Probabilistic life cycle cash flow forecasting with price uncertainty following a geometric Brownian motion

Abstract

In the Netherlands, probabilistic life cycle cash flow forecasting for infrastructures has gained attention in the past decennium. Frequencies, volume and unit prices of life cycle activities are treated as uncertainty variables for which an expert-based triangular distribution is assumed. The current research observes the absence of time-variant variables typical for infrastructure life cycles among which price (de-)escalation. Moreover, previous research has shown that price (de-)escalation and its uncertainty should not be ignored as it may lead to over or underestimation of costs, especially for public sector organisations which use low discount rates. For that reason, the current research has searched for a more data-driven approach to include price (de-)escalation and its uncertainty by adopting a price forecasting method from the financial domain, a Geometric Brownian Motion. The uncertainty variables drift and volatility are obtained from publicly available price indices. This approach is easily included in the current practice for probabilistic cost forecasting which is demonstrated on a case study. The case study shows that ignoring price increases may lead to an underestimation of total discounted costs of 13%. From an academic perspective, the current research advocates inclusion of price uncertainty in multi-objective optimisation modelling of infrastructure life cycle activities.