A Cost-Benefit Analysis of Rural Secondary School Consolidation

A Cost-Benefit Analysis of Rural Secondary School
Consolidation: A Report To Gwynedd County
Council
James Foreman-Peck
Welsh Institute for Research and Development
Cardiff Business School
April2011

A Cost-Benefit Analysis of Rural Secondary School Consolidation
Contents
Page
Executive Summary 4
1. Introduction 6
2. Measurement Issues 7
3. Cost per Pupil and School Size 7
4. ‘Empty Places’ and Cost per Student 9
5. Increased Student Travel Time 9
6. Additional Vehicle Operating Costs 11
7. Local Incomes and Employment 12
8. Disposal of School Site 14
9. Educational Achievement and School Size 14
10. Summary 16
Appendix A Gwynedd secondary school cost functions 2002-2010 18
Appendix B Pupil travel costs and times for incremental travel costing 20
2

List of Tables
Page
Table 1 Benefits and Costs from School Consolidation 6
Table 2 Ancillary Staff Costs: An Illustration for a Small Gwynedd Secondary
School 13
Table 3 Estimated Costs and Benefits from Rural Secondary School Consolidation
16
Table A1 Per pupil Gwynedd secondary school panel cost functions 2002-2010
19
List of figures
Figure 1 Budget cost per pupil in relation to school size, Wales 2009-10 8
Figure 2 Gwynedd school size and KS3 performance 22
Figure 3 Gwynedd secondary school size and predicted pupil cost 22
Figure 4 Gwynedd school predicted pupil cost and KS3 performance 23
3

A Cost-Benefit Analysis of Rural Secondary School Consolidation
Executive Summary
1. This cost-benefit analysis of rural secondary school consolidation
aims to take into account all the major relevant social and economic
impacts of the policy in accordance with H M Treasury guidelines. As
Treasury documentation makes clear in the context of central
government, an education authority focus exclusively on financial
outlays is not required by the pursuit of efficiency and effectiveness
on behalf of the taxpayer when the authority has other policies and
obligations to take into consideration as well.
2. A hypothetical example is studied in which a rural secondary school
of 350 pupils is closed and the students distributed to two others,
one a school initially also of 350 and one initially of 500. This
reconfiguration can be expected to reduce authority financial costs
per pupil and ‘empty places’. But it does so by imposing other costs
on the authority through its obligations to provide more transport
for the students who must now travel greater distances.
3. In addition greater costs are imposed upon the pupils, who must
spend more time travelling. Standard UK transport project appraisal
procedures value such extra time saved or spent and therefore
consistency in the allocation of public funds requires that school
consolidation policies should do so as well.
4. A third cost imposed by the hypothetical school closure is a loss of
local income and employment- with the attendant social disruption.
While the relocation may be expected to benefit income and
employment in other local communities, the authority may not
consider this redistribution as consistent with their social policies.
5. On the benefit side of the policy balance there may be educational
payoffs for students in larger schools of the size considered here. An
attempt is made to estimate their monetary value – that is how
much extra must be spent to obtain equivalent educational
performance in the school configuration before the hypothetical
consolidation, compared with how much after. Even more
4

uncertainty is attached to the disposal value of the hypothetical
school site. Therefore a sensitivity analysis is conducted to see what
values are sufficient to tip the net benefit balance between positive
and negative.
6. The conclusion of the study is that comparing the above costs and
benefits, calculated on as plausible and as robust assumptions as
possible, yields a negative balance from the hypothetical school
closure. What this means is that the authority would not be obliged
on grounds of efficiency and effectiveness to close the rural school.
However, if for example, the authority decided that it was
appropriate to shift the full costs of educational provision more on
to students and away from the taxpayer, it might chose to do so, at
least if other policies affecting the remaining components of the
cost-benefit analysis also pointed to such a decision.
5

A Cost-Benefit Analysis of Rural Secondary School Consolidation
1. Introduction
This report is an appraisal, broadly following the guidelines laid down in HM
Treasury's Green Book, of secondary school closure policy. The Welsh Assembly
Government is signed up to following this Treasury guidance on project and
programme appraisal and evaluation. Although the guidance refers to ‘central
government’, local authorities are mainly funded from the centre, and therefore
the use of the same principles for ensuring effectiveness, efficiency and economy
in public spending makes sense.
The Treasury states that the Green Book principles are relevant
‘to any analysis used to support a government decision to adopt a new policy, or
to initiate, renew, expand or re-orientate programmes or projects, which would
result in measurable benefits and/ or costs to the public.’ (S1.8)
The guidance recommends procedures for cost-benefit analysis – in particular for
valuations of outcomes. This involves taking into consideration wider social
impacts as well as immediate financial outlays and savings.
‘Wider social and environmental costs and benefits for which there is no market
price also need to be brought into any assessment. They will often be more
difficult to assess but are often important and should not be ignored simply
because they cannot easily be costed’. (s5.12)
Such social costs and benefits might include quality of educational provision, as
well as the educational experience of the pupil in the wider sense such as travel
time, length of day, and safety.
The present report considers the following cost and benefits of rural secondary
school consolidation;
Table 1 Benefits and Costs from School Consolidation
Benefits
Costs
Lower school cost per Greater student travel
pupil
times
Lower cost per level of Greater student travel
education achievement costs
Redundant school site Loss of rural community
disposal
income and employment
6

2. Measurement Issues
To weigh costs against benefits of secondary school consolidation both must be
in comparable time units and preferable valued in monetary terms.
Conventionally magnitudes are capitalised into present values but the present
study instead considers annual flows of benefits and costs. It does so because
education provision is a permanent obligation (there is no project end point) and
because projecting costs and benefits into the future creates additional
uncertainties and margins of error, which it is judged desirable to do without. So
implicitly this exercise assumes that conditions this year will continue into the
future.
While financial outlays are readily available, other costs and benefits are less
easily measured in monetary terms, which may explain, but not justify, why
they are often ignored in assessing the merits of a policy. In the case of travel
time, (English) Department of Transport estimates are widely used. But the
value of a local community or of the quality of educational provision is more
problematic. On occasion, as will be shown below, an analysis allows these
intangibles to be treated as residuals so that values at which the policy decision
would be altered can be calculated, and compared with policy makers’
judgements.
3. Cost per Pupil and School Size
The apparent financial advantages of school consolidation are illustrated by
figure 1. Each cross represents a particular school. The figure shows the fall in
costs per pupil with secondary school size in Wales in 2010. There is a
substantial scatter around the line of best fit because other school characteristics
may influence costs, as well as size. But the relationship is helpful because
secondary schools in Gwynedd are close to this Welsh average line.
Suppose a school of 350 pupils was closed, and 150 of those students went to
another school of similar size, raising numbers to 500. The remaining 200
students travel to a school that originally educated 500, but is now expanded to
700. The figure shows that around £200 a student is saved by putting the 150 in
7

the school of now 500 students. But also the costs of educating those 350
original students in the now expanded school are cut by around £200 a student.
This element of the consolidation then saves £100,000. The gains from the
consolidation with the larger school are greater. On the 200 students moved
there around £500 a head is saved. The costs of educating the 500 students
already attending larger schools also fall by perhaps £300. The ostensible
financial total saved by this rationalisation amounts to about £350,000 or £1000
per pupil.
Figure 1 Budget cost per pupil in relation to school size, Wales 2009-10
In Appendix A are average cost functions estimated for Gwynedd secondary
schools between 2002 and 2010. The calculation with the parameters of the
preferred equation yields about the same conclusion as above; that the
immediate financial savings from the hypothetical consolidation would be about
£1000 per affected student. Taking into account proportions of pupils entitled to
free school meals, numbers in sixth forms and percentages not achieving any
qualifications, does not significantly affect the results.
8

4. ‘Empty Places’ and Cost per Student
Education authority cost per pupil cannot be the sole index of efficiency or school
performance. A school delivering a better education may be more expensive
than another, but it is not necessarily less efficient; it may be worthwhile
incurring higher costs for a ‘better’ school. Conversely it is not necessarily fair
simply if all state schools incur the same costs per pupil. A pupil may receive
different standards of education depending on the state school attended.
Similar considerations apply to the idea of ‘empty (school) places’. This is a short
run (with given school buildings and staff) equivalent of the cost per pupil
indicator. If a school can take more students with the same resources, the
financial cost per student falls – which in itself is clearly desirable. But as an
over-riding goal of education policy it can be misleading. If students do not want
to attend a particular school for good reason, such as the quality of education or
the distance required to travel, it is likely to be an error to focus solely on filling
the empty places – rather than for instance improving school quality.
Demographic change may give rise to ‘empty places’ at particular schools but it
does not necessarily follow that such schools must be closed or that students
should be bussed in from elsewhere. The purpose of policy appraisal is to judge
whether it is. Ultimately the elected authority must make decisions about the
distribution of all the benefits and costs of school consolidation or maintaining
the status quo with the best available information about their magnitudes.
A school consolidation policy may be expected to increase travel time costs
imposed upon students in exchange for a lower financial burden for the
taxpayer. Even when the financial savings exceed the time costs, the authority is
not obliged to conclude the policy, on these grounds, is desirable. It is only
appropriate to do so if the outcome is consistent with their other objectives and
policies
5. Increased Student Travel Time
What are the wider social and economic costs and benefits? Some are easier to
quantify than others. These include greater pupil travel costs. When the
(English) Department of Transport appraises priorities for road improvements
9

the principal benefits that they weigh against the outlays are travel time and
costs and safety. They have developed procedures for measuring these in
various circumstances (Department of Transport 2009).
‘The majority of journeys ... take place .... in the traveller’s own time. However,
people implicitly put a value on their own time, in that they will trade a cheaper,
slower journey against a faster, more expensive one.’ (1.2.11)
In their guidance the Department of Transport note their valuations in their
Table 2 includes those of retired people.
It might be questioned whether non-earning school students should be treated
as equivalent to retired persons. The democratic principles under-pinning Cost-
Benefit Analysis imply that for present purposes there is no reason to treat
young people and children differently from adults, economically active or retired.
As the Transport department explain;
If values of time for appraisal are based on an individual’s willingness to pay
which are related to income, then strategies and plans will be biased towards
those measures which most benefit travellers with higher incomes ...Investment
will then be concentrated into high-income areas, and the interests of those on
lower incomes, who may already suffer from relatively lower mobility and
accessibility, will be given less weight. For this reason, multimodal transport
appraisal should normally adopt the values for non-working time which is
common across all modes and journey purposes.’(s1.2.14)
In short, the journey to and from school should not be appraised any differently
from other non-work trips.
The 2002 value recommended by the English Department for Transport for noncommuting
leisure travel time is £4.46 per hour. Uprating the leisure travel time
to 2011values takes the figure over £5 an hour. Students travel for about 5
days a week for 40 weeks a year – say 188 days. To how much extra travelling
time are students committed with a school re-organisation? In relatively sparsely
populated rural areas the position can be markedly different from in cities. There
is some evidence that an extra 20 minutes each way (Appendix B) could be
imposed on the average former pupil of a closed hypothetical school. If this were
so, then conventional cost-benefit analysis registers a cost in the hypothetical
10

example of the 350 students considered earlier, of;
350x(40/60)x5x188˜£220,000 each year.
6. Additional Vehicle Operating Costs
In addition to these extra time costs, there are those associated with the
vehicles operation. Estimating these costs requires knowledge of how many
students travel by bus, by car, by bicycle or by foot, as well as the distances of
each. Obviously the mix will change from year to year so only an average or
approximation is possible. In order to get a downward biased idea of the extra
vehicle costs, assume all the students travel the extra distance by bus (cheaper
than private cars in cost-benefit analysis). In 2009/10 bus operating costs per
kilometre in Wales were 114 pence (DfT Bus). If the same number of buses
could carry the extra student the marginal costs of the present exercise would
be zero, but, in the long run at least, certainly more buses would need to be laid
on and the marginal costs would be positive.
If 200 of the 350 hypothetical students’ journeys required more buses, with an
extra average journey per day to and from school of 20 kilometres say, and an
average bus occupancy of 8, the extra vehicle costs per year would be
£200x20x200x1.14/8˜£110,000
An alternative exercise based upon detailed consideration of particular schools,
yields an annual cost larger by almost one half. The exercise as before focuses
on closing one 11-16 Secondary school of 350 students. Pupils would transfer to
two other Secondary schools depending on where they live. Pupils are assumed
to attend their nearest school. In Appendix B are the estimates of the length of
the journey travelled and the travelling times.
Costs are based upon the use of buses (Arriva trains are not willing to put extra
carriages on their trains at present). Single deck buses must be run because the
Assembly are at present considering the abolition of the use of double-decker
buses for school transport.
Total cost of transporting pupils to their two new schools as described in the
Appendix: £270,000
11

Present costs of transporting pupils to school considered for closure by bus and
train from catchment area primary schools: £107,166.
Implementing the closure according to the above model therefore increases
travel costs by
£162,834 per annum,
a considerably higher figure than the first, rather abstract, exercise.
7. Local Incomes and Employment
‘Proposals might have differential impacts on individuals, amongst other
aspects, according to their:... geographical location.. It is important that these
distributional issues are assessed in appraisals.’ H M Treasury Green Book
(2003) Annex 5 s.1 p.91
In addition to the obligation to ensure that expenditure is efficient and effective,
spending authorities are advised to take into consideration the distributional
consequences of policies, programmes and projects.
Rural secondary school consolidation undoubtedly impacts upon local
employment and income, in view of the distances between schools and the low
incomes and part-time work of much ancillary employment. Part-time and low
income workers are less likely to find it financially feasible to travel substantial
distances to work regularly. Consequently, rural school closure would certainly
deprive local cleaners, catering assistants, maintenance staff, lunchtime
supervisors and probably classroom support workers, of sources of income.
Their pay and numbers in a particular case are given in Table 2.
It is true that the area in which the expanded schools are located would benefit
from greater income and employment opportunities as a result of school
consolidation. But authorities may not regard this redistribution as in accordance
with their policies. They are not obliged to treat losses to some people as offset
by gains to others – even when the magnitudes are balanced – if a major policy
concern, such as maintaining rural communities, was involved.
To estimate how much income and employment might be involved each year in
a rural secondary school closure, it is probably appropriate to assume teaching
and more highly paid ancillary staff would be able to commute. Though this
12

imposes an additional cost upon them, if they lived locally their job relocations
would not much affect local incomes and employment.
Taking the following ancillary staff costs (Table 2) as illustrative, even excluding
the classroom assistants and those earning more than approximately £7000, the
low and part-time incomes in the locality would be cut by about £74,000 a year
in the event of school closure. The spending of the affected people would also
support other employment – though judging by a study of Welsh National Parks
this multiplier effect is small. The National Parks Study (National Trust 2006)
estimated across all three parks an extra 20 percent of indirect income and
within the Parks perhaps an extra 2 percent. These numbers justify adding a
little on to the illustrative £74,000. The margins of uncertainty as to how much
to add are considerable so here the figure is simply rounded up to £75,000 to
include multiplier effects.
Table 2 Ancillary Staff Costs: An Illustration for a Small Gwynedd
Secondary School
Take Home Pay:
1 Administrative Officer £26,276
2 Receptionist £10,581
3 Library/Resources Assistant £9,273
4 Science Technician £13,608
5 IT Technician £10,917
6 Learning Coach/Admin £16,538
7 Caretaker £16,830
8 Clerk of Governors £1,750
9 Senior Supervisors (x2) £26,748
10 Classroom Support Workers (x11) £107,652
11 Kitchen Staff (x5) £33,261
12 Cleaners (x5) £21,072
13 Lunchtime Supervisors (x4) £6,035
Total Staff = 35 £300,541
+ Grounds Maintenance Contract
(held by a local Operator) £12,000
Total = £312,541
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8. Disposal of School Site
When a small Primary school building becomes available, it is first offered for
community use and then in the absence of takers, placed on the open market.
The building might be an pportunity for a small business premises, or a local
developer might, subject to planning permission, use the site to build houses.
Secondary school sites are, however, large and complex, with laboratories,
gymnasiums, halls and other unusual features. They might be attractive for
large developments such as supermarkets but there would otherwise be limited
demands for the site in a rural community. Local developers would not be so
easily attracted and any large housing development would not be popular or
needed- and therefore would not be granted planning permission. The site could
become a liability rather than an asset, especially in the short term.
If demolition had to be considered, then these costs could be high. Some of the
rural schools are also within the National Park which would present considerable
planning issues for any new developments. By contrast, if a school in one of the
more urban areas was considered for closure then there would be a possibility of
substantial gains.
Since the present study estimates annual costs and benefits rather than present
values, any sum from sale of the site must be converted into an annual figure.
At the 3.5 percent real discount rate recommended by the Treasury, for every
£100,000 of the net value of the site sold, the annual value would be £3,500.
9. Educational Achievement and School Size
There is evidence that many Welsh secondary schools are larger than desirable
for the best educational performance (Foreman-Peck and Foreman-Peck 2006).
However, schools in Gwynedd are generally below, close to, or not far above this
calculated optimum. A scatter plot (figure 2) of the relationship since 2002
between school size in Gwynedd and school Key stage 3 percentage score shows
no relationship between the variables. On the other hand there is a relationship
between school size and per pupil cost (as predicted by equation 1 Table A1)
(figure 3). And the (predicted) costs per pupil appear to rise with KS3 score
14

performance (figure 4). At first sight then it would seem that funding is allocated
to schools so that they may maintain a target educational standard regardless of
their size. There appears to be no size penalty once the higher running costs of
small schools are taken into account.
However, there is evidence of a cost penalty for achieving a given school Key
Stage 3 educational standard for schools of the size of the example considered
throughout this study – 350 pupils - from estimated costs function for Gwynedd
schools. The interpretation of this result is not entirely clear. Ideally an
educational value added measure would be related to school costs, but
experiments with the %tl2 score and KS3 did not yield statistically significant
results.
With the KS3 score alone the results appear to show that the cost of achieving a
given KS3 score not only decline with school size but are actually negative over
the range of pupils 300+. This raises questions as to what the KS3 score is
actually measuring. A possibility is that it is measuring an input into secondary
education rather than an output; perhaps it captures the achievements of
students arriving from primary schools. If it does then the possibility that
achieving a given standard of education is cheaper the higher the attainments
of the new students makes sense, but does not indicate stronger performance of
larger schools and an additional disadvantage of smaller schools. But the cost
functions reported in Appendix A table A1 show negative coefficient on the
interaction between school size and KS3 score. One interpretation is that larger
schools have catchment areas with higher achieving pupil intakes in Gwynedd.
The number of schools is sufficiently small that it is not possible to distinguish
this possibility from the negative marginal or average costs of KS3 score with
size option.
It turns out, in any case, that the apparent size penalty for achieving a given
percentage KS3 score is small (Appendix A). According to the preferred equation
the lower cost of achieving a given KS3 score with the larger school
configuration amounts to merely £3700.
15

10. Summary
The estimated cost and benefits of the hypothetical rural secondary school
consolidation are shown in Table 3 below (columns a). All of the figures in the
Table are surrounded by a substantial margin of uncertainty. In the case of
school site disposal it is hard to arrive at a figure other than zero at all.
However, with other the numbers in the table, a site net value of £2 million,
when converted into a permanent annual value to be commensurate with the
other figures, would not be sufficient to turn the balance of net benefits from
consolidation positive in the best estimate case of columns a.
Table 3 Estimated Costs and Benefits from Rural Secondary School Consolidation
Benefits p.a. £ Costs p.a. £
a b a b
Lower school
costs
360,000 500,000 Greater
student travel
220,000 220,000
Lower cost per
level of
education
achievement
Redundant
school site
disposal
times
3,700 3,700 Greater
student vehicle
costs
0? 35,000 Loss of rural
community
income and
employment
160,000 160,000
75,000 185,000
Totals 363,700 538,700 455,000 565,000
Balance Benefit

determine the appropriate policy, not concerns with ‘empty places’ or ‘cost per
pupil’.
True efficiency involves achieving desired objectives with the least possible
resource cost. It is important to recognise that there is usually more than one
policy objective, more than one resource and that in these circumstances priority
cannot always be claimed for policies that minimise cash outflows.
References
Department for Transport (2009) Transport Analysis Guidance Values of Time
and Operating Costs TAG Unit 3.5.6, April
Department of Transport, Bus Operating Costs
www.dft.gov.uk/pgr/.../datatablespublications/public/bus/costs/bus0409.xls
Foreman-Peck J and Foreman-Peck L (2006) Should schools be smaller? The
size-performance relationship for Welsh schools. Economics of Education Review
H M Treasury (2003) The Green Book, Appraisal and Evaluation in Central
Government: Treasury Guidance, http://www.hmtreasury.gov.uk/d/green_book_complete.pdf
National Trust (2006) Valuing our Environment: Economic Impact of the National
Parks of Wales,
http://www.nationalparks.gov.uk/voe_national_parks_summary_english.pdf
17

Appendix A Gwynedd secondary school cost functions 2002-2010 *
School costs per pupil (AC) are determined by wages (T, assumed to grow at a
steady annual rate), staffing levels, school buildings, number of pupils (Q) and
perhaps educational standards (School %Key stage 3 here, KS3). The following
cost function is estimated from a panel of 14 schools 2002-2010, with the years
2003-5 excluded.
AC=a + bQ + cQ 2 + dKS3 + e KS3*Q + fT + .. + u
Parameter restrictions; c, d, f>0, b

On top of this there is the gain on 200 students from moving from a school of
350 to one of 500, i.e. from the first calculation £267*200=£53,400. So the
total financial cost reduction from school consolidation is ;
134000+171200+53400 = £358,600,
broadly similar to the £350,000 calculated by visual inspection of figure 1.
Turning to school quality, the extra cost of achieving a given KS3 score from
having smaller schools, or the lower costs of achieving a given KS3 score with
the larger school configuration, must be calculated for the cost-benefit analysis.
Again using Eq.1 Table A1, the cost reduction for the school ending up with 500
students is; ? AC=-.0174*150= -2.61, with ? TC=1305
For the 700 pupil school ?AC = -.0174*200 =-3.48, with ? TC=-2436
Therefore total quality incremental cost is merely £3700.
Table A1 Per pupil Gwynedd secondary school panel cost functions 2002-2010
1 2 3 4 5 6
AC AC AC1 AC1 AC AC
Q pupils -2.0987*** -3.2901*** -2.5656** -4.7004*** -3.2569*** -2.0909***
Q 2 0.0016*** 0.0017*** 0.0022*** 0.0024*** 0.0017*** 0.0015***
ks3 7.2164** 7.1792** 9.1834* 8.9295 -1.9e+03** -1.8e+03**
ks3*Q -0.0174*** -0.0155*** -0.0266*** -0.0217** -0.0150*** -0.0167***
T year 179.154*** 173.131*** 231.811*** 218.476*** 114.380*** 123.241***
ks3*T - - - - 0.9579** 0.9067**
constant -3.5e+05*** -3.4e+05*** -4.6e+05*** -4.3e+05*** -2.2e+05*** -2.4e+05***
N 84 84 84 84 84 84
r2_a 0.9567 0.9583 0.8954 0.8991 0.9622 0.9611
fixed/random RE FE RE FE FE RE
legend: * p

Appendix B
Extra pupil travel costs and times for one of the incremental travel costings
.....
.....
.....
TOTAL: 217 pupils to be transported
4 extra 50 seater buses needed.
Cost: £120,000.
20

Figure 2 Gwynedd school size and KS3 performance
KS3 Performance (% Achieved CSI)
20 40 60 80
0 500 1000 1500
Number of pupils
21

Figure 3 Gwynedd secondary school size and predicted pupil cost
Linear prediction
2500 3000 3500 4000 4500 5000
0 500 1000 1500
Number of pupils
22

Figure 4 Gwynedd school predicted pupil cost and KS3 performance
Linear prediction
2500 3000 3500 4000 4500 5000
20 40 60 80
KS3 Performance (% Achieved CSI)
23