Firm Valuation with Bankruptcy Risk

Abstract

Traditional firm valuation discounts forecasted cash consequences that are understood as expected values under some scenario. It is not clear how, and to what extent, uncertainty is incorporated in the valuation. This paper constructs a new valuation model where uncertainty, in particular, bankruptcy risk, is explicitly included. At the end of each year, there is a jump to one of three possible states of the world at the end of the following year. A state is a combination of sales revenue for the firm being valued and return on the market index. The third state implies bankruptcy for the firm. The new model includes both the non-steady-state explicit forecast period and the steady-state post-horizon period and derives consistent values for the unlevered firm, the debt, the equity, the tax shields, and the levered firm. All discount rates, and the promised debt interest rate, are derived endogenously using CAPM. The model structure, in particular the manner in which sales revenue serves as driving variable, implies that one needs to perform only one discounting operation for each year, like in Fama 1977. A small annual bankruptcy probability is seen to lead to a noticeable value decrease. This paper also contains a discussion of where the bankruptcy risk is concealed in traditional firm valuation. The good news is that bankruptcy risk can actually be included in traditional firm valuation, at least approximately, by forecasting expected growth rates and discount rates that take into account the bankruptcy risk.

Keywords: Valuation, bankruptcy, free cash flow, discounting, accounting data

JEL Classification: M41, G31, G33, C63