Optimal exercise strategies for corporate warrants

In this paper, we analyse the optimal exercise strategies for corporate warrants issued by levered firms. For the analysis, we distinguish between two exercise variants, namely the traditional block exercise and competitive exercise in equilibrium. We find that the optimal exercise date under the block condition can be before or after an optimal exercise in equilibrium. Surprisingly, optimal block exercise can occur even without any dividend payments in contrast to the competitive exercise. As a consequence, the asset values and the stock volatility under block exercise fundamentally deviate from those under the competitive exercise variant. Moreover, the value of a warrant in the block case and its exercise strategy do not coincide with those of a corresponding call option which contrasts with the assumption of ‘option-like’ warrant valuation.     

Warrant pricing: a review of empirical research

Recently, several warrant pricing studies have become available for different models as well as for different countries. The most important conclusions that can be drawn from reviewing these studies are: (1) it is not necessary to make a correction on option valuation models for the dilution effect; (2) the only model that systematically outperforms the Black-Scholes (1973) type models is the Square Root model; (3) US and German warrants seem to be priced correctly, while deviations are found for English and Japanese warrants (underpriced by the market) and Swiss and Dutch warrants (overpriced by the market).     

On Testing the Assumptions of the Cash Recovery Rate Approach to the Estimation of Economic Performance

The first purpose of this paper is to investigate the necessary (as opposed to sufficient) assumptions underlying the CRR approach to the estimation of corporate economic performance. By so doing, the general circumstances in which an estimate of corporate economic performance based on CRRs will exactly equal a firm's IRR are identified. It is pointed out that these necessary assumptions are related to the concept of corporate economic performance being invoked (within the general idea that we are trying to estimate a firm's internal rate of return). Second, there is a drawing out of the empirical implications, as to the behaviour of corporate cash flows and CRRs, of the necessary assumptions for the CRR approach to produce an estimate of economic performance equal to a firm's IRR for each of these definitions of corporate economic performance. In particular, it is argued that these empirical implications depend upon the specific manner in which the CRR approach is applied in practice. A third purpose of the paper is to provide some empirical evidence as to whether an example of the practice of using the CRR approach employs data consistent with the necessary assumptions for this particular approach to be valid outlined in the paper. In fact, it turns out that this might not be the case. The evidence casts light on the extent to which CRR-based estimates of corporate economic performance are likely to be reasonable proxies of firms' IRRs.     

The Gap between the Theory and Practice of Corporate Valuation: Survey of European Experts

The valuation of companies or their assets is at the heart of most financing and investment decisions. Over the last five decades, academics have developed several simple and sophisticated models for corporate valuation. Yet valuation estimates of a firm or its assets appear to vary widely among practitioners. It is unclear whether these differences arise from practitioners' use of different valuation models or from differences in their assumptions about the inputs used in those models. To provide some insights into this issue, the authors recently surveyed 365 European finance practitioners with CFAs or equivalent professional degrees. They find that almost all survey respondents use the Discounted Cash Flow (DCF) model (along with some version of Relative Valuation that relies on the use of “comparables”). But the estimation methods of such practitioners for almost all inputs in the DCF model, including beta, the equity market risk premium, leverage, cost of debt, and terminal value, vary widely. This can be a serious problem because even small differences in inputs can cause huge variations in valuations. Such differences arise primarily because theory provides little guidance on how to estimate parameters, leaving practitioners to make their own assumptions and judgments. In sum, the authors' findings suggest that the process of estimating valuation parameters can be as important as the choice of the valuation model itself, and requires the serious attention of academics and practitioners. The authors recommend that key valuation parameter estimates be disclosed in financial and valuation reports. Their findings are also relevant to policy makers because the concept of “fair value” plays such a central role in post‐crisis regulation.     

RISK-ADJUSTED DISCOUNT RATES-EXTENSIONS FROM THE AVERAGE-RISK CASE

This paper provides an approach for developing risk-adjusted discount rates that follows naturally from the standard presentation of the weighted average cost of capital. In addition to examining the implied assumptions about the valuation of corporate debt, the paper shows the pedagogic advantages of the proposed approach.     

Impact of Imperfect Information on the Optimal Exercise Strategy for Warrants

In this paper, we determine the optimal exercise strategy for corporate warrants if investors suffer from imperfect information and we evaluate the impact of this friction on the value of a warrant. For this purpose, we address both exercises at maturity, where imperfect information about the firm value is present, and exercises before maturity which are impacted by imperfect information about the size of the dividend. We model imperfect information so that all warrant holders know that they obtain biased signals of the true state without observing the signals of other warrant holders. The optimal exercise strategy follows from a complex game among warrant holders in which every individual warrant holder must account for the potential signals of the other warrant holders and their resulting exercise decisions. The main findings are that due to imperfect information warrant holders optimally start to exercise their warrants later than without imperfect information. Moreover, a simple block exercise strategy is always an equilibrium strategy for a high degree of imperfect information before maturity, even though a partial exercise can be the unique strategy without imperfect information. Remarkably, imperfect information does not necessarily result in a lower warrant value. As long as a warrant holder has a signal that allows for correct exercise decisions, then imperfect information enhances the warrant value due to suboptimal exercises by other investors.     

Warrant exercise and bond conversion in competitive markets

We develop a theory of warrants held by competitive warrantholders not constrained to exercise their warrants as one block; the theory also applies to convertible bonds held by competitive bondholders not constrained to convert their bonds as one block. We prove that the warrant (bond) price in each of the competitive equilibria is less than or equal to the price in an economy with the block constraint; and for at least one competitive equilibrium the warrant (bond) price equals the warrant (bond) price in the block-constrained economy. We illustrate the paths of competitive warrant exercise and bond conversion and conclude that under realistic assumptions they can be long.     

Taking Real Options Beyond the Black Box

Finance theorists have long argued that DCF undervalues investment opportunities with significant flexibility to respond to future events and that real options valuation methods provide a solution to that problem. But for most corporate managers, real options analysis continues to be a "black box" when applied to real investment decisions.
This paper begins by considering why these approaches have not yet made it to the mainstream of practical application. It then shows how a traditional DCF approach can undervalue a project that provides management with operating flexibility and illustrates a case study that demonstrates to senior management how a real options valuation method with a few clear value drivers can build upon and be made consistent with the traditional DCF framework.
Critical to this process is ensuring consistency with the company's planning assumptions such as future price forecasts and discount rates. The article shows how to separate the static ("optionless") DCF value from the additional real options value that is shown to be a direct consequence of the assumptions about price dynamics.     

Share Option Rewards and Managerial Performance: an Abnormal Performance Index Model

Managerial share option schemes are widely used as a means of motivating and rewarding corporate performance. Such schemes normally adopt a static exercise price; when additional exercise criteria are employed they are often based on earnings per share. A static exercise price does not adjust for economic changes outside the control of management, and earnings per share hurdles have similar limitations. This paper presents a ‘phantom’ managerial option based on relative performance, together with a pricing model for the valuation of the option. The option is developed and demonstrated using an abnormal performance index. It offers a structure which could be used for different forms of performance measurement, and resolves some important criticisms of the reward and incentive effects of traditional schemes.     

Capital budgeting,valuation and personal taxes

This paper examines the relationship between before tax and after tax valuation and uses this to examine the literature on capital budgeting and capital structure in the presence of corporate and personal taxes, a literature which features a bewildering array of valuation formulae. Some of the variation between such formulae naturally arises out of variations in underlying model assumptions; however, in several cases, it arises because there are (by no means obvious) internal inconsistencies. The potential magnitude of the errors that might arise in a capital budgeting context is then explored through sensitivity analysis.     

Fair Terms and Fair Pricing for Multiple Warrant Issues

Abstract

Some firms utilize one or more tranches of warrant issues to supplement their capital base. Unlike exchange-traded options, the exercise of warrants requires the issuance of stock by the company, resulting in a form of dilution. Some previous studies of warrant valuation relied on “the value of the firm,” which is nonobservable, making it difficult to apply the corresponding valuation formula. This paper derives closed-form formulas to value single and multiple tranches of warrants based on the underlying stock price, its volatility, and other known parameter values. The paper first establishes the equivalence of the Black-Scholes formula for both call options and warrants in the case of a single tranche. Thereafter, it considers the impact on the value of previously issued warrants that results when a new tranche of warrants is subsequently issued, showing in each case that fair treatment of the first-issued warrant holders requires an adjustment (due to dilution) in the terms of those warrants and a corresponding modification in the warrants’ value once a second tranche of warrants is issued. To promote such fair treatment, terms of a warrant indenture would specify the nature of the adjustment required when future warrants are issued or exercised, analogous to the antidilution terms related, for example, to stock dividends. Unlike multiple issues of traded options, which are valued independently of one another, multiple warrant issues will be shown to have prices dependent on other warrants outstanding. Also examined is the sensitivity of the fair-value adjustment to changes in the underlying variables, and the theoretical fair-value prices are compared with Black-Scholes prices and with market prices of warrants in the case of two publicly traded companies, each with two warrant issues outstanding. As warrant issues modify the equity structure of a firm, the methodology of valuing warrants presented here will be useful to investment actuaries in situations in which a comprehensive market value for all of a firm’s securities is called for. In addition, risk management practices may sometimes include the use of warrant transactions to hedge stock positions similar to the way that call options are used for that purpose. This may include hedging the risk in equity-linked insurance contracts when the equity position includes stock in companies that have one or more warrant issues that are traded. The methods developed here are also applicable to multiple issues of executive stock options (ESOs) or to combinations of warrant issues and ESOs.     

ON USING THE BLACK-SCHOLES MODEL TO VALUE WARRANTS

In this paper ad hoc procedures that employ the Black-Scholes model in the valuation of warrants are examined. Findings indicate that the Black-Scholes model unadjusted for either dividends or dilution undervalues out-of-the-money warrants with short expirations. An adjustment for dilution improves the valuation for longer-term warrants of firms that do not pay dividends. For dividend-paying firms, findings suggest that it is better to adjust for dividends than for dilution when warrants are in the money or have expirations exceeding four years.     

An alternative approach to the valuation of American options and applications

In this paper we examine the structure of American option valuation problems and derive the analytic valuation formulas under general underlying security price processes by an alternative but intuitive method. For alternative diffusion processes, we derive closed-form analytic valuation formulas and analyze the implications of asset price dynamics on the early exercise premiums of American options. In this regard, we introduce useful and interesting diffusion processes into American option-pricing literature, thus providing a wide range of choices of pricing models for various American-type derivative assets. This work offers a useful analytic framework for empirical testing and practical applications such as the valuation of corporate securities and examining the impact of options trading on market micro-structure.     

Impact of partial control on policies enacted by partial targets

Numerous studies have shown that the valuation effects of corporate policies are conditioned on corporate control. A partial acquisition serves as a unique form of corporate control that has not been thoroughly researched as a control mechanism. When firms are partially acquired, the impact of their subsequent corporate policies may be affected by the degree of control imposed by the partial acquirer. Our primary objective is to test this hypothesis by (1) measuring valuation effects of the partial target and partial acquirer in response to policies enacted by the partially acquired firm (after becoming a partial target), and (2) conducting a comprehensive cross-sectional analysis for each policy which incorporate proxies for the degree of control by the partial acquirer. We find that partial targets and partial acquirers experience significant valuation effects in response to some policies enacted by the target. We also find that the valuation effects on a partial target in response to its subsequent policies are commonly conditioned by the degree of the partial acquirer's control.     

Does Corporate Governance Predict Future Performance? Evidence from Hong Kong

This study uses time‐series data to examine the relation between changes in the quality of corporate governance practices and subsequent market valuation among large listed companies in Hong Kong. The results indicate that firms that exhibit improvements in the quality of corporate governance display a subsequent increase in market valuation, whereas firms that exhibit deterioration in the quality of corporate governance practices tend to encounter a decline in market valuation. Additionally, the impact is greater for firms that are included in the MSCI index or with a China affiliation. The results provide evidence in support of the notion that good corporate governance can predict future market valuation.     

Real Asset Valuation: A Back‐to‐basics Approach

Different valuation methods can lead to different corporate investment decisions, and the conventional “static, single discount rate” DCF approach in particular is biased against many of the kinds of decisions that corporate managers tend to view as “strategic.” Reducing the bias from valuations involves two main tasks: treating risk in a way that is consistent with observed market pricing, and accounting for the ability of companies to make decisions “dynamically” over time. The authors propose two separate tools, market‐based valuation and complete decision tree analysis, for accomplishing these two improvements in valuation. The authors also suggest working with the full distribution of future cash flows, one possible realization at a time, rather than working with the aggregate measure of expected cash flow. From a technical perspective, it is necessary to work with the full distribution to value real options properly. Valuing the cash flows one realization at a time also leads to a much better understanding of the interaction between economy‐level, systematic risks and local asset‐level, technical risks. Just as important, the proposed approaches support an effective division of labor between local asset managers, who are better positioned to model technical considerations and other asset specifics, and the central finance staff, who can ensure the consistent treatment of economy‐wide risk and to create the rules of engagement for evaluating opportunities. After presenting an overview of both the valuation and the organizational issues, the authors present a case involving a corporate investment in carbon capture and storage that illustrates both the application of the proposed methods and the various sources of bias in the typical DCF analysis.     

企业价值与并购交易定价

企业价值是一个不断发展的概念,而企业价值理论也随之处在变化之中.在现代企业中企业价值代表了企业股权和债权价值,具有特殊的性质.并购交易定价实际上就是并购双方不同企业价值理念动态博弈的结果.中国国有企业的并购定价存在许多问题,根源在于对企业价值认识得不准确、不清晰.     

Corporate valuation around the world: The effects of governance,growth, and openness

The purpose of this paper is to provide a comprehensive analysis of corporate valuation around the world. Specifically, we (i) document and compare corporate valuation around the world, and (ii) identify the key factors that drive cross-country differences in valuation. In doing so, we utilize the country-level Tobin’s q (CTQ), computed as the ratio of the aggregate market value to book value of all assets held by all public firms domiciled in a country, which amounts to the Tobin’s q for the ‘market portfolio’ of the country. The key findings of the paper are: First, CTQ varies greatly across countries, ranging from 0.73 for Venezuela to 2.11 for Finland, with the international mean of 1.30 during our sample period 1999–2004. Despite the steady integration of the world economy in recent years, corporate valuation remains starkly different across countries. Second, apart from the effect of corporate governance, cross-country differences in corporate valuation are significantly driven by the growth options of countries represented by the R&D intensities, capital expenditures, and GDP growth. In addition, the degree of capital market openness has a significant, independent effect on valuation. Third, our regression analyses show that CTQ varies directly with shareholder rights, enforcement of insider trading laws, GDP growth, R&D intensity, and the degree of capital market openness. The key findings remain robust to the inclusion of inflation and industry effects.     

Employee Reload Options: Pricing, Hedging, and Optimal Exercise

Reload options, call options granting new options on exercise,are popularly used in compensation. Although the compound optionfeature may seem complicated, there is a distribution-free dominantpolicy of exercising reload options whenever they are in themoney. The optimal policy implies general formulas for numericalvaluation. Simpler formulas for valuation and hedging followfrom Black–Scholes assumptions with or without continuousdividends. Time vesting affects the optimal policy, but numericalresults indicate that it is nearly optimal to exercise in themoney whenever feasible. The results suggest that reload optionsproduce similar incentives as employee stock options and sharegrants.     

Does geographic dispersion affect firm valuation?

We find that the geographic dispersion of a corporation affects its firm valuation. Firms with subsidiaries located in different regions of the United States experience a valuation discount of 6.2% after controlling for the impact of both global and industrial diversifications. The valuation discount increases as firms expand their operations to different regions nationwide. Results show that firms with more anti-takeover provisions are more likely to be geographically diverse, and that these firms experience greater value discounts compared with their counterparts with fewer such provisions. Our overall evidence suggests that the geographic location of corporate activities is an essential component of corporate policies and has important market valuation implications.