Ebook How the corporate liquidity process affects the value of the firm
What is the impact of corporate liquidity on a firm’s value? Is the value of the firm invariant with respect to the dividend policy, as suggested fifty years ago, by Modigliani and Miller (1961)? Does the liquidative value of the assets affects the incentives of shareholders to choose the dividend policy? What is the impact of the volatility of the cash-flow on dividend policy?
This paper attempts to provide answers to these questions through a simple model in which we make a clear distinction between liquidity and solvency of the firm, which in turn allows us to properly introduce dividend policy as a fraction of the net result. Roughly speaking, solvency is the ability of the firm to redeem bondholders if the productive assets were to be sold, while liquidity is the ability of the firm to pay the current coupon to bondholders using current cash-flow. A firm may be illiquid but solvent, while another may be liquid but insolvent. The first generates low cash-flow but the liquidative value of its assets is high (e.g., an industrial firm) while the second firm generates high cash-flow but the liquidative value of its assets is low (e.g., a commercial firm).
In the structural approach to credit risk modeling, it is generally assumed that the state variable V follows some stochastic process, typically a geometric Brownian motion. One generally interprets V to represent either:
- 1. the (liquidative) value of the productive assets (e.g Merton (1974)),
2. the expected value of the future cash-flow (e.g. Fries et al.).
In the first interpretation, the scrapping value of the assets is the only economic variable. As a consequence, default comes from a “solvency trigger”. In standard structural models such as Merton (1974), Black & Cox (1976), Briys and Devarenne (1997), Leland (1994), Leland and Toft (1998), Fan and Sundaresan (2002), firms default when the liquidative value of the assets V falls below some threshold H which may be constant (Leland 1994; Fan and Sundaresan 2002); deterministic Black and Cox (1976); or stochastic Briys and Devarenne 1997). The problem with this approach is that it does not really allow default to come from a “liquidity trigger” but more importantly, as pointed out by Leland (1994) and Goldstein et al. (2001) among others, it is not clear whether or not V remains a traded asset when the firm becomes levered.
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