Report

Flavio Menezes The University of Queensland Preliminary. Comments Welcome. Matthew Ryan The University of Auckland Introduction Worldwide investment in PPPs jumped from $131 billion in the early 1990s (Thomsen,2005) to $1.2 trillion dollars globally in 2006 (World Bank PPP database). The popularity of PPPs linked to their perceived ability to shift risks from the public to the private sector. The implications of this shift in risk are not well understood About 50 percent of PPPs never reach the financing stage and, of those that do, about 50 percent are renegotiated (Bracey and Moldovan, 2007). Introduction (cont’d) In Australia, we had a couple of ‘tunnel’ bankruptcies. Administrators took over and on-sold ‘contract’ at big losses Favoured interpretation: equity was by and large wiped out, debt holders lost some, taxpayers gained. Is this right? Extension of the M1 Motorway in Hungary: Once completed, the project was at risk of default as traffic was only half the amount forecast. The project was renationalised. A successor PPP contract to build the M5 highway from Budapest to Serbia also ran into trouble for the same reason. Renegotiation led to the subsidisation of the toll by transfers from the government to the concessionaire. Does the possibility of bankruptcy (or renegotiation to avoid bankruptcy) affect the efficiency of the tender? Does it distort the choice of debt versus equity? Our Contribution Firms bid for a concession to build and operate a highway in a first-price, sealed-bid auction under demand uncertainty Construction is bundled with operation in the tender process. Bids = toll to be charged. Bidders are able to use debt strategically in order to "hold up" the Government. In low demand states, the winning firm threatens bankruptcy. If debt is not “too high”, the Government renegotiates and bails out the firm. Motivation: understand the occurrence of bail-outs in such arrangements, which will inform the design of better tenders. Our Contribution: Main Results Our model suggests that default and re-negotiation are natural outcomes of PPP first-price auctions. However, this does not result in an inefficient allocation process The winning bid may appear unrealistically attractive to the Government if it fails to anticipate the "hold-up“ Counterintuitive: More efficient firms are bailed out more often - and extract a higher expected transfer from Government -- than less efficient firms. The hold-up problem may be addressed by imposing restrictions on bidder financing. We also discuss Least Present Value of Revenue (LPVR) auctions as another potential solution. The Model: Basic Assumptions Bidders (risk neutral) have heterogeneous and privately known construction costs and complete the construction within the same timeframe; firms have common (= 0) operating costs. Each firm bids the toll it will charge while it holds the concession; The lowest bid wins, with ties resolved using uniform randomisation. The winner builds the road then operates it for the specified fixed period, charging the toll it bid into the auction. For technical convenience, we ignore discounting; the interest rate on risk-free debt is zero. Basic Assumptions (cont’d) The demand for the completed road is: = − , where is a random variable. Suppose ∈ , and its distributed according to the differentiable and strictly increasing distribution function G, with G′=g. Define = . We assume ≤ 2 so that equilibrium tolls do not exhaust demand in any state. In particular, no firm will rationally bid more than . 2 Basic Assumptions (cont’d) Firm i has construction cost ci, drawn randomly (and independently of other firms' costs) according to the common distribution F, defined on the support [c, c] , 2 where 0cc 2 F is strictly increasing and differentiable, with pdf f. (/2)² is the ex ante expected revenue of a monopolist. Basic Assumptions (cont’d) Firm i uses cash (equity) K and debt financing D = c − K to fund the construction phase; firms are not cash constrained and have access to the same competitive market for debt. Firms are distinguishable only by their construction costs. Financing is not revealed as part of the tender process; necessary to ensure costs are private information. E.g., winner finalises its finance after the auction Basic Assumptions (cont’d) The value of θ is realised at the same time as revenue is earned (not prior). Assumed for simplicity but it is not inconsequential: all revenue generated over the life of the concession is available to repay debt. Combined with no discounting, allows us to model the problem as three discrete stages: the auction, the construction phase, and the operation stage The entire period of the post-construction concession is collapsed into a single period. Endogenous financing and renegotiation Assume that there is a symmetric equilibrium bidding strategy ( ) and define , θ = ()( − ()). The Government places value > > 0 on keeping the current concession-holder in place; If − , ≤ , then renegotiation will occur with the government covering the firm’s debt shortfall. Assume Nash Bargaining ( = firm’s bargaining power) Endogenous financing and renegotiation (cont’d) As θ is continuous, expect different types renegotiate in different contingencies. Firm i may choose debt = , θ + but θ may depend on i. In states worse than θ, i declares bankruptcy and the Government will not offer a bailout, while in states better than θ the firm will either pay its debts or else renegotiate. If there is a non-zero probability of bankruptcy, debt servicing costs will rise above the risk-free rate. Given its bid and its construction cost, i chooses optimal debt. This determines the contingencies in which it is bankrupt and in which it renegotiates. These contingencies may depend on the firm's cost type; the nature of this potential dependence is not obvious a priori. Optimal leverage If firm i bids p, it will choose a financial structure to maximise its expected payoff contingent on winning. Suppose it sets its debt level at ∈ 0, . Expected profit contingent on being the winning bidder is Firm is solvent − − + Θ1 , Θ0 , Interest rate on debt − − 1 + , + + − − 1 + , Firm holds up the Government Optimal leverage Where Θ0 , = { ∈ [ , ] | [1 + (, )] ≤ ( − )┊} And Θ1 , = { ∈ [ , ]| 0 < [1 + (, )] − ( − ) ≤ ┊} Note that the optimal level of debt is independent of c given the bid p, though the latter will obviously depend on the firm's cost type in equilibrium. Optimal leverage: the cost of debt The firm declares bankruptcy and receives −( − ) when is such that: 1 + , − − > ⇔ < ([1 + (, )] + ² − )/ Thus the probability of default is: [1 + (, )] + ² − ( ) It follows that the cost of debt is the solution (in ) to: [1 + (, )] + ² − = (1 + )[1 − ( )] + [(1+)+²−] ( − ) (). Optimal leverage: Optimal Debt Level Given that the bank makes D in expected value, the firm's expected profit is given by: ( − ) − + (expected payment from the Government). Therefore, the firm chooses D to maximise its expected transfer payment from the Government, which is ([[1 + (, )] − ( − )] + ( − [[1 + (, )] − ( − )]) () Θ1 , = ( + 1 − 1 + , − − )() (∗) Θ1 , That is, for each state ∈ Θ1 , the Government pays the amount needed to clear the firm's debts, plus an additional transfer equal to this The Optimal Debt Level The Optimal Debt Level (cont’d) Given p; we can simply find the optimal left-hand end point for Θ₁, denoted by z The Optimal Debt Level (cont’d) Rather than choosing D to maximise (*), we can think of the firm choosing ∈ , to maximise {+, } [ − (1 − )( − )] () How does optimal D vary with p? ′ > The higher a firm bids in the auction, the lower its expected transfer from the Government. More efficient firms bid lower and are more likely to be ex-post bailed out Firms choose their capital structure by choosing a state (z) in which all of is needed to clear their debts. For states θ ∈ (, + ), revenue is higher so not all of is required for debt repayment. The firm can only obtain fraction α of the remainder through bargaining. Once revenue is high enough to repay all debt, the firm's claims on the Government vanish…so the expected payment that the firm can obtain depends on how quickly revenue rises with θ; the faster revenue increases with the demand state, the lower the expected transfer to the firm. For our demand structure, lower prices reduce the rate at which revenue increases with θ (see next). Optimal leverage (cont’d) To maximise payment from the Government, a firm would choose p=0 and borrow ; bailed out in every state and extract with probability one. Choosing p=0 would also maximise the firm's chances of winning the auction. However, it cannot be an equilibrium for all firms to bid p=0, since we assumed that < so the winning firm would make a loss with certainty. Trade-off between maximising revenue from hold-up and maximising toll revenue to be struck at a strictly positive toll. Since the hold-up incentive reinforces the incentive to set p low, expect more aggressive bidding by all firms than when = 0. To quantify these trade-offs, we must ascertain the optimal choice of z for each p > 0. The next Lemma characterises the optimal z for given p in the case of the uniform distribution. Optimal leverage (cont’d) Lemma 1: Let p > 0 be given. If θ is uniformly distributed, then all firms choose = . Proof: The firm is indifferent about which z ∈ ( , − ) choose. (Recall shaded area) If > − then the firm strictly prefers to set = . It is therefore without loss of generality to suppose that all firms choose = . to Optimal leverage: Conclusion It follows that creditors are exposed to zero default risk, hence r = 0, and debt satisfies D=+p(θ − ). Firms which bid higher toll rates have a (weakly) lower probability of receiving a Government bail-out, as well as a lower expected payment from the Government. A firm that bids p (and chooses its debt level optimally) receives an expected payment from the Government equal to 1 − 1 − , − ,1 = 2 − 1+ 2 , if < 2 − 1 − 1 − − 2 − ; and , if ≥ − Equilibrium bidding behaviour Given the non-differentiability in the expression above, we must be careful about assuming differentiability of the equilibrium bidding function. There are two cases in which differentiability is plausible: (i) when equilibrium bids are strictly increasing in c and bounded above by . [Low toll equilibrium] − (ii) when equilibrium bids are strictly increasing in c and bounded below by . [High toll equilibrium] − Low toll equilibrium Since hold-up incentives place downward pressure on bids, start by searching for a low toll equilibrium. In such an equilibrium, all of the winning firm's profit is obtained from exploiting the hold-up problem. If no type bids above , the winning bidder is bailed out in every state. − Suppose is a differentiable and strictly increasing equilibrium − bidding function, with ≤ . Let (, ) = ()( − ()). If i bids () and chooses its debt level optimally, its expected payoff (conditional on winning the auction) will be 1 , − + − (1 − )() − . 2 Low toll equilibrium (cont’d) 1 2 We define , = , + − 1 − − So that for an efficient mechanism solves: ∈[,] [() − ]ⁿ⁻¹(). Where c = 1 − F c . As standard, = | > , where X is the r.v. corresponding to the lowest of n-1 draws from F and . 1 , = | > − + 1 − − 2 To find , it is necessary to solve ( − ) + − () − (**) 1 2 1 − − = () ⇔ ( − ) = 1 2 Where = + (1 − ) and = − (1 − ). Low toll equilibrium: Conclusion We can solve (**) provided ≥ 0 and 2 2 ≥ − . The solution is valid provided ≤ − . These conditions will be met if weak demand or weak bargaining power for the concessionaire. In particular, a low toll can partially offset the effects of a weak bargaining position for the firm. High toll equilibrium Let be a differentiable and strictly increasing equilibrium bidding function, with ≥ . Since no type bids below and − − is strictly increasing, the winning firm is solvent with positive probability. If firm i bids , its expected payoff (conditional on winning the auction) is (1 + ) 2 , − + . 2() − The presence of a hold-up problem gives stronger incentives to lower the toll price than in the low-toll equilibrium. Once the toll reaches , marginal (hold-up) incentives for further toll reductions are − 1 constant at (1 − ) − . 2 High toll equilibrium (cont’d) In this case we have (1 + ) 2 , = | > − 2() − To find , it is necessary to solve ( − ) + 2 − (1+) 2 1+ 2 2 − (***) = () ⇔ (2 − + ()) = High toll equilibrium (conclusion) For existence we require strong demand, high returns from holdup and a strong bargaining position for the firm. Mixed equilibrium The model with a uniform θ distribution also admits equilibria that are mixtures of the "low toll" and the "high toll" variety. In these "mixed" equilibria, the bidding function is non-differentiable at a toll equal to − . It resembles the "low toll" equilibrium below this value and the "high toll" equilibrium above. Summary Firms choose debt levels strategically to hold-up the Government; winning firm threatens default with positive probability. Under our demand structure, a firm that bids lower is able to extract a higher expected bail-out from the Government. If the equilibrium bidding function is strictly increasing, more efficient firms make higher demands on the public purse (and hence charge very low tolls). We computed the equilibrium bid function when θ is uniformly distributed and verified that it is strictly increasing. I Firms never actually go bankrupt, but each firm i credibly threatens default in an interval of states of the form , ∗ for some ∗ ∈ , . ∗ When = firm i threatens default in all states, so its return on equity comes entirely from Government transfers. Summary (cont’d) Depending on parameters, we may observe: "low toll" equilibrium, in which toll bids are so low that ∗ = for every firm; "high toll" equilibrium in which ∗ < for every firm; or a "mixed equilibrium" in which more efficient firms are solvent in some states while less efficient firms threaten default in all states. Summary (cont’d) Weak demand or weak concessionaire bargaining power encourage "low toll" equilibria, while strong demand or strong bargaining power encourage "high toll" equilibria. The link between demand and tolls is natural, though the correlation between bargaining strength and equilibrium toll levels may seem counter-intuitive. The latter arises because toll reductions are a partial substitute for bargaining strength. Under our demand structure, lower tolls allow the firm to credibly threaten bankruptcy in more states and thereby increase the returns from hold-up. Conclusion We model the optimal financial structure and equilibrium bidding behaviour and show that: The auction remains efficient, but bids are lower than they would be if all bidders were equity financed, and the more efficient the winning firm, the more likely it is to require a Government bail-out and the higher the expected transfer it extracts from the Government through hold-up. These insights complement the work of Engel, Fischer and Galetovic (2001) on LPVR tenders. Conclusion A LPRV tender allocates the contract to the bidder with the lowest present value of expected revenue; the concession contract will remain in place until the firm recovers its bid. EFG argue that, unlike fixed term contracts, the LPVR mechanism results in an optimal allocation of risk -- firms are risk-averse in their model. bidders bid a "guaranteed" PVR -- not quite fully guaranteed, as demand may be so low that the winning firm holds the concession forever without earning the PVR. The Government sets the toll rate for each demand state before bids are taken. This toll rate reflects optimal congestion pricing, plus optimal risk-sharing given that the PVR is not guaranteed in every state. Conclusion EGF (2001, 2008) assume that is possible to find a mechanism that avoids further renegotiation by fully transferring the risk of default to the government Fhe firm does not default even if the revenues are not sufficient to service debt in a particular period. EFG (2001) have two models -- one with and one without "commitment". In the absence of commitment, the Government must ensure nonnegative PVR in every state (not just in expectation). They treat this as an extra constraint in the design of the optimal contract. Conclusion In each case, the Government effectively renegotiates in advance It determines the toll and concession duration as a function of the state, so there is no need to re-negotiate ex post. The Government bears the default risk (under no commitment) through agreeing up front to a state-contingent toll/transfer and concession duration. EFG consider a more complete contract than that available in our model. We assume that it is politically infeasible for governments to commit to a transfer/subsidy/toll increase even though, in practice, governments may want to avoid default As renegotiation is often inevitable, we explore its implications for the efficiency of the PPP tender and the choice of the capital structure of the firm. Conclusion Another distinction from EFG (2001, 2008) is that we do not consider differences in risk attitudes. Instead, we look at the nature of the risk. In our model the government would like to shift the risk of default to the firm. This might provide yet an alternative motivation for the introduction of a LPVR auction. The use of a LPVR tender, which could allow the firm to change either the duration of the contract or the price, would result in a greater ability for the firm to manage risk. Our future research plans includes a characterisation of equilibrium behaviour in LPVR auctions when the capital structure of the firm is endogenous.