Ebook Book Values and Market Values of Equity and Debt
This paper presents a contingent claims model to value a firmls equity and debt as functions of observable book values that appear in financial statements. This model attempts to make fuller use of information in financial statements than the existing structural models in the literature do. This attempt has practical advantages.
The model is based on observable earnings. Market values of assets and equity are driven by expected earnings, which is consistent with the theory and with the way equity analysts value equity. Market values of assets and equity also depend on the equity holdersloption to default or to voluntarily liquidate the firm. Multiples like price earnings and price to book are endogenous to the analysis, a feature that can be used in model calibration. Since the
model is based on book values, it is immediately applicable even to firms whose stock is not traded in the market.
The focus on book values makes it possible to model the dividend policy and debt covenants more accurately than in existing structural models. In fact debt covenants are normally expressed in terms of book values. Default is also made to depend on book values. The model is consistent with the way accounting ratios are used to predict bankruptcy. No estimate of the unobservable market value of the firm is required. Rather, the unobservable market value of the firmls assets is endogenous to the model. The earnings process is consistent with empirical evidence: return on assets is mean reverting and negative operative earnings are possible.
All these advantages come at the cost of not having closed form solutions for debt and equity values. Instead numerical solutions are necessary, but the computations are affordable.
The model provides theoretical insights. The options to default or liquidate the firm cause equity value to exceed the present value of expected future earnings. This is especially true in the proximity of default. Earnings volatility increases equity value and typically decreases debt value. Debt value tends to increase in earnings volatility in the proximity of default. This somehow challenges the assets substitution argument, which suggests that near default the risk shifting incentive is strongest. Equity value materially increases (decreases) with the strength of the mean reversion of profitability, when profitability is below (above) its long term level. Debt value typically rises with the strength of profitability mean reversion.
It may be in the equity holderslinterest to voluntarily liquidate the firm before default. This implies that a slow decline in profitability and small persistent losses may be more dangerous for debt holders than a sudden large decline in profitability and sudden large losses. The reason is that sudden losses would trigger voluntary liquidation, while small persistent ones would lead to default.
The paper is organised as follows. Section 2 reviews the relevant literature. Section 3 presents the valuation model. The effect of possible voluntary liquidation is analysed in Section 4. The conclusions follow in Section 5.
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