Proceedings of the 2019 World Transport Convention Beijing, China, June 13-16, 2019

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Concession period adjustment to cope with uncertainties in public-private

partnerships

Hongyu Jin Deakin University, School of Architecture and Built Environment

1 Gheringhap Street, Geelong, Victoria 3220, Australia jinho@deakin.edu.au

Shijing Liu

Deakin University, School of Architecture and Built Environment 1 Gheringhap Street, Geelong, Victoria 3220, Australia

shijing@deakin.edu.au

Chunlu Liu Deakin University, School of Architecture and Built Environment

1 Gheringhap Street, Geelong, Victoria 3220, Australia chunlu.liu@deakin.edu.au

ABSTRACT

Public-private partnerships (PPPs) have been widely used in delivering infrastructure projects. One of the most important parameters in PPP projects is the concession period that is normally predetermined by governments. However, to cope with uncertainties of project surroundings, the contractual terms should be flexible, which allows project parties adjust concession period at the post-contractual stage. Adjustment of the length of the concession period should consider not only the profits of project parties, but also the influence of the length of the concession period in risk control, which has not been studied by previous research. This paper develops a concession period adjustment method based on expanded net present value analysis, as well as the stochastic analysis of the uncertain project parameters. The project risk for project parties is expected to be controlled via concession period adjustment. Referring to a real toll road project in Australia, a numerical example is used to validate the model proposed in this research. The adjustment outcome shows that the concession period is extended by 3.2 years if the adjustment occurs at the fifth operational year, which implies that at the point of the fifth operational year, the private investors need to require for extending concession period to control the risk of suffering loss in a downturn market surrounding. The adjustment process proposed in this paper demonstrates the strong effectiveness and ability to adjust the length of the concession period at the post-contractual stage of a PPP project.

KEYWORDS：concession period adjustment; risk control; public-private partnerships; real option;

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1 INTRODUCTION

Public-private partnerships (PPPs) have been recognised as “a long-term contractual arrangement between the public and the private investors to realize public infrastructure and services more cost effectively and efficiently than under conventional procurement” (Daube et al. 2008). In the past decade, PPPs have gained popularity in delivering infrastructure projects since it is capable of alleviating government financial pressure and the role of PPP procurement in preventing cost overruns has been approved (Raisbeck et al. 2010). However, the application of PPP is not without trouble. Scholars doing research on PPP-related topics highlight the following issues. First, the market risks during the operational period need to be handled and Shan et al. (2010) have tried to control the revenue risk of the PPP project via real option design. Second, the importance of mobilising social capital participation is emphasised (Liu et al. 2016). Third, if the project market is downward or there is force majeure, the way to facilitate social capital exit while minimising the influence on governments is still an open question (Nuer 2015). Some studies have found that all these problems can be tackled through contractual term design on concession agreements, e.g. concession price, concession period and if needed, minimum revenue guarantee (Brandao and Saraiva 2008; Carbonara et al. 2014; Wang and Liu 2015).

Concession agreements are generally predetermined by governments before the bidding stage, which cannot adequately cope with uncertainties embodied in the market surroundings. Therefore, there are more and more research studies focusing on the application of flexible contracts on PPP projects. Cruz and Marques (2013) proposed a double entry matrix as a new model for contract flexibility. Liou and Huang (2008) also indicated that the concession terms towards tariff and concession period should be adjustable to achieve risk control. Nevertheless, for the type of user-paid PPPs, the decision on the tariff is usually a commercial one. Since with the increase of the price, the number of users may decrease, a stochastic price will make the prediction of the project profits even tougher. In practice, the tariff for a user-paid project can be pre-determined by governments according to the historical data gathered from similar projects or the outcome of the public hearing which gives information about the affordability of public users (Ng et al. 2007). This paper focuses on the post-contractual adjustment methodology for the concession period. The concession period as one of the most critical project parameters is usually set as a default that is the same length as in similar projects (Song et al. 2015) or decided just based on the experts’ experience (Khanzadi et al. 2012). However, these practices tend to encourage project early termination, since they neglect the fact that market surroundings can be significantly different in different projects, which implies that the concession period may need to be adjusted after signing concession agreements. This research aims to find a method that can facilitate the post-contractual adjustment of the concession period considering conditions of the market environment. The aim in adjusting the concession period is to achieve risk control for project parties and ensure that private investors can gain their expected investment return.

The longer the concession period, the higher the possibility that governments and private investors can achieve the expected return on investment. Net present value (NPV) estimation is usually used as a method to measure the profits for governments and private investors with the given concession period. For example, Hanaoka and Palapus (2012) calculated the profits of project parties for two build-operate-transfer road projects via NPV analysis, based on which concession periods were designed. However, NPV analysis neglects the value of real options in the project. Previous studies have shown that the value of real options is too enormous to neglect when making investment decisions (Garvin and Cheah 2004; Yeo and Qiu 2003). This research reviews the capital existence opportunity as an abandonment option to reflect the value of the project more accurately. Even though some research works justified the

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application of the flexible contract in BOT or PPP projects (e.g. Demirel et al. 2017), there is still a limited number of studies proposing methods in contractual terms adjustment for PPP projects, none of which considers adjusting the length of the concession period to control project risks at the post-contractual stage. This study fills the gap by proposing an adjustment method of the concession period, which gives the significance of the flexible concession period in project risk control.

2 RESEARCH BACKGROUND

2.1 NPV-based Concession Period Design

NPV analysis requires figuring out the amounts of the cash inflow and cash outflow of a project during the project lifecycle. Typical project milestones for a PPP project are shown in Figure 1, where 𝑡𝑡𝑐𝑐 indicates the instant of time when the construction stage starts. 𝑡𝑡𝑐𝑐𝑐𝑐 and 𝑡𝑡𝑐𝑐𝑐𝑐 are the instants of time when the concession period starts and ends, and 𝑛𝑛 is the end year of the project. For a PPP project, the cash outflow covers the construction cost, the operation and maintenance cost, and other implicit costs, like negotiation costs. The estimated construction cost can be paid as a lump-sum investment at the beginning of the construction stage or pay separately according to the building process. The operation and maintenance fee is usually paid annually to maintain the operation of the project. Private investors start to receive cash inflow when the project opens to the public. Overall, the NPV for private investors and governments can be calculated by:

𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑐𝑐𝑐𝑐) = ∑ (𝑅𝑅𝑡𝑡 − 𝑂𝑂&𝑀𝑀𝑡𝑡) (1 + 𝑟𝑟)𝑡𝑡⁄𝑡𝑡𝑐𝑐𝑐𝑐𝑡𝑡=𝑡𝑡𝑐𝑐𝑐𝑐 − 𝐼𝐼𝑝𝑝𝑝𝑝 (1)

𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑐𝑐𝑐𝑐) = ∑ (𝑅𝑅𝑡𝑡 − 𝑂𝑂&𝑀𝑀𝑡𝑡) (1 + 𝑟𝑟)𝑡𝑡 − 𝐼𝐼𝑔𝑔⁄𝑛𝑛𝑡𝑡=𝑡𝑡𝑐𝑐𝑐𝑐 (2)

where 𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑐𝑐𝑐𝑐) and 𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑐𝑐𝑐𝑐) indicate the function value of NPV for private investors and governments respectively with the value of the independent variable 𝑡𝑡𝑐𝑐𝑐𝑐 . 𝑅𝑅𝑡𝑡 is the gross income from operating the project at year 𝑡𝑡 . 𝑂𝑂&𝑀𝑀𝑡𝑡 is the operation and maintenance cost at year 𝑡𝑡 . 𝐼𝐼𝑝𝑝𝑝𝑝 and 𝐼𝐼𝑔𝑔 indicate the present value of the initial investment sharing for private investors and governments respectively. 𝑟𝑟 demonstrates the discount rate, which is usually calculated by the capital asset pricing model or defined by the weighted average cost of capital. However, Brealey et al. (2012) stated that the risk-free discount rate should be used in a Monte Carlo simulation since market risks have already been taken into consideration through assigning the probability distribution of the uncertain variables.

Figure 1: Typical Project Milestones for A PPP Project

At pre-contractual stage, governments usually calculate the value of 𝑡𝑡𝑐𝑐𝑐𝑐 based on NPV estimation

and put the calculated concession period into Terms of References before tendering invitation where private investors have no control over the length. Afterwards, private investors predict their profit at the biding stage based on the predetermined concession period and if and only if 𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑐𝑐𝑐𝑐) ≥𝐼𝐼𝑝𝑝𝑝𝑝 × 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑝𝑝𝑛𝑛, where 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑝𝑝𝑛𝑛 is the value of the minimal return rate on investment, private investors will consider investing the project.

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Due to the uncertainties of market surroundings, the governments or private investors may require adjusting the length of the concession period. Project milestones for a PPP project with an adjustable concession period are demonstrated in Figure 2, where 𝑡𝑡𝑎𝑎𝑎𝑎 means the instant of time when the adjustment on concession period is initiated, and 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 is the instant of time when the concession period ends after adjustment. At each time when the concession period is adjusted, both governments and private investors evaluate their profits based on:

𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝1 (𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) + 𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝2 − 𝐼𝐼𝑝𝑝𝑝𝑝

= ∑ (𝑅𝑅𝑡𝑡 − 𝑂𝑂&𝑀𝑀𝑡𝑡) (1 + 𝑟𝑟)𝑡𝑡⁄𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑡𝑡=𝑡𝑡𝑎𝑎𝑎𝑎 +∑ (𝑅𝑅𝑡𝑡 − 𝑂𝑂&𝑀𝑀𝑡𝑡) (1 + 𝑟𝑟)𝑡𝑡⁄𝑡𝑡𝑎𝑎𝑎𝑎

𝑡𝑡=𝑡𝑡𝑐𝑐𝑐𝑐 − 𝐼𝐼𝑝𝑝𝑝𝑝 (3)

𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = ∑ (𝑅𝑅𝑡𝑡 − 𝑂𝑂&𝑀𝑀𝑡𝑡) (1 + 𝑟𝑟)𝑡𝑡 − 𝐼𝐼𝑔𝑔 ⁄𝑛𝑛𝑡𝑡=𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 (4)

where 𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) and 𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) indicate the function value of NPV for private investors and governments respectively with the value of the independent variable 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 . 𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝1 (𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) is the functional present value earned by private investors with the adjusted concession period. 𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝2 is the acquired incomes for private investors before the adjustment occurs. Based on the NPV analysis, both governments and private investors can figure out the length of the concession period that they need for achieving their profit goals.

Figure 2: Project Milestones for A PPP Project with An Open Contract on Concession Period

2.2 Uncertain Variable Prediction

The primary limitation of the traditional NPV analysis is the improper treatment of project uncertainties. When estimating project NPV, there are some uncertain variables, such as the number of project user, discount rate and so on, which can significantly influence the forecast value of profits. Compared with other procurement methods, PPP projects have long lifetimes, which means that PPP projects will experience market risks over a long period so the influence of uncertain variables on the value of the profits of PPP projects cannot be neglected. Therefore, before making investment decisions, project parties usually estimate their future annual cash inflows according to the forecast of uncertain variables. Monte Carlo simulation is often used as the method for predicting the value of uncertainty variables. By assigning the corresponding probability distribution to uncertain variables, the probability distribution of NPV for governments and private investors can be generated after multiple simulations. Specifically, the trend of change in project users is usually modelled as a stochastic process, and geometric Brownian motion (GBM) is the most commonly used model in predicting the value of the stochastic variable (Dixit and Pindyck 1994). The function of the GBM model, i.e. Eq. (5), is derived based on the assumption that the expected return from the market is constant (Hull 2010):

𝑑𝑑𝑑𝑑 = 𝜇𝜇𝑑𝑑𝑑𝑑𝑡𝑡 + 𝜎𝜎𝑑𝑑𝑑𝑑𝜎𝜎 (5)

where 𝑑𝑑𝑑𝑑 is the increment value of the uncertain variable at each step in a continuous process. 𝜇𝜇 is the expected growth rate of the uncertain variable during 𝑑𝑑𝑡𝑡. 𝑑𝑑 is the current value of the uncertain variable. 𝑑𝑑𝑡𝑡 indicates the time interval. 𝜎𝜎 is the volatility of the uncertain variable during 𝑑𝑑𝑡𝑡. 𝑑𝑑𝜎𝜎 follows a Wiener process.

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If the measured uncertain variable is discrete, Eq. (5) should transfer to the format of Eq. (6):

∆𝑑𝑑 = 𝜇𝜇𝑆𝑆𝑑𝑑∆𝑡𝑡 + 𝜎𝜎𝑐𝑐𝑑𝑑𝑆𝑆√∆𝑡𝑡 (6)

where ∆𝑑𝑑 is the increment value of the uncertain variable at each step in a discrete process. ∆𝑡𝑡 indicates the time interval. 𝜇𝜇𝑐𝑐 is the expected growth rate of the uncertain variable during ∆𝑡𝑡. 𝜎𝜎𝑐𝑐 is the volatility of the uncertain variable during ∆𝑡𝑡. 𝑆𝑆 follows a standardized normal distribution. 2.3 Real Options in PPP Projects

Even though uncertain variables can be measured through Monte Carlo simulation, the value of real options embodied in the project still cannot be uncovered in a traditional NPV analysis. Trigeorgis and Reuer (2017) approved this by stating that a fatal investment decision can be made based solely on traditional NPV analysis. Leviäkangas and Lähesmaa (2002) also argued that even though NPV analysis is combined with Monte Carlo simulation, the uncertainties in a transport infrastructure project cannot be fully reflected. The sum of NPV and real option value equals the value of expanded NPV (ENPV), which can reflect the value of a project’s flexibility (Smit and Trigeorgis 2012). Thus, to better reflect the flexible value of a project, the value of real options need to be calculated first.

There are several types of real options in PPP projects. The option to expand means that if the market surroundings are experiencing an upward trend and the project is carried out in stages, the value added could come from the expansion opportunities in the future (Cheah and Garvin 2009). The option to delay is produced when the project manager decides to delay the project to receive more market information, but sometimes the cost of delaying a project is also high (Kremljak et al. 2014). In most countries carrying out PPP projects, the exit mechanism for the project is specified in the contract documents and protected by the law of the land (Bulnina et al. 2015). Hence, the project operator holds the option to abandon, which means that if the market surroundings go into extremely unfavourable conditions, they could choose to quit and receive a certain amount of money in return.

There are two main real-options pricing models used for calculating the value of real options mentioned above. One is the binomial lattice model and the other one is the Black-Scholes pricing model. The binomial lattice model assumes that there are two directions for uncertain variables to move: upward or downward. If the variable moves up, the value in the next stage should be the initial value multiplied by the quotient (u) and otherwise, multiplied by the quotient (d), and the probability of moving up is expressed as (p), where 𝑢𝑢 = 𝑒𝑒𝜎𝜎′√∆𝑡𝑡,𝑑𝑑 = 𝑒𝑒−𝜎𝜎′√∆𝑡𝑡,𝑝𝑝 = (𝑒𝑒𝑟𝑟′∆𝑡𝑡 − 𝑑𝑑) (𝑢𝑢 − 𝑑𝑑)� (Hull 2010). 𝜎𝜎′ is the volatility of underlying assets. ∆𝑡𝑡 is the step interval. 𝑟𝑟′ is the risk-free rate. However, if the project has a long lifecycle or short step intervals, the calculation of the binomial lattice model becomes complicated and it is hard to display the tree chart with large branches. In this case, the Black-Scholes pricing model is more practical. Its pricing formulas are:

𝑐𝑐 = 𝑑𝑑0𝑁𝑁(𝑑𝑑1) −𝐾𝐾𝑒𝑒−𝑟𝑟𝑟𝑟𝑁𝑁(𝑑𝑑2) (7)

𝑝𝑝 = 𝐾𝐾𝑒𝑒−𝑟𝑟𝑟𝑟𝑁𝑁(𝑑𝑑2) − 𝑑𝑑0𝑁𝑁(−𝑑𝑑1) (8)

where 𝑑𝑑1 = {𝑙𝑙𝑛𝑛(𝑑𝑑0/𝐾𝐾) + [𝑟𝑟 + (𝜎𝜎′)2/2]𝑇𝑇} 𝜎𝜎√𝑇𝑇⁄ , 𝑑𝑑2 = 𝑑𝑑1 − 𝜎𝜎′√𝑇𝑇. 𝑐𝑐 and 𝑝𝑝 indicate the value of a call option and put option respectively. The buyer of the call option has the right, but not the obligation, to buy an agreed quantity of an underlying security from the seller of the option at a certain price (a.k.a. strike price) and a certain time. A put option is an option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying security at a certain price and a certain time. 𝐾𝐾 is the value of the strike price and 𝑇𝑇 is the option term. 𝑁𝑁(𝑥𝑥) is the cumulative probability distribution

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function of the standard normal distribution variable, 𝑥𝑥. Giving the case of a PPP project, 𝑑𝑑0 stands for the profit of the project during the initial operational year.

3 CONCESSION PERIOD ADJUSTMENT PROCESS

In this part, a concession period adjustment process is proposed, which contains the following steps: first, the ENPV values for private investors and governments are calculated, based on which the concession period adjustment range is generated. All the concession periods that locates in the concession period adjustment range are defined as eligible concession periods. Second, the optimal value of the adjusted concession period is chosen from the concession period adjustment range, at the end of which the profit gap between private investors and governments is at the minimal level. Third, the capability of the optimal adjusted concession period in risk control is testified to see whether the risk of suffering loss can be controlled under the risk acceptable caps for both parties. If one project party fails in risk control with the adjusted concession period, then the length of the concession period needs to be further adjusted to transfer risks between project parties. If the optimal adjusted concession period cannot control risks for both parties or risks cannot be transferred, the capability of other eligible concession periods in risk control will be verified. The overall flow chart of the concession period adjustment process can be seen in Figure 3.

Figure 3: Flow Chart of the Concession Period Adjustment Process

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3.1 Concession Period Adjustment Range

For a PPP project, the ENPV values for project parties consist of the real option values and the NPV values, which can be shown in mathematically as:

𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑅𝑅𝑂𝑂𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) + 𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) (9)

𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑅𝑅𝑂𝑂𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) + 𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) (10)

where 𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) and 𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) are function values of ENPV for private investors and governments respectively with the assumption that the concession period ends in the year 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 . 𝑅𝑅𝑂𝑂𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) and 𝑅𝑅𝑂𝑂𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) indicate function values of real options for private investors and governments respectively with the independent variable of 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐. According to the principle that private investors expect to gain more profit through the project than the expected minimal return on investment, the lower limit of the adjusted concession period (𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑝𝑝𝑛𝑛) is decided by:

𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑝𝑝𝑛𝑛 = 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑝𝑝𝑛𝑛 − 𝑡𝑡𝑐𝑐𝑐𝑐

= 𝑀𝑀𝑚𝑚�𝒕𝒕𝒂𝒂𝒂𝒂𝒂𝒂:𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝐼𝐼𝑝𝑝𝑝𝑝 × 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑝𝑝𝑛𝑛� − 𝑡𝑡𝑐𝑐𝑐𝑐 (11)

where 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑝𝑝𝑛𝑛 is the minimal value of the year that concession period ends. 𝑀𝑀𝑚𝑚 is the mode of the number set under m-times Monte Carlo simulations since the mode is the most representative number in a non-normal distribution. All the eligible value of 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 will be stored at the number set 𝒕𝒕𝒂𝒂𝒂𝒂𝒂𝒂. No moment before this threshold will be accepted by private investors since they cannot receive the expected minimal return on investment with an insufficient time. On the other hand, governments want to avoid overly lucrative conditions for private investors via setting a cap on investment return. Thus, the upper limit of the adjusted concession period (𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑎𝑎𝑎𝑎) is calculated by:

𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑎𝑎𝑎𝑎 = 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑎𝑎𝑎𝑎 − 𝑡𝑡𝑐𝑐𝑐𝑐

= 𝑀𝑀𝑚𝑚�𝒕𝒕𝒂𝒂𝒂𝒂𝒂𝒂:𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝐼𝐼𝑝𝑝𝑝𝑝 × 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑎𝑎𝑎𝑎� − 𝑡𝑡𝑐𝑐𝑐𝑐 (12)

where 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑎𝑎𝑎𝑎 is the maximal value of the year that concession period ends. 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑎𝑎𝑎𝑎 is the value of the maximal return rate on investment. No moment after 𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑎𝑎𝑎𝑎 will be accepted by governments, as private investors can earn an excess profit in an overly long period. Moreover, a prolonged concession period squeezes the time during which governments receive revenues. The concession period cannot be indefinitely extended as governments need time to recover their initial investment. Adjusting concession period with any value locating within the interval of [𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑝𝑝𝑛𝑛, 𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑚𝑚𝑎𝑎𝑎𝑎], private investors can achieve their profit target and meanwhile governments achieve the target of limiting the private investors’ profit within a reasonable range. 3.2 The Optimal Value of the Adjusted Concession Period

The previous analysis produces the adjustment range of the concession period. To derive the optimal value of the adjusted concession period, the logic of fair sharing in project profits will be considered. According to Laffont and Martimort (2009), an excessive income gap is not conducive to the formation of long-term partnerships, and low-income partners tend to be envious of high-income partners, thereby affecting their enthusiasm for the work. Therefore, this research designs the optimal length of the adjusted concession period as the value that contributes to minimizing the difference between ENPV for private investors and government, which can be found via:

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𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑎𝑎𝑝𝑝𝑡𝑡 = 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑎𝑎𝑝𝑝𝑡𝑡 − 𝑡𝑡𝑐𝑐𝑐𝑐 = 𝑎𝑎𝑟𝑟𝑎𝑎𝑎𝑎𝑎𝑎𝑛𝑛�𝑀𝑀𝑚𝑚�𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) − 𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐)�� − 𝑡𝑡𝑐𝑐𝑐𝑐 (13)

𝑠𝑠. 𝑡𝑡. 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐 ∈ [𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑝𝑝𝑛𝑛, 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑚𝑚𝑎𝑎𝑎𝑎]

where 𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑎𝑎𝑝𝑝𝑡𝑡 is the produced optimal concession period, which is the year that locates in the concession period adjustment range while meeting the prerequisite of minimizing the profit gap and avoiding the financial deficit for governments. 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐𝑎𝑎𝑝𝑝𝑡𝑡 is calculated as the instant of time that the profit gap between project parties is minimized. �𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) − 𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐)� is the absolute value of the profit gap between project parties with the independent value 𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐. 3.3 Risk Verification and Risk Transfer

This research designs a risk verification model based on profit simulations to verify the effectiveness of the adjusted concession period in risk control. By assuming the distribution of the uncertain variables that could influence project profits, the probability of suffering loss for both project parties can be calculated. The more the times of Monte Carlo simulations, the higher the reliability of the value of risk probability. Based on the principle that the possibility of suffering loss for both parties should not exceed their risk acceptance caps, the adjusted concession period contributing to risk control must satisfy:

𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑐𝑐𝑐𝑐𝑢𝑢𝑛𝑛𝑡𝑡𝑎𝑎𝑐𝑐𝑚𝑚[𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) < 𝐼𝐼𝑝𝑝𝑝𝑝 × 𝑅𝑅𝑂𝑂𝐼𝐼𝑚𝑚𝑝𝑝𝑛𝑛] 𝑎𝑎⁄ ≤ 𝑅𝑅𝑅𝑅𝑅𝑅𝑝𝑝𝑝𝑝 (14)

𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑐𝑐𝑐𝑐𝑢𝑢𝑛𝑛𝑡𝑡𝑎𝑎𝑐𝑐𝑚𝑚[𝐸𝐸𝑁𝑁𝑁𝑁𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) < 0] 𝑎𝑎⁄ ≤ 𝑅𝑅𝑅𝑅𝑅𝑅𝑔𝑔 (15)

where 𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) and 𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) are the probability of suffering loss for private investors and governments respectively. 𝑎𝑎 is the number of simulation times. 𝑐𝑐𝑐𝑐𝑢𝑢𝑛𝑛𝑡𝑡𝑎𝑎𝑐𝑐𝑚𝑚 counts the number of times that the condition is met in m-times profit simulations. 𝑅𝑅𝑅𝑅𝑅𝑅𝑝𝑝𝑝𝑝 and 𝑅𝑅𝑅𝑅𝑅𝑅𝑔𝑔 are the risk acceptance caps for private investors and governments respectively.

This research prioritizes the verification of the capability of the optimal adjusted concession period in risk control. The risk verification process can produce different outcomes. The best case would be that the adjusted concession period can control risk occurrence rates for both parties under their risk acceptance caps while minimising the profit gaps. If only one party suffers a risk spillover, the optimal adjusted concession period needs to be re-adjusted to transfer the risk from the excess-risk bearer to low-risk bearer by a risk transfer model. For a better explanation, it is assumed that there is a risk holder 1 who suffers more risk than his risk acceptance cap. Risk holder 1 wants to transfer the excess risk to risk holder 2, who suffers less risk than his risk acceptance cap. During the risk transfer process, the concession period needs to be re-adjusted to achieve risk re-allocation. The adjusted concession period after the risk transfer process can be found following:

𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑟𝑟𝑝𝑝𝑐𝑐𝑎𝑎 = {𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐: 𝑁𝑁2(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) = 𝑅𝑅2 + 𝑅𝑅1 − 𝑅𝑅𝑅𝑅𝑅𝑅1} − 𝑡𝑡𝑐𝑐𝑐𝑐 (16)

𝑠𝑠. 𝑡𝑡. 𝑁𝑁2(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) ≤ 𝑅𝑅𝑅𝑅𝑅𝑅2

where 𝑡𝑡𝑎𝑎𝑐𝑐𝑝𝑝𝑟𝑟𝑝𝑝𝑐𝑐𝑎𝑎 is the adjusted concession period after transferring the risk. 𝑁𝑁2(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) is the probability of suffering risk that risk holder 2 holds. For a PPP project, 𝑁𝑁2(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) equals 𝑁𝑁𝑝𝑝𝑝𝑝(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐) or 𝑁𝑁𝑔𝑔(𝑡𝑡𝑎𝑎𝑐𝑐𝑐𝑐). 𝑅𝑅1 is the risk borne by risk holder 1 and 𝑅𝑅2 is the risk borne by risk holder 2. 𝑅𝑅𝑅𝑅𝑅𝑅1 and 𝑅𝑅𝑅𝑅𝑅𝑅2 are the risk acceptance caps of risk holder 1 and 2 respectively. The constraint shows the principle that the risk held by risk holder 2 should be still under his risk acceptance cap after transferring the risk. What should be noted here is that the risk transfer process could make the profit gap between private investors

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and governments deviate from the minimal level. However, the priority is given to risk control at this stage. Finally, if the optimal adjusted concession period leads to a risk occurrence rate that is higher than the risk capacity of both parties, the optimal adjusted concession period will not play a role in risk control. Under this case, the adjusted concession period will be found from other eligible concession periods and the profit gap between project parties cannot be controlled at the minimal level.

4 NUMERICAL EXAMPLE

4.1 Project Background

Referring to a real toll road project in Australia, the data used for numerical analysis are set as follows. The proposed adjustment process is applied to a toll road project named Project BA whose lifespan is 60 years. Conducted as a PPP project, the construction work is scheduled to be completed within three years and the estimated initial investment is AU$6 billion. The government invests AU$6 billion at the initial stage while the private investors are responsible for raising the remaining AU$5 billion funds. The operational cost is assumed to be AU$0.8 per vehicle before the full charge for the toll road. Afterwards, the annual operational cost is set at 35% of the annual toll revenue as a more accurate standard (Welde 2011). The expected traffic growth rate should be in line with the local yearly traffic growth rate, which is 2.9%. The discount rate used for calculating the project NPV is the risk-free rate (2.6%), which equals the 10-year yield of Australian bonds. The trial operation will last 15 months, during which the road will be toll-free for the first three months, and customers will receive 50% off the toll charge, which is AU$2.5 per vehicle, for the following one year. After reaching the fully operational stage, the full price of the toll fee will be fixed at AU$4.9. The risk acceptance cap for both the government and private investors is set at 20%. The only uncertain variable recognised in this numerical example is the annual traffic volume.

The concession period is predetermined as 19 years but considering the complicated market surroundings, the contract term on concession period is kept open. The government or private investors may initiate an adjustment towards concession period according to the current market surroundings and profit estimations. Based on the predetermined concession period, the government or private investors may require to short or extend the concession period for the proposed project, which helps to maintain the profit earning from the project and prevent risky conditions for them. To achieve this, the first thing to do is to depict the trend of the traffic volume, as all the profit estimations are based on this.

Assuming that the adjustment towards concession period occurs at the fifth operational year, the annual traffic volume in the first four years are 11 million, 10 million, 9 million and 8 million. The traffic volume from the fifth operational year is predicted via GBM modelling. The underlying asset for the GBM simulation is the traffic volume in the fifth operational year based on which the traffic volume over the rest of the project lifetime can be generated via GBM simulation. The traffic volume simulation path can be produced via:

𝑇𝑇𝑡𝑡+1 = 𝑇𝑇𝑡𝑡 × 𝑒𝑒𝜇𝜇𝑇𝑇−𝜎𝜎𝑇𝑇2

2 +𝜎𝜎𝑇𝑇𝜀𝜀 (17)

where 𝑇𝑇𝑡𝑡 indicates the current traffic volume and 𝑇𝑇𝑡𝑡+1 is the traffic volume in the next year. 𝜇𝜇𝑟𝑟 is the expected traffic growth rate during ∆𝑡𝑡. 𝜎𝜎𝑟𝑟 is the annual volatility of the traffic volume accordingly.

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4.2 Concession Period Adjustment Range and the Optimal Adjustment Value

Based on the data provided above, the ENPV function for the private investors and the government can be formed with the only unknown variable, that is, the year that the concession period ends. The real option considered in this project is the real option of abandonment, which is viewed as an American put option. American options allow option holders to exercise the option at any time prior to and including its maturity date. The real option of abandonment gives private investors the right to quit the project once the traffic revenue is 30% lower than the expected revenue in the initial year. Therefore, the executive price of the option is 70% of the value of the traffic revenue in the initial year. Since the Black-Scholes pricing model cannot be used for American options pricing, the binomial tree method is adopted.

Figures 4 and 5 give the frequent distributions of the minimum and maximum concession period after adjustment. Based on the proposed method for determining the adjustment range of the concession period, the most frequent values shown in Figures 4 and 5 are chosen as the minimal length of the adjusted concession period (20 years) and the maximal length of the adjusted concession period (23 years) respectively. Also, both distributions demonstrate that the adjusted concession period is unlikely to be less than 10 years.

Figure 4: Frequency Distribution of the Minimal Length of the Adjusted Concession Period

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Figure 5: Frequency Distribution of the Maximal Length of the Adjusted Concession Period To find the optimal value of the adjusted concession period, the logic of fair sharing in project

profits is considered. The profit gap between project parties should be minimised with the adjusted concession period. At each given length of the adjusted concession period, the profit gap between project parties is simulated by 1000-times Monte Carlo simulation and the most frequent value is recoded in Figure 6. As shown in Figure 6, if the concession period is set as 20 years, the profit gap will reach the minimal level. Namely, the optimal length of the adjusted concession period is 20 years.

Figure 6: Profit Gaps Between the Government and Private Investors

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4.3 Risk Verification and Risk Transfer

The risk of suffering loss for the government and private investors is calculated based on 1000-times Monte Carlo simulation. The risk values with different length of the adjusted concession period are shown in Figure 7. It can be seen that given the adjusted concession period of 20 years, the private investors will suffer risk that is higher than their risk acceptance cap while the risk for the government is still under control. Therefore, a risk transfer process is needed to transfer the excess risk from the private investors to the governments. According to the risk transfer model, the adjusted concession period after transferring the risk is calculated as 22.2 years. The adjusted concession period is extended by 3.2 years compared with the predetermined concession period of 19 years. The adjustment outcome implies that at the point of the fifth operational year, the private investors need to require for extending concession period to 22.2 years to control the risk of suffering loss in a downturn market surrounding.

Figure 7 The probability of suffering loss for the government and private investors respectively

5 CONCLUSION

PPP projects entail more time to be completed compared with projects under other procurement methods. In a long project lifecycle, the project risks need to be controlled properly via a flexible concession period. Previous studies paid too much attention to the design of the concession period before the project bidding stage while neglecting the method of the post-contractual adjustment towards concession period. This research proposes a concession period adjustment method aiming to serve the application of the flexible contract in PPP projects. The concession period is adjusted according to the current market surroundings and project risks for project parties are expected to be controlled through concession period adjustment. The concession period adjustment conducts in several steps. First, the concession period decision range is calculated based on the ENPV analysis instead of NPV analysis. ENPV is closer to the real project value, as it considers the values of real options. Afterwards, fair profit allocation, which means minimizing the profit gap between the two parties in the PPP project,

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contributes to finding the optimal value of the adjusted concession period. Third, the risk of suffering loss for the governments and private investors is verified respectively to see whether they suffer risks that are higher than their capacities. If the probability of suffering loss for one party exceeds his risk acceptance cap while the risk for the other project party is still under control, the risk transfer model is designed to transfer the risk under this case.

Project BA is taken as a numerical example. By passing through the concession period adjustment process, the adjusted concession period is initially set as 20 years. However, with the adjusted concession period of 20 years, the private investors suffer a risk spillover. A risk transfer process is then required to transfer the risk from the private investors’ side to the governments. The adjusted concession period after transferring the risk is 22.2 years, which is 3.2 years longer compared with the predetermined concession period. The adjustment outcome implies that to control the risk of suffering loss, private investors have to claim for extending the concession period at the point of the fifth operational year as the traffic volume has fallen to an unacceptable level.

The proposed method is testified based on the numerical example that has many assumptions on project parameters. Future research may apply the model to other PPP projects to verify the applicability of the proposed model. Another limitation of this research is that the risk of suffering loss for project parties may fail to be controlled by adjusting the concession period. Future research also should give attention to how to allow flexibilities in other contractual terms, like concession price, to support the risk control of PPP projects.

References

Berger, P.G., Ofek, E., Swary, I., 1996. Investor valuation of the abandonment option. Journal of Financial Economics, 42, 257-287.

Brandao, L. E. T., Saraiva, E., 2008. The option value of government guarantees in infrastructure projects. Construction Management and Economics, 26(11), 1171-1180.

Brealey, R.A., Myers, S.C., Allen, F., Mohanty, P., 2012. Principles of corporate finance. Noida: Tata McGraw-Hill Education.

Bulnina, I., Askhatova, L., Kabasheva, I., Rudaleva, I., 2015. Public and private partnership as a mechanism of government and business cooperation. Mediterranean Journal of Social Sciences, 6, 453.

Carbonara, N., Costantino, N., Pellegrino, R., 2014. Revenue guarantee in public-private partnerships: a fair risk allocation model. Construction Management and Economics, 32, 403-415.

Cheah, C.Y., Garvin, M.J., 2009. Application of real options in PPP infrastructure projects: opportunities and challenges. Policy, finance & management for public-private partnerships. Hoboken: Wiley-Blackwell, 229-249.

Cruz, C.O., Marques, R.C., 2013. Flexible contracts to cope with uncertainty in public–private partnerships. International Journal of Project Management, 31, 473-483.

Daube, D., Vollrath, S., Alfen, H.W., 2008. A comparison of project finance and the forfeiting model as financing forms for PPP projects in Germany. International Journal of Project Management, 26, 376-387.

Demirel, H. Ç., Leendertse, W., Volker, L., Hertogh, M., 2017. Flexibility in PPP contracts–Dealing with potential change in the pre-contract phase of a construction project. Construction Management and Economics, 35(4), 196-206.

14

Dixit, A.K., Pindyck, R.S., 1994. Investment under uncertainty. Princeton: Princeton university press. Garvin, M. J., Cheah, C. Y., 2004. Valuation techniques for infrastructure investment decisions.

Construction Management and Economics, 22(4), 373-383. Hanaoka, S., Palapus, H.P., 2012. Reasonable concession period for build-operate-transfer road projects

in the Philippines. International Journal of Project Management, 30, 938-949. Hull, J., 2010. Options, futures, and other derivatives, 7/e (with CD). Delhi: Pearson Education India,

6, 40. Khanzadi, M., Nasirzadeh, F., Alipour, M., 2012. Integrating system dynamics and fuzzy logic modeling

to determine concession period in BOT projects. Automation in Construction, 22, 368-376. Kremljak, Z., Palcic, I., Kafol, C., 2014. Project evaluation using cost-time investment simulation.

International Journal of Simulation Modelling, 13, 447-457. Laffont, J.-J., Martimort, D., 2009. The theory of incentives: the principal-agent model. Princeton:

Princeton university press. Leviäkangas, P., Lähesmaa, J., 2002. Profitability evaluation of intelligent transport system investments.

Journal of Transportation Engineering, 128, 276-286. Liou, F.-M., Huang, C.-P., 2008. Automated approach to negotiations of BOT contracts with the

consideration of project risk. Journal of Construction Engineering and Management, 134, 18-24. Liu, J., Gao, R., Cheah, C.Y., Luo, J., 2016. Incentive mechanism for inhibiting investors' opportunistic

behavior in PPP projects. InternationalJjournal of Project Management, 34, 1102-1111. Ng, S. T., Xie, J., Cheung, Y. K., & Jefferies, M. (2007). A simulation model for optimizing the

concession period of public–private partnerships schemes. International Journal of Project Management, 25(8), 791-798.

Nuer, A.T.K., 2015. Exit strategies for social venture entrepreneurs. Wageningen: Wageningen University.

Raisbeck, P., Duffield, C., Xu, M., 2010. Comparative performance of PPPs and traditional procurement in Australia. Construction Management and Economics, 28(4), 345-359.

Shan, L., Garvin, M. J., Kumar, R., 2010. Collar options to manage revenue risks in real toll public‐private partnership transportation projects. Construction Management and Economics, 28(10), 1057-1069.

Smit, H.T., Trigeorgis, L., 2012. Strategic investment: real options and games. Princeton: Princeton University Press.

Song, J., Song, D., Zhang, D., 2015. Modeling the concession period and subsidy for bot waste-to-energy incineration projects. Journal of Construction Engineering and Management, 141, 04015033.

Trigeorgis, L., Reuer, J. J., 2017. Real options theory in strategic management. Strategic Management Journal, 38(1), 42-63.

Wang, Y., Liu, J., 2015. Evaluation of the excess revenue sharing ratio in PPP projects using principal-agent models. International Journal of Project Management, 33, 1317-1324.

Welde, M., 2011. Demand and operating cost forecasting accuracy for toll road projects. Transport Policy, 18, 765-771.

Yeo, K., Qiu, F., 2003. The value of management flexibility-a real option approach to investment evaluation. International Journal of Project Management, 21, 243-250.