NZTA
Final Report 26th March 2013
Partnership Models: Analysis of Options
Prepared for
Disclaimer
Although every effort has been made to ensure the accuracy of the material and the integrity
of the analysis presented herein, Covec Ltd accepts no liability for any actions taken on the
basis of its contents.
Authorship
Tim Denne & Stephen Hoskins
[email protected] | (09) 916 1960
© Covec Ltd, 2013. All rights reserved.
Contents
Executive Summary i
1 Introduction 1
1.1 Background 1
1.2 Current Contracting Approaches (Pre PTOM) 1
1.3 Partnership Contracts under PTOM 2
2 NZTA 1 5
2.1 Description 5
2.2 Incentives for Patronage Increase 6
2.3 Incentives for Efficient Fares 7
2.4 Impacts on Subsidy 7
3 NZTA 2 8
3.1 Description 8
3.2 Incentives for Patronage Increase 9
3.3 Incentives for Efficient Fares 9
3.4 Impacts on Subsidy 9
4 AT Model 10
4.1 Description 10
4.2 Incentives for Patronage Increase 11
4.3 Incentives for Efficient Fares 11
4.4 Impacts on Subsidy 11
5 Greater Wellington (GW) 12
5.1 Description 12
5.2 Incentives for Patronage Increase 13
5.3 Incentives for Efficient Fares 13
5.4 Impacts on Subsidy 13
6 CPI Model 15
6.1 Description 15
6.2 Incentives for Patronage Increase 15
6.3 Incentives for Efficient Fares 15
6.4 Impacts on Subsidy 16
7 Patronage Payment (PP) 17
7.1 Description 17
7.2 Incentives for Patronage Increase 18
7.3 Incentives for Efficient Fares 18
7.4 Impacts on Subsidy 18
8 Comparison of Results 19
8.1 Impact of Revenue Change 19
8.2 Incentives to Increase Patronage 21
8.3 Adjusting Revenues for Fare Effects 21
8.4 Incentives for Efficient Fares 21
8.5 Subsidy Impacts 22
8.6 Summary of Effects 23
9 Sensitivity Analysis 24
9.1 Factors Analysed 24
9.2 Commerciality Ratio (CR) 25
9.3 Fares 26
9.4 Costs 26
9.5 Combinations 27
10 Summary and Conclusions 29
10.1 Model Form and Approach 29
10.2 Incentives for Patronage Increase 29
10.3 Efficient Fares 29
10.4 Subsidy Levels 29
10.5 Key Decision Choices 30
i
Executive Summary
Background
The Public Transport Operating Model (PTOM) contributes to the government’s goal of
growing patronage with less reliance on public subsidy. Consistent with this
overarching goal, a number of contract models are being considered that would ensure
both operators and councils had incentives to increase patronage. These partnership
contracts would share the potential upside rewards (or gains) and the downside risks
(or pain) between the funders of public transport (PT) and the operators. In this report
we describe a number of options being considered and analyse their effects, particularly
on patronage and subsidy level.
Partnership Model Options
The different models that have been proposed are listed in the table below. In general
they are ensuring that both parties gain when patronage increases and lose when
patronage falls. They do this by placing some revenue at risk. The different models
pursue one of two basic philosophies. They either:
Seek to share cost risk with the operator in addition to revenue risk – NZTA1,
NZTA2 and AT; or
They share revenue increases relating to patronage only on the assumption that
this is the only element that the operator can influence.
Table ES1 Model Description Summaries
Model Description
NZTA1 Operator receives a share of the difference between revenue increase (since contract
start) and indexation payment. This may be positive (revenue increase is more than indexation) or negative (revenue increase is less than indexation)
NZTA2 Works the same as NZTA1 when the operator would receive a positive payment, but the downside risk is limited.
If revenue decreases, operator risk is limited to share of the reduction in revenue;
If revenue increases less than indexation, there is zero payment to the operator.
AT Operator receives a share equal to the revenue change less the difference between gross and net indexation payments.
GW Operator receives a share of the revenue increase that is not a result of price changes (ie patronage-related revenue)
CPI Operator receives a share of any increase in revenue above that resulting from fares increasing at the rate of inflation
Patronage
Payment (PP)
Operator receives a payment equal to patronage increase in absolute terms (numbers
of passengers) times a payment per passenger. This can be set so that the patronage payment is equal to the average increase in revenue per additional passenger.
All models set aside some revenue to be shared between the council and the operator at
a pre-agreed sharing ratio. When revenues fall and there is none to share, the operator
may be required to transfer money to the council. All introduce an incentive for
operators to increase revenue via increased patronage but they all have limits to the
amount shared.
ii
Apart from the PP model, all of the models have the same basic formula:
Sharing amount = ΔR - x
Where: ΔR = change in revenue since the base year; and
x = some fixed element that constrains the quantity shared
The value for x in the different models is shown below (Table ES2). The NZTA2 model
has some constraints on this whereby it does not share anything across some outcomes.
The PP model has a different form; most simply it is expressed as:
Shared amount = ΔPax × PP
Where: ΔPax = change in passenger numbers
PP = patronage payment (ie an amount paid per passenger)
It can include a threshold also, eg in which the PP is not paid until the change in
passenger numbers exceeds some threshold. It can be defined in a way that exactly
corresponds to one of the other models through defining the value of the threshold and
the PP.
Table ES2 x-value in the different models
Model x-value Formula
NZTA1 Full indexation ΔR - I
NZTA2 Full indexation (or zero) ΔR – I (or ΔR or 0)
AT Gross minus net indexation ΔR – Ig + In
GW Revenue change that results from fare change ΔR - (R0 × ΔFn × (1 + ΔPf)) - (R0 × ΔPf)
CPI Revenue change that results if fare change = CPI ΔR – (R0 × CPI)
Notes: ΔR = change in revenue; I = indexation; Ig = gross indexation payment; In = net indexation
payment; R0 = revenue in start year; ΔFn = nominal change in fare levels; ΔPf = change in patronage as a
result of change in fares; CPI = consumer price index
We illustrate the basic approach used in the partnership models in Figure ES1. The
upward sloping solid line represents the share of revenue that goes to the operator
under a pure revenue share (Sharing amount = ΔR) in which the operator receives a
fixed percentage of the change in revenue. Here we show sharing at a ratio of 50% so
that, if revenue increases by $4,000, the operator obtains $2,000.
The introduction of an x-value shifts the line to the right. So, if x = $2,000, the line shifts
to the new dotted line; it crosses the x-axis when revenue change = $2,000 and at a
revenue increase of $4,000, the operator receives $1,000 (50% of $4,000 - $2,000).
iii
Figure ES1 Revenue Sharing
Analysis
Given the objectives relating to patronage and subsidy, we assess:
incentives on both operators and councils to increase patronage;
incentives on councils to increase fares while recognising the negative impact on
patronage;
potential impact on subsidy levels.
Impact of Revenue Change
All the models apart from the PP model are based on sharing the change in revenue and
take the same basic form, as noted above. We illustrate the effects in Figure ES2 using a
number of basic assumptions.1 It shows how a change in revenue is shared with the
operator under the different models compared with pure revenue share.2 The sharing
amount is the change in revenue minus some amount that sets a threshold. The
threshold pushes out the level of revenue change before the operator starts to receive a
positive share of revenue. This is most pronounced in the NZTA1 model for which there
is no positive flow to the operator until revenues increase by more than 7.5% under our
base assumptions. NZTA2 follows the pure revenue share line when revenue change is
below zero and the NZTA1 model above the point at which the operator receives
positive revenue. The CPI model follows the GW model exactly because we have set
fare increase equal to CPI.
1 Start AGC = $1 million; start CR = 40%; gross indexation = $30,000; CPI = 2%; fare increase = 2% 2 The Pure Revenue Share would have a formula of: sharing amount = ΔR
-$5,000
-$4,000
-$3,000
-$2,000
-$1,000
$0
$1,000
$2,000
$3,000
$4,000
$5,000
-$10,000 -$8,000 -$6,000 -$4,000 -$2,000 $0 $2,000 $4,000 $6,000 $8,000 $10,000O
pe
rato
r re
ven
ue
sh
are
Revenue increase
line shifts to the right by 'x'
Pure revenue share(Shared amount = ΔR)
Shared amount =ΔR - x
iv
Figure ES2 Impacts of Revenue Change on Operator Revenue
An important thing to note is that the angle of the line is the same in all models. The
operator obtains a share of any incremental increase in revenue and the amount is
always the same, and is also the same as they would receive with a pure revenue share.
This is because all of the models have the basic formula: a variable amount based on
revenue change, less a fixed amount. The fixed amount determines the position along
the x-axis; the variable amount determines the slope.
In some ways this makes the models all exactly equivalent. To the extent that the fixed
element of the equation cannot be influenced by the operator, it will be estimated at the
beginning of the contract and included in the initial bid price. All that matters is then
that the operator has an incentive to increase patronage.
However, if the factors determining ‘x’ are not predictable, the specification of the
formula matters.
The first three models (NZTA1, NZTA2 and AT) use indexation as the threshold. This
shares costs with the operator in addition to revenue. It is equivalent to an approach in
which, in order to be able to benefit from sharing revenue change, the operator must
accept less generous indexation.
The GW and CPI models both set a threshold equal to the revenue change expected
from the change in fare level. The GW model calculates the revenue associated with the
fare change; the CPI model assumes that fares change with CPI. Bot models isolate the
impact of patronage change from fare change (if there was zero CPI and no change in
fares, both models would be the same as the pure revenue share).
-$40,000
-$30,000
-$20,000
-$10,000
$0
$10,000
$20,000
$30,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Revenue Change (% of Start Year)
Pure revenue share
NZTA1
NZTA2
AT
GW
CPI
v
Incentives to Increase Patronage
All the models provide incentives to increase patronage, with the possible exception of
NZTA2 which, under a number of likely outcomes, will provide no patronage
incentives. In the other models any increase in patronage will result in an increase in
revenue and this marginal increase in revenue will be shared using the agreed
percentage.
Apart from PP and NZTA2, the marginal incentive is exactly the same across the
models, as shown in Figure ES2 above: an additional passenger will result in the same
level of net additional revenue for the operator. The PP model can be specified to
provide the same marginal incentive.
Adjusting Revenues for Fare Effects
Two of the models, GW and CPI, adjust the revenue changes to take account of price
(fare) effects. These isolate the impacts of revenue that are associated with patronage
and share only these with the operator. The GW model does this more explicitly and is
more complex. The CPI model operates on the assumption that fares will be increased
equal to inflation and does not share the revenue increases that result from that
adjustment. The PP model effectively isolates patronage-related revenue by measuring
patronage directly.
The other models do not isolate revenue that results from patronage change from
revenue that results from fare adjustments.
Incentives for Efficient Fares
The models differ with the extent to which they provide incentives for efficient fares.
The NZTA models and the AT model result in the council sharing any revenue
increases, whether they are patronage or fare-related, and whether or not the fare
increase is equal to, less than or more than inflation. With an estimated price elasticity of
demand of -0.4 there is always a revenue gain from increased fare levels: the revenue
gain will be greater than any negative impact on patronage. As the council gains a share
from revenue increases it benefits from all fare increases.
The GW model identifies the fare-related revenue and allocates this fully to the council.
In doing so it provides an increased incentive to a council wishing to minimise subsidy
levels to increase fares at more than the rate of inflation. It would be best introduced
with a policy to limit fare increases to the rate of inflation.
The CPI model assumes that fares will increase with inflation and all revenues up to this
point will accrue to the council; however beyond this the council has the same incentive
to increase fares as under the NZTA and AT models – it benefits by sharing a proportion
of any revenue increase.
The PP model has some incentive to maximise fares if the council wishes to minimise
subsidies because the council retains all revenues that are not associated with increases
in patronage.
vi
Subsidy Impacts
The subsidy impacts are not straightforward to estimate. In simple terms the models can
be examined in terms of how revenues are distributed, with anything distributed to
operators being equivalent to subsidy. However, this ignores two effects:
the possible incentive effects for operators to increase patronage and revenue,
such that there is a larger amount to share; and
the impacts on initial bid price. For example, expectations of increased revenue
for operators following the introduction of the sharing model would be expected
to lead to the operators bidding for a lower level of subsidy at the start of the
contract.
The expected impacts on initial bid price are further complicated by the effects of
uncertainty. Greater revenue uncertainty for operators is expected to result in greater
requirement for subsidy to compensate for risk. Uncertainty is greatest where the
revenue that the operator might earn is most affected by factors that are beyond its
control. The models all share a proportion of revenue and thus provide up-side and
down-side risk, but some models limit this to patronage-related revenue, whereas
others include all revenue and thus expose operators to price risk. In addition, three of
the models relate the payments to operators to indexation (cost change). It is likely that
the level of uncontrollable risk that the operator is exposed to will have the greatest
impact on relative subsidy levels between the sharing models.
Those that adjust the payments for indexation introduce most uncertainty, particularly
the NZTA1 model. If costs rise significantly, the operator will face a net cost unless there
is a substantial increase in revenues. And these effects are most pronounced for
contracts with low commerciality ratios. NZTA2 is more certain because there are a
number of circumstances in which there will be no sharing. The AT model has
uncertainty associated with the effects of indexation, but this is much less than under
NZTA1.
There are also uncertainties associated with the fare level decisions of councils. These
are reduced by the models that take account of fare changes (GW and CPI) and are
removed in the PP model that simply rewards patronage.
Summary of Effects
Table ES3 summarises the effects under the different models.
All share an amount that is some proportion of the change in revenue. The PP
model does not, but it is equivalent to doing so.
All include a threshold or adjust the revenues such that they are not pure
revenue share models. The GW and CPI models adjust revenue to focus on
patronage revenue only. The PP model focuses directly on patronage, and it can
be specified to include a threshold.
vii
All models provide a marginal incentive to increase patronage, although the
NZTA2 model provides no incentive across a range of outcomes.
Three models (NZTA1, NZTA2 and AT) share costs in addition to revenue and
the other three models isolate revenue from patronage.
None of the models provide incentives to change fares efficiently, that we
define as increasing at the rate of inflation. This is because, if the price elasticity
of demand is less than -1 as NZTA assumes) the council will always gain from a
fare increase. Under the GW and PP models there is a particular incentive to
raise fare levels at the expense of patronage.
Subsidy levels are most likely to be differentiated by the differences in certainty
for operators. Those that adjust the amount paid to operators with changes in
costs introduce most uncertainty, particularly NZTA1. The PP model has
greatest certainty as it limits payment explicitly to patronage. The GW and CPI
models attempt to isolate patronage revenue, but do so imperfectly.
Table ES3 Summary of Models
Factor NZTA1 NZTA2 AT GW CPI PP
Sharing amount based on change in revenue
×
Threshold/adjustment Indexation Indexation Indexation difference
Fare-related effects
Real fare change
Can be included
Marginal incentive to increase patronage
×
Shares costs × × ×
Isolates patronage × × ×
Efficient incentive to change fares
- - - × - ×
Certainty of operator outcome
×× × ×
Sensitivity Analysis
Commerciality Ratio (CR)
Low CR (and low revenues) means there is a need for a higher percentage increase in
patronage (and revenue) to overcome fixed costs. This means that the NZTA1 model, in
particular, requires a very high growth in patronage to provide sufficient revenue to
repay a share of the indexation payment. In contrast, a high CR means there is a need
for a smaller percentage increase (although the same absolute increase) in passenger
numbers to generate sufficient revenue.
Fares
If fares do not move there is a requirement for more revenue to be earned from
patronage increases to exceed the thresholds that limit payments to operators. The GW
viii
model takes account of this and adjusts the shared amount for fare changes so that an
operator is not penalised.
Costs
If costs fall, the amounts paid to operators under the GW and CPI models are
unaffected, but under the NZTA and AT models, greater amounts are shared with
operators. The NZTA1 model is affected most significantly.
Summary and Conclusions
The different models pursue one of two basic philosophies. They either:
o Seek to share cost risk with the operator in addition to revenue risk –
NZTA1, NZTA2 and AT; or
o They seek to isolate revenue increases relating to patronage only as the
only element that the operator can influence.
All the models (apart from PP) have the same basic form of:
Sharing Amount (SA) = ΔR – x
The NZTA2 model varies and across some circumstances, can be specified as
SA = Δr or SA = 0
Because x is a fixed amount, and ΔR varies with patronage, all (apart from
NZTA2 and PP) provide the same incentives for patronage increase (and PP can
be adjusted to achieve this also).
ΔR also varies with fare levels. The GW and PP models (and to a lesser extent
the CPI model – or only alongside fares policies) do not provide operators with
benefits from fare-related revenue changes.
Because demand is estimated to be inelastic (patronage levels will fall less than
price increases), increasing fares will always raise more. Councils may have an
incentive to increase fares above inflation to obtain more revenue. The GW
model isolates revenue from fare increases, but does so in a way that
incentivises more fare increases (the council retains all fare-related revenue).
Guidelines/rules on fare increases would reduce this uncertainty.
The specification of x determines how much revenue is retained by the council
before the operator receives a share of revenue (and thus potentially how low
the subsidy is), but the expectation of future x means that it will affect initial bid
prices also. Thus with perfect information all models would result in the same
level of subsidy.
Because there is not perfect information, what affects subsidy levels will be the
extent to which the models increase or decrease certainty for the operator. More
uncertainty will require more subsidy to compensate for risk. Uncertainty is
greatest when the level of x varies with costs (particularly under the NZTA1
ix
model and to a lesser extent the AT model). There is also uncertainty associated
with the councils changing of fares; as noted above these can be addressed
through fares policies.
If fare policies (that limit fare rises to CPI) are set alongside the introduction of a
partnership model, uncertainties relating to fares are largely eliminated. This then
provides a clear choice between models that either seek to isolate patronage related
revenue increases (GW, CPI, PP) and those that seek to share some underlying cost risk
(that cannot be eliminated) with the operator in addition to revenue risk.
If isolating patronage increases is desired, the PP model does this most explicitly and
simply. The GW model is somewhat complex and can deal with situations in which fare
levels vary from CPI. The CPI model is based on an assumption that fare policy is
adhered to.
If sharing cost risk, the NZTA1 model shares all of the cost risk and the AT model shares
a proportion of that risk. The NZTA2 models varies between sharing all cost risk (when
revenue growth is high) or no cost risk when it is not.
1
1 Introduction
1.1 Background
The Public Transport Operating Model (PTOM) contributes to the government’s goal of
growing patronage with less reliance on public subsidy. Consistent with this
overarching goal, a number of contract models are being considered that would ensure
both operators and councils had incentives to increase patronage. These partnership
contracts would share the potential upside rewards (or gains) and the downside risks
(or pain) between the funders of public transport (PT) and the operators. In this report
we describe a number of options being considered and analyse their effects, particularly
on patronage and subsidy level.
In this introductory section we first characterise contracts without a sharing
arrangement, setting out how the individual parties are affected by changes in revenues
and costs. We then describe six options for a partnership approach and point out the
effects of changes in the underlying factors that determine costs and revenues.
1.2 Current Contracting Approaches (Pre PTOM)
Currently contracts differ with respect to: revenue distribution and indexation.
Contracts can be set in gross or net terms with respect to revenue.
Under gross contracts the operator is paid a fee that covers their full costs, with
councils retaining the revenues. There is no incentive for the operator to increase
patronage; any incentives would be from contractual performance measures.
Under net contracts the operator retains the revenue from fares and is thus
rewarded if patronage increases. A fee is paid to make up the difference
between revenues and costs.
Indexation payments are made to compensate operators for estimated increases in costs.
These too may be in gross or net terms. In both cases they use an NZTA index which
represents an estimate of changes in costs for a bundle of relevant inputs,3
Gross indexation increases the fee by an amount equal to the previous year’s
total annual costs times the index.
Net indexation increases the fee by an amount equal to the previous year’s fee
times the index. The amount will thus differ with the commerciality ratio.
Gross indexation fully compensates for changes in costs and could be said to produce
the same outcome as if the contract was opened for competitive bidding each year
3 The Procurement Manual states that contract prices must be adjusted to compensate for fluctuations
in the price of inputs (eg wage rates, fuel prices) for any contract with a term of 12 months or more.
This is undertaken on a quarterly basis using a standard index provided by the NZTA. There are
separate indices for diesel bus and ferry contracts.
2
(assuming that the index is an accurate representation of actual cost increases). The
difference between net and gross indexation is greatest at a high commerciality ratio,
where it might also be argued that the operator is best able to take on revenue risk.
Contracts can be gross-gross, net-net, gross-net (gross contract, net indexation) or net-
gross.
In this report, and in the discussion of different partnership models, the intent is to get
away from the distinction between gross and net contracts, ie those that fix which party
obtains revenue. The partnership approach is attempting to identify what is the best
way to distribute upside and downside risks relating to patronage and revenues. For the
description of options below we use a neutral model in which there is no prior decision
on which party receives the revenue, although in practice and for consistency, we have
assumed that any excess revenue is retained by (or accrues to) the council. Indexation
can still be gross or net, reflecting local preferences.
1.3 Partnership Contracts under PTOM
1.3.1 Options
In this section we examine the different options that have been proposed for sharing
risks and rewards. The different approaches all introduce an incentive for operators to
increase revenue via increased patronage but they differ with respect to the limits to
this. The different models pursue one of two basic philosophies. They either (1) seek to
share cost risk with the operator in addition to revenue risk – NZTA1, NZTA2 and AT;
or (2) they share revenue increases relating to patronage only, assuming that this is the
only element that the operator can influence. The models are summarised in Table 1
Table 1 Model Description Summaries
Model Description Threshold
NZTA1 Operator receives a share of the difference between revenue
increase (ΔR) (since contract start) and indexation payment. This may be positive (ΔR > indexation) or negative (ΔR < indexation)
Indexation payment
NZTA2 Works the same as NZTA1 when the operator would receive a positive payment, but the downside risk is limited.
If revenue decreases, operator risk is limited to share of the reduction in revenue;
If revenue increases less than indexation, there is zero payment to the operator.
Indexation payment
AT Operator receives a share equal to the revenue change less the difference between gross and net indexation payments.
Difference between gross & net indexation
GW Operator receives a share of the revenue increase that is not a result of price changes (ie patronage-related revenue)
Revenue that
results from fare change
CPI Operator receives a share of any increase in revenue above that resulting from fares increasing at the rate of inflation
Revenue that
results if fare change = CPI
Patronage Payment (PP)
Operator receives a payment equal to patronage increase in absolute terms (numbers of passengers) times a payment per passenger.
Can be set at any level
3
The NZTA models require operators to repay a share of the indexation payment; this
functions as a threshold. Operators receive a positive share of revenues once revenue
increases are greater than indexation; they must pay the council when revenue change is
less than indexation. This is more difficult to overcome with low starting commerciality
because the threshold is set in absolute terms. For example, if starting with a 25%
commerciality ratio, for the revenue increase to be greater than indexation it would need
to be four times as much in percentage terms (eg with a 2% per annum indexation
payment, the operator would only receive a share of revenue if revenue increased by
more than 8%).
The Auckland Transport (AT) model shares risks and benefits (pain and gain) across
both revenues and costs. It shares all changes in revenues between the operator and the
council less the difference between the gross and net indexation amount.
The Greater Wellington (GW) model is based on the fare adjustment formula included
in the PTOM procurement manual. This formula is used to ensure that operators are not
made better or worse off as a result of changes to fares. It does this by estimating the
impact on revenues of changes in (real) fare levels; these revenues go to the council. This
is adapted to being a partnership model by assuming the remainder of revenues are the
result of changes in patronage levels and are shared with the operator.
The CPI model is based on a simple assumption that revenues would be expected to
remain constant in real terms (and thus to increase in nominal terms at a rate equal to
CPI). This assumes that fares increase at the rate of inflation and there is no expected
change in passenger numbers; any increase in patronage results in a real increase in
revenues and this increase is shared between operators and councils.
The Patronage Payment (PP) model is a straightforward payment for any increase in
patronage using a payment per additional passenger. A threshold can be set, eg
payments start above an x% increase in passengers. Negative payments can operate for
reductions in passengers (or reductions below the threshold).
1.3.2 Analytical Approach
We analyse the models in more detail below. Given the objectives relating to patronage
and subsidy, we assess:
incentives on both operators and councils to increase patronage;
incentives on councils to increase fares while recognising the negative impact on
patronage;
potential impact on subsidy levels.
We would expect that the partnership model would:
provide an incentive to both parties to increase patronage by both benefiting
from each additional passenger and each losing from a reduction in passengers;
take account of price changes that might affect patronage so that rewards are not
distorted by inefficient pricing;
4
not incentivise inefficient pricing – we comment below on the issue of price
elasticities of demand;
not lead to increasing levels of subsidy payment per additional passenger.
Patronage Impact
The patronage incentive can be analysed by examining the effect on the operator (and
the council) of one more passenger, or one more dollar of revenue.
Fares
The issue of fare levels is complicated because of the limited information on price
elasticity of demand. NZTA suggests that a constant elasticity of -0.4 is used, ie that
every 1% increase in price will result in a 0.4% reduction in patronage. However,
assuming an elasticity that is constant and less than 1 means that there is always an
incentive to increase fares: the increase in revenue will be greater than the reduction in
passengers in response to fare levels. Given an objective of reducing subsidy, increasing
fares might be an obvious and favoured approach. In analysis we assume instead that
efficient fares would increase at the level of inflation. This means that fare levels do not
result in any negative impact on passenger numbers and any increase in patronage is
the result of greater demand for public transport.
Subsidy Impact
The impact on subsidy levels is somewhat difficult to estimate. Simplistically, any
amount paid to an operator in a partnership model is not paid to the council and
therefore results in a need for more subsidy. However, the models are expected to
provide incentives for operators to increase patronage (and thus revenue); and any
increase in revenue in this way, that is shared by the council, will reduce subsidy. In
addition, any expectations of future flows of money (to or from the operator) will affect
the initial bid price which sets the baseline for all models. In theory, and given perfect
information, subsidy levels will be the same under any model. The models will differ if:
there are differences in how unexpected changes in revenues are distributed
(unexpected changes in costs are addressed via indexation);
there are differences in the certainty of future revenue flows under the
individual models, with greater uncertainty expected to result in greater need
for subsidy to compensate for risk. Operators will be able to predict some
market uncertainties, but the council’s approach to pricing may be
unpredictable; thus uncertainty is increased in models where operator revenue
is affected by price change.
This means that there can be no definite estimate of the impacts on subsidy levels. To
assist the analysis we provide the following pieces of information:
additional (marginal) subsidy paid per additional passenger;
uncertainty – how vulnerable is operator revenue to price change?
Below we describe a number of models that are currently being considered. In the next
sections we describe and analyse the different models; we summarise the effects in
Section 8 and undertake sensitivity analysis in Section 9.
5
2 NZTA 1
2.1 Description
The NZTA1 model shares revenue surpluses with the operator only after indexation
costs have been covered. The amount shared is defined by the formula:
Shared amount = ΔR - I
Where: ΔR = change in revenue from the commencement of the contract
I = indexation payment
All other revenue is retained by the council. It is effectively a two-part sharing model
with a fixed and a variable element. The fixed component is the share of the indexation
payment. This is based on factors outside of the controls of the council and operator.
The variable element is the change in revenue.
To illustrate the approach, we show a number of possible cases in Table 2.
Table 2 Sharing under NZTA1
All cases start with annual gross costs of $1 million in the start year and revenues of $0.4
million requiring a subsidy of $0.6 million. Costs increase in year 1 by 3% (Cases A to C)
or fall by 1% (Case D), resulting in indexation payments as shown. Patronage and fare
changes are assumed and used to estimate the change in revenue in dollar and
percentage terms.
Period Item Case A Case B Case C Case D
Description Indexation Positive Positive Positive Negative
Revenue change Positive Positive Negative Negative
Start year Annual Gross Costs $1,000,000 $1,000,000 $1,000,000 $1,000,000
Revenues $400,000 $400,000 $400,000 $400,000
Commerciality Ratio 40% 40% 40% 40%
Subsidy $600,000 $600,000 $600,000 $600,000
Year 1 Cost change 3.0% 3.0% 3.0% -1.0%
Gross indexation payment $30,000 $30,000 $30,000 -$10,000
Net indexation payment $18,000 $18,000 $18,000 -$6,000
Patronage change 6.0% 2.0% -2.0% -2.0%
Fare change 2.0% 2.0% 2.0% 2.0%
Revenue change 8.12% 4.04% -0.04% -0.04%
Revenue change $32,480 $16,160 -$160 -$160
Gross Share amount $2,480 -$13,840 -$30,160 $9,840
Indexation Revenue to council $31,240 $23,080 $14,920 -$5,080
Revenue to operator $1,240 -$6,920 -$15,080 $4,920
Net Share amount $14,480 -$1,840 -$18,160 $5,840
Indexation Revenue to council $25,240 $17,080 $8,920 -$3,080
Revenue to operator $7,240 -$920 -$9,080 $2,920
6
In Case A, the increase in revenue is greater than the increase in costs (and
indexation payment). There is a small surplus that is shared, but most of the
revenue is used to reimburse the council for the indexation payment. Under net
indexation more is shared with the operator because there is less indexation to
reimburse the council for.
In Case B there is a smaller change in patronage such that revenues do not
increase by as much as costs. As a result the council receives all of the revenue
increase ($16,160) and the difference between this and the indexation payment
($30,000 - $16,160 = $13,840 or $1,840 under net indexation) is a loss shared
between the operator and the council, ie the operator must pay back some of the
indexation payment.
Under Case C patronage and revenues fall and costs rise. The gap between
indexation payment and revenue is even greater and the operator pays back
approximately half of the indexation payment received.
Case D has both costs and revenues falling, but the costs fall by more than the
revenues. Here the indexation payment results in the operator paying the
council, but because the sharing amount is positive (revenues are less negative
than costs), the council pays the operator.
2.2 Incentives for Patronage Increase
Once the model is introduced the operator benefits from any increase in revenue, be it
patronage-related or price-related. The formula has a simple specification in which the
shared amount increases by $1 for every additional $1 of revenue. The operator and the
council will share this additional $1 using a pre-agreed percentage, so at a 50% sharing
arrangement, each additional $1 of revenue will result n the operator receiving $0.50.
Note, this is different from the potential outcome of the operator facing a net payment
despite patronage increases (Case B). The negative payment is affected by the level of
cost indexation and would shrink in size if patronage increased further. As noted above,
there is a relatively high hurdle that needs to be overcome before a positive payment is
received by an operator and it benefits from the partnership model (versus no
partnership model). Restating the example given earlier, if starting with 25%
commerciality ratio (CR), the operator would face a net penalty if the growth in
patronage is not four times greater in percentage terms than the growth in costs (and
two times at 50% CR and 1.5 times at 75% CR).
This does not change the incentive for patronage increases (that is based on how the
sharing amount changes with each additional dollar of revenue), but it does make the
model unattractive to operators versus the status quo or means that initial bid prices for
contracts will be increased to take account of this additional risk.
Some patronage increases (or decreases) may be fare-related. For example, in theory
patronage will increase if fares are not raised in nominal terms and thus drop in real
7
(inflation-adjusted) terms. Operators and councils are both rewarded under these
circumstances.
Thus NZTA1 is offering relatively efficient incentives for patronage increases by always
rewarding these increases.
2.3 Incentives for Efficient Fares
If fares increase, revenues increase and the council (and operator) gains from a share of
the increased revenue. There is no limit to this incentive and, as noted above, given a
price elasticity of demand of -0.4, fare increases will always be expected to raise more
revenue. Thus there is an incentive to raise fare levels and no disincentive to limit this to
inflation.
2.4 Impacts on Subsidy
Although it is possible to estimate the effects of the model on total subsidy levels by
calculating the level of payment to the operator relative to different starting positions
(eg gross or net contracts), in practice these expected effects will be reflected back in
initial bid prices such that the differences are not meaningful as an estimate of the final
impacts on subsidy levels. To avoid influencing the choice of model we do not present
these static effects on subsidy here. We limit the discussion of subsidy to impacts at the
margin and uncertainty.
2.4.1 Marginal Subsidy
The subsidy payment per additional passenger is equal to the revenue raised by the
passenger times the sharing amount. So if the sharing ratio is 50%, for each additional
passenger trip paying a $2.50 fare there is a subsidy of $1.25. This is regardless of the
starting level of commerciality. However, the net impact on subsidy levels depends on
what would have happened otherwise. If the additional passenger would have come
even if the operator received no revenue, then the difference between with and without
sharing is the payment of the $1.25 to the operator. However, if the passenger is
additional because of the sharing model, then effectively there is a reduction in subsidy
as a result; the council obtains $1.25 (and the $1.25 payment to the operator is not a cost
to the council – it would not have happened in the absence of the sharing model).
2.4.2 Uncertainty
As noted in Section 1.3, the main contributor to total subsidy levels will be uncertainty
of income. The NZTA1 model introduces revenue uncertainty because of the
relationship to indexation. Whereas under this model, at any time raising an additional
dollar of revenue will always benefit an operator, the net benefit to the operator of any
given level of patronage depends also on the level of indexation, and this is not certain.
To explain: if revenue increases by $30,000, whether the operator benefits depends on
whether or not costs have also increased by this amount. The aggregate uncertainty is
greater than without the sharing model and is thus likely to increase required subsidy
levels.
8
3 NZTA 2
3.1 Description
NZTA 2 is a variant on NZTA 1 that limits the downside. It has the same threshold that
applies on the up-side so that the operator does not receive a positive payment until
there is a significant increase in revenues, but the downside costs are significantly
limited. The formula used is:
Shared amount = If ΔR < 0 = ΔR
If ΔR ≥ 0 then
If I > ΔR = 0
If I < ΔR = ΔR - I
Where: ΔR = change in revenue from the commencement of the contract
I = indexation payment
When revenue falls, the shared loss is equal to the reduction in revenue and does not
take account of changes in indexation payment. When revenue rises the operator shares
the upside gain only if the revenue increase is greater than indexation, but if it is not,
there is no penalty or reward.
We use the same examples to illustrate the impacts in Table 3. The top part of the table is
unchanged and is shaded.
Table 3 Sharing under NZTA2
Period Item Case A Case B Case C Case D
Description Indexation Positive Positive Positive Negative
Revenue change Positive Positive Negative Negative
Start year Annual Gross Costs $1,000,000 $1,000,000 $1,000,000 $1,000,000
Revenues $400,000 $400,000 $400,000 $400,000
Commerciality Ratio 40% 40% 40% 40%
Subsidy $600,000 $600,000 $600,000 $600,000
Year 1 Cost change 3.0% 3.0% 3.0% -1.0%
Gross indexation payment $30,000 $30,000 $30,000 -$10,000
Net indexation payment $18,000 $18,000 $18,000 -$6,000
Patronage change 6.0% 2.0% -2.0% -2.0%
Fare change 2.0% 2.0% 2.0% 2.0%
Revenue change 8.12% 4.04% -0.04% -0.04%
Revenue change $32,480 $16,160 -$160 -$160
Gross Share amount $2,480 $0 -$160 -$160
Indexation Revenue to council $31,240 $16,160 -$80 -$80
Revenue to operator $1,240 $0 -$80 -$80
Net Share amount $14,480 $0 -$160 -$160
Indexation Revenue to council $25,240 $16,160 -$80 -$80
Revenue to operator $7,240 $0 -$80 -$80
9
The results are the same as in NZTA1 for Case A, but the other cases all have greatly
reduced effects. Case B results in no sharing; the council retains all the additional
revenue. In Case C the small revenue reduction is shared. In Case D, rather than a
positive payment to the operator, there is a negative payment equal to half the revenue
loss.
3.2 Incentives for Patronage Increase
The limitation on downside risk means that the incentives for increasing patronage and
revenue are limited also. Operators benefit from raising additional revenue only if:
The revenue increase is greater (in dollar terms) than indexation payment; or
Revenues are otherwise falling.
In other cases, the council retains all of the revenue. Thus incentives for patronage
increases are limited to periods of low inflation, or to high CR routes.
3.3 Incentives for Efficient Fares
As with NZTA1 raising fares increases revenues, but in NZTA2 there can be an even
greater incentive to do so because there are possibilities of no sharing options in which
the council retains all revenue gains, although, this is no different from a gross contract
with no sharing.
3.4 Impacts on Subsidy
3.4.1 Marginal Subsidy
As with the incentive payment, the marginal subsidy payment depends on the
circumstances with respect to costs.
If the revenue increase is greater than the cost increase then additional
passengers result in additional subsidy equal to the revenue raised times the
sharing ratio. However, as discussed above, this holds unless the additional
passengers are directly attributable to the introduction of the partnership model,
in which case there is a reduction in subsidy for each additional passenger: the
council receives a share of the extra revenue.
If revenues increase less than indexation there is no impact on subsidy levels.
If revenues fall, subsidy levels fall also as some of the revenue fall is borne by
the operator.
3.4.2 Uncertainty
The uncertainties for operators are likely to be reduced compared with NZTA1 because
in many circumstances zero sharing is likely to result, ie increasing revenue but not as
much as increases in costs. Thus the model may have little impact on subsidy or
incentives.
10
4 AT Model
4.1 Description
Under the AT model the amount paid to operators is a share of the change in revenue
and of the difference between the gross and net indexation payment. It was initially
designed for net contracts, but here we apply it to a neutral contract. The formula used
is:
Shared amount = ΔR - Ig + In (where gross indexation has been paid)
= ΔR + Ig – In (where net indexation has been paid)
Where: Ig = indexation payment that would apply under a gross contract
In = indexation payment under a net contract
ΔR = change in revenue
The model is doing two things: sharing all revenue increases or decreases, and sharing
the differences between indexation payment options in a way that results in more
sharing of cost risk. As with NZTA1 and 2, it effectively has a fixed and a variable
element: the fixed element is the difference between the indexation payments, which
cannot be influenced by the council or operator; the variable element is the revenue
change, which can.
We show the effects using the same table below.
Table 4 Sharing under AT Model
Period Item Case A Case B Case C Case D
Description Indexation Positive Positive Positive Negative
Revenue change Positive Positive Negative Negative
Start year Annual Gross Costs $1,000,000 $1,000,000 $1,000,000 $1,000,000
Revenues $400,000 $400,000 $400,000 $400,000
Commerciality Ratio 40% 40% 40% 40%
Subsidy $600,000 $600,000 $600,000 $600,000
Year 1 Cost change 3.0% 3.0% 3.0% -1.0%
Gross indexation payment $30,000 $30,000 $30,000 -$10,000
Net indexation payment $18,000 $18,000 $18,000 -$6,000
Patronage change 6.0% 2.0% -2.0% -2.0%
Fare change 2.0% 2.0% 2.0% 2.0%
Revenue change 8.12% 4.04% -0.04% -0.04%
Revenue change $32,480 $16,160 -$160 -$160
Gross Share amount $20,480 $4,160 -$12,160 $3,840
Indexation Revenue to council $22,240 $14,080 $5,920 -$2,080
Revenue to operator $10,240 $2,080 -$6,080 $1,920
Net Share amount $44,480 $28,160 $11,840 -$4,160
Indexation Revenue to council $10,240 $2,080 -$6,080 $1,920
Revenue to operator $22,240 $14,080 $5,920 -$2,080
11
4.2 Incentives for Patronage Increase
All revenue increases are shared so, in the same way as in NZTA1, every $1 of
additional revenue raised as a result of patronage increases is shared between the
operator and the council.
It does not take account of the effects of fare levels on patronage.
4.3 Incentives for Efficient Fares
As with NZTA1 there is an incentive to increase fares because it increases revenues.
There is no bound to this incentive.
4.4 Impacts on Subsidy
4.4.1 Marginal Subsidy
The marginal subsidy impact is the same as under NZTA1. This model has a fixed
element, which is the difference between gross and net indexation and this is unchanged
with changes in patronage and revenues. Each additional passenger (and quantity of
fare revenue received) results in an additional subsidy payment at the same level as
under NZTA1, ie $1.25 for every $2.50 of additional revenue.
4.4.2 Uncertainty
Uncertainty levels are similar to those under NZTA1. An operator knows it will always
gain from increasing patronage, but it final payment is dependent on factors beyond its
control, ie the levels of indexation payment.
12
5 Greater Wellington (GW)
5.1 Description
The Greater Wellington (GW) model shares revenue that is not related to changes in
fares. It uses an approach based on a formula in Section 10.28 of the Procurement
Manual that sets out the basis for resetting contracts following a change in fare levels.
The formula estimates the effects of price change on revenues by estimating:
(1) the increased (or decreased) revenue resulting from current passengers paying
the changed fare;
(2) the change in the number of passengers (increase or decrease) in response to the
change in fare level; and
(3) the effects of the price change on any additional (or fewer) passengers that has
resulted from other impacts on patronage levels.
It is described for application to a net contract as a way to estimate an amount that
would be “clawed back” from the operator to the council. However it could also be used
with a neutral contract to define the amount that went to the council with the residual
amount of revenue change being that attributed to patronage change. This patronage-
related revenue could then be shared between operator and council.
The formula is:
Sharing amount = ΔR - (R0 × ΔFn × (1 + ΔPf)) - (R0 × ΔPf)
Where: ΔR = change in revenue (as in other models)
R0 = revenue in previous year
ΔFn = change in fare level in nominal terms
ΔPf = percentage change in passenger numbers as a result of change in fares
= E × ΔFr
E = price elasticity of demand, assumed to be -0.4 based on NZTA advice
ΔFr = change in fare level in real terms
= ((1 + ΔFn)/(1 + CPI)) – 1
CPI = consumer price index
The formula has a number of elements:
It starts with the total change in revenue (ΔR) before subtracting the effects
associated with price change, which includes the following:
o the change in revenue that is based on the current number of passengers
paying more for their fares (R0 × ΔFn), ie previous year’s revenue times
the change in fare level;
o the change in the number of passengers affected (R0 × ΔFn is multiplied
by 1 + ΔPf). This adjusts the number of passengers that are assumed to
pay the increased price to only those that continue to use PT following
the change in fare level;
o the change in total revenue as a result of the change in the number of
passengers.
13
The model assumes that the remaining revenue change is as a result of increases in
patronage. This is a slight over-estimate. Where patronage has increased because of
actions taken by councils or operators to increase demand at the same time as a price
change, the changes in revenues will include an element that is the changed price paid
by these additional passengers; part of this is a price effect. However, calculating this
adds a considerable level of complexity to the analysis which is unlikely to be
worthwhile.
The impacts are shown in Table 5, including some of the intermediate steps based on
CPI of 2.5% and a price elasticity of demand of -0.4. The other items are the same as
under the previous models. The sharing amount takes no account of indexation and is
the same under gross and net approaches.
Table 5 Sharing under GW Model
5.2 Incentives for Patronage Increase
Any patronage increase increases the shared amount and provides rewards to operators
and the council. Likewise any reduction in patronage is penalised. The incentive is the
same as under the NZTA1 and AT models. However, the GW model isolates revenue
increases from changes in price and operators are not rewarded for such fare changes.
Fare-change related revenue goes to the council.
5.3 Incentives for Efficient Fares
The council receives revenue associated with fare changes whereas those associated
with patronage increases are shared with the operator. If the council wished to
maximise subsidy reduction as an objective it would have the incentive to increase fare
levels. This model may operate best with strict guidelines on fare changes, ie limiting
them to inflationary adjustments.
5.4 Impacts on Subsidy
5.4.1 Marginal Subsidy
The marginal subsidy is the same as in the other models. Each increase in patronage
(that is not directly in response to the introduction of the sharing model) results in a
subsidy equal to the revenue earned per passenger times the sharing amount, ie $1.25
Period Item Case A Case B Case C Case D
Assumptions Revenue change $32,480 $16,160 -$160 -$160
Real change in fares -0.5% -0.5% -0.5% -0.5%
ΔPf 0.2% 0.2% 0.2% 0.2%
Price element of fare change $8,796 $8,796 $8,796 $8,796
Gross Share amount $23,684 $7,364 -$8,956 -$8,956
Indexation Revenue to council $20,638 $12,478 $4,318 $4,318
Revenue to operator $11,842 $3,682 -$4,478 -$4,478
Net Share amount $23,684 $7,364 -$8,956 -$8,956
Indexation Revenue to council $20,638 $12,478 $4,318 $4,318
Revenue to operator $11,842 $3,682 -$4,478 -$4,478
14
for a $2.50 fare. However, as with the discussions above, if the patronage change is as a
result of the incentive of the sharing model, then there is a net reduction in subsidy as a
result of patronage change: the council obtains more revenue as a result.
5.4.2 Uncertainty
The GW model has far more certainty for operators because it removes the uncertainty
associated with factors outside of the control of the operators:
Cost inflation; and
Council pricing policy.
15
6 CPI Model
6.1 Description
The CPI model is a more simplistic version of the GW model that works on the
assumption that councils will raise fares with inflation. It shares all revenue that is
greater or lesser than CPI on the assumption that revenue increases equal to CPI would
be the result of fare increases. Thus the model is specified as:
Sharing amount = ΔR – (R0 × CPI)
Where: ΔR = change in Revenue
R0 = revenue in previous year
CPI = inflation rate using consumer price index
The results of using this model are exactly the same as under the GW model if fares are
increased at the same rate as CPI. The effects are shown in Table 6 with CPI of 2.5% and
fare increases of 2%.
Table 6 Sharing under CPI Model
The model is simple and takes no account of indexation. In Cases C and D above there is
an expectation of an increase in revenue because there is positive CPI (despite the PT-
specific cost index falling in Case D) but revenues fall.
6.2 Incentives for Patronage Increase
As with the other models, any increase in patronage results in an increase in revenue
shared.
6.3 Incentives for Efficient Fares
This model has effective incentives for efficient fares (fares increase at CPI) because any
revenue from fare increases above this are shared with the operator. That said, councils
will continue to benefit from additional fare increases because they benefit from doing
so by some proportion of the associated fare increase.
Period Item Case A Case B Case C Case D
Assumptions Revenue change $32,480 $16,160 -$160 -$160
Expected revenue change (R0 × CPI) $10,000 $10,000 $10,000 $10,000
Gross Share amount $22,480 $6,160 -$10,160 -$10,160
Indexation Revenue to council $21,240 $13,080 $4,920 $4,920
Revenue to operator $11,240 $3,080 -$5,080 -$5,080
Net Share amount $22,480 $6,160 -$10,160 -$10,160
Indexation Revenue to council $21,240 $13,080 $4,920 $4,920
Revenue to operator $11,240 $3,080 -$5,080 -$5,080
16
6.4 Impacts on Subsidy
6.4.1 Marginal Subsidy
The marginal subsidy effect is the same as under the other models. Each increase in
patronage (that is not directly in response to the introduction of the sharing model)
results in a subsidy equal to the revenue earned per passenger times the sharing
amount, ie $1.25 for a $2.50 fare. However, as with the discussions above, if the
patronage change is as a result of the incentive of the sharing model, then there is a net
reduction in subsidy as a result of patronage change: the council obtains more revenue
as a result.
6.4.2 Uncertainty
As with the GW model it eliminates uncertainties associated with indexation. However,
it adds some pricing uncertainty as it assumes that councils will price at CPI. It would
be improved by an associated policy to change fares with inflation.
17
7 Patronage Payment (PP)
7.1 Description
The Patronage Payment (PP) model can be expressed in different ways, but we examine
a simple representation here in which the operator receives an incentive payment for
patronage increases. For example, this might be expressed simply as a dollar payment
per additional passenger compared to a base year. The formula is shown below:
Shared amount = ΔPax × PP
Where: ΔPax = change in passenger numbers
PP = patronage payment (ie an amount paid per passenger)
In Christchurch this approach has been used alongside additional performance
indicators, but the patronage payment is only paid after the number of passengers
exceeded some threshold amount. This would be based on some assumptions about the
expected increase in patronage; such expectations would vary locally but could be
added to the formula, either in absolute terms (an expected number of passengers) or as
an expected growth rate in passenger numbers.
The formula could be expressed in absolute terms as follows:
Shared amount = (Pax – T) × PP
Where: Pax = number of passengers
T = threshold (the targeted number of passengers)
Under such an approach the threshold value might change each year. It could be
expressed in terms of an expected change in the number of passengers as follows:
Shared amount = (ΔPax – ΔT) × PP
Where: ΔT = threshold expressed as an annual change in passenger numbers
The results are shown in Table 7.
Table 7 Sharing under Patronage Payment
Period Item Case A Case B Case C Case D
Start year Passengers 160,000 160,000 160,000 160,000
Fare level $2.50 $2.50 $2.50 $2.50
Revenues $400,000 $400,000 $400,000 $400,000
Year 1 Revenue change $32,480 $16,160 -$160 -$160
Share amount $9,600 $3,200 -$3,200 -$3,200
Revenue to council $22,880 $12,960 $3,040 $3,040
Revenue to operator $9,600 $3,200 -$3,200 -$3,200
18
7.2 Incentives for Patronage Increase
There are straightforward incentives for patronage increase for the operator. It receives
a direct payment. The council also has an incentive as it retains the revenue associated
with the patronage increases.
7.3 Incentives for Efficient Fares
The council obtains all revenues associated with fare increases and thus has an incentive
to increase fares rather than patronage. As with other models this could be addressed
through fare change policies.
7.4 Impacts on Subsidy
7.4.1 Marginal Subsidy
The marginal subsidy is related entirely to the decision on the size of the patronage
payment and its relationship to fare levels. If the PP is greater than the fare level then
there is a net subsidy, but if it is lower there is a reduction in subsidy pre additional
passenger.
7.4.2 Uncertainty
This model provides considerable certainty to operators associated with patronage
increases. It is unaffected by changes in costs (indexation). However, it is affected to the
extent that fare changes made by the council affects the operators’ ability to raise
patronage.
19
8 Comparison of Results
8.1 Impact of Revenue Change
All the models apart from the PP model are based on sharing the change in revenue.
The PP model measures patronage directly. In addition all introduce some limit to the
extent to which revenues are shared. This includes those that adjust the amount to take
account of indexation (NZTA1, NZTA2 and AT) and those that take account of the
impact of fares on revenues (GW, CPI). The PP model can include an absolute threshold
in terms of expected changes in patronage.
We illustrate the effects in Figure 1 using the basic assumptions used in the tables
above.4 It shows how a change in revenue is shared with the operator under the
different models compared with a pure revenue share.5 The sharing amount is the
change in revenue minus some amount that sets a threshold. The threshold pushes out
the level of revenue change before the operator starts to receive a positive share of
revenue. This is most pronounced in the NZTA1 model for which there is no positive
flow to the operator until revenues increase by more than 7.5% with our base
assumptions. NZTA2 follows the pure revenue share line when revenue change is
below zero and the NZTA1 model above the point at which the operator receives
positive revenue. The CPI model follows the GW model exactly as we have set fare
increase equal to CPI.
Figure 1 Impacts of Revenue Change on Operator Revenue
4 Start AGC = $1 million; start CR = 40%; gross indexation = $30,000; CPI = 2%; fare increase = 2% 5 The Pure Revenue Share has a formula of: sharing amount = ΔR
-$40,000
-$30,000
-$20,000
-$10,000
$0
$10,000
$20,000
$30,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Revenue Change (% of Start Year)
Pure revenue share
NZTA1
NZTA2
AT
GW
CPI
20
An important thing to note is that the angle of the line is the same in all models. The
operator obtains a share of any incremental increase in revenue and the amount is the
same in all models, and is the same as they would receive under a pure revenue share.
This is because all of the models have the basic formula of:
Sharing amount = ΔR - x
Understanding this helps to focus the analysis on the appropriate ‘x’.
The value for x in the different models is as shown in Table 9. We do not include the PP
model here as it is specified differently, but it can be defined in a way that performs in
exactly the same way as the others. In its basic form, if the patronage payment is set
equal to 50% of the revenue received per additional passenger, it is exactly the same as
the pure revenue share. It can then approximate the others by including a threshold.
Without these modifications (eg with no threshold and an arbitrary payment per
passenger) it would be equivalent to the pure revenue share but with a different slope.
Table 8 x-value in the different models
Model x-value Formula
NZTA1 Full indexation ΔR - I
NZTA2 Full indexation (or zero) ΔR – I (or ΔR or 0)
AT Gross minus net indexation ΔR – Ig + In
GW Revenue change that results from fare change ΔR - R0 × ((ΔFn + 1) × (ΔPf + 1) - 1)
CPI Revenue change that results if fare change = CPI ΔR – (R0 × CPI)
If we regard patronage as the only variable that operators can influence, then all other
factors are essentially a fixed element in the equation. They set the absolute level of
revenue but do not change the incremental revenue received for each additional
passenger. In some ways this makes the models all exactly equivalent. To the extent that
the x-factor is fixed and cannot be influenced by the operator, it will be estimated at the
beginning of the contract and included in the initial bid price. All that matters is then
that the operator has an incentive to increase patronage.
However, if these factors are not predictable, the specification of the formula matters.
The first three models (NZTA1, NZTA2 and AT) use indexation as the threshold. This
shares costs with the operator in addition to revenue. It is equivalent to an approach in
which, in order to be able to benefit from sharing revenue change, the operator must
accept less generous indexation.
The GW and CPI models both set a threshold equal to the revenue change expected
from the change in fare level. The GW calculates the revenue associated with the fare
change; the CPI model assumes that fares change with CPI. They isolate the impact of
patronage change from fare change (if there was zero CPI and no change in fares, both
models would be the same as the pure revenue share).
21
8.2 Incentives to Increase Patronage
All the models provide reasonable incentives to increase patronage, with the exception
of NZTA2 which, under a number of likely outcomes, will provide no patronage
incentives. In the other models any increase in patronage will result in an increase in
revenue and this marginal increase in revenue will be shared using the agreed
percentage.
Apart from PP and NZTA2, the marginal incentive is exactly the same across the
models, as shown in Figure 1 above: an additional passenger will result in the same
level of net additional revenue for the operator. The PP model works in the same way
but with the amount related to the patronage payment. It can be specified to provide the
same marginal incentive.
8.3 Adjusting Revenues for Fare Effects
Two of the models, GW and CPI, adjust the revenue changes to take account of price
(fare) effects. These isolate the impacts of revenue that are associated with patronage
and share only these with the operator. The GW model does this more explicitly and is
more complex. The CPI model operates on the assumption that fares will be increased
equal to inflation and does not share the revenue increases that result from that
adjustment. The PP model effectively isolates patronage-related revenue by measuring
patronage directly.
The other models do not isolate revenue from patronage from revenue from fare
adjustments.
8.4 Incentives for Efficient Fares
The models differ with the extent to which they provide incentives for efficient fares.
The NZTA models and the AT model result in the council sharing any revenue
increases, whether they are patronage or fare-related, and whether or not the fare
increase is equal to, less than or more than inflation. With an estimated price elasticity of
demand of -0.4 there is always a revenue gain from increased fare levels, ie the revenue
gain is greater than any negative impact on patronage. As the council gains a share from
revenue increases it benefits from all fare increases.
The GW model identifies the fare-related revenue and allocates this fully to the council.
In doing so it provides an increased incentive to a council wishing to minimise subsidy
levels to increase fares at more than the rate of inflation. It would be best introduced
with a policy to limit fare increases to inflation.
The CPI model assumes that fares will increase with inflation and all revenues up to this
point will accrue to the council; however beyond this the council has the same incentive
to increase fares as under the NZTA and AT models – it benefits by sharing a proportion
of any revenue increase.
22
The PP model has some incentive to maximise fares if the council wishes to minimise
subsidies because the council retains all revenues that are not associated with increases
in patronage.
8.5 Subsidy Impacts
8.5.1 Subsidy Per Additional Passenger
In discussing the impacts per additional passenger we need to isolate two possible
effects:
1. The sharing model has no influence on patronage. Any increase in patronage
would have happened without the sharing model. Here, because each additional
amount of revenue results in a payment to the operator under all models (Figure
1), so each additional passenger results in an increase in subsidy by the same
value. This is money that otherwise would be with the council, assuming a start
point of a gross contract. Starting with a net contract, each additional passenger
results in a reduction in subsidy because it leads to a transfer to the council.
2. The sharing model influences patronage as it increases the incentive on the
operator. Here the additional revenue that comes from the patronage increase is
revenue that would not have happened otherwise; total subsidy levels reduce
per additional passenger.
These effects occur with all models. The effect is limited with NZTA2 simply because in
some instances it provides no patronage incentive.
8.5.2 Revenue Certainty
The impact on revenue certainty differs between the models. Uncertainty is greatest
where the revenue that the operator might earn is most affected by factors that are
beyond its control.
Those that adjust the payments for indexation introduce most uncertainty, particularly
the NZTA1 model. If costs rise significantly, the operator will face a net cost unless there
is a substantial increase in revenues. And these effects are most pronounced for
contracts with low commerciality ratios.
NZTA2 is more certain because there are a number of circumstances in which there will
be no sharing.
The AT model has uncertainty associated with the effects of indexation, but this is much
less than under NZTA1.
There are also uncertainties associated with the fare level decisions of councils. These
are reduced by the models that take account of fare changes (GW and CPI) and are
removed in the PP model that simply rewards patronage.
23
8.6 Summary of Effects
Table 9 summarises the effects under the different models.
Table 9 Summary of Models
Factor NZTA1 NZTA2 AT GW CPI PP
Sharing amount based on change in revenue
×
Threshold/adjustment Indexation Indexation Indexation difference
Fare-related effects
Real fare change
Can be included
Marginal incentive to increase patronage
×
Shares costs × × ×
Isolates patronage × × ×
Efficient incentive to change fares
- - - × - ×
Certainty of operator outcome
×× × ×
All share an amount that is some proportion of the change in revenue. The PP
model does not, but it is equivalent to doing so.
All include a threshold or adjust the revenues such that they are not pure
revenue share models. The GW and CPI models adjust revenue to focus on
patronage revenue only. The PP model focuses directly on patronage, and it can
be specified to include a threshold.
All models provide a marginal incentive to increase patronage, although the
NZTA2 model provides no incentive across a range of outcomes.
Three models (NZTA1, NZTA2 and AT) share costs in addition to revenue and
the other three models isolate revenue from patronage.
None of the models provide incentives to change fares efficiently, that we
define as increasing at the rate of inflation. This is because, if the price elasticity
of demand is less than -1 as NZTA assumes) the council will always gain from a
fare increase. Under the GW and PP models there is a particular incentive to
raise fare levels at the expense of patronage.
Subsidy levels are most likely to be differentiated by the differences in certainty
for operators. Those that adjust the amount paid to operators with changes in
costs introduce most uncertainty, particularly NZTA1. The PP has greatest
certainty as it limits payment explicitly to patronage. The GW and CPI models
attempt to isolate patronage revenue, but do so imperfectly.
24
9 Sensitivity Analysis
9.1 Factors Analysed
In this section we use the same basic presentation of results as in Figure 1 to show the
effects of the different models. We assess these against changes in:
commerciality ratio;
indexation;
fares;
patronage
We start with the base assumptions shown in Table 10 and we test the options listed.
Table 10 Base Assumptions and Sensitivities for Sensitivity Analysis
Factor Start Value Options
Start Year Annual Gross Costs $1,000,000
Commerciality Ratio 50% 25%, 75%
Start Revenue $500,000
Costs Increase (Gross Indexation) 3% -1%
Gross indexation $30,000
Net indexation $15,000
Fares Increase 3% 0%
CPI 2.5%
The main results are shown in Figure 2.
Figure 2 Impacts of Base Assumptions on Operator Revenue
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
25
It differs from Figure 1 in that the x-axis is equal to patronage change rather than
revenue change. Thus the pure revenue share line does not pass through the origin. At
zero patronage change there is still an increase in revenue from the change in fare levels.
We have not included NZTA2 in the chart; it can be pictured as tracking the pure
revenue share (PRS) when the PRS results in an operator payment below zero and the
NZTA1 model when it will produce a net positive payment.
9.2 Commerciality Ratio (CR)
Figure 3 and Figure 4 show the results using CRs of 25% and 75% respectively.
Changing the CR changes the slope of the lines. This is because the assumed CR changes
the estimated number of passengers in the start year. Thus a given percentage increase
results in a smaller sum in dollar terms (or larger if starting with a high CR).
Figure 3 Impacts of 25% CR + Base Assumptions on Operator Revenue
Figure 4 Impacts of 75% CR + Base Assumptions on Operator Revenue
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
26
The other main impact is to change the relative position of NZTA model. The position at
which the NZTA model crosses the x-axis shifts; all other models are unaffected. The
NZTA1 model is affected by CR because the threshold is unrelated to start year revenue.
At a low CR (low start year revenue) a very large percentage increase in revenue is
required to overcome the gross indexation cost. The AT model is different because net
indexation levels change with start year revenues, and if CR is low (and subsidy is
large) the difference between gross and net indexation is small also. If CR is high
(subsidy is small) there is a large difference between gross and net indexation.
9.3 Fares
The effects with no fare change are shown in Figure 5. The impact on all models it to
shift them to the right. In order to overcome the fixed effects there is a need for a larger
increase in patronage because there is no income coming from revenue increases.
Figure 5 Impacts of 0% fare change + Base Assumptions on Operator Revenue
The GW model results in a much smaller shift (compared with Figure 2) than the other
models because the model is correcting for the change in fares. There is still some shift
because the model does not perfectly adjust for the effects of fare changes.
9.4 Costs
Figure 6 shows the effects of a 1% reduction in costs (indexation) under the different
models. There is no impact on the GW, CPI model or pure revenue share because they
are unaffected by costs. In contrast the NZTA1 and AT models all shift upwards, ie the
x-factor threshold is reduced and a smaller increase in patronage is required to achieve
positive transfers.
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
27
Figure 6 Impacts of -1% cost change (indexation) + Base Assumptions on Operator Revenue
9.5 Combinations
For completeness we show the results for combinations of inputs below. These are 0%
fare changes at alternative commerciality ratios.
Figure 7 Impacts of 25% CR + 0% fare change + Base Assumptions on Operator Revenue
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%O
pe
rato
r R
eve
nu
e S
har
e
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%
Op
era
tor
Rev
en
ue
Sh
are
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
28
Figure 8 Impacts of 75% CR + 0% fare change + Base Assumptions on Operator Revenue
-$60,000
-$40,000
-$20,000
$0
$20,000
$40,000
$60,000
-8% -6% -4% -2% 0% 2% 4% 6% 8% 10%O
pe
rato
r R
eve
nu
e S
har
e
Patronage Change (% of Start Year)
Pure revenue share
NZTA1
AT
GW
CPI
29
10 Summary and Conclusions
10.1 Model Form and Approach
The different models pursue one of two basic philosophies. They either:
Seek to share cost risk with the operator in addition to revenue risk – NZTA1,
NZTA2 and AT; or
They seek to isolate revenue increases relating to patronage only as the only
element that the operator can influence.
All the models (apart from PP) have the same basic form of:
Sharing Amount (SA) = ΔR – x
The NZTA2 model varies and can be specified as SA = Δr or SA = 0
10.2 Incentives for Patronage Increase
Because x is a fixed amount, and ΔR varies with patronage, all (apart from NZTA2 and
PP) provide the same incentives for patronage increase (and PP can be adjusted to
achieve this also).
ΔR also varies with fare levels. The GW and PP models (and to a lesser extent the CPI
model – or only alongside fares policies) do not provide operators with benefits from
fare-related revenue changes.
10.3 Efficient Fares
Because demand is estimated to be inelastic (patronage levels will fall less than price
increases), increasing fares will always raise more revenue which is obtained by the
council (and the operator in NZTA, AT and CPI models). Councils may have an
incentive to increase fares above inflation to obtain more revenue. The GW model
isolates revenue from fare increases, but does so in a way that incentivises more fare
increases (the council retains all fare-related revenue). Guidelines/rules on fare increases
would reduce this uncertainty.
10.4 Subsidy Levels
The specification of x determines how much revenue is retained by the council before
the operator receives a share of revenue (and thus potentially how low the subsidy is),
but the expectation of future x means that it will affect initial bid prices also. Thus with
perfect information all models would result in the same level of subsidy.
Because there is not perfect information, what affects subsidy levels will be the extent to
which the models increase or decrease certainty for the operator. More uncertainty will
require more subsidy to compensate for risk. Uncertainty is greatest when the level of x
varies with costs (particularly under the NZTA1 model and to a lesser extent the AT
30
model). There is also uncertainty associated with the councils changing of fares; as
noted above these can be addressed through fares policies.
10.5 Key Decision Choices
If fare policies (that limit fare rises to CPI) are set alongside the introduction of a
partnership model, uncertainties relating to fares are largely eliminated. This then
provides a clear choice between models that either seek to isolate patronage related
revenue increases (GW, CPI, PP) and those that seek to share some underlying cost risk
(that cannot be eliminated) with the operator in addition to revenue risk.
If isolating patronage increases is desired, the PP model does this most explicitly and
simply. The GW model is somewhat complex and can deal with situations in which fare
levels vary from CPI. The CPI model is based on an assumption that fare policy is
adhered to.