Investment and the Valuation of Firms When There is an Option to Shut Down

TLDR

Classical microeconomics dictates shutting down a plant when operating revenues fall below variable costs, but this rule only matters under revenue or cost uncertainty, a feature that distinguishes the authors’ model from Sandmo’s profit‑utility framework and aligns with the broader finance literature on value‑maximizing firms. The study develops a methodology for valuing risky investment projects that include a cost‑free shut‑down option triggered when variable costs exceed operating revenues. The authors model prices and costs as continuous‑time stochastic processes, treating the firm as risk‑neutral and price‑taking while its risk‑averse investors determine the cost of capital. Risk aversion alters the cost of capital, and the explicit inclusion of a cost‑free shut‑down option leads to valuation outcomes that differ.

Abstract

An important lesson from elementary microeconomics is that a plant should be shut down if operating revenues are less than variable costs. This simple production rule has implications -which have received little attentionfor the initial decision to build the plant.2 This paper develops and studies a methodology for valuing risky investment projects, where there is an option to temporarily and costlessly shut down production (with no effect on future prices and costs) whenever variable costs exceed operating revenues. It is obvious that future revenues or costs must be uncertain if the shut-down option is to affect the investment decision otherwise, it is always known ex ante whether the plant is to be operated. Uncertainty is introduced in this paper by supposing that prices and costs follow a continuous time stochastic process.3 The firm in our model is a risk-neutral, price-taking value maximizer, which is owned by risk-averse investors. Risk aversion thus influences the investment decision by affecting the cost of capital faced by the firm. This is in contrast to the model in Sandmo [1971], in which the firm maximizes the utility of profits.4 Our treatment is descriptive of value-maximizing, publicly-owned firms and is widely used in the finance literature. The economics literature studying the effect of uncertainty on firm behavior has, however, tended to follow Sandhmo. The explicit modelling of the shut-down option and our treatment of risk aversion give us results that differ from those obtained by others who have studied the valuation of risky projects. Our principal results are: 1) Increases in the variance of the output price can either raise or lower the