and enter local average in
89 57 the second line. 7.19-7.51, D.42-D.63
Average Commercial Adult Fare: Enter the locally derived average adult commercial fare in the relevant reimbursement period for the
90 58 route/network. 7.19-7.51, D.42-D.63
Commercial journeys as a percentage of the total: The default average value provided is 60%. If there is evidence to suggest that commercial
journeys as a percentage of the total is significantly different, choose "Use Local Value" from the drop down menu and enter local value in
91 59 second line. 7.19-7.51, D.42-D.63
This is the service or frequency elasticity. It measures the responsiveness of demand to changes in frequency. It is set at 0.66 as a network
92 60 average and is applied to all routes/the network. 7.19-7.51, D.42-D.63
This is the calculated rate of marginal capacity cost per additional (generated) concessionary passenger by route or for the network. It allows
93 61 for inflation to the year of calculation and is capped at £0.00 (is not allowed to be negative) if the revenue gain from additional commercial 7.19-7.51, D.42-D.63
This is the total amount of marginal capacity cost for each route/the whole network. It is calculated as a generation factor x concessionary
94 62 trips on route/network x MCC per generated trip. Unit costs (and hence MCCs) are adjusted for inflation automatically in the calculator each 7.19-7.51, D.42-D.63
95 63 This is the total generated concessionary journeys on all routes (across all activated lines). An error message appears if the sum of all 7.19-7.51, D.42-D.63
96 64 This is the total marginal capacity costs on all routes (across all activated lines) 7.19-7.51, D.42-D.63
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98 65 Result Page (Step 6)
Observed Concessionary journeys: Displays the number of concessionary journeys observed in the relevant reimbursement period as
99 66 entered in the Start Page.
100 67 Average Fare Forgone: Displays the average fare forgone as derived in AF Model.
101 68 Reimbursement Factor: Displays the reimbursement factor as derived in the RF Model. 3.5-3.7
Total Reimbursement for Revenue Forgone: Calculated as Observed Concessionary journeys x Reimbursement Factor x Average Fare
102 69 Forgone.
103 70 Generation Factor: This is the 1- Reimbursement Factor%.
104 71 Additional Marginal Operating Cost per Journey: Displays the marginal operating cost per journey calculated in the AC Model.
105 72 Total Marginal Operating Costs: calculated as total concessionary trips x Generation Factor x MOC in pence per trip.
106 73 Display Scheme Administration Costs entered in AC model.
107 74 Total Marginal Capacity Costs calculated in MCC model.
108 75 PVR Costs: Displays Peak Vehicle Requirement Costs entered in AC Model.
Total Reimbursement for Additional Costs: Calculated as Generation Factor x Concessionary journeys x (Marginal Operating Cost per journey
109 76 + Marginal Capacity Cost per journey) + Peak Vehicle Requirement costs.
110 77 Total Reimbursement: Calculated as Total Reimbursement for Revenue Forgone + Total Reimbursement for Additional Costs.
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Start Page
1 Area Type PTE
2 Year 2009/10
3 Observed Concessionary Journeys
Average Fare Calculator
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21 Average Fare Foregone #DIV/0!
5 Discount Factor Method
Ticket prices (£)
6 Average cash fare
7 Average daily ticket price #DIV/0!
8 Average weekly ticket price
9 Discount factor before degeneration #DIV/0!
10 FINAL discount factor #DIV/0!
11 Discounted Average Fare #DIV/0!
13 Basket of Fares Method
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Type of ticket Price £ Assumed journeys Implied revenue per
per ticket purchased journey (£s)
Total
20 Weighted Average Fare:
22 Estimation of Average Fare Foregone using Discount Fare Method - Template
23 CASH FARE 24 25 26
Number of tickets
Product Single journey multiplier Total revenue (£)
sold
Total all cash fares £0
Average cash fare (per journey)
DAY TICKETS
Product Number of tickets sold Total revenue (£)
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Total all day tickets 0 £0
Average day ticket price #DIV/0!
WEEKLY TICKETS
Product Number of tickets sold Total revenue (£)
Total all weekly tickets 0 £0
Average weekly ticket price #DIV/0!
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Final allocation of tickets (after degeneration)
Ticket Type %
Cash Fare #DIV/0!
Daily #DIV/0!
Weekly #DIV/0!
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% of total journeys Weighted revenue per
with this ticket type ticket
0%
Weighted Average Fare: £0.00
Equivalent number of
journeys
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#DIV/0!
22a Reimbursement Factor Calculator
22b Choose option for change in fares
23 Area Type
24 Year
25 Current Average Fare Forgone
26 Reimbursement Factor
OPTIONS
Option (1) Percentage change in operator-specific nominal fares between 2005/6 and the current
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28 Option (2) TCA-wide change in nominal average fares
29 Enter TCA-wide percentage change in nominal fare between 2005/6 and 2010/11
30 Enter operator-specific percentage change in nominal fare between 2010/11 and current reimbursement period
31 Option (3) National Bus Fare Index
32 Percentage change in operator specific nominal fare between 2010/11 and current reimbursement period
33 New Operator
34 Enter TCA-wide percentage change in nominal fare between 2005/6 and current reimbursement period
PTE
2009/10
#DIV/0! Fare from Average Fare Model
#DIV/0!
A B C D
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A B C D E F G H I J K L M N O
1 Marginal Capacity Cost Calculator Area Type PTE
2 Year 2009/10
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Total
Cost/Veh Mean vehicle
Activate Generation Concessionary Mohring Cost /bus Mean Trip Mean route length
Network/Route icle Hour Speed (mph) occupancy (per bus
calculation Factor (%) Trips on Power mile (£) Length(miles) (miles)
(£) mile)
Network/Route
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P Q R S T U V BA BB BC BD BE BF BG BH BI BJ
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Net additional
Average Commercial Total net
Service capacity cost
commercial Journeys as a % of costs for the
elasticity per generated
adult fare (£) Total route
passenger trip
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BK BL BM BN BO BP BQ BR BS BT BU BV BW BX BY BZ CA CB CC CD
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83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
BK BL BM BN BO BP BQ BR BS BT BU BV BW BX BY BZ CA CB CC CD
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
BK BL BM BN BO BP BQ BR BS BT BU BV BW BX BY BZ CA CB CC CD
155
156
157
158
159
160
CE CF CG CH CI CJ CK CL CM CN CO CP CQ CR CS CT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
CE CF CG CH CI CJ CK CL CM CN CO CP CQ CR CS CT
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
CE CF CG CH CI CJ CK CL CM CN CO CP CQ CR CS CT
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
CE CF CG CH CI CJ CK CL CM CN CO CP CQ CR CS CT
155
156
157
158
159
160
A B C D E F G H
1 65 Result page
2
3 Area Type PTE
4 Year of Calculation 2009/10
5
6
7
8 Revenue Forgone
9
10 66 Observed Concessionary Journeys 0
11 67 Average Fare Forgone (£) #DIV/0!
12 68 Reimbursement Factor (%) #DIV/0!
13 69 Total Reimbursement for Revenue Forgone (£) #DIV/0!
14
15 Additional Costs
16
17 70 Generation Factor (%) #DIV/0!
18 71 Marginal Operating Costs (£ per trip) £0.072
19 72 Total Marginal Operating Costs (£) #DIV/0!
20 73 Scheme Administration Costs (£) £0
21 74 Total Marginal Capacity Costs (£) £0
22 75 PVR Costs (£) £0
23 76 Total Reimbursement for Additional Costs #DIV/0!
24
25
26 77 Total Reimbursement #DIV/0!