Challenges in the Evaluation of Ultra-Long-Lived Projects: Risk Premia for Projects with Eternal Returns or Costs

TLDR: In this article, the risk of ultra-long-lived investment projects implied if future pay-off's are assumed to follow geometric Brownian motion processes is discussed, and the value at risk is defined as the difference between the expected value and the boundary of the confidence interval.

Abstract: The economic evaluation of ultra-long-lived investment projects is not only challenging due to the choice of the planning horizon but also due to the discounting of future uncertain cash flows. Thus, for real world investment decisions a better understanding of the project’s risks and their effect on the project’s value is crucial. If long-term investments are modeled, stochastic processes may be used to reflect the uncertain development of future prices and cash flows. The choice of the stochastic process is consequently an essential assumption in the modeling process. This paper critically discusses the risk of ultra-long-lived investment projects implied if future pay-off’s are assumed to follow geometric Brownian motion processes. In our analysis, we distinguish between projects driven by costs and such driven by revenues. For both kind of projects we compare the value at risk with the returns of a risk-free asset. Therein, the value at risk describes the threshold value of the confidence levels of the uncertain cash flow’s probability density function. The comparison for long time horizons shows that the lower confidence interval exceeds the returns of a risk-free asset used as a benchmark for any choice of the confidence level, which implies that the returns of a “worst-case” scenario (within the assumed confidence interval) will still exceed the returns of a risk-free asset in the long-term perspective. For the case of uncertain future cost, the risk measure is defined as the difference between the expected value and the boundary of the confidence interval. This value is also found to become negative in the long-term perspective.