Capacity Planning Under Uncertainty and the Cost of Capital

Abstract

We explore how risk aversion affects optimal capacity and pricing decisions within the economic setting of Banker and Hughes (1994). A risk averse firm invests in fixed capacity and sets a product price, but can also purchase spot capacity at higher unit cost. Initial capacity and price are set by maximizing the firm’s mean-variance certainty equivalent. We find that, contrary to common intuition, optimal capacity or list prices can increase under greater risk aversion depending on exogenous fundamentals. We show how the firm’s capacity and price choices affect the economic trade-off between the mean and the risk of the firm’s uncertain payoffs. We also show that the cost of capital is affected not only by the firm’s covariance with other assets, but also by its payoff mean. The objective of minimizing the cost of capital is therefore fundamentally inconsistent with maximizing project value.

Keywords: Capital Budgeting, Pricing, Cost of Capital, Capacity Planning

JEL Classification: M41, G31