The optimal time to make a risky investment under a permanent exit option

Abstract

We study an optimal investment policy of a risky project when there exists the possibility that a firm may permanently exit the business under deeply deteriorated market conditions in the future. To capture the riskiness of the investment return rate, a Geometric Brownian motion is adopted to model the firm’s profit stream. Applying the real options framework, this paper aims at characterizing the firm’s optimal investment policy of the risky project under permanent exit option. It is shown that the investment threshold is no longer a monotonic function of the market uncertainty. Specifically, the investment threshold can decrease with market uncertainty for moderate uncertainty. And the investment threshold will eventually increase with market uncertainty if the uncertainty becomes sufficiently high. Extensive numerical experiments are conducted to check the robustness of the theoretic results. Some managerial implications are derived for investment decisions under the exit option.