Nội dung

Accounting Information, Disclosure, and the Cost of Capital Richard Lambert* The Wharton School University of Pennsylvania Christian Leuz Graduate School of Business University of Chicago Robert E. Verrecchia The Wharton School University of Pennsylvania September 2005 Revised, August 2006 Abstract In this paper we examine whether and how accounting information about a firm manifests in its cost of capital, despite the forces of diversification. We build a model that is consistent with the CAPM and explicitly allows for multiple securities whose cash flows are correlated. We demonstrate that the quality of accounting information can influence the cost of capital, both directly and indirectly. The direct effect occurs because higher quality disclosures affect the firm’s assessed covariances with other firms’ cash flows, which is non-diversifiable. The indirect effect occurs because higher quality disclosures affect a firm’s real decisions, which likely changes the firm’s ratio of the expected future cash flows to the covariance of these cash flows with the sum of all the cash flows in the market. We show that this effect can go in either direction, but also derive conditions under which an increase in information quality leads to an unambiguous decline the cost of capital. JEL classification: Key Words: G12, G14, G31, M41 Cost of capital, Disclosure, Information risk, Asset pricing *Corresponding Author. We thank Stan Baiman, John Cochrane, Gene Fame, Wayne Guay, Raffi Indjejikian, Eugene Kandel, Christian Laux, DJ Nanda, Haresh Sapra, Cathy Schrand, Phillip Stocken, seminar participants at the Journal of Accounting Research Conference, Ohio State University and the University of Pennsylvania, and an anonymous referee for their helpful comments on this paper and previous drafts of work on this topic. 1. Introduction The link between accounting information and the cost of capital of firms is one of the most fundamental issues in accounting. Standard setters frequently refer to it. For example, Arthur Levitt (1998), the former chairman of the Securities and Exchange Commission, suggests that “high quality accounting standards […] reduce capital costs.” Similarly, Neel Foster (2003), a former member of the Financial Accounting Standards Board (FASB) claims that “More information always equates to less uncertainty, and […] people pay more for certainty. In the context of financial information, the end result is that better disclosure results in a lower cost of capital.” While these claims have intuitive appeal, there is surprisingly little theoretical work on the hypothesized link. In particular, it is unclear to what extent accounting information or firm disclosures reduce non-diversifiable risks in economies with multiple securities. Asset pricing models, such as the Capital Asset Pricing Model (CAPM), and portfolio theory emphasize the importance of distinguishing between risks that are diversifiable and those that are not. Thus, the challenge for accounting researchers is to demonstrate whether and how firms’ accounting information manifests in their cost of capital, despite the forces of diversification. This paper examines both of these questions. We define the cost of capital as the expected return on a firm’s stock. This definition is consistent with standard asset pricing models in finance (e.g., Fama and Miller, 1972, p. 303), as well as numerous studies in accounting that use discounted cash flow or abnormal earnings models to infer firms’ cost of capital (e.g., Botosan, 1997; Gebhardt et al., 2001).1 In our model, we explicitly allow for multiple firms whose cash flows are correlated. In contrast, most analytical models in 1 We also discuss the impact of information on price, as the latter is sometimes used as a measure of cost of capital. See, e.g., Easley and O’Hara (2004) and Hughes et al. (2005). accounting examine the role of information in single-firm settings (see Verrecchia, 2001, for a survey). While this literature yields many useful insights, its applicability to cost of capital issues is limited. In single-firm settings, firm-specific variance is priced because there are no alternative securities that would allow investors to diversify idiosyncratic risks. We begin with a model of a multi-security economy that is consistent with the CAPM. We then recast the CAPM, which is expressed in terms of returns, into a more easily interpreted formulation that is expressed in terms of the expected values and covariances of future cash flows. We show that the ratio of the expected future cash flow to the covariance of the firm’s cash flow with the sum of all cash flows in the market is a key determinant of the cost of capital. Next, we add an information structure that allows us to study the effects of accounting information. We characterize firms’ accounting reports as noisy information about future cash flows, which comports well with actual reporting behavior. We demonstrate that accounting information influences a firm’s cost of capital in two ways: 1) direct effects – where higher quality accounting information does not affect cash flows per se, but affects the market participants’ assessments of the distribution of future cash flows; and 2) indirect effects – where higher quality accounting information affects a firm’s real decisions, which, in turn, influences its expected value and covariances of firm cash flows. In the first category, we show (not surprisingly) that higher quality information reduces the assessed variance of a firm’s cash flows. Analogous to the spirit of the CAPM, however, we show this effect is diversifiable in a “large economy.” We discuss what the concept of “diversification” means, and show that an economically sensible definition requires more than simply examining what happens when the number of securities in the economy becomes large. 2 Moreover, we demonstrate that an increase in the quality of a firm’s disclosure about its own future cash flows has a direct effect on the assessed covariances with other firms’ cash flows. This result builds on and extends the work on “estimation risk” in finance.2 In this literature, information typically arises from a historical time-series of return observations. In particular, Barry and Brown (1985) and Coles et al. (1995) compare two information environments: in one environment the same amount of information (e.g., the same number of historical time-series observations) is available for all firms in the economy, whereas in the other information environment there are more observations for one group of firms than another. They find that the betas of the “high information” securities are lower than they would be in the equal information case. They cannot unambiguously sign, however, the difference in betas for the “low information” securities in the unequal- versus equal-information environments. Moreover, these studies do not address the question of how an individual firm’s disclosures can influence its cost of capital within an unequal information environment. Rather than restricting attention to information as historical observations of returns, our paper uses a more conventional information-economics approach in which information is modeled as a noisy signal of the realization of cash flows in the future. With this approach, we allow for more general changes in the information environment, and we are able to prove much stronger results. In particular, we show that higher quality accounting information and financial disclosures affect the assessed covariances with other firms, and this effect unambiguously moves a firm’s cost of capital closer to the risk-free rate. Moreover, this effect is not diversifiable because it is present for each of the firm’s covariance terms and hence does not disappear in “large economies.” 2 See Brown (1979), Barry and Brown (1984 and 1985), Coles and Loewenstein (1988), and Coles et al. (1995). 3 Next, we discuss the effects of disclosure regulation on the cost of capital of firms. Based on our framework, increasing the quality of mandated disclosures should in general move the cost of capital closer to the risk-free rate for all firms in the economy. In addition to the effect of an individual firm’s disclosures, there is an externality from the disclosures of other firms, which may provide a rationale for disclosure regulation. We also argue that the magnitude of the cost-of-capital effect of mandated disclosure will be unequal across firms. In particular, the reduction in the assessed covariances between firms and the market does not result in a decrease in the beta coefficient of each firm. After all, regardless of information quality in the economy, the average beta across firms has to be 1.0. Therefore, even though firms’ cost of capital (and the aggregate risk premium) will decline with improved mandated disclosure, their beta coefficients need not. In the “indirect effect” category, we show that the quality of accounting information influences a firm’s cost of capital through its effect on a firm’s real decisions. First, we demonstrate that if better information reduces the amount of firm cash flow that managers appropriate for themselves, the improvements in disclosure not only increase firm price, but in general also reduce a firm’s cost of capital. Second, we allow information quality to change a firm’s real decisions, e.g., with respect to production or investment. In this case, information quality changes decisions, which changes the ratio of expected cash flow to non-diversifiable covariance risk and hence influences a firm’s cost of capital. We derive conditions under which an increase in information quality results in an unambiguous decrease in a firm’s cost of capital. Our paper makes several contributions. First, we extend and generalize prior work on estimation risk. We show that information quality directly influences a firm’s cost of capital and that improvements in information quality by individual firms unambiguously affect their non- 4 diversifiable risks. This finding is important as it suggests that a firm’s beta factor is a function of its information quality and disclosures. In this sense, our study provides theoretical guidance to empirical studies that examine the link between firms’ disclosures and/or information quality, and their cost of capital (e.g., Botosan, 1997; Botosan and Plumlee, 2002; Francis et al., 2004; Ashbaugh-Skaife et al., 2005; Berger et al., 2005; and Core et al., 2005). In addition, our study provides an explanation for studies that find that international differences in disclosure regulation explain differences in the equity risk premium, or the average cost of equity capital, across countries (e.g., Hail and Leuz, 2006). It is important to recognize, however, that the information effects of a firm’s disclosures on its cost of capital are fully captured by an appropriately specified, forward-looking beta. Thus, our model does not provide support for an additional risk factor capturing “information risk.”3 One way to justify the inclusion of additional information variables in a cost of capital model would be to note that empirical proxies for beta, which for instance are based on historical data alone, may not capture all information effects. In this case, however, it is incumbent on researchers to specify a “measurement error” model or, at least, provide a careful justification for the inclusion of information variables, and their functional form, in the empirical specification. Based on our results, however, the most natural way to empirically analyze the link between information quality and the cost of capital is via the beta factor.4 A second contribution of our paper is that it provides a direct link between information quality and the cost of capital, without reference to market liquidity. Prior work suggests an indirect link between disclosure and firms’ cost of capital based on market liquidity and adverse 3 Note that our model also does not preclude the existence of an additional risk factor in an extended or different model. This issue is left for future research. 4 See, e.g., Beaver et al. (1970) and Core et al. (2006) for an empirical analysis that relates accounting information to a firm’s beta. 5 selection in secondary markets (e.g., Diamond and Verrecchia, 1991; Baiman and Verrecchia, 1996; Easley and O’Hara, 2004). These studies, however, analyze settings with a single firm (or settings where cash flows across firms are uncorrelated). Thus, it is unclear whether the effects demonstrated in these studies survive the forces of diversification and extend to more general multi-security settings. We emphasize, however, that we do not dispute the possible role of market liquidity for firms’ cost of capital, as several empirical studies suggest (e.g., Amihud and Mendelson, 1986; Chordia et al., 2001; Easley et al., 2002; Pastor and Stambaugh, 2003). Our paper focuses on an alternative, and possibly more direct, explanation as to how information quality influences non-diversifiable risks. Finally, our paper contributes to the literature by showing that information quality has indirect effects on real decisions, which in turn manifest in firms’ cost of capital. In this sense, our study relates to work on real effects of accounting information (e.g., Kanodia et al., 2000 and 2004). These studies, however, do not analyze the effects on firms’ cost of capital or nondiversifiable risks. The remainder of this paper is organized as follows. Section 2 sets up the basic model in a world of homogeneous beliefs, defines terms, and derives the determinants of the cost of capital. Sections 3 and 4 analyze the direct and indirect effects of accounting information on firms’ cost of capital, respectively. Section 5 summarizes our findings and concludes the paper. 2. Model and Cost of Capital Derivation We define cost of capital to be the expected return on the firm’s stock. Consistent with standard models of asset pricing, the expected rate of return on a firm j’s stock is the rate, Rj, that equates the stock price at the beginning of the period, Pj, to the cash flow at the end of the period, 6 ~ V j − Pj ~ ~ ~ . Our analysis focuses on the expected rate of return, which Vj: P j (1 + Rj) = V j , or R j = Pj ~ E (V j | Φ ) − Pj ~ , where Φ is the information available to market participants to is E ( R j | Φ ) = Pj make their assessments regarding the distribution of future cash flows. We assume there are J securities in the economy whose returns are correlated. The best known model of asset pricing in such a setting is the Capital Asset Pricing Model (CAPM) (Sharpe, 1964; Lintner, 1965). Therefore, we begin our analysis by presenting the conventional formulation of the CAPM, and then transform this formulation and add an information structure to show how information quality affects expected returns. Assuming that returns are normally distributed or, alternatively, that investors have quadratic utility functions, the CAPM expresses the expected return on a firm’s stock as a function of the risk-free rate, Rf, the expected return on ~ the market, E ( Rm ), and the firm’s beta coefficient, βj: ~ E (R M | Φ ) − R f ~ ~ ~ ~ E(R j | Φ ) = R f + E(R M | Φ) − R f β j = R f + Cov ( R j , R m | Φ ) . ~ Var ( R M | Φ ) [ ] [ ] (1) Eqn. (1) shows that the only firm-specific parameter that affects the firm’s cost of capital is its beta coefficient, or, more specifically, the covariance of its future return with that of the market portfolio. This covariance is a forward-looking parameter, and is based on the information available to market participants. Consistent with the conventional formulation of the CAPM, we assume market participants possess homogeneous beliefs regarding the expected end-of-period cash flows and covariances. Because the CAPM is expressed solely in terms of covariances, this formulation might be interpreted as implying that other factors, for example the expected cash flows, do not affect the 7 firm’s cost of capital. It is important to keep in mind, however, that the covariance term in the CAPM is expressed in terms of returns, not in terms of cash flows. The two are related via the ~ ~ ⎡ ⎤ V equation Cov ( R~ j , R~M ) = ⎢Cov( j , VM )⎥ = ⎢⎣ Pj PM ⎥⎦ 1 ~ ~ Cov(V j ,VM ) . This expression implies that Pj PM information can affect the expected return on a firm’s stock through its effect on inferences about the covariances of future cash flows, or through the current period stock price, or both. Clearly the current stock price is a function of the expected-end-of-period cash flow. In particular, the CAPM can be re-expressed in terms of prices instead of returns as follows (see Fama ,1976, eqn. [83]): ~ E (VM | Φ ) − (1 + R f ) PM ~ E (V j | Φ ) − ~ Var (VM | Φ ) Pj = (1 + R f ) ⎡ ⎤ ~ J ~ Cov ( V j , ∑ Vk | Φ ) ⎥ ⎢ k =1 ⎣ ⎦, j = 1, …, J. (2) Eqn. (2) indicates that the current price of a firm can be expressed as the expected end-of-period cash flow minus a reduction for risk. This risk-adjusted expected value is then discounted to the beginning of the period at the risk-free rate. The risk reduction factor in the numerator of eqn. (2) ~ E (VM | Φ ) − (1 + R f ) PM has both a macro-economic factor, , and an individual firm component, ~ Var (VM | Φ ) which is determined by the covariance of the firm’s end-of-period cash flows with those of all ~ J ~ ⎤ is a measure of the contribution other firms. As in Fama (1976), the term ⎡Cov(V j , ∑ Vk | Φ ) ⎥ ⎢ k =1 ⎦ ⎣ J ~ ~ of firm j to the overall variance of the market cash flows, VM = ∑ Vk . k =1 Eqns. (1) and (2) express expected returns and pricing on a relative basis: that is, relative to the market. If we make more specific assumptions regarding investors’ preferences, we can 8 express prices and returns on an absolute basis.5 In particular, if the economy consists of N investors with negative exponential utility with risk tolerance parameter τ and the end-of-period cash flows are multi-variate normally distributed, then the beginning-of-period stock price can be expressed as (details in the Appendix): J ⎤ 1 ⎡ ~ ~ ~ ⎢Cov(V j , ∑ Vk | Φ)⎥ E (V j | Φ) − Nτ ⎢ ⎥ k =1 ⎣ ⎦ Pj = 1+ Rf . (3) As in eqn. (2), price in eqn. (3) is equal to the expected end-of-period cash flow minus a reduction for the riskiness of firm j, all discounted back to the beginning of the period at the riskfree rate. The discount for risk is now simply the contribution of firm j’s cash flows to the aggregate risk of the market divided by the term Nτ, which is the aggregate risk tolerance of the marketplace. The price of the market portfolio can be found by summing eqn. (3) across all 1 ~ ~ firms: (1 + R f ) PM = E (VM | Φ ) − Var (VM | Φ ) , which can also be expressed as Nτ ~ E (VM | Φ ) − (1 + R f ) PM 1 = . Therefore, the aggregate risk tolerance of the market determines ~ Nτ Var (VM | Φ ) the risk premium for market-wide risk. We can re-arrange eqn. (3) to express the expected return on the firm’s stock as follows. Lemma 1. The cost of capital for firm j is J ⎤ 1 ⎡ ~ ~ ~ ⎢ Φ + ( | ) ( , Cov V R E V j ∑ Vk | Φ )⎥ f j ~ Nτ ⎢ ⎥ E (V j | Φ ) − P j ~ k =1 ⎣ ⎦. = E ( R j | Φ) = J Pj ⎤ 1 ⎡ ~ ~ ~ ⎢Cov (V j , ∑ Vk | Φ )⎥ E (V j | Φ ) − Nτ ⎢ ⎥ k =1 ⎣ ⎦ 5 (4a) More specifically, the pricing and return formulas will be expressed relative to the risk-free rate, which acts as the numeraire in the economy. 9