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Sharing The Big Risk: An Assessment Framework for Revenue Risk 1
Sharing Mechanisms in Transportation Public-Private Partnerships 2
Ting Liu1,2, Michael Bennon3, Michael Garvin4, Shouqing Wang5 3
1. Ph.D. Candidate, Department of Construction Management，Hang Lung Center for Real Estate，Tsinghua 4
University，Beijing 100084，China 5
2. Joint-supervised Ph.D. Candidate, Stanford Global Project Center, Stanford University, CA94306, United 6
States 7
3. MBA/MSc, Stanford Global Project Center, Stanford University, CA94306, United States 8
4. Ph.D., Department of Civil and Environmental Engineering, Virginia Tech, VA24061, United States 9
5. Ph.D., Department of Construction Management，Hang Lung Center for Real Estate，Tsinghua University，10
Beijing 100084，China 11
Abstract: A number of toll roads delivered via PPPs have encountered financial distress due to 12
revenue risk with traffic levels significantly lower than those forecasts in recent years. As a result, 13
there has been a shift in PPP road procurements to models in which the government retains some or 14
all of the demand risk for the project, instead of the concessionaire. A tangible framework to guide 15
governments’ decisions in choosing among financial support mechanisms in allocating revenue 16
risks is thus a relevant development for policymakers. This paper proposes a framework to 17
evaluate fiscal support alternatives by comparing the marginal leverage they enable a project to 18
take and the level of financial exposure they allocate to the procuring government. A quantitative 19
methodology is developed that defines inputs and measurable indicators, and also incorporates 20
stochastic modeling and simulation techniques designed for use at an early stage of project 21
planning. The results of a numerical case study demonstrate that flexible term procurement does 22
little to increase project leverage, minimum revenue guarantee is most applicable to projects with 23
significant revenue volatility, while availability payment procurement is more applicable to 24
projects that are projected to have a lower volatility and lower mean revenue relative to their 25
capital investment. 26
Key words: Public-Private Partnerships (PPPs); toll road; revenue risk; government financial 27
support; borrowing capacity; value at risk 28
1. Introduction 29
As an alternative approach to traditional public procurement, Public-Private Partnerships (PPPs) 30
have been increasingly adopted by governments globally to procure infrastructure based on the 31
complete life-cycle costs of developing and maintaining the asset, and to transfer the risks 32
associated with complex infrastructure project development and operation to the private sector. 33
In the US, highways have been, to date, the predominant sector in which PPPs have been used to 34
develop new infrastructure, and prevailing PPP model used is the toll/revenue risk concession. 35
This is in part due to the fact that they are often large, complex projects but also because they are 36
funded through user-fees and entail significant risk in assessing the future demand and toll revenue 37
to support the project. These factors, and federal support programs for the PPP model, have made 38
toll roads an ideal sector for P3s in the US. However, in recent years, predominantly in the wake of 39
the global financial crisis, many toll roads delivered via PPPs have encountered financial distress. 40
Notable recent PPP bankruptcies include I-185 in South Carolina, SR125 in California, and SH130 41
in Texas, among several others. In these and other recent toll road bankruptcies one factor has 42
been cited as a predominant cause: traffic levels significantly lower than that forecast for the 43
project (See “First Amended Disclosure Statement to First Amended Plan for Adjustment of Debt 44
of I-185”, “Drop in Traffic Takes Toll on Investors in Private Roads” on the Wall Street Journal, 45
etc.). 46
Revenue risk for a toll road is the risk that low traffic levels will cause project revenue to be 47
insufficient to service the operation and maintenance costs, the debt, and the adequate rate of 48
investor return (Chiara, Garvin et al. 2007). Since the majority of toll revenue will be used in debt 49
and equity service, concession contracts with private financing are naturally very sensitive to 50
fluctuations in demand (Charoenpornpattana, Minato et al. 2002). Retrospective studies illustrate 51
that many renegotiations and cancellations of transportation projects with private participation like 52
trains and toll roads take place due to revenue risks (Guasch 2000, Charoenpornpattana, Minato et 53
al. 2002, Guasch, Laffont et al. 2003, Harris, Hodges et al. 2003). 54
Intuitively, demand for a toll road, like other critical infrastructure services, can be expected to be 55
relatively inelastic. However, this varies significantly based on the asset itself and nearby free 56
alternatives. In addition, the vast majority of toll road concessions in the US naturally include a set 57
or maximum toll schedule, so concessionaires are unable to simply adjust tolls as they see fit. In 58
addition, traffic demand in the years following the global financial crisis demonstrated that toll 59
road demand is more closely correlated to broader economic conditions than expected by many 60
investors before the recession (Bain 2009). Therefore, revenue risk is beyond concessionaires’ 61
control and thus it should not be fully allocated to concessionaires. 62
Revenue Risk for toll roads and other transportation infrastructure has also been shown to not 63
necessarily be normally distributed. A sample of 210 transportation projects in 14 nations shows 64
that traffic forecasts are so inaccurate that 90% of rail projects are overestimated by 106% on 65
average, 50% of road projects have forecast errors larger than ±20%, and forecasts have not become 66
more accurate over time (Flyvbjerg, Skamris Holm et al. 2005). Those studies show that the 67
majority of demand forecasts are not just wrong – they are more often than not too high. There are 68
several potential causes of this trend, perhaps most notably the general if not explicit pressure in 69
early stage project planning to make favorable assumptions for a new project (Bain 2009). 70
For an individual project and from the perspective of the procuring government agency, most PPP 71
bankruptcies due to revenue risk are actually an indication that revenue risk was successfully 72
transferred to the private sector – risk that otherwise would have been borne by taxpayers. Trends 73
like those in the US, however, can have regional impacts on the market and future procurements. As 74
a resul, there has been a shift in PPP road procurements to models in which the government retains 75
all or part of the revenue risk for the project, instead of the concessionaire (Parker 2011) (Cruz and 76
Marques 2012). Governments can provide financial support to mitigate the revenue risk undertaken 77
by the private sector, and increase the attractiveness of PPP contracts. Commonly adopted financial 78
supports provided by governments include Availability Payment (AP) concessions, minimum 79
revenue guarantees (MRG) and, to a lesser extent, flexible-term concessions. Each is described in 80
detail in Section 2. 81
Government financial support mitigates revenue risk transferred to the project company, but also 82
exposes the government to contingent liabilities. The guarantees offered by the Mexican 83
government in its toll road program from 1989 to 1994 resulted in an unanticipated cost of $8.9 84
billion to the government after the 1994 Mexican economic crises, when the actual project revenues 85
fell 30% below the original projections on average (Brandao and Saraiva 2008) (Ruster 1997). Also, 86
in Columbia, the adverse fiscal impact of MRGs have been very significant, where the total amount 87
of guarantees paid by government during 1995 to 2004 amounted to 70% of the investments of the 88
11 guaranteed concessions (Carpintero, Vassallo et al. 2013). In practice, some international 89
studies have identified governments’ inability to design guarantees or support mechanisms using a 90
well-founded quantitative and transparent process, which often lead to unreasonably generous 91
guarantees and ex post renegotiations (Cruz and Marques 2012) and (Xu, Yeung et al. 2014). 92
The purpose of this article is to propose a methodology through which government sponsors can 93
evaluate and compare various mechanisms for transferring or sharing revenue risk for a toll-funded 94
highway PPP. Specifically, the objectives are to (1) identify critical indicators of marginal benefit 95
and government financial exposure to establish a measurable and comparable basis for comparing 96
various government financial support alternatives, (2) outline a rationale to choose among the 97
fiscal support alternatives based on the indicators, (3) propose a stochastic model to calculate the 98
identified indicators of these fiscal supports quantitatively with Monte Carlo simulation and (4) 99
adopt a numerical case study to demonstrate the application of the proposed methodology and to 100
explore under what circumstance which fiscal support mechanism may be most applicable. The 101
following section introduces common mechanisms to allocate revenue risk. Section 3 includes a 102
literature review of approaches to evaluate revenue risk sharing mechanisms. Section 4 introduces 103
the framework. Section 5 proposes stochastic models for the mechanisms reviewed and Section 6 104
introduces a hypothetical numerical case study. The final section displays conclusions, discusses 105
the limitations of the proposed model, and identifies areas for future research. 106
2. Fiscal Support Mechanisms to Transfer or Share Revenue Risk 107
For a toll-funded road project, a “base case” toll concession would transfer revenue risk to the 108
private concessionaire. In most cases, though not always, tolling is capped at designated levels to 109
avoid excessive pricing, so total project revenue is largely driven by traffic volume. Three 110
commonly used forms of revenue risk-sharing via payments by governments to concessionaires are 111
listed below: 112
An availability payment (AP) is a public procurement mechanism in which the 113
government makes periodic performance-based and inflation-linked payments to the 114
concessionaire with monitoring of actual asset performance against predefined 115
performance specifications and quality standards (Sharma and Cui 2012). Under AP 116
procurements, the government retains all revenue risk, as well as the authority to manage 117
toll rates dynamically. It is a mechanism that generally increases competition for a 118
procurement, in that bidders are not required to take on revenue risk for the project. Under 119
AP procurements, however, concessionaires have no incentive to increase traffic for the 120
project through their design, operations, and maintenance practices. Shadow toll is 121
another mechanism that the government makes payments to the concessionaire. This 122
mechanism may not use government funds efficiently to protect investors from revenue 123
risk as payments are generally higher when traffic is high and vise versa (Fisher and 124
Babbar 1996). Therefore this paper does not dive further into shadow toll mechanism in 125
this paper. 126
Flexible-term contract is a procurement mechanism in which the duration of the 127
concession is not fixed. Instead it ends once the concessionaire achieves a target 128
cumulative revenue, “Least Present Value of Revenue (LPVR)”, as proposed by Engel, 129
Fischer et al. (1998). This approach was first introduced in the concession of the Second 130
Severn Crossing in the United Kingdom in 1990, and has since mostly been implemented 131
in Chile (Vassallo 2006). However, relatively few concessions have been awarded with 132
flexible-term contracts (Cruz and Marques 2012). The mechanism is generally more 133
complex to incorporate into a procurement than other support mechanisms, and it may 134
conflict with the maximum duration of concessions defined by local legislation. It also 135
injects uncertainty into the financing of a project when the concession duration is 136
indeterminate (Nombela and De Rus 2004) (Cruz and Marques 2012). To mitigate these 137
constraints, an adjusted version of the flexible-term concession has been proposed which 138
requires the government to pay the remaining LPVR at the end of the maximum 139
concession term (Vassallo 2004). 140
Minimum revenue guarantee (MRG) has been implemented in Chilean concessions, in 141
the early Colombian concessions (1994–1997) and in some Peruvian, South Korean 142
concessions, etc. (Vassallo 2006, Carpintero, Vassallo et al. 2013). By offering an MRG, 143
the government will make a compensation payment to the concessionaire in the case that, 144
in any one year, the actual revenue falls below the specified minimum annual revenue. 145
MRGs are sometimes implemented together with an Excess Revenue Sharing (ERS) 146
mechanism to achieve a symmetrical risk profile. Unlike payment obligations under AP 147
procurements, which are explicitly prescribed in agreements, MRGs expose governments 148
to some contingent liabilities—payments that are uncertain and driven by demand relative 149
to projections (Cebotari 2008). 150
3. Approaches to Evaluate Revenue Risk Sharing Mechanisms 151
In order to evaluate the various alternative revenue risk sharing mechanisms and support 152
government decision making, a number of researchers have made efforts to construct quantitative 153
models and instruments to value the benefits and contingent liabilities incurred by such support. 154
3.1. Incentive theory based evaluation 155
Some measure the impacts of government guarantees on projects theoretically by modeling 156
objectives, incentives and decision-making processes of the involved parties. Engel, Fischer et al. 157
(1997) Nombela and De Rus (2001) and Nombela and De Rus (2004) build up mathematical 158
bidding programming models with an asymmetric information assumption, seeking minimum life 159
cycle cost and concessionaire’s financial equilibrium objectives of both the public and private 160
sectors. The models demonstrate that auctions based on bids for the least present value of 161
revenue/net revenue with a flexible-term contract, rather than on bids for minimum price or 162
maximum payment to government, help to eliminate bias towards selecting firms with optimistic 163
demand forecasts, and help to select the most cost-efficient firm. They claim that contingent 164
concession length is a critical factor of an optimal demand risk-sharing contract. Feng, Zhang et al. 165
(2015) build a bidding model with stochastic traffic demand, assuming that private investors 166
determine toll charges, road quality, and road capacity to maximize profit. By comparing the 167
outcomes between contracts with and without government guarantees, they demonstrate that high 168
MRGs increase toll charges while decreasing road quality and road capacity. 169
3.2. Real option based evaluation 170
Other researchers have made efforts to develop quantitative evaluation methods from a financial 171
perspective. The widely used traditional Discounted Cash Flow (DCF) method to evaluate 172
engineering projects works well for short-term projects in stable markets. However, for long-term 173
and uncertain projects, the expected cash flow cannot adequately reflect market fluctuations and 174
managerial flexibility, and thus may lead to poor investment decisions (Martins, Marques et al. 175
2015). In order to remedy this defect and take flexibility into consideration, Myers (1977) derives 176
a Real Options valuation approach from the concept of options in corporate finance. 177
Other studies have proposed tools to evaluate government supports as a bundle of real options 178
(Charoenpornpattana, Minato et al. 2002), in PPPs for infrastructure investments (Garvin and 179
Cheah 2004) (Martins, Marques et al. 2015). Ho and Liu (2002) present an option-pricing based 180
model to evaluate the impacts of government loan guarantees on the financial viability of a BOT 181
(build-operate-transfer) project with project value and construction cost as two at-risk variables, 182
and argue that government guarantees will increase investment value, though this is not accounted 183
for in a DCF model. Huang and Chou (2006) demonstrate that an MRG can create substantial 184
value when modeled using real options, assuming operating revenue is a stochastic variable 185
following a generalized Wiener process. Cheah and Liu (2006) adopt a risk-neutral pricing method 186
to value governmental supports as real options, and propose to incorporate the value of such 187
supports into negotiation frameworks. Instead of structuring MRG as a series of European put 188
options (that can only be exercised at the end of its life), Chiara, Garvin et al. (2007) propose a 189
Bermudan or a simple multiple-exercise real option model, which can be exercised on 190
predetermined dates between the purchase date and the expiration date. They also employ a 191
multiple-least squares Monte Carlo technique to value the more flexible MRG. Brandao and 192
Saraiva (2008) extend the standard option pricing model to value minimum traffic guarantees by 193
using market data of project returns to estimate stochastic project parameters, and propose to put a 194
cap on total government outlays of guarantees to limit budgetary impacts of contingent liability. 195
Jun (2010) Ashuri, Kashani et al. (2011) and Iyer and Sagheer (2011) also apply real option 196
models to value MRG together with a traffic revenue cap. All of these studies conclude that MRGs 197
and other support mechanisms can create value. 198
Scholars have also applied the real option based models to measure the fiscal burden incurred by 199
taxpayers from government guarantees. Indicators frequently used include 1) the expected present 200
value of all guarantee payments, or the expected amount to be paid each year; 2) the probability 201
distributions of the amount of MRG to be paid, the excess payment with a certain confidence 202
interval, the exceedance probability, or the probability of a budget shortfall under a certain budget; 203
and 3) the probability distributions of the timing and number of times when the MRG may be 204
exercised (Ashuri, Kashani et al. 2011, Almassi, McCabe et al. 2012, Wibowo, Permana et al. 2012). 205
Wibowo and Kochendoerfer (2010) also develop a framework to quantify the contingent liability 206
of government guarantees, which allows the government to examine relationships among the 207
expected total payment, budget-at-risk allocated, and a desired confidence interval of actual 208
payment not exceeding the budget-at-risk. 209
3.3. Empirical studies 210
Despite the common conclusion drawn from theoretical studies that government financial support 211
creates value, some empirical studies show that these revenue risk sharing mechanisms are not as 212
effective as expected. Vassallo (2006) conducted interviews with government agencies, 213
concessionaires and university professors to find that the flexible-term with LPVR mechanism 214
applied in Chile initially met strong opposition from concessionaires for a variety of reasons: (1) 215
the mechanism does not improve the project’s ability to fulfill its commitments to lenders; (2) the 216
variable length of the contract makes the concession operation (resource planning) difficult to 217
organize in advance; and (3) the flexible-term procurement limits upside opportunity while not 218
always limiting downside risk. That study did, however, conclude that the LPVR procurement 219
mechanism was effective in reducing renegotiation expectations in Chile. Carpintero, Vassallo et 220
al. (2013) adopt a cross-country analysis based on project data from 1990 to 2010 in Chile, 221
Colombia, Peru, Mexico and Brazil, and find that traffic risk mitigation mechanisms, including 222
flexible-term procurements, MRGs, and APs in Latin American toll roads have not been very 223
successful in reducing renegotiation rates or in increasing the number of bidders in the tenders. 224
3.4. Optimization of individual revenue sharing mechanisms 225
Based on the evaluation researches and empirical evidences cited above, other researchers have 226
proposed models to optimize support mechanisms. Nombela and De Rus (2004) propose a way to 227
improve flexible term contracts by introducing bi-dimensional bids on LPVR, together with 228
maintenance costs, which turn into bidding on LPVNR (least present value of net revenue). 229
Vassallo (2006) suggests flexible term concessions implemented with a limit on the downside risk 230
by forcing the government to pay the LPVR left at the end, as well as a minimum concession 231
duration to make this mechanism more attractive to private bidders. Shan, Garvin et al. (2010) 232
propose a “collar option” which combines a put (MRG) and a call (ERS) option to be properly 233
matched. Ashuri, Kashani et al. (2010) Rocha Armada, Pereira et al. (2012) Sun and Zhang (2014) 234
Carbonara, Costantino et al. (2014) Wang and Liu (2015) all try to optimize the thresholds of MRG 235
and ERS by balancing the rate of investment return for the private sector and the government’s 236
cost to offer such a support. Engel, Fischer et al. (2013) propose a flexible term concession 237
mechanism with a revenue cap to be combined with a minimum income guarantee for 238
intermediate-demand projects. Sharma and Cui (2012) seek to optimize the design of concession 239
and annual payment for AP PPP projects. 240
3.5. Comparison among various revenue risk sharing mechanisms 241
Despite a number of existing studies on evaluation and optimization of individual fiscal support 242
alternatives, there are few studies that compare alternative revenue risk-sharing mechanisms 243
quantitatively or that propose a systematic rationale to choose among fiscal support alternatives. 244
Irwin (2003) suggests that choosing among different fiscal support instruments should be based on 245
comparisons of their accuracy—“accuracy” here assesses their effectiveness in internalizing 246
externalities, overcoming market failures, mitigating political and regulatory risks, circumventing 247
political constraints on prices or profits, redistributing resources to the poor, etc.—transparency, as 248
well as cost. Wibowo (2004) adopts a real option pricing model to evaluate and compare fiscal 249
supports with two dimensions of expected payoff: (1) governments’ contingent liabilities; and (2) 250
the concessionaire’s risk of having negative NPVs. The results of that study demonstrate that 251
minimum revenue/traffic guarantees can be more effective than equivalent direct subsidies; and 252
Brandão, Bastian-Pinto et al. (2012) reaches a similar conclusion. 253
Considering the circumstances under which a given financial support mechanism is most 254
appropriate should be an important issue for policymakers: Yet there remains a research gap in 255
laying out an integral and consistent framework to guide decisions on choosing among 256
government financial support mechanisms. Also, none of the above research has taken lenders’ 257
(who are critical stakeholders in project finance) perspective into consideration. This paper seeks 258
to propose such a framework based on the instruments identified and developed in the research 259
above, and critical factors reflecting governments’, concessionaires’ as well as lenders’ 260
perspectives. 261
4. A framework to evaluate and compare support mechanisms 262
Fisher and Babbar (1996) claim that the type and level of government financial support embedded 263
into PPP projects should be limited to the extent needed to attract financing and promote a 264
successful procurement. They establish a conceptual two-dimensional framework to locate the 265
spectrum of possibilities for government financial support, as illustrated in Figure 1. In this 266
framework, the higher the impact on ability to raise financing and the lower the government’s 267
financial exposure the better. The framework is cited and recommended by several subsequent 268
studies (Charoenpornpattana, Minato et al. 2002) and public reports (World Bank Group 2016) . 269
However, a model to incorporate measurable variables to plot mechanisms along those two 270
abstract dimensions is beyond the scope of these existing studies. There is a research gap to go a 271
step further to elaborate the framework into a tangible and measurable model. 272
Impact on
Ability to
Raise
Financing
High
LowGovernment Financial Exposure High
Concession Extension
Revenue Enhancement
Shadow Toll
Minimum Traffic/Revenue Guarantee
Subordinated Loan
Grant
Exchange Rate Guarantee
Debt Guarantee
Equity Guarantee
273
Figure 1. Range of Options for Government Support (reprinted from Fisher and Babbar 1996) 274
4.1. Definition of measurable indicators 275
The proposed model quantifies the implications of various options for revenue risk sharing 276
mechanisms along two dimensions: The impact of the support mechanism on the cost of capital 277
for the project, and risk exposure of the government. 278
4.1.1. Impact on cost of capital 279
Governments offer financial support to projects with revenue risk to make projects bankable and 280
reduce the weighted average cost of capital (WACC) for the project. Project WACC is determined 281
by the costs and weights of both equity and debt: WACC = w𝑒 ∗ 𝐶𝑒 +𝑤𝑑 ∗ 𝐶𝑑 . All of the 282
variables in this fomula will vary based on the project risks, and it is difficult to calculate total 283
costs of financing for a project early in the planning process. However, the revenue risk support 284
mechanisms described above can be used to decrease the cost of financing a project primarily by 285
increasing the leverage a project can take. This is a key assumption of the proposed model, in 286
using increased borrowing capacity as a proxy for reducing the financing costs of a project. 287
In practice, lenders calculate a project’s borrowing capacity based on annual cash flows available 288
for debt service (CFADS) over the loan life, and required coverage ratios such as DSCR (debt 289
service coverage ratio), and LLCR (loan life coverage ratio). CFADS is the amount of cash 290
available to service debt after all essential operating expenses have been met (see Equation 1). 291
DSCR is defined as annual CFADS divided by the annual debt service. LLCR is equal to the 292
present value of CFADS 𝑃𝑉(𝐶𝐹𝐴𝐷𝑆) over the loan life to the outstanding debt. Since annual 293
debt service and DSCR can be adjusted through structuring debt repayment schedules, the model 294
uses LLCR to determine the project’s borrowing capacity at financial close (see Equation 2). 295
CFADS and LLCR will vary with project economics, credit enhancement mechanisms (including 296
fiscal support), and the seniority of the lien. A key driver for projects with revenue risks, of course, 297
is the lenders’ evaluation of the traffic demand study for the project. Lenders and underwriters 298
generally use a very conservative probability of demand to determine CFADS, say 10% or even 5% 299
of the probability distribution. LLCRs also vary widely based on whether the project is exposed to 300
revenue risk. The required LLCR for CFADS with guaranteed revenue is generally between 301
1.2-1.3; while the market LLCR for CFADS with demand risk is generally between 1.5-1.9 (Khan 302
and Parra 2003). 303
𝐶𝐹𝐴𝐷𝑆 = 𝑅𝑜𝑏𝑢𝑠𝑡 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑜𝑓 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑂&𝑀 𝐶𝑜𝑠𝑡 (1) 304
𝐵𝑜𝑟𝑟𝑜𝑤𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 = 𝐵𝐶 =𝑃𝑉(𝐶𝐹𝐴𝐷𝑆)
𝐿𝐿𝐶𝑅 (2) 305
4.1.2. Government risk exposure 306
Fiscal supports dealing with project revenue risk may create contingent liabilities and claims for 307
the government, which increases the challenge of public budgeting. In order to better meet overall 308
fiscal constraints, a stochastic analysis is needed not only of the expected value, but also of the 309
volatility of the government’s financial exposure (Kim and Ryan 2015). A fiscal support with 310
lower expected value of government expenditure doesn’t necessarily dominate one with a higher 311
expected value, if the volatility of the former is larger than the volatility of the latter. The concept 312
of value at risk (VaR) was first introduced to improve risk management in finance and insurance 313
(Embrechts, Klüppelberg et al. 2013). VaR takes volatility into account and stands for a threshold 314
loss value given a probability level (say P5, P10). VaR offers a better understanding of 315
government liabilities in extreme cases and a more informed decision can be achieved, especially 316
when a project’s traffic forecast has an optimistic bias. Therefore, VaR is adopted as the dominant 317
indicator for government financial exposure, while expected value is used as a secondary indicator. 318
The VaR and expected value of the present value of government cash flow (CFg) can be calculated 319
through stochastic modeling and Monte Carlo simulation (see the next section “stochastic 320
modeling” for more details). 321
𝐺𝑜𝑣𝑒𝑟𝑛𝑚𝑒𝑛𝑡 𝑓𝑖𝑛𝑎𝑛𝑐𝑖𝑎𝑙 𝑒𝑥𝑝𝑜𝑠𝑢𝑟𝑒 = {𝑉𝑎𝑅[𝑃𝑉(𝐶𝐹𝑔)], 𝜇[𝑃𝑉(𝐶𝐹𝑔)]} (3) 322
These two variables can not only be used to measure government financial exposure from an 323
individual project, but could also be combined with those variables from other projects to generate 324
portfolio level measures of risk, thus improving overall, long term budgeting and deficit control. 325
4.2. Value at Risk - Borrowing Capacity comparison framework 326
To facilitate comparison, here the indicators are integrated into a two-dimensional coordinate (see 327
Figure 2). The borrowing capacity is on the Y-axis, illustrating the leverage or marginal benefit of 328
government fiscal support. Value at risk (VaR) of government expenditure is on the X-axis, 329
illustrating the maximum potential cost of fiscal support given a certain probability level, e.g.: 5%. 330
Borrowing
Capacity
Government Financial Exposure at Risk (5%)
Arrangement 1
Arrangement 2
Expenditure Income
Arrangement 3
Dominate
331
Figure 2. Value at Risk - Borrowing Capacity comparison coordinate 332
In this coordinate, a point on the top right dominates a point on the bottom left, therefore the fiscal 333
support mechanism for Arrangement 1 in Figure 2 dominates the one for Arrangement 2. However, 334
a point on the top left and a point on the bottom right cannot be directly compared via this 335
coordinate system. For example, fiscal support with Arrangement 3 has a lower cost of financing 336
than Arrangement 1, but public VaR to revenue risk is higher. In this case, external constraints 337
such as government budget for this project, maximum debt to equity ratio required by relevant 338
regulations or lenders’ policies are needed to narrow down the range of feasible options. If the 339
possible borrowing capacity with Arrangement 3 exceeds the maximum debt ratio desired by the 340
procuring agency, or the government expenditure at risk is higher than desired, then Arrangement 341
3 should be rejected because it offers more fiscal support than what is necessary or affordable. 342
However, if Arrangement 3 meets the external limits, then further analysis of the comparison 343
between Arrangement 1 and 3 in more detail is needed. Non-financial issues such as transparency, 344
accuracy of incentive mechanisms, regulatory difficulties, government’s preferences, etc. should 345
be taken into consideration. 346
In practice, each fiscal support mechanism can be arranged in various structures. For example, 347
MRG can be structured with annual minimum revenue thresholds as 70%，80%, etc. of forecasted 348
revenue. The borrowing capacity and indicators of government financial exposures with each 349
support structure can be calculated, and plotted in this coordinate system. A rough outline of the 350
results of potential structures for a certain fiscal support mechanism is shown in Figure 3. The 351
arrangements that increase borrowing capacity are compared with a “base case,” of complete 352
transfer of revenue risk to the concessionaire. This is constrained by the maximum acceptable 353
leverage ratio, and the public budget resilience within a given confidence interval (public VaR) as 354
additional feasible option frontiers for each fiscal support mechanism. The fiscal support 355
mechanism with a feasible option frontier on the top right dominates one with a feasible frontier 356
on the bottom left. As illustrated in Figure 3, fiscal support Mechanism 2 is a better choice than 357
Mechanism 1, given the constraints. 358
Borrowing
Capacity
Government Exposure
at Risk (5%)
Base Case Borrowing Capacity
Government Budget
Feasible
Options
Mechanism 1
Mechanism 2Maximum Debt Amount Allowed
IncomeExpenditure
359
Figure 3. A rough outline of the rationale for choosing among potential options 360
5. Stochastic Modeling 361
In this section, a stochastic model is built for revenue risk, and calculate borrowing capacities and 362
government financial exposures at risk with various fiscal support alternatives based on the 363
stochastic model. 364
5.1. Stochastic projection model of revenue 365
For a typical toll road concession, toll rates are adjusted annually according to a fixed schedule, 366
except for High Occupancy Toll (HOT) lanes or roads with dynamically priced tolls. A simplified 367
model is introduced for a toll road, by assuming project revenue equals to traffic multiplied by unit 368
price: 369
𝑅𝑡 = 𝑃𝑡 ∗ 𝐴𝐴𝐷𝑇𝑡 ∗ 365 (4) 370
𝑅𝑡 is the project revenue of Year t (the count starts from the beginning of the operation period); 371
𝑃𝑡 stands for the unit price predetermined in the concession agreement, and 𝐴𝐴𝐷𝑇𝑡 represents 372
the annual average daily traffic. 373
A traffic forecast for a project is developed through a Project Feasibility Study or Traffic and 374
Revenue Study. Generally, concessionaires develop their own, internal studies of potential traffic, 375
but at financial close a final traffic study is developed and often publically released by the 376
procuring agency, with lenders or bond underwriters using a conservative probable outcome from 377
that study (or their own study) to size project debt if the concession is taking some revenue risk. 378
Sponsor’s Traffic Forecast: 379
𝐴𝐴𝐷𝑇(𝑡+1)_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 = 𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 ∗ 𝑒𝛼𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 (5) 380
Pessimistic Traffic Forecast: 381
𝐴𝐴𝐷𝑇(𝑡+1)_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 = 𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 ∗ 𝑒𝛼𝑡_𝑝𝑒𝑠 (6) 382
𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 ≤ 𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 (7) 383
α𝑡- Annual traffic growth rate for Year t (in operation period). 384
A stochastic projection model is used to reflect the unknowns by adding a random time series to 385
the traditional forecast. A common assumption adopted in relevant research is that traffic follows a 386
GBM (Geometric Brownian Motion), which is a stochastic process following a Brownian Motion 387
(think about the physical phenomenon of random motion of particles suspended in a fluid) with 388
drift. It is widely used to model stock prices, and recently has been introduced to model toll road 389
traffic volumes and revenues. The drift term in GBM model could represent the traditional traffic 390
forecast based on available information, while the Brownian Motion term represents the influence 391
of unknown factors. Galera and Soliño (2010) adopt a Dickey-Fuller approach to test the GBM 392
hypothesis for highway traffic with historical traffic data of 11 highway projects and the results of 393
that study affirm their GBM hypothesis. Therefore, the model utilizes the assumption that traffic 394
follows GBM. 395
𝐴𝐴𝐷𝑇𝑡+1 = 𝐴𝐴𝐷𝑇𝑡 ∗ 𝑒(𝛼𝑡−
𝜎2
2)𝛥𝑡+𝜎ɛ√𝛥𝑡
, 𝑡 ≥ 1 (8) 396
σ stands for traffic volatility, and ε~N(0,1) is a standard Wiener process which is a 397
mathematical model commonly used to describe a Brownian Motion. 398
Also, the actual initial traffic in the first year is assumed to follow a triangular probability 399
distribution defined by the forecast of lowest, most-likely, and highest traffic for the first year (see 400
Equation 9), following Brandao and Saraiva (2008), Ashuri, Kashani et al. (2011). 401
𝑓(𝐴𝐴𝐷𝑇1|(𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡 , 𝐴𝐴𝐷𝑇1_𝑚𝑜𝑠𝑡 𝑙𝑖𝑘𝑒𝑙𝑦 , 𝐴𝐴𝐷𝑇1_ℎ𝑖𝑔ℎ𝑒𝑠𝑡)
=
{
2(𝐴𝐴𝐷𝑇1 − 𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡)
(𝐴𝐴𝐷𝑇1_𝑚𝑜𝑠𝑡 𝑙𝑖𝑘𝑒𝑙𝑦 − 𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡)(𝐴𝐴𝐷𝑇1_ℎ𝑖𝑔ℎ𝑒𝑠𝑡 − 𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡)
𝑓𝑜𝑟 𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡 ≤ 𝐴𝐴𝐷𝑇1 ≤ 𝐴𝐴𝐷𝑇1_𝑚𝑜𝑠𝑡 𝑙𝑖𝑘𝑒𝑙𝑦
2(𝐴𝐴𝐷𝑇1_ℎ𝑖𝑔ℎ𝑒𝑠𝑡 − 𝐴𝐴𝐷𝑇1)
(𝐴𝐴𝐷𝑇1_ℎ𝑖𝑔ℎ𝑒𝑠𝑡 − 𝐴𝐴𝐷𝑇1_𝑙𝑜𝑤𝑒𝑠𝑡)(𝐴𝐴𝐷𝑇1_ℎ𝑖𝑔ℎ𝑒𝑠𝑡 − 𝐴𝐴𝐷𝑇1_𝑚𝑜𝑠𝑡 𝑙𝑖𝑘𝑒𝑙𝑦)
𝑓𝑜𝑟 𝐴𝐴𝐷𝑇1_𝑚𝑜𝑠𝑡 𝑙𝑖𝑘𝑒𝑙𝑦 ≤ 𝐴𝐴𝐷𝑇1 < 𝐴𝐴𝐷𝑇1_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑜𝑝𝑡
(9)
5.2. Modeling borrowing capacity and public VaR under various supports 402
Three revenue risk sharing mechanisms are looked in this paper：(1) availability payment with 403
equal annual payment, (2) flexible term concession with LPVNR and maximum term limitation, 404
and (3) minimum revenue guarantee with excess revenue sharing. A base case is adopted as a 405
baseline for comparison. 406
5.2.1. Base case toll road without any credit enhancement 407
A base case without any credit enhancement is established in order to clarify the relative change 408
brought by government financial support. Generally, lenders will adopt both a conservative 409
probability for the forecast and a high debt coverage ratio to calculate a project’s borrowing 410
capacity if there is no credit enhancement. 411
𝐶𝐹𝐴𝐷𝑆𝑡 = 𝑅𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠 − 𝑂&𝑀𝑡 = 𝑃𝑡 ∗ 𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠 ∗ 365 − 𝑂&𝑀𝑡 (10) 412
𝑃𝑉(𝐶𝐹𝐴𝐷𝑆𝑡) = ∑𝐶𝐹𝐴𝐷𝑆𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1 (11) 413
𝐵𝐶𝑏𝑎𝑠𝑒 𝑐𝑎𝑠𝑒 =𝑃𝑉(𝐶𝐹𝐴𝐷𝑆𝑡)
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘=
∑𝑃𝑡∗𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠∗365−𝑂&𝑀𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘 (12) 414
𝑇𝐶 is the construction period, and 𝑇𝑑 is the average loan life. 𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘 is the market loan life 415
coverage ratio that lenders set for a project taking revenue risk. 416
In this case, the government has no financial exposure: 417
𝑃𝑉(𝐶𝐹𝑔)𝑏𝑎𝑠𝑒 𝑐𝑎𝑠𝑒= 0 (13) 418
𝑃𝑉(𝐶𝐹𝑔) is the present value of government cash inflow; a negative value denotes cash outflow. 419
5.2.2. Availability payment 420
Under an AP structure, the government retains all the revenue risk, and lenders will use the 421
amount of annual payment 𝐴𝑃(𝑡)1 and the relatively low coverage ratio 𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 to 422
calculate borrowing capacity. 423
𝐶𝐹𝐴𝐷𝑆𝑡 = 𝐴𝑃(𝑡) − 𝑂&𝑀𝑡 (14) 424
𝐵𝐶𝐴𝑃 =𝑃𝑉(𝐶𝐹𝐴𝐷𝑆𝑡)
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑=
∑𝐴𝑃(𝑡)−𝑂&𝑀𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 (15) 425
For the proposed model, it is assumed that the project is still toll funded but that those toll 426
revenues are collected by the government. Government cash flows consist of availability payment 427
cash outflows and toll revenue inflows. The model accounts for the fact that project toll revenue is 428
often not a completely independent variable, and is impacted by the owner of project revenue risk. 429
When all revenue risk is allocated to the government, toll revenue collected may be less than the 430
amount collected by a private concessionaire, due to incentive issues and varying public sector 431
objectives (e.g. affordability). Also, some toll revenue may be diverted to general funds rather than 432
the project itself. To account for this, a coefficient parameter 𝛽 (0 ≤ 𝛽 ≤ 1) is introduced to 433
represent these factors. Equation 16 presents the present value of government cash flows with AP 434
procurement, where 𝑟𝐺 is the capital cost of government and 𝑇𝑂 is the operation period. 435
𝑃𝑉(𝐶𝐹𝑔) = ∑𝐶𝐹𝑔(𝑡)+𝛽∗𝑅𝑡
(1+𝑟𝐺)𝑡+𝑇𝐶
𝑇𝑂𝑡=1 = ∑
−𝐴𝑃(𝑡)+𝛽∗𝑅𝑡
(1+𝑟𝐺)𝑡+𝑇𝐶
𝑇𝑂𝑡=1 (16) 436
5.2.3. Flexible term concession with LPVNR and maximum term limitation 437
Flexible term procurements introduce an additional uncertainty from the perspective of project 438
lenders, in that when revenues are much higher than expected, the concession duration actually 439
shortens, thus exposing lenders to prepayment risk. This can be mitigated for projects with bank 440
loan financing in the terms of the loan, but nevertheless a flexible term procurement should not 441
reduce default risk for project lenders in a downside scenario. This mechanism usually does not 442
change the cash flow over the loan life, therefore it should not have significant influence on 443
borrowing capacity. 444
1 We don’t consider performance deduction here for simplification. A reason behind this is the fact that the income
received by the concessionaire is expected to decrease with poor performance, no matter which procurement
mechanism is adopted.
𝐵𝐶𝑓𝑙𝑒𝑥𝑖𝑏𝑙𝑒 𝑡𝑒𝑟𝑚 = 𝐵𝐶𝑏𝑎𝑠𝑒 𝑐𝑎𝑠𝑒 =∑
𝑃𝑡∗𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠∗365−𝑂&𝑀𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘 (17) 445
This mechanism helps to reduce the uncertainty of the equity holder’s rate of return and 446
potentially to increase competition, but at the same time creates public VaR primarily via 447
termination compensation or lost revenue at the tail end of a concession, when the asset would 448
otherwise transfer to public ownership. Government contingent liabilities under this mechanism 449
occur at the end of the maximum concession term (Tmax, excluding construction period) with the 450
amount of the shortfall of the actual PVNR (present value of net revenue) compared with the 451
target LPVNR (see Equation 18, where WACC is the weighted average cost of capital for the 452
project special purpose vehicle). 453
𝑃𝑉(𝐶𝐹𝑔)𝑓𝑙𝑒𝑥𝑖𝑏𝑙𝑒 𝑡𝑒𝑟𝑚= 𝑚𝑖𝑛 {0, [PVNR(𝑇𝑚𝑎𝑥) − 𝐿𝑃𝑉𝑁𝑅] ∗（
1+𝑊𝐴𝐶𝐶
1+𝑟𝐺)𝑇𝑚𝑎𝑥+𝑇𝐶} (18) 454
PVNR(𝑇𝑚𝑎𝑥) = ∑𝑃𝑡∗𝐴𝐴𝐷𝑇𝑡∗365−𝑂&𝑀𝑡
(1+𝑊𝐴𝐶𝐶)𝑡+𝑇𝐶
𝑇𝑚𝑎𝑥𝑡=1 (19) 455
5.2.4. Minimum revenue guarantee together with excess revenue sharing 456
The relationship between the effective revenue received by the concessionaire 𝑅(𝑡) , the 457
government’s cash flow 𝐶𝐹𝑔(𝑡), and the actual project revenue 𝑅𝑡 under an MRG and ERS 458
procurement is illustrated in Equation 20 and 21, as well as Figure 4 and Figure 52. 𝑅𝑚𝑖𝑛_𝑡 and 459
𝑅𝑚𝑎𝑥_𝑡 are minimum and maximum revenue thresholds for each year as negotiated between the 460
public and private parties. 461
𝑅(𝑡) = 𝑚𝑖𝑛[𝑚𝑎𝑥 (𝑅𝑡, 𝑅𝑚𝑖𝑛_𝑡), 𝑅𝑚𝑎𝑥_𝑡] (20) 462
𝐶𝐹𝑔(𝑡) = 𝑅𝑡 − 𝑅(𝑡) = 𝑅𝑡 − 𝑚𝑖𝑛[𝑚𝑎𝑥 (𝑅𝑡, 𝑅𝑚𝑖𝑛_𝑡), 𝑅𝑚𝑎𝑥_𝑡] (21) 463
2 A full compensation MRG is more effective than partial compensation in attracting debt financing, because
robust cash flows are lenders’ major concern. However, partial revenue sharing is more efficient than a revenue cap
because the former is better in maintaining the incentive of the concessionaire to make efforts aimed at improving
service. Since debt sizing and government financial at risk are determined by downside cases, the structure of
revenue sharing won’t significantly change the result. Therefore, here we assume a full-compensation MRG and a
revenue cap for simplicity.
Rt
Project’s actual revenue
R(t)
Concessionaire's
effective revenue
Rmin_t
O
Rmin_t
Rmax_t
Rmax_t
464 Figure 4. Concessionaire’s effective revenue with MRG and excess revenue sharing 465
Rt Project’s actual revenue
CFg(t) Government’s
Cash Flow
ORmin_t
-Rmin_t
Rmax_t
466
Figure 5. Government’s cash flow with MRG and excess revenue sharing 467
Generally, lenders will use the guaranteed level of revenue and a relatively low coverage ratio 468
(𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑) to calculate the borrowing capacity of a project with MRG (Equation 22 and 23). 469
Equation 24 presents the present value of government contingent expenditures. 470
𝐶𝐹𝐴𝐷𝑆𝑡 = 𝑅𝑚𝑖𝑛 _𝑡 − 𝑂&𝑀𝑡 (22) 471
𝐵𝐶𝑀𝑅𝐺 =𝑃𝑉(𝐶𝐹𝐴𝐷𝑆𝑡)
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑=
∑𝑅𝑚𝑖𝑛 _𝑡−𝑂&𝑀𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 (23) 472
𝑃𝑉(𝐶𝐹𝑔)𝑀𝑅𝐺= ∑
𝑅𝑡− 𝑚𝑖𝑛[𝑚𝑎𝑥 (𝑅𝑡,𝑅𝑚𝑖𝑛_𝑡),𝑅𝑚𝑎𝑥_𝑡]
(1+𝑟𝐺)𝑡+𝑇𝐶
𝑇𝑂𝑡=1 (24) 473
5.3. Summary 474
The project borrowing capacity and present value of government cash flows incurred by each 475
fiscal support mechanisms are summarized in Table 1. 476
Table 1. Borrowing capacity and government financial exposure of various fiscal supports 477
Fiscal Support Borrowing Capacity Government Financial Exposure
Base case
no credit
enhancement
∑𝑅𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠 −𝑂&𝑀𝑡
(1 + 𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘
0
Availability
Payment
∑𝐴𝑃(𝑡) − 𝑂&𝑀𝑡
(1 + 𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 ∑
−𝐴𝑃(𝑡) + 𝛽 ∗ 𝑅𝑡(1 + 𝑟𝐺)
𝑡+𝑇𝐶
𝑇𝑂
𝑡=1
Flexible term with
LPVNR and
maximum term
∑𝑅𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠 −𝑂&𝑀𝑡
(1 + 𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘
𝑚𝑖𝑛 {0, [PVNR(𝑇𝑚𝑎𝑥) − 𝐿𝑃𝑉𝑁𝑅] ∗（1 +𝑊𝐴𝐶𝐶
1 + 𝑟𝐺)𝑇𝑚𝑎𝑥+𝑇𝐶}
MRG with ERS ∑
𝑅𝑚𝑖𝑛 _𝑡 − 𝑂&𝑀𝑡
(1 + 𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑔𝑢𝑎𝑟𝑎𝑛𝑡𝑒𝑒𝑑 ∑
𝑅𝑡 − 𝑚𝑖𝑛[𝑚𝑎𝑥 (𝑅𝑡, 𝑅𝑚𝑖𝑛_𝑡), 𝑅𝑚𝑎𝑥_𝑡]
(1 + 𝑟𝐺)𝑡+𝑇𝐶
𝑇𝑂
𝑡=1
It should be noted that all of the inputs for this framework are based on information available to 478
the government, and are naturally uncertain due to the nature of early stage project planning, as 479
well as the information asymmetry among the involved parties. However, the comparison is still 480
helpful during early stage project planning in enabling the government to evaluate various support 481
mechanisms for sharing in revenue risk and for creating a procurement structure designed around 482
public priorities at the outset. 483
6. Numerical Case Study 484
A case study of a hypothetical toll funded highway concession is adopted to illustrate the 485
application of the proposed framework. The concession includes a two-year construction phase and 486
a 35-year operation phase. The basic project information is described in Table 2. The interest rate 487
and growth rates of toll price and O&M cost are presented in nominal values. 488
Table 2. Project Information 489
Capital Variables
Capital Investment $110,000,000
Government’s Capital Cost rG 3%
Average Interest Rate rd 5%
Average Loan Life 25 years
LLCRguaranteed 1.2
LLCRrisk 1.5
Operating Variables
Initial Traffic Volume AADT1 (most likely) 25,000
Downside and Upside Range of AADT1 ±30% of 25,000
Continuous Annual Traffic Growth Rate αt (year 1-10) 6%
Continuous Annual Traffic Growth Rate αt (year 11-20) 3.5%
Continuous Annual Traffic Growth Rate αt (year 21-35) 2%
Initial Toll Rate $1.3
Annual Toll Growth Rate (year 1-5) 5%
Annual Toll Growth Rate (year 6-10) 3%
Annual Toll Growth Rate (year 11-35) 2%
Initial O&M Cost $6,500,000
Annual O&M Cost Growth Rate 3%
6.1. Structuring of fiscal support mechanisms 490
According to the formulas in Table 1, the borrowing capacity for base case without any credit 491
enhancement is equal to ∑
𝑅𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠−𝑂&𝑀𝑡
(1+𝑟𝑑)𝑡+𝑇𝐶
𝑇𝑑𝑡=1
𝐿𝐿𝐶𝑅𝑟𝑖𝑠𝑘, where 𝑅𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑒𝑡_𝑝𝑒𝑠 = 𝑃𝑡 ∗ 𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 ∗ 365 , 492
𝐴𝐴𝐷𝑇𝑡_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 = 𝐴𝐴𝐷𝑇𝑡−1_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 ∗ 𝑒𝛼𝑡 , 𝐴𝐴𝐷𝑇1_𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡_𝑝𝑒𝑠 = 25,000 ∗ 0.7 = 17,500 , 𝑇𝑑 = 25 , 493
𝑇𝐶=2, therefore the borrowing capacity is around $50.3 million. The expected NPV for this project 494
is $8.5 million if the required return on equity (ROE) is 12%. Government has zero expenditure in 495
this case. 496
For each fiscal support mechanism, governments may, for various reasons, need to first identify 497
appropriate structures that are able to increase the project’s borrowing capacity and at the same time, 498
keep the project attractive to equity investors. For example, annual availability payments must 499
meet market requirements for ROEs. A trial-and-error method is taken to calculate the project’s 500
borrowing capacities and the ROEs with varying levels of annual payment and find that the ROE 501
equals to 6.4%, 12.0%, 18.3%, 41.4% when the annual payment is 16.5 million, 16.75 million, 502
17.0 million and 17.5 million. Similarly, LPVNRs for flexible term contracts should be larger than 503
zero, and the expected project PVNR without any credit enhancement is taken as the value of 504
LPVNR in the analysis to facilitate comparison. Under MRG, it is assumed that the revenue 505
support and excess revenue sharing thresholds “mirror” the expected revenue projected, as is 506
common in MRG procurements (Vassallo and Soliño 2006). In other words, if the lower threshold 507
is θ% of the forecasted revenue, then the upper threshold is (2-θ%) of the forecasted revenue. It is 508
assumed that the MRG only covers the loan life, while the ERS covers the whole operation phase. 509
In order to increase the project borrowing capacity compared to the base case but not to exceed the 510
capital cost, θ% should lie in the range of 65%-88%. When θ% equals 65%, the ROE has an 511
expected value larger than 12%, but it has a probability of 19% to be lower than 5%, which is the 512
interest rate for debt financing. As θ% increases, the concessionaire is able to achieve a higher 513
return on investment. 514
6.2. Simulation results 515
As toll price limitations are set by the prevailing contract, the principal source of revenue 516
uncertainty is the traffic volume in the first and subsequent years, which can be simulated, based on 517
downside and upside ranges of initial traffic volume and traffic volatility σ.3 Initial traffic range 518
AADT1_lowest and AADT1_highest are assumed to be ±30% of 25,000. Traffic volatility σ can be (1) 519
observed from historical traffic series (for existing roads), (2) estimated and computed from a 520
Monte Carlo simulation based on historical GDP data under the standard assumption that traffic 521
levels are positively correlated with GDP (Banister 2005) (Brandão, Dyer et al. 2005). For the 522
purpose of focusing on the application of the whole comparison framework, here σ is assumed to be 523
10%, following Almassi, McCabe et al. (2012) and Carbonara, Costantino et al. (2014). It is also 524
assumed that the revenue coefficient β is 1; in other words, the actual toll revenue collected is 525
independent of the owner of project revenue risk. Sensitivity analyses are also conducted on these 526
parameters to explore under what circumstances, which fiscal support mechanism would be the 527
most advantageous choice. 528
10,000 revenue streams are randomly generated that follow GBM, and the probability 529
3 This is a simplification assumed in the proposed planning model. In practice concessionaires may choose to lower
toll prices below the limits included in the concession agreement if they determine that a lower toll will maximize
revenue. The model assumes that tolls are set at the limits in the concession.
distributions of the present value of government cash flows under different fiscal support 530
mechanisms are calculated. The figures of expected value, 5% quantile of government 531
expenditures are listed in Table 3, where negative values stand for expenditures while positive 532
value stands for incomes. 533
Table 3. Borrowing Capacities and Government Financial Exposures with Fiscal Support Alternatives 534
Fiscal Support Borrowing
Capacity (million $)
Debt to Capital
Ratio
E(GE)
(million $)
P5(GE)
(million $)
Base Case 50.325 45.75% 0 0
Flexible term
LPVNR=8.5 million
50.325
45.75%
-7.577
-25.900
MRG with ERS
65%MRG+135%ERS 51.029 46.39% 31.269 -43.827
70%MRG+130%ERS 62.907 57.19% 32.766 -57.257
75%MRG+125%ERS 74.784 67.99% 34.026 -71.210
80%MRG+120%ERS 86.662 78.78% 35.046 -86.101
85%MRG+115%ERS 98.539 89.58% 35.864 -101.620
88%MRG+112%ERS 105.670 96.06% 36.302 -111.540
Availability Payment
AP=16.50 million 90.410 82.19% 200.420 -68.105
AP=16.75 million 93.350 84.86% 190.290 -73.168
AP=17.00 million 96.290 87.53% 180.160 -78.232
AP=17.50 million 102.160 92.87% 170.040 -88.358
The simulation results are put into the “Borrowing Capacity- VaR” comparison coordinate space 535
(See Figure 6), and some potential acceptable levels of risk for a procuring agency are added for 536
illustrative purposes. This demonstrates that the acceptable risk level for the procuring agency may 537
guide them in determining which fiscal support is best for a given project. The results illustrate 538
that (1) the flexible term contract is unable to increase project’s borrowing capacity; (2) AP can 539
raise more debt financing than MRG with the same VaR of government expenditure; (3) however, 540
if the government has a tight budget constraint, AP may turn out to be unaffordable; and (4) MRG 541
is the better choice if flexibility in revenue risk allocation is preferred – MRG can be structured 542
with a low guaranteed level of revenue and a high upside threshold that gives the concessionaire a 543
chance to capture a large part of the excess revenue opportunity. 544
545 Figure 6. Borrowing Capacity- 5% VaR Comparison Framework 546
6.3. Sensitivity analysis and discussions 547
Sensitivity analysis on traffic volatility σ illustrates that, AP procurement tends to be a more 548
advantageous choice than MRG for government when the volatility σ reduces, for example, 549
σ=0.05 (see Figure 7); vice versa, for example, when σ=0.15, MRG dominates AP (see Figure 8). 550
The same results are generated when the possible range of AADT1 changes. However, when the 551
revenue uncertainty is very small, i.e. an extreme case where there is effectively no revenue 552
uncertainty, government supports in either the form of MRG or AP may be unnecessary since a 553
concession without any credit enhancement is attractive enough to lenders and equity investors. 554
555 Figure 7. Sensitivity Analysis: σ=0.05 556
557 Figure 8. Sensitivity Analysis: σ=0.15 558
As the expected return on investment for a project decreases, the feasible choices of MRG 559
structures decrease and the added flexibility of MRG is less advantageous. For example, when the 560
capital investment of this project increases to 140 million while project revenues are unchanged, 561
an MRG with a downside threshold equals 65% of the forecasted revenue will offer equity 562
investors an ROE that has an expected value of 8.5%, with a probability of 28% to be lower than 563
5%, and a probability of 41% to be lower than 7%, which is very likely not attractive to equity 564
investors. When θ% increases to 85%, the expected value of ROE increases to 12% and the 565
probability that ROE falls below 5% decreases to 15%, which is similar to the ROE distribution 566
with a 65% MRG under the original project conditions. MRGs with thresholds higher than 85% 567
are dominated by feasible AP arrangements, see Figure 9. 568
569 Figure 9. Sensitivity Analysis: I=140 million 570
Based on the sensitivity analysis and discussions, it is observed that the mean value of return on 571
investment, and the extent of revenue uncertainty may influence the optimal choice among the 572
alternative revenue risk sharing mechanisms. More specifically, if a project has an attractive return 573
on investment (a high mean revenue projection relative to its capital costs) and the revenue 574
uncertainty is very small, then a concession without any fiscal support is the best choice. If a 575
project has a high level of projected revenue volatility, MRG is more applicable. Finally, if a 576
project has a low expected return on investment (or has no viable toll revenue sources), AP is the 577
best choice if the revenue uncertainty is not very large. Figure 10 presents the fiscal support 578
mechanisms within a decision support matrix. 579
Return on Investment/ Revenue Projection Relative to Capital Cost
Revenue
Volatility
Low High
High
Low
MRG
AP Base Case
580 Figure 10. Decision Matrix 581
Our model can also account for varying toll collection incentives created by these fiscal support 582
mechanisms. This accounts for the assumption that toll revenues collected may be lower under an 583
AP procurement, in which revenue risk is held by the government, than MRG or another structure 584
in which some or all of it is allocated to the concessionaire. These are accounted for by using a β 585
coefficient less than 1 in calculating the retained risk under an AP structure. For example, if β 586
equals to 0.8, AP will be dominated by MRG, see Figure 11. 587
588 Figure 11. Sensitivity Analysis: β=0.8 million 589
7. Conclusions, Limitations and Future Research 590
This research identifies the borrowing capacity of a project as a measurable indicator of the 591
marginal benefit provided by each government fiscal support mechanism to mitigate revenue risk, 592
and the “value at risk” retained by the government sponsor as an indicator of the cost of such a 593
fiscal support. These two indicators constitute a two dimensional framework to support 594
government sponsors in evaluating and selecting fiscal support alternatives at an early stage of 595
project planning. 596
The proposed model as designed does shed light on the applicability of one support mechanism in 597
particular – the flexible term concession. As described above, under the model the flexible term 598
procurement does little to increase project leverage, and hence reduce the cost of financing. While 599
the mechanism may reduce financing costs by increasing competition under particular global 600
infrastructure market conditions, it is unlikely that this particular support mechanism will be 601
effective in a developed, federal procurement market like the United States. 602
From the numerical case study, conclusions can be drawn regarding the applicability of two 603
additional support mechanisms (MRG/ERS and AP) based on project circumstances. Specifically, 604
it is found that MRG/ERS support mechanisms to be more flexible in sharing revenue risk 605
between a public sponsor and the private concessionaire for projects with a higher expected return 606
but significant volatility. AP is more applicable to projects that are projected to have a lower mean 607
revenue relative to their capital investment and lower volatility (or, of course, that will have no toll 608
revenue sources). 609
While this model is designed for an individual project, the outcomes (regarding the expected value 610
and volatility of government expenditure) from this framework can contribute to a more 611
comprehensive approach to fiscal portfolio management, and can thus improve fiscal deficit risk 612
management. The framework is also useful as a way to clarify and organize concepts qualitatively 613
in order to consider the value and cost of alternative fiscal supports for governments to share 614
revenue risk with PPP concessionaires. Future publications planned under this research initiative 615
include applying the proposed model to other revenue risk sharing mechanisms in practice, such as 616
limited credit enhancement supports. 617
It should be noted that, for federal procurement markets like the United States, this model does not 618
address federal support mechanisms to mitigate revenue risk, such as the Transportation 619
Infrastructure Finance and Innovation Act (TIFIA) federal loan program. Federal loan and grant 620
programs that assume revenue risk can assist local procuring governments in mitigating that risk. 621
However, this model is specifically focused on the risk assumed by either the local government 622
agency procuring the asset or the concessionaire, and how those procuring governments evaluate 623
mechanisms for sharing that risk with concessionaires. It goes without saying that project sponsors 624
should pursue federal or other support programs to mitigate revenue risk for a given project 625
whenever these are available. 626
Structuring and optimizing each form of fiscal support, as well as improving the accuracy of the 627
inputs, are beyond the scope of this research. Although some relevant literature exists, these topics 628
remain a promising research opportunity. Also the framework suggested in this paper only 629
accounts for the cost of financing and public VaR in evaluating support mechanisms. There are 630
many other factors that can and should influence the allocation of revenue risk for a project. These 631
include market conditions that require one mechanism or another to generate enhanced levels of 632
competition for a procurement, which is less easily measurable. Social welfare priorities may also 633
be a relevant factor. Finally, and perhaps most importantly, the allocation of revenue risk also 634
drives incentives for bidding concessionaires to design, build, and operate a project to maximize 635
traffic demand to mitigate that risk. This is a critical factor that cannot be accounted for in the 636
quantitative evaluation framework. Deep-dive, empirical research on a set of operating toll road 637
concessions with different revenue risk sharing mechanisms is needed to assess the strength of this 638
effect. 639
Finally, as Kim and Ryan (2015) asserted, it is important to stress the importance of developing 640
precise analytical tools for evaluating fiscal supports to PPPs. Fiscal supports are a good way to 641
leverage private investment, but using them requires a clear understanding of the problems and 642
risks retained by the public. As is often the case, the devil is in the details. Adding an explicit 643
marginal benefit/risk analysis of alternative mechanisms to allocate or share revenue risk is a step 644
in the right direction in developing a project portfolio that includes both PPPs and traditionally 645
procured assets. 646
Acknowledgements 647
The author/s gratefully acknowledge the support for this research provided by the National 648
Science Foundation Grant # 1334292, the Stanford Global Projects Center, and the National 649
Natural Science Foundation of China # 71572089. All conclusions and opinions expressed in this 650
paper are those of the author/s and not of the National Science Foundation or the Global Projects 651
Center. 652
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