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Financial Restructuring
Abstract
Any company dealing with a corporate restructuring process has a lot of problems. To solve them it’s necessary to understand their nature and causes. Most problems in a company come from the operating aspects, not from the financial ones. Consequently, before trying to set up a permanent financial solution for a company, we need to understand why the company is not generating enough cash and we have to conceive a realistic and doable business plan to address the critical issues. In other words, before trying to finance an operational problem, try to solve it. Financing operating inefficiencies is the best way to end in financial distress.
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Most real-world barrier option values have no analytic solutions, either because the barrier structure is complex or because of volatility skews in the market. Numerical solutions are therefore a necessity, but options with barriers are notoriously difficult to value numerically on binomial or multinomial trees or on finite-difference lattices. Their values converge very slowly as the number of tree or lattice levels increases, often requiring unattainably large computing times for even modest accuracy. This article analyzes the biases implicit in valuing options with barriers on a lattice and suggests a method for enhancing their numerical solution. This method helps to correct these biases and works well in practice.
Contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects. Unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive. This article extends the literature on multinomial approximating models. Specifically, new multinomial models are presented that include as special cases existing models. The more general models are shown to be computationally more efficient.
A proportional hazards model with competing risks is specified and is extended to correct for the possibility of originator bias. The model is used to examine the ability of option-theoretic models of mortgage pricing to forecast commercial mortgage defaults. Among the findings, those especially of interest include the influence of contemporaneous loan-to-value and debt-service-coverage ratios on commercial mortgage default probabilities. The paper also finds that option-theoretic models of mortgage pricing are quite capable of producing default estimates that fit the actual default rates well, especially when the model is corrected for originator bias.
Most derivative securities must be priced by numerical techniques. These models contain “distribution error” and “nonlinearity error”. The Adaptive Mesh Model (AMM) sharply reduces nonlinearity error by grafting one or more small sections of fine high-resolution lattice onto a tree with coarser time and price steps. Three different AMM structures are presented, one for pricing ordinary options, one for barrier options, and one for computing delta and gamma efficiently. The AMM approach can be adapted to a wide variety of contingent claims. For some common problems, accuracy increases by several orders of magnitude with no increase in execution time.
Equilibrium in the market for real assets requires that the price of those assets be bid up to reflect the tax shields they can offer to levered firms.Thus there must be an equality between the market values of real assets and the values of optimally levered firms. The standard measure of the advantage to leverage compares the values of levered and unlevered assets, and can be misleading and difficult to interpret. We show that a meaningful measure of the advantage to debt is the extra rate of return, net of a market premium for bankruptcy risk, earned by a levered firm relative to an otherwise-identical unlevered firm. We construct an option valuation model to calculate such a measure and present extensive simulation results. We use this model to compute optimal debt maturities, show how this approach can be used for capital budgeting, and discuss its implications for the comparison of bankruptcy costs versus tax shields.
Much of the literature on pricing commercial mortgages and commercial mortgage-backed securities has assumed homogeneity in prepayment penalty structure. In this paper, we provide evidence that such an assumption is inappropriate and examine the effect of penalty structures observed in actual contracts. After conducting preliminary simulations, we present hazard models estimated from data on 1,165 multifamily mortgage loans to show how empirical prepayment rates vary with alternative penalty structures. While yield maintenance and lockout provisions are relatively more effective than fixed or step down structures in reducing or postponing prepayment, none completely eliminates the risk. Our empirical results generally confirm the theoretical findings of Kelly and Slawson (2001).
We present here an analytical process for generating the firm's value [FV] and the weighted-average cost of capital [WACC] curves, with intent to locate the optimal capital structure. The method takes into consideration the relationship between debt, equity and taxes, and places emphasis on the effects of default risk, as well as on the assumptions that underlie the curves. In relation to the proposed approach, it is shown that the conventional one, which is used more commonly in practice, is flawed. 1 --
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.
Long-established as a definitive resource by Wall Street professionals, The Complete Guide to Option Pricing Formulas has been revised and updated to reflect the realities of today's options markets. The Second Edition contains a complete listing of virtually every pricing formula_ all presented in an easy-to-use dictionary format, with expert author commentary and ready-to-use programming code.
The Second Edition of this classic guide now includes more than 60 new option models and formulas…extensive tables providing an overview of all formulas…new examples and applications…and an updated CD containing all pricing formulas, with VBA code and ready-to-use Excel spreadsheets.
The volume also features several new chapters covering such things as: option sensitivities, discrete dividend, commodity options, and two chapters on numerical methods covering trees, finite difference and Monte Carlo Simulation.
A great many people provided comments on early versions of this paper which led to major improvements in the exposition. In addition to the referees, who were most helpful, the author wishes to express his appreciation to Dr. Harry Markowitz of the RAND Corporation, Professor Jack Hirshleifer of the University of California at Los Angeles, and to Professors Yoram Barzel, George Brabb, Bruce Johnson, Walter Oi and R. Haney Scott of the University of Washington.
Pricing and hedging barrier options using a binomial lattice can be quite delicate. If the barrier is not constant, or if there are multiple barriers, then in all likelihood binomial lattices will produce erroneous answers even when a large number of time steps are used. While in some cases the time partitions of the binomial method can be carefully chosen so as to reduce the bias, for many barrier contracts more efficient procedures exist.This article explains how a very simple and extremely efficient trinomial lattice procedure can be used to price and hedge most types of exotic barriers.
This article develops a new trinomial tree model for barrier options. It is well-known that for barrier options, the positions of nodes in the tree with respect to the barrier value are critical. We use a time-dependent shift to position the tree optimally with respect to the barrier. The model is very flexible and can be used to price options with time-varying barrier structures. It can be used to price knock-in and knock-out options based on either one or two underlying assets, including those with time-varying barriers - single or double. Traditional lattice models all have difficulties when the underlying asset price is very close to the barrier. This model does not suffer from that limitation. Also, in many applications, the barrier condition is based on the daily or weekly fixings. A simple solution for the discrete-time barrier observation is advanced, which enables us to uncover the price differences among barrier options with different observation frequencies.
This paper deals with the nature of option interactions and the valuation of capital budgeting projects possessing flexibility in the form of multiple real options. It identifies situations where option interactions can be small or large, negative or positive. Interactions generally depend on the type, separation, degree of being “in the money,” and the order of the options involved. The paper illustrates, through a generic example, the importance of properly accounting for interactions among the options to defer, abandon, contract or expand investment, and switch use. It is shown that the incremental value of an additional option, in the presence of other options, is generally less than its value in isolation, and declines as more options are present. Therefore, valuation errors from ignoring a particular option may be small. However, configurations of real options exhibiting precisely the opposite behavior are identified. Comparative statics results confirm that the value of flexibility, despite interactions, manifests familiar option properties.
This paper summarizes the findings of the authors' recent survey of 392 CFOs about the current practice of corporate finance, with main focus on the areas of capital budgeting and capital structure. The findings of the survey are predictable in some respects but surprising in others. For example, although the discounted cash flow method taught in our business schools is much more widely used as a project evaluation method than it was ten or 20 years ago, the popularity of the payback method continues despite shortcomings that have been pointed out for years. In setting capital structure policy, CFOs appear to place less emphasis on formal leverage targets that reflect the trade-off between the costs and benefits of debt than on “informal” criteria such as credit ratings and financial flexibility. And despite the efforts of academics to demonstrate that EPS dilution per se should be irrelevant to stock valuation, avoiding dilution of EPS was the most cited reason for companies reluctance to issue equity.
But despite such apparent contradictions between theory and practice, finance theory does seem to be gaining ground. For example, large companies were much more likely than their smaller counterparts to use DCF and NPV techniques, while small firms still tended to rely heavily on the payback criterion. And a majority of the CFOs of the large companies said they had “strict” or “somewhat strict” target debt ratios, whereas only a third of small firms claimed to have such targets.
What does the future hold? On the one hand, the authors suggest that we are likely to see greater corporate acceptance of certain aspects of financial theory, including the use of real options techniques for evaluating corporate investments. But we are also likely to see further modifications and refinements of the theory, particularly with respect to smaller companies that have limited access to capital markets.
A general formula is derived for the price of a security whose value under specified conditions is a known function of the value of another security. Although the formula can be derived using the arbitrage technique of Black and Scholes, the alternative approach of continuous-time portfolio strategies is used instead. This alternative derivation allows the resolution of some controversies surrounding the Black and Scholes methodology. Specifically, it is demonstrated that the derived pricing formula must be continuous with continuous first derivatives, and that there is not a ‘pre-selection bias’ in the choice of independent variables used in the formula. Finally, the alternative derivation provides a direct proof of the Modigliani-Miller theorem even when there is a positive probability of bankruptcy.
Volatility, or the variability of the underlying asset, is one of the key fundamental components of property derivative pricing and in the application of real option models in development analysis. There has been relatively little work on volatility in real terms of its application to property derivatives and the real options analysis. Most research on volatility stems from investment performance (Nathakumaran & Newell (1995), Brown & Matysiak 2000, Booth & Matysiak 2001). Historic standard deviation is often used as a proxy for volatility and there has been a reliance on indices, which are subject to valuation smoothing effects. Transaction prices are considered to be more volatile than the traditional standard deviations of appraisal based indices. This could lead, arguably, to inefficiencies and mis-pricing, particularly if it is also accepted that changes evolve randomly over time and where future volatility and not an ex-post measure is the key (Sing 1998). If history does not repeat, or provides an unreliable measure, then estimating model based (implied) volatility is an alternative approach (Patel & Sing 2000). This paper is the first of two that employ alternative approaches to calculating and capturing volatility in UK real estate for the purposes of applying the measure to derivative pricing and real option models. It draws on a uniquely constructed IPD/Gerald Eve transactions database, containing over 21,000 properties over the period 1983-2005. In this first paper the magnitude of historic amplification associated with asset returns by sector and geographic spread is looked at. In the subsequent paper the focus will be upon model based (implied) volatility.
If options are correctly priced in the market, it should not be possible to make sure profits by creating portfolios of long and short positions in options and their underlying stocks. Using this principle, a theoretical valuation formula for options is derived. Since almost all corporate liabilities can be viewed as combinations of options, the formula and the analysis that led to it are also applicable to corporate liabilities such as common stock, corporate bonds, and warrants. In particular, the formula can be used to derive the discount that should be applied to a corporate bond because of the possibility of default.
This paper examines the theory of commercial mortgage default and tests it using a data set of 2,899 loan histories provided by a major multi-line insurance company. A default model is estimated which relates subsequent default incidence and timing to contemporaneous loan term, borrower, property and economic/market conditions. Maximum likelihood estimation is used to estimate a hazard function predicting conditional probability of default over time. Results confirm many expected default relationships, in particular the dominance of loan terms and property value trends over time in affecting default. The effectiveness of the model in discriminating between "good" and "bad" loans is explored. Implications for underwriting practice and credit risk diversification are noted. Finally, suggestions are made for extending these results in pricing applications. Copyright American Real Estate and Urban Economics Association.
This study examines the financing decisions of real estate investors and the choice of capital structure when acquiring income-producing properties. Drawing from the literature in finance and real estate, we develop a capital structure model for real estate investment and derive six hypotheses regarding the relationship of the overall loan-to-value ratio chosen by an investor to selected characteristics of the investment. The hypotheses are then tested using financing data from a sample of apartment and commercial transactions over a fifteen-year period in a specific real estate market. The empirical findings strongly support the importance of depreciation deductions, financial distress costs, capital constraints, tax rates, and interest rates as determinants of the capital structure of real estate investors. Copyright American Real Estate and Urban Economics Association.
This paper examines the optimal leverage strategy for real estate investors who are investing in income-producing properties. Within a discounted cash flow context, the investment objective for the equity investor is to maximize the contribution to net present value of using mortgage financing. Utilizing more debt decreases the required equity investment and increases the size of the tax shelter. On the other hand, as the loan-to-value ratio increases, the interest rate charged by the lender increases, which indicates a higher cost of debt. This paper goes beyond the simple conventional wisdom that debt financing should be used when financial leverage is positive by developing an equation that allows one to determine the optimal level of debt financing to use when positive leverage is possible. The optimal loan-to-value ratio is found to be a function of the investor's characteristics. Several hypotheses about the relationships between such an optimal loan-to-value ratio and the investor's characteristics are derived.
This article examines the cross-sectional and time-series determinants of commercial mortgage credit spreads as well as the terms of the mortgages. Consistent with theory, our empirical evidence indicates that mortgages on property types that tend to be riskier and have greater investment flexibility exhibit higher spreads. The relationship between the loan-to-value (LTV) ratio and spreads is relatively weak, which is probably due to the endogeneity of the LTV choice. However, the average LTV ratio per lender has a strong positive relation with credit spreads, which is consistent with the idea that lenders specialize in mortgages with either high or low levels of risk, and that high LTV mortgages require substantially higher spreads. Finally, we observe that spreads widen and mortgage terms become stricter after periods of poor performance of the real estate markets and after periods of greater default rates of outstanding real estate loans. Copyright 2005 by the American Real Estate and Urban Economics Association
This paper 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 [1994] 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 cost. The tax advantage of debt must be balanced against bankruptcy and agency cost 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]. The model has 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".
We develop a simple approach to valuing risky corporate debt that incorporates both default and interest rate risk. We use this approach to derive simple closed-form valuation expressions for fixed and floating rate debt. The model provides a number of interesting new insights about pricing and hedging corporate debt securities. For example, we find that the correlation between default risk and the interest rate has a significant effect on the properties of the credit spread. Using Moody's corporate bond yield data, we find that credit spreads are negatively related to interest rates and that durations of risky bonds depend on the correlation with interest rates. This empirical evidence is consistent with the implications of the valuation model. Copyright 1995 by American Finance Association.
This paper empirically investigates a contingent-claims model of commercial mortgage pricing. The authors find that the magnitude of the observed default premia for a sample of nonprepayable fixed rate bullet mortgages can be explained by the contingent-claims model. In addition, the model explains a significant proportion of the period to period changes in the default premia. However, given an assumed negative correlation between building value changes and interest rate changes, the model's risk structure tends to increase less steeply with increasing maturity than the observed risk structure. Copyright 1989 by American Finance Association.
This article examines corporate debt values and capital structure in a unified analytical framework. It derives closed-form results for the value of long-term risky debt and yield spreads, and for optimal capital structure, when firm asset value follows a diffusion process with constant volatility. Debt values and optimal leverage are explicitly linked to firm risk, taxes, bankruptcy costs, risk-free interest rates, payout rates, and bond covenants. The results elucidate the different behavior of junk bonds versus investment-grade bonds, and aspects of asset substitution, debt repurchase, and debt renegotiation. Copyright 1994 by American Finance Association.
IN A RECENT PAPER Black and Scholes [3] presented an explicit equilibrium model for valuing options. In this paper they indicated that a similar analysis could potentially be applied to all corporate securities. In other papers, both Merton [8] and Ross [11] noted the broad applicability of option pricing arguments. At the same time Black and Scholes also pointed out that actual security indentures have a variety of conditions that would bring new features and complications into the valuation process. Our objective in this paper is to make some general statements on this valuation process and then turn to an analysis of certain types of bond indenture provisions which are often found in practice. Specifically, we will look at the effects of safety covenants, subordination arrangements, and restrictions on the financing of inter
In this paper, empirical evidence with respect to both the direct and indirect costs of bankruptcy is assessed. This should be of interest for three related reasons. First, there is a need to provide further evidence as to the size of bankruptcy costs. Second, for the first time a proxy methodology for measuring indirect costs of bankruptcy is presented and actually measured. Third, a simple format for measuring the present value of expected bankruptcy costs is compared with the present value of expected tax benefits from interest payments on leverage. This comparison has important implications for the continuing debate as to whether or not an optimum capital structure exists for corporations.
This paper uses an option valuation model of the firm to answer the question, "What magnitude tax advantage to debt is consistent with the range of observed corporate debt ratios?" We incorporate into the model differential personal tax rates on capital gains and ordinary income. We conclude that variations in the magnitude of bankruptcy costs across firms can not by itself account for the simultaneous existence of levered and unlevered firms. When it is possible for the value of the underlying assets to junip discretely to zero, differences across firms in the probability of this jump can account for the simultaneous existence of levered and unlevered firms. Moreover, if the tax advantage to debt is small, the annual rate of return advantage offered by optimal leverage may be so small as to make the firm indifferent about debt policy over a wide range of debt-to-firm value ratios.
This paper studies thirty-one highly leveraged transactions (HLTs) that become financially, not economically, distressed. The net effect of the HLT and financial distress (from pretransaction to distress resolution, market- or industry-adjusted) is to increase value slightly. This finding strongly suggests that, overall, the HLTs of the late 1980s created value. We present quantitative and qualitative estimates of the (direct and indirect) costs of financial distress and their determinants. We estimate financial distress costs to be 10 to 20 percent of firm value. For a subset of firms that do not experience an adverse economic shock, financial distress costs are negligible. Copyright The American Finance Association 1998.
Loss Characteristics of Commercial Mortgage Foreclosures
- B Ciochetti