Estimating Risk‐Adjusted Costs of Financial Distress

The search for the optimal, or value‐maximizing, capital structure involves weighing the expected benefits of higher leverage against the expected “costs of financial distress.” These costs include not only the direct costs of reorganization, but less quantifiable effects of financial trouble such as damage to the firm's reputation, the loss of key employees and customers, and the loss of value from forgone investment opportunities. This article proposes a new method for valuing expected financial distress costs. While researchers have provided estimates of the costs associated with financial distress when it takes place, whether or when these costs will be incurred is, of course, unknown at the time the financing decision. As a result, the “correct” discount rate for valuing expected distress costs is difficult to derive. Instead of adjusting the discount rate to reflect historical default rate probabilities, the authors' method uses “risk‐neutral” probabilities of encountering distress that allow for discounting at the risk‐free rate. The risk‐neutral probabilities of default are derived by incorporating the systematic risk premia implicit in corporate bond yield spreads. This method results in a significant increase in estimates of financial distress costs. In a simple example presented by the authors, distress costs estimated at about 1.6% of firm value using the conventional method turn out to run about 5% after adjusting for the increased systematic risk associated with financial distress.     

Consistent valuation of project finance and LBOs using the flows‐to‐equity method

The flows‐to‐equity method is used to value transactions where debt amortizes according to a fixed schedule, requiring a formula that links the changing leverage with a time‐varying equity discount rate. We show that extant formulas yield incorrect valuations because they are inconsistent with the basic assumptions of this method. The error from using the wrong formula can be large, especially at currently low interest rates. We derive a formula that captures the effects of a fixed debt plan, potentially expensive debt, and costs of financial distress. We resolve an important issue about what to use as the cost of debt.     

Valuing Debt in a Complex Capital Structure

This article extends previous bond valuation models to account for more realistic assumptions regarding financial distress. Realized value of an individual bond under severe financial distress will reflect the expected outcome of credit-event negotiations and the relative priority listing of the security. We explicitly represent the probability rate of credit-event occurrence as a function of firm value relative to the fixed overall debt obligations of the firm. Risk premiums generated under reasonable parameter value choices fall within the range of observed bond risk premiums. Our model also provides an explanation as to why observed bond risk premia are positive after adjustment for default.     

Sovereign bond market reactions to no-bailout clauses and fiscal rules – The Swiss experience

We analyse the effects of a credible no-bailout policy and stringent sub-national fiscal rules on the risk premia of Swiss sub-national government bonds in the period from 1981 to 2007. In July 2003, the Swiss Supreme Court decided that the canton of Valais is not liable for municipal debt. This landmark decision reduced cantonal risk premia by about 26 basis points and cut the link between cantonal risk premia and the financial situation of the municipalities that existed before. The result demonstrates that a not fully credible no-bailout commitment can entail high costs for the potential guarantor. Additionally, strong and credible balanced budget rules reduce risk premia.     

Hidden insurance in a moral‐hazard economy

We analyze the general equilibrium of an economy in which a competitive industry produces nonexclusive insurance services. The equilibrium is inefficient because insurance contracts cannot control moral hazard, and welfare can be improved by policies that reduce insurance by increasing its price above marginal cost. We discuss how insurance production costs that exceed expected claim payments interact with moral hazard in determining the equilibrium's inefficiency, and show that these costs can make insurance premia so actuarially unfair as to validate the standard first‐order conditions we exploit in our analysis.     

The value, size, and momentum spread during distressed economic periods

We study the behavior of market risk, value, small cap, and momentum premia under different macro economic scenarios. If these factors are risk factors, then these factors offer high returns to investors at times when the gain (marginal utility) of additional consumption is low (good economic times) and low returns at times when the gain (marginal utility) of additional consumption is high (bad economics times). Our results show that market risk and small cap premia behave more like risk factors while value premium does not. In fact, our results show that a portfolio with a long position in value and a short position in growth is a hedge in the down market and recessionary periods. Our results also show that a momentum premium exists under different economically distressed scenarios we studied.     

Default Risk, Asset Pricing, and Debt Control

The pricing and control of firms’ debt has become a majorissue since Merton’s (1974) seminal article. Yet Mertonas well as other recent theories presume that the asset valueof the firm is independent of the debt of the firm. However,when using debt finance, firms may have to pay a premium foran idiosyncratic default risk and may face debt constraints.We demonstrate that firm-specific debt constraints and endogenousrisk premia, based on collateralized borrowing, affect the assetvalue of the firm and, in turn, the collateral value of thefirm. In order to explore the interdependence of debt financeand asset pricing of firms, we endogenize default premia andborrowing constraints in a production-based asset pricing model.In this context then the dynamic decision problem of maximizingthe present value of the firm faces an additional constraintgiving rise to the debt-dependent firm value. We solve for theasset value of the firm with debt finance by the use of numericaldynamic programming. This allows us to solve the debt controlproblem and to compute sustainable debt as well as the firm’sdebt value.     

Municipal Debt and Marginal Tax Rates: Is There a Tax Premium in Asset Prices?

We study the marginal tax rate incorporated into short‐term municipal rates using municipal swap market data. Using an affine model, we identify the marginal tax rate and the credit/liquidity spread in 1‐week tax‐exempt rates, as well as their associated risk premia. The marginal tax rate averages 38.0% and is related to stock, bond, and commodity returns. The tax risk premium is negative, consistent with the strong countercyclical nature of after‐tax fixed‐income cash flows. These results demonstrate that tax risk is a systematic asset pricing factor and help resolve the muni‐bond puzzle.     

Price uncertainty and corporate value

This study examines the sensitivity of equity values of oil producers to changes in the uncertainty of future oil prices. We document that this sensitivity is negatively correlated with a firm's debt ratio and its production costs. These results indicate that companies that are more likely to experience financial distress or underinvestment from low cash flows are adversely affected by increases in the uncertainty of future cash flows. We conclude that corporate risk management can increase shareholder value by reducing the expected costs of financial distress and underinvestment.     

An Anatomy of Commodity Futures Risk Premia

We identify two types of risk premia in commodity futures returns: spot premia related to the risk in the underlying commodity, and term premia related to changes in the basis. Sorting on forecasting variables such as the futures basis, return momentum, volatility, inflation, hedging pressure, and liquidity results in sizable spot premia between 5% and 14% per annum and term premia between 1% and 3% per annum. We show that a single factor, the high‐minus‐low portfolio from basis sorts, explains the cross‐section of spot premia. Two additional basis factors are needed to explain the term premia.     

How Big Are the Tax Benefits of Debt?

I integrate under firm-specific benefit functions to estimate that the capitalized tax benefit of debt equals 9.7 percent of firm value (or as low as 4.3 percent, net of personal taxes). The typical firm could double tax benefits by issuing debt until the marginal tax benefit begins to decline. I infer how aggressively a firm uses debt by observing the shape of its tax benefit function. Paradoxically, large, liquid, profitable firms with low expected distress costs use debt conservatively. Product market factors, growth options, low asset collateral, and planning for future expenditures lead to conservative debt usage. Conservative debt policy is persistent.     

Have the tax benefits of debt been overestimated?

We re-examine the claim that many corporations are underleveraged in that they fail to take full advantage of debt tax shields. We show prior results suggesting underleverage stems from biased estimates of tax benefits from interest deductions. We develop improved estimates of marginal tax rates using a non-parametric procedure that produces more accurate estimates of the distribution of future taxable income. We show that additional debt would provide firms with much smaller tax benefits than previously thought, and when expected distress costs and difficult-to-measure non-debt tax shields are also considered, it appears plausible that most firms have tax-efficient capital structures.     

Consumption, Dividends, and the Cross Section of Equity Returns

We show that aggregate consumption risks embodied in cash flows can account for the puzzling differences in risk premia across book‐to‐market, momentum, and size‐sorted portfolios. The dynamics of aggregate consumption and cash flow growth rates, modeled as a vector autoregression, are used to measure the consumption beta of discounted cash flows. Differences in these cash flow betas account for more than 60% of the cross‐sectional variation in risk premia. The market price for risk in cash flows is highly significant. We argue that cash flow risk is important for interpreting differences in risk compensation across assets.     

The Determination of the Seniority Structure of Debt: Theory and Evidence

The purposes of this paper are to provide a theory of determining the firm's optimal seniority structure of debt and examine the relation between the firm's seniority structure of debt and its characteristics. Unlike previous studies, we develop a theoretical model which explicitly includes the benefits and costs associated with senior debt financing, corporate taxes, risk-aversion in the capital market, and costs of financial distress. We next show how a value-maximized firm searches for the optimal trade-off among the present values of the tax advantage of debt, loss of tax credits, expected costs of financial distress, costs of senior debt financing, and benefit of limited liability. Numerical analysis results show that the firm's value is not only a strictly concave function of its capital structure (with a unique global maximum), but also a strictly concave function of its mix of senior and junior debts (with a unique global maximum). We then show that a firm's optimal seniority structure of debt (i.e. the market value of senior debt divided by the sum of the market values of senior and junior debts) increases for low levels of asset riskiness and decreases when asset riskiness becomes sufficiently great. Our model also suggests that a firm's optimal seniority structure of debt increases for low levels of growth opportunities and decreases for high levels of growth opportunities. We test the predictions of our model on the relation between the firm's seniority structure of debt and its characteristics by using the data for the firms in COMPUSTAT over the 1972 through 1991 time period. The empirical evidence is consistent with our theoretical predictions.     

An Empirical Model of Optimal Capital Structure1

The authors provide a reasonably user‐friendly and intuitive model for arriving at a company's optimal, or value‐maximizing, leverage ratio that is based on the estimation of company‐specific cost and benefit functions for debt financing. The benefit functions are downward‐sloping, reflecting the drop in the incremental value of debt with increases in the amount used. The cost functions are upward‐sloping, reflecting the increase in costs associated with increases in leverage. The cost functions vary among companies in ways that reflect differences in corporate characteristics such as size, profitability, dividend policy, book‐to‐market ratio, and asset collateral and redeployability. The authors use these cost and benefit functions to produce an estimate of a company's optimal amount of debt. Just as equilibrium in economics textbooks occurs where supply equals demand, optimal capital structure occurs at the point where the marginal benefit of debt equals the marginal cost. The article illustrates optimal debt choices for companies such as Barnes & Noble, Coca‐Cola, Six Flags, and Performance Food Group. The authors also estimate the net benefit of debt usage (in terms of the increase in firm or enterprise value) for companies that are optimally levered, as well as the net cost of being underleveraged for companies with too little debt, and the cost of overleveraging for companies with too much. One critical insight of the model is that the costs associated with overleveraging appear to be significantly higher, at least for some companies, than the costs of being underleveraged.     

Can broker-dealer client surveys provide signals for debt investing?

We use a novel data set to study return predictability in debt markets. The data are collected from J.P. Morgan’s periodic surveys on its clients’ outlook for changes in US Treasury yields and corporate credit spreads. We document that simple signals constructed from such surveys predict excess returns on debt portfolios formed on the basis of duration (2-years minus zero) or credit quality (BBB minus AAA). A linear trading strategy placing equal weight on Treasury and Credit signals has an annualized Information Ratio equal to 1.18, before transaction costs. We also show that predictability is likely to stem from private information possessed by survey respondents rather than from risk premia.     

Closing the Ledger

Using a unique, hand‐collected final dataset of 57 management buy‐outs in distress, this paper analyses the determinants of bankruptcy costs under the UK's receivership regime. We show that the direct costs of receivership consume a significant percentage of the receivership proceeds, with mean receivership costs equal to 30% of receivership proceeds. Importantly we find that while the average length of receivership was 3.0 years, 95% of repayments are made on average within 1.9 years. Our findings do not support the argument that multiple lenders create inefficiencies resulting in significantly lower secured creditor recovery rates. However, when there are multiple secured lenders, the senior secured lender gains at the expense of other secured creditors. We find that receivership costs are positively related to the proportion of secured debt repaid and that, consistent with the presence of a scale effect, the relative significance of receivership costs declines as firm size grows. Receiverships last longer the larger the amount of debt owed to the secured lenders.     

The Cost of Debt

We use exogenous variation in tax benefit functions to estimate firm‐specific cost of debt functions that are conditional on company characteristics such as collateral, size, and book‐to‐market. By integrating the area between the benefit and cost functions, we estimate that the equilibrium net benefit of debt is 3.5% of asset value, resulting from an estimated gross benefit (cost) of debt equal to 10.4% (6.9%) of asset value. We find that the cost of being overlevered is asymmetrically higher than the cost of being underlevered and that expected default costs constitute only half of the total ex ante costs of debt.     

The non-neutrality of debt in investment timing: a new NPV rule

Summary Limited liability debt financing of irreversible investments can affect investment timing through an entrepreneur’s option value, even after compensating a lender for expected default losses. This non-neutrality of debt arises from an entrepreneur’s unique investment opportunity, and it is shown in a standard model of irreversible investment that includes the equilibrium effect of a competitive lending sector. The analysis is partial, in that it takes as exogenously given an entrepreneur’s use of debt. Intuitively, limited liability lowers downside risk for the entrepreneur by truncating the lower tail of risks, and lowers the investment threshold. Compensating the lender for expected default losses reduces project profitability to the entrepreneur, and increases the investment threshold. The net effect is negative, because lower downside risk has an additional impact on the option value of delaying investment. The standard NPV rule in real options theory implicitly assumes debt to be neutral. With non-neutrality of debt, an investment threshold is higher than investment cost, but lower than the standard NPV rule. Comparisons with other standard investment thresholds show similar relationships.     

Post-Tax Capital Investment Appraisal: Plant and Machinery

Tax considerations are important for companies which are no longer tax exhausted. Taxation has a major impact upon project yield and net present value (NPV) for capital investment in plant and machinery. This paper uses the weighted average cost of capital model to demonstrate that the impact of corporate taxation upon NPV need not be in the same direction as the impact upon yield. The NPV is reduced by the nominal 35% rate of corporation tax only when the pre-tax yield is very high; for low yielding projects the post-tax NPV can range from less than zero per cent to over 100% of the pre-tax NPV depending upon the gearing. The tax deductibility of the costs of the debt finance component of capital expenditure has a major and subtle interaction with other parameters which always favours high gearing.