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.

中文翻译：

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涉及专用资产和政府补贴的多阶段PPP项目中的最佳扩张时机决策

到目前为止，多阶段公私伙伴关系（PPP）项目中的投资时机这一主题尚未引起太多关注。本研究调查了在不确定需求下多阶段PPP项目的最佳扩张时机决策，并且在PPP合同关闭后立即实施涉及专用资产的第一阶段绿地项目，而根据具体情况灵活决定了后续扩张的时机。满足需求。在这种情况下，采用最佳多重停止时序理论对扩展框架进行建模。此外，我们将政府补贴（包括投资补贴和收入补贴）整合到扩展时机决策中。通过假设的三阶段卫生排水项目投资计划，使用最小二乘蒙特卡洛模拟提供了补贴之前和之后的最佳扩展策略和多阶段项目的价值。此外，还说明了专用资产对扩张策略和项目价值的影响。另外，我们比较了补贴前后的增量值和由两种补贴产生的早期扩张。比较表明，收入补贴具有更多的增量价值，投资补贴带来了更早的扩展。我们比较了补贴前后的增量值和由两种补贴产生的早期扩张。比较表明，收入补贴具有更多的增量价值，投资补贴带来了更早的扩展。我们比较了补贴前后的增量值和由两种补贴产生的早期扩张。比较表明，收入补贴有更多的增量价值，投资补贴带来了更早的扩展。