Agency cost of debt overhang with optimal investment timing and size

The concept of debt overhang (that is, an equity‐maximizing levered firm will under‐invest relative to a firm‐value‐maximizing firm) is well established in the literature. A number of papers have demonstrated it as delayed investment (when investment size is specified) or smaller investment (when investment time is specified). However, there is no work on the underinvestment effect when the firm chooses both size and timing of investment, as it usually does in real life. This is what our paper focuses on. When the firm has the flexibility to choose both size and time, the effect is complicated by the fact that delayed investment results in larger investment, which suggests that the underinvestment problem might be mitigated. We find, however, that the effect depends on how underinvestment is measured. When measured by the expected present value of investment, flexibility can mitigate or exacerbate the underinvestment problem, depending on the cost of installing capacity. But when measured by the agency cost, flexibility always exacerbates the underinvestment problem. It is shown numerically that, at the optimal leverage ratio, the agency cost with plausible parameter values can be economically significant. Thus, with the flexibility of choosing both time and size of investment, the debt overhang problem can be of significant practical relevance in corporate investment decisions.