Optimal Capital Structure,Endogenous Bankruptcy,and the Term Structure of Credit Spreads

This article examines the optimal capital structure of a firm that can choose both the amount and maturity of its debt. Bankruptcy is determined endogenously rather than by the imposition of a positive net worth condition or by a cash flow constraint. The results extend Leland's (1994a) closed-form results to a much richer class of possible debt structures and permit study of the optimal maturity of debt as well as the optimal amount of debt. The model predicts leverage, credit spreads, default rates, and writedowns, which accord quite closely with historical averages. While short term debt does not exploit tax benefits as completely as long term debt, it is more likely to provide incentive compatibility between debt holders and equity holders. Short term debt reduces or eliminates “asset substitution” agency costs. The tax advantage of debt must be balanced against bankruptcy and agency costs in determining the optimal maturity of the capital structure. The model predicts differently shaped term structures of credit spreads for different levels of risk. These term structures are similar to those found empirically by Sarig and Warga (1989). Our results have important implications for bond portfolio management. In general, Macaulay duration dramatically overstates true duration of risky debt, which may be negative for “junk” bonds. Furthermore, the “convexity” of bond prices can become “concavity.”     

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.     

Why Have Debt Ratios Increased for Firms in Emerging Markets?

I study trends in capital structure between 1980 and 2004 in a sample of over 11,000 firms from 34 emerging markets. The average firm's market‐value debt ratio rose by 15 percentage points over this quarter century. I study how this rise in leverage was influenced by firm‐level factors and by the availability of debt financing at the country level. The central finding is that the increase in debt ratios can largely be attributed to changes in the characteristics of emerging market firms over this period. For the average firm, the most prominent determinants of capital structure – size, profitability, asset tangibility, and growth opportunities – all shifted in the direction implying a higher optimal level of debt. At the country level, increased financial development within the country is associated with lower debt ratios, but increased financial openness to foreign markets is associated with higher debt ratios.     

Capital Structure and Debt Priority

We study a defaultable firm's debt priority structure in a simple structural model where the firm issues senior and junior bonds and is subject to both liquidity and solvency risks. Assuming that the absolute priority rule prevails and that liquidation is immediate upon default, we determine the firm's interior optimal priority structure along with its optimal capital structure. We also obtain closed‐form solutions for the market values of the firm's debt and equity. We find that the magnitude of the spread differential between junior and senior bond yields is positively, but not linearly related to the total debt level and the riskiness of assets. Finally, we provide an in‐depth analysis of probabilities of default and the term structure of credit spreads.     

Managerial entrenchment, equity payout and capital structure

I develop a contingent claims model to examine the impacts of managerial entrenchment on capital structure and security valuation. The analysis shows that managers’ self-interested leverage choices deviate significantly from the optimal leverages that maximize firm values, partially explaining the suboptimal leverage ratios observed empirically (Graham, 2000). Both the extent and sensitivity of the deviations are affected by firm characteristics, debt features and default solutions. The shareholder-manager conflicts over risk level and cash payout vary dynamically with a firm’s financial health. Managerial entrenchment does not mitigate the agency problems of debt since managers’ discretionary decisions on milking properties or asset substitution could be driven by incentives to increase their own utility.     

A MULTIPERIOD MEAN-VARIANCE MODEL OF OPTIMAL CAPITAL STRUCTURE

The continuing interest in the capital structure issue among financial researchers is evidenced by the stream of capital structure models that have appeared in the literature. Much of this research has used a risk-neutral and/or a single-period framework. In this paper, we develop a capital structure model for multiperiod firms and allow for the firm's cash flows to grow over time, for the firm to issue new debt, and for two types of bankruptcy costs to occur. The types of bankruptcy costs that occur are determined by the firm's uncertain operating cash flows and negotiations between the firm and creditors. Risk is priced via the Sharpe-Lintner capital asset pricing model. Multiperiod risk-priced models, we argue, realistically represent actual firms and are thus an important step toward the development of more testable and usable models of capital structure. We execute a demonstration example in which the value of the levered firm achieves a maximum and discuss the steps the firm would take to maximize shareholder wealth within this example. The example illustrates that the value of the firm passes through an interior optimum as the promised debt payment is increased. A simulation of the effect of changes in firm-specific parameters shows that the model exhibits expected and appealing relationships between these parameters and the value of the levered firm.     

The Effect of Interest Rates on the Value of Corporate Assets and the Risk Premia of Corporate Debt

A growing number of papers have applied option pricing techniques to the valuation of risky debt. This paper deals directly with how a firm's relationship to interest rates affects its debt. A sequential binomial model is used to price the zero-coupon bonds of a firm whose value is related to interest rate changes.The results show that the strength of the relationship between firm value and interest rates (interest-rate risk) can have a significant impact on the value of a firm's debt. The model produces its most powerful results when the volatility of firm value is high and the term structure has a steep (negative or positive) slope; there is no impact when the term structure is flat. Our results indicate that empirical studies of yield spreads may have severe shortcomings if the relationship of firm value to interest rate changes is ignored.     

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.     

Dynamic Capital Structure Choice: Theory and Tests

This paper develops a model of dynamic capital structure choice in the presence of recapitalization costs. The theory provides the optimal dynamic recapitalization policy as a function of firm-specific characteristics. We find that even small recapitalization costs lead to wide swings in a firm's debt ratio over time. Rather than static leverage measures, we use the observed debt ratio range of a firm as an empirical measure of capital structure relevance. The results of empirical tests relating firms' debt ratio ranges to firm-specific features strongly support the theoretical model of relevant capital structure choice in a dynamic setting.     

Subsidiary debt,capital structure and internal capital markets

I study external debt issued by operating subsidiaries of diversified firms. Consistent with Kahn and Winton's [2004. Moral hazard and optimal subsidiary structure for financial institutions. Journal of Finance 59, 2537–2575] model, where subsidiary debt mitigates asset substitution, I find firms are more likely to use subsidiary debt when their divisions vary more in risk. Consistent with subsidiary debt mitigating the free cash flow problem, I find that subsidiaries are more likely to have their own external debt when they have fewer growth options and higher cash flow than the rest of the firm. Finally, I find that subsidiary debt mitigates the “corporate socialism” and “poaching” problems modeled in theories of internal capital markets.     

Optimal capital structure and the impact of time-to-build

We develop a dynamic investment options model with optimal capital structure and evaluate the effect of time-to-build on firm value and leverage choices. With time-to-build the firm increases initial leverage in order to reduce the impact of delayed cash flows resulting from time-to-build. The impact of time-to-build is more severe the higher the revenue volatility and competitive erosion, and when the firm issues long-term debt. Time-to-build is shown to have a substantial impact on firm values for plausible parameter values.     

Managerial Preference,Asymmetric Information,and Financial Structure

If firm performance affects managers' wealth or reputation, preferences of managers dominate firms' financing decisions. When information about real asset investment is symmetric, managers finance exclusively with equity. If managers know more about asset quality than do investors and if managers are sufficiently risk averse, they signal high-quality projects with debt. Increases in collateral value decrease risky debt use. Increases in interest rates that do not change productive opportunities increase debt use. The explanation for these and further results is based on underpricing of equity and overpricing of debt at the margin.     

Valuation of defaultable bonds and debt restructuring

In this paper we develop a contingent valuation model for zero-coupon bonds with default. In order to emphasize the role of maturity time and place of the lender's claim in a firm's debt hierarchy, we consider a firm that issues two bonds with different maturities and different seniorage. The model allows us to analyze the implications of both debt renegotiation and capital structure of a firm on the prices of bonds. We obtain that renegotiation brings about a significant change in the bond prices and that the effect is dispersed through various channels: increasing the value of the firm, reallocating payments, and avoiding costly liquidation. Moreover, the presence of two creditors leads to qualitatively different implications for pricing, while emphasizing the importance of bond covenants and renegotiation of the entire debt.     

Human Capital,Bankruptcy, and Capital Structure

We derive the optimal labor contract for a levered firm in an economy with perfectly competitive capital and labor markets. Employees become entrenched under this contract and so face large human costs of bankruptcy. The firm's optimal capital structure therefore depends on the trade‐off between these human costs and the tax benefits of debt. Optimal debt levels consistent with those observed in practice emerge without relying on frictions such as moral hazard or asymmetric information. Consistent with empirical evidence, persistent idiosyncratic differences in leverage across firms also result. In addition, wages should have explanatory power for firm leverage.     

TOWARD A MORE COMPLETE MODEL OF OPTIMAL CAPITAL STRUCTURE

Most corporate finance practitioners understand the trade-off involved in making effective use of debt capacity while safeguarding the firm's ability to execute its business strategy without disruption. But quantifying that trade-off to arrive at an optimal level of debt can be a complicated and challenging task. This paper develops a simulation model of capital structure that starts by generating multiple estimates of market rates (LIBOR, currency rates) and corresponding company operating cash flows. To arrive at an optimal capital structure, the model then incorporates the shareholder value effects of alternative financing decisions by directly measuring the costs of financial distress, including the costs of missed investment opportunities and higher working capital requirements.
The model generates both a target credit rating and a lower fallback rating that permits a higher level of debt to maintain investments and dividends when operating cash flows are weak. As the model shows, companies with volatile cash flows and significant investment opportunities can add substantial shareholder value by establishing a fallback credit rating that is one or two notches below the target rating. The model also optimizes the mix of fixed versus floating debt, the maturity structure, and the currency composition. Another distinctive feature of the model is its ability to estimate the expected cost of alternative liability structures that can provide the liquidity insurance necessary to sustain the firm through periods of severe stress. This cost turns out to be quite small relative to the total market capitalization of the average firm.     

The impact of debt on market reactions to the revaluation of noncurrent assets

This study provides evidence that noncurrent asset revaluations are differentially considered by market participants based on the level of debt in the capital structure. Contracting theory (e.g. Brown et al., Abacus 28 (1992) 36) implies that revaluations made by firms with high-debt levels may be viewed as being opportunistic, while revaluations for firms with low-debt levels may be viewed as reducing information asymmetry between the firm and capital providers. For a sample of New Zealand firm/years that excludes certain observations with extreme stock returns, we find that revaluations of fixed assets are more value-relevant for firms with low leverage than for firms with high leverage. This suggests that the value relevance of fixed asset valuations depends on management's motivation for making the revaluation. The results of the research should be considered within certain limitations such as a small sample.     

Valuing Companies with Cash‐Flow@Risk

The classic DCF approach to capital budgeting—the one that MBA students in the world's top business schools have been taught for the last 30 years—begins with the assumption that the corporate investment decision is “independent of” the financing decision. That is, the value of a given investment opportunity should not be affected by how a company is financed, whether mainly with debt or with equity. A corollary of this capital structure “irrelevance” proposition says that a company's investment decision should also not be influenced by its risk management policy—by whether a company hedges its various price exposures or chooses to leave them unhedged. In this article, the authors—one of whom is the CFO of the French high‐tech firm Gemalto—propose a practical alternative to DCF that is based on a concept they call “cash‐flow@risk.” Implementation of the concept involves dividing expected future cash flow into two components: a low‐risk part, or “certainty equivalent,” and a high‐risk part. The two cash flow streams are discounted at different rates (corresponding to debt and equity) when estimating their value. The concept of cash‐flow@risk derives directly from, and is fully consistent with, the concept of economic capital that was developed by Robert Merton and Andre Perold in the early 1990s and that has become the basis of Value at Risk (or VaR) capital allocation systems now used at most financial institutions. But because the approach in this article focuses on the volatility of operating cash flows instead of asset values, the authors argue that an internal capital allocation system based on cash‐flow@risk is likely to be much more suitable than VaR for industrial companies.     

The Determinants of Debt Maturity Structure: Evidence from France,Germany and the UK

We examine the determinants of the debt maturity structure of French, German and British firms. These countries represent different financial and legal traditions that may have implications on corporate debt maturity structure. Our model incorporates the factors representing three major theories (tax considerations, liquidity and signalling, and contracting costs) of debt maturity. It also controls for capital market conditions. The results confirm the applicability of most theories of debt maturity structure for the UK firms. However, the evidence from France and Germany are mixed. Overall the findings suggest that the debt maturity structure of a firm is determined by firm‐specific factors and the country's financial systems and institutional traditions in which it operates.     

Optimal Security Design and Dynamic Capital Structure in a Continuous-Time Agency Model

We derive the optimal dynamic contract in a continuous‐time principal‐agent setting, and implement it with a capital structure (credit line, long‐term debt, and equity) over which the agent controls the payout policy. While the project's volatility and liquidation cost have little impact on the firm's total debt capacity, they increase the use of credit versus debt. Leverage is nonstationary, and declines with past profitability. The firm may hold a compensating cash balance while borrowing (at a higher rate) through the credit line. Surprisingly, the usual conflicts between debt and equity (asset substitution, strategic default) need not arise.     

INFLATION,INVESTMENT, AND DEBT

In this paper the effect of inflation on firms' investment and debt-financing decisions is examined. Inflation affects optimal investment and financing directly through the probability of accounting loss and the real value of depreciation and interest tax shields. In addition, when corporate and differential personal taxes cause investment and financing decisions to interact, inflation has indirect effects on these decisions through their interactions. In general, the overall effects of inflation on optimal investment and debt are ambiguous in sign. For tax-exempt firms, however, optimal investment and debt are independent of inflation. For firms that are always in a tax-paying position, higher inflation reduces optimal investment without affecting optimal debt. Furthermore, inflation causes total firm value to decrease if the depreciation rate exceeds the firm's debt/asset ratio.