Article Contents
Article Contents

# Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies

• * Corresponding author: Jinghuan Li

This project was supported in part by the the Major Research Plan of the National Natural Science Foundation of China (91430108), the National Natural Science Foundation of China (11771322, 71471132, 71573189), and Tianjin Education Commission Scientific Research Plan(2017SK076, 2017KJ236)

• The topic of investment timing in multi-stage public-private partnership (PPP) projects has not been received much attention so far. This study investigates optimal expansion timing decisions in multi-stage PPP projects under an uncertain demand and where the first-stage greenfield project involving a dedicated asset is immediately implemented as the PPP contract is closed, whereas the timing of the later expansion is flexibly decided according to the demand. In this setting, the optimal multiple stopping timing theory is adopted to model the expansion framework. Furthermore, we integrate a government subsidy, including an investment subsidy and revenue subsidy, into the expansion timing decisions. Through a hypothetical three-stage investment plan for a sanitary sewerage project, the optimal expansion strategies and the value of the multi-stage project before and after the subsidy are provided using a least squares Monte Carlo simulation. Also, the influences of a dedicated asset on the expansion strategies and project value are illustrated. In addition, we compare the incremental value before and after the subsidy and earlier expansion derived from two types of subsidies. The comparisons show that there is more incremental value for the revenue subsidy, and that the investment subsidy brings an earlier expansion.

Mathematics Subject Classification: Primary: 49J20, 65C05, 65M06.

 Citation:

• Figure 1.  The schematic diagram of a three-stage PPP project

Figure 2.  The project value for different demand levels

Figure 3.  The optimal exercise boundaries for the i-th (i = 1, 2) expansions

Figure 4.  The influences of the dedicated asset ratio

Figure 5.  The project value and subsidy amount under different demands

Figure 6.  The influences of the investment subsidy proportion

Figure 7.  Revenue subsidy at different demand levels

Figure 8.  The influences of the revenue subsidy price

Figure 9.  The comparison of the subsidy amount

Figure 10.  The comparison of the incremental value

Figure 11.  The comparison of the exercise boundary under the same subsidy amount

Table 1.  Default parameters used in the calculations

 Constant Symbol Value Unit Concession Period $T_{c}$ 30 Year Investment period $T$ 10 Year Planned investment times $N$ 3 time Construction period $\nu$ 1 Year Refraction time $\delta$ 2 Year Capacity of i-th stage $m_{i}$ 40,000 $m^3$/day Unit price $p$ 1.8 CNY/$m^3$ Unit operational cost $c$ 0.8 CNY/$m^3$ Construction cost parameter $b$ 2917.8 Construction cost parameter $\gamma$ 0.9427 Drift $\alpha$ 6% Volatility rate $\sigma$ 15% Discount rate $\rho$ 8% Dedicated asset ratio $\eta$ 10%
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