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B
to the optimal endogenous default level for the case of perpetual (infinite maturity) debt.
211
A Leland [1994] modell
Leland [1994] extends Black and Cox’s [1976] endogenous default model to include a tax
advantage of debt and bankruptcy costs. Due to the consequence of debt financing, the
value U of the leveraged firm no longer coincides with the asset value V (modeled as a
geometric random walk), which latter has the interpretation of the value of an identical but
unleveraged firm. Rather, the firm value increases in the value of the tax benefits TB while
it decreases in the value of the bankruptcy costs BC. Thus minimizing the debt value – as
pronounced by Black and Cox – is no longer the optimal strategy for equity holders when
they choose the default level that maximizes their claim value. Instead, the value of equity
E is the value of the leveraged firm minus the debt value:
E = U – D = V + TB – BC – D.
Leland [1994] derives expressions for the tax benefit, the bankruptcy costs, and the debt
value for a given default boundary V B . Then he solves the equity holders’ optimization
problem and obtains the critical default boundary, assuming that default occurs as soon as
the equity value reaches zero (‘smooth-pasting condition’):
( 1−
t)
∗ c
V B
= ,
2
σ
r +
2
where t denotes the marginal corporate tax rate, c denotes the continuously paid
nonnegative coupon per instant of time, r denotes the continuous risk-free rate, and σ
denotes the volatility component in the stochastic process of the firm value V. Influencing
the riskiness of firm value, as can be seen, hence has fundamental impact on the expected
default probabilities, which makes these models so useful in analyzing and quantifying the
impact of corporate risk management decisions on firm / shareholder value.
211 Leland/Toft [1996] consider finite maturity debt that is constantly rolled over in a way that the overall
debt structure remains time-independent.
202