Public-Private Partnerships and Contract Regulation

Jorge G. Montecinos and Flavio M. Menezes

The University of Queensland, School of Economics

April, 2012

Abstract

:

This paper explores some underlying incentive issues associated with the Least-Present Value of

Revenue (LPVR) auction proposed by Engel, Fischer and Galetovic (2001) to allocate public-private

partnership contracts. We also explore the implications for the cost of capital faced by the

concessionaire when there is a risk of default. The extent of this risk also depends on the nature of

the tender and associated contract.

While the LPVR auction variable-term contract addresses the adverse selection issues associated

with ensuring that the lowest cost firm wins the tender, it fails to consider ex-post (moral hazard)

distortions that might emerge when the firm faces a guaranteed rate of return under a zero net

present value auction. We then consider a fixed-term contract, which provides the firm with an

incentive to exert an effort to boost demand (thus increasing expected revenues at the least cost).

Under a fixed-term contract the firm faces a bankruptcy risk and, therefore, potentially higher cost

of capital than under a variable-term contract.

In particular, we show that when renegotiation is not possible, a variable term contract can be

welfare dominated by a fixed term contract if the extent of moral hazard is sufficiently high to offset

any increase in the cost of capital. We extend our analysis to consider the impact of renegotiation.

We show that the positive incentives for cost reduction that exist under a fixed term contract may

disappear when renegotiation is feasible. In this case, whether a fixed-term contract welfare-

dominates a variable term contract will no longer depend only on the trade-off pointed out above

but also on the effect generated by the disutility cost that arises from the firm being subsidized by

the government to avoid default.

Key-words: public-private partnerships, infrastructure regulation, concessions.

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1. INTRODUCTION

Public-Private Partnerships (PPPs) have been employed in several countries as an alternative

mechanism for the financing and provision of public goods in areas such as transport, education

and health. They have been used as both a privatization vehicle, as construction is often bundled

with operation by a private concessionaire, and as a tool to remove debt from the government's

balance sheet.

There are several dimensions of PPPs that have attracted attention from economists. In particular,

focus is directed towards the design of the tender used to allocate the project and the choice of

contract duration. In an influential paper, Engel, Fischer and Galetovic (2001), henceforth EFG,

propose a tender mechanism to address two important issues: to provide better demand-side risk

management and to mitigate the need to renegotiate contracts.

EFG introduced the notion of a variable term concession contract implemented via a Least-Present

Value of Revenue (LPVR) auction. Under this mechanism, the tender allocates the contract to the

bidder with the lowest bid expressed as the present value of the expected revenue. Moreover, the

duration of the contract is endogenous; the concession contract will remain in place until the firm

recovers its full bid.

EFG argued that, unlike fixed term contracts, the LPVR mechanism results in an optimal allocation

of risk. The term of the contract varies endogenously to ensure that the firm recovers the full value

of its bid. Thus, under a LPVR-related contract, the firm is fully insured against demand risk.1

Arguably, the government is the best placed party to deal with demand risk and this risk is priced

competitively through the tender process. This endogenous adjustment mechanism also mitigates

the need for costly renegotiation.

The UK government was an early adopter of a variable term contract. These include, for example,

the Second Severn Bridge over the Severn River between England and Wales and the Queen

Elizabeth II Bridge across the Thames River. In both cases, the duration of the concession contract

was contingent upon achieving a particular revenue target (Foice, 1998). This approach was also

1 Nombela and De Rus (2004) propose a variation of the LPVR mechanism that includes operation and maintenance costs: the Least Present Value of Net Revenues (LPVNR) mechanism.

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adopted by the Chilean government for the concession of the Santiago-Valparaiso-Viña del Mar

Highway (Route 68).2

In addition to setting a variable term, the Chilean government went further

still by considering the level of revenues to be the main variable used to decide the winner of the

tender, awarding the concession to the bidder who proposed the least present value of the expected

revenues. The introduction of the LPVR has had mixed results with some tenders cancelled due to

lack of interest by industry.

As is clear from the above discussion, the LPVR mechanism involves both the allocation of the

contract via a tender and an endogenous duration of the contract. In this paper we abstract from the

design of the tender and assume that the tender selects the concessionary with the least expected

operational cost and that the construction costs are fixed and known to all.3

This allows us to focus

on the effects on incentives of both fixed and variable-term contracts.

Engel et al (2008) extend the analysis of the LPVR mechanism by proposing a two-threshold

auction. These thresholds refer to the levels of output that define high and low demand states, such

that, under this mechanism, the concessionary is fully insured across the three different demand

states. Under this contract, if the high demand state occurs (above the high threshold), then user

fees are sufficient to cover the investment, if the low demand state realises (below the low

threshold), then user fees are not sufficient to cover the investment and the government provides a

subsidy to cover the losses, while if intermediate demand occurs (between the high and low

thresholds), the optimal contract awards a minimum revenue guarantee. This guarantee is part of a

revenue sharing agreement, so that is isomorphic to a revenue cap in the case of high demand. The

authors show that, in the absence of moral hazard, a variable term contract based on the present

value of revenues not only achieves an optimal risk-sharing agreement but also generates a higher

expected welfare than a fixed term contract in all states of demand.

In addition to this, Engel et al (2008) consider the presence of moral hazard by allowing the

owner/manager of the firm to exert a positive effort to boost demand. In this new scenario, the

optimal contract is still implemented using a double threshold auction. However, since the

concessionaire is able to positively affect demand, the revenues collected by the concessionaire will

2 The Lusoponte Concession in Portugal was also awarded under a variable term scheme but unlike the UK the duration of the contract was contingent on achieving an accumulated traffic target (De Lemos et al., 2004). 3 We assume throughout the paper that construction is bundled with operation in the tender process. Iossa and Martimort (2008) and Martimort and Pouyet (2008) examine whether such bundling is optimal and the resulting implications for contract design.

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be unequal across the states of demand and thus, the subsidy and the revenue cap in the optimal

contract will be state-dependent.

As with EFG, Engel et al (2008) assumes that is possible to find a mechanism that would avoid

further renegotiations (by solving the adverse selection problem). However, both EFG and Engel et

al (2008) do not allow the firm to default if the revenues are not sufficient to service debt. Moreover,

the optimal contract will implement a mechanism in which the investment (representing the cost of

the project) is primarily covered with fees revenues and/or a government subsidy (representing the

sources of income). In consequence, a solution like this suffers from the fact that the government

may not effectively committ to this transfers. As argued in Laffont and Tirole (1993) incentive based

regulation has been effectively used without the government need for committing to these

transfers.

We, instead, take the viewpoint that renegotiations are often inevitable. One main reason for the

occurrence of renegotiations is the possibility of default which not only affects the firm but also the

welfare-efficiency of the contract4

, so that the introduction of a disutility cost that accounts for this

efficiency loss would introduce the incentives to the government to regenotiate the contract to

avoid the firm default. We explore this possibility by assuming that the firm funds investment with

a mix of debt and equity and allowing for a setting in which the firm may default if the revenues

collected are not sufficient to cover debt repayments. This contrasts with the analysis of Engel et al

(2008), in which it is assumed that the government subsidizes the project in the low demand state.

Moreover, unlike EFG and Engel et al (2008), we do not impose any assumptions on the degree of

risk aversion of the firm. In our view, relaxing this assumption allows us to focus our study on the

two types of contracts without introducing any biases that may result if the government faces a risk

averse versus a risk seeker firm.

Another potential downside of the endogenous variable-term mechanism is that, while they limit

the firm's upside profitability risk, the firm might still face a downside risk of going bankrupt if it

cannot pay debt holders during the duration of the contract. 5

4 Since we follow Demsetz idea for the competitive tender, any other firm taking over the project will be less efficient than the incumbent.

Although this type of contract does

allow the firm to recover the full estimated revenue at the end of the contract, short-run fluctuations

in demand or costs might lead to a period in which debt is not serviced in a timely manner. In this

paper, we do not allow for this possibility by assuming that the firm only pays debt at the end of

5 See, for example, Vassallo (2006), Gomez-Ibanez (2003), and Brealey, Cooper, and Habib (1997).

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the contract and, therefore, a variable-term contract will effectively eliminate both downside risk

and upside profitability.

Here we focus on a previously ignored perverse incentive associated with a variable-term contract.

While the EFG mechanism addresses the adverse selection ex-ante incentive issues to ensure that

the lowest cost firm wins the tender, it fails to consider ex-post moral hazard distortions that might

emerge when the concessionary faces a guaranteed rate of return under a Zero Net Present Value

auction. In contrast, under a fixed-term contract the concessionary has an incentive to boost

demand but it faces a bankruptcy risk and, potentially, a higher cost of capital than under a

variable-term contract. In particular, we show that a variable-term contract can be welfare

dominated by a fixed contract if the extent of moral hazard is sufficiently high such that it offsets

any increase in the cost of capital. This is one of the main insights of this paper.

The above result, however, assumes that the government can commit not to renegotiate with the

concessionaire when the latter becomes bankrupt under a fixed-term contract. When renegotiation

is feasible, however, we show that the positive incentives that exist under a fixed term contract to

increase the expected revenues may disappear. This result adds to the theoretical and empirical

literature on the negative effects of renegotiation on the performance of concession contracts.6

The paper is organized as follows. Section 2 introduces the benchmark model where an

unregulated monopoly chooses its effort level and the level of debt it must take on in order to

maximize profits. Section 3 introduces regulation in the form of both a fixed-term contract with

duration chosen to maximize total surplus and a variable-term contract. We show that a variable

term contract is akin to a regulatory scheme where the concessionary is guaranteed a particular rate

of return. In contrast, under a fixed term contract, the concessionary's rate of return will depend on

the realization of demand and cost uncertainty. This distinction allows us to fully explore the costs,-

including the incidence of moral hazard, of the two types of contract. Section 4 investigates the

implications of introducing renegotiations. Section 5 concludes.

2. THE MODEL

The government wants to contract a firm to build a facility and provide a service using the facility.

The firm is selected via a competitive tender and we assume that the most efficient firm wins the 6 See, for example, Guasch (2004), Guasch, Laffont and Straub (2003, 2005, 2006, 2008).

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tender with a price of . The government can either offer a fixed duration contract or a variable

term contract (also referred to as a NPV contract). We assume for simplicity that time is measured

continuously.

As in Camacho and Menezes (2010)7, the firm has to outlay $ for the construction of the facility

which is completed in one period and lasts for years. This up-front investment is funded using an

appropriate combination of debt and equity. Therefore, there is a risk of default if not enough

revenue is generated throughout the life of the project to cover the repayment of debt. Of course, by

definition, there is no risk of default under a NPV contract, which will have implications for the

cost of capital under this type of contract.

It is assumed that investment does not depreciate. Additionally, we assume that the firm is owner-

operated so that there are no agency issues inside the firm. We assume the marginal cost to operate

the infrastructure project is equal to zero which allows us to concentrate on moral hazard on the

demand side.

The inverse demand function is uncertain and inelastic with a choke price equal to ; at any

price below or equal to , the demand is either equal to or depending on the level

of effort. Effort can take one of two values, , and the cost of the effort is equal to .

Let denote the probability of high demand, , and be the probability of low

demand, . We assume . Realized demand is observable by the government but the

choice of effort is not. At a price above demand is always equal to zero. Expected demand for

and any effort level, , is then given by:

We assume that the firm holds cash on hand . This implies that, in order to fund the project,

the firm must borrow an amount We assume that lenders are risk neutral and behave

competitively so that they are subject to a zero profit constraint. This implies the rate of return

expected by lenders is the risk free rate . We further assume that the cost of equity is also equal to

. From this definition the risk free rate is referred to a period equivalent to the duration of the

contract. 7 Camacho and Menezes (2010) compare price cap and cost of service regulation in a similar model with a wealth-constrained entrepreneur who faces cost uncertainty.

7

At , the government determines the type of contract that it will offer the firm. Under a fixed

term contract, the government announces a fixed term for the duration of the contract.

Alternatively, under a variable term contract, the government announces a maximum term for the

duration of the contract and the contract terminates endogenously once the firm recovers all the

costs associated with the project, including the initial outlay. The firm then builds the infrastructure

and chooses the level of effort and the level of debt to maximize profit given the price and

taking into account the cost of debt , determined in the debt market and referred to a

period equivalent to the duration of the contract.

At , the facility starts operating, the level of demand is realized and will remain known for the

entire duration of the contract. The firm collects revenue from the users of the facility (e.g. if the

facility is a highway, revenue collection will be in the form of tolls). This revenue is then used to

cover expenditures in the same order of priority as defined in basic financial statements, namely (i)

the operational cost , which is assumed to be equal to zero for simplicity; (ii) bondholders; and

(iii) the firm. The contract expires at some , , which is determined either exogenously or

endogenously. We assume that when the contract expires, price reverts to realized marginal cost

(i.e., zero), so that profits are zero for . If the firm defaults, debt-holders take over the contract

and absorb the losses (given by the difference between net operating revenues and debt payments)

with no change in price and costs.

We assume no discounting. The expected total welfare for the duration of the contract is is equal to

, where is the expected consumer surplus, is the firm’s expected profit and

is the weight assigned to the firm’s profit.

Lemma 1: Given the choke price , the price being charged to users ( ), the life of the project ( ) and the

duration of the contract ( ), the Consumer Surplus valued at for the entire life of the project is given by

The first term in (2) represents the consumer surplus generated while the contract is outstanding,

whereas the second term in (2) corresponds to that surplus generated after the contract terminates

up until the end of the asset’s life.

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The firm's expected profits for the duration of the contract when the effort is exerted can be

written as:

The firm's expected profits under zero effort are equal to:

The participation constraint requires that . It is incentive compatible for the firm to choose

positive effort when or, equivalently, if

Condition (3) establishes that it is incentive compatible for the firm to choose the positive level of

effort when the resource cost of the effort is less than or equal to the sum of the increase in expected

demand and the difference in the total debt payment if the firm exerts high versus low effort.

Accordingly, the firm chooses to undertake only if both the participation and the incentive

constraints are satisfied. If the incentive constraint (IC) is not satisfied, then the firm undertakes

as long as .

We turn to the firm's optimal choice of debt and the associated cost of debt assuming a contract

period equal to . Given limited liability, we can calculate the firm's profits conditional on their

choice of effort and demand as follows:

Limited liability means that, if accumulated revenue at is not sufficient to cover debt

payments the firm will default, but it loses at most the equity invested, as well as the cost of effort

exerted.

Similarly, lenders' profits conditional on the choice of effort and demand are given by:

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If the revenue collected by the firm is insufficient to cover debt payments, the firm defaults and

lenders will take over the project which continues to operate for periods which allows the

lender to collect the net revenue from the project. We assume default is only possible when realized

demand is low; that is . Note that, when the price is sufficiently high that revenue can cover

debt payments in all states of nature (i.e., when ), there is no default risk and,

therefore, the cost of debt is equal to the risk-free rate. In contrast, when the firm’s revenue is

insufficient to pay debt plus interest in all states of nature (i.e., when ), the cost of debt

is determined by using expression (5) as follows:

This expression shows that the firm (borrower) cannot commit to repay debt for a period longer

than the duration of the contract, or in other words that the lender will be willing to lend an

amount of money up until the equivalent revenues that the firm can accumulate for a given

duration of the contract. Rearranging this expression yields:

We can conclude, therefore, that the cost of debt is larger than or equal to the cost of equity. When

the cost of debt is equal to the risk-free rate, the firm is indifferent between choosing any level of

debt in the interval . In this instance, we assume that the firm chooses

Alternatively, when the cost of debt is greater than the risk-free rate, then it will always be optimal

for the firm to choose This yields the following result.

Lemma 2: For a contract period equal to T (either endogenously or exogenously fixed), and since the

strategy set is restricted to those that satisfy weak dominance, the firm will weakly choose .

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Having determined the cost of debt, we can now rewrite the incentive constraint. When is such

that the risk of default is zero (i.e., when ), the cost of debt is equal to the risk-free rate

under both levels of effort and therefore (3) reduces to:

(7)

Condition (7) states that, when there is no risk of default, the positive level of effort will be chosen if

the resource cost of effort ( ) is less than the increase in the expected demand that happens under

positive effort. Meanwhile if the risk of default is positive regardless of the level of effort chosen by

the firm (i.e., ), the cost of debt is given by (6) and (3) can be rewritten as:

(8)

Where , i.e., .

Note that represents the difference in the cost of debt under positive effort and

under zero effort. This difference is greater than zero since a positive effort increases the probability

of a high demand scenario ( ) and decreases the risk of default. The result below

characterizes the optimal choice of effort for the firm.

Lemma 3: Table 1 below summarizes the threshold levels that must satisfy in order for the firm to

undertake .

Table 1: Threshold levels for

where

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3. FIXED VERSUS VARIABLE TERM CONTRACTS

In this section we determine the socially optimal duration of a fixed term contract, and equilibrium

welfare outcomes under both fixed and variable term contracts.

3.1 FIXED-TERM CONTRACTS

We note first that, under a fixed-term contract, the firm's expected gross revenue is fixed as has

been set by the tender. Therefore, there is a natural analogy between a fixed-term contract and a

price-cap regime in a standard regulatory economics framework. This insight allows us to rewrite

Lemma 3 in terms of the duration of the contract rather than the price.

Lemma 4: Table 2 below summarizes the threshold levels that must satisfy in order for the firm to

undertake .

Table 2: Threshold levels for

where

Recall that for, , there is no risk of default whereas, if , there is a

risk that the firm defaults on its debt and loses its effort, net revenue and equity in the project. This

risk is priced in terms of a higher cost of debt.

The government's problem when choosing the optimal duration for a fixed-term contract can be

written as:

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where is the contract duration set by the government during the tender, (PR) stands for the

participation constraint and (IC) for the incentive compatibility constraint.

Given limited liability, expected profits is given by,

;

.

Then, can be rewritten as:

;

The proposition below determines the optimal fixed-term contract duration and the associated

choice of effort by the firm. The proof is in the appendix.

Proposition 1: Table 3 below characterizes the optimal fixed-term contract duration ( ) for all

combinations of the IC and PR conditions.

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Table 3: Optimal Term Cap

Constraints Effort

Proposition 1 has important implications for the relationship between the duration of the contract,

the firm’s cost of capital and optimal effort induction. The nature of this relationship will depend

on parameter values. When there is no risk of default (rows one and three of Table 3), the firm’s

cost of capital is equal to the risk-free rate and, thus, does not depend on the level of effort. Thus,

the regulator will set the lowest duration of the contract possible (i.e. set duration such that the

firm’s participation constraint is binding) to extract all expected rent. In this instance there is no

trade-off between rent extraction, optimal effort choice and the cost of capital. The firm’s expected

profit is zero which allows us to obtain total welfare by replacing the duration in rows one and

three of Table 3 in as follows:

The optimal choice of effort in equation (9) will depend on parameter values as described in rows

one ( ) and three ( ) of Table 3.

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Alternatively, for other parameter values (rows two and four of Table 3), by reducing the duration

of the contract to extract rents, the government may affect the optimal choice of effort and the firm’s

cost of capital. In this case, it is optimal for the regulator to set the minimum duration such that the

participation constraint is satisfied with equality and, therefore, the firm’s cost of capital is given by

equation (6), reflecting a higher cost of capital than the risk-free rate. The firm’s expected profit is

zero and we obtain total welfare by substituting the duration expressions from rows two and four

of Table 3 into :

If ; and,

If

The optimal choice of effort in equations (10a) and (10b) will depend on parameter values as

described in rows two ( ) and four ( ) of Table 3.

3.2. VARIABLE TERM CONTRACTS

A variable term contract has the property that the duration of the contract is endogenous. Under

this type of contract the firm is fully insulated against cost and demand uncertainty; profits will be

zero, ex-post, regardless of the realization of demand. Under these circumstances, there are no

incentives for cost reduction. There is, therefore, a natural analogy between a variable-term contract

and a cost-plus regime in a standard regulatory economics framework. This insight allows us to

characterise the optimal choice of effort by the firm.

At the firm determines the level of effort, , that it is going to exert. At , demand is

realized. Since the regulated term for the contract adjusts endogenously depending on the observed

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demand, it will be the case that operational and capital costs are always being covered. Hence, there

is no risk of default and the firm’s cost of capital is always equal to the risk-free rate, . In this

setting then, it holds that the firm is indifferent between any levels of debt . As

discussed in the previous section, we assume that the firm chooses .

The following proposition characterizes the choice of effort by the firm and the ex-post durations,

contingent on the realisation of demand, under a variable term contract. The proof of this

proposition is offered in the appendix.

Proposition 2: Under a Variable Term Contract the firm always chooses . The ex-post contract

duration terms are given by , when ; and , when .

Proposition 2 establishes that society bears the full extent of moral hazard under a variable term

contract. This proposition also allows us to compute the expected overall welfare for the variable

term contract evaluated at , as the level of welfare that is obtained at the expected duration of

the contract for each state of cost/demand described in Proposition 2, as follows:

3.3. WELFARE COMPARISON

In this section we compare the welfare generated by a fixed term contract against that generated by

a variable term contract. Proposition 3 below provides this comparison for all potential model

parameterizations. The proof is in the appendix.

Proposition 3: Table 4 below compares the welfare generated by fixed and variable term contracts for all

feasible parameter values expressed in terms of the incentive constraint (IC) and participation constraint (PR)

faced by the firm under a fixed term contract.

Table 4: Optimal Regulation

Constraints Optimal type of contract

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, if

, otherwise.

Proposition 3 establishes that whether a fixed term or a variable term contract is welfare superior

depends on the trade-off between higher revenues (which result from increased demand) under a

fixed term contract and a lower cost of capital under a variable term contract. When there is no risk

of default, such that the cost of capital is the minimized, then if the firm chooses to exert a positive

effort, , a fixed term contract will be welfare superior as it boosts demand at no extra cost in

terms of an increase in the cost of capital. In contrast, if the firm chooses to exert effort then

both types of contract generate the same level of welfare. If the model is parameterized such that

there exist default risk, there will be a trade-off between the higher cost of capital the firm faces

under a fixed term contract and lower demand under the variable term contract. More specifically,

if the firm undertakes under a fixed term contract, whether the fixed term contract is welfare

superior to the variable term contract will depend on parameter values as given in the second row

of Table 4. Further, if the firm undertakes under a fixed term contract, then a fixed term

contract yields the same expected demand as a variable term contract but still leads to a higher cost

of capital. Therefore, in this case, the fixed term contract is welfare dominated by a variable term

contract.

This potential trade-off between higher expected demand/revenues and a lower cost of capital has

yet to be explored in the PPP literature. This trade-off it is likely to be more significant in concession

contracts where the increase in revenues in response to the increased demand is larger than the

increase in capital costs. It should be noted, however, that this trade-off has been studied in other

contexts. Camacho and Menezes (2010) show that the question of whether price-cap regulation

welfare dominates cost-of-service regulation depends precisely on the trade-off between a higher

cost efficiency under price cap and a lower cost of capital (or a lower entrepreneur’s rent) under

cost of service regulation.

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4. ALLOWING FOR RENEGOTIATION

As discussed above, the firm might only default when low demand eventuates. In contrast to the

previous section, we now assume that there is scope for renegotiation in the event the firm defaults.

We explore the impact of such renegotiations on equilibrium behavior and the impact this may

have on the resulting welfare realized under fixed term versus variable term contracts.

First, recall that the firm defaults when low demand eventuates only when , or

equivalently, in terms of the duration, when

For any contract duration that is at least as large as the right hand side of equation (12), the firm

never defaults, even when demand is low. If a default occurs at the end of the duration of the

contract, the shortfall in revenue required to fully cover the debt repayment at the end of the

contract is given by:

Notice that equation (13) simply represents the gap between debt payments, given that the firm

chooses , and net operational revenue.

To avoid default, the government needs to transfer an amount equal to to the firm when low

demand eventuates and the original contract duration satisfies equation (12). In this model, we

suppose that this transfer occurs at time . As indicated above, demand is observable which implies

that there is no scope for a second round of moral hazard arising from contract renegotiation.

However, full observability also means that, if default does occur, it will happen at when

demand is realized.

We maintain the assumption that, if the firm defaults, the contract reverts to debt holders who

forego part of their wealth but continue to manage the project in the same fashion in order to

recover net operating revenue. We also assume that the government faces a disutility cost given by

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. This cost is meant to capture the negative future impact of the firm’s default on its cost of capital

and how this will affect the government who has then, the incentives to avoid the firm default

preventing the loss of welfare. Default is avoided by extending the original contract duration from

to . We assume henceforth that, .

When renegotiation is possible, the limited liability constraint becomes:

To sum up, when the firm renegotiates the contract with the government to avoid default, it

receives a transfer which is implemented through an extension of the contract term from to .

The firm continues to operate the project but profits are zero (ex-post). It follows then that debt

holders’ payoff is equal to

Thus, under the above assumptions, the risk of default disappears such that . This result is

summarized in the following Lemma.

Lemma 5: In the case of default, if renegotiation involving a transfer of L to the firm, then .

Furthermore, ex-post profits under default are equal to zero.

Lemma 5 has some important implications for the optimal choice of effort for the firm under a fixed

term contract. This is established in the next proposition with proof provided in the appendix.

Proposition 4: Table 5 below characterizes optimal contract duration ( ) given the IC and PR conditions

and the optimal choice of effort if renegotiation is allowed for.

Table 5: Optimal Term Cap under renegotiation

Constraints Effort

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Or

Or

The optimal choice of effort for the firm given above is factored in by the government when

choosing the optimal duration for a fixed-term contract, which is given by the solution to the

following optimization problem:

where is set by the government prior to the realization of demand. From Lemma 5, we know

that debt is paid under all states of nature such that the firm’s cost of capital does not depend on the

level of effort and is equal to the risk-free rate. Moreover, the regulator sets the lowest duration of

the contract possible (again, at the point in which the participation constraint is binding), so that the

expected profit is zero, and, there is no trade-off between rent extraction, optimal effort choice and

the cost of capital. Total welfare is then given by:

Equation (16) allows us to compare the welfare generated by both types of contracts when

renegotiation is possible. Proposition 5 below provides such comparison. The proof is in the

appendix.

Proposition 5: Table 6 below compares the welfare generated by fixed and variable term contracts for all

parameter values when renegotiation is allowed for, expressed in terms of the incentive constraint (IC) and

participation constraint (PR) faced by the firm under a fixed term contract.

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Table 6: Optimal Regulation under Non-Commitment

Constraints

if

if

Or

Or

Proposition 5 shows that under renegotiation, whether a fixed-term contract welfare dominates a

variable term contract will no longer depend entirely upon the trade-off between higher revenues

under a fixed term contract and a lower capital cost under a variable term contract as was the case

in section 3. Instead, when there is no risk of default and the effect of the disutility cost ( ) is small,

then we have the same result that was found in section 3: if the firm chooses to exert a positive

effort , then a fixed term contract is welfare superior as it still drives higher revenues at no

extra cost in terms of an increase in the cost of capital. However, if the disutility cost is larger than

the advantage of the fixed term contract with respect to the variable term contract under full-

commitment, then the variable term contract generates more welfare. If the firm chooses to exert

effort , then both types of contracts generate the same level of welfare.

When there is a risk of default, the particular form of renegotiation studied above implies that the

cost of capital remains minimized. Moreover, Proposition 4 shows that the optimal duration for the

fixed term contract is identical to that of a variable term contract when renegotiation is feasible. In

this instance, the firm has no incentives to exert a positive effort to avoid default and, as a result, the

21

fixed term contract is dominated by the variable term contract (both generate the same cost of

capital and expected marginal cost but the former entails a disutility cost ).

5. CONCLUSION

This paper investigates a perverse incentive associated with the Least-Present Value of Revenue

(LPVR) auction proposed by Engel, Fischer and Galetovic (2001) to allocate public-private

partnerships contracts. While the LPVR auction variable-term contract addresses the adverse

selection issues associated with ensuring that the lowest cost firm wins the tender, it fails to

consider ex-post (moral hazard) distortions that might emerge when the firm faces a guaranteed

rate of return under a zero net present value auction. We consider a fixed-term contract, which

provides the firm with an incentive to provide the service at the least cost. However, under a fixed-

term contract the firm faces a bankruptcy risk and, therefore, potentially higher cost of capital than

under a variable-term contract.

We have established that, when renegotiation is not possible, a variable term contract can be

welfare dominated by a fixed term contract if the extent of moral hazard is sufficiently high such

that it offsets any increase in the cost of capital. We extend our analysis to consider the impact of

renegotiation and find that the positive incentives for cost reduction that exist under a fixed term

contract may disappear when renegotiation is feasible. In this case, whether a fixed-term contract

welfare-dominates a variable term contract will no longer depend only on the trade-off pointed out

above but also on the effect generated by the disutility cost that arises from the firm being

subsidized by the government to avoid default.

REFERENCES

Brealey, R. A., Cooper, I. A., & Habib, M. A. (1997). Investment Appraisal in the Public Sector.

Oxford Review of Economic Policy, 13, 12-29.

Camacho, F., & Menezes, F. (2010). Price Regulation and the Cost of Capital. School of Economics,

University of Queensland, Discussion Paper No. 413.

De Lemos, T., Eaton, D., Betts, M., & De Almeyda, L. T. (2004). Risk Management in the Lusoponte

Concession - A Case Study of the Two Bridges in Lisbon, Portugal. International Journal of Project

Management, 22, 63-73.

22

Engel, E., Fischer, R., & Galetovic, A. (2001). Least-Present-Value-of-Revenue Auction and Highway

Franchising. Journal of Political Economy, 109, 993-1020.

Engel, E., Fischer, R., & Galetovic, A. (2008). The Basic Public Finance of Public-Private

Partnerships. Forthcoming in the Journal of the European Economics Association. Center discussion

Paper No. 957, Economic Growth Center, Yale University, New Haven, CT (USA)

Foice, D. (1998). Second Severn Crossing. Paper presented at the Seminar in PPP Risk Management

for Big Transport Projects, Ministerio de Fomento, Spain.

Gomez-Ibanez, J. A. (2003). Regulating Infrastructure: Monopoly, Contracts and Discretion. Cambridge,

MA: Harvard University Press.

Guasch, J. L. (2004). Granting and Renegotiating Infrastructure Concessions: Doing it Right. Washington,

DC: World Bank Institute.

Guasch, J. L., Laffont, J. J., & Straub, S. (2003). Renegotiations of Concession Contracts in Latin

America. The World Bank.

Guasch, J. L., Laffont, J. J., & Straub, S. (2005). Concessions of Infrastructure in Latin America:

Government-led Renegotiation. The World Bank.

Guasch, J. L., Laffont, J. J., & Straub, S. (2006). Renegotiation of Concessions Contracts: A

Theoretical Approach. Review of Industrial Organization, 29, 55-73.

Guasch, J. L., Laffont, J. J., & Straub, S. (2008). Renegotiation of Concessions Contracts in Latin

America. Evidence from the Water and Transport Sectors. International Journal of Industrial

Organization, 26, 421-442.

Iossa, E., & Martimort, D. (2008). The Simple Micro-Economic of Public-Private Partnerships.

Center for Economic and International Studies.

Laffont, J. J., & Tirole, J. (1993). A Theory of Incentives in Procurement and Regulation, MIT Press.

Cambridge, MA (USA)

Martimort, D., & Pouyet, J. (2008). To Build or not to Build: Normative and Positive Theories of

Public-Private Partnerships. International Journal of Industrial Organization, 26, 393-411.

Nombela, G., & De Rus, G. (2004). Flexible-Term Contracts for Road Franchising. Transportation

Research Part A, 38, 163-179.

Vassallo, J. M. (2006). Traffic Risk Mitigation in Highway Concession Projects, The Experience of

Chile. Journal of Transport Economics and Policy, 40, 359-381.

23

APPENDIX

Proof of Proposition 1

We begin by identifying all the cases that need to be examined. From Lemma 2 we know that the

concessionaire chooses only one level of effort within the range of possible durations. In

fact, the decision of whether or not to undertake a positive effort will depend only on the cost of

undertaking that level of effort ( ) being less than or equal to the expected benefit in terms of higher

expected demand .

First, assume that the minimum duration for the contract that satisfies the participation constraint is

greater than or equal to . In this situation, the government can set the minimum

duration of the contract to extract all rents from the firm. Thus, to find this duration, we substitute

in and set . The optimal duration cap is then given by,

Where the firm chooses when, , and when,

.

Secondly, assume that the minimum duration that satisfies the participation constraint is lower

than . It continues to hold that the government will set the minimum feasible

duration for the contract to extract maximum rents. Therefore, we find the optimal duration cap by

substituting in and setting . If we calculate , we get:

24

If no default:

If default:

Since, , then

Therefore, the previous condition is analogous to:

Then, the optimal duration will depend on the condition between and .

If we have that rearranging for yields

25

where the firm chooses when,

, and when,

.

In the other hand, when we have that the minimum duration for the contract will be given

by equals to:

Proof of Proposition 2

Under a variable term contract, the duration is endogenous and will depend on the realisation of

demand. The firm’s state contingent net) revenues, which depend on whether or low or high

demand state realised, are given by:

Since the regulated term for the contract adjusts endogenously depending on the observed costs

and realized demand, it holds that operational and capital costs are always able to be covered.

Hence, there is no risk of default and the firm’s cost of capital is always equal to . Then, the

expression for profits reduces to

26

Fix , and at any level such that, the ex-ante expected revenues for the high and low demand

scenarios are the same, regardless of the level of effort, i.e., . Then, from

the expression above, the firm never chooses , as it can always guarantee higher profits by

choosing . It follows that the welfare maximizing regulated ex-post durations for the contract

(the ones that guarantee zero profits and maximize consumer surplus) are equal to ;

and .

Notice that since in all cases, then ; where , and,

is given by,

Rearranging this expression, we have that,

Proof of Proposition 3

We proceed to prove Proposition 3 using the cases outlined in Proposition 1 and comparing each

result with what we obtained in Proposition 2.

Case 1: and

We know from Proposition 1 that under these market conditions the optimal duration cap is given

by, , while the welfare generated is given by equation (9) ( ). It is then possible to

compare this welfare against the welfare obtained under a variable term contract. By taking the

difference between equation (9) ( ) and equation (11) we find that the fixed term contract

always generates at least the same welfare as the variable term contract.

27

Rearranging,

Since,

Therefore,

Case 2: and

We know from Proposition 1 that, under these market conditions, the optimal duration cap is

. By taking the difference between equation (10) ( ) and equation (11)

we find that:

Rearranging,

If we define Z as,

Consequently, , if

28

But, , therefore the above condition is equivalent to,

Which can be written as,

Rearranging,

So, if this condition is met, then,

Case 3: and

We know from Proposition 1 that, under this model parameterisation, the optimal term cap is

. By taking the difference between equation (9) ( ) and equation (11) we find that

the fixed term contract generates the same welfare as the variable term contract.

Case 4: and

We know from Proposition 1 that, under these market conditions, the optimal term cap is

. By taking the difference between equation (10) ( ) and equation (11) we

find that:

29

Rearranging,

After rearranging this expression we get:

According to this, whether the fixed term contract welfare dominates the variable term contract will

depend on the difference . Since , we have that:

If , then , and the fixed term contract will generate a higher

welfare than the variable term contract. But if, , then , and we

conclude that the variable term contract generates a higher welfare than the fixed term contract.

Proof of Proposition 4

From Lemma 2 we know that the concessionaire chooses only one level of effort within

the range of possible durations. We must also consider Lemma 6, which states the choice of effort

for the firm when there is no risk of default, since it is possible to renegotiate the contract.

As in Proposition 1, assume initially that the minimum duration for the contract that satisfies the

participation constraint is greater than or equal to . In this situation, the government

sets the minimum duration of the contract to extract all rents from the firm, and the optimal

duration cap is given by

30

where the firm chooses when, , and when,

.

On the other hand, when the minimum duration that satisfies the participation constraint is lower

than , the government can still set the minimum duration of the contract such that it

extracts all rents. According to Lemma 6, the optimal duration cap can be found by substituting

in and setting , such that the participation constraint is binding. Solving for in

this manner yields

where the firm chooses . This follows from the fact that, since the risk of default is covered by

the government allowing for the possibility of renegotiation, the firm has no incentives to exert a

positive effort.

Proof of Proposition 5

To prove Proposition 5 we use the cases obtained in Proposition 4 and we compare each result with

the results obtained in Proposition 2. Note that Proposition 4 provides only two distinct cases to

analyze:

Case 1: and

We know from Proposition 4 that, under these market conditions, the optimal duration cap is given

by, . Moreover, from equation (16) we know that, .

Since under a variable term contract there is no risk of default, it holds that . Therefore,

31

We know from Proposition 3 that, for this case, . Then, the question of whether the fixed

term contract will dominate the variable term contract will depend on parameter values. If

, then . Finally, if

, then .

Case 2: and ;

and ;

and

We know from Proposition 4 that, under these market conditions, the optimal term cap is

. From equation (16) we know that, . Since under a

variable term contract there is no risk of default, . Therefore, . Replacing, we

have that, which implies that