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

Jinghuan Li; Yu Li; Shuhua Zhang

doi:10.3934/jimo.2019043

Article Contents

2020, Volume 16, Issue 5: 2065-2086. Doi: 10.3934/jimo.2019043

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

1.
Department of Mathematics, Tianjin University of Commerce, Tianjin 300134, China
2.
Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

^* Corresponding author: Jinghuan Li
^* Corresponding author: Jinghuan Li

Received: August 31, 2018

Revised: December 31, 2018

Early access: May 2019

Published: August 2020

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)

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Abstract

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.

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

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

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Figure 2. The project value for different demand levels

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

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Figure 4. The influences of the dedicated asset ratio

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

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Figure 6. The influences of the investment subsidy proportion

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Figure 7. Revenue subsidy at different demand levels

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Figure 8. The influences of the revenue subsidy price

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Figure 9. The comparison of the subsidy amount

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Figure 10. The comparison of the incremental value

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

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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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