Corporate investment and financing with uncertain growth opportunities

This paper develops a continuous‐time model of a firm's sequential investments. The firm has an option to expand revenue after the initial investment. However, the timing of exercising the growth option depends not only on the underlying cash flows but also on the uncertainty of the growth opportunity. We show that the uncertainty of growth opportunity has a positive effect on the initial investment. In particular, the investment threshold has a nonmonotonic (U‐shaped) relation with the arrival rate of the growth opportunity, in that it starts to decrease and then increase with the arrival rate. The outcome is driven by the tradeoff between benefit and cost of the prospective expansion, and the magnitude of that rests on the level of arrival rate. For optimally levered firm, the financial leverage ratio displays a U‐shaped relation with the arrival rate. It is caused by the interaction between future growth uncertainty and debt overhang problem. Furthermore, we show that the optimal leverage, depending on the level of growth uncertainty, may or may not display inverse relation with the growth size. Our results shed valuable light on the empirical implication of testing the existence of debt overhang.