Modeling Dynamic Redemption and Default Risk for LBO Evaluation: A Boundary Crossing Approach
58 Pages Posted: 15 Feb 2015 Last revised: 15 Jun 2016
Date Written: January 7, 2016
We analyze corporate financial policies in leveraged buyouts (LBOs) in the presence of default risk. Our model captures the LBO-specific stepwise debt reduction, either with predetermined or cash-flow dependent (cash sweep) principal payments, and thus allows for dynamic redemption. These dynamics imply stochastic, discontinuous default boundaries. Our framework enables us to derive explicit-form solutions for the net present value (NPV) and the internal rate of return (IRR) of an LBO investment. We show that in scenarios with high entry debt and high redemption payments, the flexibility associated with dynamic redemptions creates value for investors, while fixed redemptions yield higher NPV and IRR values for moderate redemption due to lower debt yields. Moreover, we discuss optimal corporate financial policies implied by NPV or IRR maximization and find that the latter always results in increased leverage with higher default probability. The model of piecewise linear boundaries developed in this article is sufficiently flexible to be applied to a wide range of problems in corporate finance.
Keywords: Default at first passage, Dynamic redemption, Barrier options, Brownian motion, Numerical integration, Leveraged buyouts
JEL Classification: C61, C63, G12, G13, G32, G33
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