Abstract
Abstract We develop a theory of multiperiod debt structure. A simple trade-off between the termination threat required to make debt repayments incentive compatible and the desire to avoid early liquidation determines the number of repayments, their timing, and amounts. As firms increase their borrowing, they add periodic risky repayments from the back of the maturity structure, with the time between repayments increasing in cash-flow risk. Cash-flow growth or a significant risk-free cash-flow component limits the number of risky repayments. Firms with a significant risk-free cash-flow component choose dispersed maturity profiles with smaller, relatively safe repayments every period, rather than riskier periodic repayments. Received May 31, 2017; editorial decision October 8, 2018 by Editor Stijn Van Nieuwerburgh.
Highlights
How do firms choose the term structure of their debt? While a large literature has investigated why firms use debt to raise financing for investments,1 we know much less about the determinants of the number of repayment dates, their timing, and the respective repayment amounts
Cash flows are left to the entrepreneur, the entrepreneur’s payoff from continuing past date T − 2 is given by VT −1 = 2∆, which provides the upper bound for the incentive compatible repayment at
This paper provides a model of optimal debt structure in a multi-period setting
Summary
Consider a risk neutral entrepreneur who seeks to undertake an investment project. At date t = 0, the investment requires an outlay of I. Vt = ∆ + Pr(Xt ≥ Rt) (−Rt + Vt+1) This recursive formulation reflects that, at each date t, the entrepreneur generates an expected cash flow of ∆ and continues to the period, by making the contractual repayment Rt, whenever Xt ≥. Cash flow to repay debt, so that the firm is liquidated at the first instance that Xt < Rt. Given risk neutrality, the entrepreneur chooses the repayment schedule R to maximize V1, the value of equity at the beginning of the project. The binary cash-flow distribution combined with the assumption that the entrepreneur cannot save or refinance allows us to simplify the above maximization problem With these assumptions in place, the relevant choice variable for the entrepreneur reduces to whether to promise a positive repayment at any particular date t. Lemma 1 states that if two debt contracts R and R have identical repayment dates and the same expected value to creditors, they yield the same expected payoff to the entrepreneur.
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