Abstract
This paper applies the standard risk-neutral valuation framework to tax shields generated by dynamic debt policies. We derive a partial differential equation (PDE) for the value of the debt tax shield. For a class of dynamic debt policies that depend on the asset's free cash flows, value, and past performance, we obtain closed-form solutions for the PDE. We also derive the tax-adjusted cost of capital for free cash flows and analyze the conditions under which the weighted average cost of capital is an appropriate discount rate. Finally, we derive closed-form solutions for equity betas, which differ from the formulas that have traditionally been used to lever and unlever equity betas.
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