Explicit investment rules with time-to-build and uncertainty

TL;DR

This paper derives explicit optimal investment rules considering time-to-build and uncertainty, analyzing demand models and highlighting biases affecting capacity decisions.

Contribution

It provides the first explicit formulas for optimal investment with time-to-build under demand uncertainty, incorporating biases and offering economic insights.

Findings

Committed capacity should not fall below demand predictor minus biases.

Biases include discounting bias and precautionary bias related to volatility.

Analytical formulas are derived for different demand models.

Abstract

We establish explicit socially optimal rules for an irreversible investment deci- sion with time-to-build and uncertainty. Assuming a price sensitive demand function with a random intercept, we provide comparative statics and economic interpreta- tions for three models of demand (arithmetic Brownian, geometric Brownian, and the Cox-Ingersoll-Ross). Committed capacity, that is, the installed capacity plus the in- vestment in the pipeline, must never drop below the best predictor of future demand, minus two biases. The discounting bias takes into account the fact that investment is paid upfront for future use; the precautionary bias multiplies a type of risk aversion index by the local volatility. Relying on the analytical forms, we discuss in detail the economic effects.