A Theory of Debt Maturity

In our paper, A Theory of Debt Maturity: The Long and Short of Debt Overhang, forthcoming in the Journal of Finance, we study the effects of the debt maturity on current and future real investment decisions of an owner of equity (or a manager who is compensated by equity). Our analysis is based on debt overhang first analyzed by Myers (1977), who points out that outstanding debt may distort the firm’s investment incentives downward. A reduced incentive to undertake profitable investments when decision makers seek to maximize equity value is referred to as a problem of “debt overhang,” because part of the return from a current new investment goes to make existing debt more valuable.

Myers (1977) suggests a possible solution of short-term debt to the debt overhang problem. In part, this extends the idea that if all debt matures before the investment opportunity, then the firm without debt in place can make the investment decision as if an all-equity firm. Hence, following this logic, debt that matures soon—although after relevant investment decisions, as opposed to before—should have reduced overhang.

However, short-term debt is known to have several disadvantages. For firms without access to outside funds to meet debt repayments, short-term debt can lead to early firm closure and liquidation (e.g., Diamond (1991), Gertner and Scharfstein (1991)). More relevant to our paper, Gertner and Scharfstein (1991) show that, conditional on ex-post financial distress, making a fixed promised debt payment due earlier (i.e., shorter-term) raises the market value of the debt and thus the firm’s market leverage, leading to more debt overhang ex-post. In addition, certain drawbacks of short-term debt have also been suggested by some quantitative models (Titman and Tsyplakov (2007), Moyen (2007)) that focus on equity holders’ differential abilities and incentives to adjust leverage in response to new information given different debt maturity structures.

Our paper aims to provide a thorough analysis on the effects of debt maturity on the equity incentives to undertake both current and future investments, and, more importantly, to identify the forces that determine overhang. We show why the ideas based on Myer’s suggestion have merit, and show how and why they can be reversed under different settings.

Debt maturity influences investment incentives in a more nuanced way than suggested by existing analysis. By definition, investment incentives are weak (and debt overhang is severe) when very little of the return from investment accrues to equity. For a single immediate investment, we show in a Black-Scholes-Merton model that shorter maturity debt is less sensitive to increased firm value from a new investment. This provides an intuition why shorter-term debt may impose less overhang, because the difference between the total return from investment and the part accruing to equity is the change in the value of debt. When investment opportunities are present in the future, this intuition is incomplete. Less risk shared with existing shorter-term debt makes equity values and debt overhang more volatile, which affects future investment incentives.

We illustrate three ways in which shorter-term debt can impose stronger overhang. First, when volatility of firm value is sufficiently higher in bad times than good times, shorter-term debt can lead to higher overhang even for a single immediate investment decision taken just after the debt is issued. Second, in a dynamic setting with future investment opportunities, the reduction in equity value (and increased market leverage) due to the combination of bad times and shorter-term debt is so large that equity holders’ investment incentives suffer greatly, and they may choose to default earlier. Third, because shorter-term debt induces earlier future default and elimination of future growth, it hurts equity holders’ incentives to invest (maintain) today when investment benefits are inter-temporally linked.

There is an interesting application combining all of our results. For reasons other than the effects on debt overhang, banks and other financial institutions issue short-term debt such as deposits, matching well with our exogenous constant refinancing structure, and fund debt contracts such as loans, implying high asset volatility in bad times. Our model then suggests that the effects of debt overhang in bad times will be extremely large for banks. This is for different reasons than the risk of runs and asset illiquidity leading to severe short-term debt overhang in Diamond and Rajan (2011). Adding our results to theirs suggests that the debt overhang problem for banks may be very severe.

The link between investment incentives and debt maturity is important for firms where future investments are important. Besides offering several testable implications for future empirical research, our paper suggests that managers who understand only one part of effect of debt maturity on investment incentives could make poor choices of debt maturity structure.

The full paper is available for download here.