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.     

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).     

Dividends,research and development expenditures,and the value relevance of book value for UK loss-making firms

We extend prior research on the value relevance of accounting information for loss-making firms by allowing the coefficient of book value to vary across three distinct set of loss-making firm observations in our valuation model. Our key findings are, first, that book value is a less important determinant of equity value for either high R&D-intensive firms or dividend-paying firms, relative to firms with low R&D-intensity and zero dividends. Prior literature suggests that book value is a strong indicator of firm value for loss-making firms. This reasoning stems from book value's role as: (i) a proxy for the value of the possibility of abandoning or adapting the firms' net assets; and/or (ii) a proxy for expected future normal earnings. Our work suggests that this prior literature does not fully capture the valuation role of book value for loss-making firms. Second, we also find that dividends are value relevant, but generally only when the valuation role of book value is contextualised by allowing its coefficient to vary across high R&D-intensive firms, and dividend-paying, loss-making firms.     

Valuation of Callable Warrants

A simple valuation model for callable warrants is derived and tested. The model is expressed in closed form except for one term which can be evaluated numerically. Predictions of 78 warrant prices are compared to market prices and the average error is -.224 percent. By contrast, the Black-Scholes model applied to the same warrants produces an average error of 31.44 percent. Thus the callability feature cannot safely be ignored in determining warrant values.     

Dividend Policy and Corporate Performance

Substantial research has been conducted to determine the signal that results from dividend initiations and omissions. Our study extends from previous research by measuring the long-term valuation effects following dividend initiations and omissions. We find that firms initiating dividends experience favorable long-term share price performance. Conversely, firms omitting dividends experience unfavorable long-term share price performance. The long-term valuation effects resulting from dividend initiations are more favorable for firms that are smaller, that overinvest, and that had relatively poor performance prior to the initiations. The long-term effects resulting from dividend omissions are more unfavorable for large firms and for firms experiencing relatively large dividend omissions.     

Valuation of American call options on dividend-paying stocks: Empirical tests

This paper examines the pricing performance of the valuation equation for American call options on stocks with known dividends and compares it with two suggested approximation methods. The approximation obtained by substituting the stock price net of the present value of the escrowed dividends into the Black-Scholes model is shown to induce spurious correlation between prediction error and (1) the standard deviation of stock return, (2) the degree to which the option is in-the-money or out-of-the-money, (3) the probability of early exercise, (4) the time to expiration of the option, and (5) the dividend yield of the stock. A new method of examining option market efficiency is developed and tested.     

Personal Taxation in Firm Market Valuation: Theory and Test*

In this paper, I extend Ohlson's 1995 firm market valuation model to incorporate personal taxes: the taxes on dividends and the taxes on capital gains. Without personal taxes, firm market value can be expressed as the present value of future benefits received by the shareholders (dividends, in this case). With personal taxes, the benefits received by the shareholders should be classified into three categories (due to their different tax treatments): dividends, share repurchases, and new share issues (i.e., contributed capital). The extended model shows the effects of personal taxation on firm market valuation: retained earnings are valued less than contributed stocks, both dividends taxes and capital gains taxes affect retained earnings valuation and firm market value, and firms choose cash distribution methods (paying dividends and repurchasing shares) to increase their retained earnings valuation, therefore increasing their market value. An empirical test using a sample from the Disclosure Select Canada and Financial Post Card data bases for the years 1995‐98 supports these personal tax effects.     

New Evidence That Taxes Affect the Valuation of Dividends

This paper uses British data to examine the effects of dividend taxes on investors' relative valuation of dividends and capital gains. British data offer great potential to illuminate the dividends and taxes question, since there have been two radical changes and several minor reforms in British dividend tax policy during the last 30 years. Studying the relationship between dividends and stock price movements during different tax regimes offers an ideal controlled experiment for assessing the effects of taxes on investors' valuation of dividends. Using daily data on a small sample of firms, and monthly data on a much broader sample, we find clear evidence that taxes affect the equilibrium relationship between dividend yields and market returns. These findings suggest that taxes are important determinants of security market equilibrium and deepen the puzzle of why firms pay dividends.     

Value relevance of earnings,book value and dividends in an emerging capital market: Kuwait evidence

This study examines the value relevance of book value, earnings and dividends for a sample of all non-financial firms listed on the Kuwait Stock Exchange (KSE) over the period 2003–2009. After controlling for the impact of the global financial crisis, empirical results provide evidence on the value relevance of book value and earnings in the KSE. The results indicate that dividends are not a value-relevant in the presence of earnings in the valuation model. However, when dividends are used as a substitute for earnings they become value-relevant. The explanatory power of the model including both book value and earnings is almost indistinguishable from that of book value and dividends. Furthermore, splitting earnings into dividends declared (or paid) and earnings retained results in each of the two variables becoming value-relevant. The average dividend pay-out ratio tends to increase over time, indicating that dividend policies do matter in the KSE and that dividends in Kuwait are used to boost investors' confidence and support share price, noticeably during the global financial crisis period.     

The Pricing of Dividends in Equity Valuation

Abstract:   This study uses Ohlson's (1995 and 2001 ) accounting‐based equity valuation model to structure tests of four explanations for the anomalously positive pricing of dividends reported by Rees (1997) and Fama and French (1998) . First, we find that dividends are not simply a proxy for publicly available information that helps predict future abnormal earnings. Second, although dividends act as if they signal managers' private information about future profitability, they remain positively priced for firms with low incentives to signal. Third, dividends do not signal management's willingness to abstain from incurring agency costs. Fourth, however, controlling for one‐year‐ahead realized forecast errors yields a pricing of dividends that is very close to that of dividend displacement. After showing that dividends are not simply a proxy for analysts' misforecasting, we conclude that dividends appear to be positively priced because they are a proxy for the mispricing by investors of current earnings or book equity.     

Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives

This paper uses a sample of over 25,000 daily warrant prices to empirically investigate potential problems with the commonly used warrant pricing model proposed by Black and Scholes as an extension of their call option model. One problem seems to be especially important: the constant variance assumption of the dilution adjusted Black-Scholes model appears to cause biases in model prices for almost all warrants and over the entire sample period. We show that more accurate price forecasts are obtained with a specific form of the constant elasticity of variance model.     

Effects of tax reform on drop-off ratios and on the ex-dividend and ex-right prices

The main purpose of this paper is to examine the impact of the integrated tax system introduced in Taiwan on the valuation of dividends. Based on Elton and Gruber??s (Rev Econ Stat 52:68?C74, 1970) model, the ratio of ex-day price drop to cash dividend per share (i.e., the drop-off ratio) should reflect the relative taxes on dividends and capital gains. In Taiwan, the suspension of capital gains taxes, the coexistence of taxable and non-taxable stock dividends, and the change in tick sizes allow us to control for the influences of non-tax factors on drop-off ratios. In this paper, we find significant increases in drop-off ratios for both cash dividends and taxable stock dividends after Taiwan??s tax reform (in 1998), while we find no significant changes in drop-off ratios for non-taxable stock dividends. These results provide further evidence to support the argument that tax affects the valuation of firms.     

Strategic Decision Making of the Firm Under Asymmetric Information

This paper develops a simple signaling model whereby high valuation firm uses levels of investment, debt and dividends to convey information to the market regarding its valuation. Conditions are determined under which investment, debt and dividends are employed in a separating Nash equilibrium. Unlike many other signaling models where the source of asymmetric information concerns only the mean of the firms' cash flow, our model allows for two sources of asymmetric information: the mean and the variance of the cash flow. This paper finds that the choice of signals depends on the relative importance of these two sources of informational asymmetry. For example, we show that high valued firms signal their values by decreasing their debt if the source of asymmetric information is mainly driven by the variance of the cash flows. This latter result differs from the debt signaling models found in the literature. The findings of this paper are consistent with extensive empirical evidence.     

Signaling, Free Cash Flow and "Nonmonotonic" Dividends

Many argue that dividends signal future earnings or dispose of excess cash. Empirical support is inconclusive, potentially because no model combines both rationales. This paper does. Higher quality firms pay dividends to eliminate the free cash-flow problem, while firms that outsiders perceive as lower quality pay dividends to signal future earnings and reduce the free cash-flow problem. In equilibrium, dividends are nonmonotonic with respect to the signal observed by outsiders; the highest quality firms pay smaller dividends than lower perceived quality firms. The model reconciles the existing literature and generates new empirical predictions that are tested and supported.     

Earnings Quality and Market Values of Indonesian Listed Firms

We find that earnings quality (EQ) is reliably negatively correlated with the market values of equity of firms listed on the Jakarta Stock Exchange (IDX). The financial reporting process produces earnings viewed as increasingly ‘incomplete’ for valuation purposes by the capital market despite moves towards high‐quality financial reporting standards (IFRS) during the sample period 1995–2015. Time‐series analyses reveal that EQ decreases rather than increases through time. The role of earnings in valuation is replaced by other attributes, most notably net dividends. Firms that pay out dividends are valued significantly higher, and firms that issue equity are valued lower. These results are robust regardless of other accounting, market and governance controls. Large and closely held firms are valued higher than smaller firms, consistent with some aspects of the political cost hypothesis. Shares with higher idiosyncratic risk are valued higher, consistent with option value, as are shares where the volume of shares traded is more volatile. Collectively, the results indicate that the mere adoption of high‐quality accounting standards (IFRS) and other nominal changes in capital market regulations do not automatically increase the quality of the financial reporting process.     

Modeling dividends,earnings, and book value equity: An empirical investigation of the ohlson valuation dynamics

This study empirically investigates the information dynamics of the Ohlson valuation framework. Single-period lagged linear autoregressive relationships among dividends, earnings, and book values of equity are estimated for a sample of stochastically stationary firms and are found not to support the valuation framework. This study further extends the empirical analysis to a multilagged vector autoregressive linear information system. Consistent with the Ohlson valuation framework,the past time series of all three variables are generally found to be relevant for firm valuation. This study brings into question empirical research utilizing the Ohlson framework that presupposes a single-period lagged information dynamic.     

A Re-Examination of Shareholder Wealth Effects of Calls of Convertible Preferred Stock

Common stock price reactions to announcements of 67 calls of in-the-money convertible preferred stocks are examined, and a significant average abnormal return of ?1.6 percent is documented. The finding is robust to the choice of estimation period and the assumed return-generating process. Annual dividend obligations for the called preferred issues in the sample typically are greater than the dividends for the common shares into which they are converted, and announcement-period abnormal returns are negatively correlated with changes in dividends. Moreover, calls that result in dilution of voting rights appear to have greater adverse valuation effects than calls that do not alter voting rights concentration.     

The Informativeness of Dividends and Associated Tax Credits

This paper investigates the informativeness of dividends and the associated tax credits with respect to earnings persistence. After confirming that dividend‐paying firms have more persistent earnings than non‐dividend‐paying firms, we show that the taxation status of the dividend is also important. Firms that pay dividends with a full tax credit attached have significantly more persistent earnings than firms that pay dividends which carry no associated tax credit. Consistent with higher levels of tax credits identifying more mature firms, those paying dividends with full tax credits have significantly less persistent losses than firms that pay dividends with only partial tax credits. Further, market pricing tests confirm that the incremental information in dividends and tax credits contributes to reductions in market mispricing of the persistence of earnings and earnings components. Our results are robust to alternative model specifications and controlling for dividend size and firm age.     

Option pricing using a binomial model with random time steps (A formal model of gamma hedging)

This paper provides a new option pricing model which justifies the standard industry implementation of the Black-Scholes model. The standard industry implementation of the Black-Scholes model uses an implicit volatility, and it hedges both delta and gamma risk. This industry implementation is inconsistent with the theory underlying the derivation of the Black-Scholes model. We justify this implementation by showing that these adhoc adjustments to the Black-Scholes model provide a reasonable approximation to valuation and delta hedging in our new option pricing model.