Pitfalls in Levering and Unlevering Beta and Cost of Capital Estimates in DCF Valuations1

The “levering” and “unlevering” of estimates of beta and various costs of capital are routine steps in estimating the discount rates used in DCF valuations. But as the authors demonstrate by reviewing the existing research on the subject, the levering and unlevering formulas that are most commonly used in practice are not appropriate for valuing many companies. They also illustrate the shortcomings of—and substantial valuation errors that can result from—the common practices of assuming that the betas of securities like debt and preferred stock are equal to zero and ignoring the effects of equity‐linked securities such as employee stock options, warrants, and convertible debt. The authors offer alternative levering formulas that are more appropriate for valuing most companies than—and as readily implemented as—the formulas commonly used today. They also provide a relatively easy way to estimate betas for debt and preferred stock that can be used in the levering and unlevering formulas. The authors discuss how properly to account for equity‐linked securities such as employee stock options, warrants, and convertible debt while demonstrating the potential importance of ignoring such equity‐linked securities in the levering and unlevering formulas. Finally, the authors show why it is appropriate to standardize the treatment of contractual obligations such as leases across comparable companies in order to get consistent estimates of the unlevered cost of capital.     

Employee stock ownership and the cost of capital

This paper investigates the relationship between employee stock ownership and the cost of capital, the main determinant of shareholder value creation computed through economic value added (EVA). By reducing agency conflicts within the firm, we hypothesize that employee share ownership reduces the firm’s cost of capital by affecting its two components, i.e. the cost of equity and the cost of debt. We test this hypothesis in France, a leading country in terms of employee ownership, based on a panel of the 120 largest listed companies for the 2000–2011 period. We find: (i) no significant relationship between employee stock ownership and the cost of equity; (ii) a negative curvilinear relationship between employee stock ownership and the cost of debt; (ii) a negative curvilinear relationship between employee stock ownership and the weighted average cost of capital. These results suggest debtholders regard ESO as positive as long it is moderate because it shifts risk from them to employees and that this effect is still perceptible in the weighted average cost of capital.     

CONVERTIBLE BONDS: MATCHING FINANCIAL AND REAL OPTIONS

For companies whose value consists in large part of “real options”‐ growth opportunities that may (or may not) materialize‐convertible bonds may offer the ideal financing vehicle because of the matching financial options built into the securities. This paper proposes that convertible debt can be a key element in a financing strategy that aims not only to fund current activities, but to give companies access to low‐cost capital if and when their real investment options turn out to be valuable. In this sense, convertibles can be seen as the most cost‐effective solution to a sequential financing problem‐how to fund not only today's activities, but also tomorrow's growth opportunities (some of them not yet even foreseeable). For companies with real options, the ability of convertibles to match capital inflows with corporate outlays adds value by minimizing two sets of costs: those associated with having too much (particularly equity) capital (known as “agency costs of free cash flow”) and those associated with having too little (“new issue” costs). The key to the cost‐effectiveness of convertibles in funding real options is the call provision. Provided the stock price is “in the money” (and the call protection period is over), the call gives managers the option to force conversion of the bonds into equity. If and when the company's investment opportunity materializes, exercise of the call feature gives the firm an infusion of new equity (while eliminating the debt service burden associated with the convertible) that enables it to carry out its new investment plan. Consistent with this argument, the author's recent study of the investment and financing activities of 289 companies around the time of convertible calls reports significant increases in capital expenditures starting in the year of the call and extending three years after. The companies also showed increased financing activity following the call, mainly new long‐term debt issues (many of them also convertibles) in the year of the call.     

Employee sentiment and stock option compensation

The use of equity-based compensation for rank-and-file employees is a puzzle. We analyze whether the popularity of option compensation may be driven by employee optimism, and show that optimism by itself is insufficient to make option compensation optimal. The crucial insight is that firms compete with financial markets as suppliers of equity to employees and that employees’ access to the equity market restricts firms’ ability to profit from employee optimism. Firms must be able to extract some of the implied rents even though employees can purchase company equity in the financial markets. Such rent extraction becomes feasible if employees prefer the stock options offered by firms to the equity offered by the market, or if the traded equity is overvalued. We provide empirical evidence that firms use broad-based option compensation when boundedly rational employees are likely to be excessively optimistic about company stock, and when employees are likely to strictly prefer options over stock.     

Convertible securities in merger transactions

This paper provides a rationale for the use of convertible securities as the medium of exchange in corporate change-of-control transactions. We argue that convertible securities can resolve the information asymmetry about the bidder’s value while at the same time mitigating the information asymmetry about the target’s value. In contrast, deals with cash or stock can only address one information asymmetry or the other but not both. Empirically, we find that a bidder is more likely to offer convertible securities, rather than all cash or all stock, when both the bidder and its target face large asymmetric information problems. We also find that both bidders and targets in convertible deals enjoy positive abnormal stock returns around takeover announcements. These findings provide empirical support for the use of convertible securities to resolve the double-sided asymmetric information problem. Finally, we find that bidder returns in convertible deals are larger than in all-cash and all-stock deals, but that target returns in convertible deals are smaller than in all-cash and all-stock deals.     

CAPM for estimating the cost of equity capital: Interpreting the empirical evidence

We argue that the empirical evidence against the capital asset pricing model (CAPM) based on stock returns does not invalidate its use for estimating the cost of capital for projects in making capital budgeting decisions. Because stocks are backed not only by projects in place, but also by the options to modify current projects and undertake new ones, the expected returns on stocks need not satisfy the CAPM even when expected returns of projects do. We provide empirical support for our arguments by developing a method for estimating firms' project CAPM betas and project returns. Our findings justify the continued use of the CAPM by firms in spite of the mounting evidence against it based on the cross section of stock returns.     

The Information Content Of Calls Of Debt: Evidence From Long-Run Stock Returns

We examine the long‐run performance of the common stock of firms following calls of both straight and convertible debt from 1945 to 1995. Using a sample of 718 calls of straight debt, we find an average abnormal return in the five years following the call of between 0.16% and 0.34% per month, which compounds to an economically and statistically significant 11% to 22% over the five‐year period. This evidence of overperformance following calls shows a distinct symmetry between the straight debt and equity markets. Issues of debt and equity are both followed by long‐term underperformance, whereas stock repurchases and debt calls are both followed by long‐run overperformance. For our sample of 713 calls of convertible debt, we find little systematic evidence of abnormal performance following the call. Some researchers suggest that calls of convertible debt provide negative signals to the market. Our results provide no support for this claim. In contrast, our evidence of marginal positive long‐run returns provides weak support for the model that calls of convertible debt signal the realization of profitable investment options, and for the price pressure hypothesis.     

Risk and return in convertible arbitrage: Evidence from the convertible bond market

In this paper, we identify and document the empirical characteristics of the key drivers of convertible arbitrage as a strategy and how they impact the performance of convertible arbitrage hedge funds. We show that the returns of a buy-and-hedge strategy involving taking a long position in convertible bonds (“CBs”) while hedging the equity risk alone explains a substantial amount of these funds' return dynamics. In addition, we highlight the importance of non-price variables such as extreme market-wide events and the supply of CBs on performance. Out-of-sample tests provide corroborative evidence on our model's predictions. At a more micro level, larger funds appear to be less dependent on directional exposure to CBs and more active in shorting stocks to hedge their exposure than smaller funds. They are also more vulnerable to supply shocks in the CB market. These findings are consistent with economies of scale that large funds enjoy in accessing the stock loan market. However, the friction involved in adjusting the stock of risk capital managed by a large fund can negatively impact performance when the supply of CBs declines. Taken together, our findings are consistent with convertible arbitrageurs collectively being rewarded for playing an intermediation role of funding CB issuers whilst distributing part of the equity risk of CBs to the equity market.     

Is backdating executive stock options always costly to shareholders?

We use a binomial model to investigate the cost to shareholders of backdating employee stock option (ESO) grants to award in‐the‐money rather than at‐the‐money options to a manager. When the expected return of the stock underlying an ESO is sufficiently close to the risk‐free rate, a backdating arrangement can always be structured to simultaneously improve shareholders’ wealth and the manager's utility. The smaller the manager's non‐option wealth, personal income tax rate or risk tolerance, the more likely a backdating arrangement can be welfare improving.     

Employee stock options in compensation agreements: A financing explanation

We develop a model for the use of stock options in compensation agreements based on a financing explanation. Our model is consistent with the extensive use of options for non-executive employees. Simulation results from our model show an optimal use of options of about 9.3% of total compensation for a non-executive employee with a compensation of US$50,000. Finding an optimal level of options as part of compensation in this context requires a balancing of two opposing factors—the benefit of a lower capital issuance cost versus a higher compensation cost as a result of the discount that an employee places on options because of an undiversified position.     

Resolving the Agency Problems of External Capital through Options

This paper investigates the role of stock options in resolving the agency problems of external capital as originally identified by Jensen and Meckling (1976). These problems are precipitated by managerial incentives a) to consume excessive non-pecuniary benefits or perquisites beyond the optimal level for sole ownership and b) to engage in risk shifting in productive decisions so as to transfer wealth from external capital contributors. These incentive problems can be resolved through a strategy that judiciously combines call and put options retained by the owner-manager and external financiers, respectively. The resolution of the agency problems through this mechanism provides an economic rationale for the existence of managerial stock options and convertible debt.     

Stock Returns and Operating Performance of Securities Issuers

We examine long‐run stock returns and operating performance around firms’ offerings of common stock, convertible debt, and straight debt from 1985 to 1990. We find that pre‐issue abnormal returns are positive and significant for stock issuers, but not for convertible and straight debt issuers. The post‐issue mean returns show that common stock and convertible debt issuers experience underperformance during the post‐issue periods, but straight debt issuers do not. Consistent with these results, common stock issuers experience the best pre‐issue operating performance among all three types of issuers, and operating performance declines during the post‐issue periods for common stock and convertible debt issuers. Using a new approach in linear model estimations to correct heteroskedasticity and to adjust for finite sample, we find a positive relation between post‐issue operating performance and issue‐period stock price reactions. The results suggest that future operating performance is anticipated at the issue and that securities issues provide information on issuers’ future performance.     

Do executive stock options induce excessive risk taking?

We examine whether executive stock options can induce excessive risk taking by managers in firms’ security issue decisions. We find that CEOs whose wealth is more sensitive to stock return volatility due to their option holdings are more likely to choose debt over equity as a capital-raising vehicle. More importantly, the pattern holds not only in firms that are underlevered relative to their optimal capital structure but also in overlevered firms. This evidence is inconsistent with executive stock options aligning the interests of managers and shareholders; rather, it supports the hypothesis that stock options sometimes make managers take on too much risk and in the process pursue suboptimal capital structure policies.     

不确定性、信息不对称与风险投资契约工具选择

现代契约理论认为，契约结构在很大程度上由信息分布决定。由于人力资本内生不确定性导致的信息不对称，使得可转换优先股在风险投资契约中被广泛使用。本文认为，其原因在于可转换优先股隐含了更多的选择权，可以更好地适应风险投资过程中的不确定性。     

Entrepreneurial finance: Banks versus venture capital

We analyze how entrepreneurial firms choose between two funding institution: banks, which monitor less intensively and face liquidity demands from their own investors, and venture capitalists, who can monitor more intensively but face a higher cost of capital because of the liquidity constraints that they impose on their own investors. Because the firm's manager prefers continuing the firm over liquidating it and aggressive (risky) continuation strategies over conservative (safe) continuation strategies, the institution must monitor the firm and exercise some control over its decisions. Bank finance takes the form of debt, whereas venture capital finance often resembles convertible debt. Venture capital finance is optimal only when the aggressive continuation strategy is not too profitable, ex ante; the uncertainty associated with the risky continuation strategy (strategic uncertainty) is high; and the firm's cash flow distribution is highly risky and positively skewed, with low probability of success, low liquidation value, and high returns if successful. A decrease in venture capitalists’ cost of capital encourages firms to switch from safe strategies and bank finance to riskier strategies and venture capital finance, increasing the average risk of firms in the economy.     

Financial reporting for employee stock options: liabilities or equity?

This study seeks to determine whether employee stock options share key characteristics of liabilities or equity. Consistent with warrant pricing theory, we find that common equity risk and expected return are negatively associated with the extent to which a firm has outstanding employee stock options, which is opposite to the association for liabilities. We also find the following. (1) The association is positive for firms that reprice options and less negative for firms that have options with longer remaining terms to maturity, which indicates that some employee stock options have characteristics that make them more similar to liabilities. (2) Leverage measured based on treating options as equity has a stronger positive relation with common equity risk than leverage measured based on treating options as liabilities. (3) The sensitivity of employee stock option value to changes in asset value mirrors that of common equity value and is opposite to that of liability value. Also, we find that, unlike liabilities, employee stock options have substantially higher risk and expected return than common equity. Our findings are not consistent with classifying employee stock options as liabilities for financial reporting if classification were based on the directional association of a claim with common equity risk and expected return. Rather, our findings suggest the options act more like another type of equity.     

Analysts’ estimates of the cost of equity capital

We explore a large sample of analysts' estimates of the cost of equity capital (CoE) to evaluate their usefulness as expected return proxies (ERP). We find that the CoE estimates are significantly related to a firm's beta, size, book-to-market ratio, leverage, and idiosyncratic volatility but not other risk proxies. Even after controlling for the popular return predictors, the CoE estimates incrementally predict future stock returns. This predictive ability is better explained as the CoE estimates containing ERP information rather than reflecting stock mispricing. When evaluated against traditional ERPs, including the implied costs of capital, the CoE estimates are found to be the least noisy. Finally, we document CoE responses around earnings announcements, demonstrating their usefulness to study discount-rate reactions of market participants. We conclude that analysts' CoE estimates are meaningful ERPs that can be fruitfully employed in a variety of asset pricing contexts.     

The buyers’ perspective on security design: Hedge funds and convertible bond call provisions

We provide evidence that security design reflects the interplay of capital supplier and security issuer preferences. While call provisions have historically been the default option in convertible security design, only a minority of post-2005 issues are callable. Because hedge funds dominate the market for new convertibles today and because convertible arbitrage is less risky without callability, the recent diminution in the frequency of call provisions in new convertible bond issues illustrates the importance of the preferences of the suppliers of capital in security design.     

Employee stock options as warrants

Previous studies ignore the fact that employee stock options are warrants because these options have been an insignificant component of firms’ capital structures. I show that this assumption is no longer correct. For example, for more than 36% of my sample firms, employee stock options represent a more significant claim on firm value than the firm’s debt and preferred stock combined. Moreover, in contrast to the suggestions of previous research, I show that employee stock options are a significant claim on firms throughout the economy, including larger firms, older firms, and firms in “Old Economy” industries. Finally, I show that the presumption in prior studies that employee stock options are not warrants causes a potential misunderstanding of the risk-shifting interests of securityholders and biases the analysis of capital structure issues.     

Financing decisions: The case of convertible bonds

Research studying firms' motivations to issue convertible bonds remains far from complete. This paper aims to provide further understanding of firms' motives behind issuing convertible bonds. We propose a theoretical model that explains issuers' choice between convertibles and equity when raising a required amount of capital by comparing the cash flow streams of both alternatives in order to maximize the firm's value for the current shareholders. We derive a closed form solution of our theoretical model both in absence and presence of default risk. Our model suggests that issuing convertible bonds is preferred to a direct stock issuance if the expected return of convertible bonds is lower than the expected return of common stocks. Empirical findings confirm our theoretical predictions.