Effect of incorporating capacity constraints on government guarantees in PPP infrastructure projects

Public Private Partnerships (PPPs) are widely adopted for financing and implementing infrastructure projects, especially under long-term concession models such as DBFOT (Design-Build-Finance-Operate-Transfer). The demand/revenue uncertainty in such capital-intensive projects often results in significant financial risks to private entities. Governments usually offer Minimum Revenue Guarantees (MRGs) for downside protection against revenue shortfalls to safeguard private entities from such risks. Existing approaches for valuing MRGs predominantly rely on financial option pricing theory, which models the underlying asset using Geometric Brownian Motion (GBM). While GBM offers analytical convenience, it assumes continuous unbounded exponential growth and fails to account for physical capacity constraints typical to infrastructure assets such as highways, ports, and energy grids, resulting in incorrect revenue projections and sub-optimal guarantee valuations. To address these limitations, this study proposes two alternative stochastic models: a Capacity-Constrained GBM (CC-GBM), which imposes an upper cap on growth, and a 4-Parameter Logistic Brownian Motion (4 P-LBM), which integrates logistic growth dynamics with stochastic volatility. Monte Carlo simulation is used to model stochastic demand/revenue paths to evaluate expected revenues and guarantee payouts under each modelling approach. The proposed models are applied to a highway PPP case study to conduct a comprehensive scenario analysis by varying initial traffic levels and growth rates. The results indicate that while all models yield comparable outputs when the initial demand remains well below the capacity, GBM significantly starts to overestimate concessionaire revenues and government liabilities when the demand approaches or exceeds the capacity. The 4 P-LBM consistently provides the most conservative and realistic valuations.