A Multistage Linear Stochastic Programming Model for Optimal Corporate Debt Management

Large corporations fund their capital and operational expenses by issuing bonds with a variety of indexations, denominations, maturities and amortization schedules. We propose a multistage linear stochastic programming model that optimizes the bond issuance policy to fund a predetermined project portfolio. Cash flows are uncertain, affected by financial, macroeconomic and business specific risk factors. Our objective function combines a mean-risk trade-off measured at the end of the planning horizon and penalties for highly leveraged debt portfolios at each intermediate stage. Avoiding the curse of dimensionality common in long term multistage stochastic models, the full event tree representation of uncertainty is used only in the initial planning stages. The remainder of the horizon uses independent path sub-samples, adopting a fixed-rule policy approximation. Assuming null cash returns, an illustrative example presents a sensitivity analysis of the first stage solution and the stochastic efficient frontier of mean-risk trade-off. Based on a realistic example with stochastic cash returns, we underscore the importance of the intermediate penalties in obtaining suitable solutions. Based on the proposed model, a financial planning software tool has been implemented and deployed in Brazilian oil company Petrobras.