Partnership models: analysis of options - NZ …...7 Patronage Payment (PP) 17 7.1 Description 17...

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




4 AT Model 10

4.1 Description 10




5 Greater Wellington (GW) 12

5.1 Description 12




6 CPI Model 15

6.1 Description 15




7 Patronage Payment (PP) 17

7.1 Description 17




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


8.5 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


10.3 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


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





Revenues $400,000 $400,000 $400,000 $400,000


Subsidy $600,000 $600,000 $600,000 $600,000

Year 1 Cost change 3.0% 3.0% 3.0% -1.0%




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.


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.


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.



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





Revenues $400,000 $400,000 $400,000 $400,000


Subsidy $600,000 $600,000 $600,000 $600,000

Year 1 Cost change 3.0% 3.0% 3.0% -1.0%




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


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


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.


As with NZTA1 there is an incentive to increase fares because it increases revenues.

There is no bound to this incentive.



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


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.


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.



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


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



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.


As with the other models, any increase in patronage results in an increase in revenue

shared.


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.


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



Net Share amount $22,480 $6,160 -$10,160 -$10,160



16



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


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


18


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.


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.



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.


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


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


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


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


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


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


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


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.

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