A New Approach to the Irreversible Investment Problem

This paper solves the irreversible investment decision problem under uncertainty by a new real options method. It yields a Shadow Net Present Value rule such that the investment is triggered only when the shadow revenue of the investment reaches the investment cost. This paper hence corrects and extends the conventional Net Present Value (NPV) rule by figuring out the proper NPV of the investment. Meanwhile, the investment policy is shown to be correct and consistent with the real options theory since the shadow revenue records the economic value of the investment by deducting the option premium of waiting from the real revenue. This method allows for a generalization of the conventional analysis to all semi-martingale processes with deterministic or stochastic discount rates. Especially, we provide an explicit characterization of the threshold value when the uncertainty is specified as an exponential L´evy process. To highlight the significance of risk preferences on the decision rule, this paper also addresses the utility-based extension of the standard real option model. The investment policy in such a model is identified in the same form as that in the profit-maximization problem but signalled by the shadow utility process. The joint effect of risk aversion and jumps on the trigger value is analyzed through examples.