Public private partnership with government included demand risk a case study from viet nam

Public-Private Partnerships with governmentinduced demand risk: A case study from
Vietnam
Vinh-Thang HOANG 1

ABSTRACT
This research considers the Phu My Bridge in Ho Chi Minh City (Vietnam) in a context of
increasing private-sector participation in Vietnam’s infrastructure sector. It analyzes the
bridge’s financial distress as the consequence of the public sector’s failure to deliver on its
commitment to complete city’s ring road project on time. The paper’s model considers the
private-sector investor and the government in a two-party interaction, where the government
may overstate its capability to deliver supporting infrastructure. If this is the case, the
private sector party makes a loss to the extent that it is misled. Furthermore, even if the
government chooses to rescue the private sector party, its own commitment would increase
but would not reach the no-deviation scenario. These results call for more transparency as
well as improved communication channels between the parties. Finally, the paper discusses
other important issues of the project that the model voluntarily leaves out.
Keywords: Vietnam, Phu My Bridge, Public-private partnerships, Demand risk

1. INTRODUCTION
Over the last decade, infrastructure has gathered renewed interest, especially from
institutional investors given its particular characteristics as an investment (Sawant 2010).
However, roads, bridges or aqueducts have been around for millennia, constructed by

Université Paris-Dauphine
Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16
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civilizations both ancient and modern to drive trade, integration and progress. Once being
the responsibility of the governing body, with time the private sector is increasingly called
upon as well.
On the other hand, as the ongoing AIIB (Asian Infrastructure Investment Bank) initiative is
any indication, emerging markets and particularly Asia is where a significant portion of
infrastructure demand will be. This demand is estimated at USD 800 billion per year from
2010 to 2020 (Bhattacharyay 2010). Asian countries such as Vietnam are also massively
turning towards the private sector to finance their infrastructure.
In this paper, the author has chosen to explore this link between infrastructure and
emerging markets by providing a case study of the Phu My Bridge in Vietnam. Located in Ho
Chi Minh City whom it connects two key districts, the bridge had been one of the largest in
Vietnam at the time of its construction. However, it is in financial distress for reasons
detailed later in this paper. Understanding these reasons will therefore provide valuable
lessons for Vietnam in enlisting the private sector in infrastructure development, and this is
the first reason that motivates this paper.
From an academic standpoint, the Phu My Bridge is also worth considering. The paper will
argue that the public sector’s behavior may be interpreted as opportunistic and this has
contributed to the bridge’s financial difficulty. For this, the paper will develop a theoretical
model and show even with simplifying assumptions we can come upon a number of results
worth interpreting.
The remainder of this paper is organized as follows. Section 2 provides a background to this
research. Section 3 develops a theoretical model to analyze the behavior of the government in
this project. Section 4 points out the limitations of the model compared to real life and what
we may learn from them. The final section concludes.

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2. BACKGROUND TO THE STUDY
2.1. Background on Vietnam

2.1.1. Economic context
Since the country’s opening up during the late 80s, Vietnam has made some great strides on
creating a market economy. Real GDP growth averaged 6.9% from 1990 to 2013, according to
the World Bank’s data. In parallel, vast institutional changes were introduced to attract
foreign investments, resulting in Vietnam becoming one of the top destinations for foreign
direct investments (FDI) in the region. FDI commitments amounted to USD 22.4 billion in
2013 (Báo Đầu Tư 2014).
The private sector in Vietnam was also a big beneficiary of the sweeping reforms. The
number of State-Owned Enterprises (SOEs) declined from 6545 in 1992 to about 3000 in
2010 and they only account for about 10% of the country’s employment (Le Hoang Cuong,
Helen and Ruhul 2014). The private sector’s contribution to the national economy, on the
other hand, rose to between 57% and 67% of the GDP (ADB 2005).

2.1.2. Private participation in infrastructure development
When the reforms began in Vietnam, the country’s infrastructure was in shambles due to
lack of investment. However, over the next two decades the country has ramped up its
infrastructure spending, which now represents a significant percentage of GDP. According to
Vietnam’s General Statistics Office (GSO), the country spent on average 10.6% of its GDP on
infrastructure from 2009 to 2011. This estimate is on the higher end of the regional range, as
a research report showed none of Vietnam’s emerging neighbors in the ASEAN2 spent more
than 10% of GDP (Goldman Sachs 2013).
Faced with this intensifying need in infrastructure spending, Vietnam’s government budget
is currently under increasing scrutiny from the public and capital markets, and the budget
deficit was estimated at 5.5% in 2013 (ADB 2014). Domestic bank financing have become
2

ASEAN: Association of Southeast Asian Nations

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more difficult since 2008 with rates sometimes as high as 20%. Foreign bank financing is
also challenging due to more stringent international banking regulations. The Bank for
International Settlement itself admitted emerging countries were “particularly concerned”
about Basel III’s impact on the availability of funds (Bank for International Settlements
2014).
Consequently, Vietnam is relying more and more on the private sector to keep up with
infrastructure demand, something recognized very early by the government. The first
amendment of the country’s Law on Investment in 1992 introduced the first legal framework
for BOT (Build-Operate-Transfer) contracts. Subsequent Decisions issued by the government
detailed other frameworks such as BT (Build-Transfer), BOO (Build-Own-Operate) or BTO
(Build-Transfer-Own). Since then, 82 projects with private participation reached financial
close in Vietnam until 2013, with a total cost of USD 11.6 billion (World Bank 2014).

2.2. The Phu My Bridge
2.2.1. The context
The Phu My Bridge connects Districts 2 and 7 of Ho Chi Minh City, Vietnam’s economic
powerhouse with 9% of the national population and 20% of the national GDP in 2012. At the
time of its construction, the bridge had been one of the largest infrastructure projects ever
undertaken in the city. After completion, it would create a profound impact both for the city
and for Vietnam as a whole. Being part of the city’s ongoing ring road project, the Phu My
Bridge provides a quick way to move from East to West of the city, and in the near future the
bridge would link up two major sections of Vietnam’s 1800-km under-construction national
expressway (VnExpress 2014).
A map of the Phu My Bridge’s location is provided below:

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Figure 1: Location of the Phu My bridge and the ring road project – (Tang Quoc Cuong 2010, 139)

2.2.2. Implementation
The Phu My Bridge was constructed under the BOT (Build-Operate-Transfer) model, for a
projected investment of VND 1800 billion (USD 115 million at the time). The World Bank
defines a BOT project as one where “the public sector grantor grants to a private company the
right to develop and operate a facility or system for a certain period (the "Concession Period"),
in what would traditionally be a public sector project” (World Bank 2014). For the Phu My
Bridge, the developer is Phu My Bridge Corporation (PMC), an entity backed by a number of
investors.
The main EPC (Engineering, Procurement & Construction) contract was awarded to BBBH
consortium, which consisted of Germany’s Bilfinger Bergerm and Australia’s Balderstone
Hornibrook. The main debt financing package was co-syndicated by two French banks
Société Générale and Crédit Agricole CIB. It consisted of a USD 60 million buyer credit and
another untied USD 34 million loan. The buyer credit is insured by Germany’s Euler Hermes

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and reinsured by France’s Coface and Australia’s EFIC3, and the entire debt facility is lent to
Ho Chi Minh City Finance & Investment Company (HFIC), a public entity established by the
city’s government. HFIC then lent the proceeds to PMC, thus allowing the latter to benefit de
facto from the guarantee of the City’s government (this technique is known as on-lending).
Loan repayments from HFIC are in turn guaranteed by Vietnam’s Ministry of Finance
(MoF). The lending contract was signed in 2005 and entered into force in 2007. However, a
number of domestic banks such as BIDV and Sacombank also provided financing to PMC.
Below is a summary of the key parties:

People’s Committee of
HCMC
Ticket price regulator &

BOT contract signatory
Guarantor
Lenders

MoF

Société
Générale
Crédit
Agricole

Other
domestic
lenders

Phu My Bridge Corporation
Domestic shareholders
On-lender
HFIC

End-users

Main contractors
Bilfinger Bergerm,
Baulderstone Hornibrook

Export finance guarantors
Coface, Euler Hermes, EFIC

Sub-contractors

Freyssinet, CC620

Figure 2: Summary of the main parties involved

Euler Hermes, Coface and EFIC are examples of Export Credit Agencies (ECA), public or quasipublic entities that engage in export financing and international credit insurance.
3

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Construction started in 2005, was delayed by two years due to in land acquisition issues but
wrapped up successfully in 2009. PMC began to collect tolls starting from April 2010, after
the ticket price was approved by the City’s government.

2.2.3. Financial distress
After the bridge’s opening, it became clear to PMC that its viability was threatened. Two
factors explain the bridge’s financial distress:
First, the actual investment amount has been heavily revised upwards. In 2010, just a few
months after the bridge’s opening, PMC asked government of Ho Chi Minh City to approve a
new investment amount of VND 3030 billion, a 68% increase over the initial approved
amount of VND 1800 billion, citing various unplanned costs such as interest during
construction, revised costs due to inflation and foreign exchange loss. The city government
appointed an independent accounting firm to audit the total project cost. The result was
published in May 2013 and placed the investment made by PMC at VND 3250 billion (Tuoi
Tre News 2014).
Second, fee revenue has been largely underneath what was needed to repay loans and recoup
the initial investment. Ho Chi Minh City-based economist Nguyen Xuan Thanh investigated
real traffic going through the bridge and found out that in terms of Passenger Car Units
(PCU), real traffic only represented 53.7% of traffic assumptions made in the initial financial
plan (Nguyen Xuan Thanh 2013). In a letter addressed to the city government in 2011, PMC

put the blame on the city for low traffic demand. According to the company, the ring road
projects of Ho Chi Minh City were incomplete and the city government had not prohibited
heavy vehicles from going through the city center (VnEconomy 2011).
From an economic standpoint, these claims are not without merit. The rationale behind the
project was to capture traffic from the South and West of the City to the North (see Figure 12
below). As the Eastern ring road project (managed by the city’s government) is not yet
completed (dotted line on Figure 12), vehicles would choose to follow the old National Road

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1A (red line) or going through the busy city center instead of the Phu My Bridge. (VnExpress
2014). As of February 2015, there were still at least one bridge to be constructed to close the
ring road completely, and construction would only begin in the future (Official Journal of Ho
Chi Minh City 2015).

Phu My Bridge

Figure 3: Uncompleted sections of the ring road project (VnExpress 2014)

Initially, the government had agreed in the initial contract to have the Eastern ring road
ready three years after the bridge’s completion at the latest (Nguyen Xuan Thanh 2013). If
this is not the case, the government would receive back the project and reimburse PMC for the
investment outlay plus interest. This outcome, however, would have to be pronounced by a
court. Although PMC seems to have an advantage in this situation, there are actually
reasons to believe the company had allegedly committed violations of the initial contract
itself by overleveraging the project, all of which will be the topic of a later section of the
paper. At present, therefore, two parties are pursuing negotiation to resolve the issue.

2.3. Theoretical background and contribution

Public-private partnerships (PPPs) have long been a focus of research both in academia and
in international organizations, but there is no clear-cut definition of a PPP both in academic
research (De Clerck, Demeulemeester and Herroelen 2012) and in publications by

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international organizations (World Bank PPP IRC 2015), (OECD 2008). There seems to be
agreement, however, on the necessity to analyze PPPs as mechanisms of risk allocation by
which each risk is borne by the party better positioned to do so.
PPPs are themselves contract, and they been the subject of a particular strand of contract
theory literature. One of the earliest references on the subject was done by Jean Tirole and
Jean-Jacques Laffont, who provided a game-theoretic analysis of regulation and procurement
contracts (Laffont and Tirole 1993). One of the concepts proposed by Laffont and Tirole to
analyze the public sector’s decision-making process is called shadow cost of public funds,
which will be used again later on in this paper. This provided the groundwork necessary for
subsequent authors’ research. In a 2005 paper, the economists Dewatripoint and Legros
showed if it was too costly to avoid cost overruns then letting cost overruns happen would be
a better solution overall. PPPs are therefore not a silver bullet to cure the ills of
infrastructure projects. The role of institutions is crucial in opening up public projects for
competition and ensuring the latter is respected by all stakeholders (Dewatripont and Legros
2005). In another study, it is shown that PPP might be less efficient than other financing
modes due to transaction costs that may be incurred by choosing the PPP model. These
transaction costs come from three sources: (1) principal-principal problems, (2) renegotiation
and hold-up problems, and (3) soft budget constraints (Ho and Tsui 2009).
Renegotiation was the particular focus in an earlier paper by Ping Ho (S. P. Ho 2006), which
used a game structure. First, the project encounters an unfavorable event such that the
developer can either request a public subsidy or let it go bankrupt. The government may
choose to negotiate to lower the subsidy or reject the request altogether. If the project goes
bankrupt, the government has a negative payoff reflecting political costs of restructuring the

project. If the subsidy request is accepted, then the government suffers from another type of
political costs due to budget spending to rescue a private sector company. These
specifications reflect shadow cost of public funds, a concept used later in this paper’s model.

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The recent PPP market in Vietnam has not so far captured interest from researchers, with
the exception being a short case study by economist Nguyen Xuan Thanh specifically about
the Phu My Bridge itself (Nguyen Xuan Thanh 2013). Therefore this paper, by focusing on
the Phu My Bridge, is making a contribution as it is among the firsts to study PPPs in
Vietnam and the first to do so with a formalized analysis of a particular project. Secondly,
while some papers may focus on the moral hazard of the private-sector party who is
supposedly better informed, this paper studies a possible moral hazard of the public sector
concerning their ability to deliver and realize its prior commitment. As the paper would try
to demonstrate, such decision to deliver (or not) may be interpreted as an equilibrium
decision.
In short, the paper’s approach is pragmatic: it starts from a real project, presents a simple
theoretical model and uses the model to analyze one key aspect of the project which is the
possible opportunistic behavior of the public sector. In doing so, it voluntarily departs from
other issues. The paper asks the following questions: What is the motivation of the
government in the Phu My Bridge? Why would the government be induced to not give an effort
in constructing the ring roads? And finally, what lessons can Vietnam learn from the project?
By searching for answers to these questions, the paper tries to contribute to both the existing
literature and Vietnam’s still nascent PPP market.

3. THE MATHEMATICAL MODEL
3.1. Preliminary assumptions
We consider two parties, the government of Ho Chi Minh City (public sector) and Phu My
Corporation (private sector). The government wants to have a bridge constructed across the

Saigon River, and at the same time it also has to invest in the City’s ring road project. Each
party has no information on the real intents of the other party and do not make assumptions
regarding the behavior of their co-signatory.

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Construction cost of the Phu My Bridge project is assumed to be fixed, known perfectly
in advance by all and consists only in the initial investment outlay 𝐾:
𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝐾
𝜕𝑇𝐶

There is no variable cost, and marginal cost ( 𝜕𝑄 ) is zero. To simplify further, we normalize 𝐾
at 1, therefore 𝑇𝑜𝑡𝑎𝑙 𝐶𝑜𝑠𝑡 = 𝐾 = 1. This feature is a departure from real life, where the
project cost was not certain and subject to dispute.
We also make other simplifying assumptions regarding operations:


Under public management, the city allows free access to the bridge for everyone;



The bridge has unlimited capacity;



The government only allows toll pricing at average cost so that PMC can break even4.

We consider traffic demand to be completely inelastic with regards to toll price (this is
also a simplification). However, we suppose the traffic level on the Phu My Bridge will

depend on the government’s investment on the city’s ring road project:
𝑄 = 𝛼𝐼
Where:


𝑄 is actual traffic demand.



𝐼 is the investment made by the city’s government in the ring road projects. Traffic
demand is an increasing function of this investment.



𝛼 is a parameter and measures the sensitivity of demand on 𝐼, i.e. 𝛼 =

𝑑𝑄
.
𝑑𝐼

The higher

𝛼 is, the higher the impact of each unit invested in the ring road on the Phu My
Bridge’s traffic demand. We suppose 𝛼 > 1.

The government cannot make Phu My Corporation provide free access by sacrificing the project’s
financial viability, but at the same time we assume the government does not want to leave out rent to
PMC either.
4

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There is a timeline but no discounting and other time-related matters. The timeline of the
project depends on whether it is under public or BOT management and is visualized below:
Timeline (A): Public management
0
1

∞

Construction


Timeline (B): BOT management
0
Construction



Public management
 At 𝑡 = 1, construction is completed
 Traffic demand is 𝑄 = 𝛼𝐼

The public manager begins construction
of the Phu My bridge and the ring road
project at 𝑡 = 0

At 𝑡 = 0, the parties sign the contract
Each party proceeds to invest/construct

accordingly without observation of and
from the other party

1

2

∞

Concession period (BOT)

Public management

 At 𝑡 = 1 , information about effective
demand arrives
 Demand during the concession period is
𝑄
𝛼𝐼
𝑄1 = = (half of total demand)

 At 𝑡 = 2, the project is transferred back
to public management
𝑄
 Demand during this period is 𝑄 2 = =

2

2

𝛼𝐼

2

2

(the other half of total demand)

Figure 4: Timelines used in the model

These two timelines were inspired by a paper about BOT concessions by two French
economists (Auriol and Picard 2013), where the authors used a continuous-time framework
with separate intervals that represent the concession period the post-transfer period.

3.2. Baseline model (0): Public management
In this first model denoted with the subscript 0, we assume complete public-sector financing
and management. Timeline (A) above is therefore the relevant one.
Being responsible for financing two projects at once (Phu My bridge plus the ring road), the
government’s expenditure consists in two components:


Investment in the Phu My Bridge project, normalized at 1.



Investment in the ring road, denoted 𝐼.

From 𝑡 = 1 (when construction is over) to 𝑡 → ∞, the public manager will make the bridge
available free of charge for all (𝑃0 = 0 where the subscript 0 denotes model 0). As such, the
bridge produces no revenue for the city’s government at all levels of traffic (and we suppose
that no tax is being raised to directly finance the project). The P&L of the government is:
Π0𝐺 = 𝑃0 𝑄 − 𝐾 = 𝑄 × 0 − 1 = −1

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The government makes a loss equal to the initial investment outlay. This loss, or in other
words the investment outlay itself, has to be drawn from the government’s budget. However,
in so doing the government subjects itself to “shadow cost of public funds”, which is now
developed in more details.
This notion was used in a theoretical paper (Auriol and Picard 2013) to model the total cost
of public fund and this approach is also similar to (S. P. Ho 2006). The authors gave the
notion’s origin to Laffont and Tirole’s book (Laffont and Tirole 1993). In this paper, we
consider a slightly modified specification for shadow cost of public funds.
Definition of shadow cost of public funds: Let 𝑥 be the amount the government spends to
develop infrastructure. The real cost of this spending from the government’s perspective,
denoted 𝐿(𝑥), will be:
𝐿(𝑥) = 𝑥 + 𝛽𝑥 2 where 𝛽 > 0
The real cost of 𝑥 units of public infrastructure equals 𝑥 plus a political cost of 𝛽𝑥 2 . The
political cost component assumes a parabolic form, suggesting each additional unit spent will
𝜕2 𝐿

be more politically costly than the last (𝜕𝑥 2 = 2𝛽 > 0). This interpretation is consistent with
reality, where deficits and budgets are given increasing scrutiny. The positive parameter 𝛽
plays a crucial role in the model, as it determines the government’s sensitivity to this budgetrelated political loss.
The government’s welfare takes the following form:
𝑊0𝐺 = ⏟
𝑄 − 𝐿(𝐾) − 𝐿(𝐼)
=𝛼𝐼

In other words, the government would be “happier” if more people use the bridge, but it has
to balance this with the cost to invest in two infrastructure projects at once. The control
variable for the government is 𝐼, the amount invested in the ring road project. However, in

contrary to certain models of benevolent governments such as (Auriol and Picard 2013), the
government in our model does not take into account consumer surplus since the demand
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function is absolutely inelastic. Absolute price inelasticity (zero elasticity) means consumers
would not modify their demand no matter the price, and therefore there is no consumer
surplus.
The optimal investment 𝐼0∗ is solution to maximizing the government’s welfare:
𝐌𝐚𝐱
𝐼0

(1 + 𝛽) − ⏟
(𝐼0 + 𝛽𝐼02 )
𝑊0𝐺 = 𝛼𝐼0 − ⏟
=𝐿(𝐾)

=𝐿(𝐼)

The first-order condition is:
𝜕𝑊0𝐺
𝜶−𝟏
= 𝛼 − 1 − 2𝛽𝐼 = 0 ⟹ 𝑰∗𝟎 =
𝜕𝐼
𝟐𝜷
Recall that we assumed 𝛼 > 1, therefore 𝐼0∗ is positive.
Verification of the second-order condition:

𝜕2 𝑊0𝐺
𝜕𝐼2

= −2𝛽 < 0 . Therefore 𝐼0∗ maximizes the

government’s welfare.
Having the investment amount at equilibrium, we can compute the other variables. Traffic
demand resulting from the investment is:

𝑄0∗ = 𝛼𝐼0∗ =

𝛼(𝛼 − 1)
2𝛽

The maximum welfare amount of the city government is:

𝑊0𝐺∗ =

(𝛼 − 1)2 𝛼(𝛼 − 1) (𝛼 − 1)2 𝛼 − 1
𝛼(𝛼 − 1)
𝛼−1
−𝛽−1−
−𝛽×
=
−
−
−𝛽−1
2𝛽
2𝛽
4𝛽 2
2𝛽
4𝛽

2𝛽

=

3.3. Model

(𝛼 − 1)2 (𝛼 − 1)2
(𝛼 − 1)2
−
−𝛽−1=
−𝛽−1
2𝛽
4𝛽
4𝛽

(1):

BOT

management

without

government

opportunism
From this point on in the paper, we will use timeline (B), since we are now considering
private-sector participation. The model in this section takes the subscript 1.

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We suppose that when the city’s government and Phu My Corporation sit together, they
agree to maximize their collective welfare (recall that there is no consumer surplus). The
general expression of collective welfare (public and private) is defined as the following:
𝑊1 = Government ′ s welfare + Profit of PMC = 𝑊1𝐺 + Π𝑃𝑀𝐶
Two comments/assumptions are made to simplify the expression of 𝑊:


The government’s welfare takes the same form as in model 0 and they still have no
revenue from both projects since there is no toll under public management;



Section 3.1 (Preliminary assumptions) supposes the BOT regulatory framework
allows PMC to price toll at a level which allows them to recoup the initial investment
of 𝐾 = 1, but not more. Therefore Π𝑝𝑟𝑖𝑣𝑎𝑡𝑒 = 0 in the expression above. In other words,
there is no profit maximization for Phu My Corporation.

These simplifications gives the following form for 𝑊1 :
𝑊1 = 𝛼𝐼1 − (𝐼1 + 𝛽𝐼12 )
The term −(1 + 𝛽) is no longer present in 𝑊1 , as the government no longer has to spend its
budget to construct the Phu My bridge. At the signing of the contract between the
government and PMC, the parties agree to maximize this expression:
𝐌𝐚𝐱
𝐼1

𝑊1 = 𝛼𝐼1 − (𝐼1 + 𝛽𝐼12 )

First-order condition is the same as in model (0):

𝜕𝑊1
𝜶−𝟏
= 𝛼 − 1 − 2𝛽𝐼 = 0 ⟹ 𝑰̅𝟏 =
𝜕𝐼
𝟐𝜷
The overhead bar ( ̅ ) notation designates a feature written in the contract between the two
parties. In this section, we suppose the government honors this commitment to make an
investment equal to 𝐼̅1 for the ring road project. By using the superscript ∗ to designate an
actual quantity, we can write 𝑰̅𝟏 = 𝑰∗𝟏 .

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The traffic amount resulting from an investment of 𝐼1∗ is:
𝑄1∗ =

𝛼(𝛼 − 1)
2𝛽

Notice that 𝑄1∗ = 𝑄0∗ and 𝐼1∗ = 𝐼0∗ , therefore so far nothing has changed compared to model (0).
The government invests the same amount into the ring road. Other results have changed,
however, as detailed below.
First, toll price during the concession period has changed. The traffic demand
addressed to PMC between 𝑡 = 1 and 𝑡 = 2 is:
𝑄1𝟏∗ =

𝑄1∗ 𝛼(𝛼 − 1)
=
2
4𝛽

The superscript 1 indicates this is the demand during the concession period.
Since the company prices the toll to break even, the implied toll price is:

Π1 = 0 ⟹ 𝑃1∗ 𝑄11∗ = 𝐾 ⟹ 𝑷∗𝟏 =

𝑲
𝟒𝜷
=
𝟏∗
𝜶(𝜶 − 𝟏)
𝑸𝟏

In the previous section, under public management the Phu My Bridge could be used free of
charge, in other words 𝑃0∗ = 0 < 𝑃1∗ . Introducing a private sector company increases the price
charged to consumers.
After 𝑡 = 2, the project is given back to Ho Chi Minh City’s government who again collects no
toll.
Second, collective welfare has also changed, since the government no longer has to
spend its own money on the Phu My Bridge, while the private project developer is able to
charge a breakeven price. The new welfare level is calculated as:
𝑊1∗ = 𝑄1∗ − (𝐼1∗ + 𝛽𝐼1∗ 2 ) =

(𝛼 − 1)2
𝛼(𝛼 − 1)
𝛼−1
−[
+𝛽
]
2𝛽

2𝛽
4𝛽 2

(𝛼 − 1)2
𝛼−1
𝛼−1
=
(𝛼 − 1 −
)=
2𝛽
2
4𝛽
16


Note that 𝑊0∗ =

(𝛼−1)2
4𝛽

− 𝛽 − 1, hence 𝑊1∗ > 𝑊0∗ .

The two changes explained above can be interpreted as follows:


This simple model shows it is possible to attain the same level of infrastructure
investment (Bridge plus ring road: 𝐼0∗ + 𝐾 = 𝐼1∗ + 𝐾) by delegating financing and
construction to the private sector. This interpretation is consistent with the growing
trend of private participation in infrastructure projects in Vietnam and elsewhere.



By inviting PMC to participate in the project, collective welfare is higher by an
amount of (𝛽 + 1). Therefore from a welfare point of view, private participation in
infrastructure is desirable.



However, this increase in welfare has been made in detriment of consumers who
“suffer” from a price hike (𝑃0∗ < 𝑃1∗ ). Again, the impact of this price increase is not
considered in our model since consumers have zero price elasticity, but this point is
worth mentioning.



In our model, toll price regulation (Π𝑝𝑟𝑖𝑣𝑎𝑡𝑒 = 0) is there to “protect” consumers from
price increase. In reality, price regulations are commonly seen in infrastructure
projects. In the case of the Phu My Bridge, if PMC wants to increase toll price or start
collecting toll on motorcycles, they have to secure the city government’s approval.

3.4. Model

(2):

BOT

management

with

government

opportunism
A preliminary comment on the 𝛼 and 𝛽 is in order. The interpretation of 𝛽 and 𝛼 are
different, insofar as 𝛼 can arguably be measured with less difficulty, as opposed to 𝛽. Indeed,
𝛼 measures the impact of each unit spent to construct the ring road on Phu My Bridge’s
traffic demand and its impact can be more easily estimated in an objective way.
On the other hand, 𝛽 measures the government’s sensitivity to political loss related to budget
spending. This private nature creates a difficulty for Phu My Corporation to accurately

17


estimate 𝛽 . What is more, Vietnam’s institution quality and transparency has much to
improve, which exacerbates the problem.
We make two additional assumptions regarding 𝛽:


The government does not reveal its true sensitivity 𝛽 to PMC. Instead, before signing
the contract the company believes the sensitivity of the government to shadow cost of
public funds is another value, 𝛽̅. This inaccurate value of 𝛽̅ is used in the contract and
forms the basis of the city government’s obligations.



Furthermore, we suppose Phu My Corporation is unsuspecting of this behavior. This
is a simplifying assumption, but it supports the paper’s perspective which is to focus
on the public sector’s opportunism.

Let us look at the model as two key phases: signing of the contract and life of the contract.

3.4.1. Signing of the contract
The collective welfare’s expression is similar to model (1), with the only difference being the
sensitivity parameter used. At this stage (signing), the relevant sensitivity is the one
revealed by the city government, which is 𝛽̅ and not 𝛽. The parties maximize the expression:
𝐌𝐚𝐱
𝐼2

̅ 𝐼22 )
𝑊2 = 𝛼𝐼2 − (𝐼2 + 𝜷

Which yields the following results:

𝐼̅2 =

𝛼−1
(𝛼 − 1)2
⟹ ̅̅̅̅
𝑊2 =
2𝛽̅
4𝛽̅

Recall that the overhead bar ( ̅ ) designates a contracted feature, which may or may not be
honored.
In private, the government decides using 𝜷 as the relevant parameter. It maximizes its
own welfare (collective welfare and the government’s welfare have the same expression given
our assumptions):

18

𝑊2𝐺 = 𝛼𝐼2 − 𝜷𝐼22

𝐌𝐚𝐱
𝐼

And therefore:

𝐼2∗ =

𝛼−1
(𝛼 − 1)2
⟹ 𝑊2𝐺∗ =
2𝛽
4𝛽

The superscript * indicates actual results (not contractual results). By investing 𝐼2∗ and not 𝐼̅2 ,
the government has deviated in private.
Why would the government choose to deviate? To answer this question, we can
compare the welfare corresponding to each option. If the government sticks to its word, then
its welfare is ̅̅̅̅̅
𝑊2𝐺 =

(𝛼−1)2
̅ ,
4𝛽

whereas deviating would give a welfare of 𝑊2𝐺∗ =

(𝛼−1)2

.
4𝛽

A quick

comparison between the two expressions allow us to conclude that:
̅<𝜷
Deviation ⟺ 𝛽̅ is revealed but 𝛽 is used ⟺ 𝑊2𝐺∗ > ̅̅̅̅̅
𝑊2𝐺 ⟺ 𝜷
In other words, the government voluntarily understates its sensitivity to shadow cost of
public funds. In doing so, they overstate their ability to bear political costs that stem from
public expenditure. The government has the incentive to misrepresent 𝛽 because this would
improve their welfare.
For the remainder of the paper, we assume 𝛽̅ < 𝛽.
What are the consequences of this misrepresentation? First, we calculate every
quantity implied by the contract between the government and PMC.
First, since 𝛽̅ < 𝛽 we can conclude that 𝐼2∗ < 𝐼̅2 , or in other words the city government underinvests compared to the contract.
Implied traffic demand is:
̅𝑄̅̅2̅ =

𝛼(𝛼 − 1)
2𝛽̅

19


This demand is split evenly between the concession period and the public management
period:
𝛼(𝛼 − 1)
̅̅̅̅

𝑄21 = ̅̅̅̅
𝑄22 =
4𝛽̅
Toll price charged by PMC during the concession period:

̅̅
Π̅̅2 = 0 ⟹ ̅̅̅
𝑃2 ̅̅̅̅
𝑄11 = 𝐾 ⟹ ̅̅̅
𝑃2 =

𝐾
4𝛽̅
=
̅̅̅̅
𝑄1 𝛼(𝛼 − 1)
1

These values are summarized in the following table:
Contracted quantities

Value

Investment made by the city government in the
ring road project

𝛼−1
2𝛽̅
𝛼(𝛼 − 1)
̅𝑄̅̅2̅ =

2𝛽̅
̅̅̅2̅ 𝛼(𝛼 − 1)
𝑄
̅̅̅1̅ = 𝑄
̅̅̅1̅ =
𝑄
=
2
2
2
4𝛽̅

Implied traffic demand after construction’s
completion
Implied traffic demand in each period

𝐼̅2 =

̅ 𝑃𝑀𝐶 = 0
Π

Profit of Phu My Corporation

4𝛽̅
𝛼(𝛼 − 1)
𝛼(𝛼 − 1)
̅̅̅̅2 =
𝑊
4𝛽̅
̅̅̅

𝑃2 =

Toll price during concession period
Collective welfare

Table 1: Model (2) - Features implied by the contract between the city government and Phu My
Corporation

These contracted quantities are not realized during the life of the contract.

3.4.2. Life of the contract
Between the signature at 𝑡 = 0 and 𝑡 = 1 when construction is complete, each party deploys
its resources to construct their respective projects. The actual commitment of the
government is not verified by PMC, and the government puts in an insufficient investment.
At 𝒕 = 𝟏, construction of both projects is finished and traffic demands across the bridge
becomes known. Since the government invested 𝐼2∗ =
demand is lower than expected:

20

𝛼−1
2𝛽

instead of 𝐼̅2 =

𝛼−1
̅
2𝛽

and 𝐼2∗ < 𝐼̅2 , traffic

𝑄2∗ =

𝛼(𝛼 − 1) 𝛼(𝛼 − 1)
<
= ̅𝑄̅̅2̅
2𝛽
2𝛽̅

Demand during the concession period is therefore: 𝑄21∗ =

since 𝛽̅ < 𝛽
𝑄2∗
2

=

𝛼(𝛼−1)
4𝛽

Faced with lower demand than anticipated, Phu My Corporation still has to charge the
agreed-upon toll price ̅̅̅
𝑃2 . The company’s profit is calculated as:
Π2∗ = ̅̅̅
𝑃2 𝑄21∗ − 𝐾 =

=

4𝛽̅

𝛼(𝛼 − 1)
×
−1
𝛼(𝛼 − 1)
4𝛽

̅
𝜷
−𝟏 <𝟎
𝜷
⏟
̅ <𝛽
𝛽

Therefore PMC is making a loss due to insufficient investment by the government. In the
expression of profit above, notice that if the government reveals its real sensitivity then
𝛽̅ = 𝛽 and Π2∗ = 0: PMC is breaking even again.
From a welfare standpoint, the government has improved its own welfare compared to the
initial contract, but it has done so in detriment of PMC. Collective welfare is calculated as:

𝑊2∗ = 𝑊2𝐺 + Π2∗ =

(𝛼 − 1)2
𝛽̅
+ ( − 1)
4𝛽
𝛽

(< 𝑊1∗ )

These results are linked to the real-life Phu My Bridge in two key ways:
First, this issue of insufficient investment by the government has been one of the key
drivers that push the Phu My Bridge into financial distress. Due to parts of the ring road
still being under construction six years after the bridge is put into use, traffic demand has
never reached initial projections.
̅̅̅2 ) despite weaker-than-expected
Second, notice that PMC did not increase toll price (𝑃
demand, as in our model they are assumed to adhere to the contract. In reality, Phu My
Corporation has twice sent proposals to the city government to (i) increase toll price, (ii)

21


prolong the concession period, but both proposals were rejected (Dantri International News
2011).
These two elements were mentioned when PMC executives were asked about the reasons to
the project’s financial failure:
“In 2012, toll revenues totaled VND 95 billion, while the contract requires that they reach VND 158
billion. Similarly, last year the toll collection reached VND 102 billion rather than the required VND 180
billion.
Thai said toll revenues are low because the roads connecting the bridge to main traffic are not
completed, resulting in few vehicles passing by the bridge, while the operator is not allowed to charge
tolls on motorbikes.” [emphasis mine] (Tuoitre News 2014)
The next section will now consider the possibility that the government may rescue PMC.

3.5. Model

(3):

BOT

management

with

government

opportunism and rescue feature
We now introduce the rescue feature properly.
In his paper on the project, the economist Nguyen Xuan Thanh outlined the government’s
obligations according to Clause 7.4.4 of the contract as follows:


If the Second Ring Road Project is completed no more than three years after the Phu
My Bridge’s opening and traffic demand is lower than forecasts made in the initial
financial plan, then the city government must use its budget to compensate for any
revenue shortfall experienced by the project.



If the Second Ring Road Project is completed more than three years after the bridge’s
completion, then the city government has to receive back the project and reimburse
the sponsor of all expenses made for construction plus a predefined margin capitalized
at a contractual interest rate (Nguyen Xuan Thanh 2013).

22


In the paper’s model, however, “rescue” is defined as the government reimbursing Phu My
Corporation of the losses the company may make during the concession period due to

insufficient investment leading to weak demand. We further suppose that the intention to
rescue is unknown to PMC for simplification.
If the government chooses to rescue, spending taxpayers’ money to bail out a private-sector
company may be politically challenging. This is why we have to subject the rescue money to
shadow cost of public funds. However, the political pressure in this case is interpreted
differently since it entails rescuing a private sector company and not simply building
infrastructure. This is why the expression of political cost is distinguished by a new
parameter 𝛾.
Definition of shadow cost of rescue funds: Let 𝑧 be the amount the city government uses to
reimburse Phu My Corporation for it loss, then the real total cost of 𝑧 from the government’s
perspective will be:
𝐿rescue (𝑧) = 𝑧 + 𝛾𝑧 2
The model is adjusted to accommodate these additional assumptions below.

3.5.1. Key results
As in the previous model, the parties maximize the apparent collective welfare 𝑊3 = 𝛼𝐼3 − 𝐼 −
𝛽𝐼32 , which gives the result:
𝐼̅3 =

𝛼−1
2𝛽̅

As before, the features implied by the contract are:

Contracted quantities

Value

Investment made by the city government in the
ring road project

𝛼−1
2𝛽̅
𝛼(𝛼 − 1)
̅𝑄̅̅3̅ =
2𝛽̅
̅𝑄̅̅3̅ 𝛼(𝛼 − 1)
̅̅̅1̅ = 𝑄
̅̅̅1̅ =
𝑄
=
3
3
2
4𝛽̅

Implied traffic demand after construction’s
completion
Implied traffic demand in each period

23

𝐼̅3 =


̅ 𝑃𝑀𝐶 = 0
Π

Profit of Phu My Corporation

4𝛽̅
𝛼(𝛼 − 1)
(𝛼 − 1)2
̅̅̅̅3 =
𝑊
4𝛽̅
̅̅̅
𝑃3 =

Toll price during concession period
Collective welfare

Table 2: Model (3) - Quantities written in or implied by the contract

We demonstrate a simple intermediate result: Let 𝐼 ̅ be the investment specified in the
contract and 𝐼 ∗ be an investment level such that 𝐼 ∗ < 𝐼 ,̅ so that PMC is loss-making. Then the
loss amount is Π =

𝐼∗
𝐼̅

𝐼∗

− 1 < 0 and the rescue amount is 𝑅 = | 𝐼 ̅ − 1| = 1 −

𝐼∗
𝐼̅

>0

1
Proof: Actual traffic demand is 𝑄 ∗ = 𝛼𝐼 ∗ , ticket price under contract is 𝑃̅ = 𝛼𝐼 ̅ .
∗

1
𝐼
Revenue of PMC is therefore 𝑃̅𝑄 ∗ = 𝛼𝐼 ∗ × 𝛼𝐼 ̅ = 𝐼 ̅ . Given that the cost of constructing

the Phu My bridge is 1, profit is Π ∗ =

𝐼∗
𝐼̅

− 1 . This is a loss (Π ∗ < 0) since the

assumption is that 𝐼 ∗ < 𝐼 ̅. Assuming the government injects money into PMC to
𝐼∗

restore breakeven, if 𝑅 denotes the rescue amount and 𝑅 > 0, then 𝑅 = | 𝐼 ̅ − 1|. End of
proof.
This result is simply general than the loss expression from the preceding section. Indeed,
replacing generic 𝐼 ∗ and 𝐼 ̅ with 𝐼2∗ and 𝐼̅2 from the previous model gives back the familiar
̅
𝛽

result Π2∗ = 𝛽 − 1.
If the city government knows beforehand they would deviate, they are also able to anticipate
𝐼∗

in advance the rescue amount of 𝑅 = 1 − 𝐼 ̅ . Hence this rescue amount and any shadow cost

associated to it must be considered in the government’s decision-making. The definition of
shadow cost of rescue funds above allows us to calculate the total cost of rescuing Phu My
𝐼
𝐼3

𝐼
𝐼3

2

Corporation as 𝐿rescue (𝑅) = 𝑅 + 𝛾𝑅 2 = ( 3̅ − 1) + 𝛾 ( ̅3 − 1) .
In private, the city government maximizes their welfare function where there is a
new term representing the cost of rescuing Phu My Corporation:

24


2
𝐼3
𝐼3
2)
𝑊𝐺 = 𝛼𝐼3 − (𝐼
+
𝛽𝐼
−
[(
−
1)
+
𝛾

(
−
1)
]
⏟3
3
𝐼3̅
𝐼̅3
⏟
L(Invest)
L(Rescue)

𝛼−1
Since 𝐼̅3 is already stipulated by the contract and 𝐼̅3 = 2𝛽̅ , the expression above becomes:

𝑊𝐺 =

𝛼𝐼3 − (𝐼3 + 𝛽𝐼32 ) −

2
2𝛽̅
2𝛽̅
𝐼 − 1) + 𝛾 (
𝐼 − 1) ]
[(
𝛼−1 3
𝛼−1 3

The government’s welfare maximization has first- and second-order conditions as follows:
𝜕𝑊𝐺

2𝛽̅
4𝛾𝛽̅
2𝛽̅
= 𝛼 − (1 + 2𝛽𝐼3 ) − [
+
𝐼 − 1)] = 0
(
𝜕𝐼3
𝛼−1 𝛼−1 𝛼−1 3
𝜕 2 𝑊𝐺
8𝛾𝛽̅ 2
=
−2𝛽
−
< 0 , this is true given assumptions
2
(𝛼 − 1)2
{ 𝜕𝐼3
Solving

𝜕𝑊𝐺
𝜕𝐼3

= 0 will therefore allow us to determine the optimal investment by the

government for the ring road project. The negative second-order derivative ensures 𝑊𝐺 is
maximized.
𝜕𝑊𝐺
2𝛽̅
4𝛾𝛽̅

2𝛽̅
= 0 ⟺ 𝛼 − (1 + 2𝛽𝐼3 ) − [
+
𝐼 − 1)] = 0
(
𝜕𝐼3
𝛼−1 𝛼−1 𝛼−1 3

⟺ 2𝛽𝐼3 +

8𝛾𝛽̅ 2
2𝛽̅
4𝛾𝛽̅
𝐼
=
𝛼
−
1
−
+
3
(𝛼 − 1)2
𝛼−1 𝛼−1

̅
𝟐𝜷
𝛼 − 1 − 𝜶 − 𝟏 (𝟏 − 𝟐𝜸)
⟺ 𝐼3∗ =
̅𝟐
𝟖𝜸𝜷

2𝛽 +
(𝜶 − 𝟏)𝟐
Total traffic demand is:

𝑄3∗ =

2𝛽̅
𝛼 [𝛼 − 1 − 𝛼 − 1 (1 − 2𝛾)]
2𝛽 +

25

8𝛾𝛽̅ 2
(𝛼 − 1)2