Irreversibility, mean reversion, and investment timing

This paper examines the effect of irreversibility on investment under mean reversion. We develop a continuous-time model wherein a risk-neutral firm is endowed with a perpetual option to invest in a project at any time by incurring a fixed investment cost at that instant. The project, once undertaken, generates a stream of cash flows that are governed by a mean-reverting stochastic process. The firm is then allowed to liquidate its project at any time to partially recover the fixed investment cost. The recovery rate of the fixed investment cost inversely gauges the degree of irreversibility of investment. Using a real options approach, we derive an analytical solution to the value of the firm that is analogous with an American compound option. We show that greater irreversibility of investment induces the firm to raise its investment trigger, thereby deferring the undertaking of the project. We further show that greater irreversibility of investment has a detrimental effect that makes the firm less valuable.